Principles of Instrumental Analysis sixth edition [6 ed.] 0495012017, 9780495012016

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Principles of Instrumental Analysis Douglas A. Skoog S t a n fo r d

U n iv e r s i~ }·

F James Holler U n ive r s ity

o f K e n tu c kJ '

Stanley R. Crouch M ic h ig a n

S ta te

U n ive r s ity

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T H O IV IS O N

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B R O O K S /C O L E

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Holler.

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Publisher: David Harris Development Editor: Sandra Kiselica Editorial Assistant: Lauren Oliveira Technology Project Manager: Lisa Weber Marketing Manager: Amee Mosley Project Manager, Editorial Production: Belinda Krohmer Creative Director: Rob Hugel Art Director: John Walker Print Buyer: Rebecca Cross

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© 2007.1998. Thomson Brooks/Cole, a part of The Thomson Corporation. Thomson, the Star logo, and Brooks/Cole arc trademarks used hercin under license.

Thomson

Higher

Instrumental Analysis in ActionMonitoring i\lercuf) :__ t31

Education

10 Da"is

DriVt'

Belmont,

CA 94002-:3093

lISA

CHAPTER

Circuits

Electrical

TW O

Components

Molecular Spectroscopy

and

:2()

CHAPTER

ALL RIGHTS RESERVED. No part of this work covered by the copyright hereon may bc reproduced or used in any form or by any means - graphic, electronic, or mechanical, including photocopying, recording, taping, web distribution, information storage and retrieval systems, or in any other manner ~ without the written permission of the publisher.

CHAPTER

Operati(H1al Amplifiers

THREE

in Chemical

CHAPTER CHAPTER

FOUR

Computers

80

Digital Electronics

and

Signals and Noise

F IV E

Instrumental Electronic

110

Anal)'sis in Actioo-

For permission to use material from this text or product, submit a request online at http://www.thomsonrights.com. Any additional questions about permissions can be submitted bye-mail to thomson righ [email protected].

;_-nh

Analytical

Laboratory

CHAPTER

127

'\-lolecular

;Hi?

LuminesCf'IlCe

:39C) S IX T E E N

Spectrometry CHAPTER

of l i1tra\iolet-

Spectrolllt'try

Absorption

F IF T E E N

Sprctrometry The

Printed in Canada. 1 2 3 4 5 6 7 11 10 09 08 07 For more information about our products, contact us at: Thomson Learning Academic Resource Center 1-800-423-0563

ldtravlo[cl-

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Spectrollwlry

ApplicatiollS

FOURTEEN

Visible i\lolecular CHAPTER

CHAPTER

In tr o d u c tio ll

Absorption

sq

Instrumentation

ISBN-13: 978-0-495-01201-6 ISBN-lO: 0-495-01201-7

An

T H IR T E E N

Visible ~rolccular

An Introduction

1 0 Illfr a r r d

4:lO Applications

SEVENTEEN

Spectrometry

of

In fra re d

457>

Atomic Spectroscopy An Introduction

CHAPTER

S IX

\[eth",b

]:12

CHAPTER

SEVEN

C ( ) m p o J H ~ n r : 'i

of

Optical

Nudear

N IN E T E E N

Spectro~copy

EIGHT

Spectrometry CHAPTER

CHAPTER

\-lagllHic

B(,:-;oW:Hln~

4gB

CHAPTER

TWENTY

CHAPTER

T W "E N T Y -O N E

.\-Ioircillar

:\Ias-'i

S llC ( 't n llll( 'lr ~

;");-){)

16;.

III;;;truments CHAPTER

to Spectrometric

:::!

N IN E

flU(IH'SCt'IH'(,

An Introduction

to Optical

Atomic

Sprctroscnpy

.'-illrLict'

and l\licros('op~

Charadnizal

ion

h~

"~8q

1;) Atomic Ab:-iorptioll and

Slwi'tronwtr~

230

A to m ic

In!'itrumeutal Analvsi:"O in AdionAssessin~ the Al1tl;enticit~· of tht~ ,"iulan.1 'lap: Surfact~ .~nalysis Art. and Forensics

ill the S.'n"if'e of Ifistoq-. ( l~ - t

Instrtllllental Anah'sis

A"IJ·lamide

in .-\dion-()iscon~rin(J'

890"

~

E leet roallal,·rieal Chemistry CHAPTER

Contents

():2"7

T W E N T Y -T W O

Elt~nrfJallalytical

.\ll

Chf'lIIi . ;,tr~

~ liscellaneous !\lethods 89.3

1 1 Ir r n d l!I.,ti( ) [\ In

(I~(l

CHAPTER

Instrumental

Analysis

in .\ction-i\lt·asuring-

the Parts to hlrophysiometer

,-) CHAPTER

Separation CHAPTER

1\1ethocls

T W E N T Y -S IX

Chromatographic

Instrumental Analysis in ActionVollman Case 964

:\11 IllrroJlt(_~tion to

Separarion.:;

CHAPTER

T W E N T Y -S E V E N

CHAPTER

T W E N T Y -E IG H T

'0 : 2

Cas ChnlllliHngraphy

....33

ONE

Evaluation of Aualytical Data

A P P E N D IX

TW O

Activity CoefficicIlb

A P P E N D IX

THREE

CHAPTER

CHAPTER

APPENDIX S U f 1 t 'f c r i t i , 'a l

and Extraction

T H IR T Y

96~

9 (H

and Furmal

IA 18 IC ID IE

Classification of Analytical Methods Types of Instrumental Methods 2 Instruments for Analysis 3 Calibration of Instrumental Methods Selecting an Analytical Method 17 Questions and Problems 22

Capillary

(:apillary Elcctnwhromatography. Fractionation 367

F illill

R")()

EIt:'ctrupllOfC:3i::i.

and Ficld-FIO\\

Preparation

Elements

11

Compuunds RecollllnendeJ for tile of Stant lard Solutions of Some Common

1001

TW O

Eleetl"ieal Components

and CiI"ellils

2D Power Supplies and Regulators 2E Readout Devices 51 Questions and Problems 54 CHAPTER

SO

90

26 CHAPTER

2A Direct-Current Circuits and Measurements 28 Alternating Current Circuits 32 2C Semiconductors and Semiconductor ·Devices 43

and Computel"s

4A Analog and Digital Signals 81 4B Counting and Arithmetic with Binary Numbers 81 4C Basic Digital Circuits 83 4D Computers and Computerized Instruments 4E Components of a Computer 92 4F Computer Software 95 4G Applications of Computers 103 4H Computer Networks 104 Questions and Problems 108

FOUR

CHAPTER

FOUR

Bigital Electronics

L iq u id

8th

T W E N T Y -N IN E

Chromarography

Some Standard 997

ONE

Intl"odlletion CHAPTER

A P P E N D IX

Electrode Potentials ChrolllJ.wgraphr

The John

Applications of Operational Amplificrs to Comparison 74 Questions and Problems 74

26

49

F IV E

Signals and Noise

110

5A The Signal-to-Noise Ratio 110 58 Sources of Noise in Instrumental Analyses 5C Signal-to-Noise Enhancement 113 Questions and Problems 124 Instrumental Analysis in AdionThe Electronic Analytical Laboratory

111

127

THREE

Opentlional Amplifiers in Chemieal hlStl"lImentation ;" ) < )

.. t01l11e'Jlwetroscopy \

3A Properties of Operational Amplifiers 59 3B Operational Amplifier Circuits 62 3C Amplification and Measurement of Transducer Signals 65 3D Application of Operational Amplifiers to Voltage and Currcnt Control 70 3E Application of Operational Amplifiers to Mathematical Operations 71

CHAPTER

"C '

S IX

.\n IlItl"odlietioli to Spl'cll'onwtric "('(hods \:32 6A General Propertics of Electromagnetic Radiation 132 68 Wavc Properties of Electromagnetic Radiation 133

1 ."'-'~1

6C Quantum-Mechanical Properties of Radiation 144 60 Quantitative Aspects of Spectrochemical Measurements 157 Questions and Problems 159 C H A P T E R

of Optical Instnlmenb

164

General Designs of Optical Instruments Sources of Radiation 166 W avelength Selectors 175 Sample Containers 190 Radiation Transducers 19J

7F Signal Processors and Readouts 7G Fiber Optics 202

164

C H A P T E R

140 Quantitative Analysis by Absorption Measurements 374 14E Photometric and Spectrophotometric Titrations 379 14F Spectrophotometric Kinetic Methods 14G Spectrophotometric Studies of Complex Ions 384 Questions and Problems 390

2111

Some General Features of Atomic Mass Spectrometry 281 lIB Mass Spectrometers 283 II C Inductively Coupled Plasma Mass Spectrometry 291 110

Spark Source Mass Spectrometry

llE llF

Glow Discharge Mass Spectrom~try Other Mass Spectrometric Methods Questions and Problems 301

C H A P T E R

202

T W

12A 12B 12C 120 12E

212

E IG H T

299 300 301

Instrumental Analysis in AetionMonitorin;; Me •.c nry 332

C H A P T E R

8C Sample-Introduction Methods Questions and Problems 228 C H A P T E R

N IN E C H A P T E R

Atomie Ahsorption and Atomie FItIOI'escence Speetmlllcli'y 2;30 9A Sample Atomization

Techniques

230

9B Atomic Absorption Instrumentation 9C Interferences in Atomic Absorption Spectroscopy 241

I3A

237

I3B

90 Atomic Absorption Analytical Techniques 9E Atomic Fluorescence Spectroscopy 249 Questions and Problems 250

247

C H A P T E R

;3;36

and

13C The Effects of Instrumental Noise on Spectrophotomctric Analyses 343 130 Instrumentation 348 362

T E N

Atomic Emission SpeetronH'tl')

C H A P T E R

F O U R T E E N

Based on Plasma

lOB Emission Spectroscopy Sources 269

Based on Arc and Spark

IOC Miscellaneous Spectroscopy

Sources for Optical Emission 273

Questions

276

\pplications of l;ltnl\·iolet- \isihle \lolecuhu'\hs''''l'tion Speetromt'tr) 14A The Magnitude of Molar Absorptivities 1413 Absorbing Species 367 14C Qualitative Absorption

:16-:'

431

367

Applications of Ultraviolet-Visible Spectroscopy 372

T W

E N T Y -O N E

hy Speetros('upy

21A 21B 21 C 210 21 E 21F

Introduction to the Study of Surfaces 589 Spectroscopic Surface Methods 590 Electron Spectroscopy 591 Ion Spectroscopic Techniques 602 Surface Photon Spectroscopic Methods 604 Electron-Stimulated Microanalysis Methods 607 21G Scanning Probe Microscopes 613 Questions and Problems 622 I":;tr,,mental Analysis in Aetion.\.ss••ssing the Authenticity of th •• Vinland

E IG H T E E N

~Iap: Su •.fa" •• Analysis in the S ••niee lIistory .. \1'1. and Fo •.•.n sies 624

4 3 1

18A Theory of Raman Spectroscopy 481 18B Instrumentation 487 18C Applications of Raman Spectroscopy

5.50

551

20C Mass Spectrometers 563 200 Applications of Molecular Mass Spectrometry 577 20E Quantitative Applications of Mass Spectrometry 583 Questions and Problems 585

Sudan' Chanu'terizatioll and i\Iiel'Oseopy 589

S E V E N T E E N

Haman Sp""'I'OS"'IP~

E N T Y

20A Molecular Mass Spectra 20B Ion Sources 551

Mid-IR Absorption Spectrometry 455 Mid-IR Reflection Spectrometry 469 Photoacoustic IR Spectroscopy 472 Near-IR Spectroscopy 473 Far-IR Spectroscopy 476 IR Emission Spectroscopy 476 IR Microscopy 477 Questions and Problems 477

C H A P T E R

T W

'\Iuleeulm' M ass Speeiromelr'y

2 ;")4

lOA Emission Spectroscopy Sources 255

and Problems

C H A P T E R

Applicatiulls of Infrato•.d Spedloumdry 4;')5 17A 17B 17C 170 17E I7F 17G

499

Environmental Effects on NMR Spectra 510 NMR Spectrometers 521 Applications of Proton NMR 526 Carbon-13 NMR 529 Application of NMR to Other Nuclei 533 Multiple Pulse and Multidime~sional NMR 534 19H Magnetic Resonance Imaging 537 Questions and Problems 542

C H A P T E R

Measurement of Transmittance Absorbance 336 Beer's Law 337

Questions and Problems C H A P T E R

and

T H IR T E E N

An Introduetion to Lltradolet-Visihle M oh"'ular Ahsorption Speetnllnelr'y

N IN E T E E N

,",ndl'ar "Ia~n('tie HesonHn('t' Spedrus('UI;y 491l . 19A Theory of NMR

S IX T E E N

16A Theory of IR Absorption Spectrometry 16B IR Instrumentation 438 16C IR Sources and Transducers 449 Questions and Problems 452

Molecular Spectroscopy

223

493

19B 19C 190 19E 19F 19G

An Intmduetioll tu Infroared 4:30 Speetrometry

8A Optical Atomic Spectra 215 8B Atomization Methods 223

Other Types of Raman Spectroscopy Questions and Problems 495

C H A P T E R

381

F IF T E E N

15A Theory of Fluorescence and Phosphorescence 400 15B Instruments for Measuring Fluorescence Phosphorescence 411 15C Applications of Photoluminescence Methods 418 150 Chemiluminescence 422 Questions and Problems 426

:3();3

Fundamental Principles 303 Instrument Components 310 X-ray Fluorescence Methods 317 X-ray Absorption Methods 325 The Electron Microprobe 328 Questions and Problems 328

An Intmdnetion to Optical Atomic Spt'etrometry 215

C H A P T E R

180

I\lolet:nlar LumilH'sct'nct' Speetrometr) ;399

E L V E

\tomic X-r'ay Spectnlllwtry·

7H Types of Optical Instruments 203 7I Principles of Fourier Transform Optical Measurements 204 Ouestions and Problems

E L E V E N

IIA

S E V E N

Components 7A 7B 7C 70 7E

C H A P T E R

Atomic \lass Spectmmet,·y

492

of

25E 25F

Electroanalytical Chemistry 62:

25G Applications of Voltammetry 25H Stripping Methods 748 251

C H A P T E R

T W

E N T Y -T W

O

An Introduction to Electroallalytical Chcmistry 628 . 22A Electrochemical

Cells

22E Currents in Electrochemical Cells 647 22F Types of Electroanalytical Methods 653 Questions and Problems 653 T W

T W

6.'59

24B An Introduction Analysis 701

during an

to Coulometric

24C Controlled-Potential Coulometry 240 Coulometric Titrations 707 Questions and Problems 712

Methods of

Applications of Chromatography Questions and Problems 785

C H A P T E R

(;11>;

T W

E N T Y -S E V E N

Chl'Omatogmphy

788

Columns and Stationary

27F

Gas-Solid Chromatography 810 Questions and Problems 811

716

Excitation Signals in Voltammetry 717 Voltammetric Instrumentation 718 Hydrodynamic Voltammetry 723 Cyclic Voltammetry 737

28A Scope of HPLC

816

816

Column Efficiency in LC 817 LC Instrumentation 818 Partition Chromatography 828 Adsorption Chromatography 837 Ion Chromatography 839 Size-Exclusion Chromatography 844

T H IR T Y -T H R E E

29A Properties of Supercritical Fluids 856 29B Supercritical Fluid Chromatography 857 29C Supercritical Fluid Extraction 862 Questions and Problems 865

33B Flow Injection Analysis 931 33C Micronuidics 940 33D Discrete Automatic Systems 942 Questions and Problems 948

C H A P T E R

C H A P T E R

T H IR T Y

30A 30B 30C 300 30E

An Ovcrview of Electrophoresis 867 Capillary Electrophoresis 868 Applications of CE 875 Packed Column Electrochromatography Field-Flow Fractionation 884 Questions and Problems 888 Instrumental Analysis in AdionDiscovering

Aerylamide

890

'\/liscellaneous

C H .!\P T E R

31A 31 B 31 C 31 D

894

T H IR T Y -T W

l{ad ioehemical

O

'Ietlwds

32A Radioactive Nuclides 32B Instrumentation

916

9.50

34A Introduction to Particle Size Analysis 950 34B Low-Angle Laser Light Scattering 951 34C Dynamic Light Scattering 955 34D Photosedimentation 958 Questions and Problems 962 Instrumental Analysis in AdionThe John Vollman Case 964 1 E,"aillation of Analytical Data Precision and Accuracy 967 Statistical Treatment of Random Errors Hypothesis Testing 983 Method of Least Squares 985 Questions and Problems 988

A P P E N D IX

alA alB alC aID

a2C The Debye-HUckel Equation

Thermogravimetric Analysis 894 Differential Thermal Analysis 897 Differential Scanning Calorimetry 900 Microthermal Analysis 904 Questions and Problems 906

C H A P T E R

T H IR T Y -F O U R

Pal,tiele Size Determination

883

Cl29

929

9h7 971

A P P E N D IX

T H IR T Y -O N E

\Iethods

:\Iethods of Analysis

33A Overview

2 Actiyity Coefficients 444 a2A Properties of Activity Coefficients 994 a2B Experimental Evaluation of Activity Coefficients 995

893

E N T Y -E IG H T

Li1luid Chl'onJatognlphy 28B 28C 28D 28E 28F 28G

E N T Y -N IN E

Automated

Thcl'mal

Applications of GC 806 Advances in GC 808

T W

C H A P T E R

T W

Supercritical Fluid Chl"Olllatography and Extraction 856

Methods

270 27E

C H A P T E R

C H A P T E R

781

703

E N T Y -F IV E

\'oltammetl"y 25A 25B 25C 250

762

26C Band Broadening and Column Efficiency 768 260 Optimization of Column Performance 775 26E Summary of Chromatographic Relationships 781

27C Gas Chromatographic Phases 800

697

24A Currcnt- Voltage Relationships Electrolysis 697

T W

E N T Y -S IX

An lutroduction to Chromatogmphi,' S('pamtions 762

26F

32C Neutron Activation Methods 918 32D Isotope Dilution Methods 924 Questions and Problems 925

Capilhll'y Electrophoresis. Capillary E1ectl"Oehromatography, and Field-Flow fmctionation 867

27 A Principles of GLC 788 27B Instruments for GLC 789

E N T Y -F O U R

Coulomelry

C H A P T E R

T W

26A General Description of Chromatography 26B Migration Rates of Solutes 765

General Principles 659 Reference Electrodes 660 Metallic Indicator Electrodes 662 Membrane Indicator Electrodes 664 Ion-Selective Field-Effect Transistors 675 Molecular-Selective Electrodc Systems 677 Instruments for Measuring Cell Potcntials 684 Direct Potentiometric Measurements 686 Potentiometric Titrations 691 Questions and Problems 692

C H A P T E R

C H A P T E R

M ethods

E N T Y -T H R E E

Potclltiomefl"y 23A 23B 23C 230 23E 23F 23G 23H 231

Measuring the Parts to Understand the W hole: The l\1icrophysiOlIll·ter 757

Separation

28H Affinity Chromatography 848 281 Thin-Layer Chromatography 848 Questions and Problems 851

746

Voltammetry with Microelectrodes 751 Questions and Problems 753 Instrumental Analysis in Aetion-

628

22B Potentials in Electroanalytical Cells 633 22C Electrode Potentials 635 220 Calculation of Cell Potentials from Electrodc Potentials 645

C H A P T E R

Pulse Voltammetry 742 High-Frequency and High-Speed Voltammetry 745

9 ()9

909

A P P E N D IX

Potentiab

3

80me Standard 9'J7

995

amI Formal Electrode

4 COltll'olll"b Heconllllen,kd for the Pn:'paralion of Standard Solutions of SO Ill(' Coltlluon E"'merlts 100 I

A P P E N D IX

Preface

Today, there is a wide and impressive array of powerful and elegant tools for obtaining qualitative and quantitative information about the composition and structure of matter. Students of chemistry, biochemistry, physics, geology, the life sciences, forensic science, and environmental science must develop an understanding of these instrumental tools and their applications to solve important analytical problems in these fields. This book is addressed to meet the needs of these students and other users of analytical instruments. W hen instrument users are familiar with the fundamental principles of operation of modern analytical instrumentation, they then will make appropriate choices and efficient use of these measurement tools. There are often a bewildering number of alternative methods for solving any given analytical problem, but by understanding the advantages and limitations of the various tools, users can choose the most appropriate instrumental method and be attuned to its limitations in sensitivity, precision. and accuracy. In addition, knowledge of measurement principles is necessary for calibration, standardization. and validation of instrumental methods. It is therefore our objective to give readers a thorough introduction to the principles of instrumental analysis. including spectroscopic. electrochemical, chromatographic, radiochemical, thermal, and surface analytical methods. By carefully studying this text, readers will discover the types of instruments available and their strengths and limitations.

•

Section 1 contains four chapters on basic electrical circuits, operational amplifiers, digital electronics and computers, signals, noise, and signal-to-noise enhancement.

•

Section 2 comprises seven chapters devoted to various atomic spectrometric methods, including an introduction to spectroscopy and spectroscopic instrumentation, atomic absorption, atomic emission, atomic mass spectrometry, and X-ray spectrometry.

•

•

•

•

Section 3 treats molecular spectroscopy in nine chapters that describe absorption, emission, luminescence, infrared, Raman, nuclear magnetic resonance, mass spectrometry, and surface analytical methods. Section 4 consists of four chapters that treat electroanalytical chemistry, including potentiometry, coulometry, and voltammetry. Section 5 contains five chapters that discuss such analytical separation methods as gas and liquid chromatography, supercritical fluid chromatography, electrophoresis, and field-flow fractionation. Section 6 consists of four chapters devoted to miscellaneous instrumental methods with emphasis on thermal, radiochemical, and automated methods. A chapter on particle size analysis is also included in this final section.

Since the first edition of this text appeared in 1971. the field of instrumental analysis has grown so large and diverse that it is impossible to treat all of the modern instrumental techniques in a one- or even twosemester course. Also, instructors have differing opinions on which techniques to discuss and which to omit in their courses.

This text is organized in sections similar to the fifth edition. After the brief introductory chapter. the hook is divided into six sections.

Because

of this. we have

included

more material in this text than can bc covered in a single instrumental analysis course, and as a result. this comprehensive text will also be a valuable reference

nieal assistance for years to come. An important advantage of organizing the material into sections is that instructors have flexibility in picking and choosing topics to be included in reading assignments. Thus, as in the previous edition, the sections on atomic and molecular spectroscopy, clectrochemistry, and chromatography begin with introductory chapters that precede the chapters devoted to specific methods of each type. After assigning the introductory chapter in a section, an instructor can select the chapters that follow in any order desired. To assist students in using this book, the answers to most numerical problems are provided at the end of the book.

•

•

•

W e have included a new chapter on particle size determination (Chapter 34). The physical and chemical properties of many research materials and consumer and industrial products are intimately related to their particle size distributions. As a result, particle size analysis has become an important tech-

•

Throughout the text, we have attempted to present material in a student-friendly style that is active and engaging. Examples are sprinkled throughout each chapter to aid in solving relevant and interesting problems. The solutions to the problems in each example are indicated so that students can easily separate the problem setup from the problem solution.

~ Spreadsheet applications have been included throughout to illustrate how thesc powerful pro-

· I I I The book's companion wensite at

www.thom

son ••du,corn/chemistr}'/skoog includes more than 100 interactive tutorials on instrumental methods,

proach is required or supplemental reading is appropriate, readers are referred to our companion book, Applications of Microsoft') Excel in Analytical Chemistry (Belmont, CA: Brooks/Cole, 2(04), for assistance in understanding these applications.

simulations of analytical techniques, exercises, and animations to help students visualize important concepts. In addition, Excel filcs containing data and sample spreadsheets are available for download. Selected papers from the chemical literature

The hook is now printed in two colors. This particularly aids in understanding the many figures and diagrams in the text. The second color clarifies graphs; aids in following the data flow in diagrams;

are also availanle as PDF files to engage student interest and to provide background information for

provides keys for correlating data that appear in multiple charts, graphs, and diagrams; and makes •

•

nique in many research and industrial laboratories. Exciting new Instrumental Analysis in Action features have been added at the end of each of the six sections. These case studies describe how somc of the methods introduced in each section can be applied to a specific analytical problem. These stimulating examples have been selected from the forensic, environmental, and biomedical areas.

grams can be applied to instrumental methods. Problems accompanied by this icon ~ encourage thc use of spreadsheets. W hen a more detailed ap-

•

•

ter and requires reading the original literature of analytical chemistry, derivations, extensive analysis of real experimental data, and creative problem solving. All chapters have been revised and updated with recent references to the literature of analytical chemistry. Among the chapters that have been changed extensively are those on mass spectrometry (Chapters II and 20), surface characterization (Chaptcr 21), voltammetry (Chapter 25), chromatography (Chapters 26 and 27), and thermal analysis (Chapter 31). Throughout the hook, new and updated methods and techniques arc described, and photos of specific commercial instruments have been added where appropriate. Some of these modern topics include plasma spectrometry, fluorescence quenching and lifetime measurements, tandem mass spectrometry, and hiosensors. Many new and revised charts, diagrams, and plots contain data, curves, and waveforms caleulaied from theory or obtained from the originalliteratuce to providc an accurate and rcalistic representation.

for a more pleasing overall appearance. An open-ended Challenge Problem provides a capstone research-oriented experience for each chap-

study. Throughout the book, this icon b l l alerts and encourages students to incorporate the wensite into their studies. •

An Instructor's Manual containing the solutions to all the text problems and online images from the text can he found at www.thomsonedu.com/ ('hclllis(ry/skoog.

W e wish to acknowledge the many contributions ofreviewers and critics of all or parts of the manuscnpt. Those who offered numerous helpful suggestions and corrections

include:

Larrv Bowman, University of Alaska, Fairbanks John'Dorsey, Constantinos

Florida State University E. Efstathiou, University of Athens

Dale Ensor, Tennessee Tech University Doug Gilman, Louisiana State University . Michael Ketterer, Northern Arizona UniverSity Robert Kiser, University of Kentucky Michael Koupparis, University of Athens David Rvan, University of Massachusetts-Lowell Alexand~r Scheeline, University of Illinois at UrbanaChampaign Dana Spence, W ayne State University Apryll Stalcup, University of Cincinnati Greg Swain, Michigan State UnIvcrslty Dragic Vukomanovic, UniverSity of MassachusettsDartmouth Mark W ightman, University of North Carolina Charles W ilkins, University of Arkansas Steven Yates, University of Kentucky W e are most grateful for the expcrt assistance of Professor David Zellmer, California State UniverSity, Fresno, who reviewed most of the chapters and served as the accuracy reviewer for the entire manuscnpt. HIS efforts are most heartily appreciated. W e owe special thanks to Ms. Janette Carver, head of the University of Kentucky Chemistry/PhysIcs LIbrarv, who, in addition to serving as a superb reference libr;rian,

provided essential library scrvices and tech-

in the use of the many electronic

re-

sources at our disposal. Numerous manufacturers of analytical instruments and other products and services related to analytical chemistrv havc contributed by providing diagrams, application' notes, and photos of their products. W e are particularly grateful to Agilent TechnologIes, BlOanaIvtical Svstems, Beckman Coulter, Inc .. Bnnkman Ins'trume;ts, Caliper Life Sciences, Hach Co., Hamamatsu Photonics, InPhotonics, Inc., Kaiser Optical Svstems, Leeman Labs, LifeScan, Inc., MettlerToledo, Inc., National Instruments Corp .. Ocean Optics, Inc., Pcrkin-Elmer Corp., Post nova Analytics, Spectra Analytical Instruments, T. A. Instrume~ts, Thermo-Electron Corp., and Varian, Inc. for provldmg photos. W e are cspecially indebted to the many members of the staff of Brooks/Cole-Thomson Learning who provided excellent support during the production of this text. Our development editor, Sandra Kiselica: did a wonderful job in organizing the project, in keepmg the authors on task, and in making many important comments and suggestions. W e also thank the many people involved in the production of the book. W e arc grateful to Katherine Bishop, who served as the project coordinator, and to Belinda Krohmer, the project manager at Brooks/Cole. Finally, we wish to acknowledgc the support and assistance of our publtsher DaVid Harris. His patience, understanding, and guidance were of great assistance in the completion of the project. Douglas A. Skoog F. J ames Holler Stanley R. Crouch

1A

I n tr o d u c tio n

CLASSIFICATION METHODS

OF ANALYTICAL

Analytical methods are often classified as being either or i/ls tr u m e llta l. Classical methods, so';;etimes called w e t- c h e m ie a l m e th o d s , preceded instrumental methods by a century or more.

c la s s ic a l

A .

yie ld s

.•.•

n. .a ../y.tic . a l. C he..~ . .i..s.tr y d .e... a... ls w ith m e th o d s fo r d e te r m in in g

in [ c : ; m a tio n

m o le c u la r ~ p e c ie s s a m p le .

th e c h e m ic ( ll

,s ~ r n p le s 0 fl! lfltte r .

a lJ e u t th e id ~ fltity o r th e fu n c ti~ n fl

I lg u a n tita tivt.

m e th o d :

p r o vid e s n ,m e r ic a l.in fo r m a tio ~ a s ( lm o u n t

r7l lQ.J

c o m p o s itio n

of

A I J u .a lita tive ' fle th o d o f a lfJ m ic o r

groups

in th e

in c o n tr a s t, to th e r ~ la tive

o f ( m e o r m o r e o f th e s ( n io m p o n e n ls .

Throughout the book, this logo indicates an opportunity for online self-study. Visit the book's cOfilpanion website at www.thomsonedu.com/ ehemistrylskoog to view interactiVe tutorials, guided simulations, and exercises.

In the early years of chemistrv, most analvses were carried out by separating the c'omponents ~f interest (the a n a lyte s ) in a sample by precipitation. extraction, or distillation. For qualitative analyses, the separated components were then treated with reagents that yielded products that could be recognized by their colors, their boiling or melting points, their solubilities in a series of solvents, their odors, their optical activities, or their refractive indexes. For quantitative analyses, the amount of analyte was determined by g r a vim e tr ie or by vo lu m e tr ic measurements. In gravimetric measurements, thc mass of the analytc or some compound produced from the analyte was determined. In volumetric, also called titr im e tr ic , procedures, the volume or mass of a standard reagent required to react completely with the analyte was measured. These classical methods for separating and determining analytes are still used in many laboratories. The extent of their general application is, however, decreasing with the passage of time and with the advent of instrumental methods to supplant them.

Early in the twentieth century, scientists began to exploit phenomena other than those used for classical methods for solving analytical problems. Thus, measurements of such analyte physical properties as conductivity, electrode potential, light absorption or cmission, mass-to-charge ratio, and fluorescence began to be used for quantitative analysis. Furthermore, highly efficient chromatographic and electrophoretic techniques began to replace distillation, extraction, and precipitation for the separation of components of complex mixtures prior to their qualitative or quantitative determination. These newer methods for separatiilg and determining chemical species are known collectively as in s tr u m e /lta l m e th o d s o f a /la lr s is .

Many methods

of the phenomena

underlying

have

for

been

known

Their

application

by most

layed

by lack of reliable

In fact, the growth analysis tronics

scientists, and

has paralleled

the

more. was de-

forms

of the

of

elec-

industries.

application to the analyte

of the analyte

by the analyte; teraction

TYPES OF INSTRUMENTAL METHODS

then rate,

let

us first consider

some

of the chemical

characteristics

that are useful

tative

Table

analysis.

properties

that

analysis. require

a source from

for qualitative

emission

excited-state

to seJect

an optimal

method

used

for

magnetic

the atoms then

radiation,

the instrument. of a rapid

which

Sources

thermal

electromagnetic

change radiation

instrumental

listed

to stimulate For

emit

a measurable

example,

gaseous to higher

in the table

of the analyte

energy

is the quantity

instrumental

classical

eombinations mental

states.

The

a gravimetric

electro-

measured

may -take

bv

the for~ example;

a selected

region

interferencc. convenience, cult to draw. costly

pr~perties

properties ratio,

are

reaction

from

physical

among

are

tions.

Thus.

violet

and

electrical

approach

in-

that

sophisticated

diffi-

instrumenor

more

Emission spectroscopy (X-ray, UV, visible, electron. Auger); fluorescence, phosphorescence, and luminescence (X-ray, Uv, and visible)

of radiation

Refractometry;

Diffraction

of radiation

X-ray and electron

tion

ahout analyte

and

interpreted

of radiation

Electrical

poten tial

Potcntiomctry:

Electrical

charge

('oulomctry

Electrical

current

Ampcromdry:

Electrical

resistance

('onductometry

ratio

Rate of reaclion Thermal

Polarimetry;

Gravimetry

Mass-to-charge

charactcristic"i

the physical

diffraction

spectroscopy:

because studied

we these

output

produced

is contained

lengths circular dichroism

extent

of visible

the analyte, is usuallv

mcchanical,

the system

and physics.

under

dcvices

Before

The

in-

systems

be-

ment

To

Figure

it is

a sample

how information

hy the analyte.

whose

resulting

scheme

characmodcs

based

understanding

of

A classi-

d a r a d o m a in s .

the analysis

such

s ig n a ls ,

"arious

developed

1-2. data domains

on this con-

of instrumental of the measure-

in the data-domain may be broadly

map

classified

of

into

n o n e le c tr ic a l d o rn a ifls and e le c tr ic a l d o m a in s .

that result of

The

measurement

from

resides

in these

A fa-

acteristics

\\ia\'e~

to measure The intensity

the

,tuJ~

experimenter.

shOWing the overall process

domains.

in noninfor-

experiment

Among

these

chemical

and others

to make

char-

composition, listed

a measurement

entirely

in the first

of the mass

balance

of the object.

units

who provides

the

domains.

of the mass

equal-arm

of an obi'1\ o"es

which

a

is placed

masses

rlaced on a

repr(,sL'ntin~

IhL' mass of

pan. with standard

in standard

by ha"ing

in nonelectrical

the determination

ran. The information

the object

ends chemical

in a particular

density,

a mcchanical

on one balance

and and

I-I.

reside

unda

begins

physical

of light. pressure,

using

second

data

length,

of Tablc

It is possible

of

The

is of interest

arc

intensity column

process

domains. that

Sptcrn

Block diagram

The

it

can be e n -

and chemical

are called

As shown

function,

e le C lr ic a l

and charge.

and promotes

mation

(ljuartz crystal microbalance)

1-1

by

has heen

process.'

electrical

infor-

l\fass spec[fOmetr~/

of an instrumental measurement.

by physical

particularly

of

to an-

stimulus

study

band

by a wide variety from one form

how instruments

information

fication

is aided

information

voltage,

comparison

FIGURE

to

can he repre-

investigating

For instance,

Acti\"ation and isotope dilution methods

it is instructi"e

of interest

in the

with thc analyte.

a narrow

light through

thermal

analvte

Dr graphical

to understand

and

ject

differential

process

that convert

polarography

s'l

PrD~J;:;rtie3 of SH!con

snd

G:9j·rJ~2Hli\jnl 5·am!co{1thA,;:;x~)?'5

Silicon thus

and have

formation.

germanium f(~ur valence

arc

Gruup

electrons

In a silicon crvstal.

IV' dements available

and

for bond

cach of these electrons

is

k-

localized

hy comhination

with an electron

silicon atom to form a co\-aknt there

are no free electrons

material

would

howe\·er. bonded

state, leaving

lattice

and

termed

agitation

an occasional

leal'es

The hole. however.

to the electrical

crystal.

The mechanism

bound

electron

dircction

motion

conquctivity

can be greatly

icon

amount

by diffusion,

crystal.

conductor arsenic

is stepwise;

silicon

atom

a

electrons

in onc

is doped

as indium element

replaces

When

a silicon

atom

of thermal

this electron

for conduction,

Group

because

there

energy

is little

a covalent

tion,

A semiconductor

for electrons to this nonbonding

that

has been

electrons

type) hecause

negatively

charged

crvstaL

which

con atoms.

but their

the number

of electrons:

number thus,

as

such V un-

\\'ith represent

(positive

type)

when silicon or germanium ement. Here,

which holes

joining ated parts

silicon a

only

introduced

atoms

jump

\\'Ith the impurity'

~vlovcment atOIn.

contains are

is doped

negative of the

as described

valence electrons

to the vacant

atum.

charge holes

three

:\ote that to

from

earlier.

the

con'ititlltcs

the f! region

is created

in the

diffuse

that

into

reverse

is separation

region,

which

causes

in the opposite

from the diffusion

a migration

direction,

it

II-typ e

tion region

to

m illo r-

tential a

p ll

junction,

electrons.

td

hand,

the

atoms. silicon in

p ll

of the materidiodes,

voltage

is little resistance to the n-type

junction

offers

in the opposite

in the On the

a high resistance

direction

it

across

to current materiaL

to

and is thus a

2-15b illustrates

the symbol

for a diode,

arro\\" points

in the direction

of low resistance

tin: currents.

The triangular

portiun

hol may be imagined rent in a conductin§,Figure charge

~-15c shows

when

tu point

The

to po:-;i-

of the diode

in the direction

is called

by application

sym-

of cur-

carriers

the influence where The

combine

ne"ative

trons

i:to

hand,

terminal process;

extracts

the p region

is made

of conduction

positi\'e

of

with respect

tance

present under

in each

reverse

conductance

each

injects

which

can 'then

the positive

terminal.

othcr.

new elec-

continue

thc

on the other

from the p region,

thus creat-

toward

the p n

is r n a s e b lilsed , as in Figure

carriers

to form Only

2-15,1.

in each region drift away from the

the depiction

layer.

drifts

forward

toward

the junc-

Consequentlv,

bias is tvpically

under

C u rre n t-V o lta g e

conduc-

10 "tLl 10'

that of

bias,

C u rv e s fo r

S e m ic o n d u c to r

D io d e s

Figure

2-16 shows

the hehayior

ductor

diode

forward

ward

under

bias, the current

with voltage.

which

the small concentration

contains

of minority

nium diode

Learn more: about diodes.

under

\'l)lu.i!!t'

range.

of a typical

and reverse

increases

For some

power

nearly diodes,

c:xpnnentially' forward

of sC\'tT'-

in thc

or

fo l l o l \ ' e r ,

will be a dc

three

different

vo !tilg e

fo l l o l l ' ( ' r

-~-

~

signaL in the case of a dc

input. the output as the input.

are

c o m p a r a to r

and the

of p h a s e with the signal at

input of an amplifier,

\'-,-

~lGUriE 8.:3 Operational amplifier current follower.

operatmg

3-5 Voltage follower. The amplifier output is connected directly back to the amplifier inverting Input. The input voltage ", is connected to the noninverting Input. The output voltage is the sum of the input voltage and the difference voltage ",. If the output voltage is not at limit, v , is very small. Therefore, I'" = 1', and the output voltage follows the input voltage. FlOUR

range

38-1

I

Comparators

[n the comparator used

mode, without

o p e n !o a p ,

the operational any feedback

ure 3-4a, [n this mode,

the amplifier

(often

:'::15-V

inputs. A(v_

supply

supplies).

Usually,

the

directly

to the two 01' amp

amplifier

1 '_ ) .

If A

limits V/1 0

6

range

-13IJV in Figure

1 '+

+

is givcn

1 '0

by

for example,

,

+ 13

would

for a small region

V,

2-

v , is in the

tells us whether

1 '_

than

13 IJV. the output

FKmRE 3-4 (a) Comparator mode. Note that the , operational amplifier has no feedback and is thus an open-loop amplifier. (b) Output voltage v " of operational amplifier as a function of input difference voltage ",. Note that only a very small voltage difference at the two inputs causes the amplifier output to go to one limit or the other.

>

or

v _

1 '+




v.

is at negative

( -13 V). Some applications of comparator given in Sections 31" and 4C.

limit

circuits

are

A typical shown

operational

in Figure

3-5. Modern,

amplifiers

have

and output

impedances

voltage

input

source

not loaded

by circuits

follower

impedance

source

2A-3,

the

and distorting

vent such loading, device

the inherent ternal

resistance,

a

I'()!w g e

circuit

internal

the voltage

electrodc,

its output

a voltage

was discussed.

must

resistance

source

be much

larger

of the voltage

is a transducer to introduce

to prelent

To prethan

source.

with high in-

a circuit

the loading

or pion known

When

as

error.

is a nearly

devices

Furthermore, ideal buffer

signal

cuits. There

v,

must always the output

we can write,

from

high-

amplifier

follower,

signal

input

~

being

loaded

in Section

amplifier

is not

+ 13

IJV to

' " 0.13%.

v

Not~ gain

that,

is called the outso that it

=

(1 '0 1 1 ',

but low output

I"IR ) v"

I

10 m V, the

2-

purposes,

1 '0

has a unit

amplifier

substitute

Vi'

voltage

mput

To show

=

Imped-

the effect

let us detine

the

the out-

and Pi IS the IIlput

the power

law into this delJmllon

law ( P

~

/1'

[n the

This

mode

used them

provides

to the current on current

to

measure

III the

zero

and prevents

device

or circuit.

measurements

or

C llr r e n t

a nearly

source

by a measuring

fo l -

resIsit from

The ef-

was descnbed

2A-3.

~

and recall

that

the same in a voltage

fol-

F o llo w e r

operational

amplifier

the output

is connected

a

r e s is to r

fe e d b a c k

piifier ence

gain be-

Po is the powerof

where

are approximately

lower. we obtain

high

in impedance,

the operational

If we then

have

impedances.

difference

and Ohm's v,

if 11'0

this circuit

amplifiers

gain as P j P "

and

be quite

l), it can have a very large power

ances

power.

Therefore,

although

operational

power

v , must

IJV for an 01' amp with a gain 01

For all practical

cause

of this large

at limit,

be

(3 -2 )

is kept voltage

the potential to that input

Rf as shown

within

at the inverting

at the noninverting is connected

amplifier

to be m O il

3-6. II the am-

limits,

ii is equal

amplifier

input

Kirchhoff's

equal

If the nOl1lnvertIllg

common,

at circuit

Hence,

is essentially

the inverting

common

current

to the feedback

in-

as long as the lI1put

or at

th e c ir c u it c o m m o n

From

p o te n ti,; ! .

the differ-

as we have seen. input

mode,

input through

is not at limit. The noninvertll1g

vir tu a l/va t

current

supply

input.

to circuit

put is kept very nearly

follower

in Figure

its power

is very small,

1',

current

to the inverting

IS

said

com -

Vir tu a l

law, the input

current

i, plus

the

it,.

bias current

the expression

n e g a til'e

With

fe e d b a c k .

follower given by

of the amplifier.

v"

For the

\'oltagc

10

cir-

Ia\\',

where

Zi and Z" are the input

of the operational because

amplifier.

it means

impedances

lI' point

IS Important

tial. it follows

most no current

from an input: the internal amplifier

ilmpliiicr

ever. can supplv

large currents

amplifier.

1\111 draw alT.

follower

the operational erational

-15

and output

that the voltage and

modern "-10

This result

'The'

limih [u whIch Ih~ op dmp .:-an be dri\,;'n ,He \Jtlcn slightly ks~ than rilL' pO\\cr sllrply \olt;)g~~!:: L'i \. ) bcc 0 by more

v,

few microvolts,

"s shown

amplifier

of 1.0

for the following

3-17a

If

with output

resistance

3-5 By means

is

v ;".

in Figure

and other

hy 10 V for an input

ratio of the amplifier?

tance of 10.0 kll. Find the percentage

- Limit

is compared

and in (b) the comparison

c r o s s i n g d e t e c t o r because

response

versus

in (a), the input voltage

with the circuit The

response

rejection

For a comparator

"3-4 An operational

he-

I)

tion 3B-1. Figure

mode

for comp"rators

changes

gain A need to he to keep the absolute

sign"1

was introduced

ratio is important voltage

ana-

of the bounda[\'

domains.

rejection

If the output

age \', of 500 flV and hy 1.0 Y for a common

signals.

circuits,

mode

ence amplifiers.

of applications

detection

at the interface

"3-2 The common

FO"" [

Limit

of op-

analog

in a wide variety

circuits,

levels, and circuits

'· ,. I~:n:jJ1

+Lil1l~:

does

v_

has output supply.

have to exceed

at limit if th~ open-loop

using spreadsheets.

mltage

limits

If the amplifier l'_

gain A is

ancll

j

Design

a current

of -+ 13 Vand

-14

l'_

(hi

Y when

to be used in a current bias current

follower

follower

of 2.5 nA.

that will produce

a 1.0 \" output

for a 10.0 flA input

for the amplifier

What

is the effective

input resistance

of the current

follower

designed

for the circuit

designed

in part

in

part (al.

hy what to be

iCI

What

is the percentage

input

current

(a)

200.000

3-9 An operational

(b)

500.00n

open-loop

(C)

15

age range

X 10"

amplifier

10 and an input

current.

is used as a comparator.

have to exceed

X

relative

error

(a) for an

of 25 flA" amplifier

gain A ~ 1.0

to be used in an inverting X

105 an input

of :'C 10 V. and an input

bias current

resistance

amplifier

configuration

of 5,U nA. a linear

of I.n X 10"

n.

has an

output

volt-

(a)

Design R,

3-10

an inverting

amplifier

\Vith a gain of 25 such that the input

resistance

is 10 kll.

(b)

Determine

Ic)

Find the input

(d)

How Clluld you avoid a loading input resistance found in (cr?

A low-frequency the anticipated

the range

of usable

resistance

input voltages

of the inverting error

for the amplifier

amplifier

if the voltage •

sine wave voltage is the input output of each circuit.

designed source

to the following

in (a). in (a).

were loaded

circuits.

bv the .

Sketch

(a) (b)

write an expression

and the various

resistances.

indicate

the mathematical

operation

200 ki1: R , 3-17

:'3-11 Calculate

the slew rate and the rise time for an operational

50-ME Iz bandwidth

in which

the output

-\1 ;,

3-13

Design a circuit plied by 1000

for calculating

=

3 \1 ;

changes

amplifier

=

R"

Show the algebraic the [allowing

3-18

that gives the output

voltages

=

400 kll: R ,

relationship

=

voltage

performed

50 kll: R ,

between

=

in terms

of the three

by the circuit

when R,

input

=

R I\

the output

voltage

and input

voltage

for

circuit:

For the circuit

below, sketch

but is switched

to a constant

the outputs positive

at V,,-, and v,," if the input

voltage

is initially

zero

at time zero.

with a

by 10 V

+ W, - 6V,

the average

value

of three

input

voltages

multi-

""'"~ /

3-20

Show that when

suhtractin~

=

10 kll.

;L "

the four reSistances

circuit.

are equal.

the following

circuit

hecomes

a

(a)

What

is the function

(b)

What

function

(c)

Assume

of this signal

are closed interval (d) R,

During

signal

is a linearly

is desired,

During

and switch

a second

54 opens.

slide wire A S in the circuit

its length should contact C be placed of the Weston cell is 1.02 V

consecutive

and S3 closes.

At the end of the second

shown

has a length

to provide

exactly

of 100 em. Where 3.00 Vat

along

What

amplifier

would

What

(i)

What

(j)

The circuit

be the result

would

~[,

= v"

= ~ t,

during

switch

this second

that will produce

1 '0

a circuit

the following

v"

+

= 4.0fV'ldt o

that will produce

=

output:

r

('v,d t

5.0

-u

the following

2.0

VI d t

output:

6.0(

---

+ ",)

v,

II

3-24 Plot the output

voltage

shown

below

described

is an integrating

by E. M. Cordos.

1968,40,1812-1818. R

I, J. 5. and 7 s after

of an integrator

is 2.0 MIl, the feedback

if the input resistor voltage is 4.0 mV

capacitor

American

Chemical

~.;~ .

r---o

V

R

52

'I

i~O\

~

and H. V

Societv,

'-(4

r--(//

the start

,0 - - 1

R

c"1

of intearation

is 0.25 flF. and the inp:t

type of differentiator

5. R. Crouch,

~

,-A/'4.-'-i>l,

SI opens,

disconnecting

the input

at the end of the measurement

1'0

based

on a circuit

r..•.lalmstadt,

An a /.

above

ratemeters

measurement

desirable

for

Refer

of this circuit

of Figure signal

cycle

over the normal

3-16do

were to change

2 ; lt

if the two time intervals

by a time delay

be the result shown

The total

Hint: a circuit

switch

and disadvantages

if the input

were separated

what limitations

C h e r n .,

~tl

this

slope

during

the

cycle?

eral automatic

originally

time period

and plot the output

voltage

differentiator

happen

would

instead

The circuit

during

.

(h)

3-25

51 and S2

1'0

V :;! The voltage

measurement

Design

and the rate of

~tl' switches

is given by

(g)

3-23

voltage

and plot the output

and identical

interval.

Show that the output

operational

Design

increasing

the first period

Describe

Now describe

(0 What are the advantages

3-22

I?

2 perform'?

interval. signal.

The linear

amplifier amplifier

~ ll'

52 opens (e)

*3-21

operational

that the input

change

I',o--A /"

of operational

does

if the two time intervals with consecutive

to part

be imposed

(g), above.

but

enzyme

is 2 .! .t . Discuss

In measuring

if the measurement

duration?

was the basis of sev-

for measuring

instruments

to be as long as possible. might

not consecutive

were of different

time intervals

used in instruments time for these

were

~tJo

enzyme time

kinetics,

wby it is kinetics,

is too 10ngO

rale

The

of growth

and computer

D ig ita l E le c tr o n ic s

Computers tories

tirst hegan

to program

computer

to appear

hut they were

with

devices,

It has heen

mass-produced

however,

that has brought

are found

the scientist

about

high-speed

connection

computers

in the

to the

data analysis, but

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FIGURE 4-17

Computer display of GRAMS IAI being used to fit peaks and baselines

for several overlapping peak-shaped

Signals (Courtesy of Thermo Electron Corp.)

F IG U R E

LabVIEW front panel for a data-acquisition system allows the user to choose such as sampling rate, sample length, and filtering values. (Reprinted with of National Instruments Corporation.)

4 -1 8

parameters permission

F IG U R E 4 -1 9 LabVIEW block diagram of data-acquisition and measurement (Reprinted with permission of National Instruments Corporation.)

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solution of several simultaneous equations, curve fit ting, averaging, and Fourier t ransformat ions. Data storage is another important passive function of computers. For example, a powerful tool for the analysis of complex mixtures results when gas chromatography (GC) is linked with mass spectrometry (MS) (see Chapters 11,20, and 27). GC separates mixtures on the basis of the time required for the individual components to appear at the end of a suitably packed column. MS permits identification of each component according to the mass of the fragments formed when the compound is bomharded with one of a number of different types of particles such as electrons. Equipment for G C /M S may produce data for as many as 100 spectra in a few minutes, with each spectrum being made up of tens to hundreds of peaks. Conversion of these data to an interpretable form (a graph) in real time is often impossihle. Thus, the data are usually stored in digital form for subsequent processing and presentation in graphical form. Identification of a species from its mass spectrum involves a search of files of spectra for pure compounds until a match is found; done manually, this process is time consuming, hut it can be accomplished quickly by using a computer. Here, the spectra of pure compounds, stored on a hard disk, are searched until spectra are found that are similar to the analyte. Several thousand spectra can be scanned in a minute or less. Such a search usually produces several possihle compounds. Further comparison of the spectra by the scientist often makes identification possible. Another important passive application of the power of computers in GC IM S uses the high-speed data fetching and correlating capabilities of the computer. Thus, for example, the computer can be called on to display on a monitor the mass spectrum of anyone of the separated components after the component has exited from a gas chromatographic column.

In active applications only part of the computer's time is devoted to data collection, and the rest is used for data processing and control. Thus, active applications are real-time operations. Most modern instruments contain one or more microprocessors that perform control functions. Examples include adjustment of (I) the slit width and wavelength settings of a monochromator, (2) the temperature of a chromatographic column, (3) the potential applied to an electrode.

(-I) the rate of addition of a reagent, and (5) the time at which the integration of a peak is to begin. For the G C I MS instrument considered in the last section, a computer is often used to initiate the collection of mass spectral data each time a compound is sensed at the end of the chromatographic column. Computer control can he relatively simple, as in the examples just cited, or more complex. For example, the determination of the concentration of elements by atomic emission spectroscopy involves the measurement of the heights of emission lines, which arc found at wavelengths charactcristic for each element (see Chapter 10). Here, the computer can cause a monochromator to rapidly sweep a range of wavelengths until a peak is detected. The rate of sweep is then slowed to better determine the exact wavelength at which the maximum output signal is obtained. Intensity measurements are repeated at this point until an average value is obtained that gives a suitable signal-to-noise ratio (see Chapter 5). The computer then causes the instrument to repeat this operation for each peak of intere~ in the spectrum. Finally, the computer calculates and sends to the printer the concentrations of the elements present. Because of its great speed, a computer can often control variables more efficiently than can a human operator. Furthermore, with some experiments, a computer can be programmed to alter the way the measurement is being made, according to the nature of the initial data. Here, a feedback loop is used in which the signal output is converted to digital data and fed back through the computer, serving to control and optimize how later measurements arc performed.

The connection of two or more computers produces a computer network, or simply a n e tw o r k. In today's world, computer networks arc all around us. We get money from an ATM. access the Internet for information. and watch programs on digital cable television. Each of these examples requires a computer network. Todav, networks significantly increase the efficiency with which information can be transmitted and manipulated."

4H.1 Network

Types

Networks encompass an enormous number of possible interactions between computers, hut they can be classifIed into local area networks, wide area networks, and the Internet. None of the physical networks described here will operate without the approprIate software on all the interconnected machines. L o c a l A re a N e tw o rk S

A lo c a l a r e a n e tw o r k, or LAN, is the least complex type of network. A LAN is a group of linked computers all located at a single site. The usual LAN has a high data-transfer rate ranging from a few megabits per second (Mbps) to gigabits per second (Gbps) .. Manv LANs are physically connected by wires. More r~cently, wireless networks have becomepopular, allowing computers to interact through radiO w~ves sent from a transmitter to receivers. In the past, Wired LANs employed a bus-type architecture, in which computers were connected to a long cable (the bus) With taps along its length as shown in Figure 4-20a. If any of the links between computers were broken in a bus topology, the entire network went down. Coaxial Ethernet networks (IOBase5 and 10Base2) were examples of bus networks. These have been replaced in more modern networks by star topology networks. Twistedpair Ethernet networks (IOBaseTor IOOBaseT) use the star topology shown in Figure -I-20b. Star networks are more robust and less prone to interruptIOns than

~jJ

bus-type networks. Ring networks use a configuration similar to the star network, but in the rmg network information circulates in a ring around the network. The IBM Token Ring network and the tiber-optic distributed-data interface (FDDI) network use ring structures. The computers in a network where users work are called w o r ks ta tio n s . A computer whose resources are shared with other computers on the network is called a s e r ve r . In addition to these physical devices, hubs, access units, network cards, and the appropriate wlflng and cabling arc needed along with software to establish a LAN W id e A re a N e tw o rk s

A second type of network is the I" id e a r e a n e t" ,o r k, or WAN. With a WAN, the computers involved are geographically scattered. These networks are usually LANs joined hy high-speed interconnectIOns and devices called r O llte r s that manage data tIow. WANs are usuall y accessed by leased d igital phone Iim:s (Tccarner lines) operating in the United States at /.) Mbps (T-! lines) or45 Mbps (T-3 or DS3Iines). These leased hnes can be quite expensive, running thousands of dollars per month for T-I lines. T h e In te rn e t

Finally, there is the Internet, which is capable of rapidly transmitting digital representations of an almost unbelievable variety of textual, graphical, audiO, and

1

W~'J:'i::C

is Server

Nelwork printer

FIGURE 4-20 Network topologies. In (a), the bus topology is shown. Here, computers ~S..::.:.for ,::CHllpk 1. HJhr,jlo;cn ;mJ M. fL.Jydcn, S l1 tn \ T e a c h Yo u n e l! \:t'l!'" o rk l1 lj{ III _'4 IfO ljrJ , frH ..haniJpolis. fN: 5ams Puhljshmg. 2f)(j.J; L L Peterson and R S. Da\il', C O n /p U .tt'f Xc r w o r k..L A S U !I:'n o Ap p r o a c h . 3rd ed ~l'W York: Ebc\'ieL 2o(J.1: ..\. S. Tanenhaum. C O n /rU fe r St' ( w u r ks -hh ed .. L'pper Saddle RI\LT N J . Pedhon,Prl.'llIice-Hall PTR. 2002.

w c mmunlcate along a physical bus. Software is necessary on the variouS deVices to alia c~mmunlcation. In (b), a star topology is shown. Here, a junction box or hub connects n computers to one another. In (c), a token-ring topology Is shown. Information Circulates I a ring around the network. MAU ~ multlstatlon access Unit.

Samples

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may If a test fails

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appropriate

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can ensure

are individuallv

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the set may

4-22 Block diagram of an enfire automated laboratory system. (Reprinted with permission from E. L. Cooper and E. J. Turkel, A m e r. L a b ., 1988,20 (3), 42. Copyright 1988 by International Scientific Communications, Inc.) FIGURE

-

be reviewed.

When all required approvals

are performed,

the standard reports

set of

is printed. All samples Updating

Validated, results

approved

are indexed

and stored subsequent

Requests standard rcports serviced

for retrieval.

and long term 4

archiving and recall

and

test data may be archived

and

recalled

from

low-cost media

storage at any time.

for A number

or ad hoc may be at any time.

Generation of user-

of

user-wfltten report

formats

may

designed

be specified,

stored,

repofts

and executed

at any

time. FIGURE 4-21 L1MSdata and sample management overview. (Reprinted with permission fromF.I. Scott, Amer. L a b ., 1987. 19 (11),50. Copyright 1987 by Intemational Scientific C ommUnlCat,ons,Inc.)

video information throughout the world. The Internet is really a network of networks. [( can be accessed in several different ways: by a standard dial-up telephone lIne, by a cable modem employing the same coaxial cable lines that provide cable television signals, and bv a d ig ita l s u b s c r ib e r lin e (DSL). which is a private te'le-

phone line partitioned for data transmission. The dialup line is usually limited to a 56 kilobaud transmission rate. The cable modem and DSL connections are usually termed b r o a d b a n d connections. A cable modem is much faster than dial-up, with a maximum throughput of 2.8 Mbps. However, because cable communications

are based on a shared network topology, bandwidth is not always available when needed. One type of DSL, the asymmetric DSL, can provide downloading speeds to the subscriber of more than 6 Mbps and uploading speeds of more than 600 kilobits per second (kbps). Because DSL uses a private phone line, there is no degradation of speed as the number of users increases. The speed does, however, depend on the distance of the subscriber from the central telephone office. Security is also less of an issue with DSL than with cable modems. The Internet will eventually deliver information to virtually every home via high-speed (hundreds of megabits per second) cables or telephone lines. Today, much of the world's information, including scientific data, journals. and other types of reports, is already available on the Internet.

4H-2 Laboratory Management

Information

Systems

Networking computers in a laboratory environment can result in enormous quantities of data to be handled, manipulated. and stored. In addition, govern·

mcnt regulations, sample validation, and quality control dictate that data be archived and readily recalled at any time. A laboratory information management system (LIMS) can address these concerns.' A well-designed LIMS keeps track of all of the information about all of the samples and projects that have been completed or arc in progress. Figure 4-21 summarizes many of the processes that might be controlled by a LIMS in a testing laboratory and provides an overview of some of the options that might be exercised as a sample is processed. Finally, Figure 4-22 is a block diagram of a computer system designed to totally automate an entire laboratory. Note that at the bollom of this figure entire laboratories are designated by boxes; within each of these laboratories a LAN would be used to coordinate activities and communicate with the next level in the hierarchy. In this system we see that two different types of LIMSs are used; those designated DM are standard for datamanagement LIMSs, and the SM designation stands for system-sample management. Essentially the only

difference between these coordinating computers, or servers, is the software that controls the communication and the data handling. The SNA (systems network

architecture) gateway represents a means of connecting this laboratory's cluster of computers with the primary server at the corporatc headquarters.

*4-12 According to the Nyquist sampling criterion (see Section 5 C -2 ), a signal must bc digitized at a rate at least twice that of the highest frequency m the sIgnal to aVQld a sampling error. If a particular 12-bit ADC hasa conversIOn tlmeof 8 ~s, what IS the highest frequency that can be accurately dIgItIzed whIle satlsfymg the NyqUIst criterion? C h a lle n g e

*Answers are provided at the end of the book for problems marked with an asterisk.

00

Problems with this icon are best solved using spreadsheets.

*4-1

Convert each of the following decimal numbers to its binary equivalent. (a) 24 (b) 91 (c) 135 (d) 396

*4-2

Convert each of the decimal numbers in Prohlem 4-1 into binary-coded-decimal (BCD) numbers.

4-3

Based on your results in Problems 4-1 and 4-2, which is more efficient in expressing decimal numbers in the fewest number of bits, binary or BCD? Why is the less efficient coding scheme still very useful"

*4-4

Convert each of the following binary numbers into its decimal equivalent. (a) 101 (b) 10101 (c) 1110101 (d) 1101011011

*4-5

Convert each of the following BCD numbers into its decimal equivalent. (a) 0100 (b) 1000 1001 (c) 0011 0100 0111 (d) 100101101000

4-6

*4-7

Based on your results in Problems 4-4 and 4-5, which of the two coding schemes is easier to convert to decimal, binary or BCD? Why? Perform the following calculations using binary numbers and convert the result back to decimal. (a)9+6

*4-8

4-9

(b) 341+29

(c) 47+16

(d)3x8

Threc ADCs all have a range of 0 to 10 V and a digitization uncertainty of :!: 1 LSB. What is the maximum uncertainty in the digitization of a 10-V signal if the converters have (a) 8 bits? (b) 12 bits') (c) 16 bits? Repeat Problem 4-8 if a I-V signal is being digitized with the same three ADCs and the input signal is (a) not amplified and (b) amplified by 10 to bring it to full scale.

4-10 The maximum percentage error of a voltage processed by an ADC is given by the following equation:

If the same ADC is used, how do the percentage errors in measured voltages compare if the measured voltages arc 10 V and 1 V" *4-11 ADCs digitize at different rates. What conversion rate is required if a chromatographic peak is to be sampled and digitized 20 times between the first positive deflection from the baseline until the peak returns to the baseline? The total baseline-to-baseline time is (a) 20 s and (b) I s.

4-13 Use and (a) (b)

P ro b le m

a search engine such as Google to find information about Gordon E. Moore Moore's law, the famous law about technological advances that he proposed. What is Moore's law? Give a brief description in your own words. Who is Gordon E. Moore? What was hIs pOSItIon at the tIme he first proposed Moore's law? What company did he later cofound? WIth whom dId he

cofound this company? . . (c) In what field did Gordon E. Moore obtain his BS degree? At what unIversity did he receive his BS degree? Where did he obtain his PhD degree? In what field was his PhD degree? (d) What Nobel Prize-winning

. . physicist gave Gordon E. Moore hIS first Job

opportunity? , (e) What was the number of the first microprocessor developed at Moorc s company and how many transistors did it have? When was it introduced", _ (0 One important benchmark of computatIonal progress ISthe performance-to price ratio (PPR) of computers" The PPR is the number of bIts per word dIvided by the product of cycle time (l/clock speed) and pnce. The ongmal IBM PC (1981) with an 8-bit word length, a 4.77 MHz clock, and a pnce tag of $5000 came in with a PPR of ~ 7600. Computers based on other Important processors are listed in the table below. Calculate the PPR of each of these computers. Does Moore's law hold for the PPR? How did you come to your conclusion? Clock Speed,

P rocessor

Type 286 486 P e n tiu m

Pentium 11 Pentium III Pentium 4

Year

1982 1989 1993 1997 1999 2000

MHz

Bits/Word

6.0 25 60 266 700 3000

16 32 32 32 32 64

Computer Price, $ 5000 4fXlO 3500 3000 2500 2000

Signal~a n d

.

E

..

.

N o is e

The effect of noise I on a signal is shown in Figure 5.la, which is a strip-chart recording of a tiny direct current of about 10 -" A. Figure 5·1 b is a theoretical plot of the same current in the abscnce of noise.' The difference between the two plots corresponds to the noise associated with this experiment. Unfortunatelv, noise-free data, such as that shown in Figure 5-lb, ~an never be realized in the laboratory because some types of noise arise from thermodynamic and quantum effects that are impossible to avoid in a measurement. In most measurements, the average strcngth of the noise N is constant and independent of the magnitude of the signal S. Thus, the effect of noise on the relative error of a measurement becomes greater and greater as the quantity being measured decreases in magnitude. For this reason, the signa l-lo·noise r a lio (SIN) is a much more useful figure of merit than noise alone for describing the quality of an analytical method' or the performance of an instrument

.

ver ya na lyjica l mea ~~ement

Aima de

up of

,two c0Tnf.'.()nents. O n; : -compon~Bt"thesig-

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tha t is ofinter est'i8the

scient~t. The s~~~nd, ca iled

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tha t

detected.ln thisc~~pter we~~cr ibe s~~: -of the common sour c~i of noise ,a nd how their effects

-

Note that the signal-to-noise ratio xis is the reciprocal of the relative standard deviation, RSD (see SectIon a18-I, Appendix 1), of the group of measurements. That is, S N

1

IThe term noise ,is derived f~om fildio eng.ineering where the presence of an unwanted SIgnal IS mamfesteJ as audio static, or noise. The term is applied.now throughout science and engineering to describe the random fluctuatIons ohsen'cd whenever replicate measurements are made on sivnab that are monitored continuously. Random f1uctuation.~ are Jescrib:~ and treated by statistical methods (see Section aiR. A.rrendix 1 )

Throughout this chapter, this logo indicates

:thomsonedu,com/chemistry/skoog. linkingyou to interactIve tutorials, simulations, and exercises.

Chemical analyses are affected by two types of noise: chemical noise and instrumental noise.

(a)

FIGURE 5-1 Effect of noise on a current measurement:

(a)experimental strip-chart recording of a 0.9 x 10 -15 A direct current. (b) mean of the fluctuations. (Adapted from T.Coar, J. C h e m . E d u c ., 1968. 45, A594. With permission.)

:Por a more detailed discussion of noise, see T. Coor,1. C h"n!. E duc"

1968-

45. A533. ASH3: G. M. HieftJc. AI/a l C her n., 1972. -/.4liSI, SI A: A. Bczcgh and 1. Janata. Ana l. C hem .. 1987.59. 494A; ~1. E. Green, I C hem E du~.. 1984,61.600: H. V Malrnstadt. C. G. Enke. and S. R. Crllu.:h. M /uocomP U ll''''':

and

E lectr unic

lnstmmenta t/ofl:

V,Iashmgton. DC American

200 Frequency, Hz FIGURE 5-2 Effect of signal-to-noise ratio on the NMR

spectrum of progesterone: A, SIN = 4.3; B, SIN (Adapted from R. R. Ernst and W. A. Anderson, In s t., 1966,37,101. With permission.)

=

43. Sci.

R ev.

RSD

For a recorded signal such as that shown in Figure 5-la, the standard deviation can be estimated easily at a 99% confidence level by dividing the difference

r;;'l

Time. h

Chemical noise arises from a host of uncontrollable variables that affect the chemistry of the system being analyzed. Examples include undetected variations in temperature or pressure that affect the position of chemical equilibria, ftuctuations in relative humidity that cause changes in the moisture content of samples, vibrations that lead to >tratification of powdered solids, changes in light intensity that affect photosensitive materials, and laboratory fumes that interact with samples or reagents. Details on the effects of chemical noise appear in later chapters that deal with specific instrumental methods. In this chapter we focus exclusively on instrumental noise.

standard deviation

ca n be minimized.

IQ.J an opportunityfor online self-study atwww

SOURCES OF NOISE IN INSTRUMENTAl ANALYSES

mean

S N

a nd pr ecision ofa .~·; a na lysis~n; da lso plgces a ofa ~a lYte thb; tca n be

58

For a dc signal, such as th~t shown in Figur~ 5-1 a, the magnitude of the noise is convenientlv defined as the standard deviation s of numerous m~asurements of the signal strength, and the signal is given by the mean x of the measurements. Thus, SIN is given by

is unwa nted becC f~$eit degr a ,~esthe a 4¥: r a c y lower limit on thea ~ount

of about 4.3. In the lower plot the ratio is 43. At the smaller signal-to-noise ratio, only a few of the several peaks can be recognized with certainty.

.\la kinr ;

the Rir ; hl C O flnect/ollY.

Chcmi(:al SOCiCl". 1,)9~

between the maximum and the minimum signal by five. Here, we assume that the excursions from the mean are random and can thus be treated by the methods of statistics. In Figure aI-5 of Appendix I, it is seen that 99% of the data under the normal error curve lie within :+:2.5(J" of the mean. Thus, we can say with 99% certainty that the difference between the maximum and minimum encompasses 5". One fifth of the difference is then a good estimate of the standard deviation. As a general rule, it becomes impossible to detect a signal when the signal-to-noise ratio becomes less than about 2 or 3. Figure 5-2 illustrates this rule. The upper plot is a nuclear magnetic resonance (NMR) spectrum for progesterone with a signal-to. noise ratio

Noise is associated with each component of an instrument - that is, with the source, the input transducer, all signal-processing elements, and the output transducer. Furthermore, the noise from each of these elements may be of several types and may arise from several sources. Thus, the noise that is finally observed isacomplex composite that usually cannot be fully characterized. Certain kinds of instrumental noise are recognizable: (l) thermal, or Johnson, noise; (2) shot noise; (3) flicker, or I1f, noise; and (4) environmental noise. A consideration of the properties of the four kinds of noise is useful. T h e rm a l

N o is e ,

or Johnson

N o is e

Thermal noise is caused by the thermal agitation of electrons or other ch3rge carriers in resistors, capacitors, radiation transducers, electrochemical cells, and other resistive elements in an instrument. Thi, agitation of charged partides is random and periodically creates charge inhorngeneities, which in turn create voltage fluctuations that then appear in the readout as

noise. It is important to note that thermal noise is present even In the absence of current in a resistive element and disappears only at absolute zero. The magnitude of thermal noise in a resistive circuit element can be derived from thermodynamic considerations' and is given by V,m; = V 4kTRJ .f

(5-3)

where v,m; is the root-mean-square noise voltage lying In a frequency bandwidth of J.f Hz, k is Boltzmann's constant (1.38 x to -21 1 1 K ) , T is the temperature in kelvIns, and R is the resistance of the resistive element in ohms. In Section 3B-4 we discussed the relationship between the rise time t, and the bandwidth tif of an operational amplifier. These variables are also used to characterize the capability of complete instruments to transduce and transmit information, because

The rise time of an instrument is its response time in seconds to an abrupt change in input and normally is taken as the time required for the output to increase from 10% to 90% of its final value. Thus, if the rise time is 0.01 s, the bandwidth t1 f is 33 Hz. Equation 5-3 suggests that thermal noise can be decreased by narrowing the bandwidth. However, as the bandwidth narrows, the instrument becomes slower to respond to a signal change, and more time is required to make a reliable measurement.

What is the effect on thermal noise of decreasing response time of an instrument from [ s to [ /1s')

the

instrument circuiLs and by lowering the temperature of IIlstrument components. The thermal nOLsein transducers is often reduccd by cooling. For example, lowerIng the temperature of a UV -visible photodiode arra\, from room temperature (298 K) to the temperature ,;f liqUId Illtrogen (77 K) will halve the thermal noise. It is important to note that thermal noise, although dependent on the frequency bandwidth. is independent of frequency itself. For this reason, it is sometimes termed white noise by analogy to white light, which contains all visible frequencies. Also note that thermal noise in resistive circuit elements is independent of the physical size of the resistor.

I

10'

1~ ~'

-

>,

H ~ :::.

c:

D o .)

611-

C hange

of

ISIl-

cla"ses

I

I

I

E lt '\a t o r

H o u rI

10'

10' E n v im n r n e n la l n O is e

1 10-'

10

b

10-'

la '

10-2 Hz

--

S h o t N o is e

Shot noise is encountered wherever electrons or other charged particles cross a junction. [n typical electronic CirCUits,these junctions arc found at pn interfaces; in photocells and vacuum tubes, the junction consists of the evacuated space between the anode and caihode. The currents comprise a series of quantized evdnts, the transfer of individual electrons across the junction. These events occur randomly, however, and the rate at which they occur is thus subject to statistical fluctuations, which are described by the equation 1 m"

=

V2/~-s.7

current fluctuawhere i,m, is the root-mean-square tion associated with the average direct current, I; c is thecharge on the electron of 1.60 x 10 19 C; and J.fis agam the bandwidth of frequencies being considered. LIke thermal noise, shot noise is white noise and is thus the same at any frequency. Equation 5-5 suggests that shot noise in a current measurement can be minimized only by reducing handwidth. F lic k e r

As shown by Equation 5-3, thermal noise can also be reduced by lowering the electrical resistance of

I

F re q u e n c y ,

S o lu tio n

If we assume that the response time is approximatelv cqual to the rise time, we find that the bandwidth ha~ been cha"..ged from I Hz to 10' Hz. According to EquatIOn )-3, such a change will cause an increase in the noise by (1 0 6 /1 ) I!2,or IOOO-fold.

P o w e r lin e

T em p.

N o is e

Flicker noise is characterized as having a magnitude that IS Inversely proportional to the frequency of the SIgnal bemg ohserved; it is sometimes termed IIf(oneover -fJ nOISe as a consequence. The causes of flicker noise are not totally understood; it is ubiquitous, howe_ver,and is recognizable bv its frequency dependence. Fhcker noise hecomes significant at frequencies lower than about 100 Hz. The long-term drift observed in de amplifiers, light sourecs, voltmeters, and current meters is an example of flicker noise. Flicker noise can be reduced

s ig n ific a n tly

in

S O ffit:

cases

b y u s in g w ir e -w o u n d

F I G U R E 5-3 Some sources of environmental noise in a universIty laboratory. Note the frequency dependence and regions where various types of interference occur. (From T. Coor, J . C h e m . E d u c ., 1 9 6 8 ,4 5 , A540. With permission.)

or metallic-film resistors rather than the more common carbon-composition type. E n v ir o n m e n ta l

N o is e

Environmenta[ noise is a composite of different forms of noise that arise from the surroundings. Figure 5-3 suggests typical sources of environmental noise in a university laboratory. Much environmental noise occurs because cach conductor in an instrument is potentially an antenna capable of picking up electromagnetic radiation and converting it to an electrical signal. There are numerous sources of electromagnetic radiation in the em·ironment. induding ac power lines, radio and TV stations, gasoline-engine ignition systems, arcing switches, brushes in electric motors, lightning, and ionospheric disturbances. Note that some of these sources, such as power lines and radio stations, cause noise with relatively narrow frequency bandwidths. Note that the noise spectrum shown in Figure 5-3 contains a large, continuous noise region at low frequencies. This noise has the properties of flicker noise: its sources arc not fully known. Superimposed on the flicker noise are noise peaks associated with yearlv and daily temperature fluctuations and other periodic phenomena associated with the use of a laboratory building. Finally, two quiet-frequency regions in which environmental noise is low are indicated in Figure 5-3: the region extending from about 3 Hz to almost 60 Hz and

the region from about f kHz to about 500 kHz, or a frequency at which AM radio signals arc prevalent. Often, signals arc converted to frequencies in these regions to reduce noise during signal processing.

Many laboratory measurements require only minimal effort to maintain the signal-to-noise ratio at an acceptable level. Examples include the weight dcterminations made in the course of a chemical synthesis or the color comparison made in determining the chlorine content of the water in a swimming pool. For both examples, the signal is large relative to the noise and the requirements for precision and accuracy are minimal. When the need for sensitivity and accuracy increases, however, the signal-to-noise ratio often becomes the limiting factor in the precision of a measurement. Both hardware and software methods are available for improving the signal-to-noise ratio of an instrumental method. Hardware noise reduction is accomplished hy incorporating into the instrument design components such as filters, choppers, shields, modulators, and synchronous detectors. These devices remove or attenuate the noise without affecting the analytical signal significantlv. Software methods are based on "arious computer algorithms that permit extraction of signals from noisy data. As a minimum. software methods require sufficient hardware to condition the output

signal from the instrument and convert it from analo to digital form. Typically, data arc collected by using; computer equipped with a data·acquisition module'as described in Chapter 4. Signals may then be extracted from noise by using the data-acquisition computer or another that ISconnected to it via a network.

Narrow-band electronic filters are also available to attenuate noise outside an expected band of signal frequencies. We have pointed out that the magnitude of fundamental noise is directly proportional to the square root of the frequency bandwidth of a signal. Thus, significant noise reduction can be achieved by restricting the input signal to a narrow band of frequencies and using an amplifier that is tuned to this band. It is important to note that the bandpass of the filter must be sufficiently wide to include all of the signal frequencies.

5C-1 Som e Hardware Devices for NO ise Reduction

We briefly describe here some hardware devices and techniques used for enhancing the signal-to-noise ratio. G r o u n d in g

M o d u la tio n

a n d S h ie ld in g

Noise that arises from environmentally generated electromagnetic radiation can often be substantially reduced by shleldmg, grounding, and minimizing the lengths of conductors within the instrumental system. Shleldmg consists of surrounding a circuit, or the most CrItical conductors in a circuit, with a conducting material that is attached to earth ground. Electromagnetic radiation is then absorbed by the shield rather than by the enclosed conductors. Noise pickup and pOSSibly amplification of the noise by the instrument CirCUItmay thus be minimized. It may be somewhat surprIsmg that the techniques of minimizing noise through grounding and shielding are often more art than science, particularly in instruments that involve both analog and digital circuits. The optimum configuralion IS often found only after much trial and error4 Shielding becomes particularly important when the output of a high-resistance transducer, such as the glass electrode, is being amplified. Here, even minuscule randomly induced currents produce relatively large voltage fluctuations in the measured signal. D iffe r e n c e

FIGURE 5-4 An instrumentation amplifier for reducing the effects of nOIsecommon to both inputs. The gain of the CirCUitIS controlled by resistors R,Ia and KR,.

a n d In s tr u m e n ta tio n

A m p lifie r s

Any noise generated in the transducer circuit is particularly CrItical because it usually appears in an amplified form in the instrument readout. To attenuate this type of noise, most instruments employ a difference amplIfier, such as that shown in Figure 3-13, for the first stage of amplification. Common-mode noise in the

~For an excelkm discussion of groundlllQ. and shielding see H \/ M' I _ stadt, C. G. Enke, and S. R. Crouch. ,V/; r ncompulen- a 'nd E le~lr ~ni; ~~_ ,'-la kmg the Right C onnections, pp . .tOl --9, W is the p h a se a n g le, a term defined in Section 2B-I, page 34. The angular velocity of the vector w is related to the frequency of the radiation v by the equation

A

F I G U R E 6-4 Superposition of sinusoidal wave: (a) Al < A" (1)1 - 1>,) = 20', = (b) Al < A" (1)1 - 1>,) ~ 200', = v,. In each instance, the black curve results fro~ the combination of the two other curves. VI

V ,;

VI

Substitution yields

6 8 -4

of this relationship

S u p e rp o s itio n

into Equation

6-4

of W aves

The p r in cip le o f su p er p o sitio n states that when two or more waves traverse the same space, a disturbance occurs that is the sum of the disturbances caused by the individual waves. This principle applies to electromagnetic waves, in which the disturbances involve an electric Held, as well as to several other types of waves, in which atoms or molecules are displaced. When n electromagnetic waves differing in frequcncy, amplitude, and phase angle pass some point in space simultaneously, the principle of superposition and Equation 6-5 permit us to write y = Al sin(21Tl'lt

+.

+ dJI) +

. + An sin(21Tv"t

A, sin(21Tv2t

+

two waves are completely in phase - a situation that occurs whenever the phase difference between waves (.

F IG U R E

~ ~ \

Eo

A,

Line Spectra

Line spectra in the ultraviolet and visible regions are produced when the radiating species are individual atomic particles that are well separated in the gas

1.0

A

metal.

E,

are superimposed on this continuum. The source of the continuum is described on page 152. Figure 6-20 is an X-ray em~sion spectrum produced by bombarding a piece of molybdenum with an energetic stream of electrons. Note the line spectrum superImposed on the continuum. The source of the continuum is described in Section 12A-I.

0.8

0.6 W a v e le n g th .

F IG U R E 6-19 Emission spectrum of a brine sample obtained with an oxyhydrogen flame. The spectrum consists of the supenmposed line, band, and continuum spectra of the constituents of the sample. The characteristic wavelengths of the species contributing to the spectrum are listed beside each feature. (R. Hermann and C . T" J Alkema d e, C h'emlcal AnalysIs. by Flam e Ph t o orne try, 2nd ed., p. 484. New York:Interscience, 1979.)

frequency. Figure 6-19 illustrates a typical emission spectrum, which was obtained by aspirating a brine solulton Into an oxyhydrogen flame. Three types of spectra appear In the figure: lin es, b a n d s. and a co n tin u u m The line spectrum is made up of a series of sharp, well~ defined peaks caused by excitation of individual atoms. The band spectrum consists of several groups of lines so closely spaced that they are not completely resolved. The source of the bands consists of small molecules or radicals. Finally, the continuum portion of the spectrum IS responSible for the increase in the background that is evident above about 350 nm. The line and- band spectra

= (E, -

Al = h d (E ,

(a)

Band Spectra

C ontinuum

Band spectra are often encountcred in spectral sources when gaseous radicals or small molecules are present. For example, in Figure 6-19 bands for OH, MgOH, and MgO are labeled and consist of a series of closely spaced lines that are not fully resolved by the instrument used to obtain the spectrum. Bands arise from numerous quantized vibrational levels that are superimposed on the ground-state electronic energy level of a molecule. Figure 6-21b is a partial energy-level diagram for a molecule that shows its ground state E o and two of its excited electronic states, E , and E ,. A few of the many vibrational levels associated with the ground state are also shown. Vibrational levels associated with the two excited states have been omitted because the lifetime of an excited vibrational state is brief compared with that of an electronically excited state (about 10-15 s versus 10- 8 s). A consequence of this tremendous difference in lifetimes is that when an electron is excited to one of the higher vibrational levels of an electronic state, relaxation to the lowest vibrational level of that state occurs before an electronic transition to the ground state can occur. Therefore, the radiation produced by the electricalor thermal excitation of polyatomic species nearly always results from a transition from the lo west vib r a tio n a l level o f a n excited electr o n ic sta te to any of the several vibrational levels of the ground state. The mechanism by which a vibrationally excited species relaxes to the nearest electronic state involves a transfer of its excess energy to other atoms in the system through a series of collisions. As noted, this process takes place at an enormous speed. Relaxation from one electronic state to another can also occur by collisional transfer of energy, but the rate of this p,,;_ cess is slow enough that relaxation by photon release is favored. The energy-level diagram in Figure 6-21b illustrates the mechanism by wbieh two radiation bands that consist of five closely spaced lines are emitted by a molecule excited by thermal or electrical energy. For a real molecule. the number of individual lines is much larger because in addition to the numerous vibrational states, a multitude of rotational states would be superimposed On each. The differences in energy among the rotationa I levels is perhaps an order of magnitude smaller than that for vibrational states. Thus. a real molecular band would be made up of many more lines than we have shown in Figure 6-2Ib. and these lines would be much more closely spaced.

Spectra

As shown in Figure 6-22, truly continuum radiation is produced when solids are heated to incandescence. Thermal radiation of this kind, which is called b la ckb o d y r a d ia tio n , is characteristic of the temperature of the emitting surface rather than the material of which that surface is composed. Blackbody radiation is produced by the innumerable atomic and molecular oscillations excited in the condensed solid by the thermal energy. Note that the energy peaks in Figure 6-22 shift to shorter wavelengths with increasing temperature. It is clear that very high temperatures are needed to cause a thermally excited source to emit a substantial fraction of its energy as ultraviolet radiation. As noted earlier, part of the continuum background radiation exhibited in the flame spectrum shown in Figure 6-19 is probably thermal emission from incandescent particles in the flame. Note that this background decreases rapidly as the ultraviolet region is approached. Heated solids are important sources of infrared, visible, and longer-wavelength ultraviolet radiation for analytical instruments.

According to quantum theory, atoms, molecules, and ions have only a limited number of discrete energy levels; for absorption of radiation to occur, the energy of the exciting photon must exa ctly match the energy difference between the ground state and one of the excited states of the absorbing species. Since these energy differences are unique for each species, a study of the frequencies of absorbed radiation provides a means of characterizing the constituents of a sample of matter. For this purpose, a plot of absorbance as a function of wavelength or frequency is experimentally determined (a b so r b a n ce, a measure of the decrease in radiant powcr, is defined by Equation 6-32 in Section 6D-2). Typical absorption spectra are shown in Figure 6-23. The four plots in Figure 6-23 reveal that absorption spectra vary widely in appearance; some are made up of numerous sharp peaks, whereas others consist of smooth continuous curves. In general, the nature of a spectrum is influenced by such variables as the complexity, the physical state, and the environment of the absorbing species. More fundamental, however, are

6C-5 Absorption of Radiation

When radiation passes through a layer of solid, liquid, or gas, certain frequencies may be selectively removed by a b so r p tio n , a process in which electromagnetic energy is transferred to the atoms, ions, or molecules composing the sample. Absorption promotes thcse particles from their normal room temperature state, or ground state, to one or more higher-energy excited states.

{",'"""]Ml 588

589

590

10'

>.

103

~ ~ "

>

~

.. : ~"-I -~-fungs-t~nfamp ..

arc

Nerrist

spectra for atoms

Absorption

The passage of polychromatic ultraviolet or visible radiation through a medium that consists of mono atomic particles, such as gaseous mercury or sodium, results in the absorption of but a few well-defined frequencies (see Figure 6-23a). The relative simplicity of such spectra is due to the small number of possible energy states for the absorbing particles. Excitation can occur only by an electronic process in which one or more of the electrons of the atom are raised to a higher energy leveL For example, sodium vapor exhibits two closely spaced, sharp absorption peaks in the yellow region of the visible spectrum (5H9.0 and 589.6 nm) as a result of excitation of the 3s electron to two 3 p states that differ only slightly in energy. Several other narrow absorption lines, corrcsponding to other allowed electronic t;ansitions, are also observed. For example, an ultraviolet peak at about 285 nm results from the excitation of t~e 3s electron in sodium to the excited 5 p state, a process that requires significantly greater energy than docs excitation to the 3 p state (in fact, the peak at 285 nm is also a doublet; the energy difference between the two peaks is so small, however, that most instruments cannot resolve them). Ultraviolet and visible radiation have enough energy to cause transitions of the outermost, or bonding, electrons only. X-ray frequencies, on the other hand, are several orders of magnitude more energetic (see Example 6-3) and are capable of interacting with electrons that are closest to the nuclei of atoms. Absorption peaks that correspond to electronic transitions of these innermost electrons are thus observed in the X-ray region. Absorption

Absorption spectra for polyatomic molecules, particularly in the condcnsed state, are considerably more complex than atomic spectra because the number of energy states of molecules is generally enormous when compared with the number of energy states for isolated atoms. The energy E associated with the bands of a moleculc is made up of three components. That is,

glower

10'

0;

"

Atom ic

M olecular

xe.n..o..n.. ,arc Carbon

the differences between absorption and those for molecules.

10

FIGURE

spectra.

6·23

Some typical ultraviolet absorption

where Eelectmoic describes the electronic energy of the molecule that arises from the energy states of its several bonding electrons. The second term on the right refers

to the total energy associated with the multitude of interatomic vibrations that are prescnt in molecular species. Generally, a molecule has many more quantized vibrational energy levels than it does electronic levels. Finally. E m""o",' is the energy caused bv various rotational motions within a molecule; again the number of rotational states is much larger than the number of vibrational states. Thus, for each electronic energy state of a molecule, there are normally several possible vibrational states. For each of these vibrational states, in turn, numerous rotational states are possible. As a consequence, the number of possible energy levels for a molecule is normally orders of magnitude greater than the number of possible energy levels for an atomic particle.

tronic energy); the lines labeled E, and E, represent the energies of two excited electronic states. Several of the many vibrational energy levels (eo, e" ... , en) are shown for each of these electronic states. Figure 6-24 shows that the energy difference between the ground state and an electronically excited state is large relative to the energy differences between vibrational levels in a given electronic state (typically, the two differ by a factor of 10 to 100), The arrows in Figure 6-24a depict some of the transitions that result from absorption of radiation. Visible radiation causes excitation of an electron from E o to any of the n vibrational levels associated with E, (only five of the n vibrational levels are shown in Figure 6-24), Potential absorption frequencies are then given by n equations, each with the form

Figure 6-24 is a graphical representation of the energy levels associated with a few of the numerous electronic and vibrational states of a molecule. The heavy line labeled E o represents the electronic cnergy of the molecule in its ground state (its state of lowest elec-

=

Vi

h(E ,

+

e; -

where i = 1,2,3, ... , n .

£2

!

Visihle

CJ,

Excited

R

t tI

electronic state I

'

IT'! I

e1#

i !

~ e

!

__

__

i~

,.,.-

-

--- -----

_

I•... ' _~ __

t,

t,

;

Ground Eo

electronic state

(al

2

;

£1

energy

e,

electronic Slate

::l ,

(h)

mulated as

E o)

Excited

Vibrational

where i = 1,2, 3, ... , m . Finally, as shown in Figure 6-24a, the less energetic near- and mid-infrared radiation can bring about transitions only among the k vibrational levels of the ground state. Here, k potential absorption frequencies are given by k equations, which may be for-

Figure 6-23d. Solvent effects are considered

(e)

FIGURE 6-24 Partial energy-level diagrams for a fluorescent organic molecule.

I

where i = 1,2,3, ... , k. Although they are not shown, several rotational energy levels are associated with each vibrational level in Figure 6-24. The energy difference between the rotational energy levels is small relative to the energy difference between vibrational levels. Transitions between a ground and an excited rotational state are brought about by radiation in the 0.01- to l-cm-wavelength range, which includes microwave and longer-wavelength infrared radiation. fn contrast to atomic absorption spectra, which consist of a series of sharp, well-defined lines, molecular spectra in the ultraviolet and visible regions are ordinarily characterized by absorption regions that often encQmpass a substantial wavelength range (see Figure -6-23b, c). Molecular absorption also involves electronk transitions. As shown by Equations 6-23 and 6-24, however, several closely spaced absorption lines will be associated with each electronic transition, because of the existence of numerous vibrational states. Furthermore, as we have mentioned, many rotational energy levels are associated with each vibrational state. As a result, the spectrum for a molecule usually consists of a series of closely spaced absorption lines that constitute an a b so r p tio n b a n d , such as those shown for benzene vapor in Figure 6-23b. Unless a high-resolution instrument is employed, the individual peaks may not be detected, and the spectra will appear as broad smooth peaks such as those shown in Figure 6-23c. Finally, in the condensed state, and in the prcsence of solvent molecules, the individual lines tend to broaden even further to give nearly co n tin u o u s sp ectr a such as that sh()\vn in

in later

chapters. Pure vibrational absorption is observed in the infrared region, where the energy of radiation is insufficient to cause electronic transitions. Such spectra exhibit narrow, closely spaced absorption peaks that result from transitions among the various vibrational quantum levels (see the transition labeled IR at the bottom of Figure 6-24a). Variations in rotational levels may give rise to a series of peaks for each vibrational state; but in liquid and solid samples rotation is often hindered to such an extent that the effects of these small energy differences are not usually detected. Pure rotational spectra for gases can, however, be observed in the microwave region. Ab so r p tio n

I

-~,~-~--

;

Similarly, if the second electronic state has m vibrational levels (four of which are shown), potential absorption frequencies for ultraviolet radiation are given by m equations such as

In d u ced

by

a M a g n etic

F ield

When electrons of the nuclei of certain elements are subjected to a strong magnetic field, additional quantized energy levels can be observed as a consequence of the magnetic properties of these elementary particl,,,. The differences in energy between the induced states are small, and transitions between the states are brought about only by absorption of long-wavelength (or low-frequency) radiation. With nuclei, radio waves ranging from 30 to 500 MHz (A = 1000 to 60 em) are generally involved; for electrons, microwaves with a frequency of about 9500 MHz (A = 3 em) are absorbed. Absorption by nuclei or by electrons in magnetic fields is studied by n u clea r ma g n etic r eso n a n ce (NMR) and electr o n sp in r eso n a n ce (ESR) techniques, respectively; NMR methods are considered in Chapter 19.

Ordinarily, the lifetime of an atom or molecule excited by absorption of radiation is brief because there are several r ela xa tio n p r o cesses that permit its return to the ground state. No n r a d ia tive

Rela xa tio n

As shown in Figure 6-24b, n o n r a d ia tive r ela xa tio n involves the loss of energy in a series of small steps, the excitation energy being converted to kinetic energy by collision with other molecules. A minute increase in the temperature of the system results. As shown by the blue lines in Figure 6-24c, relaxation can also occur by emission of fluorescence radia· tion. Still other relaxation processes arc discussed in Chapters IS, 18, and 19.

Fluorescence

and Phosphorescence

R elaxation

Fluorescence and phosphorescence are analytically important emission processes in which species are excited by absorption of a beam of electromagnetic radiation: radiant emission then occurs as the excited species return to the ground state. Fluorescence occurs more rapidly than phosphorescence and is generally complete after about 10 -5 S from the time of excitation. Phosphorescence emission takes place over periods longer than 10 -5 S and may indeed continue for minutes or even hours after irradiation has ceased. Fluorescence and phosphorescence are most easilv observed at a 90° angle to the excitation beam. . Molecular fluorescence is caused by irradiation of molecules in solution or in the gas phase. As shown in Figure 6-24a, absorption of radiation promotes the molecules into any of the several vibrational levels associated with the two excited electronic levels. The lifetimes of these excited vibrational states are, however, only on the order of 10-15 s, which is much smaller than the lifetimes of the excited electronic states (10-8 s). Therefore, on the average, vibrational relaxation occurs before electronic relaxation. As a consequence, the energy of the emitted radiation is smaller than that of the absorbed by an amount equal to the vibrational excitation energy. For example, for the absorption labeled 3 in Figure 6-24a, the absorbed energy is equal to (£2 - £0 + whereas the energy of the fluorescence radiation is again given by (£2 - £0)' Thus, the emitted radiation has a lower frequency, or longer wavelength, than the radiation that excited the fluorescence. This shift in wavelength to lower frequencies is sometimes called the Sto kes sh ift as mentioned in connection with Raman scattering in Figure 6-1K Phosphorescence occurs when an excited molecule relaxes to a metastable excited electronic state (called the tr ip let sta te), which has an average lifetime of greater than about 10-5 s. The nature of this type of excited state is discussed in Chapter 15.

Section 68-4. Applications of this principle will be found in several later chapters that deal with spectroscopic methods.' Let us suppose that we wish to determine the frequency VI of a monochromatic beam of radiation by comparing it with the output of a standard clock, which is an oscillator that produces a light beam that has a precisely known frequency of 1 '2 ' To detect and measure the difference between the known and unknown frequencies, tJ .v = VI - V" we allow the two beams to interfere as in Figure 6-5 and determine the time interval for a beat (A to B in Figure 6-5). The minimum time tJ .t required to make this measurement must be equal to or greater than the period of one beat, which as shown in Figure 6-5, is equal to lItJ .v. Therefore, the minimum time for a measurement is given by

60

c (P e gives

QUANTITATIVE ASPECTS OF SPECTROCHEMICAL MEASUREMENTS

As shown in Table 6-2, spectrochemical methods fall into four major categories. All four require the measurement of radiant p o wer P , which is the energy of a beam of radiation that reaches a given area per second. In modern instruments, radiant power is determined with a radiation detector that converts radiant cnergy into an electrical signal S. Generally 5 is a voltage or a current that ideally is directly proportional to radiant power. That is,

where k is a constant. Many detectors exhibit a small, constant response, known as a dark current, in the absence of radiation. In those cases, the response is described by the relationship

Note that to determine tJ.v with negligibly small uncertainty, a huge measurement time is required. If the observation extends over a very short period, the uncertainty will be large. Let us multiply both sides of Equation Planck's constant to givc

6-25 by

where k d is the dark current, which is generally small and constant at least for short periods of time. Spectrochemical instruments are usually equipped with a compensating circuit that reduces kd to zero whenever measurements are made. With such instruments, Equation 6-27 then applies.

=

kc). Combining this equation with Equation 6-27

where k' is a constant that can be evaluated by exciting analyte radiation in one or more standards and by measuring S. An analogous relationship also applies for luminescence and scattering methods. 60-2 Absorption Methods

As shown in Table 6-2, quantitative absorption methods require two power measurements: one before a beam has passed through the medium that contains the analyte (Po) and the other after (P). Two terms, which are widely used in absorption spectrometry and are related to the ratio of P o and P , are tr a n smitta n ce and a b so r b a n ce.

Transm ittance

Figure 6-25 depicts a beam of parallel radiation before and after it has passed through a medium that has a thicl«less of b cm and a concentration c of an absorbing species. As a consequence of interactions between the photons and absorbing atoms or molecules, the power of the beam is attenuated from Po to P. The tr a n smitta n ce T of the medium is then the fraction of incident radiation transmitted by the medium: l' T = Po

e'; - e;,),

6C-7 The Uncertainty Principle

The u n cer ta in ty p r in cip le was first proposed in 1927 by Werner Heisenberg, who postulated that nature places limits on the precision with which certain pairs of physical measurements can be made. The uncertainty principle, which has important and widespread implications in instrumental analysis, is readily derived from the principle of superposition, which was discussed in

From Equation 6-17, it is apparent that tJ .E = h tJ .v

Equation 6-26 is one of several ways of formulating the Heisenberg uncertainty principle. The meaning in words of this eq uation is as follows. If the energy E of a particle or system of particles - photons, electrons, neutrons, or protons, for example - is measured for an exactly known period of time tJ .t, then this energy is uncertain by at least h i tJ .t. Therefore, the energy of a particle can be known with zero uncertainty only if it is observed for an infinite period. For finite periods. the energy measurement can never be more precise than h ltJ .t. The practical consequences of this limitation will appear in several of the chapters that follow.

60-1 Emission, Luminescence, and Scattering Methods

Transmittance

As sn copy Vols. 1-3. San Diego: Acad~mic Press. 2000: J. \\:. Robillslm, cd., P r a cliwl H a ndhook ufSpectr oscoP : I', Buca Raton, fL: eRr Press. 1\)91; E, J. ~1cchan, in Tr elllise on Ana lvIlc,ll C hemistr y, P. 1. Elving. E. 1. Meehan. and L M. Kolthll(f. eds" Part!. Vol. 7. Chap. 3. New York:-\\,iky, 19,s1; 1. D, Ingle Jr. and S. R. Crouch. SpeC /l'O ellemlwl Ar wlr sls. Chaps. J and~. Upper S A,), is shown. This radiation enters the monochromators via a narrow rectangular opening, or SUI; is collimated; and then strikes the surface of the dispersing element at an angle. For the grating monochromator, angular dispersion of the wavelengths results from diffraction, which occurs at the reflective surface; for the prism, refraction at the two faces results in angular dispersion of the radiation, as shown. In both designs, the dispersed radi-

~

Exer c~e:

Learn more about monochromators.

of M onochrom ators

Figure 7-18 illustrates the optical elements found in all monochromators, which include the following: (I) an entrance slit that provides a rectangular optical image,

/"

(

Hnlographic

~nterfcrencc

mlh:h lilter

filter

~ 60

g

I

Orange cutoff 40

filter

Effective handwidth \bsorpllOri

L/~

-10 nm

~~

filter

Entrance ~ht

Collimating lens

z~7

__

~~-~"A~ Prism

Focusing lens

FIGURE 7-17 Comparison of various types of absorption filters for visible radiation.

~~a~~

~~R

A~ /

.I

/' Ex.it silt

A

7-18 Two types of monochromators: (a) Czerney-Tumer grating monochromator and (b) Bunsen prism monochromator. (In both instances, Al > A,.) FIGURE

Grating 200

300

400

500

600

A,nm

700

800

----------,

Diffracted

beam

at

reflected

angle

r 2

la}

200 A,nm

Absorption

200

r..1onochromatic

Glass prism

350

400

500

600800

beams

--i-.--H

J

Quartz

300

- -+-------

angle 350

400

at

3

incident

prism

250

A,nm

450

j

500 600800

I

i

i

,

(b}

A

B

I

0

5.0

10.0

15.0

20.0

FIGURE 7-19 Dispersion for three types of monochromators. The points in (c) correspond to the points shown in Figure 7-18.

25.0

A

and

B

on the scale

Prism M onochrom ators

Prisms can be used to disperse ultraviolet, visible, and infrared radiation. The material used for their construction differs, however, depending on the wavelength region (see Figure 7-2b). Figure 7-20 shows the two most common types of prism designs_ The first is a 60° prism, which is usually fabricated from a single block of material. When crystalline (but not fused) quartz is the construction material, however, the prism is usually formed by cementing two 30° prisms together, as shown in Figure 7-20a; one is fabricated from right -handed quartz and the second from left-handed quartz_ [n this way, the optically active quartz causcs no net polarization of the emitted radiation; this type of prism is called a C or nu pr ism. Figure 7-18b shows a Bunsen monochr oma tor , which uscs a 60° prism, likewise often made of quartz. As shown in Figure 7-20b, the !.iU r a ", pr ism, which permits more compact monochromator designs, is a 30° prism with a mirrored back. Refraction in this type of prism takes place twice at the same interface so that the performance characteristics are similar to those of a 600 prism in a Bunsen mount. G rating

FIGURE 7-20 Dispersion by a prism: (a) quartz Cornu type and (b) Litlrow type.

mon type_ Replica gr a tings, which are used in most monochromators, are manufactured from a ma ster gr a ting. ' ] A master grating consists of a hard, optically flat, polished surface that has a large number of parallel and closely spaced grooves, made with a diamond tool. A magnified cross-sectional view of a few typical grooves is shown in Figure 7-2L A grating for the ultraviolet and visible region typically has from 300 to 2000 grooves/mm, with 1200 to 1400 being most common. For the infrared region, gratings typically have 10 to 200 grooves/mm; for spectrophotometers designed for the most widely used infrared range of S to IS Ilm .

M onochrom ators

Dispersion of ultraviolet, visible, and infrared radiation can be brought about by directing a polychromatic beam through a tr a nsmission gr a ting or onto the surface of a r eflection gr a ting; the latter is by far the more COIll-

,; For an interesting and informative discu);sion u1' the manufacture, testing, and performance characteristics of gratings, see D iffr a ction G r a ting H a ndbook, 6th cd" Irvine. CA: Newport Corp .. ~005 (v,.'ww.newport,com l For a historical pt:rspecti\'c nil the imparlance of gratings in the' aJ\'anccmenl of science. see A. G. Ingalls. Sd. Amer .. 195!. 186 (6), 45

a grating with about 100 grooves/mm is suitable. The construction of a good master grating is tedious, timeconsuming, and expensive because the grooves must be of identical size, exactly parallel, and equally spaced over the length of the grating (3 to 10 cm). Replica gratings are formed from a master grating by a liquid-resin casting process that preserves virtually perfectly the optical accuracy of the original master grating on a clear resin surface. This surface is usually made reflective by a coating of aluminum, or sometimes gold or platinum. The Echellette Grating, Figure 7-21 is a schematic representation of an echelieue-type grating, which is grooved, or bla zed, such that it has relatively broad face~ from which reflection occurs and narrow unused face~_This geometry provides highly efficient diffraction of radiation, and the reason for blazing is to concentrate the radiation in a preferred direction_I' Each of the broad faces can be considered to be a line source of radiation perpendicular to the plane of the page; thus interference among the reflected beams 1,2, and 3 can occur. For the interference to be constructive, it is necessary that the path lengths differ by an integral multiple n of the wavelength A of the incident beam. [n Figure 7-21, parallel beams of monochromatic radiation I and 2 are shown striking the grating at an incident angle i to the gr a ting nor ma l. Maximum constructive interference is shown as occurring at the re-

f1ected angle r. Beam 2 travels a greater distance than beam 1 and the difference in the paths is equal to (CB + BD) (shown as a blue line in the figure). For constructive interference to occur, this difference must equal nA_ That is,

where n, a small whole number, is called the diffraction or der . Note, however, that angle C AB is equal to angle i and that angle DAB is identical to angle r . Therefore, from trigonometry, we can write

where d is the spacing between the rellecting surfaces_ It is also seen that

Substitution of the last two expressions into the first gives the condition for constructive interference. Thus.

Equation 7-6 suggests that there are several values of A for a given diffraction angle r. Thus, if a first-order line

(n = I) of 900 nm is found at r, second-order (4S0-nm) and third-order (300-nm) lines also appear at this angle. The flfSt-order line is uo;ually the most intense; indeed, it is possible to design gratings with blaze angles and sh:lpes that concentrate as much as 90% of the incident intensity in this order. Filters can generally remove the higher-order lines. For example, glass, which absorbs radiation below 3S0 nm. eliminates the higher-order spectra associated with first-order radiation in most of

e visible

region.

The example

that follows

illustrates

Holographic

lese points.

gratings,

tion with rcspect spectra

that

arc relatively

ghosts

I douhle

images).

In the -\n echellette rradiated angle

grating with

48' to the grating

lengths

1450 bla zesimm

thatcontams

a polychromatic

of radiation

beam

normal.

that would

Calculate appear

of + 20, + 10, and 0' (angle

reflection

was

at an incident the wave-

at an angle

r . Figure

of

7 -21).

beams toresist.

angles

heams

sensitize

solved,

leaving

7-6. we write

altered

=~~

d

X 10" _~m_ = 6li9.7 nm mm blaze

1450 blazes

=

A

689.7 nm . ~-n~' (sin 48 + sm 20)

or other

the wavelengths

order

reflections

Further lowing

and third-

are 748, 374, and 244 nm, respectively.

calculations

of a similar

kind yield

the fol-

n = 2

pattern

on the surface

minum.

Nearly

at a relatively

741\

374

249

632

316

2!!

0

513

256

171

cave surface

in much

face. A concave chromator mirrors

or lenses

hecause

the energy

in numhcr

throughput

a concave

sur-

of a monoand

concave

focuses

is advantageous

the rcduction

that contains

the design

The quality

Holographic

Gratings.

in ever-incrcasing

focusing

surface

both

it on the exit slit. in terms of optical

of cost: surfaces

of a monochromator

grating.

instruments,

even

some

H ologr a phic gr a cings'; are apof the

absorption

output,

last property

usually

Purity. radiation

of Gratin!:

to separate

on its disper sion.

to

The angular

grating.

El\uation

at any given angle

are reflections

m modern

less expensive

optical ones.

dA

dcosr

wavelength

I is

the focal lcngth

dispersion

wave-

power, and its spectral

band-

in Section

can he related

tical parts

surfaces

result

parts

are minimi7Cd

sources

optical

also causes

along

to the angular

in

by introducing

adjacent

in wavelength.

D =

A is the average

where

hench-top

useful

mcasure

dispcrsion

hy

dA

linea r disper sion D

-I

is thc r ecipr oca l

of dispersion

of

the

.r

are often

-I

dr

that the resolving

1,1

when

n is the diffraction hlazes

slit. Thus.

longer

gratings,

letle

better

to ra-

in appro-

ranges

power

of a grat-

orders.

This

and N is the number

by radiation

el\uation

from

applies

(see later discussion)

and higher to both

nm/mm

or A/mOl

in

tcctor

7-7 into Equation

lincar

dispersion

for

7-'1 we a grating

Il'

"ower

of Monochromators,

the signal-to-noise

echel-

energy

be as large as possible. a mcasure

collect

that reaches

The {"umber

of the ahility

the radiation

To in

ratio of a spectrometer,

that the radiant

slit. The f.numbcr

where

F . or spec,

of a monochromat'

that emerges

is defined

it i the d,

from the enlran

hj'

lis the focal length of the collimating The

mirror

light-gathering

po'

or all optical device increases as the iO\'t:rsc squar, that

tance

d Od\\'ccn

the angular

lines per millimeter

I'For

di_~ClJ_'i-;lOlJ tlf

raJi;llil)O. sc,'

W

dispersion

rulings

A/hit

increases

as thc dis-

decreases. as th~ number

increases.

the Jd,;dion.

K;Jw

C hem __t91U.)',.'.N,.-\

of dif-

gratings.

monochromator:

Note

of

the en-

is a characteristic

blaze spacings,

lens} and d is its diameter.

radiation

of typ-

nN

resolution

smaller

and echellc

=

order

illuminated

trance

necessary

par-

of spurious

power

monochromators

R = .~

provides

Equation

reciprocal

of thc two images

ing is given bv the exprcssion

crease

region.

By suhstituting have

1 dA

= d,,- =

f)

a slight

where

dy

the UV -visible

have

The rcsolving

liV -visihle

Ught-Gathering

The dimcnsions

that

10' to 10'-

fraction A more

the limit of its

by definition

wavelength

the lincar

Idr

di.

images

Here.

r esolving

The

describes

the

or on the

baffles

separate

7-18. If

manufacture.

stray

the effects

parts

from op-

imperfections, during

in the atmosphere

reach the exit slit. Generally. diation

radiation

these

Reflections

mechanical introduced

by dust particles of optical

Among

from various

housing.

from

in gratings.

This unwanted

sources.

from

10

grating

is

of scattered

far different

of Monochromators.

and t.A is tbeir ditference.

in Figure

is

monochro-

..\A

i con-

holding

to the variation

as shown

simplifies

A R = ~~~-

7C-3.

of a monochromator

Power

can be obtained

of the monochromator.

on the purity adjacent

selling.

of the beam

in wavelength

of y, the distance

as a (unction

dl'

dcpends

ability

from

D refers

r is small.

design.

It can be shown"

linea r disper sion

The

if the angle

that greatly

polI'er R of a monochromator

ical

n

purposes,

a properly

difference

thc relationship

with small amounts

and the monochromator

of

of incidence,

dr

(7-11)

of a gr a tin!: nl0nochronlalO r

7-20 and 7-21.

7-6 while

line AS of the focal planes

grating.!h

for all practical

Rcsoh'ing is

in the angle

of a grating

=.d.

1

ability

wavelengths

a change

1

=

nf the linea r disper sion

a ngula r disper sion

in Figures

dispersion

bv differentiating stant. Thus,

with

r is defined

with as replica

[)

Thus.

certain

The

dr is the change

or refraction

dA. The angle

in this way

holographic

is discussed

to several

under

different

The

r

approximately

still

can have serious

Monochromators.

7 -I 0 becomes

thcse

The grat-

holographic

with wavelengths

that of the instrument can be traced

radiation

mator Dispersion

(> 2()"), cos

At small angles of dilIraction

and E4uation

(,O ll.l'/anl,

given by dr ldA, where

test that can distinguish

The exit beam

contaminated

or stray

spurious

conditions."

D' Spectral

the

the slits

Despitc

measurements

heams

of a thin

gratings

its ahility to resolve

its light-gathering

over

and fumes.

some

creases.

by coating

In addition.

we shall see that its presence on

such as alu-

can be manufactured

of a monochromator

The

ticularly

numhers

substance

and a replica

however,

of a monochromator

Characteristics

of its radiant

Scattering pearing

appears:

by gener-

of the grating.

no optical

a mastcr

precautions,

and

paint.

with windows

of dust

depends

is developed

large (~50cm)

is sealed

entrance

can be

in Fig-

low cost. As with ruled gratings.

is apparently

monochromator

effects

monochromator

with flat hlack

on a con-

way as on a plane

collimating the

and

Such an arrangement increases

permits

auxiliary

the radiation

in addition.

can he formed

the same

grating

without

disperses

Gratings

perfect.

in the

surfaces

of G rating M onochrom ators

width. Gratings.

structure

can be cast from a master

lengths, Concave

which

with a reflective

many as 6000 lines/mm

Perform ance

lIJ

material.

the grooved

n=3

20

7C-l and illustrated

ating

between n= 1

of thc two laser

are produced

There

r,O

to produce

gratings

gratings

data:

substance

ure 7-14. holographic

provide

nm

spots

interior

reflection

in Section

an interference

priate

it can be dis-

that can be coated of the grooves

the angle

film of photosensitive

= ~'.;-'

for thc lirst-, secondo,

reflecting

The spacing

to bear

with pho-

from the two

so that

structure

the

to one another.

As descrihed

748.4

coated

fringes

the photoresist a grooved

ing is then coated and

interfercnce

by changing

with respect

and

gratings.

lasers are hrought

on a glass surface

grating.

perfecprovidc

radiation

of holographic

The resulting

a reflection

d in Equation

free of stray

from a pair of identical

at suitable

of their greater and dimcnsions,

to prevent

preparation

with aluminum To obtain

hecause

to line shape

the

or as the focallcngth

IllC;JSIH.'nwnl,

(,heln ..

llJfH,q.

alll\

22HL

Ihl.' dlc,\~

~t

R

the f-number.

of

light than

in-

chromalurs

il\ ....tLI\

ShMpc, And!

Thus. an f/2

lens gathers

an ('4 lens. Thc {numbers lii: in the 1 ID 10 f:.lngc'.

four times n for m"ny

ill
$150,000) installations that permit the simultaneous detection and determination of as many as twenty-four elements. In these instruments, individual channels consisting of an appropriate crystal and a detector are arranged radially around an X-ray source and sample holder. The crystals for all or most of the channels are usually fixed at an appropriate angle for a given analyte line; in some instruments, one or more of the crystals can be moved to permit a spectral scan. Each transducer in a multichannel instrument has its own amplifier, pulse-height selector, scaler, and counter or integrator. These instruments are equipped with a computer for instrument control, data processing, and display of analytical results. A determination of twenty or more elements can he completed in a few seconds to a few minutes. Multichannel instruments are widely used for the determination of several components in industrial materials such as steel, other alloys, cement, ores, and petroleum products. Both multichannel and singlechannel instruments arc equipped to handle samples in the form of metals, powdered solids, evaporated films, pure liquids, or solutions. When necessary, the materials are placed in a cell with a Mylar or cellophane window. E n e rg y-D isp e rsive

Electronics X-ray detector Alpha detector Collimator Alpha sourCe Door Contact

ring

APXS Front View x_raYdeteClor Alpha detector . ..

with collimator .

•

..

Alpha source Contact

ring

FIGURE 12-13 Energy-dispersive X-ray fluorescence spectrometer. Excitation by X-rays from (a) an X-ray tube and (b) a radioactive substance (curium-244, a 5.81 MeV alpha particle and X-raysource) as shown in the sensor head for the Mars alpha proton X-ray spectrometer. The X-ray detector is a new room-temperature type. (Reprinted with permission from R. Gellert et aI., J. G eophys. R es., 2006, 111, E02S05.)

diffractor, as well as the closeness of the detector to the sample, result in a 100-fold or more increase in energy reaching the detector. These features permit the use of weaker sources such as radioactive materials or low-power X-ray tubes, which arc cheaper and less likely to cause radiation damage to the sample. Generally, energy-dispersive instruments cost about one fourth to one fifth the price of wavelength-dispersive systems. Figure 12-13b shows the sensor head from the Mars rover missions of 2004. The head contains a curium244 source that emits X-rays and 5.81 MeV alpha particles. The X-rays cause fluorescence in Martian rock samples, and the alpha particles stimulate X-ray emission as well. X-ray emission stimulated by bombardment by alpha and other subatomic particles such as protons is called pa r ticle induced X-r a y emission, or PIXE. The X-ray detector is a new room-temperature type, which in the low temperature of the Martian night (below -40'C) exhibits low noise and high signal-to-noise ratio for excellent resolution and sensitivity. Note the concentric design of the sensor head with six Cm-244 sources arranged around the central detector. The X-ray spectrum of Figure 12-14 was acquired with the sensor head. In a multichannel, energy-dispersive instrument. all of the emitted X-ray lines are measured simultane-

In stru m e n ts

As shown in Figure 12-13a, an EDXRF spectrometer consists of a polychromatic source - which may be either an X-ray tuhe or a radioactive materiala sample holder, a semiconductor detector, and the various electronic components required for energy discrimination. 11 An obvious advantage of energy-dispersive systems is the simplicity and lack of moving parts in the excitation and detection components of the spectrometer. Furthermore, the ahsence of collimators and a crystal

lOFor a review of recent X-ray fluorescence instruments. see P. J. Potts. A T. Ellisb. P. Kregsamerc. C Strelic, C. Vanhoofd, M. ""este. and P. Wobrauschekc, 1. Ana l. Atomic Spectr ometr y. 2005, 20, 1124

~

....

... P)

ously. Increased sensitivity and improved signal-tonoise ratio result from the Fellgett advantage (see Section 71-1). The principal disadvantage of energydispersive systems, when compared with crystal spectrometers, is their lower resolutions at wavelengths longer than about 1 A. On the other hand, at shorter wavelengths, energy-dispersive systems exhibit superior resolution. Figure 12-15a is a photo of a basic, commercial, henchtop EDXRF instrument that is used for the routine determination of a broad range of elements from sodium to uranium in samples from many industrial processes. The diagram of Figure 12-15b shows a closeup of the bottom of the sample turntable, which is visible from the top in the photo of Figure 12-15a, and the optical layout of the instrument. Radiation from the X-ray tube passes through an appropriate filter hefore striking the boltom of the rotating sample. The X-ray fluorescence emitted by the sample passes to the silicon detector, which provides the signal for the multichannel counting system. The system is equipped with a rhodium anode X-ray tube, five programmable filters, a helium purge system, a twelve-position sample changer, and a spinner to rotate each sample during the dataacquisition process. Spinning the sample reduces errors due to sample heterogeneity. We describe a quantitative application of this instrument in Section 12C-3.

AI

i

Sol 357 Wish stone RAT2 --data --fl(

1.00

--

all components of theoretical model

-g

~ ~ c.. §

0.10

8

I

X-ray

tube

(b)

0.01 0.16

~ juations for absorption and fluorescence, matrix effects: the crystal reflectivity (in a WDXRF instrumene), instrument aperture, the detector efficiency, and so forth. The XRF spectrum of the standard is measured, and in an iterative process the instrument variables are refined and combined with the fundamcntal variables to obtain a ca libr a tion function for the analysis. Then the spectrum for an unknown sam pic is measured, and the iterative process is repeated using initial estimates of the concentrations of the analytes. Iteration continues until the calculated spectrum matches the unknown spectrum according to appropriate statistical criteria. This method gives good results with accuracies on the order of 1 %~ 4 % but is generally considered to be less accurate than derived

or regression methods." So-called swnda r dless a na lyusing variations on fundamental calibration methods. Instruments are carefully characterized, and instrument and fundamental parameters are stored in the computer. Spectra are then calculated and matched with samples by iterative methods to estimate concentrations of analytes. Derived methods simplify calculations of the fundamental method by lumping detailed fundamental calculations into generalized parameters to account for instrument functions, but the calculation of fluorescence intensities from analyte concentration is the same as in fundamental methods. Derived methods often show some improvement in accuracy and precision over fundamental methods. Regression methods rely on models of the form

sis is accomplished

W i = Bi

+

K J,[

I

+

tl

m ,jW ij]

where B i is the background, K, is a sensitivity coefficient, Ii is the intensity due to clement i, m ij is the bina r y influence coefficient that describes the matrix effect of element j on analyte i, and w,j is the average composition of the sample in i and j. To calibrate an instrument, spectra are acquired for standards and regression analysis is performed to determine Ki, Bi, and m ij for each binary combination of elements in the standards. These parameters are then used in a regression analysis of spectral data from unknown samples to determine the unknown concentrations W ;. A broad range of models and algorithms for regression analysis in XRF are available, and many commercial instruments use combinations and variations on tbese algorithms in their software suites." Accuracies and precisions attained using these methods are typically 1 % or better under optimal conditions. Regression methods were used to analyze the data of Figure 12-14 from the Mars rover to determine by EDXRF the concentrations of many elements in rocks and soil. In the early days of XRF, influence correction methods were difficult and time-consuming because sufficient computational power to accomplish them was available only on large. expensive mainframe computers. With the advent of powerful. low-cost, dedicated computers. sophisticated data analysis is now

1 L de Vrks and B. A. R. Vrebo,>. in R. E. Van Grieken and A. A. !\.-larkowicz, cds., Ha ndbook of X·r a l Specr r omctn'. 2nd ed .. New York Marcel Dekker. 2002. p. 37H . ;\Ibid .. pp .. 141- ..WS 14

routine, and all commercial instruments have mature software suites for instrument operation, calibration, data reduction, and analysis.

With proper correction for matrix effects, X-ray fluorescence spectrometry is one of the most powerful tools available for the rapid quantitative determination of all but the lightest elements in complex samples. For example, Rose, Bornhorst, and Sivonen 16 have demonstrated that twenty-two elements can be determined in powdered rock samples. with a commercial EDXRF spectrometer in about 2 hours (I hour instrument time), including grinding and pellet preparation. Relative standard deviations for the method are better than I % for major elements and better than 5% for trace elements. Accuracy and detection limits as determined by comparison to results from international standard rock samples were comparable or better than other published procedures. For an excellent overview of XRF analysis of geological materials, see the paper by Anzelmo and Lindsay. 17 X-ray methods arc also applied widely for quality control in the manufacture of metals and alloys, Because of the speed of the analysis in these applications, it is possible to correct the composition of the alloy during its manufacture. X-ray fluorescence methods are easily adapted to liquid samples. Thus, as mentioned earlier, methods have been devised for the direct quantitative determination of lead and bromine in aviation fuel samples. Similarly, calcium, barium, and zinc have been determined in lubricating oils by exciting fluorescence in the liquid hydrocarbon samplcs. The method is also convenient for the direct determination of pigments in paint samples. X-ray fluorescence methods are being widely applied to the analysis of atmospheric pollutants. For example, one procedure for detecting and determining contaminants involves drawing an air sample through a stack consisting of a micropore filter for particulates and three filter paper disks impregnated with orthotoIidine, silver nitrate, and sodium hydroxide, respectively. The reagents retain chlorine. sulfides, and sulfur dioxide in that order. The filters containing trapped

analytes then serve as samples for X-ray fluorescence analysis. As an example of the routine application of EDXRF for determining the elemental composition of foodstuffs, consider the data plots of Figure 12-15c and 12-15d.18 In this analysis, iron, copper, and zinc were determined in rice using the spectrometer shown in Figure 12-15a. The spectrometer was calibrated using nine standard samples of rice. The standards were ground into fine powders, pressed into pellets, and loaded into the sample turntable. Each sample was irradiated with X-rays (Rh anode) through an aluminum filter for 5 minutes, and data were acquired to produce spectra such as the one shown in Figure 12-15c. The instrument computer then analyzed the data and calculated the areas under the various peaks in the spectrum as shown by the shaded areas in the figure, and calibration curves similar to Figure 12-15d were produced for each of the analytes. Determination of the analytes in another well-characterized' sample yielded concentrations of 73.49 ppm, 7.46 ppm, and 38.95 ppm for iron, copper, and zinc, respectively. Relative accuracies for the three elements were 0.9% (Fe), 5% (Cu), and 0.3% (Zn) as determined by comparison with values determined by optical spectroscopic methods. . Another indication of the versatility of X-ray fluorescence is its use for the quantitative determination of elements heavier than sodium in rocks and soil encountered near the landing site of the Mars Pathfinder mission.19 The Pathfinder's microrobot Sojour ner was equipped with a sensor head that could be placed flat against a material to be analyzed. The head contained curium-244, which emitted a particles and X-rays that bombarded the sample surface as in Figure 12-l3b. The X-ray emission from the sample struck the transducer of an energy-dispersive spectrometer in which the radiant power was recorded as a function of energy, was transmitted from Mars to Earth, and ultimately was analyzed on Earth. Lighter clements were determined by backscattering or proton emission. With these three methods of detection, all of the elements in the periodic table but hydrogen can be determined at concentration levels of a few tenths of a percent. In 2004 two new rovers, Spir it and Oppor tunity, landed on Mars with X-ray fluorescence spectrometers aboard.") As we write this, the rovers have

lilW. I. Rose, T. 1. Bornhorst, and S. 1. Sivon.:n. t-m.\' Spea r ometr v. 1986, 15, :55 1- J. E. Anzelmo and J. R Lindsay,J. Cher n. Educ .. 1987.6.J . A181 and A200.

V. Sethi, M. t\'lizuhira. and Y. Xiao, G.I. T. Ll.J .bur a tor y J our na l, 2005, 6. 22. IQ"Mars Pathfinder," 1997. http://mars.jpl.nasa.govIMPF' (25 July 1997). ""'Spirit and Opportunity," 200...J, hltpJ/mpf\\.ww.jpl.nasa.gu\'/missions I present /2003.html (13 Oct 2(05)

S o m e Q u a n tita tive

A p p lica tio n s

o f X -ra y F lu o re sce n ce

I~

spent nearly 2 years moving about their respective landing sites, and the spectrometers continue to send data to Earth revealing the elemental composition of Mars rocks and soil. The spectrum shown in Figure 12-14 was transmitted from one of the rovers to a ground station where the data were analyzed using a regression algorithm, and concentrations of the various elements in the sample were extracted from the data. Details of the intricate calibration procedure appear in the paper by Gellert et al.21 A d va n ta g e s

a n d D isa d va n ta g e s

o f X -ra y F lu o re sce n ce

M e th o d s

X-ray fluorescence offers a number of impressive advantages. The spectra are relatively simple, so spectralline interference is minimal. Generally, the X-ray method is nondestructive and can be used for the analysis of paintings, archaeological specimens, jewelry, coins, and other valuable objects without harm to the sample. Furthermore, analyses can be performed on samples ranging from a barely visible speck to a massive object. Other advantages include the speed and convenience of the procedure, which permit multielement analyses to be completed in a few minutes. Finally, the accuracy and precision of X-ray fluorescence methods often equal or exceed those of other methods.22 X-ray fluorescence methods are generally not as sensitive as the optical methods discussed earlier. In the most favorable cases, concentrations of a few parts per million or less can be measured. More often, however, the concentration range of the method is from about 0.01% to 100%. X-ray fluorescence methods for the lighter elements arc inconvenient; difficulties in detJ:ction and measurement become progressively worse as atomic numbers become smaller than 23 (vanadium), in part because a competing process, called Auger emission (see Section 2IC-2), reduces the fluorescence intensity (see Figure 21-7). Today's commercial instruments have a lower atomic number limit of 5 (boron) or 6 (carbon). Another disadvantage of the X-ray emission procedure is the high cost of instruments, which ranges from less than $10,000 for an R. (,e1krt, R. Rieder, 1. BrUckner, B. C. Clark, G. Dreibu$, G. KlingclhOfer, G. Lugmair, D. W. Ming, H. Wanke, A. Yen, J. Zipfel, and S. W Squyres. 1. Geophys. Res., 2(4)6, J 11. E02S05 22For a comparison of X-ray fluorescence and inductively coupled plasma for the analysis of environmental samples, see T. H. Nguyen, 1. Boman, and t\t Lecrmakers, X-Ra y Spectr ometr y, 1998,27,265. 21

r::il lQJ

Tutor ia l: Learn more about applications of X-ray fluorescence.

energy-dispersive system with a radioactive source to well over $500,000 for automated and computerized wavelength-dispersive systems.

In contrast to optical spectroscopy, where absorption methods are most important, X-ray absorptionapplications are limited when compared with X-ray emission and fluorescence procedures. Although absorption measurements can be made relatively free of matrix effects, the required techniques are somewhat cumbersome and time-consuming when compared with fluorescence methods. Thus, most applications are confined to samples in which matrix effects are minimal. Absorption methods are analogous to optical absorption procedures in which the attenuation of a band or line of X-radiation is the analytical variable. Wavelength selection is accomplished with a monochromator such as that shown in Figure 12-9 or by a filter technique similar to that illustrated in Figure 12-8. Alternatively, the monochromatic radiation from a radioactive source may be used. Because of the width of X-ray absorption peaks, direct absorption methods arc generally useful only when a single element with a high atomic number is to be determined in a matrix consisting of only lighter elements. Examples of applications of this type are the determination of lead in gasoline and the determination of sulfur or the halogens in hydrocarbons.

120-1 X-ray Diffraction Methods Since its discovery in 1912 by von Laue, X-ray diffraction has provided a wealth of important information to science and industry. For example, much of what is known about the arrangement and the spacing of atoms in crystalline materials has been determined directly from diffraction studies. In addition, such studies have led to a much clearer understanding of the physical properties of metals, polymeric materials, and other solids. X-ray diffraction is one of the most important methods for determining the structures of such complex natural products as steroids, vitamins, and antibiotics. The details of these applications are beyond the scope of this book. X-ray diffraction also provides a convenient and practical means for the qualitative identification of crystalline compounds. The X-ray powder diffraction method is the only analytical method that is capable of

providing qualitative and quantitative information about the compounds present in a solid sample. For example. the powder method can determine the percentage KBr and NaCl in a solid mixture of these two compounds. Other analytical methods reveal only the percentage K-. Na-, Br-, and Cl- in the sample." Because each crystalline substance has a unique X-ray diffraction pattern, X-ray powder methods are well suited for qualitative identification. Thus, if an exact match can be found between the pattern of an unknown and an authentic sample, identification is assured.

120-2 Identification of Crystalline Compounds S a m p le P re p a ra tio n

For analytical diffraction studies, the crystalline sample is ground to a fine homogeneous powder. In such a form, the enormous number of small crystallites are oriented in every possible direction; thus, when an X-ray beam passes through the matcrial, a significant number of the particles are oriented in such ways as to fulfill the Bragg condition for reflection from every possible interplanar spacing. Samples are usually placed in a sample holder that uses a depression or cavity to mount the sample. These mounts are commonly made of aluminum, bronze, Bakelite, glass, or Lucite. Cavity mounts are most commonly side loaded or back loaded. A frostcd glass surface, ceramic, or caJdboard is placed over the front, and the sample is carefully added via the open side or back. Top-loading mounts are also available as are special mounts known as zero background mounts. Alternatively, a specimen may be mixed with a suitable noncrystalline binder and molded into an appropriate shape. A u to m a tic

P h o to g ra p h ic

R e co rd in g

The classical photographic method for recording powder diffraction patterns is still used, particularly when the amount of sample is small. The most common instrument forthis purpose is the Debye-Scher r er powder camera, which is shown schematically in Figure 12-17a. Here, the beam from an X -ray tube is filtered to produce a nearly monochromatic beam (often the copper or molybdenum Ka line), which is collimated by passage through a narrow tube. Figure 12-8 shows how a filter can be used to produce a relatively monochromatic beam_ Note that the Kf3 line and most of the continuum from a Mo target are removed by a zirconium filter with a thickness of about 0.01 em. The pure K a line is then available for diffractometry. Several other target-filter combinations have been developed to isolate one of the intense lines of the targct material. The undiffracted radiation T then passes out of the camera via a narrow exit tube as shown in Figure 12-17a. The camera itself is cylindrical and equipped to hold a strip of film around its inside wall. The inside diameter of the cylinder usually is 5.73 or 11.46 em, so that each lineal millimeter of film is equivalent to 1.0' or 0.5' in 8, respectively. The sample is held in the center of the beam by an adjustable mount. Figure 12-17b shows the appearance of the exposed and developed film; each set of lines (0" 0" and so forth) represents diffraction from one set of crystal planes. The Bragg angle 8 for each line is easily evaluated from the geometry of the camera.

D iffra cto m e te rs

Diffraction patterns are generally obtained with automated instruments similar in design to that shown in Figure 12-9. In this instrument, the source is an X-ray tube with suitable filters. The powdered sample, however, replaces the single crystal on its mount. In some instances. the sample holder may be rotated to increase the randomness of the orientation of the crystals. The

a more detailed Jisformation regarding the substances and materials,inbluding name, formula (if appropriate), compositio'n, color, line strengths, melting point, mineral classification, density, and a host of other characteristics of the materials as well as bibliographic information. A variety of presentation modes are available so that graphs and other important images may be viewed and printed." If the sample contains two or more crystalline compounds, identification becomes more complex. Here, various combinations of the more intense lines are used until a match can be found. Computer searching and matching of data greatly facilitates this task. One very important application is the determination of the percentage crystallinity of materials. In the analysis of polymeric and fibrous materials, determin-

ing the crystalline-to-amorphous ratio has long been of importance, and X-ray powder methods have unique advantages in these determinations. In the pharmaceutical area, the degree of crystallinity can influence the long-term stability of a formulation as well as its bioactivity. X-ray diffraction methods are being increasingly applied to pharmaceuticals. Crystalline materials produce well-defined diffraction peaks whose widths are related to the crystalline "quality." High-quality materials produce sharp peaks, and poor-quality materials give rise to more diffuse diffraction peaks. Amorphous phases come in different forms depending on how they were formed. A glassy phase produces a diffraction signal that is the radial distribution of nearest neighbor interactions. An amorphous phase derived from a crystalline phase usually corresponds to a poor-quality, or paracrystalline, material. Both glassy and para crystalline specimens produce a low-frequency halo, which can appear as a broad background. One approach to determining the crystalline-toamorphous ratio is to use conventional quantitative analysis methods. Non-overlapped X-ray diffraction peaks arc chosen for the phase to be analyzed. Either peak height or peak area is used for quantitative analysis. Standards of known concentration are then used to prepare a calibration curve. In the Vainshtein approach, the amorphous phase is used as a normalizing factor for the integrated

intensities of the crystalline peaks." This eliminates the effects of sample preparation and instrumcnt drift. Analysis is based on Va inshteins la w. which states that the diffracted intensity from a material is independent of its state of order within identical regions of reciprocal space. To apply the law. a single standard with a known percentage of crystallinity is used to establish the normalization ratio between the integrated crystalline peaks and the amorphous "background." The same measurements are then made on thc specimen of unknown crystallinity. The percentage crystallinity of the unknown is thcn found from (C IA )" ] % C" = %C"d [ (C/A)"d

where % C" and %C"d are the percentage crystallinities of the unknown and standard respectively, and CIA

!jB_ K. Vainshtein (1~21-1996) \lias a prominent Russian X-ray crystallographer. His monograph Diffr a ccion of X-r a ys by Cha in MoLecules (Amsterdam: Elsevier. 1966) played an important role in the development of structural studies of polymers.

is the ratio of the integrated intensity of the crystalline phase C to the amorphous background A. Yet another approach is to use Fourier transform methods to split the power spectrum into low- and high-frequency regions. The amorphous phase is associated with the low-frcquency region, and the crystalline phase is associated with the high-frequency region. After filtering the undesired region, the inverse transform gives the amorphous intensity and the crystalline intensity. Standards are used to dctcrmine the width and frcquencies of the filters.

*12-7 Aluminum is to be used as windows for a cell for X-ray absorption measurements with the Ag Ka line. The mass absorption coefficient for aluminum at this wavelength is 2.74; its density is 2.70 g/cm '. What maximum thickness of aluminum foil could be used to fabricate the windows if no more than 3.5% of the radia tion is to be absorbed by them ry *12-8 A solution of I, in ethanol had a density of 0.794 g/cm '. A 1.50-cm layer was found to transmit 27.3% of the radiation from a Mo Ka source. Mass absorption coefficients for I. C, H, and 0 are 39.2,0.70.0.00, and 1.50, respectively. (a) Calculate the percentage of I, present, neglecting absorption by the alcohol. (b) Correct the results in part (a) for the presence of alcohol. *12-9 Calculate the goniometer setting, in terms of 20. required to observe the Ka, lines for Fe (1.76 A), Se (0.992 A), and Ag (0.497 A) when the diffracting crystal is (a) topaz, (b) LiF, (c) NaCI.

An important method for the determination of the elemental composition of surfaces is based on the electr on micr opr obe. In this technique, X-ray emission from the elements on the surface of a sample is stimulated by a narrowly focused beam of electrons. The resulting X-ray emission is detected and analyzed with either a wavelength or an energy-dispersive spectrometer. This method is discussed in detail in Section 21F-1.

12-10 Calculate the goniometer setting, in terms of 20, required to observe the LI3, Iincs for Br at 8.126 A when the diffracting crystal is (a) ethylenediamine d-tartrate. (b) ammonium dihydrogen phosphate. *12-11 Calculate the minimum tube voltage required to excite the following lines. The numbers in parentheses are the wavelengths in A for the corresponding absorption edges. (a) K lines for Ca (3.064) (b) La lines for As (9.370) (c) Ll3lines for U (0.592) (d) K lines for Mg (0.496)

*Answers are provided at the end of the book for problems marked with an asterisk. ~

Manganese was determined in samples of geological interest via X-ray fluorescence using barium as an internal standard. The fluorescence intensity of isolated lines for each element gave the following data:

Problems with this icon are best solved using spreadsheets.

*12-1

What is the short-wavelength limit of the continuum produced by an X-ray tube having a silver target and operated at 90 kV?

*12-2

What minimum tube voltage would be required to excite the KI3 and LI3series of lines for (a) U, (h) K, (c) Rh, (d) W? The Ka, lines for Ca, Zn, Zr, and Sn have wavelengths of 3.36,1.44,0.79, and 0.49 A, respectively. Calculate an approximate wavelength for the Ka lines of (a) V, (h) Ni, (c) Se, (d) Br, (e) Cd, (f) Sh. The La lines for Ca. Zn, Zr, and Sn have wavelengths of 36.3, 11.9.6.07, and 3.60 A, respectively. Estimate the wavelengths for the La lines for the elements listed in Prohlem 12-3.

*12-5

*12-6

The mass ahsorption coefficient for Ni, measured with the Cu Ka line, is 49.2 cm 2/g. Calculate the thickness of a nickel foil that was found to transmit 47.8% of the incident power of a beam of Cu Ka radiation. The density of Ni is 8.90 g/cm '. For Mo Ka radiation (0.711 A), the mass absorption coefficients for K, L H. and 16.7.39.2.0.0, and 1.50 cm '/g, respectively. (a) Calculate the mass ahsorption coefficient for a solution prepared by mixing 11.00 g of Kl with 89.00 g of water. (h) The density of the solution described in (a) is 1.086 g/cm 3 What fraction of the radiation from a Mo Ka source would be transmitted hy a 0.60-cm layer of the solution')

o arc

Wt.%Mn

Ba

Mn

0.00 0.10 020 0.30 0.40

156 160 159 160 151

80 1116 129 154 167

What is the weight percentage manganese in a sample that had a Mn-to-Ba count ratio of 0.735') ~

C h a lle n g e

P ro b le m

12-13 As discussed in Section 12C-3, the APXS, or alpha proton X-ray spectrometer, has been an important experiment aboard all of the Mars exploration rovers. Journal articles provide details of the APXS experiments on the most recent missions in 2004 and compare the instrumentation and measurement strategies with those on board the Pathfinder mission of 199726 ,~S. W. Squyres et aI., 1. Genphys. Res .. 2003. 108. S06::!;R. Rieder et al.. 1. Ge{)ph.~·5.Res .. 2003. J 08. 8066: 1. Bruckner et aL, 1. (;eophys. Res .. 2003, lOS, 809·l; R. Gellert et aL Science, 200·t 305, 829: H. Y. McSween et al., Science. 2004, 305. 8--12;S. W Squyres et a\., Science, 2004. 306, 1709; L A. Soderblom et aL Science, 2004, 306. 1723: G. Khngelhofer ct aL, Scienef:'. 200·1. 306.1740; R. Rieder et al.. Sciena . 2004. 306.1746; A. Banin, Science, 2005. 309. 888.

(a) Consult the cited articles, and describc the construction and operation of the deteclor head on the Spir ic and Oppnr cu/lity ro\·ers. Illustrate your answer with basic diagrams of Ihe instrument components, and describe the function of each. (b) What determines the selectivity and sensitivity of the APXS system') (c) What elements cannot be determined by APXSo Why notO (d) Characterize the general elemental composition of all of the Martian landing sites. What are the similarities and differences among the sites. What cxplanation do these workers and others givc for the similarities? (e) How Were the APXS measurements limited bv the time in the Martian day when the experiments were completed" Expl~in the cause of these Iimita-tions. How and why were the APXS experiments terminated? (f) What effect did temperature have on the results of the X-ray mode of the APXS experiments? How does this effect relate to your discussion in (e)? (g) The APXS experiments were used to compare the surface composition with the composition of the interiors. How was this accomplished? What differences were discovered? What explanation was given for the differences? (h) Halogen fractionation was apparent in the Martian rock samples. What explanation was given for this phenomenon? (i) Characterize the overall precision and accuracy of the APXS experiments. The APXS team states that "accuracy is mainly determined by precision." Explain what is meant by this statement. Under what circumstances is it true? (j) Explain in some detail the calibration procedure for the APXS experiments. What calibration standards were used on Mars, and where were they located? How Were individual element peaks extracted from the X-ray spectra? (k) Figure 12-18 shows a plot of corrected calibration data for Fe from the APXS experiments. Note that there are uncertainties in both the x and y data. The 22 20

18 V;

C

~ g ;

§

~

2 ;

~

16 14 12 10

x

~ "

'"'

~

6

0..

4

l()

12

14

W e ig h t

FIGURE

12-18

APXS

R. Rieder et aI., J.

16

l~

:20

'l,

~4

26

28

)0

percentag~

calibration curve for Fe corrected for attenuation coefficient. (From 2003. 108,8066, with permission.)

G eophys. R es.,

data from the plot are tabulated in the table below. Carry out a normallcastsquares analysis of the data using Excel. Determine the slope, intercept, correlation coefficient, and the standard deviation about regression. Peak Area

(T

M ass

%

(T

2.36

0.28

2.12

0.13

7.04

0.54

5.75

0.13

6.68 8.01

0.54 0.39

5.85

0.13

8.42

0.44

7.14 7.45

0.13

0.10

7.87 13.20

0.10

15.58 20.24

0.18 0.21

1.18

20.71

0.23

1.26

20.55

0.18

9.04

0.44

14.74

0.74

17.93 21.27

0.90 1.05

23.22 25.02

0.10

(I) Carry out a weighted least-squares analysis of the data using a procedure similar to the one described in Problem 10-14 that allows for uncertainties in both the x and y variables. Compare your results to those obtained in (k).

w~¥

Instrumental Analysis in Action

:""~,~~::;>:

_ ~ -,..~ '"'t'~ ~

t-.fercury is an extremely

important

ment, in foods, and in industrial scares concerning

is a small industrial

containing

firm in Minamata,

into Minamata

1968. As a result, thousands

of local residents, whose norsymproms

poisoning. The disease became known as

disea se. Since then, there have been many warn-

Mina ma ta

are found in large fish such as swordfish and sharks.

the

Bay from 1932 to

mal diet included /ish from the bay, developed of methylmercury

by the life span

town on the coast of the

dumped some 37 tons of mercury-

compounds

of mercury are determined

Bay disaster in Japan in 1956.

Shiranui Sea. The major industrial Chisso Corporation,

concentrations

of the fish and its feeding habits. The highest concentrations

mercury have been many since the best-

known case, the Minamata Minamata

element in the environ-

processes. The health

Because of its importance reliable determinations determination

accurate,

of the various forms that mercury takes in

the environment measurements

in the environment,

of mercury are crucial. Although

is of interest, current

regulations

focus on

of total mercury, which is in itself challeng-

ing. The challenge arises because in complex environmental

ings ahout eating /ish and shellfish known to contain high

samples mercury is present in very small amounts. The EPA

levels of mercury. The most recent recommendations

has established

United States Environmental

Protection

and the Food and Drug Administration child-bearing

of the

Agency (EPA) warn women of

age and young children not to eat shark,

swordfish, king mackerel,

or tilefish. These agencies also

water ecosystems

and 25 ppt as the limit for saltwater. The

National Toxics rule of the EPA

2

recommends

quently, concentrations

lower than this criterion

seawater. Some ocean surface waters have been found to

such as shrimp, canned lUna, salmon, pollock, and cat/ish.

have concentrations

apply to fish from certain

plus organic forms) in

lower than 0.05 ppt, and intermediate

water layers can have levels as high as 2 ppt. These low concentrations

can be near or lower than the limits of detection

for many analytical techniques. higher concentrations

In freshwater

have been observed.

systems, much In some Califor-

nia lakes, for example, levels of 0.5 to 100 ppt have been deMercury is, of course, a naturally occurring element. How-

termined.

ever, industrial

can be quite a challenge for analytical chemists.

poHution is a major source of environmental

mercury. The pollution coal-burning

In any case, detection

of these ultra trace levels

liquid reagents from the mercury vapor, which is transferred

to Hg(lI). Stannous chloride (SnCI,) is then used to reduce

to the observation

the Hg(ll)

intensity mercury vapor lamp excites atomic fluorescence.

observation

to elemental

mercury, which is swept into the

cell of the atomic absorption

ure 1A2-1 for mercury detection.'

achieve sub-parts-per-billion

systems, the digestion-oxidation

sensitivity but gives nonlinear

responses. EPA method 7474 uses a microwave digestion

The digestion

The method can achieve a detection

and has a range from about 1 ppb to several

Beca.lJsc regulatory requirements in

are becoming more strin-

gent, -it is desirable to have a more sensitive method for

the United States and the United Kingdom are in the parts-

mercury. Atomic fluorescence

per-trillion

tion 9E) can achieve the required detection

The Clean Air

range and lower. However, conventional

analyti~

bined with newly developed

Act, first enacted in 1970 in the United Srates, mandated

cal methods such as flame atomic absorption,

levels of air pollution, including mercury. Likewise, the EPA

coupled plasma atomic emission, and inductively coupled

instrument

has set water-quality

plasma mass spectrometry

on atomic fluorescence

criteria for levels of mercury in both

inductively

cannot achieve parts~per-trillion

that individual states achieve safe concentration

samples to the atomizer is quite inefficient (often only 2%

for mercur\, monitoring

or less of the sample is transferred).'

generation' techniques

like mercury.

Mercury from the air or from water sources accumulates in streams and lakes. Bacteria cury into methylmercury,

in the water convert the mer-

which is readily absorbed

by in-

sects and other aquatic organisms. The mercury-containing compounds

Cold-vapor sometimes

atomic absorption

(see Section 9A-3) can

achieve sub-parts-per-billion

In the most sensitive EPA cold-vapor method, the sample is digested

to transfer

detection

limits.

atomic absorption

with a permanganate-

rapidly move up the food chain as small fish

eat the small organisms and big fish eat the small fish. The

http://w\\''-''.epa.govimcrcury/reporLhtm J"Monitoring the Mercury Menace," p. Stockwdl. Toda .vs Chemisla ! Wor k. p. 27. November 2003: http://pub5.acs.org/subscrihe/journals/ tC3w/12/i 11ipdf,-1103instruments.pdf. !

detection

instrument

sand trap by

uses an atomic

system and claims a working range

from

1000

= eb c = A

13B-1 Application of Beer's Law to Mixtures

A total

= At

+

= e[ l> c

5

After converting to base 10 logarithms and inverting the fraction to change the sign, we obtain

x

Beer's law also applies to a medium containing more than one kind of absorbing substance. Provided that the species do not interact, the total absorbance for a multicomponent system is given by

-In!.. = a n Po

13-7 yields

Finally, the constants in this equation can be colleeted into a single term e to give lo g p

P

with Equation

= 6.02 X 1 0 " a b c

g P

Recall, now, that d 5 is the sum of the capture areas for particles within the section; it must therefore be proportional to the number of particles, or

-r

moUl

lO " V

Az

+

+ ... +

e2 b c

An

+ ... +

en l> c

(1 3 -9 )

where the subscripts refer to absorbing components 1 ,2 , ...

, n.

13B-2 Limitations to Beer's Law

Few exceptions are found to the generalization that absorbance is linearly related to path length. On the other hand, deviations from the direct proportionality between the measured absorbance and concentration frequently occur when I> is constant. Some of these deviations, called r e a l d e via tio lls, are fundamental and represent real limitations of the law. Others are a result of how the absorbance measurements are made (in str u m e n ta l d e via tio n s) or a result of chemical changes that occur when the concentration changes (c h e m ic a l d e via tio n s).

anI>

2 .3 0 3 V

Note that IlIV is the number of particles per cubic centimeter, which has the units of concentration. We can then convert IlIV to moles per liter because the number of moles is given by number mol ~

n p;>HielcS -------. 6.02 X 1021 p .a r-fictl!S 1 m o l

R e a l L im ita tio n s

to

B e e r's

Law

Beer's law describes the absorption behavior of media containing relatively low analyte concentrations; in this sense, it is a limiting law. At high concentrations (usually >0.01 M), the extent of solute-solvent interactions. solute-solute interactions, or hydrogcn bonding can

r::"iI ~

E xe r c ise : Learn more about absorption spectrophotometry.

affect the analyte environment and its absorptivity. For example. at high concentrations, the average distances between the molecules or ions responsihle for absorption are diminished to the point where each particle affects the charge distribution of its neighbors. Thcse solute-solute interactions can alter the ability of the analyte species to absorb a given wavelength of radiation. Because the extent of interaction depends on concentration, deviations from the linear relationship hetween absorbance and concentration occur. A similar effect is sometimes encountered in media containing low ahsorber concentrations but high concentrations of other species, particularly electrolytes. The proximity of ions to the absorber alters the molar absorptivity of the latter by electrostatic interactions; the effect is lessened by dilution. Although the effect of molecular interactions is ordinarily not significant at concentrations below 0.0 I M, some exceptions oceur among certain large organic ions or molecules. For example, the molar ahsorptivity at 436 nm for the cation of methylene blue in aqueous solutions is reported to increase by 88% as the dye concentration is increased from 1O·5to 10-2 M; even below 10-6 M, strict adherence to Beer's law is not observed. Deviations from Beer's law also arise because absorptivity depends on the refractive index of the medium.' Thus, if concentration changes cause significant alterations in the refractive index n of a solution, departures from Beer's law are observed. A eorrection for this effect can be made by substituting the quantity e n l(n 2 + 2)2 for e in Equation 13-8. In general, this correction is never very large and is rarely significant at conc!ntrations less than 0.01 M. A p p a re n t

C h e m ic a l

D e v ia tio n s

Apparent deviations from Beer's law arise when an analyte dissociates, associates, or reacts with a solvent to produce a product with a different ahsorption spectrum than the analyte. A common example of this behavior is found with aqueous solutions of acid-base indicators. For example, the color change associated with a typical indicator Hln arises from shifts in the equilibrium

Example 13-1 demonstrates how the shift in this equilibrium with dilution results in deviation from Beer's law.

Solutions containing various concentrations of the acidic indicator Hln with K , = 1.42 X 1 0 - 5 were prepared in 0.1 M HCI and 0.1 M NaOH. In both media, plots of absorbance at either 430 nm or 570 nm versus the total indicator concentration are nonlinear. However, in both media, Beer's law is obeyed at 430 nm and 570 nm for the individual species HIn and In-. Hence, if we knew the equilibrium concentrations of H In and In -, we eould compensate for the dissociation of Hln. Usually, though, the individual concentrations are unknown and only the total concentration cta,,! = [Hln] + IIn-] is known. We now calculate the absorbance for a solution with CIO rr* transitions generally range between 1000 and is.OOOL mol 1 cm -I Typical absorption spectra are shown in Figure 1.\-2. Saturated organic compounds containing such heteroatoms as oxygen, nitrogen, sulfur. or halogens have non bonding electrons that can be excited by radiation in the range of 170 to 250 nm. Table 14-2 lists a

100,0000 80,000

f3

60,000 -l0 000 20000

o

~arOh:ne

[;0

TABLE 14-2 Absorption by Organic Compounds Containing Heteroatoms with Nonbonding Electrons

~ ••••••.•_-

350 400 450 500 550 600 650

-l00

CH,oH

500

(CH,hO CH,Cl CH,' (CH,hS CH,NH2 (CH,hN

210230250270290310330350 Wavelength.

FIGURE

14-2

om

Absorption spectra for typical organic

compounds.

depend on the Iigands bonded to the metal ions. The energy differences between these d-orbitals (and thus the position of the corresponding absorption maximum) depend on the position of the element in the periodic table, its oxidation state, and the nature of the ligand bonded to it, Absorption spectra of ions of the lanthanide' and actinide transitions series differ substantially ffOLDthose shown in Figure 14-3. The electrons responsible for absorption by these elements (4fand Sf, respectively) are shielded from external influences by electrons that occupy orbitals with larger principal quantum numbers. As a result, the bands tend to be narrow and relatively

l[~l

few examples of such compounds. Some of these compounds, such as alcohols and ethers, are common solvents, so their absorption in this region prevents measuring absorption of analytes dissolved in these compounds at wavelengths shorter than 180 to 200 nm. Occasionally, absorption in this region is used for determining halogen and sulfur-bearing compounds.

400

500

600

700

10'000[8000 6000 4000 2000 ;: 0 0. 400

o

~ A number of inorganic anions exhibit ultraviolet absorption bands that are a result of exciting nonbonding electrons. Examples include nitrate (313 nm), carbonate (217 nm), nitrite (360 and 280 nm), azido (230 nm), and trithiocarbonate (500 nm) ions. In general, the ions and complexes of elemenls in the first two transition series absorb broad bands of visible radiation in at least one of their oxidation states and are, as a result, colored (see, for example, Figure 14-3). Here. absorption involves transitions between filled and unfilled d-orbitals with energies that

Zl I~J

'I t o

!

-lOO

-l00

500

600

V\"avekngth. FIGURE

14-3

700

mil

Absorption spectra of aqueous solutions

of transition metal ions.

:0:: ,""I -l00

500

Wavelength,

600

700

nm

FIGURE 14-4 Absorption spectra of aqueous solutions of rare earth ions.

unaffected by the species bonded by the outer electrons (see Figure 14-4).

For quantitative purposes, charge-transfer absorption is particularly important because molar absorptivities are unusually large (£ > 10,0(0), which leads to high sensitivity. Many inorganic and organic complexes exhibit this type of absorption and are therefore called charge-transfer complexes. A charge-transfer complex consists of an electrondonor group bonded to an electron acceptor. When this product absorbs radiation, an electron from the donor is transferred to an orbital that is largely associated with the acceptor. The excited state is thus the product of a kind of internal oxidation-reduction process. This behavior differs from that of an organic chromophore in which the excited electron is in a molecular orbital shared by two or more atoms. Familiar examples of charge-transfer complexes include the phenolic complex of iron(IlI). the 1,10-

[l]

Simula tion:

Learn more about absorption spectra.

phenanthroline complex of iron(II), the iodide complex of molecular iodine, and the hexacyanoferrate(II)hexacyanoferrate(III) complex responsible for the color of Prussian blue. The red color of the iron(l1l)thiocyanate complex is a further example of chargetransfer absorption. Absorption of a photon results in the transfer of an electron from the thiocyanate ion to an orbital that is largely associated with the iron(lll) ion. The product is an cxcited species involving predominantly iron(II) and the thiocyanate radical SeN. As with other types of electronic excitation, the electron in this complex ordinarily returns to its original state after a brief period, Occasionally, however, an excited complex may dissociate and produce photochemical oxidation-reduction products. Three spectra of charge-transfer complexes are shown in Figure 14-5. In most charge-transfer complexes involving a metal ion, the metal serves as the electron acceptor. Exceptions are the 1,10-phenanthroline complexes of iron(II) and copper(l), where the ligand is the acceptor and the metal ion the donor. A few other examples of this type of complex are known, Organic compounds form many interesting chargetransfer complexes, An example is quinhydrone (a 1: 1 complex of quinone and hydroquinone), which exhibits strong absorption in the visible region. Other examples include iodine complexes with amines, aromatics, and sulfides. 5000 4000 3000 2000 1000

Fe(SCN)2+

o

400 450 500 550 600 650 700

~ 12,000 ~ 108~~~ ~ 6000 ~ 4000 ~ 2000 '0 0 ::;: -l00 450 500 550 600 650 700

~H~.

~StarChlj-

•

10,000 5000

o

-l00 -l50 500 550 600 650 700 \Vavelength.

nm

FIGURE 14-5 Absorption spectra of aqueous chargetransfer complexes.

14C

QUAliTATIVE APPliCATIONS OF ULTRAVIOLET-VISIBLE ABSORPTION SPECTROSCOPY

Even though it may not provide the unambiguous identification of an organic compound, an absorption spectrum in the visible and the ultraviolet regions is nevertheless useful for detecting the presence of certain functional groups that act as chromophores. For example, a weak absorption band in the region of 280 to 290 nm, which is displaced toward shorter wavelengths with increased solvent polarity, strongly indicates the presence of a carbonyl group. Such a shift is tcrmed a hypsochr omic, or bLlle,shift. A weak absorption band at about 260 nm with indications of vibrational finc structure constitutes evidence for thc existcnce of an aromatic ring. Confirmation of the presence of an aromatic amine or a phenolic structure may be obtained by comparing the effects of pH on the spectra of solutions containing the sample with those shown in Table 14-4 for phenol and aniline. The ultraviolet spectra of aromatic hydrocarbons are characterized by three sets of bands that originate from 'IT --+ 'IT ' transitions. For example, benzene has a strong absorption peak at 184 nm (em" = 60,000): a weaker band, called the E, band, at 204 nm (com" ~ 7900); and a still weaker peak, termed the B band, at256 (emax = 200). The long-wavelength bands of benzene vapor, 1,2,4,5-tetrazine (see Figure 14-la), and many other aromatics contain a series of sharp peaks duc to the superposition of vibrational transitions on the basic electronic transitions. As shown in Figure 14-1, solvents tend to reduce (or sometimes eliminate) this fine structure as do certain types of substitution.

~ 0.4

Spectrophotometric measurements with ultraviolct radiation are useful for detecting chromophoric groups, such as those shown in Table 14-1.' Because large parts of even the most complex organic molecules are transparent to radiation longer than 180 nm, the appearance of one or more peaks in the region from 200 to 400 nm is clear indication of the presence of unsaturated groups or of atoms such as sulfur or halogens. Often, the identity of the absorbing groups can be determined by comparing the spectrum of an analyte with those of simple molecules containing various chromophoric groups" Usually, however, ultraviolet spectra do not have enough fine structure to permit an analyte to be identified unambiguously. Thus, ultraviolet qualitative data must be supplemented with other physical or chemical evidence such as infrared, nuclear magnetic resonance, and mass spectra as well as solubility and melting: and boiling-point information.

Ultraviolet spectra for qualitative analysis are usually measured using dilute solutions of the analyte. For volatile compounds, however, gas-phase spectra are often more useful than liquid-phase or solution spectra (for example, compare Figure 14-1a and b). Gas-phase spectra can often be obtained by allowing a drop or two of the pure liquid to evaporate and equilibrate with the atmosphere in a stoppered cuvette. In choosing a solvent, consideration must be given not only to its transparency, but also to its possible effects on the absorbing system. Quite generally, polar solvents such as water, alcohols, csters, and ketones tend to obliterate spectral fine structure arising from vibrational effects. Spectra similar to gas-phase spectra (see Figure 14-6) are more likely to be observed in

3For a detailed discussion of ultraviolet absorption spectroscopy in the identification of organic functional groups, see R. M. Silverstein, G. C Bassler, and T. C. Morrill, S p e c rro m e rric Id e fl(~ fic a lio n uf O rg a n ic C o m pounds, 5th ed., Chap. 6, !"iew York: Wiley, 1991. ~I-L H. Perkampus. [ lV-VIS AlIa s of Or ga nic Compnlll!ds. 2nd ed .. Hoboken. NJ: WHey-VCH.I992. In addition. in the past. several organizations have published catalogs of spectra that may still be useful, including American Petroleum Institute, Ultraviolet Spectral Data, AP .l. Resea r ch P r oject 44. Pittsburgh: Carnegie Institute of Techno log v: Sa dtler Ha ndbook of Ultr a ~'iolet Spectr a , Philadelphia: Sadtler Research-Laboratories: American Society for Testing ~'iaterials. Committee E-D. Philaddphia.

1.4

;; -E 0.3 o

~ -< 0.2

" c

~ 1.2 ~

:;(

0.1

1.6

FIGURE 14-7 Spectra for reduced cytochrome c at four

spectral bandwidths. (1) 20 nm, (2) 10 nm, (3) 5 nm, and (4) 1 nm. (Courtesy of Varian, Inc., Palo Alto, CA.)

FIGURE 14-6 Effect of solvent on the absorption

trophotometry include water, 95% ethanol, cyclohexane, and lA-dioxane. For the visible region, any colorless solvent is suitable.

spectrum of acetaldehyde. nonpolar solvents such as hydrocarbons. In actctttion, the positions of absorption maxima arc influenced by the nature of the solvent. As a rule, the same solvent must be used when comparing absorption spectra for identification purposes. Table 14-3 lists some common solvents and the approximate wavelength below which they cannot be used because of absorption. These wavelengths, called the cutoff wa velengths, depend strongly on the purity of the solvent.' Common solvents for ultraviolet spec-

The effect of variation in slit width, and hence effective bandwidth, was shown previously for gas-phase spectra in Figure 13-8. The effect on solution spectra is illustrated for reduced cytochrome c in Figure 14-7. Clearly, peak heights and separation are distorted at wider bandwidths. Because of this, spectra for qualitative applications should be measured with minimum slit widths.

'i Most major suppliers of reagent chemicals ill the United States offer spectrochemical grades of solvents. Spectral-grade solvents have been treated to remove absorbing impurities and meet or exceed the requirements set forth in Rea gent Chemica ls, 9th cd., Washington, DC: American Chemical Society, 2000. Supplements and updates are available at http://pubs.acs .org/reagentslindex.html

TABLE14-3 Solvents for the Ultraviolet and Visible Regions Lower Wavelength Solvent Water Ethanol Hexane

Cyclohexane Carbon tetrachloride

L im it ,n m

180 220 200 200 260

Solvent Diethyl ether Acetone Dioxane

Cellosolve

Lower Wavelength Limil,nm 210 330 320 320

B Band

E, Band Compound Benzene

Toluene m-Xylene Chlorobenzene Phenol Phenolate ion Aniline A n ilin iu m

ion

Thiophenol Naphthalene Styrene

A ..-x ,

C 6H 6 C6H,CH, C6H,(CH,), C.H,Cl C.HsOH c"H,OC.HsNH2 C.H,NH; C.H,SH CIOHs C.H,CH=CH2

om

emax

204 207

7900 7000

210 211 235 230 203 236 286 244

7600 6200 9400 8600 7500 10.000 9300 12,000

A m a l,n m

256 261 263 265 270 287 280 254 269 312 282

E max

200 300 300 240 1450 2600 1430 160 700 289 -\50

All three of the characteristic bands for benzene are strongly affected by ring substitution: the effects on the two longer-wavelength bands are of particular interest because they can be studied with ordinary spectrophotometric equipment. Table 14-4 illustrates the effects of some common ring substituents. By definition, an a uxochr ome is a functional group that does not itself absorb in the ultraviolet region but has the effect of shifting chromophore peaks to longer wavelengths as well as increasing their intensities. Such a shift to longer wavelengths is called a ba thochr omic, or r ed, shift. Note in Table 14-4 that -OH and - NH, have an auxochromic effect on the benzene ch~omOphore, particularly with respect to the B band. AUXDchromic substituents have at least one pair of n ele~tro~s capable of interacting with the 7T electrons of the ring. This interaction apparently has the effect of - stabilizing the 7T* state, thereby lowering its energy, and increasing the wavelength of .the corresponding band. Note that the auxochromic effect is more pronounced for the phenolate anion than for phenol itself, probably because the anion has an extra pair of unshared electrons to contribute to the interaction. With aniline, on the other hand, the nOnbonding electrons are lost by formation of the anilinium cation, and the auxochromic effect disappears.

140

QUANTITATIVE ANALYSIS BY ABSORPTION MEASUREMENTS

Absorption spectroscopy based on ultraviolet and visible radiation is one of the most useful tools available to the scientist for quantitative analysis6 Important characteristics of spectrophotometric and photometric methods include (1) wide applicability to both organic and inorganic systems, (2) typical detection limits of lO-4 to lO-5 M (in some cases, certain modifications can lead to lower limits of detection).' (3) moderate to high selectivity, (4) good accuracy (typically, relative uncertainties are 1% to 3%, although with special precautions. errors can be reduced to a few tenths of a percent), and (5) ease and convenience of data acquisition. "For a wealth of detailed. practical information on spectrophotometriC" practices, see Techniques in Visible a nd (jltr a ~'iolet Spea r omer r y. \'01. I. Sumda r ds in Absor ption Spectr oscopy, C. Burgess and A. Knowles. eds .. London: Chapman & Hall, 1981; 1. R. Edisbury. P r a ctica l If/nls Oil Absor ption Spea r omelr .r . New York: Plenum Press, 1968. 'See. for example, T. D. Harris. Ana l. Cher n .. 1982,54, 7.HA,

140-1

Scope

The applications of quantitative, ultraviolet-visible absorption methods not only are numerous but also touch on everv field that requires quantitative chemical information.' The reader can obtain a notion of the scope of spectrophotometry by consulting the series of review articles that were published in Ana lytica l Chemistr y' as well as monographs on the subject.9 A p p lic a tio n s

to

A b s o rb in g

S p e c ie s

Tables 14-1, 14-2, and 14-4 list many common organic chromophoric groups. Spectrophotometric determination of any organic compound containing one or more of these groups is potentially feasible. Many examples of this type of determination are found in the literature. A number of inorganic species also absorb UVvisible radiation and are thus susceptible to direct determination. We have noted that many ions of the transition metals are colored in solution and can .thus be determined by spectrophotometric measurttment. In addition, a numbcr of other species show charactcristic absorption bands, including nitrite, nitrate, and chromate ions, the oxides of nitrogen, the elemental halogens, and ozone. A p p lic a tio n s

to

N o n a b s o rb in g

S p e c ie s

Numerous reagents react selectively with nonabsorbing species to yield products that absorb strongly in the ultraviolet or visible regions. The successful application of such reagents to quantitativc analysis usually requires that the color-forming reaction be forced to near completion. If the amount of product is limited by the analyte, the absorbance of the product is proportional to the analyte concentration. Color-forming reagents are frequently employed as well for the determination of absorbing species, such as transitionmetal ions. The molar absorptivity of the product is frequently orders of magnitude greater than that of the species before reaction. A host of complexing agents are used to determine inorganic species. Typical inorganic reagents include thiocyanate ion for iron, cobalt, and molyhdenum; ~L. G. Hargis.]. A. Howell. and R E. Sutlon. Alta i. Cher n. (Rc\lcwl.1996. 68.169: 1-:\. Howell and R. E. Sutton, Ana l. Cher n .. (Re\'i.:w).1998. 7{j. 107 9H. Onishi, P ho[ omeIr ic Dner mina tlon of Tr a ces of :\-fe ta L I. Part IIA. Part lIB. -Ilh ed .. :-';ew York: \Viky. 1986. 1989: Color imetr ic Deter mina tion of Nonmeta ls. 2nd ed .. D. F. Boltz. ed., New Ymk: Intcrscicnce. 197.s: E. B Sandell and H. Onishi. P hotometr ic D e te rm in a tiO fl of T ra l"e S of .\kr tlis. ..loth ed .. New York: Wiley. 1978: F D. Snell. P h o lU m e rric a n d F lu o r(J m < !(ril ,\.fer hods o(Ana lysis. New York: Wiley. 1978

hvdrogen peroxide for titanium, vanadium, and chromium; and iodide ion for bismuth, palladIUm, and tellurium. Of even more importance are organicchelating agents that form stable, colored complexes WIth cations. Common examples include dlethyldlthlOcarbamate for the determination of copper. diphenylthiocarbazone for lead, I,lO-phenanthrolene for iron, and dimethylglyoxime for nickel. In the application of the last reaction to the photometric determinatIOn of nickel, an aqueous solution of the cation is extracted with a solution of the chelating agent in an immiscible organic liquid. The absorbance of thc resulting bright red organic laycr serves as a measure of the concentration of the metal.

enees that can result from scratches, etching, and wcar. It is equally important to use proper cell-cleaning and drying techniques. Erickson and Surles 10 recommend the following cleaning sequence for the outSide Windows of cells. Prior to measurement, the cell surfaces should be cleaned with a lens paper soaked in spectrograde methanol. While wiping, it is best to hold the paper with a hemostat. The methanol is then allowed to evaporate, leaving the cell surfaces free of contamtnants. Erickson and Surles showed that thiS method was superior to the usual procedure of wiping the cell surfaces with a dry lens paper, which can leave ltnt and a film on the surface. D e te rm in in g

th e R e la tio n s h ip

140-2

A b s o rb a n c e

a n d C o n c e n tra tio n

Procedural

Details

A first step in any photometric or spectrophotometric analysis is the developmcnt of conditions that yield a reproducible relationship (preferably linear) between absorbance and analyte concentration. S e le c tio n

of W a v e le n g th

For highest sensitivity, spcctrophotometric absorbance measuremcnts are ordinarily made at a wavelength corresponding to an absorption maximum because the change in absorbance per unit of concentratIOn ISgreatest at this point. In addition, the absorbance tS nearly constant with wavelength at an absorption maximum, which leads to close adherence to Becr's law (sce Figure 13-5). Finally, small uncertainties that arise from failing to reproduce precisely the wavelength setting of the instrument have less influence at an absorptIOn maximum. V a ria b le s T h a t In flu e n c e

A b s o rb a n c e

Common variables that influence the absorption spectrum of a substance include the naturc of the solvent, the pH of the solution, the temperature, high electroIvte concentrations, and the presence of interfering s~ubstances. The dIects of these variables must be known and conditions for the analysis must be chosen such that the absorbance will not be materially influenced by small. uncontrolled variations in their magnitudes. C le a n in g

a n d H a n d lin g

of C e lls

Accurate spectrophotometric analysis requires the use of good-quality, matched cells. These should be regularlv calibrated against one another to detect dlffer-

b e tw e e n

The method of external standards (see Section 10-2) is most often used to establish the absorbance versus concentration relationship. After deciding on the conditions for the analysis, the calibration curve is prepared from a series of standard solutions that bracket the concentration range expected for the samples. Seldom, if ever, is it safe to assume adherence to Beer's law and use only a single standard to determine the molar absorptivity. It is never a good idea to base the results of an analysis on a literature value for the molar absorptivity. . Ideally, calibration standards should approximate the composition of the samples to bc analyzed not only with rcspect to the analyte concentration but als~ WIth regard to the concentrations of the other spectes In the sample matrix. This can minimize thc effects of vanous components of the sample on the measured absorbance. For example, the absorbance of many colored complexes of metal ions is decreased to a varying degree in the presence of sulfate and phosphate Ions because these anions can form colorlcss complexes with metal ions. The desired reaction is often less complete as a consequence, and lowered absorbances are the result. The matrix effect of sulfate and phosphate can often be counteracted by introducing into the standards amounts of the two species that approximate the amounts found in the samples. Unfortunately. matrix matching is often impossible or quite difficult when complex materials such as soils, minerals, and tissues are being analyzcd. When this is the case. the sta nda r da ddition method is often helpful in counteracttng

matrix effects that affect the slope of the calibration curve. However, the standard-addition method does not compensate for extraneous absorbing species unless they are present at the same concentration in the blank solution. T h e S ta n d a rd -A d d itio n

M e th o d

The standard-addition method can take several forms.l1 The one most often chosen for photometric or spectrophotometric analyses, and the onc that was discussed in some detail in Section 10-3, involves adding one or more increments of a standard solution to sample aliquots. Each solution is then diluted to a fixed volume before measuring its ahsorbance. Example 14-1 illustrates a spreadsheet approach to the multiple-additions method for the photometric determination of nitrite.

Nitrite is commonly determined by a spectrophotometric procedure using the Griess reaction. The sample containing nitrite is reacted with sulfanilimide and N(I-naphthyl)ethylenediamine to form a colored species that absorbs radiation at 550 nm. Five-milliliter aliquots of the sample were pi petted into five 50.00-mL volumetric flasks. Then, 0.00, 2.00, 4.00, 6.00, and 8.00 mL of a standard solution containing 10.00 flM nitrite were pipetted into each flask, and the color-forming reagents added. After dilution to volume, the absorbance for each of the five solutions was measured at 550 nm. Thc absorbances were 0.139, 0.299, 0.486, 0.689, and 0.865, respectively. Devise a spreadsheet to calculate the nitrite concentration in the original sample and its standard deviation.

The spreadsheet is shown in Figure 14-8. Note that the final result indicates the concentration of nitrite in the original sample is 2.8 :+: 0.3 flM. The standard deviation is found from the regression line 12 bv using an extrapolated x value of ~ 1.385 mL and a v ~'alue;f 0.000 as illustrated in Example 1-1 of Chapt~r 1.

I i

In the interest of saving time or sample, it is possible to perform a standard-addition analysis using only two increments of sample. Here, a single addition of V; mL of standard would he added to one of the two samples. This approach is based on Equation 14-1 (see Section 10-3).

See M. Rader, I Cher n. Educ.. 1980. 5~. 70.3.

leFor more information on sprcadsh~e( ilpproach~s {u standard additIon methods. see S. R. Crouch and F J Holler. ApplicillWIZS of .\licr osoW:' Excel in Ana (\,'licill Chemistn Chaps. 4 and l~. BdmlmL c.-\ Brooks Cole.200.t.

A,c\.Vs C,

The single-addition ample 14-2.

=

(A , ~ -A I)V '

method

is illustrated

in Ex-

A 2.00-mL urine specimen was treated with reagent to generate a color with phosphate, following which the sample was diluted to 100 mL. To a second 2.00-mL sample was added exactly 5.00 mL of a phosphate solution containing 0.0300 mg phosphate/mL, which was treated in the same way as the original sample. The absorbance of the first solution was 0.428, and th;t of the second was 0.538. Calculate the concentration of phosphate in milligrams per millimeter of the specimen.

01W1

.'

I

c=-.Mool ~--. -2 00

0.00

2.00

S o lu tio n

=

C

,

(0.428)(O~OJOOmg PO/"/mL)(5.00 =

A n a ly s is

mL)

(0.538 - 0.428)(2.00 mL sample) 0.292 mg PO.'-

o f M ix tu re s

I mL

o f A b s o rb in g

sample

S u b s ta n c e s

The total absorbance of a solution at any given wavelength is equal to the sum of the absorbances of the individual components in the solution (Equation 13-9). This relationship makes it possible in principle to determine the concentrations of the individual components of a mixture even if their spectra overlap completelv. For example, Figure 14-9 shows the spectrum of a solution containing a mixture of species M and species N as well as absorption spectra for the individual components. It is apparent that there is no wavelength where the absorbance is due to just one of these components. To analyze the mixture, molar absorptivities for M and Narc tlrst determined at wavelengths A, and A2 with sufficient concentrations of the two standard solutions to be sure that Beer's law is obeved over an absorbance range that encompasses the ab;orbance of the sample. Note that the wavelengths selected are

ones at which the molar absorptivities of the two components differ significantly. Thus, at A" the molar absorptivity of component M is much larger than that for component N. The reverse is true for A2. To complete the analysis, the absorbance of the mixture is determined at the same two wavelengths. From the known molar absorptivities and path length, the following equations hold: (14-2)

AI

(14-3) where the subscript 1 indicates measurement at wavelength AI' and the subscript 2 indicates measurement at wavelength A,. With the known values of e and b, Equations 14-2 and 14-3 represent two equations in two unknowns (c" and eN) that can be solved. The relationships are valid only if Beer's law holds at both wavelengths and the two components behave independently of one another. The greatest accuracy is obtained by choosing wavelengths at which the differences in molar ahsorptivities are large.

f7l lQ.j

lluor ia l: Learn more about sis of mixtures.

c a lib r a t io n

and

analy~

Mixtures containing more than two absorbing species can be analyzed. in principle at least, if a further absorbance measurement is made for each added component. The uncertainties in the resulting data become

.........•.

/-; ;/

..••.

/

'

"

" ••• __

,

~+N

\

FIGURE 14-9 Absorption spectrum of a two-component mixture (M + N) with spectra of the individual components. Vertical dashed lines indicate optimal wavelengths for determination of the two components.

greater, however, as the number of measurements increases. Some array-detector spectrophotometers are capable of reducing these uncertainties by overdetermining the system. That is, these instruments use many more data points than unknowns and effectivelv match the entire spectrum of the unknown as closely' as possible by least-squares techniques using the methods of matrix algebra. The spectra for standard solutions of each component are required for the analysis. Computer data-processing methods based on factor analysis or principal components analysis have been developed to determine the number of components and their concentrations or absorptivities in mixturesl3 These methods are usually applied to data obtained from array-detector-based spectrometers.

14E

Section 3E-4). Another technique uses mechanical oscillation of a refractor plate to sweep a wavelength interval of a few nanometers repetitively across the exit slit of a monochromator while the spectrum is scanned, a technique known as wa velength modula tion. Alternatively, the spectrum can be scanned using two wavelengths offset by a few nanometers, which is called dua /-

Photometric or spectrophotometric measurements are useful for locating the equivalence point of a titration, provided the analyte, the reagent, or the titration product absorbs radiation. IS Alternatively, an absorbing indicator can provide the absorbance change necessary for location of the equivalence point.

wa velength speetr ophotometr y. A p p lic a tio n s

o f D e riv a tiv e

S p e c tra

Many of the most important applications of derivative spectroseopy in the ultraviolet and visible regions have been for qualitative identification of species. The enhaneed detail of a derivative spectrum makes it possible to distinguish among compounds having overlapping spectra, a teehnique often called fea tur e enha ncement. Figure 14-10 illustrates how a derivative plot can reveal details of a spectrum consisting of three overlapping absorption peaks. It should be noted that taking a derivative enhances noise, and so high-quality spectra are a must for using this technique. If high-quality spectra are not used, derivative spectra can sometimes cre 0

7 r \: '7 L £A=£l:::O

(f)

~

fA =

a

FIGURE 14-12 Typical photometric titration curves. Molar absorptivities of the analyte, the product, and the titrant are given by 'A' 'P, 'T, respectively. the intersection of the extrapolated linear portions of the curve. End points can also be determined automatically by titration to a fixed absorbance or by taking the derivative to convert the linear-segment curve to a sigmoid-shape curve. Figure 14-12 shows typical photometric titration curves. Figure 14-12a is the curve for the titration of a nonabsorbing species with an absorbing titrant that reacts with the analyte to form a nonabsorbing product. An example is the titration of thiosulfate ion with triiodide ion. The titration curve for the formation of an absorbing product from nonabsorbing reactants is shown in Figure 14-12b; an example is thc titration of iodide ion with a standard solution of iodate ion to form triiodide. The remaining figures illustrate the curves obtained with various combinations of absorbing analytes, titrants, and products. To obtain titration curves with linear portions that can be extrapolated, the absorbing systems must obey Beer's law. In addition, absorbances must be corrected for volume changes by multiplying the observed absorbance by (V + ,.)IV , where V is the original volume of the solution and v is the volume of added titrant. Many methods, however, use only changes in absorbance to locate the endpoints by various techniques. With these, strict adherence to Beer's law is not a necessity.

Photometric titrations are ordinarily performed with a spectrophotometer or a photometer that has been modified so that the titration vessel is held stationary in the light path. Alternatively, a probe-type cell. such as that shown in Figure 13-18, can be employed. After the

instrument is set to a suitable wavelength or an appropriate filler is inserted, the 0% r adjustment is made in the usual way. With radiation passing through the analyte solution to the transducer, the instrument is then adjusted to a convenient absorbance reading hy varying the source intensity or the transducer sensitivity. It is not usually necessary to measure the true absorbance because relative values are perfectly adequate for endpoint detection. Titration data are then collected without changing the instrument settings. The power of the radiation source and the response of the transducer must remain constant during a photometric titration. Cylindrical containers are often used in photometric titrations, and it is important to avoid moving the cell. so that the path length remains constant. Both filter photometers and spectrophotometers have been used for photometric titrations. Several instrument companies currently produce photometric titration equipment.

Photometric tit rations often provide more accurate results than a direct photometric analysis because the data from several measurements are used to determine the end point. Furthermore, the presence of other absorbing species may not interfere, because only a change in absorbance is being measured. An advantage of end points determined from linear-segment photometric titration curves is that the experimental data are collected well away from the equivalence-point region where the absorbance changes gradually. Consequently, the equilibrium constant for the reaction need not be as large as that required for a sigmoid titration curve that depends on observations near the equivalence point (for example, potentiometric or indicator end points). For the same reason, more dilute solutions may be titrated using photometric detection. The photometric end point has been applied to many types of reactions. For example, most standard oxidizing agents have characteristic ahsorption spectra and thus produce photometrically detectable end points. Although standard acids or bases do not absorb, the introduction of acid-base indicators permits photometric neutralization titrations. The photometric end point has also been used to great advantage in titrations with EDTA (cthylenediaminetelraacetic

r::;l

l2J

S .im ~ lla (i~ )fl: Learn r le h t r a t lo n s .

more about

sp e c tr o p h o to m e t-

acid) and other complexing agentsl9 Figure 14-Ba illustrates the application of this technique to the determination of total hardness in tap water using Eriochrome Black T as the indicator. The ahsorbance of the indicator is monitored at 610 nm.'lJ The photometric end point has also been adapted to precipitation titrations. In tur bidimetr ic titr a tions, the suspended solid product causes a decrease m the radiant power of the light source by scattering from the particles of the precipitate. The end point is observed when the precipitate stops forming and the amount of light reaching the detector becomes constant. The end pomt in some precipitation titrations can also be detected as shown in Figure 14-13b by addition of an indicator. Here, the Ba2+ titrant reacts with SO, ,- to form insoluble BaSO,. Once the end point has been reached, the excess Ba2+ ions react with an indicator, Thorin, to form a colored complex that absorbs light at 523 nm.21

14F

I(J

from its thiourea complex:

BiY- + 6tu + 2H+

where tu is the thiourea molecule (NHz),CS. Predict the shape of a photometric titration curve based on this process, given that the Bi(III) or thiourea complex is the only species in the system that absorbs light at 465 nm, the wavelength

+ $6$34'85)

---+ -

==t -

Cell F12=SUM(FS

acid abstracts bismuth(IIl)

Bi(tu)/'

Documentation Cell 1

•

•

for the

electronic the first (S ,) The

one on

the case, the energy

is ex-

spin

of

of the first elec-

or a tr ip le t s ta te is

unpaired

represent

state is less energetic singlet state.

state,

of a molecule

tem-

of most

levels

excited

elec-

slightly

is nor-

At room

The two lines on the left represent

second

called

photoluminescent

in a solution.

upper

the right tronic

heavy

energy

this state

the molecules

states.

of -~10-8 s for an ex-

The lowest

the ground-state

trip-

lifetime

M o le c u le s

a J a b lo n s ki d ia g r a m . for a typical

com-

of an excited

10-' to several

Phosphorescence

of such a process.

15-2 is a partial

molecule.

an

from an excited

state for a free

for the odd

can be represented

of singlet,

from

electronic

the average

may range

no splitting

imparts

level. a singlet

is still paired

the arrows

differ

let state

that

however.

is a d o u b le t s ta te because

hand,

In the triplet

glet statc.

when

one of a pair of electrons

need

state

Occurs

spins

see.

molecules.

a result

P h o to lu m in e s c e n t

Figure

singlet-

can be populated

of certain

is often

E n e r g y-Le ve l

FIGURE

a consequence,

field, and each

The properties l'h(J.;,phort>..:cnc T ,) as shown in Figure I S-2 , As with internal conversion, the probability of intersystem crossing is enhanced if the vibrational levels of the two states overlap. Note that in the singlettriplet crossover shown in Figure 1S -2 the lowest singlet vibrational level overlaps one of the upper triplet vibrational levels and a change in spin state is thus more probable, Intersystem crossing is most common in molecules that contain heavy atoms, such as iodine or bromine (the h e a vy-a to m e ffe c t), Spin and orbital interactions increase in the presence of such atoms, and a change in spin is thus more favorable, The presence of paramagnetic species such as molecular oxygen in solution also enhances intersystem crossing with a consequent decrease in fluorescence, P h o s p h o re s c e n c e

Deactivation of electronic excited states may also involve phosphorescence, After intersystem crossing to the triplet state, further deactivation can occur either by internal or external conversion or by phosphorescence, A triplet -> singlet transition is much less probable than a singlet-singlet conversion, Transition probability and excited-state lifetime are inversely related. Thus, the average lifetime of the excited triplet state with respect to emission is large and ranges from 10'4 to 10 s or more. Emission from such a transition may persist for some time after irradiation has ceased. External and internal conversion compete so successfully with phosphorescence that this kind of emission is ordinarily observed only at low temperatures in highly viscous media or by using special techniques to protect the triplet state.

15A-4 Variables Affecting Fluorescence and Phosphorescence

Both molecular structure and chemical environment influence whether a substance will or will not luminesce. These factors also determine the intensity of

Y ie ld

The q lla lllilm yie ld , or q u a n tu m e ffic ie n c y, for fluorescence or phosphorescence is simply the ratio of the number of molecules that luminesce to the total number of excited molecules. For a highly fluorescent molecule such as fluorescein, the quantum efficiency approaches unity under some conditions. Chemical species that do not fluorescc appreciably have efficiencies that approach zero. Figurc IS-2 and our discussion of deactivation processes suggest that the fluorescence quantum yield '" for a compound is determined by the relative rate constants k , for the processes by which the lowest excited singlet state is deactivatcd. These processes are fluorescence (k,), intersystem crossing (k;). external conversion (k e e ), internal conversion (k i,), predissociation (kpd), and dissociation (k d ). We can expre~s these relationships by the equation k '" =.

t

kf + k i + k e c + k ic + kpd + kd

(IS-I)

where the k terms are the respective rate constants for the various deactivation processes. Equation IS- I permits a qualitative interpretation of many of the structural and environmental factors that inlluence fluorescence intensity. Those variables that lead to high values for the fluorescence rate constant k, and low values for the other k x terms enhance lluorescence. The magnitude of k" the predissociation rate constant kpd, and the dissociation rate constant k mainly depend on chemical structure. Environment and to a somewhat lesser extent structure strongly inlluence the remaining rate constants. d

T ra n s itio n

T y p e s in F lu o re s c e n c e

It is important to note that fluorescence seldom results from absorption of ultraviolet radiation of wavelengths shorter than 2S0 nm because such radiation is sufficiently energetic to cause deactivation of the excited states by predissociation or dissociation. For example, 200-nm radiation corresponds to about 140 kcallmol. Most organic molecules have at least some honds that can be ruptured by energies of this magnitude. As a consequence, fluorescence due to u * ~ if transitions is seldom observed. Instead. such emission is confined to the less energetic

17* ~

iT

and rr*

--+

n

processes.

As we havc noted, an electronically excited molecule ordinarily returns to its lo w e st e xc ite d sta te by a series of rapid vibrational relaxations and internal conversions that produce no emission of radiation. Thus, fluorescence most commonly arises from a transition from the lowest vibrational level of the first excited electronic state to one of the vibrational levels of the electronic ground state. For most fluorescent compounds. then, radiation is produced by either a 1 T* -> n or a 1 T* -> 1 T transition, depending on which of these IS

may also exhibit fluorescence, but the number of these is smaller than the number in the aromatic systems. Most unsubstituted aromatic hydrocarbons fluoresce in solution, the quantum efficiency usually increasing with the number of rings and their degree of condensation. The simple heterocyclics, such as pyridine, furan, thiophene, and pyrrole,

0

the less energetic.

pyridine

Q u a n tu m

E ffic ie n c y

a n d T ra n s itio n

likelv. It; summarv, then. fluorescence is more commonly associated wi(h the 1 T, 1 T* state because such excited states exhibit relatively short average lifetimes (k, is larger) and because the deactivation processes that compete with lluorescence are less likely to occur. F lu o re s c e n c e

a n d S tru c tu re

The most intense and the most useful fluorescence is found in compounds containing aromatic functional groups with low-energy r. ---7 7T* transitions. Compounds containing aliphatic and alicyclic carbonyl structures or highly conjugated double-bond structures

furan H

Type

It is observed empirically that fluorescence is more commonly found in compounds in which the lowest energy transition is of a 1 T -> 1 T* type (1 T, 1 T* excited singlet state) than in compounds in which the lowest energy transition is of the n -> 1 T* type (n , 1 T* eXCited state): that is, the quantum efficiency is greater for 1 T* ~ 1 T transitions. The greater quantum efficiency associated with the 1 T. 1 T* state can be rationalized in two ways. First, the molar absorptivity of a 1 T -> 1 T* transition is ordinarily 100- to WOO-fold greater than for an n -> 1 T* process, and this quantity represents a measure of the transition probability. Thus, the inherent lifetime associated with the 1 T, 1 T* state is shorter (10'7 to 10-9 s compared with lO S to 10-7 s for the n , 1 T* state) and k , in Equation IS- I is larger. The most efficient phosphorescence often occurs from the n , 1 T* excited state, which tends to be shorter lived and thus less susceptible to deactivation than a 1 T , 1 T* triplet state. Also. intersystem crossing is less probable for 1 T. 1 T* excited states than for n , 1 T* states because the energy dilIerence between the singlet and triplet states is larger and spin-orbit coupling is less

0

0

s

0 thiophene

I N

0 pyrrole

do not exhibit fluorescence. On the other hand, fusedring structures ordinarily do fluoresce. With nitrogen heterocyclics, the lowest -energy electronic transition is believed to involve an n -> 1 T* system that rapidly converts to the triplet state and prevents fluorescence. Fusion of benzene rings to a hcterocyclic nucleus, however, results in an increase in the molar absorptivity of the absorption band. The lifetime of an excited state is shorter in such structures, and fluorescence is observed for compounds such as quinoline, isoquinoline, and indole. H

I

CO Substitution on the benzene ring causes shifts in the wavelength of absorption maxima and corresponding changes in the fluorescence emission. In addition, substitution frequently alIects the quantum efficiency_ Some of these effects are illustrated by the data for benzene derivatives in Table IS -I. The influence of halogen substitution is striking: the decrease in fluorescence with increasing molar mass of the halogen is an example of the heavy-atom effect (page 404), which increases the probability for intersystem crossing to the triplet state. Predissociation IS thought to play an important role in iodobenzene and in nitro derivatives as well, because these compounds

Wavelengtb of Compound

Formula

B enzene

C,li" C,H,CH3 c"H,C3H, CoHsF C,H,Cl C,H,Br C,HsI C,H,OH C,HsOC,H,OCH, C,HsNH2 c"HsNH3 ' C,H,COOH C,H,CN C,H,N02

Toluene Prapylbenzenc Fluorabenzene Chlorabenzene B ro m o b e n ze n e

Iodobenzene Phenol Phenolate ion A n is o le

Aniline A n ilin iu m B e n z o ic

lo n a c id

B e n z o n itr ile N itr o b e n z e n e

have easily ruptured bonds that can absorb the excitation energy following internal conversion. Substitution of a carboxylic acid or carbonyl group on an aromatic ring generally inhibits fluorescence. In these compounds, the energy of the n -> 7T* transition is less than in the 7T -> 7T* transition, and as discussed previously, the fluorescence yield from the n -> 7T* systems is ordinarily low. E ffe c t

of S tru c tu ra l

Fluorescenc~

om

Relative IntensitI o f flu o r e s c e n c e

270-310

10

270-320

17

270-320

17

270-320

10

275-345

7

290-380

5 0

285-365

18

310-400

10

285-345

20

310-405

20

310-390

3

280-360

20

0

O·

metal ion. For example, the fluorescence intensity of 8-hydroxyquinoline is much less than that of its zinc complex:

R ig id ity

It is found empirically that fluorescence is particularly favored in molecules with rigid structures. Forexample, the quantum efficiencies for fluorene and biphenyl are nearly 1.0 and 0.2, respectively, under similar conditions of measurement. The difference in behavior is largely a result of the increased rigidity furnished by the bridging methylene group in fluorene. Many similar examples can be cited.

Lack of rigidity in a molecule probably causes an enhanced internal conversion rate (k,c in Equation 15-1) and a consequent increase in the likelihood for radiationless deactivation. One part of a nonrigid molecule can undergo low-frequency vibrations with respect to its other parts: such motions undoubtedly account for some energy loss. T e m p e ra tu re

The influence of rigidity has also been invoked to account for the increase in fluorescence of certain organic chciating agents when thev arc complcxed with a

The fluorescence of a molecule is decreased by solvents containing heavy atoms or other solutes with such atoms in their structure: carbon tetrabromidc and ethyl iodide are examples. The effect is similar to that which occurs when heavy atoms are substituted into fluorescing compounds: orbital spin interactions result in an increase in the rate of triplet formation and a corresponding decrease in fluorescence. Compounds containing heavy atoms are frequently incorporated into solvents when enhanced phosphorescence is desired.

a n d S o lv e n t E ffe c ts

The quantum efficiency of fluorescence in most molecules decreases with increasing temperature because the increased frequency of collisions at elevated temperatures improves the probability for deactivation by external conversion. A decrease in solvent viscosity also increases the likelihood of external conversion and leads to the same result.

E ffe c t of p H o n F lu o re s c e n c e

The fluorescence of an aromatic compound with acidic or basic ring substituents is usually pH dependent. Both the wavelength and the emission intensity arc likely to be different for the protonated and unprotonated forms of the compound. The data for phenol and aniline shown in Table 15-1 illustrate this effect. The changes in emission of compounds of this type arise from the differing number of resonance species that are associated with the acidic and basic forms of the molecules. For example, aniline has several resonance forms but anilinium has only one. That is, H H

H

H

'" {

H

V/

H

HHIH

V/

'" /

6-6-6 6 The additional resonance forms lead to a more stable first excited state; fluorescence in the ultraviolet region is the consequence. The fluorescence of certain compounds as a function of pH has been used for the detection of end points in acid-base titrations. For example, fluorescence of the phenolic form of l-naphthol-4-sulfonic acid is not detectable by the eye because it occurs in the ultraviolet region. When the compound is converted to the phenolate ion by the addition of base, however, the emission band shifts to visible wavelengths, where it can readily be seen. It is significant that this change occurs at a different pH than would be predicted from the acid dissociation constant for the compound. The explanation of this discrepancv is that the acid dissociation constant for the excited molecule differs from that for the same species in its ground state. Changes in acid or base dis-

r71

.Sim u la tio n :

Learn

lQ.J spectroscopy.

more about

lu m in e s c e n c e

sociation constants with excitation are common and are occasionally as large as four or five orders of magnitude. These observations suggest that analytical procedures based on fluorescence frequently require close control of pH. The presence of dissolved oxygen often reduces the intensity of fluorescence in a solution. This effect mav be the result of a photochemically induced oxidatio~ of the fluorescing species. More commonly, however, the quenching takes place as a consequence of the paramagnetic properties of molecular oxygen, which promotes intersystem crossing and conversion of excited molecules to the triplet state. Other paramagnetic species also tend to quench fluorescence. E ffe c t

of C o n c e n tra tio n

F lu o re s c e n c e

on

In te n s ity

The power of fluorescence emission F is proportional to the radiant power of the excitation beam that is absorbed by the system. That is,

where P o is the power of the beam incident on the solution, P is its power after traversing a length b of the medium, < P c is the quantum efficiency of the fluorescence process, and K " is a constant dependent on geometry and other factors. The quantum efficiency of fluorescence is a constant for a given system, and so the product ,

g

100

~

T h e M e rc u ry

>.

~ 50 11m),none of the thermal sources just described provides sufficient radiant power for convenient detection. Here, a high-pressure mercury arc is used. This device consists of a quartz-jacketed tube containing mercury vapor at a pressure greater than I atmosphere. Passage of electricity through the vapor forms an internal plasma source that provides continuum radiation in the far-IR region. T h e T u n g s te n

F ila m e n t

D io x id e

IR transducers are of three general types: (I) pyroelectric transducers, (2) photoconducting transducers, and (3) thermal transducers. The first is found in photometers, some FTIR spectrometers, and dispersive spectrophotometers. Photoconducting transducers are found in many FTIR instruments. Thermal detectors are found in older dispersive instrumcnts but are too slow to be used in FTIR spectrometers.

Lam p

An ordinary tungsten filament lamp is a convenient source for the near-IR region of 4000 to 12,800 em-l (2.5 to 0.78 11m). T h e C a rb o n

target. Some of the radiation is then reflected back to the lidar instrument where it is analyzed and used to obtain information about the target. By means of lidar, distance, speed, rotation, chemical composition, and concentration of remote targets can be obtained.

L a s e r S o u rc e

A tunable carbon dioxide laser is used as an IR source for monitoring the concentrations of certain atmospheric pollutants and for determining absorbing species in aqucous solutions." A carbon dioxide laser produccs a band of radiation in the range of 900 to 1100 cm-l (11 to 9 11m), which consists of about 100 closely spaeed diserete lines. As described in Section 7B-3, anyone of these lines ean be chosen by tuning the laser. Although the range of wavelengths available is limited, the region from 900 to 1100 cm-l is one particularly rich in absorption bands arising from the interactive stretching modes of CO2, Thus, this source is useful for quantitative dctermination of a number of important species such as ammonia, butadiene, benzene, ethanol, nitrogen dioxide, and trichloroethylene. An important property of the laser source is the radiant power available in each line, which is several orders of magnitude greater than that of blackbody sources. Carbon dioxide lasers are widely used in remotesensing applications such as light detection and ranging (lidar). The operating principle of lidar is similar to that of radar. The lidar system transmits radiation out to a target where it interacts with and is altered by the 12Sce A. A. Demido\". in I n tr o d u c tio n to L a s e r S p e c tr w c o p y, 2nd ed., D. L Andrews and A. A. Demido\". eds_. New York: Kluwer Academic/Plenum Press, 2002: Z. Zding.:r. M. Strizik. P. KuhaCand S. C h is ,An a l. C h im . Ad a , 2000.422. t 79: P. L r.,.·1t:yt:cM . ,"'. Sigrist. R t' I ,' . S e i. I n s lr u m .. 1990.61, l779

P y r o e le c tr ic

T ra n s d u c e rs

Pyroelectric transducers are constructed from single crystalline wafers of pyroelectric materials, which are insulators (dielectric materials) with very special thermal and electrical properties. Triglycine sulfate H,SO, (usually deuterated or with (NH,CH2COOHh' a fraction of the glycines replaced with alanine), is the most important pyroelectric material used for IRdetection systems. When an electric field is applied aeross any dielectric material, polarization takes place, with the magnitude of the polarization being a function of the dielectric constant of the material. For most dielectrics, this induced polarization rapidly decays to zero when the .external field is removed. Pyroelectric substances, in co~trast, retain a strong temperature-dependent pola'rization after removal of the fteld. Thus, by sandwiching the pyroelectric crystal between two electrodes, one of which is IR transparent. a temperaturedependent capacitor is produced. Changing its temperature by irradiating it with IR radiation alters the charge distribution across the crystal, which can be detected as a current in an external electrical circuit connecting the two sides of the capacitor. The magnitude of this current is proportional to the surface area of the crystal and the rate of change of polarization with temperature. Pyroelectric crystals lose their residual polarization when they are heatcd to a temperature called the C u r ie p o in /. For triglycine sulfate. the Curie point is 4rC Pvroelectric transducers exhibit response times that ~re fast enough to allow them to track the changes

in the time-domain signal from an interferometer. For this reason, many FTIR spectrometers for the mid-IR region employ this type of transducer. P h o to c o n d u c tin g

T ra n s d u c e rs

IR photoconducting transducers consist of a thin film of a semiconductor material, such as lead sulfide, mercury telluride-cadmium telluride (MCT), or indium antimonide, deposited on a nonconducting glass surface and sealed in an evacuated envelope to protect the semiconductor from the atmosphere. Absorption of radiation by these materials promotes nonconducting valence electrons to a higher energy-conducting state, thus decreasing the electrical resistance of the semiconductor. Typieally, a photoconductor is placed in series with a voltage source and load resistor, and the voltage drop across the load resistor serves as a measure of the power of the beam of radiation. A lead sulfide photoconductor is the most widely used transducer for the near-IR region of the spectrum from 10,000 to 333 cm - t (1 to 311m). It can be operated at room temperature. For mid- and far-IR radiation, MCT photoconductor transducers are used. They must be cooled with liquid nitrogen (77 K) to minimize thermal noise. The long-wavelength cutoff, and many of the other properties of these transducers, depend on the ratio of the mercury telluride to cadmium telluride, which can be varied continuously. The MCT transducer is faster and more sensitive than the de ute rated triglycine sulfate transducer discussed in the previous section. For this reason, the MCT transducer also finds widespread use in FTlR spectrometcrs, particularly those requiring fast rcsponse times, such as spectrometers interfaced to gas chromatographs. T h e rm a l

T ra n s d u c e rs

Thermal transducers, whose responses depend on the heating effect of radiation, are found in older dispersive spectromcters for detection of all but thc shortest IR wavelengths. With these deviees, the radiation is absorbed hy a small blackbody and the resultant temperature rise is measured. The radiant power level from a spectrophotometer beam is minute ( ]( r 7 to 10-9 W), so that the heat capacity of the absorbing clement must be as small as possible if a detectable temperature change is to be produced. Under the best of circumstances, temperature changes are confined to a few thousandths of a kelvin.

The problem of measuring IR radiation by thermal means is compounded by thermal noise from the surroundings. For this reason. thermal transducers are housed in a vacuum and are carefully shielded from thermal radiation emitted by other nearby objects. To further minimize the effects of extraneous heat sourccs, the beam from the source is always chopped. [n this way, the analyte signal, after transduction, has the frequency of the chopper and can be separated electronically from extraneous noise signals, which are ordinarily broad band or vary only slowly with time. Thermocouples. In its simplest form, a thermocouple consists of a pair of junctions formed when two pieces of a metal such as bismuth are fused to each end of a dissimilar metal such as antimony. A potential difference between the two junctions varies with their difference in temperature. The transducer junction for [R radiation is formed from very fine wires or alternatively by evaporating the metals onto a nonconducting support. In either case, the junction is usually blackened (to improve its heatabsorbing capacity) and sealed in an evacuated chamber with a window that is transparent to [R radiation. The response time is typically about 30 ms.

The reference junction, which is usually housed in the same chamber as the active junction, is designed to have a relatively large heat capacity and is carefullv shielded from the incident radiation. Because thc anaIyte signal is chopped, only the difference in temperature between the two junctions is important; therefore. the reference junction does not need to be maintained at constant temperature. To enhance sensitivity. several thermocouples may be connected in series to give what is called a th e r m o p ile .

*16-5 The wavelength of the fundamental N-H stretching vibration is about 1.5 I-'m. What is the approximate wavenumber and wavelength of the first overtone band for the N-H stretch'? *16-6 Sulfur dioxide is a nonlinear molecule. How many vibrational modes will this compound have" How many IR absorption bands would sulfur dioxide be expected to have'!

* 16-7 Indicate whether the following vibrations are active or inactive in the lR spectrum.

Bolometers. A bolometer is a type of resistance thermometer constructed of strips of metals, such as platinum or nickel, or from a semiconductor. This type of semiconductor device is sometimes called a th e r m is to r , Semiconductor materials exhibit a relatively large change in resistance as a function of temperature. The responsive element in a bolometer is kept small and blackened to absorb the radiant heat. Bolometers are not so extensively used as other [R transducers for the mid-IR region. However, a germanium bolometer, operated at 1.5 K, is an excellent transducer for radiation in the range of 5 to 400 cm 1 (2000 to 25 I-'m). The response time is a few milliseconds.

(aJCH J-CH 3

c ~ C stretching

(hi CH, - CCI,

C -

le;SO,

Symmetric

(dICH,=Ctl,

C -

C stretching stretching

H stretching:

" H •..• /

/

C=C

H

•..•

H

H

/'

'\

/

00

...•

H

"

CH 2 wag: -1'

"!J

H

•..•

/

tl

sC=cg

•..•

/

H

H

,Ii

*16-2 Gaseous HCl exhibits an IR absorption at 2890 cm 1 due to the hydrogenchlorine stretching vibration. (a) Calculate the force constant for the bond. (b) Calculate the wavcnumber of the absorption band for HCl assuming the force constant is the same as that calculated in part (a).

'IJ

CH2t\l,.'ist rl

,;.

H•..• / s'

*16-4 The wavelength of the fundamental O-H strctching vibration is about lAl-'m. What is the approximate wavcnumbcr and wavelength of the first overtone band for the O-H stretch')

C=C

H

,/

*16-1 The IR spectrum of CO shows a vibrational absorption band centered at 2170cm·1 (a) What is the force constant for the CO bond'? (b) At what wavenumber would the corresponding peak for I'CO occur'!

16-3 Calculate the absorption frequency corresponding to thc -C -H stretching vibration treating the group as a simple diatomic C-H molecule with a force constant of k = 5.0 x 10' N/m. Compare the calculated value with the range found in correlation charts (such as thc one shown in Figure 17-6). Repeat the calculation for the deuterated bond.

/

H

Problems with this icon are best solved using spreadsheets.

" /'

H •..•

* Answers are provided at the end of the book for problems marked with an asterisk.

/'

H

/

C=C

H

•..•

H '"OJ

16-8 What are the advantages of an FTIR spectrometer instrument?

[iJ

compared with a dispersive

16-9 What length of mirror drive in an FTIR spectrometer would be required to provide a resolution of (a) 0.050 cm -1, (b) 0040 cm -1, and (c) 4.0 cm -10

*16-10 It was stated that at room temperature (25°C) the majority of molecules are in the ground vibrational energy level (v = 0). (a) Use the Boltzmann equation (Equation 8-1) to calculate the excited-state and ground-state population ratios for HCl: N(v = 1 )/N(v = 0). The fundamental vibrational frequency of HCl occurs at 2885 cm-1 (b) Use the results of part (a) to find N(v = 2 )/N(v = 0). 16-11 Why are nondispersive IR instruments often used for the determination rather than dispersive IR spectrometers?

of gases

As shown in Table 17-1, the applications of TR spectrometry fall into three major categories based on the three IR spectral regions. The most widely used region is the mid-IR, which extends from about 670 to 4000cm -I (2.5 to 14.9 11m).Here, absorption, reflection, and emission spectra arc employed for both qualitative and quantitative analysis. The near-IR region, from 4000 to 14,000 cm-I (0.75 to 2.5 11m),also finds considerable use for the routine quantitative determination of certain species, such as water, carbon dioxide, sulfur, low-molecular-weight hydrocarbons, amine nitrogen, and many other simple compounds of interest in agriculture and in industry. These determinations are often based on diffuse-reflectance measurements of untreated solid or liquid samples or absorption studies of gases. The primary use of the far-IR region (15 to 1000 11m)has been for the determination of the structures of inorganic and metal-organic species based on absorption measurements.

Applications of Infrared Spectrometry

16-12 The first FTIR instruments used three different interferometer systems. Briefly. describ~ how it has been possible to simplify the optical systems in more contemporary instruments. *16-13 In a particular trace analysi5 via FTIR, a set of sixteen interferograms were collected. The signal-to-noise ratio ( S I N ) associated with a particular spectral peak was approximately 5: 1. How many interferograms would have to be collected and averaged if the goal is to obtain a S I N = 20: I? ~

*16-14 If a Michelson interferometer has a mirror velocity of 1.00 cm/s, what will be the frequency at the transducer due to light leaving the source at frequencies of (a) 4.8 X 1013 Hz" (b) 4.9 x 1013 Hz, and (c) 5.0 X 1013 Hz? What are the ~orresponding wavenumbers of these frequencies? ' odem C h a lle n g e

P r o b le m

16-15 (a) The IR spectrum of gaseous N,O shows three strong absorption bands at 2224 cm -1,1285 cm-I, and 2089 cm-I. In addition two quite weak bands are observed at 2563 cm-I and 2798 cm-l It is known that N,O is a linear molecule, but assume it is not known whether the structure is N-N---D or N-O-N. Use the IR data to decide between the two structures. What vibrations can be assigned to the strong absorption bands? What are possible causes of the weak absorptions? (b) The IR spectrum of HCN shows three strong absorption bands at 3312 cm-I, 2089 cm-I, and 712 cm-1 From this information alone, can you deduce whether HeN is linear or nonlinear? Assuming that HCN is linear, assign vibrations to the threc absorption bands. (c) How many fundamental vibrational modes are expected for BF]? Which of these are expected to be IR active? Why? Sketch the vibrations. (d) How many fundamental vibrational modes would you predict for (I) methane, (2) benzene, (3) toluene, (4) ethylene, and (5) carbon tetrachloride?

; .

M

IR sp e c tr o m e tr y

.... to o l th a tisa p p lie d .. a n d q u a n tita tive sp e c ie s o f~ (l

fir st fo c u s

o n th e u se s o f m id -Ill

o f m o le c u la r pounds

compoun& ,

tJ P e s. [ T/th is c h a p te r

th e n e xa m in e a p p lic a tio n s

q .b so r p tio n

st~ tU r a l p a r ti~ u la r ly

a n c i sp e c ie s o f in te r e st

MID-IR ABSORPTION SPECTROMETRY

.•. ·.·.to .. .th e q u a l.t.·.t.a tive . d e te r m in a tiQ n o f

m o le c u la r

te fle c tio n sp e c tr o m e tr yfo r

17A

is a ve r sa tile

we

a nd

in ve ~ tig a tio n s

Mid-IR absorption and reflection spectrometry are major tools for determining the structure of organic and biochemical species. In this section we examine mid-IR absorption applications. Section 17B is devoted to mid-IR reflectance measurements. 1

o r g a n ic c o m -

W b io c h e m istr y.

in le ss d e ta il se Vli" r a lo f th e o th e r o f IR sp e c tr o sc o p y.

We

As we have seen in earlier chapters, ultraviolet and visible molecular spectra are obtained most conveniently from dilute solutions of the analyte. Absorbance measurements in the optimal range are obtained by suitably adjusting either the concentration or the cell length. Unfortunately, this approach is often not applicable for IR spectroscopy because no good solvents arc transparent throughout the region of interest. As a consequence, sample handling is frequently the most difficult and time-consuming part of an IR spectrometric analysisZ In this section we outline some of the common : For further reading see R. M. Silverstein, F X. Webster. and D. Kiemle. I d e n r ( f ic a r i( J f l o f O r g a n ic C o m p o u n d s, 7th cd .. Chap. 2, New York: Wiky. 2005; B. Schrader, J llfr u r e d Q n d Ru m a n 5 p e c r r o sc o p y, New York: VOL 1995; N. B_ Colthup, L. H. Daly. and S. E. Wiberley. ln r m d u e l/o n LO In fr a r e d a n d Ra m a n Sp e c tr m l-" o p ). 3rd cd_. San Diego: Academic Press, 1990. ~See P r a c tic e d Sa m p lifJ f: F e c lm iq u l's (o r Illfr a r e d Alla lysis. P. B. Coleman. ed .. Boca Raton, FL: eRe Press. 1993: T J. Porro and S. C Pattacini, Sp e c · r r o sc o p y. 1993. tl (7). 40: Ibid., 8 IRL 39: A. L Smith, Ap p lie d In fr a r e d Sp e c tr o sc o p y. New York: Wiley, 1979, Chap_ 4

Sp e c tr o m e tr ic

r-:::¥I

Throughout this chapter, this logo indicates

l2.J an opportunity for online self-study at www .thomsonedlLcom /chemistry/skoog, linking you to interactive tutorials, simulations, and exercises.

the basis of cost, range of transparency, solubility in the solvent, and reactivity with the sample or solvent. Sodium chloride and potassium bromide windows are most commonly employed and are the least expensive. Even with care, however, their surfaces eventually become fogged because of absorption of moisture. Polishing with a buffing powder returns them to their original condition. For samples that arc wet or aqueous, calcium and bariuin fluoride are suitable, although neither transmits well throughout the entire mid-IR region. Silver bromide is often used, although it is more expensive, is

TABLE17-1 Major Applications of IR Spectrometry Applicable Samples Near-lR Mid-IR

Quantitative

Solid or liquid comm~rcial materials

Quantitative

Gaseous

Pure solid, liquid, or gases Complex liquid, solid, or gaseous mixtures

Reflectance

Qualitative Quantitative Chromatographic Qualitative

Emission

Quantitative

Atmospheric

Absorption

Qualitative

Pure inorganic or organometallic

Diffuse reflectance Absorption Absorption

Complex

mixtures

liquid. solid, or gaseous mixtures

Pure solids or liquids samples species

2500 2000 Wavenumber.

techniques for preparation tion measurements.

limited in its applications, ity of solvents transparent the IR.

of samples for IR absorp-

however, by the availabilover significant regions in

G ases

Solvents. Figure 17-1 lists several common S(?lvents employed for IR studies of organic compoun,ds. This figure illustrates that no single solvent is transparent throughout the entire mid-IR region. Water and the alcohols are difficult to use as solvents in IR spectrometry. Water shows several strong absorption bands in the IR region, as can be seen in Figure 17-2. Here, the spectrum of water is shown along with the spectrum of an aqueous solution of aspirin. The computer-calculated diflerence spectrum reveals the spectrum of the water-soluble aspirin. Water and alcohols also attack alkali-metal halides, the most common materials used for cell windows. Hence, water-insoluble window materials, such as barium tluoride, must be used with such solvents. Care must also be taken to dry the solvents shown in Figure 17-1 before use with typical cells.

The spectrum of a low-boiling-point liquid or gas can be obtained by permitting the sample to expand into an evacuated cvlindrical cell equipped with suitable windows. For this purpose, a variety of cylindrical cells are available with path lengths that range from a few centimeters to 10 m or more. The longer path lengths are obtained in compact cells by providing reflecting internal surfaces, so that the beam makes numerous passes through the sample before exiting the cell (see Figure 16-13). S o lu t io n s

When feasible, a convenient way of obtaining IR spectra is on solutions prepared to contain a known concentration of sample, as is generally done in ultravioletvisible spectrometry. This technique is somewhat

\Vavenumber,

em

Carhon

disulfide

tetrachloride

Cells. Because of the tendency for solvents to absorb IR radiation, IR liquid cells are ordinarily much narrower ( O m to I mm) than those employed in the ultraviolet and visible regions. Often, relatively high sample concentrations (from 0.1 % to 10%) are required because of the short path lengths and the low molar absorptivities of IR bands. Liquid cells are frequently designed for easy disassembly and use Teflon spacers to allow variation in path length (see Figure 17-3). Fixed-path-Iength cells can be filled or emptied with a hypodermic syringe. A variety of window materials are available as listed in Table 17-2. Window materials are often chosen on

Barium fluoride

Thallium bromideiodide, KRS-5 Silver bromide Zinc sulfide, Irtran-2 Zinc selenidc, Irtran-4 Polyethylene

Water Solubility, g/lOOg H,O,

cm--1

20"C

40,000-625 40,000-385 40,000-500 40,000-200 50,000-2,500 50,000-1,100 50,000-770 16,600-250

36.0 65.2 34.7 160.0 Insoluble 1.51 x 10-3 0 .1 2 (2 S" C )

8.3 1 1 m ) . L im it a t io n s

to

th e

U s e o f C o r r e la t io n

To summarize, correlation charts serve only as a guide for further and more careful study. Several excellent monographs describe the absorption characteristics of functional groups in detail.' A study of these characteristics, as well as the other physical properties of the sample, may permit unambiguous identification. IR spectroscopy, when used in conjunction with mass spectrometry, nuclear magnetic resonance, and elemental analysis, usually leads to positive identification of a species. C o lle c t io n s

o f S p e c tra

As just noted, correlation charts seldom suffice for the positive identification of an organic compound from its IR spectrum. However, several catalogs of IR spectra are available that assist in qualitative identification by providing comparison spectra for a largc number of pure compounds.' Manually searching large catalogs of spectra is slow and tedious. For this reason, computer-based search systems are widely used. • C o m p u te r

S e a rc h

Systems

Virtually all IR instrument manufacturers now offcr computer search systems to aid in identifying compounds from stored IR spectral data'" The position and relative magnitudes of peaks in the spectrum of the analyte are determined and stored in memory to give a peak profile, which can be compared with profiles of pure compounds stored on disk or CD-ROM. The computer then matches profiles and prints a list of compounds having spectra similar to that of the analyte. Usually, the spectrum of the analyte and that of each potential match can be shown simultaneously on the computer display for comparison, as shown in Figure 17-7. In 1980 the Sad tier Standard IR Collection and the Sadtler Commercial IR Collection became available as

C h a rts

The unambiguous establishment of the identity or the structure of a compound is seldom possible from correlation charts alone. Uncertainties frequently arise from overlapping group frequencies, spectral variations as a function of the physical state of the sample (that is, whether it is a solution, a mull, in a pelleted form, and so forth), and instrumental limitations. In using group frequencies, it is essential that the entire spectrum, rather than a small isolated portion, be considered and interrelated. Interpretation based on one part of the spectrum should be confirmed or rejected by studying other regions.

~R. M. Silverstein, F. X. Webster, and D. Kienle, Sp e c tr o m e tr ic Id e n o f O r g a n ic C o m p o u n d s, 7th ed., New York: Wiley. 2005; B. Schrader, In fr a r e d a n d Ra m a n Sp e c tr o sc o P J ', New York: veil 1995: N. B. Colthup, L. H. Daly, and S. E. Wiberley, In tr o d u c tio n to In fr a r e d a n d Ra .r n a n Sp e c tr o sc o p y, 3rd ed., San Diego: Academic Press, 1990. sSee Informatics/Sadtler Group, Bio-Rad Laboratories, Inc., Philadelphia, PA; c.1. Pouchert, Th e Ald r ic h Lib r a r y o f In fr a r e d Sp e c tr a . 3rd ed .. Milwaukee. Wl: Aldrich Chemical Co., 1981; Thermo Galactic, Sp e c r r a O n lin e (http://spectra.galactic,com). 6See E. Pretsch. G. Toth, M. E. Monk. and M. Badertscher. C o m p u te r tific a tio n

Aid e d

Str u c tu r e

E lu c id a tio n :

Sp e c tr a

In te r p r e ta tio n

a n d Str u c tu r e

FIGURE 17-7 Plot of an unknown spectrum and the best match from a computer search report. (Courtesy of Informatics/Sadtler Group, Bio-Rad Laboratories, Inc., Philadelphia, PAl

software packages. Currently. this library contains more than 220,000 spectra.' Included are vapor-phase spectra and condensed-phase spectra of pure compounds. Individual databases in application areas such as polymers, industrial products, pure organic compounds, forensic sciences, and the environment are available. Several manufacturers of Fourier transform IR (FTIR) instruments have now incorporated these packages into their instrument computers, thus creating instantly available IR libraries of hundreds of thousands of compounds. The Sadlier algorithm consists of a search system in which the spectrum of the unknown compound is first coded according to the location of its strongest absorption peak; then each additional strong band (% T < 60%) in ten regions 200 cm-I wide from 4000 to 2000 cm -I are coded by their location. Finally, the strong bands in seventeen regions 100 cm -I wide from 2100 to 400 cm -I are coded in a similar way. The compounds in the library are coded in this same way. The data are organized by the location of the strongest band with only those compounds having the same strongest

G e n e r u .-

2003: B. C Smith, In fr a r e d Sp e c tr a l In te r p r e tm io n : A Systl!m a tic Ap p r o a c h , Boca Raton, FL eRe Press, 1998. Chap. 9; \\'. O. George and H. \Villis, C o m p llle r M e th u d s in U 1 /, ~ Tisib le a n d IR Sp e c tr o sc o p .,-" , ?\itW York: Springer-Verlag, 1990. tio n , New York: VCH-Wiley,

r::;;'l

Tu r o r ia /:

Learn more about IR spectral interpre-

leJ tation and identification.

band being considered in any sample identification. This procedure is rapid and produces a list of potential matches within a short period. For example, only a few seconds are required to search a base library of 50,000 compounds by this procedure. In addition to search systems. artificial intelligencebased computer programs seek to determine the structure or substructure from spectral profiles. Some of these programs use data from different types of instruments (nuclear magnetic resonance, mass, and IR spectrometers, etc.) to determine structuresS

Quantitative IR absorption methods differ somewhat from ultraviolet-visible molecular spectroscopic methods because of the greater complexity of the spectra, the narrowness of the absorption bands, and the instrumental limitations of IR instruments. Quantitative data obtained with older dispersive IR instruments were generally significantly inferior in quality to data obtained with UV -visible spectrophotometers. The precision and accuracy of measurements with modern FTIR instruments, however, is distinctly better than those

ments. In either casc, quantitative analysis usually requires that empirical calibration curves be used. A b s o rb a n c e

M e a s u re m e n t

Matched absorption cells for solvent and solution are ordinarily employed in the ultraviolet and visible regions, and the measured absorbance is then found from the relation Psolvent

A

= I og--~

P"olulion

The use of the solvent in a matched cell as a reference absorber has the advantage of largely canceling out the effects of radiation losses due to reflection at the various interfaces, scattering and absorption by the solvent, and absorption by the container windows, This technique is seldom practical for measurements in the IR region because of the difficulty in obtaining cells whose transmission characteristics are identicaL Most IR cells have very short path lengths, which are difficult to duplicate exactly. In addition, the cell windows are readily attacked by contaminants in the atmosphere and the solvent. Because of this, their transmission characteristics change continually with use. For these reasons, a reference absorber is often dispensed with entirely in IR work, and the intensity of the radiation passing through the sample is simply compared with that of the unobstructed beam, In either case, the resulting transmittance is ordinarily less than 100%, even in regions of the spectrum where no absorption by the sample occurs (see Figure 17-5), For quantitative work, it is necessary to correct for the scattering and absorption by the solvent and the celL Two methods are employed. In the so-called cellin·cell·out procedure, spectra of the pure solvent and the analyte solution are obtained successively with respect to the unobstructed reference beam. The same cell is used for both measurements. The transmittance of each solution versus the reference beam is then determined at an absorption maximum of the analyte. These transmittances can be written as

Time (a)

1.0 0.8

~

g 0.6 u

ge 0.4 f-.

0.2

0.0 4000

3200

3600

2800

2400

2000

Wavenumber,

1600

1200

800

400

cm--I

(b)

FIGURE 17-8 (a) Interferogram obtained from a typical FTIRspectrometer for methylene chloride. The plot shows detector signal output as a function of time or displacement of the moving mirror of the interferometer. (b) IR spectrum of methylene chloride produced by the Fourier transformation of the data in (a). Note that the Fourier transform takes signal intensity collected as a function of time and produces transmittance as a function of frequency after subtraction of a background interferogram and proper scaling. with dispersive instruments. Meticulous attention to detail is, however, essential for obtaining good-quality results9 D e v ia t io n s

fro m

B e e r 's

Law

With IR radiation, instrumental deviations from Beer's law are more common than with ultraviolet and visible wavelengths because IR absorption bands are ~For a discussion of quanlilative F u n d a m e n r a ls

o f F o u r ie r

FTIR spectroscopy.

Tr a n sfo r m

In fr a r e d

see B. C. Smith,

Sp e c tr o sc o p y,

FL: eRe Press, 1995; P. R Griffiths and 1. A. deHasech. fo r m

In fr a r e d 5 p e c r r o m e tr ,,-. 'ew

York:

\\'lley,

1986.

Boca

Raton,

F o u r ie r

Tr a n s-

relatively narrow. Furthermore, with dispersive instruments, the low intensity of sources and low sensitivities of transducers in this region require the use of relatively wide monochromator slit widths; thus. the bandwidths employed are frequently of the same order of magnitude as the widths of absorption peaks. We have pointed out (Section 13B-2) that this combination of circumstances usually leads to a nonlinear relationship between absorbance and concentration. As discussed in Section 16B-l, FTIR instruments have better performance characteristics. Hence, Beer's law deviations are not quite as serious as with dispersive instru-

the transmittance of the sample with respect to the solvent can be obtained by division of the two equations. That is, T = T ,n ;,

T y p ic a l A p p lic a t io n s

With the exception of homo nuclear molecules, all organic and inorganic molecular species absorb radiation in the IR region. IR spectrophotometry thus offers the potential for determining an unusually large number of substances. Moreover, the uniqueness of an IR spectrum leads to a degree of specificity that is

A

== log !JJ ::: log !!.!J T,

where P , is the power of the unobstructed beam and 'I i) and T , are the transmittances of the solvent and analvte solution. respectively, against this reference. If P , remains constant during the two measurements. then

.tie.·...

= P IP "

With modern FTIR spectrometers, the reference interferogram is obtained with no sample in the sample cell. Then, the sample is placed in the cell, and a second interferogram obtained. Figure 17-8a shows an interferogram collected using an FTIR spectrometer with methylene chloride, CH,Cl" in the sample cell. The Fourier transform is then applied to the two interferograms to compute the IR spectra of the reference and the sample. The ratio of the two spectra can then be computed to produee an IR spectrum of the analyte such as the one illustrated in Figure 17-8b, An alternative way of obtaining P o and T for a single absorption band is the baseline method. For an instrument that displays transmittance, the solvent transmittance is assumed to be constant or at least to change linearly between the shoulders of the absorption peak, as illustrated in Figure 17-9. The quantities To and T, are then obtained as shown in the figure, For direct absorbance readout, as is shown in Figure 17-7, the absorbance is assumed to be constant or to change linearly under the absorption band. The peak absorbance is then obtained by subtracting the baseline absorbance,

P

FIGURE 17 -9 The baseline method for determining the absorbance of an absorption maximum.

Minimum Detectable Concentration, ppmt

12 FIGURE

17-10

13

l-l

15

12

14

15

A, ,Llln

A , t lm

Spectra of C8H IO isomers in

13

cyclohexane.

Carbon disulfide Chloroprene Diborane Ethylenediamine Hydrogen cyanide Methyl mercaptan Nitrobenzene Pyridine Sulfur dioxide Vinyl chloride

4.54 11.4 3.9 13.0 3.04 3.38 11.8 14.2 8.6 10.9

Courtesy of Thermo Electron Corp. *1992-1993 OSHA exposure limits for 8-h weighted average. tFor a 20.25-01 cell. fShort·term

12

13

A,

matched or exceeded by relatively few other analytical methods. This specificity has found particular application to analysis of mixtures of closely related organic compounds. Two examples that typify these applications follow. Analysis of a Mixtnre of Aromatic Hydrocarbons. A typical application of quantitative IR spectroscopy involves the resolution of CHHIO isomers in a mixture that includes v-xylene, m-xylene, p-xylcne, and ethylbenzene. The IR absorption spectra of the individual components in the range of 12 to 15 flm in cyclohexane solvent is shown in Figure 17-10. Useful absorption bands for determination of the individual compounds occur at 13.47,13.01,12.58, and 14.36 flm, respectively. Unfortunately, however, the absorbance of a mixture at anyone of these wavelengths is not entirely determined by the concentration of just one component because of overlapping absorption bands. Thus, molar absorptivities for each of the four compounds must be determined at the four wavelengths. Then. four simultaneous equations can be written that permit the calculation of the concentration of each species from four absorbance measurements (see Section 14D-2). Alternatively. chemometric techniques. such as factor analvtical

14

15

pm

methods, 10 can use entire spectral regions to determine the individual components. Such methods can be used even when the relationship between absorbance and concentration is nonlinear (as frequently occurs in the IR region). Determination of Air Contaminants. The recent proliferation of government regulations with respect Lo atmospheric contaminants has demanded the development of sensitive, rapid. and highly specific methods

TABLE

17-4

An Example of IR Determinations of Air

Contaminants

Contaminant

Conen,

Found,

Relative

ppm

ppm

Error, %

Carbon monoxide

50.0

49.1

Methyl ethyl ketone Methanol Ethylene oxide Chloroform

1000

98.3

18 1.7

100.0

99.0

1.0

50.0

49.9

100.0

99.5

0.2 0.5

CourteSy of Thermu Ekc!ron

Curp

exposure limit: is-Olin time-weighted

average that shall not be exceeded at any time during the work day

for a variety of chemical compounds. IR absorption procedures appear to meet this need better than any other single analytical tool. Table 17-4 demonstrates the potential of IR spectroscopy for the analysis of mixtures of gases. The standard sample of air containing five species in known concentration was analyzed with a computerized version of the instrument shown in Figure 16-13; a 20-m gas cell was employed. The data were printed out within a minute or two after sample introduction. Table 17-5 shows potential applications of IR filter photometers (such as that shown in Figure 16-13) for the quantitative determination of various chemicals in the atmosphere for the purpose of assuring compliance with Occupational Safety and Health Administration (OSHA) regulations. Of the more than 400 chemicals for which maximum tolerable limits have been set by OSHA, more than half appear to have absorption charaeteristics suitable for determination by means of IR filter photometers or spectrophotometers. With such a large number of absorbing compounds, we expeet overlapping absorption bands. However, the method can provide a moderately high degree of selectivity. D is a d v a n t a g e s

and

to

IR M e th o d s

Q u a n t it a t iv e

L im it a t io n s

There are several disadvantages to quantitative analysis by IR spectrometry. Among these are the frequent nonadherence to Beer's law and the complexity of spectra.

The richness of spectral features enhances the probability of overlapping absorption bands. In addition, with older dispersive instruments, the narrowness of bands and the effects of stray radiation make absorbance measurements critically dependent on the slit width and the wavelength setting. Finally, the narrowpath-length cells required for many analyses are inconvenient to use and may lead to significant analytical uncertainties. For these reasons, the analytical errors associated with a quantitative IR analysis often cannot be reduced to the level associated with ultraviolet and visible methods, even with considerable care and effort.

178

MID-IR REFLECTION SPECTROMETRY

IR reflection spectrometry has found a number of applications, particularly for dealing with solid samples that are difficult to handle, such as polymer films and fibers, foods, rubbers, agriculture products, and many others." Mid-IR reflection spectra, although not identical to the corresponding absorption spectra, are similar in general appearance and provide the same information as do their absorption counterparts. Reflectance spectra can be used for both qualitative and See F. M. Mirabella, cd .. M o d e r n Te c h n iq u e s in Ap p lie d M o le c u la r Sp e c · New York: Wiley, 1998; G. Kortum, Re fle c ta n c e Sp e c tr o sc o p y, New York: Springa, 1969: N. J. H:trrick, / n t e r f U l l Re fle c tio n Sp e c tr o sc o p y, New York: Wiley, 1967. II

tr o sc o p y,

quantitative analysis. Most instrument manufacturers now offer adapters that fit into the cell compartments of IR absorption instruments and make it possible to obtain reflection spectra readily.

Reflection of radiation is of four types:

sp e c u la r

r e fle c -

and a tte n u a te d to ta l r e fle c ta n c e (ATR). Specular reflection occurs when the reflecting medium is a smooth polished surface. Here, the angle of reflection is identical to the incident angle of the radiation. If the surface is made up of an IR absorber, the relative intensity of reflection is less for wavelengths that are absorbed than for wavelengths that are not. Thus, a plot of reflectance R, which is the fraction of the incident radiant energy reflected, versus wavelength or wavenumber provides a spectrum for a compound similar in general appearance to a transmission spectrum for the species. Specular reflection spcctra find some use for examining and characterizing the smooth surfaces of solids and coated solids but are not as widely used as diffuse- and total-reflection spectra. We will, therefore, focus on the latter two types of spectra. tio n . d iffu se

r e fle c tio n ,

in fe r n a l

r e fle c tio n ,

Diffuse-reflectance IR Fourier transform spectrometry (D RIFTS) is an effective way of directly obtaining IR spectra on powdered samples with a minimum of sample preparation.12 In addition to saving time in sample preparation, it permits conventional IR spectral data to be gathered on samples not appreciably altered from their original state. The widespread use of diffuse-reflectance measurements had to await the general availability of FTIR instruments in the mid1970s because the intensity of radiation reflected from powders is too low to be measured at medium resolution and adequate signal-to-noise ratios with dispersive instruments. Diffuse reflection is a complex process that occurs when a beam of radiation strikes the surface of a finely divided powder. With this type of sample, specular rcflection occurs at each plane surface. However, because there are many of these surfaces and they are random Iv oriented, radiation is reflected in all direcinformation, see M. Milosevic. S. L. Berets. Ap p L Sp e c }..p ; P. R. Griffiths and M. P. Fuller in A d l 'a f l C e S in Sp e c tr o sc u p y, R. 1. H. Clark and R. E. Hester. cds .. \"ul. 9. Chap_ 2.LDndon: Heydon and Sons, 19x2 L

tions. Typically, the intensity of the reflected radiation is roughly independent of thc viewing angle. A numbcr of models have bcen developed to describe in quantitative terms the intensity of diffuse reflected radiation. The most widely used of these models was developed by Kubelka and MunklJ Fuller and Griffiths in their discussion of this model show that the relative reflectance intensity for a powder f(R'x) IS given bV 14 f(R ' ..

)

=

(I

R ') ' 2 R 'x

5

where R'x is the ratio of the reflected intensity of the sample to that of a non absorbing standard, such as finely ground potassium chloride. The quantity k is the molar absorption coefficient of the analyte, and s is a scattering coefficient. For a diluted sample, k is related to the molar absorptivity e and the molar concentration of the analyte c by the relationship k = 2 .3 0 3 e c

Reflectance spectra then consist of a plot sus wavenumber (see Figure 17-12b). I n s t r u m e n t a t io n

C o m p a r is o n

of

FIGURE 17-11 A diffuse-reflectance attachment for an FTIRspectrometer.

finely ground mixture of carbazole in potassium chloride. Note that the peak locations are the same in the two spectra but that the relative peak heights differ considerably. The differenccs arc typical, with minOr peaks generally appearing larger in reflection spectra.

ver-

o f f ( R 'x , )

Currently, most manufacturers of FTIR instruments offer adapters that fit in cell compartments and permit diffuse-reflectance measurements. Figure 17-11 illustrates one type of adapter. The collimated beam from the interferometer is directed to an ellipsoidal mirror and then to the sample. The sample is usually ground and mixed with KBr or KCI as a diluent. The mixture is then placed in a sample cup 3-4 mm deep and about 10-15 mm in diameter. A complex combination of reflection, absorption, and scattering occurs before the beam is directed to the detector. To obtain a spectrum with a single-beam instrument, the signal for the sample is first stored. A reference signal with a good reflector. such as finely ground KBr or KCl, is then recorded in place of the sample. The ratio of these signals is thcn taken to give the reflectance.

a n d R e f le c t io n

I n s t r u m e n t a t io n

= ~

-x

x,

ATR. The resulting ATR spcctrum resembles that of a conventional IR spectrum with some differcnces.

A b s o r p t io n S p e c tra

Figure 17-12 compares the conventionallR absorption spectrum for carbazole obtained bv mcans of a KBr pellet with the diffuse-reflectance spectrum of a 5%

For additional

Internal-reflection spectroscopy is a technique for obtaining IR spectra of samples that are difficult to deal with, such as solids of limited solubility, films, threads, pastes, adhesives, and powders15

Figure 17-13 shows an apparatus for ATR measurements. As can be seen from the upper figure, the sample (here, a solid) is placed on opposite sides of a transparent crystalline material of high refractive index. By proper adjustment of the incident angle, the radiation undergocs multiple internal reflections before passing from the crystal to the detector. Absorption and attenuation takc place at each of these reflections. Figure 17-13b is an optical diagram of an adapter that fits into the cell area of most IR spectrometers and permits ATR measurements. Cells for liquid samples are also available. A T R S p e c tra

ATR spectra are similar but not identical to ordinary absorption spectra. In gencral, although the same bands are observed, their relative intensities differ.

l.00

~ c "~ ~ 0.75

O;;JCJ ::--.IN 1 ....-; H

carbazole

.Q

P r in c ip le s

Whcn a beam of radiation passes from a more dense to a less dense medium, reflection occurs. The fraction of the incident beam reflected increases as the angle of incidence becomes larger; beyond a certain critical angle, reflection is complete. It has been shown both theoretically and experimentally that during the reflection process the beam penetrates a small distance into the less dense medium beforc reflection occurs. The depth of penetration, which varies from a fraction of a wavelength up to several wavelengths, depends on the wavelength, the index of refraction of the two materials, and the angle of the beam with respcct to the interfacc. The penetrating radiation is called the e va n e sc e n t wa ve . At wavelengths where thc less dense medium absorbs the evanescent radiation, attenuation of the beam occurs, which is known as a tte n u a te d to ta l r e fle c ta n c e , or See E M. Mirabella. cd .. M o d e m Te c h n iq u e s in Ap p lie d M o le c u la r Sp e c New York: Wiley, 1998: (j-, Kortum, Re ffc c u m c e Sp e c tr m -c o p y, New 'r"orlc Springer. lY69: N. 1. H a r r ic K.lr u e m ill Re fle c tio n Sp I: Y[ (m c o p .'"

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FIGURE 17 -12 Comparison of the absorption spectrum (a) for carbazole with its diffuse-reflectance spectrum (b).

FIGURE 17-13 ATRapparatus. In (a) a solid sample is shown mounted on an internal reflection crystal of high refractive index. The materials used as ATRcrystals include KRS-5, AgCI, Ge, Si, and the Irtran materials. Solid samples can be pressed against the crystal to obtain optical contact. In (b), a typical attachment for ATR is shown. With many attachments, the internal reflection plate can be positioned in the holder to provide several incident angles.

With ATR spectra, the absorbances, although dependent on the angle of incidence, are independent of sample thickness, because the radiation penetrates only a few micrometers into the sample. The e ffe c tive p e n e tr a tio n d e p th dp depends on the wavelength of the beam, the refractive indexes of the crystal and the sample, and the beam angle. The penetration depth can be calculated from

where A, is the wavelength in the crystal (Aln ,), 0 is the angle of incidence, and n , and n , are the refractive indexes of the sample and crystal, respectively. Note that the effective penetration depth can be changed by changing the crystal material, the angle of incidence, or both. It is possible to obtain a depth profile of a surface using ATR spectroscopy. In practice, a multireflection crystal with a 45' angle can accommodate most routine samples. One of the major advantages of ATR spectroscopy is that absorption spectra are readily obtainable on a wide variety of sample types with a minimum of preparation. Threads, yarns, fabrics, and fibers can be stud-

ied by pressing the samples against the dense crystal. Pastes, powders, or suspensions can be handled in a similar way. Aqueous solutions can also be accommodated provided the crystal is not water soluble. There are even ATR flow cells available. ATR spectroscopy has been applied to many substances, such as polymers, rubbers, and other solids. It is of interest that the resulting spectra are free from the interference fringes mentioned previously. The spectra obtained with ATR methods can differ from [R absorption spectra because of distortions that occur near strong absorption bands where the sample refractive index may change rapidly. Also, the orientation of the sample on the ATR crystal can influence band shapes and relative intensities. However, the ATR band intensity is usually proportional to concentration so that quantitative measurements can be made.

17e

PHOTOACOUSTIC IR SPECTROSCOPY

Photoacoustic spectroscopy (PAS) provides a way to obtain ultraviolet, visible, and IR absorption spectra of solids, semisolids, or turbid liquids." Acquisition of spectra for these materials by ordinary methods is usually difficult at best and often impossible because of light scattering and reflection.

PAS is based on a light absorption effect that was first investigated in the 1880s by Alexander Graham Bell and others. This effect is observed when a gas in a closed cell is irradiated with a chopped beam of radiation of a wavelength that is absorbed by the gas. The absorbed radiation causes periodic heating of the gas, which in turn results in regular pressure fluctuations within the chamber. If the chopping rate lies in the acoustical frequency range, these pulses of pressure can be detected by a sensitive microphone. The photoacoustic effect has been used since the turn of the century for the analysis of absorbing gases and has recently taken on new importance for this purpose with the advent of tunable IR lasers as sources. Of greater importance, however. has been the use of the photo-

components of mixtures separated by thin-layer and high-performance liquid chromatography and for monitoring the concentrations of gaseous pollutants in the atmosphere.

:".1odulated beam from FfIR

FIGURE 17-14 Diagram of a photoacoustic attachment for an FTIR spectrometer.

acoustic effect for obtaining solids and turbid liquids.

absorption

spectra

of

Photoacoustic IR spectroscopy saw limited application before the advent of FT[R instruments. Now, several manufacturers make photoacoustic accessories for FTIR instruments. [n photoacoustic measurements, the sample is placed in a small sample cup within the photoacoustic attachment as illustrated in Figure 17-14. The photoacoustic spectrometer chamber is tilled with a high-thermal-conductivity gas such as helium or nitrogen and placed in the FTIR sample compartment. The mirror shown deflects the modulated beam onto the sample. Absorption of the IR beam by the sample can result in nonradiative decay of the excited vibrational states of the sample molecules. This can transfer heat to the surface of the sample and result in the generation of a modulated acoustic wave in the gas inside the chamber. A very sensitive microphone then detects the acoustic wave. Photoacoustic spectra are normally plotted in a format similar to absorption spectra as shown in Figure 17-15. The spectra are usually plotted as a ratio to a background scan of a totally absorbing material such as carbon black. Although the frequencies of transitions are the same as in absorption spectra, relative intensities depend on wavelength and modulation frequency. Photoacoustic spectra can be obtained on samples with essentially no sample preparation. The only requirement is that the sample must fit within the sample cup. fn addition to solids and turhid liquids, photoacoustic methods have been used for detecting the

The near-IR (NIR) region of the spectrum extends from the upper wavelength end of the visible region at ahout 770 nm to 2500 nm (13,000 to 4000 cm-I)." Absorption bands in this region are overtones or combinations (Section 16A-4) of fundamental stretching vibrations that occur in the region of 3000 to 1700 cm-I. The bonds involved are usually C- H, N - H, and a-H. Because the bands are overtones or combinations, their molar absorptivities are low and detection limits are on the order of 0.1 %. In contrast to mid-[R spectrometry, the most important uses of NIR radiation are for the routine q u a n tita tive determination of species, such as water, proteins, low-molecular-weight hydrocarbons, and fats, in products of the agricultural, food, petroleum, and chemical industries. Both diffuse-reflection and transmission measurements are used, although diffuse reflectance is by far the more widely used.

I"For a general reference on NIR, see H a n d b o o k o f Ne a r -in fr a r e d An a lyand E. W. Ciurczak, cds .. New York: Marcel Dekker, 2001. For a review of commercial instrumentation, see C. M. Henry. An a L C h e r n ., 1999, 7/. 625A. In the literature of NlR spectromelry, the abscissa is usually wm /e !e n g lh in nanometers or micrometers in contrast to mid-IR spectra in which the abscissa is wa ve n u m b e r in units of

sis. 2nd ed., D. A. Burns

(cm)-I

FIGURE 17-15 Photoacoustic IRspectra of (a) a pulverized coal sample and (b)an extruded polymer pellet. (From P r a c t ic a l S a m p lin g Techniques f o r I n f r a r e d A n a ly s is , P. B. Coleman, ed., Boca Raton, FL:eRC Press, 1993.)

Four different types of instruments are available for the NIR region. Grating instruments are similar to those used for UV-visible absorption spectroscopy. There are also discrete filter instruments usually containing filter wheels for selecting different wavelengths. These are less flexible than other instruments but useful for fixed, well-characterized samples. In addition, acoustooptic tunable filter (AOTF) instruments are available. The acoustooptic filter is a solidstate device that diffracts radiation at wavelengths determined by a radio frequency signal applied to the crystal. Speed and ruggedness are the main advantages of AOTF devices. Fourier transform spectrometers are also available commercially for NIR spectrometry. The advantages normally associated with FT instruments in the mid-IR region, such as high throughput and resolution, are less applicable in the NIR region. However, the wavelength reproducibility and signalto-noise-ratio characteristics are major advantages of FTsystems. Most spectrometers use tungsten-halogen lamps with quartz windows. Cells for absorption measurements are usually quartz or fused silica transparent up to about 3000 nm. Cell lengths vary from 0.1 to 10 cm. Detectors range from PbS and PbSe photoconductors to InSb and InAs photodiodes. Array detectors, such as InGaAs detectors, have also become available for the region. Several commercial UV-visible spectrophotometers are designed to operate from 180 to 2500 nm and can thus be used to obtain NIR spectra. Several solvents are used for NIR studies. Some of these are listed in Figure 17-16. Note that only carbon tetrachloride and carbon disulfide are transparent throughout the entire NIR region.

170-2 Data Processing in NIR spectrometry

NIR spectral bands are normally broad and often overlapping. There are rarely clean spectral bands that allow simple correlation with analyte concentration. Instead, multivariate calibration techniques are usedl' Most commonly, partial least squares, principal components regression, and artificial neural networks are em-

'~For a discussion of multivariate techniques, see K. R. Beebe. R J PeiL and M. B. Seashohz, C h e m o m c r r ic s: A P r a c tic a l G u id e . Chap. 5. :'\ew York Wiley, 1998: H. Martens and T. NaC's M l l l r i m r i a t e C < 1 l i b r i l t i o f l . :\'ew )"ork Wiley, 1989.

ployed. Such calibration involves development of a calibration model through obtaining results on a "training set" that includes as many of the eonditions encountered in the samples as possible. Problems and pitfalls in developing the models have been diseussedl' The manufacturers of NIR instruments include software packages for developing calibration models. In addition, third-party software for multivariate calibration is readily available.

Wavelength,

10

1.2

14

16

18

J..lffi

2.0

2.2

2.4

I--

t-t

--i

FIGURE 17-16 Some useful solvents for NIR spectroscopy. Solid lines indi-

cate satisfactory transparency for use with '-cm cells.

170-3 Applications of NIR Absorption Spectrometry

In contrast to mid-IR spectroseopy, NIR absorption spectra are less useful for identification and more useful for quantitative analysis of compounds containing functional groups made up of hydrogen bonded to carbon, nitrogen, and oxygen. Such compounds can often be determined with accuracies and precisions equivalent to ultraviolet-visible spectroscopy, rather than mid-IR spectroscopy. Some applications inthtde the determination of water in a variety of samples, including glycerol, hydrazine, organic films, and fuming nitric acid; the quantitative determination of phenols, aleohols, organic acids, and hydroperoxides based on the ftrst overtone of the 0 - H stretching vibration that absorbs radiation at about 7100 cm] (1.4 Jlm); and the determination of esters, ketones, and carboxylic acids based on their absorption in the region of 3300 to 3600 cm-] (2.8 to 3.0 Jlm). The absorption in this last case is the first overtone of the carbonyl stretching vibration. NIR spectrophotometry is also a valuable tool for identification and determination of primary and secondary amines in the presence of tertiary amines in mixtures. The analyses are generally carried out in carbon tetrachloride solutions in IO-cm cells. Primary amines are determined directly by measurement of the absorbance of a combination N - H stretching band at about 5000 cm-' (2.0 Jlm); neither secondary nor tertiary amincs absorb radiation in this region. Primary and secondary amines have several overlapping absorption bands in the 3300 to 10,000 cm-' (I to 3 Jlm) region due to various N -H stretching vibrations and their overtones, whereas tertiary amines can have no such bands. Thus. one of these bands gives the second·

I"For example. ~ee.\1. A. Arnvld. J J BurmeIster. dnd G. W. SOl;)I!. An a l L Zhang. ( j \ \ ' . Small. and \1. A.. :\cncussiollS of the theory and practice of Raman spectroscopy. see J. R. Ferraro, K. Nakamoto, and C. \V. Brown, Inr wduclor v Rllman SpedTOsclJpl·. 2nd ed" San Diego: Academic Pre

MH,'

+ CH4

+ MH

-->

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C,H5 + + MH

-->

M+ + C,H6

C,H5'

+ C 2H 4

proton transfer proton transfer hydride transfer

(b)

20B-2 Chemical Ionization Sources and Spectra

FIGURE 20-4 Electron-impact mass spectra of (a) methylene chloride and (b) 1-pentanol.

Abundance of Other Isotopes Relative to 100 Parts of the Most Ahundant"

Most Abundant Isotope

Element' Hydrogen Carbon Nitrogen Oxygen

'H

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associated with a particular sample. The results are reported to the user, and if desired. the reference spectra can be displayed on a monitor or printed for visual comparison.

200-2

Analysis

Mass Spectral

of Mixtures

by Hyphenated

Methods

Applications

Although ordinary mass spectrometry is a powerful tool for thc identification of pure compounds. its usefulness for analysis of all but the simplest mixtures is limited because of the immense number of fragments of differing m lz values produced. It is often impossible to interpret the resulting complex speetrum. For this reason, chemists have developed methods in which mass spectrometers are coupled with various efficient separation devices in so-called hyphena ted methods. Chrom atography-M ass

Spectrom etry

Gas chromatography-mass spectrometry (GC/MS) has become one of the most powerful tools available for the analysis of complex organic and biochemical mixtures. In this application. spectra are collected for compounds as they exit from a chromatographic column. These spectra are then stored in a computer for subsequent processing. Mass spectrometry has also been coupled with liquid chromatography (LC/MS) for the analysis of samples that contain nonvolatile constituents. A major problem that had to be overcome in the development of both of these hyphenated methods is that the sample in the chromatographic column is highly diluted by the gas or liquid carrying it through the column. Thus, methods had to be developed for removing the diluent before introducing the sample into the mass spectrometer. Instruments and applications of GC/MS and LC/MS are described in Sections 27B-4 and 28C-6, respectively. Capillary Electrophoresis-M ass

directly into an electrospray ionization device. and the products then enter a quadrupole mass filter for analysis. Continuous ftow FAB has also been used for ionization in some applications. Capillary electrophoresis-mass spectrometry is discussed in more detail in Section 30B-4

Spectrom etry

The first report on coupling capillary electrophoresis with mass spectrometry was published in 1987.oxSince then. it has become obvious that this hyphenated method will become a powerful and important tool in the analysis of large biopolymers. such as proteins, polypeptides, and DNA species. In most of the applications reported to date, the capillary effluent is passed

.:~1. A,. Oli\ares, N. T Nguyen. N. T. '(onkcr, and R. D. Smith. Ana l. Chern., 1987,51),1230. See also R. D. Smith. 1. A. Olivares, N. T Nguyen. and H. R Hudseth, Ana l. Chern .. 1988.60,436

of Tandem M ass Spectrom etry

Dramatic progress in the analysis of complex organic and biological mixtures began when the mass spectrometer was first combined with gas chromatography and subsequently with liquid chromatography. Tandem mass spectrometry offers some of the same advantages as GC/MS and LC/MS but is significantly faster. Separations on a chromatographic column are achieved in a time scale of a few minutes to hours, but equally satisfactory separations in tandem mass spectrometers are complete in milliseconds. In addition. the chromatographic techniques require dilution of the sample with large excesses of a mobile phase and subsequent removal of the mobile phase, which llreatly enhances the probability of introduction of interferences. Consequently, tandem mass spectrometry is potentially more sensitive than either of the hyphenated chromatographic techniques because the chemical noise associated with its use is generally smaller. A current disadvantage of tandem mass spectrometry with respect to the other two chromatographic procedures is the greater cost of the required equipment; this gap appears to be narrowing as tandem mass spectrometers gain wider use. For some complex mixtures the combination of GC or LC and MS does not provide enough resolution. In recent years, it has become feasible to couple chromatographic methods with tandem mass spectrometers to form GC I MS I MS and LC I MS I MS systems.29 There have also been reports of LC/MS" instruments.'o To date, tandem mass spectrometry has been applied to the qualitative and quantitative determination of the components of a wide variety of complex materials encountered in nature and industry. Some examples include the identification and determination of drug metabolites, insect pheromones, alkaloids in plants, trace contaminants in air. polymer sequences. :"For recent JL:\'dopments in LC~fSil\.IS. See R. Thomas, Specrroscopy. 2001, 16, 28 ·'tlS ee. for example. 1. C A. WUllloud, S. R. GratL B. M. Gamble, and K. A. Wolnik. Ana lysr. 2004.129.150; E. W. Taylor. W lia. M. Bush, and G. O. O\)llinger, Ana l. Chern .. 2002. 74. 3232: L. Ho\\.ells and M. 1. Sauer. A na(nl, 2 0 0 L /26.155.

petrochemicals, polychlorinated biphenyls, prostaglandins. diesel exhausts. and odors in air. One of the most promising areas of applications is that of protea mics, the study of proteins produced by a cell or by a species." 20E

QUANTITATIVE APPLICATIONS OF MASS SPECTROMETRY

Applications of mass spectrometry for quantitative analyses fall into two categories. The first involves the quantitative determination of molecular species or types of molecular species in organic, biological, and occasionally inorganic samples. The second involves the determination of the concentration of elements in inorganic and, less commonly, organic and biological samples. In the first type of analysis, all of the ionization sources listed in Table 20-1 are used. Mass spectroscopic elemental analyses, which are discussed. in detail in Chapter 11, are currently based largely on inductively coupled plasma sources, although glow discharge, radio-frequency spark, laser, thermal, and secondary ion sources have also found use. 20E-1 Quantitative of Molecular

Determination

Species

Mass spectrometry has been widely applied to the quantitative determination of one or more components of complex organic (and sometimes inorganic) systems such as those encountered in the petroleum and pharmaceutical industries and in studies of environmental problems. Currently. such analyses are usually performed by passing the sample through a chromatographic or capillary electrophoretic column and into the spectrometer. With the spectrometer set at a suitable m lz value, the ion current is then recorded as a function of time. This technique is termed selected ion monitoring. In some instances, currents at three or four m lz values are monitored in a cyclic manner by rapid switching from one peak to another. The plot of the data consists of a series of peaks, with each appearing at a time that is characteristic of one of the several components of the sample that yields ions of the chosen value or values for m lz. Generally. the areas under the peaks are directly proportional to the component concentrations and are used for determinations. In this type of

procedure, the mass spectrometer simply serves as a sophisticated selective detector for quantitative chroma togra phic or electrophoretic a na lyses. Further details on quantitative gas and liquid chromatography are given in Sections 27B-4 and 28C-6. The use of a mass spectrometer as a detector in capillary electrophoresis is described in Section 30B-4. In the second type of quantitative mass spectrometry for molecular species, analyte concentrations are obtained directly from the heights of the mass spectral peaks. For simple mixtures, it is sometimes possible to find peaks at unique m lz values for each component. Under these circumstances. calibration curves of peak heights versus concentration can be prepared and used for analysis of unknowns. More accurate results can ordinarily be realized, however, by incorporating a fixed amount of an internal standard substance in both samples and calibration standards. The ratio of the peak intensity of the analyte species to that of the internal standard is then plotted as a function of analyte concentration. The internal standard tends to reduce uncertainties arising in sample preparation and introduction. These uncertainties are often a major source of indeterminate error with the small samples needed for mass spectrometry. Internal standards are also used in GC/MS and LC/MS. For these techniques, the ratio of peak areas serves as the analytical variable. A convenient type of internal standard is a stable, isotopically labeled analog of the analyte. Usually, labeling involves preparation of samples of the analytc in which one or more atoms of deuterium, carbon-13, or nitrogen-iS have been incorporated. It is then assumed that during the analysis the labeled molecules behave in the same way as do the unlabeled ones. The mass spectrometer easily distinguishes between the two. Another type of internal standard is a homolog of the analyte that yields a reasonably intense ion peak for a fragment that is chemically similar to the analyte fragment being measured. With low-resolution instruments, it is seldom possible to locate peaks that are unique to each component of a mixture. In this situation. it is still possible to complete an analysis by collecting intensity data at a number of m lz values that equal or exceed the number of sample components. Simultaneous equations are then developed that relate the intensity of each m lz value to the contribution made hy each component to

U l Tutoria l: Learn more about quantitative applicaIQj tions of MS.

this

intensity.

the

desired

chemometric principal

equations

analysis

provides

In environmental

Alternatively,

such as partial

least squarcs

ing use or

are used.

of quantitative

mass spectral

just described

2% and 10% relative. considerably

the mixture ponents,

analyzed

For gaseous

ranges accuracy

on the complexity

and the nature

hydrocarbon

ing five to ten components, mole percent

usually

The analytical

depending

being

measure-

mixtures

absolute

of

of its com-

errors

contain-

of 0.2 to 0,8

are typical.

of TOF,

transform

analysis.

ionization

tion

and

methods

quantitative

nated

diphenyl

water

disinfection,

ethers,

isms

carried

now

compounds

of interest

In forensic are widely

for drugs

etry tended dustrial

materials

quantitative many

diverse

vironmental

areas,

industrial

samples,

materials.

is widely

has been the method

techniques

such

powerful

application,

the

products

for polymer sample heating

of a direct

a single fragment:

natural

rubber,

styrene

from polyethylene,

can

molecular

the

for analyon the

from

isoprene

polystyrene,

can provide

from

In the tandem

which depend

in

temperature.

Studies

information

regard-

bonds,

clinical

as well as the ap-

mass distribution.

mass spectrometry

plication,36

GC/MS

The

urinary

tools

metabolic

disorders.

becoming

the standard

for metabolic

disease.'7

are replacing

Many trometry been

other

20·Z

How do the spectra for electron-impact, sources differ from one another"

ZO-3

Describe the difference desorption sources.

ZO-4

The following figure impact source.

enzymes

ever, intact

proteins

been

directly

try."

Electrospray

spectrometry

by tandem

ionization

field Fourier useful

transform

is now playing

of each'!

and chemical

ionization

is a simplified

field ionization

diagram

sources

of a commercially

and field

available

electron-

~

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Accelerating plates and slit

(a)

MS

immunological determinaof mass

(b)

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how-

fragments

have

to

Mass

a magnetic

x

*20-6

and target

so that elec-

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SS (sample

source)

will

to a molecule

that diffuses

toward

the filament

and is ion-

instrument

was operated

energy"

sector

3

What

range

tween

16 and 250, for singly charged

What

Calculate charged

of field strengths

would

range

of accelerating

with an accelerating

to focus the CH,

be required

+

voltage

on the detector.

to scan the mass range

ions, if the accelerating

\)5. D. Richardson, Annl. Chen!. 2004, 7n, 3337 '~w.D. Smith. Anill. Chl'm .. 2002. 7-1. 462.-\ Boca Raton.

the accelerating in Example

The ion-accelerating

would

be required

voltage

be-

is held

voltage

that would

be required

an instrument

to direct

that is identical

in a particular

quadrupole

that the initial

of the rod assembly"

plane

Assume

ion to travel velocitv

is the

of the ion

is zero.

On page 288 a qualitative

xz

singly to the one

mass spectrometer

15.0 em length

in the

is

20-·t voltage

cyclohexane

direction

to scan the mass

ions, if the field strength

5.00 V How long will it take a singly charged in the:: ZO-8

voltages

16 and 250, for singly charged

ions of mass 7,500 through

described

*ZO· 7

"'See D. H. Chace. Ch01/. Rev.. 2 0 0 1 . IOJ. ~-l5 "K. C Kooky. Chll. B/ochem .. 2003. 36 . .171. ;'G. E. Reid and S. A. ~teLuckcy. 1. .\fa5S Spec(ron! ,2002 . .17. 6fi:;

the filament

at the point

10 V, a field of 0.126 T was required

range between held constant?

with high

a major role in the field of

of Muss Spedrometry.

between

with molecules

constant? (b)

spectromeappears

When (a)

with

Recently,

MS/MS

must be applied

What will happen ized at point P?

3.00

particularly

determinations.

voltage interacting

spec-

has always

mass

What trons

have 70 c V of kinetic

proteomics.

Applica tions

What are the advantages

now

and tandem

in conjunction

in such

gaseous

__

babies

from digestions

and large protein

analyzed

are

newborn

identification, as trypsin.

between

to

and toxicology.

derived

such

used

MS methods

applications

in protein

differ"

field ionization,

of having

Mass spectrometry

of peptides

proteolytic

suspected

in quantitative

biological

important

he particularly

ap-

drug monitoring

are appearing.

in the analysis

increasing

some traditional

methods

tions involving

sources

FIlament]

is widely

LC/MS

and desorption

Mass spec-

arc finding

The

using spreadsheets.

in the forensic and

for screening

with an asterisk.

horses

LC/N1$.,

Tandem

marked

eviden-

GC/MS,

of patients

for problems

body fluids

in testing

and fibers."

technique

profiles

I'See J. Yinon. Forensit' FL eRe Press. 1995 l= See P. tv!. Peacock and C ;-..:.McEwen, AWl!. Chern .. 2004, 7(" J.t17~ H. Pasch and W. Schrcpp .. lUl.D/[0,..- ,Has.\" Speetm m ern' of SynrhclI( P olymers. lkrlin: Spring,er-\'crlag. ~()(J3

and GC I MS

and in examining

laboratory,

with this icon are best solved

How do gaseous

laboratory.

magnetic

ethylene

from Kel-F. Other

products,

of the various

In this and

yield es-

and kind on the pyrolysis

ing the stabilities

are

be performed

and CF,=CFCI

effects

sub-

Some polymers

for example,

yield two or more

of temperature

pyrolyzed,

into GC/MS

inlet system.

sentially

polymeric with GC/MS

characterization.

is first

are admitted

sis. Alternatively,

proximate

complex combined

events,

Problems

20-1

and materials

fires, in analyzing

such as paints

and fluorometric

MS are very

of

surfactants,

security.'"

for drugs,

at the end of the hook

spectrometric

explosives

athletes

~

microorgan-

mass

are now indispensable

methods

of size exclusion

with MALDI

methods

mass spec-

of choice. 32Hyphenated

for characterizing

also quite popular

amount

to

polymeric

MALDI

as the combination

Pyrolysis

polymers

en-

used for the characteri-

applications,

and liquid chromatography

probe

polymers,

and increasingly

of high-molecular-mass

In recent

trometry

volatile

to

byproducts

mass spectrometry

in setting

materials

widely

is also used to determine

in detecting

at equine

trometers

analyze

and analysis

stances.

years,

applied

materials.

Mass spectrometry zation

has been

including

and forensic

and on in-

In recent

spectrometry

tiary

of mass spectromproducts

characterization:

mass

biological

applications

to focus on petroleum

using

in homeland

science,

used

and hair, in testing The early quantitative

out

are provided

polybromi-

and various

Mass spectrometry

* Answers

Detec-

of such

algal toxins,

arsenic,

Fourier

to desorp-

as MALDp3

pharmaceuticals,

pesticides,

ether,

are

in addition

such

increas-

and

as perfluoroorganics,

methyl-r-butyl methods.

has been

ion-trap,

determination

contaminants

used by arsonists

Applications

there

quadrupole,

mass spectrometers

tion

diverse

by the procedure

between varies

then

information.

and Accuracy

precision

ments

these

methods

component

Precision

The

Solving quantitative

(positive

discussion dc potential

described plane)

how a positive

of a quadrupole

ion would

behave

mass filter. Con-

of

struct a similar argument for the behavior of positive ions in the tive dc potential plane).

yz

plane (nega-

20-9 Why do double-focusing mass spectrometers give narrower peaks and higher resolutions than single-focusing instruments'! 20-10 Discuss the differences between quadrupole Fourier transform ICR mass spectrometers.

ion-trap mass spectrometers

Challenge

Problem

20-19 Figure 20-27 shows the mass spectrum of the same compound from an e1ectronimpact ionization source and an ionization source.

!OO

and

*20-11 Calculate the resolution required to resolve peaks for (a) CH,N (ell = 28.0187) and N; (At = 28.0061). (b) C,H"' p( = 28.0313) and CO' (ell = 27.9949). (c) CjH,N1' (JH = 85.0641) and C,H90+ (At = 85.0653). (d) androst-4-en-3,17,-dione (M') at m lz = 286.1930 and an impurity at 286.1240.

SO

""~ C

-0

60

~ "

40

>

;;

~ 20

~

20-12 What mass differcnces can just be resolved at m values of 100, 500, 1500,3000, and 5000 if the mass spectrometer has a resolution of (a) 500. (h) WOO. (c) 3000. (d) 5000?

0 0

*20-13 Calculate the ratio of the (M + 2)' to M' and the (M + 4)+ to M peak heights for (a) ClllH,Br" (b) C,H7CIBr, (c) C6H"C1,. 20-14 In a magnetic sector (single-focusing) mass spectrometer, it might be reasonahle under some circumstances to monitor one mlz value, to then monitor a second m lz. and to repeat this pattern in a cyclic manner. Rapidly switching between two accelerating voltages while keeping all other conditions constant is called pea k ma tching.

(a) Derive a general expression that relates the ratio of the accelerating voltages to the ratio of the corresponding m lz values. (b) Use this equation to calculate m lz of an unknown peak if m lz of the ion used as a standard, CF1', is 69.00 and the ratio of VU"knuwn/V;"nd'Cd is 0.965035. (c) Based on your answer in part (b), and the assumption that the unknown is an organic compound that has a mass of 143, draw some conclusions about your answer in part (b), and about the compound. 20-15 Measuring the approximate mass of an ion without using a standard can he accomplished via the following variant of the peak-matching technique described in Prohlcm 20-14. The peak-matching technique is used to alternately cause the pion and the (P + I) + ions to reach the detector. It is assumed that the difference in mass hetween p+ and (P + I) - is due to a single 'JC replacing a 12Catom. (a) If the accelerating voltage for (P + 1)+ is laheled V, and that for P' is V" derive a relationship that relates the ratio V,W, to the mass of P'. (h) If V,W, = 0.987753, calculate the mass of the P+ ion. 20-16 Discuss the major differences between a tandem-in-space mass spectrometer and a tandem-in-time mass spectrometer. Include the advantages and disadvantages of each type. 20-17 Identifv the ions responsible for the peaks in the mass spectrum shown in Figure 20-20b. 20-18 Identifv the ions responsihle for the four peaks having greater mass-to-charge ratios than the M - peak in Figure 20-4a.

IIKl SO

" 'j

~

§

60

"

40

-fl > .~

"iJ

x

20

0 0

FIGURE 20-27 Electron-impact spectrum (a) and chemical ionization spectrum (b) of the same biologically important compound. (From H. M. Fales, H. A. Lloyd, and G. A. W. Milne, J. Amer, Chem . Soc., 1970,92,1590-1597. American Chemical Society.)

(a) Which mass spectrum would be hest for determining the molecular mass of the compound? Why? (b) Which mass spectrum would he best for determining the chemical structure') Whvo (c) Th; electron-impact source was a pulsed source used with a Tal' mass analvzer. If the flight tube were 1.0 m long and the accelerating voltage were 3000 V. what \~ould the flight time be for the ion at m/z = 58', (d) For two ions of m/z values m,/z and m,/z. derive an equation for the difference in flight times .lIF as a function of the two masses. the charges. and the accelerating voltage. (e) For the same Tal' analyzer as in part (c). calculate the difference in flight times between ions of m lz = 59 and m /z = 58.

(f) To get more structural information, the compound of Figurc 20-27 was subjected to tandem mass spectrometrv. Which ionization source, electronimpact or chemical. would be most suitable for this purpose? Why" (g) Using the ionization source chosen in part (f), describe the types of mass spectra that could he obtained from an MS/MS experiment by: (I) holding the first mass analyzer constant and scanning the second analyzer. (2) scanning both analyzers with a small m lz offset between them. (3) scanning the first analyzer while holding the second analyzer constant. (4) scanning the second mass analyzer for every mass selected by the first analyzer.

21A

u r fa c e

INTRODUCTION TO THE STUDY OF SURFACES

Before considering how surfaces are characterized, wc first need to define what constitutes the surface of a solid that is in contact with a gaseous or liquid second phase.

h a r a c te r iz a tio n

y .$pe~tro~copy

I n your answer, use features of the mass spectrum of Figure 20-27 to illustrate your description.

n d :M ic r o s c o p y

he~ ur fa ce

';0-:'

ola

solid in conta ct

'f'

.

I

sf.Witia lly fr tJ m the inter ior

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usua lly

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br a nes.

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methods. fa ces,

liquid-ga s

r3l

pr oper ties, mem-

dea ls with the investiga tion

the empha sis

some of the techniques

to other inter fa ces,

a nd technol-

mecha nisms,

of biologica l

by spectr oscopic

Although

thin-film

embr ittlement

a nd functions

of solid suifa ces

is often

including

a lso a ids in under -

cor r osion a nd a dhesion

(Lnd beha vior

of fields,

sensor development

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"p g y. Such cha r a cter iza tion

a ctivity

pr oper ties.

of t/lese sur fa ce pr oper ties

~ eter oge,,: ~ ous ca ta lysis,

sta nding

of the solid both

a nd physica l

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"? pplica ti0tlf,

with a liqdiffer s sub-

a nd micr oscopic is on solid sur -

a r e a lso a pplica ble

such a s liquid-liquid

a nd

inter fa ces.

Throughout this chapter, this logo indicates an opportunity for online self-study at www .t h o m s o n e d o .c o m / c h e m i s t r y / s k o o g , linking you to interactive tutorials, simulations, and exercises. ~

We will consider a sur fa ce to be the boundary layer between a solid and a vacuum, a gas, or a liquid. Generally, we think of a surface as a part of the solid that differs in composition from the average composition of thc bulk of the solid. By this definition, the surface comprises not only the top layer of atoms or molecules of a solid but also a transition layer with a nonuniform composition that varies continuously from that of the outer layer to that of the bulk. Thus, a surface may be several or even several tens of atomic layers deep. Ordinarily, however, the difference in composition of the surface layer does not significantly affect the measured overall average composition of the bulk because the surface layer is generally only a tiny fraction of the total solid. From a practical standpoint, it appears best to adopt as an operational definition of a surface that volume of thc solid that is sampled by a specific measurement technique. This definition recognizes that if we use several surface techniques, we may in fact be sampling different surfaces and may obtain different, alheit useful, results.

During the last century, a wide variety of methods have heen developed for characterizing surfaces. The classical methods, which are still important, provide much useful information about the physica l nature of surfaces but less ahout their chemical nature. These methods involve obtaining optical and electron microscopic images of surfaces as wcll as measurements of adsorption isotherms. surface areas, surface roughness, pore sizes, and reflectivity. Beginning in the 1950s, spectroscopic surface methods began to appear that provided information about the chemical nature of surfaces. This chapter is divided into several major parts. After an introduction to surface methods in Section 21B. we then discuss electron spectroscopic techniques, ion spectroscopic techniques. and photon spectroscopic tcchniques to identify the chemical species making up

the surface of solids and to determine their concentrations. Sections 21F and 21G describe modern microscopic methods for imaging surfaces and determining their morphology and their physical features.

Primary Beam

Detected Beam

I n fo r m a tio n

X-ray photons

Electrons

Chemical composition Chemical structure

Electrons

Chemical composition

Electron energy-lossspectroscopy (EELS)

Electrons or X-ray photons Electrons

Electrons

Electron microprobe (EM) Secondary-ion mass spectrometry (SIMS)

Electrons Ions

X-ray photons Ions

Ion-scattering spectroscopy (ISS) and Rutherford backscattering

Ions

Ions

Chemical structure Adsorbate binding Chemical composition Chemical composition Chemical structure Chemical composition

Laser-microprobe

Photons

Ions

Method and Acronym X-ray photoelectron spectroscopy (XPS). or electron spectroscopy

218

analysis (ESCA) Auger electron spectroscopy (AES)

SPECTROSCOPIC SURFACE METHODS

Generally, the chemical composition of the surface of a solid differs, often significantly, from the interior or bulk of the solid. Thus far in this text, we have focused on analytical methods that provide information about bulk composition of solids only. In certain areas of science and engineering, however, the chemical composition of a surface layer of a solid is much more important than is the bulk composition of the material. Spectroscopic surface methods provide both qualitative and quantitative chemica l information about the composition of a surface layer of a solid that is a few tenths of nanometers (a few angstroms) to a few nanometers (tens of angstroms) thick. In this section we describe some of the most widely used of these spectroscopic techniques'

21 B-1 Spectroscopic

Surface

Experiments

Figure 21-1 illustrates the general way spectroscopic examinations of surfaces are performed. Here, the solid sample is irradiated with a pr ima r y bea m made up of photons, electrons, ions, or neutral molecules. Impact of this beam on a surface results in formation of a seconda r y bea m also consisting of photons, electrons, molecules, or ions from the solid surface. The secondary beam is detected by the spectrometer. Note that the type of particle making up the primary beam is not necessarily the same as that making up the secondary beam. The secondary beam. which results from scattering, sputtering, or emission, is then studied by a variety of spectroscopic methods. The most effective surface mcthods are those in which the primary beam. the secondary beam, or both is made up of either electrons, ions, or molecules and not photons because this limitation assures that the measurements are restricted to the surface of a sample and not to its bulk. For example, the maximum penetration depth of a beam of J-ke V electrons or ions is For a d~scription of surface spectroscopic techniques, see Sur fa ce Ana {ylis - Th e P r in cip a l Tech n iq u es, 1. C Vickerman. ed .. Chichester, CK: Wiley. 1997: Specr mscopy of Sur fa ces, R. G. H. Clark and R. E. Hester. cds., 'ew York: \\'ile\. 19RB.

for chemical

FIGURE 21-1 General scheme for surface spectroscopy. Beams may be photons. electrons. ions. or neutral molecules.

approximately 2.5 nm (25 A), whereas the penetration depth of a photon beam of the same energy is about 1000 nm (l0' A). Thus, for many methods that involve two beams of photons, such as X-ray fluorescence (see Chapter 12). infrared reflection spectroscopy (see Chapter 17), ellipsometry, or resonance Raman spectroscopy (see Chapter 18), precautions must be taken to limit the measurements to a surface layer. The techniques involving primary and detected (secondary) beams of photons discussed in this section are surface plasmon resonance, nonlinear optical spectroscopy, and ellipsometry. There are several ways to classify surface techniques. Many of these are based on the nature of the primary and detected beams. Table 21-1 lists the most widely used spectroscopic techniques. These will be discussed further in this section.

21B-2

Sampling

Surfaces

Regardless of the type of spectroscopic surface method being used, three types of sampling methods are employed. The first involves focusing the primary beam on a single small area of the sample and observing the secondary beam. Often, the spot is chosen visually with an optical microscope. The second method involves mapping the surface, in which a region of the surface is scanned by moving the primary beam across the surface in a r a ster pa tter n of measured increments and observing changes in the secondary beam that result. The mapping may be linear or two dimensional. The third technique is known as depth profiling. Here, a beam of ions from an ion gun etches a hole in the surface by sputtering. During this process a finer primary beam produces a secondary beam from the center of the hole. which provides the analytical data on the surface composition as a function of depth.

mass

spectrometry (LMMS) Surface plasmon resonance (SPR)

Atomic structure Chemical composition

Chemical structure Photons

Photons

Sum frequency generation (SFG)

Photons

Photons

Ellipsometry

Photons

Photons

Most of the surface spectroscopic techniques require a "vacuum" environment. High vacuum conditions ensure that the particles used have long mean free paths to interact with the surface of interest. The vacuum environment also keeps the surface free from adsorbed gases during the surface analysis experiment. The exceptions to the high vacuum requirement are the photon-photon techniques given in the last three rows of Table 21-1. These allow examination of surfaces under conditions more akin to those used in applications such as catalysis. sensing, and corrosion studies. A problem frequently encountered in surface analyses is contamination of the surface by adsorption of components of the atmosphere, such as oxygen, water, or carbon dioxide. Even in a vacuum, this type of contamination occurs in a rclatively short time. For example, at a pressure of Hj' torr (1 torr = 133 Pal, a monolayer of gas molecules will cover a clean surface in just 3 s. At 10-; torr. coverage occurs in about 1 h. At 10-10 torr. 10 h is required.' Because of adsorption

Composition

and concentration

of thin films Interface structure. adsorbate binding Thin-film thickness

problems, provisions must often be made to clean the sample surface, usually in the chamber used for irradiating the sample. Cleaning may involve baking the sample at a high temperature; sputtering the sample with a beam of inert gas ions from an electron gun; mechanical scraping or polishing of the sample surface with an abrasive; ultrasonic washing of the sample in various solvents; and bathing the sample in a reducing atmosphere to remove oxides. In addition to atmospheric contamination, the primary beam itself can alter the surface as a measurement progresses. Damage caused by the primary beam depends on the momentum of the primary beam particles. Thus, of the beams listed in Table 21-1, ions are the most damaging and photons the least.

h

III

Tutor ia l:

Learn more ahout surface methods.

The lirst three methods listed in Table 21-1 arc based on detection of emitted electrons produced by incident beams. Here. the signal from the analvte is encoded in a beam of electrons rather than photons. The spectrometric measurements then consist of the determination of the power of this beam as a function of the energy h v or frequency v of the electrons. This type of spectroscopy is termed electr on spectr oscopy.

Although the basic principles of electron spectroscopy were well understood a century ago, the widespread application of this technique to chemical problems did not occur until relatively recently. Studies in the field were inhibited by the lack of technology necessary for performing high-resolution spectral measurements of electrons having energies varying from a few tenths to several thousand electron volts. By the late 19605, this technology had developed, and commercial electron spectrometers began to appear in the marketplace. With their appearance, an explosive growth in the number of publications dcvoted to electron spectroscopy occurred.' There are three types of electron spectroscopy for the study of surfaces. The most common type, which is based on irradiation of the sample surface with monochromatic X-radiation, is called X-r a y photoelectr on spectr oscopy (XPS). It is also termed electr on spectr oscopy for chemica l a na lysis. Much of the material in this chapter is devoted to XPS. The primary beam for photoelectron spectroscopy can also consist of ultraviolet photons, in which case the technique is called ultr a violet photoelectr on spectr oscopy (UPS). Here, a monochromatic beam of ultraviolet radiation causes ejection of electrons from the analyte. This type of electron spectroscopy is not as common as the other two, and we shall not discuss it further. The second type of electron spectroscopy is called Auger (pronounced oh-ZHAY) electr on spectr oscopy (AES). Most commonly, Auger spectra are excited by a beam of electrons, although X-rays are also used. Auger spectroscopy is discussed in Section 21C-2. The third type of electron spectroscopy is electron energy-loss spectroscopy (EELS), in which a low-energy beam of electrons strikes the surface and excites vibrations. The resultant energy loss is then detected and related to the vibrations excited. We briefly describe EELS in Section 21C-3. Electron spectroscopy is a powerful tool for the identification of all the elements in the periodic table with the exception of hydrogen and helium. More important, the method permits determination of the oxidation state of an element and the type of species to which it is bonded. Finally, the technique provides useful information about the electronic structure of molecules. see 1. F. \Vatts and 1. \Volstenholme, An Intr oduction to Sur fa ce Ana (vsLs by XP S a nd AE S, Chichester. CK: Wiley, 2003; D Briggs and M. P. Scah, P r a ctica l Su r fa ce An a lysis h ,\ Au g er a n d X·r a y P hotoelectr on Spectr oscop-",,'. 2nd ed .. Chichester. UK: \Viky, 1990. 3

For additional

information,

Electron spectroscopy has been successfully applied to gases and solids and more recently to solutions and liquids. Because of the poor penetrating power of electrons, however, these methods provide information about solids that is restricted largely to a surface layer a few atomic layers thick (2 to 5 nm). Usually, the composition of such surface layers is significantly different from the average composition of the entire sample. Indeed, the most important and valuable current applications of electron spectroscopy are to the qualitative analysis of the surfaces of solids, such as metals, alloys, semiconductors, and heterogeneous catalysts. Quantitative analysis by electron spectroscopy finds somewhat limited applications.

FIGURE 21-2 X-ray photoelectron spectrum of tetrapropylammoniumdifluoridethiophosphate. The peaks are labeled according to the element and orbital from which the emitted electrons originate.

21C-1 X-ray Photoelectron Spectroscopy

It is important to emphasize the fundamental difference between electron spectroscopy (both XPS and AES) and the other types of spectroscopy we have thus far encountered. In electron spectroscopy, thl'l ~netic energy of emitted electrons is recorded. The spectrum thus consists of a plot of the number of emitted electrons, or the power of the electron beam, as a function of the energy (or the frequency or wavelength) of the emitted electrons (see Figure 21-2). P rinciples

of X P S

The use of XPS was pioneered by the Swedish physicist K. Siegbahn, who subsequently received the 1981 Nobel Prize in Physics for his work.· Siegbahn chose to call the technique electron spectroscopy for chemical analysis (ESCA) because, in contrast to the other two electron spectroscopies, XPS provides information about not only the atomic composition of a sample but also the structure and oxidation state of the compounds being examined. Figure 21-3 is a schematic representation of the physical process involved in XPS. Here, the three lower lines labeled E b , E b , and E;; represent energies of the inner-shell K and L electrons of an atom. The upper three lines represent some of the energy levels of the outer shell, or valence, electrons. As shown in the illustration, one of the photons of a monochromatic X-ray beam of known energy h v displaces an electron ~For a brief description of the hislory of XPS, see K. Siegbahn, Science, 1981, 217, 111: D. Nt Hercules, 1. C her n. E duc., 2004, 81, 1751. For monographs, see S. Hufner, P hotoelectr on Spectr oscopy: P r inciples a nd Applica tions, Berlin: Springer-Verlag, 1995; T. L. Barr, M oder n E SC A: The P r inciples a nd P r a ctice of X-Ra y P hotoelectr on Spectr oscopy. Boca Raton, FL: eRe Press, 199..t.

500 Binding

400 energy

e - from a K orbital of energy E b • The process can be represented as

where A can be an atom, a molecule, or an ion and AU is an electronically excited ion with a positive charge one greater than that of A.

Eb

Schematic representation of the ESCA process. The incident beam consists of monoenergetic X-rays. The emitted beam is made up of electrons. FIGURE

21-3

The kinetic energy of the emitted electron E k is measured in an electron spectrometer. The binding ener gy of the electron E b can then be calculated by means of the equation

In this equation, IV is the IV ork function of the spectrometer, a factor that corrects for the electrostatic environment in which the electron is formed and measured. Various methods are available to determine the value of IV. The binding energy of an electron is characteristic of the atom and orbital that emit the electron. Figure 21-2 shows a low-resolution, or survey, XPS spectrum consisting of a plot of electron-counting rate as a function of binding energy E b . The analyte consisted of an organic compound made up of six elements. With the exception of hydrogen, well-separated peaks for each of the elements can be observed. In addition, a peak for oxygen is present, suggesting that some surface oxidation of the compound had occurred. Note that, as expected, the binding energies for Is electrons increase with atomic number because of the increased positive charge of the nucleus. Note also that more than one peak for a given element can be observed: thus peaks for both 2s and 2p electrons for sulfur and phosphorus can be seen. The large background count arises

because associated with each charactcristic peak is a tail of ejected electrons that ha\·c lost part of their energy by inelastic collisions within the solid sample. These electrons have lcss kinetic energy than their nonscattered counterparts and will thus appear at lower kinetic encrgies or higher binding energies (Equation 21-2). It is evident from Figure 21-2 that XPS provides a means of qualitative identification of the elements present on the surface of solids. Instrum entation

Instruments for electron spectroscopy are offered by several instrument manufacturers. Thesc products differ considerably in types of components. configurations. and costs. Some are designed for a single type of application, such as XPS, and others can be adapted to AES and UPS by purchase of suitable accessories. All are expensive ($300,000 to >$106). Electron spectrometers are made up of components whose functions are analogous to those encountered in optical spectroscopic instruments. These components include (1) a source; (2) a sample holder; (3) an analyzer, which has the same function as a monochromator; (4) a detector; and (5) a signal processor and readout. Figure 21-4 shows a typical arrangement of these components. Electron spectrometers generally require elaborate vacuum systems to reduce the pressure in all of the components to as low as 10-8 to 10-10 torrS

Sources. The simplest X-ray sources for XPS spectrometers are X-ray tubes equipped with magnesium or aluminum targets and suitable filters. The K a lines for these two elements have considerably narrower bandwidths (0.8 to 0.9 eV) than those encountered with higher atomic number targets; narrow bands arc desirable because they lead to enhanced resolution. Nonmonochromatic sources typically illuminate a spot a few centimeters in diameter. Relatively sophisticated XPS instruments, such as that shown in Figure 21-4. employ a crystal monochromator (Section 12B-3) to provide an X-ray beam having a bandwidth of about 0.3 e V. Monochromators eliminate bremsstrahlung background, thus improving signal-to-noise ratios. They also allow much smaller spots on a surface to be examined (spot sizes ~50 11m). 'Specifications for several representative commercial instruments are given in D. Nuble. AM /. C h er n . 1995, 67, 675A. For a perspc:ctive on commercial XPS instrumenlalion. set: M ... \_ Kelly. 1. C h e r n . F d u c 20(}4, 81.1716

Thc increased availability of synchrotron radiation in recent years has given XPS experimenters another useful source. The synchrotron produces hroadband radiation that is highly collimated and polarized. Such sources when used with a monochromator can provide a source of X-rays that is tunahle for photoelectron experiments.

Sample Holders. Solid samples are mounted in a fixed position as close as possible to the photon or clectron source and the entrance slit of the spectrometer (see Figure 21-4). To avoid attenuation of the electron beam, the sample compartment must be evacuated to a pressure of 10-5 torr or less. Often, however, much better vacuums (10-9 to 10-10 torr) are required to avoid contamination of the sample surface by substances such as oxygen or water that react with or are adsorbed on the surface. Gas samples are leaked into the sample area through a slit of such a size as to provide a pressure of perhaps 10-2 torr. Higher pressures lead to Jx"Cssive attcnuation of the electron beam, which is due to inelastic collisions: on the other hand, if the sample pressure is too low, weakened signals are obtained.

Analyzers. The analyzer consists of the collection lens or lenses and the electron energy analyzer, which disperses the emitted electrons according to their kinetic energy. The lens system usually allows a wide collection angle (-30') for high efficiency. In some angleresolved experiments, an aperture reduces the angles collected. Such experiments are used in depth-proliling studies. Typically, photoelectron experiments are carried out in constant analyzer energy mode, in which electrons are accelerated or retarded by the lens system to sOme user-defined energy as they pass through the analyzer (the pass energy, E in Figure 21-4). Often, pass energies of 5-25 eV will give high-resolution spectra, and 100-200 eV pass energies are used for survey scans. The signal intensity decreases as the pass energy decreases. Most energy analyzers are of the type illustrated in Figure 21-4, in which the electron beam is deflected by the electrostatic field of a hemispherical capacitor. The electrons thus travel in a curved path from the lens to the multichannel transducer. The radius of curvature depends on the kinetic energy of the electrons and the magnitude of the electrostatic field. An entire spcc-

21-4 Principle of a modern ESCA instrument using a monochromatic X-ray source and a hemispherical field spectrometer. FIGURE

trum is obtained by varying the field so as to focus electrons of various kinetic energies on the transducer. Transducers. Most modern electron spectrometers are based on solid-state, channel electron multipliers, which consist of tubes of glass that have been doped with lead or vanadium. When a potential difference of several kilovolts is applied across these materials, a cascade or pulse of 106 to 108 electrons is produced for each incident electron. The pulses are then counted electronically (see Section 4C). Several manufacturers are now offering two-dimensional multichannel electron detectors that are analogous in construction and application to the multichannel photon detectors described in Section 7E-3. Here, all of the resolution elements of an electron spectrum are monitored simultaneously and the data stored in a computer for suhsequent display. The advantages of such a system are similar to those realized with multichannel photon detectors. Data Systems. Modern XPS instruments have nearly all components under computer control. Thus. electron guns, ion guns, valves, lens voltages, sample position, and analyzer parameters are all selected by the computer. Current software on XPS instruments al-

lows many data-analysis options, including peak finding, peak identification, and peak intensity measurement. Many packages also include chemometric data analysis such as multivariate statistical processing and pattern recognition. A pplications

of

XPS

XPS provides qualitative and quantitative information about the elemental composition of matter, particularly of solid surfaces. It also often provides useful structural information.6 Qualitative Analysis. Figure 21-2 shows a low-resolution, wide-scan XPS spectrum, called a sur vey spectr u m, which serves as the basis for the determination of the elemental composition of samples. With a magnesium or aluminum K a source, all elements except hydrogen and helium emit core electrons having characteristic binding energies. Typically, a survey spectrum encompasses a kinetic energy range of 250 to 1500 eV. which corresponds to binding energies of about 0 to ~For reviews of applicatIons of XPS (and AES 1. Wolstenholme, An lmr o d u ctio fl to Su r /a ce Chichester. UK: Wiley. 2003: N, H. Turner C her n" 2000, 72. 9YR: 1998. 70, 129K 1996 Hercules, I C h f'/1 t.b lu c-. 200,t.sf, 1751

as w'ell). see J. F Walts and An a lysis b y XP S a n d AE S,

and 1. A. Schreifels, An a l 68. 309R. See also D. M

F I

Elementb

0 II

H I

H I

F-y-\~-o(~-T\H -2

Nitrogen (Is) Sulfur (15) Chlorine (2p) Copper (Is) Iodine (45) Europium (3d) • All shifts

afc

-1

0

*0' -2.0

+1 +4.5'

+2

+3

+5

F \ \

+7

I

*0

+3.8

I

/

+5.8

+4.5 +0.7

+6

+8.0

+5.1

*0 *0

+4

+9.5

+5.3

+6.5

H; /

\ \ \

/

+7.1

I\H \

+4.4

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in electron votts measured relative to the oxidation states indicated by (*). (Reprinted 28A. Copyright 1970 American Chemical Society.)

with permission from D. M. Hercuks.

Ana L C her n., 1970,42,

GType of electrons given in parentheses. C

Arbitrary

zero for measurement,

end nitrogen in NaN;.

dMiddle nitrogen in NaN,.

1250 eY. Every element in the periodic table has one or more energy levels that will result in the appearance of peaks in this region. [n most instances, the peaks are well resolved and lead to unambiguous identification provided the element is present in concentrations greater than about 0.1 %. Occasionally, peak overlap is encountered such as 0(15) with S b(3d) or AI(2s, 2p) with Cu(3s, 3p). Usually, problems due to spectral overlap can be resolved by investigating other spectral regions for additional peaks. Often, peaks resulting from Auger electrons are found in XPS spectra (see, for example, the peak at about 610 eV in Figure 21-2). Auger lines are readily identified by comparing spectra produced by two X-ray sources (usually magnesium and aluminum K a). Auger lines remain unchanged on the kinetic energy scale but photoelectron peaks are displaced. The reason for the behavior of Auger electrons will become apparent in the next section. Chemical Shifts and Oxidation States, When one of the peaks of a survey spectrum is examined under conditions of higher energy resolution. the position of the maximum depends to a small degree on the chemical environment of the atom responsible for the peak. That is, variations in the number of valence electrons, and the type of bonds they form, influence the binding energies of core electrons. The effect of the number of valence electrons and thus the oxidation state is demonstrated by the data for several elements shown in Table 21-2. Note that in each case. binding energies increase as the oxidation state becomes more positive. This chemica l shift can be explained by assuming that the attraction of the nucleus for a core electron is di-

minished by the presence of outer electrons. When one of these electrons is removed, the effective charge sensed for the core electron is increased, and an increase in binding energy results. , One of the most important applications of ~PS has been the identification of oxidation states of elements in inorganic compounds. Chemical Shifts and Structure. Figure 21-5 illustrates the effect of structure on the position of peaks for an element. Each peak corresponds to the 15 electron of the carbon atom indicated by dashes above it in the structural formula. Here, the shift in binding energies can be rationalized by taking into account the influence of the various functional groups on the effective nuclear charge experienced by the Is core electron. For example, of all of the attached groups, fluorine atoms have the greatest ability to withdraw electron density from the carbon atom. The effective nuclear charge felt by the carbon Is electron is therefore a maximum, as is the binding energy. Figure 21-6 indicates the position of peaks for sulfur in its several oxidation states and in various types of organic compounds. The data in the top row clearly demonstrate the effect of oxidation state. Note also in the last four rows of the chart that XPS discriminates between two sulfur atoms contained in a single ion or molecule. Thus, two peaks are observed for thiosulfate ion (S,o,"). suggesting different oxidation states for the two sulfur atoms. XPS spectra provide not only qualitative information about types of atoms present in a compound but also the relative number of each type. Thus, the nitro-

FIGURE21-5 Carbon 1s X-ray photoelectron spectrum for ethyl trlfluoroacetate. (From K. Siegbahn et aI., E S C A : A tom ic, M olecular, and S olid-S tate

S tudies by Means

of E lectron S pectroscopy, p. 21, Upsala: Almquist and Wiksells, 1967. With permission.)

162 I

I S'I SO RSH(2)H

I SOj'- SO}'H HRS ...• O(3)

RSR(3)H

(3)

RSO,R'H(9) RSOj-H

520/I--i RSiSO)RI----1 (3)

I

I Precision of I---l RS(SO,)R (4)

measurement

Quanlitative Applications. Once, XPS was not considered to be a very useful quantitative technique. However, there has been increasing use of XPS for determining the chemical composition of the surface region of solids.7 If the solid is homogeneous to a depth of several electron mean free paths, we can express the number of photoelectrons detected each second I as

/--I RSO; is)

ArSR(3)H RSSR (3) H I

gen Is spectrum for sodium azide (Na+Nj') is made up of two peaks having relative areas in the ratio of 2: 1 corresponding to the two cnd nitrogens and the center nitrogen, respectively. It is worthwhile pointing out again that the photoelectrons produced in XPS are incapable of passing through more than perhaps 1 to 5 nm of a solid. Thus, the most important applications of electron spectroscopy, like X-ray microprobe spectroscopy, are for the accumulation of information about surfaces. Examples of some of its uses include identification of active sites and poisons on catalytic surfaces, determination .of surface contaminants on semiconductors, analysis of the composition of human skin, and study of oxide surface layers on metals and alloys. It is also evident that the method has a substantial potential in the elucidation of chemical structure (see Figures 21-5 and 21-6). Information from XPS spectra is comparable to that from nuclear magnetic resonance (NMR) or [R spectroscopy. The ability of XPS to distinguish among oxidation states of an clement is noteworthy. Note that the information obtained by XPS must also be present in the absorption edge of an X-ray absorption spectrum for a compound. Most X-ray spectrometers, however, do not have sufficient resolution to permit ready extraction of this structural information.

I

RSS03-

I

I

I

162

164

166

FIGURE21-6 Correlation chart for sulfur 2s electron binding energies. The numbers in parentheses indicate the number of compounds examined. (Reprinted with permission from D. M. Hercules, A nal. C hem ., 1970, 42, 35A. Copyright 1970, American Chemical Society.)

where n is the number density of atoms (atoms cm -3) of the sample, 1> is the flux of the incident X-ray beam (photons cm" S'l), a is the photoelectric cross section for the transition (cm'/atom), e is the angular efficiency factor for the instrument, '7 is the efficiency of producing photoelectrons (photoelectrons/photon), A is the area of the sample from which photoelectrons are detected (em '), T is the efficiency of detection of

~For a review of 4uantitati\'e applications of XPS and AES, see K. W. :\ebesnv, B. L !\faschhoff, and 1'\. R. Armstrong, Ana l. C her n .. 1989,61. 469.-\. For a discussion of the reliability of XPS, see C 1. Powell. 1. C her n. E dtlC ".. 2004, 8/. 1734.

the photoelectrons, and I is the mean free path of the photoelectrons in the sample (cm). For a given transition, the last six terms arc constant, and we can write the atomic sensitivity factor S as

For a given spectrometer, a set of relative values of S can be developed for the elements of interest. Note that the ratio liS is directly proportional to the concentration n on the surface. The quantity I is usually taken as the peak area, although peak heights are also used. Often, for quantitative work, internal standards are used. Relative precisions of about 5 % are typical. For the analysis of solids and liquids, it is necessary to assume that the surface composition of the sample is the same as its bulk composition. for many applications this assumption can lead to significant errors. Detection of an element by XPS requires that it be present at a level of at least 0.1 %. Quantitative analysis can usually he performed if 5% of the element is present. 21 C-2

Auger Electron

Spectroscopy

In contrast to XPS, AES' is based on a two-step process in which the first step involves formation of an electronically excited ion A-* by exposing the analyte to a beam of electrons or sometimes X-rays. With X-rays, the process shown in Equation 21-1 occurs. For an electron beam, the excitation process can be written

where e, represents an incident electron from the source, e; - represents the same electron aftcr it has interacted with A and has thus lost some of its energy, and eA represents an electron ejected from one of the inner orbitals of A. As shown in Figure 21-7a and h, relaxation of the excited ion A ~* can occur in two ways:

Here, e A corresponds to an Auger c-Iectron and represents a fluorescence photon. ~St.:C 1. F \Valts

and

J \\'Obl107 V/cm) that electrons are produced by a qua ntum mecha nica l tunneling pr ocess 10 in which no thermal energy is required to free the electrons from the potential barrier that normally prevents their emission. Field emission sources provide a beam of electrons that have a crossover diameter of only 10 nm compared with 10 flm for LaB. rods and 50 flm for tungsten hairpins. The disadvantages of this type of source are its fragility and the fact that it also requires a better vacuum than does an ordinary filament source. Electron guns produce a beam of electrons with energies of 1 to 10 keY, which can be focused on the surface of a sample for Auger electron studies. One of the special advantages of Auger spectroscopy is its capability for very high spatial-resolution scanning of solid surfaces. Normally, electron beams with diameters ranging from 5 to 500 flm are used for this purpose. 'OJ In quantum mechanics, there is a finite probahility that a particle can pass through a potential ~nergy barrier and appear in a region forbidden by classical mechanics. This process is called tunneling. It can be an important process for light particles, such as protons and electrons.

of A E S

Qualitative Analysis of Solid Surfaces. Typically, an Auger spectrum is obtained by bombarding a small area (5 to 500 flm diameter) of the surface with a beam of electrons from a gun. A derivative electron spectrum, sueh as that shown in Figure 21-8, is then obtained with an analyzer. An advantage of Auger spectroscopy for surface studies is that the low-energy Auger electrons (20 to 1000 e V) are able to penetrate only a few atomic layers, 0.3 to 2 nm (3 to 20 A) of solid. Thus, whereas the electrons from the electron guns penetrate to a considerably greater depth below the sample surface, only those Auger electrons from the first four or five atomic layers escape to reach the analyzer. Consequently, an Auger spectrum is likely to reflect the true surface composition of solids. , • The two Auger spectra in Figure 21-8 are for samples of a 70% Cu to 30% Ni alloy, which is often used for structures where saltwater corrosion resistance is required. Corrosion resistance of this alloy is markedly enhanced by preliminary anodic oxidation in a strong solution of chloride. Figure 21-8A is the spectrum of an alloy surface that has been pa ssi va ted in this way. Spectrum B is for another sample of the alloy in which the anodic oxidation potential was not great enough to cause significant passivation. The two spectra clearly reveal the chemical differences between the two samples that account for the greater corrosion resistance of the former. First, the copper-to-nickel ratio in the surface layer of the nonpassivated sample is approximately that for the bulk, whereas in the passivated material the nickel peaks completely overshadow the copper peak. Furthermore, the oxygen-to-nickel ratio in the passivated sample approaches that for pure anodized nickel, which also has a high corrosion resistance. Thus, the resistance toward corrosion of the alloy appears to result from the creation of a surface that is largely nickel oxide. The advantage of the alloy over pure nickel is its significantly lower cost.

FIGURE21-10 Schematic representation of the simultaneous use of ion sputter etching and Auger spectroscopy for determining depth profiles. (Courtesy of Physical Electronics, USA, Chanhassen, MN.)

ter is the more common. Figure 21-10 shows schematically how the process is carried out with a highly focused Auger microprobe with a beam diameter of about 5 flm. The microprobe and etching beams are operated simultaneously, with the intensity of one or more of the resulting Auger peaks being recorded as a function of time. Because the etching rate is related to time, a depth profile of elemental composition is obtained. Such information is of vital importance in a variety of studies such as corrosion chemistry, catalyst behavior, and properties of semiconductor junctions.

Line Scanning. Line scans are used to characterize the surface composition of solids as a function of distance along a straight line of 100 flm or more. For this purpose, an Auger microprobe is used that produces a beam that can be moved across a surface in a reproducihle way. Figure 21-12 shows Auger line scans along the surface of a semiconductor device. In the upper ligure, the relative peak amplitude of an oxygen peak is recorded as a function of distance along a line; the lower figure is the same scan produced when the analyzer was set to a peak for gold.

u

~

(4.00 X 1 0 -' M),Cr3'(2.00 x 1 0 -' M),H+(0.100 M)lpt (b) UO,'+(0.200 M),UH (O.I00 M),H'(0.500 M)lpt

*22-8

PtIY(OHl:(2.67

*22-9

PtIFe(CN):-(4.42 is 3.85

+ 2e' ~

+

N i(s)

X

0.cJ03215 0.004488 0.005619 0.007311 0.009138 0.011195 0.013407 0.01710 0.02563 0.05391 0.1238

to".

the process

given that K,p for BiOCI has a value of 8.1 xl()'

+ H,O

19

*22-12 Calculate the standard potential for the half-reaction AI(C,O.),'

+ 2 c,o l-

+ 3e- ->AI(s)

if the formation constant for the complex is 1.3 x to

l1.

*22-13 From the standard potentials TI+ + e- ~TI(s) TICl(s) + e' ~

£0

=

TI(s) + Cl-

-0.336 V £"

=

-0.557 V

*22-14 From the standard potentials

+ 2e' ~ Ag' + e ~

2Ag(s) + SeO,' Ag(s)

EO

x 1O-3MlIIAg'(5.75

x 1O-'M)!Ag

y±

0.9418 0.9328 0.9259 09173 0.9094 0.9031 0.8946 0.8843 0.8660 0.8293 0.7877

E

EO

0.52053 0.50384 0.49257 0.47948 0.46860 0.45861 0.44974 0.43783 0.41824 0.38222 0.34199

0.22255 0.22251 0.22241 0.22236 0.22250 0.22258 0.22248 0.22247 0.22260 0.22256 0.22244

22-1."

I!l

C h a lle n g e

P ro b le m s

22-19 As a part of a study to measure the dissociation constant of acetic acid, Harned and Ehlers 16 needed to measure EO for the following cell:

calculate the solubility product constant for TICL

Ag,SeO.(s)

1O-'M),Fe(CNl6'-(8.93

(a) Create a spreadsheet to calculate the standard electrode potential for the Ag-AgCI electrode using the method described in Example 22-1. Make columns for the activity coefficients and the standard potential. Calculate y values for H' and CI . for each molality. Then find y" at each molality. Use the measured values of E to find EO at each molality. (b) Compare your values for the activity coefficients and standard potential with those of Mac[nnes, and if there are any differences between your values and those in the table above, suggest possible reasons for the discrepancies. (c) Use the Descriptive Statistics function of Data Analysis Toolpak15 to find the mean, standard deviation, 95% confidence interval, and other useful sta, tistics for the standard potential of the Ag-AgCI electrode. (d) Comment on the results of your analysis and, in particular, the qualitv of Mac[nnes's results. .

*22-11 Calculate the standard potential for the half-reaction Bi(s) + Cl

X

n. Calculate the initial potential when 0.0442 A is drawn from this cell.

c H O ,m

*22-10 The solubility product constant for Pb[, is 7.1 x 10-9 at 25"C. Calculate EO for

BiOCI(s) + 2H+ + 3e- ~

x lO-'Ml.

IiJ 22-18 The following data are similar to those given in Example

4CW

given that the formation constant for the complex is 1.0

x 1O-'M),vO"(3.42

x 10-' MlIICu2+(2.50 x 1O-'M)!Cu

*22-17 The resistance of the galvanic cell

Compute EO for the process Ni(CN)}-

n. Calculate

has an internal resistance of 3.81 n. What will be the initial potential if a current of 0.0750 A is drawn from this cell?

x 10-5 M)IISn2+(5.50 x 10-' M),

Calculate the theoretical potential of each of the following cells. [s the ccll reaction spontaneous as written or spontaneous in the opposite direction? (a) BiIBiO+(0.0400 M),W(0.200 M)III'(O.100 M),Ag[(sat'd)!Ag (b) Zn\Zn'+(7.50 X 10" M)IIFe(CN)6'-(4.50 x 10-' M),Fe(CN)6'-(7.00 x to-' M)\Pt • (c) Pt,H,(0.200 atm)IHCI(7.50 X 10-· M), AgCI(sat'd)!Ag

10'1 M)IIBr-(o.0850 M).AgBr(sat'd)IAg

*22-16 The cell

Calculate the theoretical potential of each of the following cells. Is the cell reaction spontaneous as written or spontaneous in the opposite direction? (a) PtICr3+(1.00 x 1 0 -' M),Cr"(2.00 x 1 0 - 3 M)IIPb"(5.60 x to' M)lpb (b) HgIHg,'+(2.00 x to-' M)IIH+(1.00 x to-' M),vJ+(3.00 x 10-' M),VO" (2.00 x 103 M)!Pt (c) PtIFe3+(4.00 x 10-2M),Fe2+(3.00 Sn'+(3.50 x 10-' M)lpt

X

As a result of its design, the cell has an internal resistance of 4.87 the initial potential of the cell.

H'(4.81 *22-7

105 M),y2+(4.48

E " = 0.355 V =

0.799 V

: ~ D . A. Macinnes. Th e P r in cip les o f E lectr o ch emistr y, Table I. p. 187, New York: Reinhold, 1939 ·'S. R. Crouch aoL1F. J Holler. Ap p lica tio n s o f M icr o so fr ~ E xcel in An a lytica l C h emistr y, Bdmont, 2004. pp. 32--34 ~H. S. Harned and R. \\.:. Ehlers. 1. Am_ C h er n . Sa c., 1 9 3 2 ,5 4 (4),1350-57

C\: Brt)oksiCole.

(a) Write an expression for the potential of the cell. (b) Show that the expression can be arranged to give E

=

E

o

-

RT F In YH,O'Yu mll,o' mu

where mH;O' and mn are the molal (mole solute per kilogram solvcnt) concentrations. (c) Under what circumstances is this expression valid: (d) Show that the expression in (b) may be written E

+

2 k log m

= E" -

2 k log Y±

where k = In lO R T I F. (e) A considerably simplificd version of the Debye:!:Iilckel cxpression that is valid for very dilutc solutions is log Y = -0.5 \I'm + b m , wherc c \s a constant. Show that the expression for the cell potcntial in (d) may be written as E

+ 2klogm

- kvm

=

E " - 2 kcm

(f) The previous expression is a "limiting law" that becomes linear as the concentration of the electrolyte approaches zero. The equation assumes the form y = a x + b , where y = E + 2 klo g m - kvm; x = m, the slope; a = ,-2 kc; and the y-intercept b = F'. Harned and Ehlers very accurately measured the potential of the cell without liquid junction presented at the beglOOing of the problem as a function of concentration of HCI (molal) and temperature and obtained the data in the following table. For example, they measured the potential of the cell at 25'C with an HCl conccntration of 0.01 m and obtained a value of 0.46419 volts.

Construct a plot of E + 2 k log m -- k \1 m versus m. and note that the plot is quite linear at low concentration. Extrapolate the line to the y-intcrcept, and estimate a value for En Compare your value with the value of Harned and Ehlers, and explain any difference. Also compare the value to the one shown in Table 22-1. The simplest way to carry out this exercise is to place the data in a spreadsheet. and use the Exccl function INTERCEPT(known_y's, known_x's) to determine the extrapolated value for E n " Use only the data from 0.005-0.01 m to find the intcrcept. (g) Enter the data for all temperatures into the spreadsheet and determine values for EO at all temperatures from ye to 35"C. Altcrnatively, you may download an Excel sprcadsheet containing the entire data table. Use your web browser to conncct to http://www.thomsonedu.com/chemistry/skoog. and select your course, Instrumcntal Analysis. Finally, navigate to the links for Chapter 22, and click on the spreadsheet link for this problem. (h) Two typographical errors in the preceding table appeared in the original published paper. Find the errors, and correct them. How can you justify these corrections: What statistical criteria can you apply to justify your action? In your judgment, is it likely that these errors have been detected previously? Explain your answer. (i) Why do you think that these workers used molality in their studies rather than molarity or weight molarity? Explain whether it matters which of these concentration units are used. As we saw in Problem 22-19, as a preliminary experiment in their effort to measure the dissociation constant of acetic acid, Harned and Ehlers 18 measured EO for the cell without liquid junction shown. To complete the study and determine the dissociation constant, these workers also measured the potential of the following cell:

Potential Measurements of Cell Pt,H2(1 atm)IHCI(m),AgCI(sat'dj!Agwithout Liquid Junction as a Function of Concentration (molality)and Temperature COG) E ,., volts

m, molal

E.

£,

E ••

E"

E ,.

E 25

E ,.

E"

0.005

0.48916

0.49138

0.49338

0.49521

0.44690

0.49844

0.49983

0.50109

0.006

0.48089

0.48295

0.48480

0.48647

0.48800

0.48940

0.49065

0.49176

0.007

0.4739

0.47584

0.47756

0.47910

0.48050

0.48178

0.48289

0.48389

0.008

0.46785

0.46968

0.47128

0.47270

0.47399

0.47518

0.47617

0.47704

0.009

0.46254

0.46426

0.46576

0.46708

0.46828

0.47103

0.4578

0.45943

0.46084

0.46207

0.46319

0.46937 0.46419

0.47026

0.01

0.46499

0.46565

0.02

0.42669

0.42776

0.42802

0.42925

0.42978

0.43022

0.43049

0.43058

0.03 0.04

0.40859

0.40931

0.40993

0.41021

0.41041

0.41056

0.41050

0.41028

0.39577

0.39624

0.39666

0.39638

0.39595

0.05

0.38586

0.06

037777

0.39673

0.39673

0.38616

0.39668 0.38641

0.38631

0.38614

0.38589

0.38543

0.38484

0.37793

037802

0.37780

0.37749

0.37709

0.37648

0.37578

0.36965 0.36320

0.36890

0.36808

0.36285

0.36143

0.35658

0.35556

0.35140

0.35031

0.2191~

0.21591

0.07

0.37093

0.37098

037092

0.37061

0.37017

0.08 0.Q9

0.36497

0.36495

0.36479

0.36438

0.35976

0.35963

0.35937

0.35888

0.36382 0.35823

0.1

0.35507

0.35487

0.33451

0.35394

03532l

0.35751 0.35240

EO

0.23627

0.23386

0.23126

0.22847

022550

022239

where YH,O'and Ycl are the activity coefficients of hydronium ion and chloride ion, respectively, and mll,o' and mo are their respective molal (mole solute per kilogram solvent) concentrations. (b) The dissociation constant for acctic acid is given by K

Yu/rYoAc- tnH,o' mo Ac-

= .------

-~-.-

YHOAc

..-

mHOAc

where Yo", and YIlO.', arc the activity coefficients of acetate ion and acetic acid, respectively, and mo" and mHO\' are their respective eqUilibrium

1'5. R. Crouch and}-. 1. Hdlkr. 2iX}4, p 67 IKS ee note 16

A p p liC l.J.fio n s

of

,iflc ro .,0 fr·)

L'xa ! in A n a l •..tlcu ! C h n n istn ,', l i d m o n t . CA: Brooks/Cok,

molal (mole solute per kilogram solvent) concentrations. potential of the cell in part (a) is given by E -

EU

+ RT in

IIlHOA,mCl

F

= _

mo:... c

Show that the

RT In YH,O'YCl-YHOA, F

YillO'

_

The equipment required for potentiometric methods is simple and inexpensive and includes an in d ica to r electr o d e, a r efer en ce electr o d e, and a p o ten tia l mea su r in g d eVice. The deSign and properties of each of these components are described in the initial sections of this chapter. Following these discussions, we investigate analytical applications of potentiometric measur';-ments. L -

P o t e n t io m e t r y

RF T InK

'YOAc

(c) As the ionic strength of the solution approaches zero, what happens to the right-hand side of the preceding equation': (d) As a result of the answer to part (i) in Problem 22-19, we can write the righthand side of the equation as -(R T /F )ln K '. Show that K'

=

exp [ __U_: _-_E_o_l_F In

(_m_H_OA_,_IIl_C_I-)

]

m OA'-

RT

In Chapter 22, we state that absolute values for individual half-cell potentials cannot be determined in the laboratory. That is, only relative cell potentials can be measured experimentally. Figure 23-1 shows a typical cell for potentiometric analysis. This cell can be represented as

(e) The ionic strength of the solution in the cell without liquid junction calculated by Harned and Ehlers is I-'-= cN,n + [H"] + [OAc"] Show that this expression is correct. (f) These workers prepared solutions of various molal analytical concentrations of acetic acid, sodium acetate, and sodium chloride and measured the potential of the cell presented at the beginning of this problem. Their resljlts are shown in the following table.

reference

P

Potential Measurements of Cell Pt,H,(1 atmjIHOAc(cHoAc),NaOAc(cN,oAc),NaCI(cN,d, AgCI(sat'd)IAgwithout Liquid Junction as a Function of Ionic Strength (molality)and Temperature ("C)

o ten tio metr ic

meth o d s

...

,i< ; d wm iwl" ," ' wi" ¥ !d m wi~ .p p ~

E,

E,

E ••

E 15

£20

E"

E".

E"

0.62392

0.62789

0.63183

0.63580

0.63959

0.64335

0.64722

0.011582

0.012326

0.59826

0.60183

0.60538

0.60890

0.61922

0.62264

0.021516

0.58528

0.58855

0.59186

0.60792

tio n s h a ve b een mea su r ed

0.04737

0.05042

0.56546

0.56833

0.57128

0.58257

0.07796

0.08297

0.55388

0.55667

0.56189

0.56712

0.56964

0.09056

0.08716

0.09276

0.55128

0.55397

0.55928 0.55661

0.58529 0.57213

tia l o f a n io n -selective

0.08101

0.57699 0.56456

0.60154 0.57977

0.60470

0.04922

0.59508 0.57413

0.61241 0.59840

0.61583

0.020216

0.55912

0.56171

0.56423

0.56672

0.56917

0.012035 0.021006

o felec-

~ ia b le cu r r en t. F o r n ea r ly a cen tu r y, p o ten tio metr ic

0.61995

0.004599

th e p o ten tia l

are

b a sed o n mea su r in g

c N lIC I,m

c N .O A c 'm

0.004779

o f a n a lysis

.

0.004896

c H O A c 'm

tech n iq u esh a ve

b een u sed fo r

p O in ts in titr a tio n s,

~gr e

tize lo ca tio n p !en d

r ecen tly,

io n co n sen tr a -

d ir ectlyfr o m

memb r a n e

electr o d es a r e r ela tively fr ee fr o ~ p r o vid e a r a p id a n d co n ven ien t ta tive estima tio n s

Calculate the ionic strength of each of the solutions using the expression for the K , of acetic acid to calculate [H,O"], [OAc"], and [HOAc] with the usual suitable approximations and a provisional value of K , = 1.8 X 10"'. Use the potentials in the table for 25°C to calculate values for K ' with the expression in part (j). Construct a plot of K ' versus 1-'-,and extrapolate the graph to infinite dilution (I-'- = 0) to find a value for K , at 25°C. Compare the extrapolated value to the provisional value used to calculate 1-'-.What effect docs the provisional value of K , have on the extrapolated value of K ,? You can perform these calculations most easily using a spreadsheet. (g) If you have made these computations using a spreadsheet, determine the dissociation constant for acetic acid at all other temperatures for which data are available. How does K , vary with temperature" At what temperature does the maximum in K , occur?

electrode Isalt bridgel analyte

'----v-----'

th ep o ten -

electr o d e,'Su ch in teifer en ce

a nd

mea n s fo r q u a n ti-

o f n u mer o u s imp o r ta n t

a n io n s

a n d ca tio n s,

'----v----'

solution Iindicator

electrode

The r efer en ce electr o d e in this diagram is a half-cell with an accurately known electrode potential, E "" that is mdependeM of the concentration of the analyte or any other lOns m the solution under study. It can be a standard hydrogen electrode but seldom is because a standard hydrogen electrode is somewhat troublesome to maintain and use. By convention, the reference electrode is always treated as the left-hand electrode in potentiometric measurements. The in d ica to r electr o d e which is immersed in a solution of the analyte, develop~ a potential, E;nd, that depends on the activity of the analyte. Most indicator electrodes used in potentiometry are selective in their responses. The third component of a potentiometric cell is a salt bridge that prevents the components of the analyte solution from mixing With those of the reference electrode. As noted in Section 22B-2, a potential develops across the liquid junctlOns at each end of the salt bridge. These two potentials tend to cancel one another if the mobilities of the cation and the anion in the bridge solution are approximately the same. Potassium chloride is a nearlv ideal electrolyte for the salt bridge because the mobilities of the K· ion and the 0- ion are nearly equal. The net potential difference across the salt bridge E is thereby reduced to a few millivolts Or less. For most electroanalvtical methods, the junction potential is small enough -to be J

~

Throughout this chapter, this logo indicates an opportunity for online self-study at www :thomsooedu.com/chemistry/skoog,linking you to tnteracllve tutorials, simulations, and exercises.

: For more information. see R S. Hutchms and L. G. Bacha_~.l0H a n d b o o k o f In Slmmema i

T e ch n iq iU :'Y

fo r

An a lytica l

C h e m isr n , F

A. StHIe

Chap. 3b. pp. 727--l.,s.l:ppcr Saddle Ri\"CT. NJ: Preolic1 Ca", >1 Sr2+, >0.5 Sr2', 1 X 10-2 Zn" Hg" and Ag' (poisons electrode at >10-7 M), Fe" (at >0.1[Cd2'], Pb" (at >[Cd2+], Cu2'(possible) 10-5 Pb2+. 4 X 10-' Hg2' H' 6 X 10-' Sr"· 2 X 10-2 Fe2+·4 X 10-' Cu'" 5 X 10-2 2'; 0.2 NH,; 0.2 N~'; 0.3 Tris'; 0.3 Li'; 0.4 K'; 0:7 Ba"; 1.0Zn"';

Ni

1.0 Mg2'

Maximum allowable ratio of interferent to [cq: OH- 80, Br- 3 X 10-', [- 5 X 10-7,52- 10-6, CN- 2 X 10-7, NH, 0.12, 5,0,'- 0.01 5 X 1O-7C[O,-; 5 X 10-6 r; 5 X 10-5 ClO, -; 5 X 10-' CN-; 10'" Br-; 10-' N02-; 5 X 10-' NO,-; 3 X 10-' HCO,-, 5 X 10-2 CI-; 8 X 10-2 H,PO,-, HPO,'-, pol-; 0.2 OAc-; 0.6 P-; 1.0 50,'10-7 CIO,-; 5 X 10-61-; 5 X 10-' ClO, -; 10-4 CN-; 7 X 10-' Br-; 10-' HS-; 10-2 HCO,-, 2 X 10-2 CO,'-; 3 X 1O-'CI-; 5 X 10-2 H2PO,-, HPO,'-; pol-; 0.2 OAc-; 0.6 P-; 1.0 SO,'7 X 10-1 salicylate,2 X 10-' r, 10-1 Br-, 3 X 10-1 ClO, -,2 X 10-[ acetate, 2 X 10-1 HCO,-,2 X 10-1 NO,-,2 X 10-1 SO,'-, 1 X 10-1 CI-, 1 X 10-[ 00.-,

1.4 X 10-6 to 3.6 X 10-6

1

K' Water hardness (Ca2+ + Mg2+)

10° to 1 X 10-6 10-' to 6 X 10-6

All electrodes are the plastic-membrane

X

10-1 F-

•

2 X 10-" r; 2 X 10-2 CIO,-; 4 X 10-2 CN-, Br-; 5 X 10-' NO, -, NO, -; 2 HC~,-, CO,'-; CI-, H2PO,-. HPO,'-, pol-, OAc-, F-, 50,'3 X 10-4 Cst; 6 X 10-' NH.', TI'; 10-2 H'; 1.0 Ag', Tris'; 2.0 Li', Na' 3 X 10-5 Cu2', Zn2'; 10'" Ni2'; 4 X 10-' Sr'; 6 X 10-' Fe"; 6 x 10-' Ba2+; 3 X 10-2 Na'; 0.1 K'

type.

'From product catalog, Boston, MA: Thermo Orion, 2006. With permission of Thermo Electron Corp., Waltham. MA. (From product instruction

manuals, Boston, MA: Thermo Orion. 2003. With permission of Thermo Electron Corp .. Waltham. MA.

channel. As shown in Figure 23-11. instead of the usual metallic contact, the gate of the [SFET is covered with an insulating layer of silicon nitride (SiJN4). The analyte solution, containing hydrogen ions in this example, is in contact with this insulating layer and with a reference electrode. The surface of the gate insulator functions very much like the surface of a glass electrode. Protons from the hydrogen ions in the test solution are adsorbed on available microscopic sites on the silicon nitride. Any change in the hydronium ion concentration of the solution results in a change in the concentration of adsorbed protons. The changc in concentration of adsorbed protons then gives rise to a changing electrochemical potential between the gate and source, which in turn changes the conductivity of the channel of the [SFET. The conductivity of the channel can be monitored electronically to provide a signal that is proportional to the logarithm of the concentration of H' in the solution. Note that the entire [SFET except the gate in-

sulator is coated with a polymeric encapsulant to insulate all electrical connections from the analyte solution.

The ion-sensitive surface of the ISFET is naturally sensitive to pH changes, but the device may be rendered sensitive to other species by coating the silicon nitride gate insulator with a polymer containing molecules that tend to form complexes with species other than hydronium ion. Furthermore, several ISFETs may be fabricated on the same substrate so that multiple measurements may be made simultaneously. All of the [SFETs may detect the same species to enhance accuracy and reliability, or each [SFET may be coated with a different polymer so that measurements of several different species may be made. ISFETs offer a number of significant advantages over mcmbrane electrodes, including ruggedness, small

23F-1 Gas-Sensing Probes

size, inertness toward harsh environments. rapid response. and low electrical impedance. [n contrast to membrane electrodes, ISFETs do not reqUire hydration before use and can be stored indefimtely m ~he dry state. Despite these many advantages, no ISFETspecific-ion electrode appeared on the market untllthe early 19905, more than 20 years after their Illvenlion. The reason for this delay is that manufacturers were unable to develop the technology of encapsulatlllg the devices to create a product that did not exh[blt dnft and instability. The only significant disadvantage of ISFETs other than drift appears to be that they reqUire a more or less traditional reference electrode. This reqUIrement places a lower limit on the size of the ISFET probe. Work continues on the development of a differential pair of ISFETs, one selective for the analyte Ion and the other not. The second reference [SFET IScalled a REFET, and a differential amplifier is used to measure the voltage difference between the ISFET and the REFET, which is proportional to pX.[S Many [SFETbased devices have appeared on the market over the past decade for the determination of pH, and research has continued on the development of deVices that are selective for other analytes. Well over 150 [SFET patents have been filed over the last three decades, and more than twenty companies manufacture [SFETs 10 various forms. The promise of a tiny, rugged sensor that can he used in a broad range of harsh and unusual env[ronments is being achieved as the reference electrode problem is being sol ved." l~

P. Bergveld,

I~lbid_,

pp.

Sens Actua tor S. B. 2O(H, 88. 9.

1 8 ·1 1 }

During the past three decades. several gas-sensing electrochemical devices have become available from commercial sources. In the manufacturer literature, these devices are often called gas-sensing "electrodes." Figure 23-12 shows that these devices are not, III fact, electrodes but instead are electrochemical cells made up of a specific-ion electrode and a reference electrode immersed in an internal solution retamed by a thm gas-permeable membrane. Thus, ga s-sensing pr obes [S a more suitable name for these gas sensors. . Gas-sensing probes are remarkably selective and sensitive devices for determining dissolved gases or

NaHCOJ NaCI internal solution

Internal solution of glass electrode

Thin

film

of internal solution

FIGURE 23-12 Schematic of a gas-sensing probe for carbon dioxide.

M e m b ra n e

P ro b e

C O ,(g) ~

C O ,(a q)

rnembrane por~s

int¢Tnal jolution

+ 2H,O ~

C O ,(a q)

D e s ig n

G a s - P e r m e a b le

Equilibrium iu Internal Solution

HCO, - + H]O'

InternJI

Figure 23-12 is a schematic showing details of a gassensing probe for carbon dioxide. The heart of the probe is a thin, porous membrane, which is easily replaceable. This membrane separates the analyte solution from an internal solution containina sodium bicarbonate and sodium chloride. A pH-se~sitive glass electrode having a fiat membrane is held in position so that a very thin film of the internal solution is sandwiched between it and the gas-permeable membrane. A silver-silver chloride reference electrode is also located in the internal solution. It is the pH of the film of liquid adjacent to the glass electrode that provides a measure of the carbon dioxide content of the analyte solution on the other side of the membrane.

then

interllal sulution

50[uti RCOCOOH + NH; + H20, NH,-gas sensor L-Glutamine ---> glutamic acid + NH3 NH,-gas sensor Adenosine

deaminase

an important routine clinical test. In the presence of the enzyme urease, urea is hydrolyzed according to the reaction (NH2),CO + H30' + H,O->2NH4+

II

+ HCO,' +

Amygdalin Glucose Penicillin $

Penicillinase

----* inosine + NH3 NH,-gas sensor

L-Glutamate ---> GABA + CO, amygdalin ---> HCN + 2CJI,,06 + benzaldehyde glucose + 0, ---> gluconic acid + H,O, Penicillin ---> Penicilloicacid

From E. Bakker and f\.t. E. Meyerhoff, in E ncyclopedia

eN-solid-state H+-glass or polymer H+-glass or polymer

A.1. Bard., Ed., \01. 9, Bloe1ecr r ochemISITy, G. S. Wilson, Ed., New of £leC ITochemutr y,

York: Wiley, 2002, p. 305, with permission

211,0

2NH3 + 2H36~

Glutamate decarboxylase I3-Glucosidase Glucose oxidase

NH. + glass or polymer NH r gas sensor H' -glass or polymer NH, +-glass or polymer

(23-23)

The electrode in Figure 23-13a is a glass electrode that responds to the ammonium ion formed by the reaction shown in the upper part of Equation 23-23. The electrode in Figure 23-13b is an ammonia gas probe that responds to the molecular ammonia in equilibrium with the ammonium ion. Unfortunately, both electrodes have limitations. The glass electrode responds to all monovalent cations, and its selectivity coefficients for NH4 + over Na+ and K' are such that interference occurs in most biological media (such as blood). The ammonia gas probe has a different problem - the pH of the probe is incompatible with the enzymc. The cnzyme requires a pH of about 7 for maximum catalytic activity, but the sensor's maximum response occurs at a pH that is greater than 8 to 9 (where essentially all of the NH, + has been converted to NH3). Thus, the sensitivity of the electrode is limited. Both limitations are ovcrcome by use of a fixedbed enzyme system where the sample at a pH of about 7 is pumped over the enzyme. The resulting solution is then made alkaline and thc liberated ammonia determined with an ammonia gas probe. Automated instruments (see Chapter 33) based on this technique have been on the market for several years. Factors that affect the detection limits of enzymebased biosensors include the inherent detection limits of the ion-selective electrode coupled with the enzyme layer, the kinetics of the enzyme reaction, and the mass-

transfer rate of substrate into the layer.24 Despite a large bod y of research on these devices and, as shown m Table 23-6, the several potentially useful enzyme-based membranes, there have been only a few commerCial potentiometric enzyme electrodes, due at least in part to limitations such as those cited previously. The enzymatic determination of urea nitrogen in clinical applications discussed in the following paragraphs is an exceptional example of this type of sensor. A number of commercial sources offer enzymatic electrodes based on voltammetric measurements on various enzyme systems. These electrodes are discussed in Chapter 25.

A p p lic a t io n s

in C lin ic a l

A n a ly s is

An example of the application of a potentiometric enzyme-based biosensor in clinical analySIS ISan automated monitor designed specifically to analyze blood samples at the bedside of patients. The i-STAT Portable Clinical Analyzer, shown in Figure 23-14a, IS a handheld device capable of determining a broad range of clinically important analytcs such as potas~~E. Bakker and M. E. Meyerhoff, in E ncyclopedw of E leclr o~ hemi~ lr }' A.1. Bard, ed .. Vol. 9, Bioelectr ochemi~ ln', G, S. \Vllson, cd .. Nev. 'turk Wiley, 2002. p. 3fH, P. W. Carr and L. D. Bl)WCrS, I m m o b I lI ~ e d E nzym ey. in Ana lytica l a nd C lir lica { C hemistr y __F unda menta ls

York: \Viley, 1980.

a nd Appftca tlO ns. Nc\\

sium, sodium, chloride, pH, pCO" pO" urea nitrogen, and glucose. In addition, the computer-based analyzer calculates bicarbonate, total carbon dIOXide, base excess 0, saturation, and hemoglobin in whole blood. Rel~tiv~ standard deviations on the order of 0.5% to 4% are obtained with these devices. Studies have shown that results are sufficiently reliable and cost effective to substitute for similar measurements made m 'c a traditional, remote clinicallaboratory.25 Most of the analytes (pCO" Na+, K+, Ca- , urea nitrogen, and pH) are determined by potentiometric measurements using microfabricated membranebased ion-selective electrode technology. The urea nitrogen sensor consists of a polymer layer contaming urease overlying an ammonium ion-selective electrode. The chemistry of the BUN determmatlOn ISdescribed in the previous section. The hematocnt IS measured by electrolytic conductivity detection, and pO, is determined with a Clark voltammetnc sensor (see Section 25C-4). Other results are calculated from these data. The central component of the mom tor IS the single-use disposable electrochemical i:STAT sensor array depicted in Figure 23-14b. The mdlvldual sensor electrodes are located on silicon chips along a narrow flow channel, as shown in the figure. The

~ _

Polyimide Ion-selective

_HEMA _AgCl _Ag C]Au _Cr CJ Kapton _SolidKCl

membra

R,;.~~~;;~~~i~~'~l;~ ".

--------1IDiii/~;~,;,~u:;

&

>

FIGURE23-15 A microfabricated potentiometric sensor for in vivo determination of analytes. The sensor was fabricated on a flexible plastic substrate using thick-film techniques. There are nine ion-selective electrodes (ISEs)on one side of the film and corresponding reference electrodes on the opposite side. (From E. Lindner and R. P. Buck, A n a l. C h e m . , 2000, 72, 336A, with permission. Copyright 2000 American Chemical SoCiety.)

(b)

~~T~RE 23-14 (a) Photograph of i-STAT1 portable clinical analyzer. (b) Exploded view of I :r sensor array cartridge. (Abbott Point of Care Inc.)

integrated biosensors are manufactured by a patented mIcrofabncation process.'" .Each new sensor array is automatically calibrated pnor to the measurement step. A blood sample withdrawn from the patient is deposited into the sample entry well, and the cartridge is inserted into the i-STAT analyzer. The cali brant pouch, which contains a standard buffered solution of the analytes, is punctured by the i-STAT analyzer and is compressed to force the calibrant through the flow channel across the surface of the sensor array. When the calibration step is complete, the analyzer compresses the air bladder, which lorces the blood sample through the flow channel to ex-

pel the calibrant solution to waste and to bring the blood (20 fIL to 100 fIL) into contact with the sensor array. Electrochemical measurements are then made, and the results are calculated and presented on the liquid crystal display of the analyzer. The results are stored in the memory of the analyzer and may be transmitted to the hospital laboratory data management system for permanent storage and retrieval (see Section 4H-2). Cartndges are available that are configured for different combinations of more than twentv different analytes and measurements that can be ~made with this system. Instruments similar to the i-STAT bedside monitor have heen available for some time [or in vitro potentlOmetnc determination of various analytes in biomedIcal and biological systems. In recent years, there

has been much interest in the development of miniature potentiometric sensors for in vivo studies as well. Figure 23-15 shows a small array (4 x 12 mm) of nine potentiometric electrodes fabricated on a thin Kapton® polyimide filmY Nine separate electrodes (along with corresponding reference electrodes on the opposite side of the array) are fabricated by thick-film techniques similar to those used for printed circuit boards. A chromium adhesion layer and a gold layer are vapor deposited on the polymer to provide electrical connection to the sensor areas. The array is next coated with photoresist and exposed to UV light through a mask that defines the electrode areas. The photoresist is developed to expose the electrode pads. Silver is then deposited electrochemically followed by silver chloride to form the internal reference electrode for each sensor. A mixture of hydroxyethyl methacrylate (HEMA) and an electrolyte is added to provide a salt bridge between the internal reference electrode and the ionselective memhrane. Finally, the ion-selective membrane is applied ovcr the internal reference electrode along with a protective layer of polyimide. The sensor array has been used successfully to monitor H ~, K Na +, Ca " , and other analytes in heart muscle.

Other disposable electrochemical cells based on ion-selective electrodes, which are designed for the routine determination of various ions in clinical samples, have been available for some time. These systems are described briefly in Section 33D-3. L ig h t A d d r e s s a b le

P o t e n t io m e t r ic

Sensor

An intriguing and useful application of semiconductor devices and potentiometric measurement principles is the light addressablc potentiometric sensor (LAPS)." This device is fabricated from a thin, flat plate of p- or n-type silicon with a 1000-A-thick coating of silicon oxynitride on one side of the plate. If a bias voltage is applied between a reference electrode immersed in a solution in contact with the insulating oxynitride layer and the silicon substrate, the semiconductor is depleted of majority carriers (see Section 2C-l). When light from a modulated source strikes the plate from either side, a corresponding photocurrent is produced. By measuring the photocurrent as a function of bias voltage, the surface potential of the device can be determined. Because the oxynitride layer is pH sensitive. the surface potential provides a measure of pH with a nernstian response over several decades. '~D_ A. Haf~man, 1 . J O . l1 1 '\ 2 .

1- W. Parce, and H. M. McConnelL

Science.

1988.

· The versatility of the device is enhanced by attachIng to the underside of the silicon substrate an arrav of lIght-emIttIng diodes. By modulating the diodes in'sequence: dIfferent regions of the surface of the device can be Interrogated for pH changes. Furthermore, by applyIng membranes containing various ionophores o-r enzymes to the oxynitride layer, each LED can monitor a different analyte. When this device is used to monItor the response of living cells to various biochemIcal stImuli, it is referred to as a micr ophysiomel e r . For a more complete description of the LAPS and Its blOanalytical applications, see the Instrumental Analysis in Action feature following Chapter 25.

23G

INSTRUMENTS FOR MEASURING CELL POTENTIALS

An important consideration in the design of an instrument for measuring' cell potentials is that its resistance be large with respect tot he cell. If it is not, the I R drop !lI the cell producesslgmficant error (see Section 2A -3). We demonstrate thIS effect in the example that follows.

The true potential of a glass-calomel electrode system IS0.800 V; ItS!lite mal resistance is 20 MO. What would be the relative error in the measured potential if the measunng device has a resistance of 100 Mfl? Solution

The following schematic diagram shows that the measurement circuit can be considered as a voltage source E , and two resIstors in series: the source resistance R and the internal resistance of the measuring device R,,'

where I is the current in this circuit consisting of the cell and the measurIng de"ice . The current is then given by I

0.800:v'._~ __ (20 + 100) X 10' l! --6.67

= ~_

E,

=

IR, + IR"

10-' A

The potential drop across the measuring device (whIch IS the potential indicated by the device E ) ., -." is IR". Thus, EM

= (6.67

x 10 'A)(IOO

X

10" 0) = 0667 V

and 'I 0.667 V - O.80()V re error = ---0.800\;--~ . X 100%

=

-'0.133 V O BO O -V- X 100%

-17%

":e can easily show that to reduce the loading error to I Yo, the resistance of the yoltagc measuring device must be about 100 times greater than tbe cell resistance; for a rclative error of 0.1 %, the res'isrance must be WOOtimes greater. Because the electrical resistan~e of cells containing ion-selective electrodes may be 100 Mfl or more, voltage measuring devices to be 'used WIth these electrodes generally have internal resistances of at least 1012 n. It is important to appreciate that an error in measured voltage, such as that shown in Example 23-1 (-0.133 V), would have an enormous effect on the accuraey.of a concentration measurement based on that potentIaL Thus, as shown in Section 23H-2, a 0.001 V uncertainty in potential leads to a relative error of about 4% in the determination of the hydrogen ion concentratIOn of a solution by potential measurement WIth a glass electrode. An error of the size found in Example 23-1 would result in a concentration uncertamty of two orders of magnitude or more. Direct-reading digital voltmeters with high internal reSIstances are used almost exclusively for pH and pIon measurements. We descrihe these devices in the next section. 23G-1 Direct-Reading

From Ohm's law, we may write

X

Instruments

Numerous direct-reading pH meters are available comme.rcially. Generally. these are solid-state devices With a fIeld-effect transistor or a voltage follower as the first amplilier stage to provide the necessary high input resIstance. FIgure 23-16 is a schematic of a simple. batten-operated pH meter that can be huilt for about

Frn",

reference

eteelrode

~

FIGURE 23-16 A pH meter based on a quad Junction-FETinput operational amplifier

integrated circuit. Resistors R ,-R, and potentiometers P ,-P , are 50 kll. The circuit may be powered by batteries as shown or an appropriate power supply. See the original paper for descriptions of the circuit operation and the calibration procedure. (Adapted from D. L. Harris and D. C. Harris, J. C h e r n . E d u c . , 1992, 69, 563. With permIssion.)

$10, exclusive of the pH prohe and digital multimeter, which is used as the readout.'9 The output of the probe is connected to a high-resistance voltage follower A (see Sections 3B-2 and 3C-2), which has an input resistance of to 12 fl. Operational amplifiers Band C provide gain (slope, or temperature control) and offset (calibration) for the circuit readout. The inverting amplifIer C (see Section 3B-3) inverts the sense of the signal so that an increase in pH produces a positive increase in the output voltage of the circuit. The circuit is calibrated with buffers to display a range of output voltages extending from 100 to 1400 m Y , corresponding to a pH range of 1 to 14. The three junction-FET operational amplifiers are located in a single quad integrated circuit package such as the LF347 (made hy National Semiconductor).

The range of pion meters available from instrument manufacturers is simply astonishing.''' We can classify four groups of meters based on price and readability. '''D. L !farris and D C. H;uns, J C her n. E duc.. J992. 69. :'i6; ~JT

-

" -0.5

~ i5. ~ ." ~

U

F IG U R E 2 4 -2 Changes in cathode potential during the deposition of copper with a constant current of 1.5 A. The cathode potential is equal to E , + '1".

ions to maintain the desired current. When this occurs, further increases in E,ppl cause rapid changes in 1)" and thus the cathode potential; codeposition of hydrogen (or other reducible species) then takes place. The cathode potential ultimately becomes stabilized at a level fixed by the standard potential and the overvoltage for the new electrode reaction; further large increases in the cell potential are no longer necessary to maintain a constant current. Copper continues to deposit as eopper(II) ions reach the electrode surface; the contribution of this process to the total current, however, becomes smaller and smaller as the deposition becomes more and more nearly complete. An altcrnative process, such as reduction of hydrogen or nitrate ions, soon predominates. The changes in cathode potential under constant current conditions are shown in Figure 24-2.

2 4 A -3

E le c tr o ly s is

W o r k in g

E le c tr o d e

a t C o n s ta n t P o te n tia ls

From the Nernst equation, we see that a tenfold decrease in the concentration of an ion bcing deposited requires a negative shift in potential of only 0 .0 5 9 2 /n V. Electrolytic methods, therefore, are reasonablv selective. For example, as the copper concentration ~f a solution is decreased from 0.10 M to 10" M, the thermodynamic cathode potential E , changes from an initial value of +0.31 to +0.16 V. In theory, then, it should be feasible to separate copper from any elcment that does not deposit within thisO.IS-V potential

range. Species that deposit quantitatively at potentials more positive than +0.31 V could be eliminated with a prereduction; ions that require potentials more negative than +0.16 V would not interfere with the copper deposition. Thus, if we are willing to accept a reduction in analyte concentration to 10-6 M as a quantitative separation, it follows that divalent ions differing in standard potentials by about 0.15 V or greater can, theoretically, be separated quantitatively by electrodeposition, provided their initial concentrations are about the same. Correspondingly, about 0.30- to 0.10- V differences are required for univalent and trivalent ions, respectively. An approach to these theoretical separations, within a reasonable electrolysis period, requires a more sophisticated technique than the ones thus far discussed because concentration polarization at the cathode, if unchecked, will prevent all but the crudest of separations. The change in cathode potential is governed by the decrease in I R drop (Figure 24-1b). Thus, for instances in which relatively large C\lrrents are applied initially, the change in cathode potential can ultimately be expected to be large. On the other hand, if the cell is operated at low current levels so that the variation in cathode potential is decreased, the time required for completion of the deposition may become prohibitively long. A straightforward solution to this dilemma is to begin the electrolysis with an applied cell potential that is sufficiently high to ensure a reasonable current; the applied potential is then continuously decreased to keep the cathode potential at the level necessary to accomplish the desired separation. Unfortunately, it is not feasible to predict the required changes in applied potential on a theoretical basis because of uncertainties in variables affecting the deposition, such as overvoltage effects and perhaps conductivity changes. Nor, indeed, docs it help to measure the potential across the two electrodes, because such a measurement gives only the overall cell potential, E,ppl' The alternative is to measure the potential of the working electrode against a third electrode whose potential in the solution is known and constant -that is, a reference electrode. The voltage applied across the working electrode and its counter electrode can then be adjusted to the level that will control the cathode (or anode) at the desired potential with respect to the reference electrode. This technique is called c o n tr o lle d - p o te n tia l e le c tr o lys is , or sometimes p o te n tio s ta tic e le c tr o lys is .

2 4 -3 Apparatus for controlled-potential electrolysis. The digital voltmeter monitors the potential between the working and the reference electrode. The voltage applied between the working and the counter electrode is varied by adjusting contact C on the potentiometer to maintain the working electrode (cathode in this example) at a constant potential versus a reference electrode. The current in the reference electrode is essentially zero at all times. Modern potentiostats are fullyautomatic and often computer controlled. The electrode symbols shown (-0 Working, --> Reference, Counter) are the currently accepted notation. F IG U R E

f-

Experimental details for performing a eontrolledcathode-potential electrolysis are presented in Section 24C-1. For the present, it is sufficient to note that the potential difference between the reference electrode and the cathode is measured with a voltmeter. The voltage applied between the working electrode and its counter electrode is controlled with a voltage divider so that the cathode potential is maintained at a level suitable for the separation. Figure 24-3 is a schematic of a manual apparatus that permits deposition at a constant cathode potential. An apparatus ofthe type shown in Figure 24-3 can be operated at relatively high initial applied potentials to give high currents. As the electrolysis progresses, however, a decrease in the voltage applied across AC is required. This decrease, in turn, decreases the current. Completion of the electrolysis is indicated by the approach of the current to zero. The changes that occur

III

T u to r ia l:

Learn more about electrolysis.

in a typical constant -cathode-potential electrol ysis are depicted in Figure 24-4. [n contrast to the electrolytic methods described earlier, implementing this technique manually would demand constant attention. Fortunately, the constant-potential electrolysis method can be readily automated. A potentiostat, such as that shown in Figure 24-6, is suitable for the control of the working electrode potential with respect to the reference electrode.

248

AN INTRODUCTION TO COULOMETRIC METHODS OF ANALYSIS

Coulometry encompasses a group of analytical methods that involve measuring the quantity of electricity (in coulombs) needed to convert the analyte quantitatively to a different oxidation state. Like gravimetric methods, coulometry has the advantage that the

proportionality constant between the measured quantity (charge in coulombs) and the mass of analyte can be computed from known physical constants; thus, calibration or standardization is not usually necessary. Coulometric methods are often as accurate as gravimetric or volumetric procedures, and they are usually faster and more convenient than gravimetric methods. Finally, coulometric procedures are easily automated.'

248-1

Units for Quantity

A constant current of 0.800 A was used to deposit copper at the cathode and oxygen at the anode of an electrolytic cell. Calculate the mass of each product that was formed in 15.2 min, assuming that no other redox reactions occur.

The equivalent masses are determined half-reactions

of Electricity

The quantity of electricity or charge is measured in units of coulombs (C). A coulomb is the quantity of charge transported in one second by a constant current of one ampere. Thus, for a constant current of I amperes for t seconds, the charge in coulombs Q is given by the expression

Cu'+

i,

Q

(2 4 -4 )

F

=

= 96,485~1

mo e

'

nF

nc" = nF

anout

methods, see J A. Dean, l-l, pp. I..U 18-1,UJ3, Nev.

COulOfficlric

Section 1995; D. 1. Curran. in f- a b o r a c o r y T e c h n iq u e s in E le c 2nd ed., P. T. Kissinger and W R. Heinemann, cds., pp. 739-68, :"Iew York: Marcd Dekker. 1996; 1. A. Plambeck. E le c tr o a n a lytjc a ! C h e m is tr \,. Chap. t2. New )'t)rk: Wiky. 1982

An a lytic a l

C h e m i.n r y H a n d b o o k,

York: McGraw-HilL

C h e m is e r y,

X

15.2 min

X

60 s lm in

729M! =

2~

Im o l

Cu X 96,485 e /~

= 3.781 X 10 3 mol Cu

Q no,

=

nF

=

4~

Im o l

729.6 e 0, X 96,485 e /~

= 1.890 X 10'3 mol 0,

m c " = n c " .M .c " =

mo,

where n is the number of moles of clectrons in the analyte half-reaction. As shown in Example 24-1, we can use these definitions to calculate the mass of a chemical species that is formed at an electrode by a current of known magnitude.

lr o a n a lyr jc a l

0.800 A

We can find the number of moles of Cu and 0, from Equation 24-5:

Q n A= ~

information

=

The masses of Cu and 0, are given by

Faraday's law relates the numbcr of moles of the analyte n A to the charge

~For additional

+ 2e' ---.C u ( s ) + O ,( g ) + 4H+

Q

6.02214 X lO23~e_- - X 1.60218 X 10,19 ~ mole' e'

2H,O 2CHCIJ + Hg,Cl,(s) 2

24-3 It is desired to separate and determine hismuth, copper, and silver in a solution that is 0.0550 M in BiO+, 0.125 M in Cu 2+, 0.0962 M in Ag', and 0.500 M in HCIO~. (a) Using 1.00 x 10-6 M as the criterion for quantitative removal, determine whether separation of the three species is feasible by controlled-potential electrolysis. (b) If any separations are feasible, evaluate the range (versus Ag-AgCI) within which the cathode potential should be controlled for the deposition of each. 2 4 -4

At a potential of --1.0 V (versus SCE), carhon tetrachloride rcduced to chloroform

At -1.80 V, the chloroform further reacts to givc methanc: 2CHCl3 + 6H+ + 6e- + 6Hg(l)

---->

2CH~ +

3 H g ,C l,( s )

Several 0.750-g sampies containing CCl" CHCI" and inert organic species were dissolved in methanol and electrolyzed at -1.0 V until the current approached zero. A coulometer indicated the charge required to complete the reaction, as given in the second column of the following tahle. The potential of the cathode was then adjusted to -1.80 V. The additional charge reqUired to complete the reaction at this potential is given in the third column of the table. Calculate the percent CCl~ and CHClJ in each mixture. Charge Required at-1.DV.C

Charge Required at-1.8V,C

11.63

68.60

21.52

~5.33

.1

6.22

4

12.92

4598 55.31

Sample No.

A 6.39-g sample of an ant-control preparation was decomposed by wet ashing with H 2S0 4 and HNO J. The arsenic in the reSidue was reduced to the trIvalent

state with hydrazine. After the excess reducing agent had been removed, the arsenic(III) was oxidized with electrolytically generated I, in a fa in tly a lka lin e m e d iu m :

HAsO/-

+ I, + 2HCO) -

--> HAsO,z-

+ 21- + 2CO + H 0 2

The titration was complete after a constant current of 127.6 mA had been passed for II min and 54 s. Express the results of this analysis in terms of the percentage As,O) in the original sample. A O.0809-g sample of a purified organic acid was dissolved in an alcohol-water mixture and titrated with coulometrically generated hydroxide ions. With a current of 0.0441 A, 266 s was required to reach a phenolphthalein end point. Calculate the equivalent mass of the acid.

A digital chloridometer was used to determine the mass of sulfide in a wastewater sample. The chloridometer reads out directly III ng Cl . In chlonde de: terminations, the same generator reaction is used, but the tltratton reach~n IS Cl- + Ag' -> AgCl(s). Derive an equation that relates ~he deSired quantity, mass 5 2- (ng), to the chloridometer readout m mass CI (ng). _ A particular wastewater standard gave a readmg of 1689.6 ng CI . What ,total charge in coulombs was required to generate the Ag' needed to preCIpitate the sulfide in this standard? . . The following results were obtained on 20.00-mL samples contammg known amounts of sulfide.17 Eaeh standard was analyzed in triplicate and t~= mass of chloride recorded. Convert each of the chloride results to mass S (ng). Known Mass 5 2-, ng

*24-11 Traces of aniline can be determined generated Br,:

c"HsNH, + 3Br, --> c"H,Br)NH,

+ 3H' + 3Br-

6365

10447.0

10918.1

4773

8416.9

8366.0

8416.9

3580

6320.4

6638.9 3936.4

The polarity of the working electrode is then reversed, and the excess bromine is determined by a coulometric titration involving the generation of CU(I):

1989

6528.3 3779.4

796

1682.9

1713.9

Br2 + 2Cu' --> 2Br- + 2Cu2+

699

1127.9

Suitable quantities of KBr and copper(II) sulfate were added to a '25.0-mL sample containing aniline. Calculate the mass in micrograms of C 6H sNH 2 in the sample from the accompanying data: Working Electrode Functioning As

Generation Time (min) with a Constant Current of 1.00 mA

Anode

3.76

Cathode

0.270

Construct a eoulometric titration curve of 100.0 mL of a I M H,S04 solution containing Fe(lI) titrated with Ce(IV) generated from 0.075 M Ce(III). The titration is monitored by potentiometry. The initial amount of Fe(lI) present is 0.05182 mmol. A constant current of 20.0 mA is used. Find the time corresponding to the equivalence point. Then, for about ten values of time before the equivalence point, use the stoichiometry of the reaction to calculate the amount of Fe" produced and the amount of Fe'+ remaining. Use the Nemst equation to find the system potential. Find the equivalence point potential in the usual manner for a redox titration. For about ten times after the equivalence point, calculate the amount of Ce 4+ produced from the electrolysis and the amount of Ce 3+ remaining. Plot the curve of system potential versus electrolysis time. ~

Mass CI- Determined, ng

by reaction with an excess of electrolytically

C h a lle n g e

P r o b le m

24-13 Sulfide ion (S'· ) is formed in wastewater by the action of anaerobic bacteria on organic matter. Sulfide can be readily protonated to form volatile, toxic H,S. In addition to the toxicity and noxious odor, sulfide and H,S cause corrosion problems because they can be easily converted to sulfuric acid when conditions change to aerobic. One common method to determine sulfide is by coulometric titration with generated silver ion. At the generator electrode, the reaction is Ag -> Ag' + eO. The titration reaction is S'- + 2Ag' -> Ag,5(s).

3763.9

466

705.5

1180.9 736.4

373

506.4

521.9

233 0

10654.9

1669.7 1174.3 707.7 508.6

278.6

278,6

247.7

-22.1

-19.9

-17.7

Determine the average mass of 5'- (ng), the standard deviation, and the % RSD of each standard. Prepare a plot of the average mass of 5'- determined (ng) versus the actual, mass (ng). Determine the slope, the intercept, the standard error, and the R value. Comment on the fit of the data to a linear modeL . (f) Determine the detection limit (ng) and in parts per mllhon usmg a k factor of2 (see Equation 1-12). _ An unknown wastewater sample gave an average reading of 893.2 ng Cl . What is the mass of sulfide (ng)? If 20.00 mL of the wastewater sample was introduced into the titration vessel, what is the concentration of 5' m parts per million?

V o lta m m e tr y

.. \I

olta mmetr y

compr ises a gr oup of electr o-

·a na lytica l.methods

in which infor ma tion

a bout the a .na (r te is obta ined

ing cur r ent a s a junction conditions

by mea sur -

of a p~lied potentia l

tha t pr odlOte pola r iza tion

under

of a n indica -

tor , or [ cor king, electr ode. When cur r entpr opor tiona l to a na lyte coijcentr a tion potentia ~

the technique

is monitor ed a t fl:I:ed

is ca lled a mper ometr y.

Gener a lly, to enha nce pola r iza tion, tr odes in volta mmetr ya nd

wor king elec-

a r nper ometr yha ve

sur -

fa ce a r ea s of a few squa r e millimeter s a t the most a nd, in SOme a pplica tions,

a few squa r e micr ometer s

or less.

01 I2J

Throughout this chapter, this logo indicates an opportunity for online self-study at www .thomsouedu.com/chemistry/skoog, linking you to interactive tutorials, simulations, and exercises. 716

Let us begin by pointing out the basic differences between voltammetry and the two types of electro_ chemical methods that we discussed in earlier chapters. Voltammetry is based on the measurement of the current that develops in an electrochemical cell under conditions where concentration polarization exists. Recall from Section 22E-2 that a polarized electrode is one to which we have applied a voltage in excess of that predicted by the Nernst equation to cause oxidation or reduction to occur. In contrast, potentiometric measurements are made at currents that approach zero and where polarization is absent. Voltammetry differs from coulometry in that, with coulometry, measures are taken to minimize or compensate for the effects of concentration polarization. Furthermore, in voltammetry there is minimal consumption of analyte, whereas in coulometry essentially all of the analyte is converted to another state. Voltammetry is widely used by inorganic, physical, and biological chemists for nonanalytic:il purposes, including fundamental studies of oxidation and reduction processes in various media, adsorption processes on surfaces, and electron-transfer mechanisms at chemically modified electrode surfaces. Historically, the field of voltammetry developed from pola r ogr a phy, which is a particular type of voltammetry that was invented by the Czechoslovakian chemist Jaroslav Heyrovsky in the early 1920s1 Polarography differs from other types of voltammetry in that the working electrode is the unique dr opping mer cur y electr ode. At one time, polarography was an important tool used by chemists for the determination of inorganic ions and certain organic species in aqueous solutions. In the late 1950s and the early 19605,however, many of these analytical applications were replaced by various spectroscopic methods, and polarography became a less important method of analysis except for certain special applications, such as the determination of molecular oxygen in solutions. In the mid-1960s, several major modifications of classical voltammetric techniques were developed that enhanced significantly the sensitivity and selectivity of the method. At about this same time, the advent of low-cost operational amplifiers made possible the commercial development of relatively inexpensive instruments that incorporated many of these modifications and made them available to all chemists. The result was a resurgence of interest in

11. Hevrovsh Cher n. Ust}', 1922.16.256. Ht:\Tovsh 'A'asawarded the 1959 Nobel Priz~ in Chc~jstry for his discO\"ery a~d development of polarograph~

Type of voltammetry

{2J

Differcntialpulse vo!tammetry

r~\ I

EI.!

I

/

\

\

\

Time-----.FIGURE

25-1

Voltage versus time excitation signals used in voltammetry.

applying polarographic methods to the determination of a host of species, particularly those of pharmaceutical, environmental, and biological interest.' Since the invention of polarography, at least 60,000 research papers have appeared in the literature on the subject. Research activity in this field, which dominated electroanalytical chemistry for more than five decades, peaked with nearly 2,000 published journal articles In 1973. Since that time, interest in polarographIc methods has steadily declined, at a rate nearly twice the rate of growth of the general chemical literature, until In 2005 only about 300 papers on these methods appeared. This decline has been largely a result of concerns about the use oflarge amounts of mercury in the laboratory as well as in the environment, the somewhat cumbersome nature of the apparatus, and the broad availability of faster and more convenient (mainly spectroscopIc) methods. For these reasons, we will discuss polarographv only briefly and, instead, refer you to the many so~rces that are available on the subject.' Although polarography declined in importance, voltammetry and amperometry at working electrodes ~A. Bond.

Br oa dening

Eleecr ochemica l

Hor izons:

P r inciples a nd illustr a -

tion of \/olta mmetr ic a nd Rela ted Techniques. New York:

Oxford,

2003;

(:. M. A. Brett and A. M. Oliveira Brett. In Encyclopedw of Electr ochemi~-tr v A. J. Bard and M. Stratmann, eds .. Vol. 3. Insr r nmenta tlOfI a nd £It: c~r oa na lvtica l Chemistr y, P. Unwin, ed., New York: WIley. 2002, pp. 105 -24> A. 1. Bard and L R. Faulkner, Elecrrochemu:.a l ~elhods: 2nd ed. New York: Wile .•..2001. Chap. 7. pp. 261-30-4; La bor a tor .\ .Technl~Ue5 in t:leclr oa na lvr ica l Chemistr y, 2nd ed., P. T Kissinger and \\'. R. Hememan. -:ds.. Ne~- York: Dekker. 1996, pp. 4-W -61.

other than the dropping mercury electrode have grown at an astonishing pace' Furthermore, voltammetry and amperometry coupled with liquid chromatography have become powerful tools for the analysis of complex mixtures. Modern voltammetry also continues to be an excellent tool in diverse areas of chemistry, biochemistry, materials science and engineering, and the environmental sciences for studYing oXIdatIon, reduction, and adsorption processes.'

25A

EXCITATION SIGNALS IN VOLTAMMETRY

In voltammetry, a variable potential excitation signal is impressed on a working electrode in an electrochemIcal cell. This excitation signal produces a charactenstlc current response, which is the measurable quantity III this method. The waveforms of four of the most common excitation signals used in voltammetry are shown in Figure 25-1. The classical voltammetric excitation JFrom 1973 to 2005. the annual numbc:r of journal articles on \'o~tammetrv and amperometry grew at three times and two and on:-half tlmes, res~ectivelY, the rate of production of articles ~n all of chemistry. 'Some general references on voltammetry IOclu~e ~-\.,1. ~a~'i:;\~ ~~~: faulkner Elecr r ochomca l Mer hods, 2nd ed., Ne\\ .lork. .' - _ ' S. p, Ko~naves, in Ha ndbook of Instr umenta l Te~hntq~es for Ana lyt!ca l Chemistr y, Frank A. Settle. ed., Upper Saddle RIVC:r.1\1: Pren~lCe-Hal~, 1997 . 711-28' La bor a tor y Techmques In ElectfOu.na lj tica l ChemlSr r }. , pp K.' . d W R Heineman. eds .. "ew York: Dekker. . " _ 'Jew York: 2nd ed .. P. T. Issmger an 1996; Ana lytua l F olta mmer r y. \-1. R. Smyth and F G. \ o~. eds.,. Elsener,

1992

signal is the linear scan shown in Figure 25-1 a, in which the voltage applied to the cell increases linearly (usually over a 2- to 3-V range) as a function of time. The current in the cell is then recorded as a function of time, and thus as a function of the applied voltage. In amperometry, current is recorded at fixed applied voltage. Two pulse excitation signals are shown in Figure 25-1 band c. Currents are measured at various times during the lifetime of these pulses. With the triangular waveform shown in Figure 25-1 d, the potential is cycled between two values, first increasing linearly to a maximum and then decreasing linearly with the same slope to its original value. This process may be repeated numerous times as the current is recorded as a function of time. A complete cycle may take 100 or more seconds or be completed in less than 1 second. To the right of each of the waveforms of Figure 25-1 is listed the types of voltammetry that use the various excitation signals. We discuss these techniques in the sections that follow.

Figure 25-2 is a schematic showing the components of a modern operational amplifier potentiostat (see Section 24C-1) for carrying out linear-scan voltammetric measurements. The cell is made up of three electrodes immersed in a solution containing the analyte and also an excess of a nonreactive electrolyte called a suppor ting electr olyte. One of the three electrodes is the work-

ing electrode, whose potential is varied linearly with time. Its dimensions are kept small to enhance its tendency to become polarized (see Section 22E-2). The second electrode is a reference electrode (commonly a saturated calomel or a silver-silver chloride electrode) whose potential remains constant throughout the experiment. The third electrode is a counter electrode, which is often a coil of platinum wire that simply conducts electricity from the signal source through the solution to the working electrode. The signal source is a linear-scan voltage generator similar to the integration circuit shown in Figure 3-16c. The output from this type of source is described by Equation 3-22. Thus, for a constant dc input potential of E i, the output potential E" is given by Ei

Eo = ~ RiCe

i' 0

E,t

dt = - RiCe

The output signal from the source is fed into a potentiostatic circuit similar to that shown in Figure 25-2 (see also Figure 24-6c). The electrical resistante.ofthe control circuit containing the reference electrode is so large (> 10" 0) that it draws essentially no current. Thus, the entire current from the source is carried from the counter electrode to the working electrode. Furthermore, the control circuit adjusts this current so that the potential difference between the working electrode and the reference electrode is identical to the output voltage from the linear voltage generator. The resulting current, which is directly proportional to the potential difference between the working electrode-reference

r:::il l.Q.J

Tutor ia l: Learn more about voltammetric instrum e n ta tio n

and

waveforms.

Linear sweep generator

Dal3 acquisition sysh::m

FIGURE 25-2 An operational amplifier potentiostat. The three-electrode cell has a working electrode (WE).reference electrode (RE),and a counter electrode (CE).

electrode pair, is then converted to a voltage and recorded as a function of time by the data-acquisition system.' It is important to emphasize that the independent variable in this experiment is the potenllal of the working electrode versus the reference electrode and not the potential between the working electrode and the counter electrode. The working electrode is at virtual common potential throughout the course of the experiment (see Section 38-3).

~ 0.75 em

I I j

I I

I

7.5 em

Hg

I I

258-1 Working Electrodes

The working electrodes used in voltammetry take a variety of shapes and forms.' Often, they are small flat disks of a conductor that are press filled into a rod of an inert material, such as Teflon or Kel-F, that has embedded in it a wire contact (see Figure 25-3a). The conductor may be a noble metal, such as platinum or gold; a carbon material, such as carbon paste, carbon fiber, pyrolytic graphite, glassy carbon, dia~ond,. or carbon nanotubes; a semiconductor, such as tm or mdlUm oxide; or a metal coated with a film of mercury. As shown in Figure 25-4, the range of potentials that can be used with these electrodes in aqueous solutions varies and depends not only on electrode material but also on thc composition of the solution in which it is immersed. Generally, the positive potential limitations arc caused by the large currents that develop because of oxidation of the water to give molecular oxygen. The negative limits arise from the reduction of water to produce hydrogen. Note that relatively large negative potentials can be tolerated with mercury electrodes because of the high overvoltage of hydrogen on this metal.

6Earty vohammetry was performed with a two-electrode system rather than the three-electrode system shown in Figure 25-2. With a t •••. 'oelectrode syskm, the second electrode is either a large metal. electr~de or a reference electrode large enough to prevent its polarization dunng an experiment. This second electrode combines the functiom of the rcference electrode and the counter electrode in Figure 25-2. 1n the twoelectrode system, we assume that the potential of this second electrode is constant th'rouohout a scan so that the working ekctrode potential is simply the differe~ce be~ween the applied.potentialand the potential of the second electrode. With solutions of high electncal resistance, ho .••.e\cr, this assumption is not valid because the IR drop is significant and increases as the current increases. Distorted voltammograms are the result. ..••• Im{)st aU .•.. oltammetry is now performed with three-electrode systems ) Manv of the ~'orking electrodes that we dt:scribe in this chapter have -di· mensi'ons in the millimeter range. There is nnw intense interest in studies ""ith electrodes having dinwnsions in the mi...:romet~r range and smaller We will term ~uch electrodes micr oelectr odes. Such electr odes have seVeral ad\'antages ewer classical working e1ectrodes_ Vie descrihe some of the uni4ue characteristics ,)f microelectfl)des in Section 25[

I .I

-I ~ 6mm

\ (bl

(a)

(e)

FIGURE 25-3 Some common types of commercial

voltammetric electrodes: (a) a disk electrode; (b) a hanging mercury drop electrode (HMOE);(c) a microelectrode; (d) a sandwich-type flow electrode. (Electrodes (a], [c], and [d]courtesy of Bioanalytical Systems, Inc., West ~afayetle, IN. with permission.)

Mercury working electrodes havc been widely used in voltammetrv for several reasons. One IS the relatively largc n;gative potential range just described.

I M H,SO, ------~I

tochemical, or electrochemical polymerization methods. Immobilized enzyme biosensors, such as the amperometric sensors described in Section 25('-4. are a type of modified electrode. These can be prepared by covalent attachment, adsorption, or gel entrapment. Another mode of attachment for electrode modification is by self-a ssembled m",wla yer s, or SAMs.' In the most common procedure, a long-ehain hydrocarbon with a thiol group at one end and an amine or carboxyl group at the other is applied to a pristine gold or mercury film electrode. The hydrocarbon molecules assemble themselves into a highly ordered array with the thiol group attached to the metal surface and the chosen functional group exposed. The arrays may then be further functionalized by covalent attachment or adsorption of the desired molecular species. Modified electrodes have many applications. A primary interest has been in the area of electrocatalysis. In this application, electrodes capable of reducing oxygen to water have been sought for use in fuel cells and batteries. Another application is in the production of e1ectrochromic devices that change color on oxidation and reduction. Such devices are used in displays or sma r t windows and mir r or s. Electrochemical devices that could serve as molecular electronic devices, such as diodes and transistors, are also under intense study. Finally, the most important analytical use for such electrodes is as analytical sensors selective for a particular species or functional group (see Figure 1-7).

I Pt)

pH 7buffer iPtI

1M NaOH (Ptl 1M H,SO,iHgl

--------

FIGURE25-4 Potential ranges for three types of electrodes in various supporting electrolytes. (Adapted from A. J. Bard and L R. Faulkner, E lectrochem ical M ethods, 2nd ed., back cover, New York:Wiley, 2001. Reprinted by permission of John Wiley & Sons, Inc.)

O,or.

...•1 1 M KCI (Hg)

t-----------II

,.

electrochemICal OXidation

l t \t NaOH \HgJ

>---------- P from a stirred solution of A. See Figure 25-6 for potentials corresponding to curves X , Y, and Z.

FIGURE 25-13

P rofiles

for E lectrodes

in S tirred S olutions

Let us now consider concentration-distance profiles when the reduction described in the previous section is performed at an electrode immerscd in a solution that is stirred vigorously. To understand the effect of stirring, wc must develop a picture of liquid flow patterns in a stirred solution containing a small planar electrode. We can identify two types of flow depending on the average flow velocity, as shown in Figure 25-11. Lam inar flow occurs at low flow velocities and has smooth and regular motion as depicted on the left in the figure. T urbulent flow, on the other hand, happens at high velocities and has irregular, fluctuating motion as shown on the right. In a stirred electrochemical cell, we have a region of turbulent flow in the bulk of solution far from the electrode and a rcgion of laminar flow

close to the electrode. These regions are illustrated in Figure 25-12. In the laminar-flow region, the layers of liquid slide by one another in a direction parallel to the electrode surface. Very near the electrode, at a distance D centimeters from the surface, frictional forces give rise to a region where the flo~ velocity is essentially zero. The thin layer of solution"i.n this region is a stagnant layer called the N ernsr diffusion layer. It is only within the stagnant Nernst diffusion layer that the concentrations of reactant and product vary as a function of distance from the electrode surface and that there are concentration gradients. That is, throughout the laminar-flow and turbulent-flow regions, convection maintains the concentration of A at its original value and the concentration of P at a very low level.

Ii D is ta n c e

x

fr o m

e le c tr o d e ,

em

Ii N ern st

d iffu s io n

laye~

_

of:~a:~:~: :~I~l:~:ion { j FIGURE

25-12 Flow patterns and regions

of interest near the working electrode in hydrodynamic voltammetry.

0( 0(

•

0(

J 1

Figure 25-13 shows two sets of concentration profiles for A and P at three potentials shown as X, Y, and Z in Figure 25-6. In Figure 25-13a, the solution is divided into two regions. One makes up the bulk of the solution and consists of both the turbulent- and laminar-flow regions shown in Figure 25-12, where mass transport takes place by mechanical convection brought about by the stirrer. The concentration of A throughout this region is CA, whcreas Cp IS essentially zero. The second region is the Nernst diffUSIOnlayer, which is immediately adjacent to the electrode surface and has a thickness of D centimeters. Typically, 8 ranges from to -, to 10-3 cm, depending on the efficiency of the stirring and the viscosity of the lIqUid. Within the static diffusion layer, mass transport takes

place by diffusion alone, just as was the case with the unstirred solution. With the stirred solutIOn, however, diffusion is limited to a narrow layer of liquid, which even with time cannot extend indefinitely into the solution. As a result, steady, diffusion-controlled currents appear shortly after applying a voltage. . As is shown in Figure 25-13, at potential X , the equIlibrium concentration of A at the electrode surface has been reduced to about 80% of its original value and the equilibrium concentration P has increased by an equivalent amount; that is, c~ = c~ - c~ . At potential Y, which is the half-wave potential, the equilibrium concentrations of the two species at the surface arc approximately the same and equal to CAlL Finally. at potential Z and beyond, the surface concentration of A

approaches zero, and that of P approaches the original concentration of A, CA' Thus, at potentials more negative than Z, essentially all A ions entering the surface layer are instantaneously reduced to P. As is shown in Figure 25-13b, at potentials greater than Z the concentration of P in the surface laver remains constant at c~ = C A because of diffusion ~f P back into the stirred region.

This derivation is based on an ovcrsimplified picture of the diffusion layer in that the interface between the moving and stationary layers is viewed as a sharply defined edge where transport by convection ceases and transport by diffusion begins. Nevertheless, this simplified model does provide a reasonable approximation of the relationship between current and the variables that affect the current.

. Earpl

The current at any point in the electrolysis we have just discussed is determined by the rate of transport of A from the outer edge of the diffusion layer to the electrode surface. Because the product of the electrolysis P diffuses from the surface and is ultimately swept away by convection, a continuous current is required to maintain the surface concentrations demanded by the Nernst equation. Convection, however, maintains a constant supply of A at the outer edge of the diffusion layer. Thus, a steady-state current results that is determined by the applied potential. This current is a quantitative measure of how fast A is being brought to the surface of the electrode, and this rate is given by dcA ldx where x is the distance in centimeters from the electrode surface. For a planar electrode, the current is given by Equation 25-4. Note that dcA ldx is the slope of the initial part of the concentration profiles shown in Figure 25-13a, and these slopes can be approximated by (cA - c~)IS . When this approximation is valid, Equation 25-4 reduces to . I

=

nF AD" ~-S~

(c, - c~)

=

k,(c,-

c~)

(25-5)

where the constant kA is equal to nF AD A/S. Equation 25-5 shows that as c1 becomes smaller as a result of a larger negative applied potential the current increases until the surface concentration approaches zero, at which point the current becomes constant and independent of the applied potential. Thus, when c~ ---> 0, the current becomes the limiting current i" and Equation 25-5 reduces to Equation 25-6." . II

liCarcful

nF AD, = ~-S~

c,

=

k,c,

(25-6)

analysis of the unib of the variables in thIS equation leads to

' mol e - ) - mo ana)te

n ( ----I-I.

F

(

C "J . '(' --. - --:- Afcm-jIJ A" _mol e ,

em'"J (mol ,nalyte - c.•.. ---- ---~ em},

) /ij

for R eversible

R eactions

il

0_

CA

-

-

i

--,;;,-

The surface concentration of P can also be expressed in terms of the current by using a relationship similar to Equation 25-5. That is, nF ADp i =

,

---S~(cp

-

r

c~)

where the minus sign results from the negative slope of the concentration proftle for P. Note that Dp is now the diffusion coefficient of P. But we have said earlier that throughout the electrolysis the concentration of P approaches zero in the bulk of the solution and, therefore, when Cp = 0, . I

where kp

=

-nfADpc~

= --S---

-nF ADp/S.

II

= kpcp

Rearranging gives c~ = ilkp

Substituting Equations 25-7 and 25-10 into Equation 25-3 yields, after rearrangement, E

- EO

,ppl-

"A -

0.0592 -~Iog-kn

kA

0.0592 - -~Iog-.--.

'p

n

i II -

- E", I

(25-11) When i = i, /2, the third term on the right side of this equation becomes equal to zero, and, by definition, E,pplis the half-wave potential. That is, _

_ -

(I

EA

-

0.0592 ~--log n

kA - - E"r kp

(25-12)

Substituting this expression into Equation 25-11 gives an expression for the voltammogram in Figure 25-6. That is,

----;.;

-1

og

_.!.1

_

i

1

species A

V oltage

for Irreversible

To develop an equation for the sigmoid curve shown in Figure 25-6, we substitute Equation 25-6 into Equation 25-5 and rearrange, which gives

E,ppl - E II2 (em)

R elationships

00592 -

Often, the ratio kA 1kl' in Equation 25-11 and in Equation 25-12 is nearly unity, so that we may wflte for the

currentC urrent-V oltage

= El!2

R elationships R eactions

Many voltammetrie electrode processes, particularly those associated with organic systems, are lfreverslble, which leads to drawn-out and less well-defined ·waves. To describe these waves quantitatively reqUIres an additionalterm in Equation 25-12 involving the activation energy of the reaction to account for the kmetlcs of the electrode process. Although half-wave potentials for irreversible reactions ordinarily show some dependence on concentration, diffusion currents remaIll linearly related to concentration. Some IrreverSible processes can, therefore, be adapted to quantltatlve analysis if suitable calibration standards are available. V oltam m ogram s

for M ixtures

of R eactants

The reactants of a mixture generally behave independently of one another at a working electrode, Thus, a voltammogram for a mixture is just the sum of the waves for the individual components. Figure 25-14 shows the voltammograms for a pair of two-component mixtures. The half-wave potentials of the two reactants differ by about 0.1 V in curve A and by about 0.2 Y 1lI curve B . Note that a single voltammogram may permit the quantitative determination of two or more speclCs provided there is sufficient difference between succeeding half-wave potentials to permit evaluatIOn of md,vldual diffusion currents. Generally, a difference of 0.1 to 0.2 Y is required if the more easily reducible species undergoes a two-electron reduction; a minimum of about 0.3 V is needed if the ftrst reduction is a one-electron process. A nodic

and M ixed

FIGURE 25-14 Voltammograms for two-component

mixtures. Half-wave potentials differ by 0.1 V in curve and by 0.2 V in curve B . Fe2~ ~Fe3t-

A,

+ e~

As the potential is made more negative, a decrease in the anodic current occurs; at about -0.02 Y, the current becomes zero because the oxidation of iron(II) ion has ceased. Curve C represents the voltammogram for a solution of iron(III) in the same medium. Here, a cathodiC wave results from reduction of iron(Ill) to iron (II). The half-wave potential is identical with that for the anodic wave, indicating that the oxidation and reduc-

t

----+

Fe2+

~ c

"~

0

u

::I:

l

A nodic-C athodic

+0.4

V oltam m ogram s

Anodic waves as well as cathodic waves arc encountered in \'oltammetry. An example of an anodic wave IS iIlust~ate-d in curve A of Figure 25-15, where the electrode reaction is the oxidation of iron( II) to iron( Ill) in the presence of citrate ion. A limiting current IS observed at about +0.1 Y (versus a saturated calomel electrode [SeED, which is due to the half-reaction

+0.2

0.0 E appl' V

-0.2 \'s.

-0.4

-0.6

-0.8

SeE

FIGURE 25-15 Voltammetric behavior of iron(t1)and

iron(lIl)in a citrate medium. Curve A : anodic wave for a solution in which CFe" ~ 1 x 10 -4 M. Curve B : anodlccathodic wave for a solution in which CFel- = CFe3- == 0.5 x 10 -, M. Curve C: cathodic wave for a solution in which (Fe)-

=

1 x 10 --4 M.

Inlet

moved by passing an inert gas through the analyte so. lulton for several mmutes (spa r ging). A stream of the same gas, usually mtrogen, ISpassed over the surface of the solulton during analysis to prevent reabsorption of oxygen. The lower curve in Figure 25-16 is a voltam_ mogram of an oxygen-free solution. 25C-4 Applications

Electrical connection to counter electrode block

of Hydrodynamic

Voltammetry

o

-0.4

-0.8

-1.2

Eappl' V vs.

-1.6

-2.0

seE

FIGURE 25-16 Voltammogram for the reduction of oxygen in an air-saturated a.l-M KCIsolution. The lower curve IS for a a.l-M KCIsolution in which the oxygen is removed by bubbling nitrogen through the solution.

The most important uses of hydrodynamic voltammetry Include (1) detection and determination of chemical species. as they exit from chromatographic columns Or f1ow-InJeclton apparatus; (2) routine determination of oxygen and certain species of biochemical interest. such as gluc?se, lactose, and sucrose; (3) detection of end POlOtS 10 eoulometrie and volumetric titrations; and (4) fundamental studies of electrochemical processes. V oltam m etric

D etectors

and F low -Injection

tion of the two iron species are perfectly reversible at the working electrode. Curve B is the voltammogram of an equimolar mixture of lron(II) and iron(III). The portion of the curve below the zero-current line corresponds to the oxidatIOn of the iron(II); this reaction ceases at an applied potential equal to the half-wave potential. The upper portIOn of the curve ISdue to the reduction of iron(III). 25C-3

Electrical connection to working electrode

in C hrom atography

A nalysis

Hydrodynamic voltammetry is widely use'd.ior de teelton and determination of oxidizable or reducible compounds or ions that have been separated by liquid

Oxygen Waves

Dissolved oxygen is easily reduced at many working elect~odes. Thus, as shown in Figure 25-16, an aqueous solulton saturated with air exhibits two distinct oxygen waves. The first results from the reduction of oxygen to hydrogen peroxide: 02(g)

+ 2H' + 2e' ~

FIGURE25-17 (continued) (b) Detail of a commercial flow cell assembly. (c) Configurations of working electrode blocks. Arrows show the direction of flow in the cell. ([b]and [c] courtesy of Bioanalytical Systems, Inc., West Lafayelle, IN.) chromatography or that are produced by flow-injection methods. 16 A thin-layer cell such as the one shown schematically in Figure 25-17a is used in these applications. The working electrode in these cells is usually embeddcd in the wall of an insulating block separated

H20,

The second wave corresponds to the further reduction of the hydrogen peroxide: H20,

+ 2H' + 2e- ~2H20

Because both reactions are two-electron reductions the two waves are of equal height. ' Voltammetric measurements offer a convenient and widely used method for determining dissolved oxygen In solutions. However, the presence of oxygen often Interferes with the accurate determination of other species. Thus. oxygen removal is usuallv the first step in amperometrie procedures. Oxygen c~n be re-

16Voitammetric detectors are a particular type of transducer called /im iJtr a nsducer s. In this dIScussion and subsequent discussions involving voltammetric transducers. we use the more common tcrm volram metr ic de/ector . When a voltammetric transducer is inherently selective for a particular speCies by virtue of control of various experimental variables or ""hen it is co\ereu with a chemically selective layer of polymer or other membranous material. we rder to It as a volta mmecr ic sensor . For a discussion of transducc:rs. detectors. sensors. and their definitions, see

in g -C IIrrm t

(a)

FIGURE 25·17 (a) A schematic of a voltammetric system for detecting eiectroactive species as they elute from a coiumn. The cell volume is determined by the thickness of the gasket.

Section 1C4.

from a counter electrode by a thin spacer as shown. The volume of such a cell is typically 0.1 to I ilL. A voltage corresponding to the limiting-current region for analytes is applied between the working electrode and a silver-silvcr chloride reference electrode that is located downstream from the detector. We present an exploded view of a commercial flow cell in Figure 25-17b, which shows clearly how the sandwiched cell is assembled and held in place by the quick -release mechanism. A locking collar in the counter electrode block, which is electrically connected to the potentiostat, retains the reference electrode. Five different configurations of working electrode are shown in

Figure

25-l7c.

These

tIon of dctector mental

conditions.

trode

configurations

sensitivity

under

Working

materials

optimizaof experi-

electrode

are described

detection in Section

blocks

in Section

type of application of voltammetry has detection limits as low as 10-' cuss. voltammetric phy rn more detail

pcrmit a variety

is an immobilized

and elec-

25B-1.

This

in this example.

acetate

membrane.

immersed

chromatogra-

(see Section The inner peroxide.

in a glucose-containing

fuses through

the outer

lized enzyme,

where

used as labels in immunoassays,

23F-2). glucose

been

layer is a cellulose

which is permeable

cules, such as hydrogen

(or amperometry) to W- w M. We dis-

for liquid 28C-6.

enzyme

oxidase

to small mole-

When

this device

solution,

glucose

dif-

In Section

and A m perom etric

23F-2,

potentIometriC molecular There

we described

sensors

catalytic

piezoelectric

reaction

much

research

A number mercially

systems

for the determination

rndustrlal,

biomedical,

applications.

These

devices

or detectors

metric

cells and are better that

years

of specific and

are sometimes referred

com-

called

elec-

two

avaIlable sensors and one that is under this rapidly expanding field.

The

In the

commercially

development

in

R tlY the

~/a liquid.r hese

cla ssified bX sepfr a tion

typel.Q-r e often

ffl~qha nismgr by

txpe of$ta tiona r ypha se.

the

TfUiva r ietiesitMude

(1) pa r tition

chr o",,#togr a ph(f2)

a ds~#tion,

liquid-solid

chr o"fftogr a plzr -r (3)

ion~iicha nge,

or ion c~r oma toglJ fl!h)";

(4)~!~e-exclufi(J n

ma togr a ph)";

cht~ma togr a p~,a nd

(5)fi!jnil)"

(6 ) chir a l chr oma t~gr a ph)".

chr o-·.

of these impor ta nt

TMpna l

ever , pr e.sents a br ie/descr iption chr oma togr a phy

sect~~~ how-

of pla llwliquid

beda use this technique pr ovides a

simple a nd inexpensive

wa y

01 deter mining

likely-

optima l conditions for column sepa r a tions.

Y1

Throughout this chapter, this logo indicates an opportunity for online self-study at www :thomso.nedu.com IcltetnistrylskOQg,linking you to interactive tutorials, simulations, and exerciseS.

12.J

or

;~ost of t!ti.f9'wpter

dea ls with columna pplica tior s types o/chr oma togr a phy.

. Early in the development of liquid chromatography, SCIentIsts realIzed that major increases in column ef. ~ciency coU~d be achieved by decreasing the particle SIze of packmgs. It was not until the late 1960s, how. ever,. that the technology for producing ~nd using packlngs WIth particle diameters as small a~ 3 to 10 j.1m was developed. This technology required sophisticated instruments operating at high pressures, which con. trasted markedly with the simple glass columns of clas. sic gravity-flow liquid chromatography. The name hi~h-per for ma nce liquid chr oma togr a phy (HPLC) Was ongmally used to distinguish these newer procedures from the original gravity-flow methods. Today, virtu. ally all LC is done using pressurized flow. and We use the abbreviations LC and HPLC interchangeablyl

LC is the most widely used of all of the analytical sepa. ration techniques. The reasons for the popularity of the method are its sensitivity. its ready adaptability to accurate quantitative determinations, its ease of automation, its suitability for separating nonvolatile species or thermally fragile ones, and above all, its widespread applIcabIlity to substances that are important to industry, to many fields of science, and to the public. Examples of such materials include amino acids, proteins, nucleic acids, hydrocarbons, carbohydrates, drugs, terpenoids, pesticides, antibiotics, steroids, metal-organic species, and a variety of inorganic substances. I

For detailed discussions of HPLC, see L R. Snyder and 1. 1. Kirkland, In-

tr oductIOn to Moder n LiqUid Chr oma togr a phy,

1979; R. P. W Scott. Liquid Chr oma togr a phy Dekker, 1995.; S. Lindsay. High P er for ma nce New York: Wiley, 1992.

2nd ed., New York: Wiley, for the Ana lyst. New York: Liquid

Chr oma togr a phy.

Organic soluble Soluble in

I Hexane 11 MeOH I

~I_T_HF_~I!

Nonionic

I

~1_[_O_ni_c ~

FIGURE 28-1 Selection of LC modes. Methods can be chosen based on solubility and molecular mass. In most cases for nonionic small molecules (At < 2000), reversedphase methods are suitable. Techniques toward the bottom of the diagram are best suited for species of high molecular mass (M > 2000). (Adapted from H ig h P e rfo rm a n ce L iq u id C h ro m a fo g ra p h y, 2nd ed., S. Lindsay and J. Barnes, eds., New York:Wiley,1992. With permission.)

Figure 28·1 reveals that the various liquid chromatographic procedures are complementary in their application. Thus, for solutes having molecular masses greater than 10,000, size-exclusion chromatography is often used, although it is now becoming possible to handle such compounds by reversed-phase chromatography as well. For lower-molecular-mass ionic species, ion-exchange chromatography is widely used. Small polar but nonionic species are best handled by reversed-phase methods. In addition, this procedure is frequently useful for separating members of a homologous series. Adsorption chromatography was once used for separating nonpolar species, structural isomers, and compound classes such as aliphatic hydrocarbons from aliphatic alcohols. Because of problems with retention reproducibility and irreversible adsorption, adsorption chromatography with solid stationary phases has been largely replaced by normal-phase (bonded-phase) chromatography. Among the special. ized forms of LC, affinity chromatography is widely used for isolation and preparation of biomolecules, and chiral chromatography is employed for separating enantiomers.

The discussion on band broadening in Section 26C- 3 is generally applicable to LC. Here, we illustrate the important effect of stationary-phase particle size and describe two additional sources of zone spreading that are sometimes of considerable importance in LC. 288-1 Effects of Particle Size of Packings

The mobile-phase mass-transfer coefficient (see Table 26-3) reveals that eM in Equation 26-23 is directly related to the square of the diameter d p of the particles making up a packing. Because of this, the efficiency of an LC column should improve dramatically as the particle size decreases. Figure 28-2 is an experimental demonstration of this effect, where it is seen that a reduction of particle size from 45 to 6 j.1mresults in a tenfold or more decrease in plate height. Note that none of the plots in this figure exhibits the minimum that is predicted by Equation 26·23. Such minima are, in fact, observable in LC (see Figure 26-8a) but usually at flow rates too low for most practical applications.

2.0 L in e a r

v e lo c ity .

em/s

Effect of particle size of packing and flow rate on plate height H in LC. Column dImensIons: 30 cm x 2.4 mm. Solute: N,N'-diethyl-p-aminoazobenzene. Mobile phase: mixture of hexane, methylene chloride, isopropyl alcohol. (From R. E. Majors, J. C h ro m a to g r. SCI., 1973, 11,88. With permission.) F IG U R E

2 8 -2

F IG U R E

2 8 B - 2 E x t r a c o lu m n B a n d B r o a d e n in g in L C

LC. significant band broadening sometimes occurs outside the column packing itself. This extr a column ba nd br oa dening occurs as the solute is carried through open tubes such as those found in the injection system, the detector region, and the piping connecting the various components of the system. Here, broadening arises from differences in flow rates between layers of liquid adjacent to the wall and the center of the tube. As a result, the center part of a solute band moves more rapidly than the peripheral part. I n GC, extracolumn spreading IS largely offset by diffusion. Diffusion in liquids. however, is significantly slower, and band broadening of this type often becomes noticeable. It has been shown that the contribution of extracolumn effects H " to the total plate height is given by' In

,

H

=

"

M

ing made as small as feasible to minimize this source of broadening.

Pumping pressures of several hundred atmospheres are required to achieve reasonable flow rates with packings of 3 to !O 11m,which are common in modern LC. Because of these high pressures, the equipment for HPLC tends to be more elaborate and expensive than equipment for other types of chromatography. FIgure 28-3 is a diagram showing the important components of a typical LC instrument. 2 8 C - 1 M o b ile - P h a s e R e s e r v o ir s a n d S o lv e n t T r e a t m e n t S y s t e m s

7r r -u

24D

o.o!O inch or less, and the length of extracolumn tub-

(28-1)

where u is the linear-flow velocity (cm /s), r is the radius of the tube (cm), and D M is the diffusion coefficient of the solute in the mobile phasc (cm 2 /s). Extracolumn broadening can become quite serious when small-bore columns are used. Here, the radius of the extracolumn components should be reduced to

A modern LC apparatus is equipped with one or more glass reservoirs, each of which contains SOO mL or more of a solvent. Provisions are often included to remove dissolved gases and dust from the liquids. Dissolved gases can lead to irreproducible flow rates and band spreading; in addition, both bubbles and dust interfere with the performance of most detectors. Degassers may consist of a vacuum pumping system, a distillation system, a device for heating and stirring, or as

2 8 -3

Block diagram showing components of a typical apparatus for HPLC. (Courtesy

of Perkin-Elmer Corp., Norwalk, Cl). shown in Figure 28-3, a system for spa r ging, in which the dissolved gases are swept out of solution by fine bubbles of an inert gas that is not soluble in the mobile phase. Often the systems also contain a means of filtering dust and particulate matter from the solvents to prevent these particles from damaging the pumping or injection systems or clogging the column. It is not necessary that the degassers and filters be integral parts of the HPLC system as shown in Figure 28-3. For example, a convenient way of treating solvents before introduction into the reservoir is to filter them through a millipore filter under vacuum. This treatment removes gases as well as suspended matter. An elution with a single solvent or solvent mixture of constant composition is termed an isocr a tic elution. In gr a dient elution, two (and sometimes more) solvent systems that differ significantly in polarity are used and varied in composition during the separation. The ratio of the two solvents is varied in a preprogrammed way, sometimes continuously and sometimes in a series of steps. Modern HPLC instruments are often equipped with proportioning valves that introduce liquids from two or more reservoirs at ratios that can be varied continuously (Figure 28-3). The volume ratio of the solvents can be altered linearly or exponentially with time.

Figure 28-4 illustrates the advantage of a gradient eluent in the separation of a mixture of chlorobenzenes. Isocratic elution with a SO:SO (v/v) methanolwater solution yielded the curve in Figure 28-4b. The curve in Figure 28-4a is for gradient elution, which was initiated with a 40:60 mixture of the two solvents; the methanol concentration was then increased at the rate of 8% /min. Note that gradient elution shortened the time of separation significantly without sacrificing the resolution of the early peaks. Note also that gradient elution produces effects similar to those produced by temperature programming in gas chromatography (see Figure 27-7).

2 8 C -2

P u m p in g S y s t e m s

The requirements for liquid chromatographic pumps include (1) the generation of pressures of up to 6000 psi (lb/in.'), or 414 bar, (2) pulse-free output, (3) flow rates ranging from 0.1 to 10 mUmin, (4) flow reproducibilities of O.S% relative or better, and (S) resistance to corrosion by a variety of solvents. The high pressurcs

f7I lQ.J

Simula r ion:

Learn more about

chromatography.

liq u id

Two major types of pumps are used in LC: the serew-dnven synnge type and the reciprocating pump. ReCIprocatIng pumps are used in almost all modern commercial chromatographs.

dition. the output is pulse free. Disadvantages include limited solvent capacity (- 250 mL) and considerable inconvenience when solvents must be changed. F lo w C o n tro l

R e c ip ro c a tin g

I. Benzene 2. Monochlorobenzene 3. Orthodichlorobenzene 4.

1,2,3-trichlorobenzene

5.

1,3,5-trichlorohenzene

6. 1.2.4-trichlorobenzene 7. 1,2,3,4-tetrachlorobenzene

8. l,2,4.5-tetrachlorobenzene 9. Pentachlorobenzene 10. Hexachlorobenzene

Pum ps

Reciprocating pumps usually consist of a small chamber in which the solvent is pumped by the back and forth motion of a motor-driven pis Ion (see Figure 28-5). Two ball check valves, which open and close alternatelv. control the /low of solvent into and out of a cylinde~. The solvent is in direct contact with the piston. As an alternative, pressure may he transmitted to the solvent via a /lexible diaphragm. which in turn is hydraulically pumped by a reciprocating piston. Reciprocating pumps have the dIsadvantage of producing a pulsed /low, which must be damped because the pulses appear as baseline noise on the chromatogram. Modern LC instruments use dual pump heads or elliptical cams to minimize such pulsations. The advantagesy! reciprocatIng pumps include their small internal volume (35 to 400 flL). their high output pressures (up to 10.000 psi). thelf adaptabIlity to gradient elution. their large solvent capacities. and their constant /low rates. which are largely independent of column back pressure and solvent viscosity. D is p la c e m e n t

Pum ps

Displacement pumps usually consist of large, syringelIke chambers equipped with a plunger activated by a screw-driven mechanism powered by a stepping motor. DIsplacement pumps also produce a flow that tends to be independent of viscosity and back pressure. In adFIGURE28-4 Improvement in separation effectiveness by gradient elution. Column: 1 m x 2.1 mm inside-diameter. precision-bore slainless steel; packing: 1 % Permaphase" ODS (C,al.Sample: 5 ~L of chlorinated benzenes in isopropanol. Detector: U V photometer (254 nm). Conditions: temperature. 60°C. pressure. 1200 psi. (From J. J. Kirkland. M o d e m P ra c tic e o f L iq U id C h ro m a to g ra p h y . p. 88. New

York:Interscience. 1971. Reprinted by permission of John Wiley& Sons. Inc.) generated by liquid chromatographic pumps are not an explosion hazard because liquids are not verv compressible. Thus. rupture of a component results ~nlv in solvent leakage. However. such leakage may constitute a fire or environmental hazard with some solvents.

a n d P ro g ra m m in g

S y s te m s

As part of their pumping systems, many commercial instruments are equipped with computer-controlled devices for measuring the flow rate hy determining the pressure drop across a restrictor located at the pump outlet. Any difference in signal from a preset value is then used to increase or decrease the speed of the pump motor. Most instruments also have a means for varying the composition of the solvent either continuously or in a stepwise fashion. For example. the instrument shown in Figure 28-3 contains a proportioning valve that permits mixing of up to four solvents in a pre programmed and continuously variable way.

28C-3

Sample-Injection

Systems

Often. the limiting factor in the precision of liquid chromatographic measurements is the reproducibility with which samples can he introduced onto the column packing. The problem is exacerbated hy band broadening, which accompanies a lengthy sample injection plug. Thus, sample volumes must be very small- a few tenths of a microliter to perhaps 500 flL. Furthermore, it is convenient to he able to introduce the sample without depressurizing the system. The most widely used method of sample introduction in LC is based on sampling loops, such as that shown in Figures 28-6 and 27-5. These devices are often an integral part of liquid-chromatographic equipment and have interchangeable loops providing a choice of sample sizes from 1 flL to 100 flL or more. Sampling loops of this type permit the introduction of samples at pressures up to 7000 psi with relative standard deviations of a few tenths of a percent. Most chromatographs today are sold with autoinjectors. Such units are capable of injecting samples into the LC [rom vials on a sample carousel or from microtiter plates. They usually contain sampling loops and a syringe pump for injection volumes from less than I flL to more than 1 mL. Some have controlledtemperature environments that allow for sample storage and for carrying out derivatization reactions prior to injection. Most are programma hIe to allow for unattended injections into the LC system.

FIGURE28-6 A sampling loop for Le. With the valve handle as shown on the left, the loop is filledfrom the syringe. and the mobile phase flows from pump to column. When the valve is placed in the position on the right. the loop is inserted between the pump and the column so that the mobile phase sweeps the sample onto the column. (Courtesy at Beckman-Coulter. Inc.)

Liquid-chromatographic columns' are usually constructed from smooth-bore stainless steel tubing. HPLC columns are sometimes made from heavywalled glass tubing and polymer tubing, such as polyetheretherketone (PEEK). In addition, stainless steel columns lined with glass or PEEK are also available. Hundreds of packed columns differing in size and packing are available. The cost of standard-sized. nonspeciality columns ranges from $200 to more than $500. Specialized columns, such as chiral columns, can cost more than $1000.

'For more mfdrmathHl. s Na' > H' > Li'. For divalent cations, the order is Ba" > Pb" > Sr" > Ca" > Ni" > Cd'- > Cu2+ > Co" > Zn" > Mg" > VO ,". For anions, K" for a strong-base resill decreases in the order sol' > C,O/- > 1-> NO] - > Iir" > CI- > HCO, - > CH,CO, - > OH" > F . This sequence somewhat depends on the type of resin and reaction conditions and should thus be considered only approximate.

[RSO, -B' ],[H ' ],q K " = [RSO]W].[B'k

(28-6) 2 8 F -2

Here, [RSO] -B -], and [RSO, -H-L arc concentrations (strictiy activities) of B' and H' in the solid pha se. Rearranging yields

During the elution, the aqueous concentration of hydrogen ions is much larger than the concentration of the singly charged B' ions in the mobile phase. Also, the exchanger has an enormous number of exchange sites relative to the number of B ' ions being retained. Thus, the overall concentrations [H'L q and [RSOJ-H'l, arc not affected signilicantly by shifts in the equilibrium 28-5 Therefore, when [RSO, - H' j, 'b [RSO J -B 'L and [H'L q 'b [B 'la q , the right-hand side of Equation 2X-7is substantially constant. and we ean write

where K is a constant that corresponds to the distribution constant as defined by Equations 26-1 and 26-2. All of the equations in Table 26-5 (Section 26E) can then bc applied to ion-exchange chromatography in

lo n - E x c h a n g e

P a c k in g s

Historically, ion-exchange chromatography was performed on small, porous beads formed during emulsion copolymerization of styrene and divinylbenzene. The presence of divinylbenzene (usually -8%) results in cross-linking, which makes the beads mechanically stable. To make the polymer active toward ions, acidic or basic functional groups are bonded chcmieally to the structure. The most common groups are sulfonic acid and quaternary amines. Figure 28-22 shows the structure of a strong acid resin. Note the cross-linking that holds the linear polystyrene molecules together. The other types of resins have similar structures except for the active functional group. Porous polymeric particles are not entirely satisfactory for chromatographic packings because of the slow rate of diffusion of analyte molecules through the micropores of the polymer matrix and because of the compressibility of the matrix. To overcome this problem, two ncwer types of packings have been developed and arc in more general use than the porous polymer type. One is a polymeric bead packing in which the bead surface is coated with a synthetic ion-exchange

28-22 Structure of a cross-linked polystyrene ion-exchange resin. Similar resins are used in which the -SO, -H' group is replaced by -COO 'W, ~NH;OH', and -N(CH,), +OH groups.

F IG U R E

resin. A second type of packing is prepared by coating porous mieroparticles of silica, such as those used m adsorption chromatography, With a thm film of the exchanger. Particle diameters are typically 3-10 J.lm. With either type, faster diffusion in the polymer film leads to enhanced efficiency. Polymer-based packmgs have higher capacity than silica-based packings and can bc used over a b ro a d pH range. Silica-based ,on exchangers give higher efficiencies, but suffer from a limitcd pH range of stability and an incompatiblhty WIth suppressor-based detection (see next sectIOn).

2 8 F -3

In o r g a n ic - Io n

C h ro m a to g ra p h y

The mobile phase in ion-exchange chromatography must have the same general properties required for other types of chromatography. That is, it must dissolve the sample, have a solvent strength that leads to reasonable retention times (appropriate k values), and mteract with solutes in such a way as to lead to selectivity (suitable" values). The mohile phases in ion-exchange chromatography arc aqueous solutions that may contain moderate amounts of methanol or other watermiscible organic solvents; these mobile phases also contain ionic species, often in the form of a buffer. Solvent strength and selectivity are determined by the kmd and concentration of these added ingredients. In general, the ions of the mobile phase compete with analyte ions for the active sites on the ion-exchange packing. Two types of ion chromatography are currently in use: suppr essor ,ba sed and sillgle-columll. They differ in the method used to prevent the conductivity of the eluting electrolyte from interfering with the measurement of analyte conductivities.

.,.

Io n C h ro m a to g ra p h y

B ased

on Suppressors

As noted earlier, the widespread application of ion chromatography for the determination of inorganic species was inhibited by the lack of a good general detector, which would permit quantitative determmallon of ions on the basis of chromatographic peak areas, Conductivity detectors are an obvious choice for this task. Thev can be highly sensitive, they are unIversal for charg~d species, and as a general rule, they respond in a predictable way to concentration changes: Furthermore, such detectors are simple, inexpenSive to construct and maintain, easy to miniaturize, and ordInarily give prolonged, trouble-free service. The only limitation to conductivity detectors proved to be a serious one, which delayed their general use. This limitation arises from the high electrolyte concentration required to elute most analyte ions in a reasonablc time. As a result, the conductivity from the mobIle-phase components tends to swamp that fro m analyte ions, which greatly reduces the detector sensitivity. In 1975 the problem created by the high conductance of eluents was solved by the introduction of an eluent suppr essor columll immediately following. the ionexchange column." The suppressor column IS packed with a second ion-exchange resin that effectIvely converts the ions of the eluting solvent to a molecular species of limited ionization without affecting the conductivity due to analyte ions. Forexample, when cations are being separated and determined, hydrochlortc aCId IS chosen as the eluting reagent, and the suppressor column is an anion-exchange resin in the hydroxide form.

The product of the reaction in the supprcssor is water. That is

Concentrations. PFormate

H + (a q )

+ CI

(a q )

+ rcsin-OH

BrO,'

(s)-.

Ct'

resin' CI

(s)

+ ficO

The analyte cations are not retained by this second column. For anion separations. the suppressor packing is the acid form of a cation-exchange resin and sodium bicarbonate or carbonate is the eluting agent. The reaction in the suppressor is N a + (a q )

+ HCO

j

(a q )

+ resin'H;

ppm 3 S 10 4

NO,'

III

HPO,'

30

Br

30

1';0,'

30

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25

Concentrations, Ca2+ t

ppm J

Mg: Sr:"!+

J 10

Ba2+

25

:.;

~

~~ .~

8 ~

50

C

~

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FIGURE29-11 Comparison of extraction efficiencies obtained by using CO, and CO, modified with methanol. A soil sample was used. Allextractions were for 30 min. Diuron is a common herbicide that is an aromatic substituted derivative of urea. TCDD is 2,3,7 ,8-tetrachlorodibenzo-p-dioxin. LAS is linear alkylbenzenesulfonate detergent.

Material

Analyte*

Soils River sediments Smoke, urban dust Railroad bed soil Foods Spices, bubble gum Serum Coal, fly ash Polymers Animal tissue

Pesticides PAHs PAHs PCBs,PAHs Fats Aromas and fragrances Cholesterol PCBs, dioxins Additives and oligomers Drug residues

ure 29-10). Analytes have also been collected on adsorbents, such as silica. The adsorbed analytes are then eluted with a small volume of a liquid solvent. In either case the separated analytes are then identified by any of several optical, electrochemical, or chromatographic methods. In the on-line method, the effluent from the restrictor, after depressurization, is transferred directly to a chromatograph system. In most cases the latter is a GC or an SFC instrument, although occasionally an HPLC system has been used. The principal advantages of an on-line system are the elimination of sample handling between the extraction and the measurement and the

Supercritical Fluid

Extradion Time, Off-line (1 ),

min

CO, C O ,1 5 % M e O H

CO, C O , lM e O H C O , lM e O H

CO, CO, CO, CO, CO,

9

2 9 C -5

T y p ic a l

A p p lic a tio n s

and critical pressure of a gas.

29-2 What properties of a supercritical fluid are important in chromatography? Two types of methods have been used to collect analytes after extraction: o ff- l i n e and o n - l i n e . In off-line collection, which is the simpler of the two, the analytes are collected by immersing the restrictor in a few milliliters of solvent and allowing the gaseous supercritical fluid to escape into the atmosphere (see Fig-

1 1 2 1 1 2 1 2 2 1

of SFE

Hundreds of applications of SFE have appeared in the literature. Most applications are for the analysis of environmental samples. Others have been for the analysis of foods, biomedical samples, and industrial samples. Table 29-3 provides a few typical applications of off-line and on-line SFE. In addition to the analytical uses of SFE, there are many preparative and isolation uses in the pharmaceutical and polymer industries.

Problems with this icon are best solved using spreadsheets.

29·1 Define (a) critical temperature (b) supercritical fluid.

(2 )

potential for enhanced sensitivity because no dilution of the analyte occurs.

* Answers are provided at the end of the book for problems marked with an asterisk. ~

20 120 15 45 12 10 30 15 15

On-line

29-3 How do instruments for SFC differ from those for (a) HPLC and (b) GC? 29-4 Describe the effect of pressure on supercritical fluid chromatograms. 29-5 List some of the advantageous properties of supercritical CO, as a mobile phase for chromatographic separations.

29-6 Compare SFC with other column chromatographic

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29-7 For supercritical carbon dioxide, predict the effect that the following changes will have on the elution time in an SFC experiment: (a) increasing the flow rate (at constant temperature and pressure). (b) increasing the pressure (at constant temperature and flow rate). (c) increasing the temperature (at constant pressurc and flow rate). 29-8 For SFE, differentiate between (a) on-line and off-line processes. (b) static and dynamic extractions. 29-9 List the advantages and any disadvantages of SFE compared to liquid-liquid extractions.

C hallenge

[n capillary electrophoresis and electrochromatography, separations occur in a buffer-filled capillary tube under the influence of an electric field as seen in the schematic of Figure 30-1. Separations in field-flow fractionation, on the other hand, occur in a thin ribbon-like flow channel under the influence of a sedimentation. electrical, or thermal field applied perpendicular to the flow direction.

30A

P roblem

29-11 In a recent paper, Zheng and coworkers (J. Zheng, L. T. Taylor, J. D. Pinkston, and M. L. Mangels, J. C h r o ma to g r . A, 2005, 1 0 8 2 , 220) discuss the elution of polar and ionic compounds in SFC. (a) Why are highly polar or ionic compounds usuallv not eluted in SFC? (b) What types of mobile-phase additives have been' used to improve, the elution of highly polar or ionic compounds? . (c) Why is ion-pairing SFC not often used? (d) Why arc ammonium salts sometimes added as mobile-phase modifiers in SFC? (e) The authors describe an SFC system that uses mass spectrometry (MS) as a detector. Discuss the interfacing of an SFC unit to a mass spectrometer. Compare the compatibility of SFC with MS to that of HPLC and GC with MS. (f) The authors studied the effect of column outlet pressure on the elution of sodium 4-dodecylbenzene sulfonate on three different stationary phases with five mobile-phase additives. What effect was observed, and what was the explanation for the effect? (g) What elution mechanisms were considered by thc authors? (h) Which mobile-phase additive gave the fastest elution of the sulfonate salts? Which provided the longest retention times? (i) Did a silica column give results similar to or different from a cyano bondedphase column?

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AN OVERVIEW OF ELECTROPHORESIS

E lectr o p h o r esis is a separation method based on the differential rate of migration of charged species in ao applied dc electric field. This separation technique was first developed by the Swedish chemist Arne Tiselius in the 1930s for the study of serum proteins; he was awarded the 1948 Nobel Prize in Chemistry for this work. Electrophoresis on a macro scale has been applied to a variety of difficult analytical separation problems: inorganic anions and cations, amino acids, catecholamines, drugs, vitamins, carbohydrates, peptides, proteins, nucleic acids, nucleotides, polynucleotides, and numerous other species. A particular strength of electrophoresis is its unique ability to separate charged macromolecules of interest in biochemical, biological, and biomedical research and the biotechnology industry. For many years, electrophoresis has been the powerhouse method for separating proteins (enzymes, hormones, antibodies) and nucleic acids (DNA, RNA) with unparalleled resolution. For example, to sequence DNA it is necessary to distinguish between long-chain polynucleotides that have as many as perhaps 200 to 500 bases and that differ by only a single nucleotide. Only electrophoresis has sufficient resolving power to handle this problem. Without electrophoresis, for example, the Human Genome Project would have been nearly impossible because human DNA contains some three billion nucleotides. An electrophoretic separation is performed by injecting a small band of the sample into an aqueous buffer solution contained in a narrow tube or on a flat porous support medium such as paper or a semisolid gel. A high voltage is applied across the length of the buffer by means of a pair of electrodcs located at each

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species are eluted from one cnd of the capillary. so quantitative detectors, similar to those found in highperformance liquid chromatography (HPLC), can bc used instead of the cumbersome staining techniqucs of slab electrophoresis. I

FIGURE30-1 Schematic of a capillary electrophoresis system.

30B-1 Migration Rates in CE end of the buffer. This field causes ions of the sample to migrate toward one or the other of the electrodes. The rate of migration of a given species depends on its charge and its size. Separations are then based on differences in charge-to-size ratios for the various analytes in a sample. The larger this ratio, the faster an ion migrates in the electric field.

Electrophoretic separations are currently performed in two quite different formats: one is called sla b electr o p h o r esis and the other ca p illa r y electr o p h o r esis. The first is the classical method that has been used for many years to separate complex, high-molecular-mass species of biological and biochemical interest. Slab separations are carried out on a thin flat layer or slab of a porous semisolid gel containing an aqueous buffer solution within its pores. This slab has dimensions of a few centimeters on a side and, like a chromatographic thinlayer plate, is capable of separating several samples simultaneously. Samples are introduced as spots or bands on the slab, and a dc electric field is applied across the slab for a fixed period. When the separations are complete, the field is discontinued and the separated species are visualized by staining in much the same way as was described for thin-layer chromatography in Section 281-2. Slab electrophoresis is now the most widely used separation tool in biochemistry and biology. Monographs, textbooks, and journals in the life sciences contain hundreds of photographs of developed electrophoretic slabs. Capillary electrophoresis, which is an instrumental version of electrophoresis, was dcveloped in the mid-to-late 1980s. It has bccome an important tool for a wide variety of analytical separation problems. In many cases, this new method of performing electrophorctic separations is a satisfactory substitute for slab electrophoresis with several important advantages that are described later in this chapter.

30A·2 The Basis for Electrophoretic Separations The migration rate v of an ion (cm/s) in an electric field is equal to the product of the field strength E (V cm '1) and the electrophoretic mobility M, (cm 2 V-I S'I). That is,

The electrophoretic mobility is in turn proportional to the ionic charge on the analyte and inversely proportional to frictional retarding factors. The electric field acts on only ions. If two species dil'fej cither in charge or in the frictional forces they experience while moving through the buffer, they will be separated from each other. Neutral spccies are not separated. The frictional retarding force on an analyte ion is determined by the size and shape of the ion and the viscosity of the migration medium. For ions of the same size, the greater the charge, the greater the driving force and the faster the rate of migration. For ions of the same charge, the smaller the ion, the smaller the frictional forces and the faster the rate of migration. The ion's ch a r g e-to -size r a tio combines these two effects. Note that in contrast to chromatography, only one phase is involved in an electrophoretic separation.

As Equation 30-1 shows, the migration rate of an ion v depends on the electric field strength. The electric field in turn is proportional to the magnitude of the applied voltage V and inversely proportional to the length L over which it is applied. Thus

This relationship indicates that high applied voltagcs are desirable to achieve rapid ionic migration and a fast separation. It is desirable to have rapid separations, but it is even more important to achieve highresolution separations. So we must examine the factors that determine resolution in electrophoresis.

30B-2 Plate Heights in CE In chromatography, both longitudinal diffusion and mass-transfer resistance contribute to band broadening. However, because only a single phase is used in electrophoresis, in theory only longitudinal diffusion needs to be considered. In practice, however, Joule heating can add variance as well as the injection process. Although CE is not a chromatographic process, separations are often described in a manncr similar to chromatography. For example, in electrophoresis, we caleulate the plate count N by MeV

N =W As useful as conventional slab electrophoresis is, this type of electrophoretic separation is typically slow, labor intensive, and difficult to automate. Slab electrophoresis does not yield very precise quantitative information. During the mid-to-late 1980s, there was explosive growth in research and application of electrophoresis performed in capillary tubes, and several commercial instruments appeared. C a p illa r y electr o p h o r esis (CE) yields high-speed, high-resolution separations on exceptionally small sample volumes (0.1 to 10 nL in contrast to slab electrophoresis, which requires samples in the flL rangc). Additionally, the separated

where D is the diffusion coefficient of the solute (cm' S'I). Because resolution increases as the plate count increases, it is desirable to use high applied voltages to I

For additional discussion of CE, see An a lysis a n d D etectio n by C apillllr.r M. L. Marina, A. Rios. and M. Valcarcel, eds., Vol. 45

E lectr o p h o r esis,

of C o m p r eh en sive An a lytica l C h em istr y, D. Barcelo. ed., Amsterdam: Elsevier, 2005; C a p illa r y E lectr o p h o r esis o f P r o tein s a n d P ep tid es. M. A Strege and A. L L.agu. eds., Totowa. NJ: Humana Press. 2004; C lin ica l a n d F o r en sic Ap p lica tio n s o f C a p il1 a r y E lectr o p h o r esis. J. R. Petersen and A. A. Mohamad, eds .. Totowa. NJ: Humana Press. 2001; R. Weinberger. P r a ctica l C a p illa r y E lectr o p h o r esis. 2nd ed .. New York: Academic Press. 2000: H ig h P er fo r ma n ce C a p illa r )' E lectr o p h o r esis. M. G. Khaledi. ed .. New York: Wiley. 1998.

achieve high-resolution separations. Note that for electrophoresis, contrary to the situation in chromatography, the plate count does not increase with the length of the column. With gel slab electrophoresis, joule heating limits the magnitude of the applied voltage to about 500 V. Here, one of the strengths of the capillary format compared with the slab format is realized. Bccause the capillary is quite long and has a small cross-sectional area, the solution resistance through the capillary is exceptionally high. Because power dissipation is inversely proportional to resistance (P = [2/R), much higher voltages can be applied to capillaries than to slabs for the same amount of heating. Additionally, the high surface-to-volume ratio of the capillary provides efficient cooling. As a result of these two factors, band broadening due to thermally driven convective mixing does not occur to a significant extent in capillaries. Electric fields of 100-400 V/cm are typically used. High-voltage power supplies of 10-25 kV are normal. The high fields lead to corresponding improvements in speed and resolution over those seen in the slab format. CE peak widths often approach the theoretical limit set by longitudinal diffusion. CE normally yields plate counts in the range of 100,000 to 200,000, compared to the 5,000 to 20,000 plates typical for HPLC. Platc counts of 3,000,000 have been reported for capillary zone electrophoresis of dansylated amino acids,' and plate counts of 10,000,000 have been reported for capillary gel electrophoresis of polynucleotides.'

A unique feature of CE is electr o o smo tic flo w. When a high voltage is applied across a fused-silica capillary tubc containing a buffer solution, electroosmotic flow usually occurs, in which the bulk liquid migrates toward the cathode. The rate of migration can be substantial. For example. a 50 mM pH 8 buffer flows through a 50-cm capillary toward the cathode at approximately 5 cm/min with an applied voltage of25 kV4 As shown in Figure 30-2, the cause of electroosmotic flow is the electric double layer that develops at the silica-solution interface. At pH values higher than 3, the ~R. D. Smith.J. A. Olivares, N. T. Nguyen. and H. R. Udseth,A/laL

C h er n .•

1988,60.436 J A. GUltman. A. S. Cohen. D. N. Hciger, and R. L Karger. An a l. C h er n .. 1990.62,137 ~J. D. Olechno. J M. Y. Tso. 1. Thayer, and A. \\/ainright. Am er . La b ., 1990,22(171.51

The number of theoretical plates in the presence of electroosmotic flow can be found from an expression analogous to Equation 26-21:

+1

N =

FIGURE 30-2 Charge distribution at a

silica-capillary interface and resulting electroosmotic flow. (From A. G. Ewing, R. A. Wallingford,and T. M Olefirowicz, Anal. C hern., 1989, 61, 298A. Copyright 1989 American Chemical Society.)

inside wall of a silica capillary is negatively charged because of ionization of the surface silanol groups (Si-OH). Buffer cations congregate in the electrical double layer adjacent to the negative surface of the silica capillary. The cations in the diffuse outer layer of the double layer are attracted toward the cathode, or negative electrode, and because they are solvated, they drag the bulk solvent along with them. As shown in Figure 30-3, electroosmosis leads to bulk solution flow that has a flat profile across the tube because flow originates at the walls of the tubing. This profile is in contrast to the laminar (parabolic) profile observed with the pressure-driven flow encountered in HPLC. Because the profile is essentially flat, electroosmotic flow does not contribute significantly to band broadening the way pressure-driven flow does in liquid chromatography. The rate of electroosmotic flow is generally greater than the electrophoretic migration velocities of the individual ions and effectively becomes the mobile-phase pump of CEo Even though analytes migrate according to their charges within the capillary, the electroosmotic flow rate is usually sufficient to sweep all positive, neutral, and even negative species toward the same end of the capillary, so all can be detected as they pass by a common point (see Figure 30-4). The resulting electr o p h er o g r a m looks like a chromatogram but with narrower peaks.

The electroosmotic flow velocity v is given by an equation similar to Equation 30-1. That is,

16(~Y

where W, as in chromatography, is the peak width measured at the base of the peak. It is possible to reverse the direction of the normal electroosmotic flow by adding a cationic surfactant to the buffer. The surfactant adsorbs on the capillary wall and makes the wall positively charged. Now buffer anions congregate near the wall and are swept toward the cathode, or positive electrode. This ploy is often used to speed up the separation of anions. Electroosmosis is often desirable in certain types of CE, but in other types it is not. Electroosmotic flow

In the presence of electroosmosis, the velocity of an ion is the sum of its migration velocity ahQ. the electroosmotic flow velocity. Thus,

As a result of electroosmosis, order of elution in a typical electrophoretic separation is, first, the fastest cation followed by successively slower cations, then all the neutrals in a single zone, and finally the slowest anion followed by successively faster anions (see Figure 30-4). In some instances, the rate of electroosmotic flow may not be great enough to surpass the rate at which some of the anions move toward the anode, in which case these species move in that direction instead of toward the cathode. The migration time tm in CE is the time it takes for a solute to migrate from the point of introduction to the detector. If a capillary of total length L is used and the length to the detector is I, the migration time is

I tm

=

(J -Le

+

J -Leofi

(J -L,

+

J -LwlV

As shown in Figure 30-1, the instrumentation for CE is relatively simple5 A buffer-filled fused-silica capillary, typically 10 to 100 flm in internal diameter and 30 to 100 cm long, extends between two buffer reservoirs that also hold platinum electrodes. Like the capillary tubes used in gas chromatography (GC), the outside walls of the fused-silica capillary are typically coated with polyimide for durability, flexibility, and stability. The sample is introduced at one end and detection occurs at the other. A voltage of 5 to 30 kV dc is applied across the two electrodes. The polarity of this high voltage can be as indicated in Figure 3D-lor can be reversed to allow rapid separation of anions. Highvoltage electrophoresis compartments are usually safety interlocked to protect the user. Although the instrumentation is conceptually simple, significant experimental difficulties in sample introduction and detection arise due to the very small volumes involved. Because the volume of a normal capillary is 4 to 5 flL, injection and detection volumes must be on the order of a few nanoliters or less. S am ple Introduction

IL

=

can be minimized by modifying the inside capillary walls with a reagent like trimethylchlorosilane that bonds to the surface and reduces the number of surface silanol groups (see Section 280-1).

FIGURE 30-4 Velocitiesin the presence of electroosmotic flow.The length of the arrow next to an ion indicates the magnitude of its velocity;the direction of the arrow indicates the direction of motion. The negative electrode is to the right and the positive electrode to the left of this section of solution.

Simu la tio n : Learn more about capillary

electrophoresis.

The most common sample-introduction methods are electr o kin etic in jectio n and p r essu r e in jectio n . With electrokinetic injection, one end of the capillary and its electrode are removed from their buffer compartment and placed in a small cup containing the sample. A voltage is then applied for a measured time, causing the sample to enter the capillary by a combination of ionic migration and electroosmotic flow. The capillary end and electrode are then returned to the regular buffer solution for the duration of the separation. This injection technique discriminates by injecting larger amounts of the more mobile ions relative to the slowermoving ions. In pressure injection, the sample-introduction end of the capillary is also placed in a small cup containing the sample, but here a pressure difference drives the sample solution into the capillary. The pressure difference can be produced by applying a vacuum at the de-

tector end, by pressurizing the sample, or by elevating the sample end (hydrodynamic injection). Pressure injection does not discriminate because of ion mobility, but it cannot be used in gel-filled capillaries. For both electrokinetic injection and pressure injection, the volume injected is controlled by the duration of the injection. Injections of 5 to 50 nL are common, and volumes below 100 pL have been reported. For a buffer with density and viscosity near the values for water, a height differential of 5 cm for 10 s injects about 6 nL with a 75-!lm inside-diameter capillary. Microinjection tips constructed from capillaries drawn to very small diameters allow sampling from picoliter environments such as single cells or substructures within single cells. This technique has been used to study amino acids and neurotransmitters from single cells. Other novel injection techniques have been described in the literature6 Commercial CE systems are available with thermos tatted multiposition carousels for automated sampling.

75-J.L1ll capillary

Shim with

Spectrometry Absorption' Fluorescence

1-1000 1-0.01

Thermal lens'

10

1000 1':0.0001 1-0.01

Ramant Chemiluminescence

t

Mass spectrometry Electrochemical Conductivity' Potentiometry t Amperometry

Because the separated analytes move past a common point in most types of CE, detectors are similar in design and function to those described for HPLC. Table 30-1 lists several of the detection methods that have been reported for CEo The second column of the table shows representative detection limits for these detectors. Absorption Methods. Both fluorescence and absorption detectors are widely used in CE, although absorption methods are more common because they are more generally applicable. To keep the detection volume on the nanoliter scale or smaller, detection is performed on-column. In this case a small section of the protective polyimide coating is removed from the exterior of the capillary by burning or etching. That section of the capillary then serves as the detector cell. Unfortunately, the path length for such measurements is no more than 50 to 100 !1m,which restricts detection limits in concentration terms; because such small volumes are involved, however, mass detection limits are equal to or better than those for HPLC. Several cell designs have been used for increasing the measurement path length to improve the sensitivity of absorption methods. Three of these are shown in

300-p.m hole

Capillary

"~

\ 0

ce

30-5 Three types of cells for improving the sensitivity of absorption measurements in CEo(a) a 3-mm z cell, (b) a 150-~m bubble cell, (c) a multireflection cell.

FIGURE

/-/

B. Huang. 1. J. Li, L. Zhang, 1. K. Cheng, Anal. C hern., 1996, 68.2366; S. C. Beale, An a l. C h er n ., 1998, 7 0 , 279R. S. N. Krylov and N. 1. Dovichi, An a l. C h er n ., 2000, 72, III R; S. Hu and N. 1. Dovichi. An a l. C h er n ., 2002, 74, 2833.

Sources:

* Detection limits quoted have been determined with injoction volumes ranging from IX pL to 10 nL.

D etection

/

Representative Deteetion Limit * (attomoles detected)

Mass detection limit converted using a I-nL injection volume t

from concentration

dete~tion limit

Figure 30-5. In the commercial detector shown in Figure 30-5a, the end of the capillary is bent into a Z shape, which produces a path length as long as ten times the capillary diameter. Increases in path length can lead to decreases in peak efficiency and thus resolution. In some cases, special lenses, such as spherical ball lenses, are inserted between the source and the z cell and between the cell and the detector.' Such lenses improve sensitivity by focusing the light into the cell and onto the detector. Figure 30-5b shows a second way to increase the absorption path length. In this example, a bubble is formed near the end of the capillary. In the commercial version of this technique, the bubble for a 50-!lm capillary has an inside diameter of 150 !1m,which gives a threefold increase in path length. A third method for increasing the path length of radiation by reflection is shown in Figure 30-5c. In this technique, a reflective coating of silver is deposited on the end of the capillary. The source radiation then undergoes multiple reflections during its transit through the capillary, which significantly increase the path length.

Source

Silver

coating

-\N\J&'ZsDetector

Commercial CE systems are available with diode array detectors that allow spectra to be collected over the UV -visible range in less than 1 s. Indirect Detection. Indirect absorbance detection has been used for species of low molar absorptivity that are difficult to detect without derivatization. An ionic chromophore is placed in the electrophoresis buffer. The detector then receives a constant signal due to the presence of this substance. The analyte displaces some of these ions, just as in ion-exchange chromatography, so that the detector signal decreases during the passage of an analyte band through the detector. The analyte is then determined from the decrease In absorbance. The electropherogram in Figure 30-6 was generated by using indirect absorbance detection with 4-mM chromate ion as the chromophore; this ion absorbs radiation strongly at 254 nm in the buffer. Although the peaks obtained are negative (decreasing A) peaks, they appear as positive peaks in Figure 30-6 because the detector polarity was reversed. Fluorescence Detection. Just as in HPLC, fluorescence detection yields increased sensitivity and selec, tivity for fluorescent analytes or fluorescent derivatives.

Laser-based instrumentation is preferred to focus the excitation radiation on the small capillary and to achieve the low detection limits available from intense sources. Laser-induced-fluoreseence attachments are

30-6 Electropherogram of a six-anion mixture by indirect detection with 4-mM chromate ion at 254 nm. Peak: (1)bromide (4 ppm), (2) chloride (2 ppm). (3)sulfate (4 ppm), (4)nitrate (4 ppm), (5)fluoride (1 ppm), (6)phosphate (6 ppm). FIGURE

sections that follow illustrate typical applications

of

each of these techniques. LOO-em-Iong,

lOO-l'm·

i.d. fused-silica

capillary

\

~£2'

/~~ Melahz~fused silica

SampLe High-voltage (interlocked automated

1) III

r

/

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CE buffer region with injection)

FIGURE30-7 An instrument for CE/MS. The high-voltage (anode) end was maintained at 3050 kV in an electrically isolated. interlocked box. Electrical contact at the low-voltage (cathode) end was made by silver deposited on the capillary and a stainless steel sheath. This electrical contact was at 3 to 5 kVwith respect to common, which also charged the electrospray. The flow of nitrogen at -70'C for desolvation was 3 to 6 Llmin. (From R. D. Smith, J. A. Olivares, N, T. Nguyen, and H. R. Udseth, Anal. C hern., 1988, 60, 436, With permission.)

available that couple with commercial CE instruments. Laser-induced fluorescence has allowed detection of as little as 10 zeptomoles, or 6000 molecules." Electrochemical Detection. Two types of electrochemical detection have been used with CEo conductivity and amperometry. One of the problems with electrochemical detection has been that of isolating the detector electrodes from the high voltage required for the separation. One method for isolation involves inserting a porous glass or graphite joint between the end of the capillary and a second capillary containing the detector electrodes. Mass Spectrometric Detection. The very small volumetric flow rates of less than I flL/min from electrophoresis capillaries make it feasible to couple the effluent directly to the ionization source of a mass spectrometer. The most common sample-introduction and ionization interface for this purpose is currently electrospray (Section 20B-4), although fast atom bombardment, matrix-assisted laser desorption-ionization (MALDI) spectrometry, and inductively coupled plasma mass spectrometry (ICPMS) have also been used. Because the liquid sample must be vaporized before entering the mass spectrometry (MS) system,

it is important that volatile buffers be used. Capillary electrophoresis-mass spectrometry (C E /M S) systems have become quite important in the life sciences for determining large biomolecules that occur in nature, such as proteins, DNA fragments, and pep tides.' Figure 30-7 is a schematic of a typical electrospray interface coupled to a quadrupole mass spectrometer. Note that the capillary is positioned between the isolated high-voltage region and the electrospray source. The high-voltage end of the capillary was at 30 to 50 k V with respect to common. The low-voltage end was maintained at 3 - 5 k V and charged the droplets. Similar electrospray instruments are available commercially coupled with either quadrupole or ion-trap mass spectrometerslO Ion-trap mass spectrometers can allow CE IM S I MS or CE I MS n operation. Figure 30-8 shows the electrospray mass spectrum obtained for vasotocin, a polypeptide having a molecular mass of 1050. Note the presence of doubly and triply charged species. With higher-molecular-mass species, ions are often observed with charges of + 12 or more. Ions with such large charges make it possible to detect high-molecular-mass analytes with a quadru"For more information on mass spectromctnc detectIOn, see 1. C Seyas and R. D. Smith, in H a n d b o o k o fC a p ilia r y E lectr o p h o r esis, 2nd ed., 1. P. Landers, ed., Chap. 28, Boca Raton, FL: CRC Press, 1997. 10 Agilent Technologies, Wilmington, DE; Beckman Coulter, Inc .. Fullerton,CA.

200 400 600 800 1000 1200

Zone Electrophoresis

In capillary zone electrophoresis (CZE), the buffer composition is constant throughout the region of the separation. The applied field causes each of the different ionic components of the mixture to migrate according to its own mobility and to separate into zones that may be completely resolved or that may be partially overlapped. Completely resolved zones have regions of buffer between them as illustrated in Figure 30-9a. The situation is analogous to elution column chromatography, where regions of mobile phase are located between zones containing separated analytes.

ml'; .

FIGURE30-8 Electrospray ionization mass spectrum for vasotocin. (From R. D. Smith, J. A. Olivares. N. 1. Nguyen, and H. R. Udseth, Anal. C hern., 1988. 60. 436. With permission.)

pole instrument with a relatively modest mass range. Typical detection limits for CE/MS are ofa few tens of fcmtomoles for molecules with molecular masses of 100,000 or more. C om m ercial

C E Systems

Currently, fewer than ten companies worldwide manufacture CE instruments. Some two dozen companies offer supplies and accessories for CEo The initial cost of equipment and the expense of maintenance for CE are generally significantly lower than those for ion chromatographic and atomic spectroscopic instruments. Thus, commercial CE instruments with standard absorption or fluorescencc detectors cost $10.000 to $65,0001l Addition of mass spectrometric detection can raise the cost significantly.

Capillary electrophoretic separations can be performed in several different modes. These include capillarv zone electrophoresis, capillary gel electrophoresis. capillary isoelectric focusing, capillary isotachophoresis. and micellar electrokinetic chromatography. The

S eparation

of S m all Ions

For most electrophoretic separations of small ions, the smallest analysis time occurs when the analyte ions move in the same direction as the electroosmotic flow. Thus. for cation separations, the walls of the capillary are untreated and the electroosmotic flow and the cation movement are toward the cathode. For the separation of anions, on the other hand, the electroosmotic flow is usually reversed by treating the walls of the capillary with an alkyl ammonium salt, such as cetyl trimethylammonium bromide. The positively charged ammonium ions become attached to the silica surface, yielding a positively charged. immobile surface layer. This, in turn, creates a negatively charged, mobile solution layer, which is attracted toward the anode, reversing the electroosmotic flow. In the past, the most common method for analysis of small anions has been ion chromatography. For cations, the preferred techniques have been atomic absorption spectroscopy and ICPMS. Figure 30-10 illustrates the speed and resolution of electrophoretic separations of small anions. Here, thirty anions were separated cleanly in just more than 3 minutes. Typically, an ionexchange separation of only three or four anions can be accomplished in this brief period. Figure 30-11 further illustrates the speed at which separations can be carried out. In this example, nineteen cations were separatcd in less than 2 minutes. CE methods were once predicted to replace the more established methods because of lower equipment costs, smaller-sample-size requirements. and shorter analysis times. However, because variations in electroosmotic flow rates make reproducing CE separations difficult, LC methods and


i

• 1 :'D- 2

pI = -log[H,o

]i'o =

-

10gK w

+

10gK b )

2

.

(30-9) (pK,

The first reaction constitutes a kind of internal acidbase reaction and is analogous to the reaction one would observe between a simple carboxylic acid and an amine. The typical aliphatic amine has a base dissociation constant of 10-4 to 10-5, and many carboxylic acids have acid dissociation constants of about the same magnitude. The result is that the first reaction proceeds far to the right, with the product or products being the predominant species in the solution. The amino acid product in thc first reaction, bearing both a positive and a negative charge, is called a zw itlerion. As shown by the equilibrium constants for the second and third reactions (Equations 30-8 and 30-9), the zwitterion of glycine is stronger as an acid than as a base. Thus, an aqueous solution of glycine is somewhat acidic. The zwitterion of an amino acid, containing as it does a positive and a negative charge, has no tendency to migrate to an electric field, but the singly charged anionic and cationic species are attracted to oppositely charged electrodes. No net migration of the amino acid occurs in an electric field when the pH of the solvent is such that the concentrations of thc anionic and cationic forms are identical. The pH at which no net migration occurs is called the isoelectric point (pI) and is an important physical constant for characterizing amino acids. The isoelectric point is readily related to

pI

+

=

pK w

2

-

pK b)

(30-12)

from the anode compartment toward the cathode. Hydroxide ions from the cathode begin to move in the opposite direction. If a component of the ampholyte or the analyte has a net negative charge, it migrates toward the positive anode. As it migrates it passes into continuously lower pH regions, where progressive protonation of the species occurs, which lowers its negative charge. Ultimately, it reaches the pH where its net charge is zero (its isoelectric point). Migration of the species then ceases. This process goes on for each ampholyte species and ultimately provides a continuous pH gradient throughout the tube. Analyte ions also migrate until they reach their isoelectric points. These processes then result in the separation of each analyte into a narrow band that is located at the pH of its isoelectric point (see Figure 30-9c). Very sharp focusing is realized in such systems. Note that isoelectric focusing separations are based on differences in equilibrium properties of the analytes (K" K b ) rather than on differences in rates of migration. Once each analyte has migrated to a region where it is neutral, the positions of bands become constant and no longer change with time. M obilization

For glycine, pK , = -log(2 and pK w = 14.0. Thus, p[

=

x 10-1°)

= 9.7, pK b = 11.7

(9.7 + 14.0 - 11.7)/2

=

6.0

Hence, the isoelectric point pi for glycine occurs at a pH of 6.0. S eparation

of A m phiprotic

S pecies

[n isoelectric separation of amphiprotic species, the separation is performed in a buffer mixture that continuously varies in pH along its length. This pH gradient is prepared from a mixture of several different am pholytes in an aqueous solution. Ampholytes are amphoteric compounds usually containing carboxylic and amino groups. Ampholyte mixtures having different pH ranges can be prepared or are available from several commercial sources. To perform an isoelectric focusing experiment in a capillary tube, the analyte mixture is dissolved in a dilute solution of the ampholytes, which is then transferred to the tube. One end of the capillary is then inserted in a solution of strong base, such as sodium hydroxide, that also holds the cathode. The other end of the tube is immersed in a solution of a strong acid, such as phosphoric, that also holds the anode. When the electric field is applied. hydrogen ions begin to migrate

of Focused B ands

To detect the focused bands in a capillary isoelectric focusing separation, it is necessary to move, or mobilize, the contents of the capillary so that the bands pass the detector located at one end. This mobilization can be accomplished by applying a pressure difference, just as for sample loading, or by simply changing the solution in the electrode compartment. During the focusing step, equal numbers of H+ and OH- ions enter opposite ends of the capillary, so the pH gradient remains stable. Suppose that sodium chloride is added to the sodium hydroxide solution after focusing is finished. Now both CI- and OH- migrate into the cathode end of the column, and the sum of these two concentrations is balanced by H+ entering the opposite end. That means that there is now less OH- than H+ flowing into the capillary. The pH decreases at the cathode end. The pH gradient is no longer stable. It moves toward the cathode end, and along with it go the focused bands. The bands that pass the detector first are the ones corresponding to proteins with the most alkaline isoelectric points. Figure 30-16 shows an electropherogram for the separation of several proteins by capillary isoelectric focusing. The pi for each protein is shown above the peak. Mobilization was accomplished by adding sodium chloride to the anode compartment.

1111".' i !

I:.

f

!

!

'I

I', I.

"

f

~-~

6.00 Time,

9.00

min

FIGURE30-16 Capillary isoelectric focusing of proteins. lsoelectric pi listed above the peaks. Detection was by UVabsorption. (From T. Wehr, M. Zhu, R. Rodriguez, D. Burke, and K. Duncan, Am er. Biotech. Lab., 1990, 8, 22. With permission.)

30C·5 Micellar Electrokinetic Chromatography In 1984, Terabe and collaborators 17 described a modification of CE that permitted the separation of lowmolecular-mass aromatic phenols and nitro compounds with equipment such as shown in Figure 30-1. M icella r electr o kin etic ch r o ma to g r a p h y (MEKC) is a type of CE that offers several unique featuresl" Like CE, MEKC provides highly efficient separations on mierovolumes of sample solution without the need for PS. Terabe, K. Otsuka, K. Ichikawa. A. Tsuchlya, and T. AnJo, An a l. C h er n " 1984, 56,111; S. Terabe, K. Otsuka, and T. Ando, An a l. C h er n . 1985.57, 841. See ~Iso K. R. Nielsen and 1. P. Foley. in C a p ilia r y E lec-' FL: eRe Press, 1993, Chap. 4. l~For a brief reHew, see S. Terahe. An a l. C h er n .. 2004, 7 t), 2-tOA

tr o p h o r e s~ , P. C~milleri, ed., Boca Raton,

the high-pressure pumping system required for HPLC Unlike normal CE, however, MEKC allows uncharged speCies to be separated as well as charged species. In MEKC a mobile phase is transported across a stationary phase by electroosmotic flow. As shown in Fia_ ute 30-3, electroosmotic pumping leads to a flat-pl~g profile rather than the parabolic profile of pressureinduced flow. The flat profile of osmotic pumping leads to narrow bands and thus high separation efficiencies. M icelles form in aqueous solutions when the concentration of an ionic species having a long-chain hydrocarbon tail is increased above a certain level called the cr itica l micelle co n cen tr a tio n (CMC). At this point the surfactant begins to form spherical aggregates made up of 40 to 100 ions with their hydrocarbon tails in the interior of the aggregate and their charged ends exposed to water on the outside. Micelles constitute a stable second phase that can incorporate nonpolar compounds in the hydrocarbon interior of the particles, thus so lu b ilizin g the nonpolar s('e·cies. SolubiIIzalton IS commonly encountered when It' greasy matertal or surface is washed with a detergent solution. In MEKC, surfactants are added to the operating buffer in amounts that exceed the CMC. For most applIcations to date, the surfactant has been sodium dodecyl sulfate (SDS). The surface of an ionic micelle of this type has a large negative charge, which gives it a large electrophoretic mobility. Most buffers, however, exhibit such a high elcctroosmotic flow rate toward the negative electrode that the anionic micelles are carried toward that electrode also, but at a much reduced rate. Thus, during an experiment, the buffer mixture consists of a faster-moving aqueous phase and a slower-moving micellar phase. When a sample is introduced into this system, the components distribute themselves between the aqueous phase and the hydrocarbon phase in the interior of the micelles. The positions of the resulting equilibria depend on the polarity of the solutes. With polar solutes the aqueous solution is favored; with nonpolar compounds, the hydrocarbon environment is preferred. The phenomena just described are quite similar to what occurs in an LC column except that the "stationary phase" moves along the length of the column but at a much slower rate than the mobile phase. The mechanism of separation is identical in the two cases and depends on differences in distribution constants for analytes between the mobile aqueous phase and the hydrocarbon p seu d o s!a tio n a r y p h a se. The process is thus true chromatography; hence, the name "micellar

2

4

5

I

7

10 II

5

3

o.oo~ AU

I

2 3 78

~

9

I

'I

I

1 I

A I

1

~ I

"

FIGURE30-17 Typical separations by MEKC.(al Some test compounds: 1 = methanol, 2 = resorcinol, 3 = phenol, 4 = p-nitroaniline, 5 = nitrobenzene, 6 ~ toluene, 7 ~ 2-naphthol, 8 = Sudan III;capillary, 50-~m inside diameter, 500 mm to the detector; applied voltage, -15 kV;detection UVabsorption at210 nm. (b) Analysis of a cold medicine: 1 = acetaminophen, 2 = caffeine, 3 ~ sulpyrine, 4 = naproxen, 5 = guaiphenesin, 10 = noscapine, 11 = chloropheniramine and tipepidine; applied voltage, 20 kV;capillary, as in (a);detection UVabsorption at 220 nm. (From S. Terabe, Trends Anal. C hem ., 1989, 8,129. With permission.) electrokinetic ch r o ma to g r a p h y." Figure 30-17 illustrates two typical separations by MEKC. MEKC has become important for chiral separations.l" Here, chiral resolving agents are used as in HPLC to preferentially complex one of the isomers. Either a chiral resolving agent with detergent properties, such as a bile acid, is used to form the micelles or a resolving agent, such as a cyclodextrin, is added to a detergent that is itself achiral. In many aspects, chiral separations are easier to develop by MEKC than by LC, although LC is still the dominant technique in industry because of its familiarity. MEKC appears to have a promising future. One advantage that this hybrid technique has over HPLC is much higher column effkiencies (100,000 plates or more). In addition, changing the second phase in MEKC is simple, involving only changing the micellar composition of the buffer. In contrast. in HPLC, the second phase can be altered only by changing the type

of column packing or column, The MEKC technique appears particularly useful for separating small molecules that are impossible to separate by traditional gel electrophoresis. Recent advances include on-line preconcentration to enhance sensitivity and mass spectrometric detection.20

300 PACKED COLUMN ELECTROCHROMATOGRAPHY Electrochromatography is a hybrid of HPLC and CE that offers some of the best features of the two methods. Like HPLC and MEKC, it is applicable to the separation of neutral species or charged species. Electrochromatography with packed columns is, however, the least mature of the various electroseparation techniques. In this method, a polar solvent is usually driven by electroosmotic flow through a capillary packed with

FIGURE 30-18 Electrochromatogram showing the electrochromatographic separation of t6 PAHs (-to-6 to 10- 8 M of each compound). The peaks are identified as follows: (1) naphthalene, (2) acenaphthylene, (3) acenaphthene, (4)fluorene, (5) phenanthrene, (6)anthracene, (7)fluoranthene, (8) pyrene, (9) benz[a]anthracene, (10) chrysene, (11) benzo[b]f1uoranthene, (12) benzo[k]fluoranthene, (13) benzo[a]pyrene, (14) dibenz[a,h]anthracene, (15) benzo[ghi]perylene, and (16) indeo[1,2,3-ed]pyrene. (From C. Yan, R. Dadoo, H. Zhao, D. J. Rakestroaw, and R. N. Zare, Anal. C hem ., 1995, 67, 2026. With permission.)

a reversed-phase HPLC packing. Separations depend on the distribution of the analyte species between the mobile phase and the liquid stationary phase held on the packing. Figure 30-18 shows a typical electrochromatogram for the separation of sixteen polyaromatic hydrocarbons (PAHs) in a 33-cm-long capillary having an inside diameter of 75 J.lm.The mobile phase consisted of acetonitrile in a 4-mM sodium borate solution. The stationary phase consisted of 3-J.lm octadecylsilica particles.

Field-flow fractionation (FFF) describes a group of analytical techniques that are becoming quite useful in the separation and characterization of dissolved or suspended materials such as polymers, large particles, and colloids. Although the FFF concept was first described by Giddings in 1966,21only recently have practical applications and advantages over other methods been shown.22

Separations in FFF occur in a thin ribbon-like flow channel such as that shown in Figure 30-19. The channel is typically 25-100 em long and 1-3 em wide. The thick211.

C. Giddjng, Sep . Sei., 1966. 1, 123.

:!2For a review of FFF methods, see 1. C Giddings. 67.592A

A M I.

C h er n ,

1995.

AGURE 30-19 Schematic diagram of FFF flow channel sandwiched between two walls. An external field (electrical, thermal, centrifugal) is applied perpendicular to the flow direction.

ness of the ribbon-like structure is usually 50-500 J.lm. The channel is usually cut from a thin spaEer and sandwiched between two walls. An electrical, thermal, or centrifugal field is applied perpendicular to the flow direction. Alternatively, a cross flow perpendicular to the main flow direction can be used. In practice, the sample is injected at the inlet to the channel. The external field is next applied across the face of the channel as illustrated in Figure 30-19. In the presence of the field, sample components migrate toward the a ccu mu la tio n wa ll at a velocity determined by the strength of the interaction of the component with the field. Sample components rapidly reach a steadystate concentration distribution near the accumulation wall as shown in Figure 30-20. The mean thickness of the component layer I is related to the diffusion coefficient of the molecule D and to the field-induced velocity U toward the wall. The faster the component moves in the field, thc thinncr the laycr near the wall. The larger the diffusion coefficient, the thicker the layer. Because the sample components have different values of D and U , the mean layer thickness will vary among components. Once components have reached their steady-state profiles near the accumulation wall, the channel flow is begun. The flow is laminar. resulting in the parabolic profile shown on the left in Figure 30-20. The main carrier flow has its highest velocity in the center of the channel and its lowest velocity near the walls. Components that interact strongly with the field are com-

pressed very near the wall as shown by component A in Figure 30-21. Here, they are eluted by slow-moving solvent. Components Band C protrude more into the channel and experience a higher solvent velocity. The elution order is thus C, then B, then A. Components separated by FFF flow through a UV-visible absorption, refractive index, or fluorescence detector located at the end of the flow channel and similar to those used in HPLC separations. The separation results are revealed by a plot of detector response versus time, called a fr a cto g r a m, similar to a chromatogram in chromatography.

I w

1-When the field is applied in FFF,components migrate to the accumulation wall where an exponential concentration profile exists as seen on the right. Components extend a distance y into the channel. The average thickness of the layer is I, which differs for each component. The main channel flow is then turned on and the parabolic flow profile of the eluting solvent is shown on the left.

FIGURE 30-20

Simu la tio n : Learn more about field ftow fractionation.

Different FFF sub techniques result from the application of different types of fields or gradients.23 To date, the methods that have' been developed are sed imen ta tio n F F F , electr ica l F F F , th er ma l F F F , and flo w F F F . S edim entation

FFF

Sedimentation FFF is by far the most widely used form. In this technique, the channel is coiled and made to fit inside a centrifuge basket as illustrated in Figure 30-22. Components with the highest mass and density are driven to the wall by the sedimentation (centrifugation) force and elute last. Low-mass species are eluted first. There is relatively high selectivity between particles of different size in sedimentation FFF. A separation of polystyrene beads of various diameters by sedimentation FFF is shown in Figure 30-23. Because the centrifugation forces are relatively weak for small molecules, sedimentation FFF is most applicable for molecules with molecular masses exceeding 106 Such systems as polymers, biological macromolecules, natural and industrial colloids, emulsions, and subcellular particles appear to be amenable to separation by sedimentation FFF. E lectrical

FFF

In electrical FFF, an electric field is applied perpendicular to the flow direction. Retention and separation occur based on electrical charge. Species with the liFor a discussion of tht: various FFF methods. see J. C. Giddings, U m fied Sep a r a tio n 5 c ie n a , New York Wiley, 1991. Chap. 9~ M. E. Schimpf, K CaldwelL and 1. C. Giddings. eds., F ield -F lO l\' F r a ctio n a tio n H a n d b o o k, \lew

York:

Wiley,

2000.

FIGURE 30-21 Three components A, B, and C are shown compressed against the accumulation wall in FFF to different amounts because of different interactions with the extemal field. When the flow is begun, component A experiences the lowest solvent velocity because it is the closest to the wall. Component B protrudes more into the channel where it experiences a higher flow velocity. Component C, which interacts the least with the field, experiences the highest solvent-flow velocity and thus is displaced the most rapidly by the flow.

FIGURE 30-24 Separation of three proteins

by flow FFF.Three separate injections are shown. In the experiment shown, the sample was concentrated at the head of the channel by means of an opposing flow.BSA ~ bovine serum albumin. (From H. Lee, S. K. R. Williams,and J. C. Giddings, Anal. C hern., 1998,70,2495. Copyright 1998 American Chemical Society.)

FIGURE 30-22 Sedimentation FFF apparatus. (Courtesy of Postnova Analytics.)

highest charge are driven most effectively toward the accumulation walL Species of lower charge are not as compacted and protrude more into the higher-flow region. Hence, species of the lowest charge are eluted first, with highly charged species retained the most. Because electric fields are quite powerful, even small ions should be amenable to separation by electrical FFE However, electrolysis effects have limited the application of this method to the separation of mixtures of proteins and other large molecules. ThermalFFF FIGURE 30-23 Fractogram illustrating separation of polystyrene beads of various diameters by sedimentation FFF.The channel flow rate was 2 mLlmin. (Courtesy of FFFractionation, LLC,Salt Lake City, UT.)

In thermal FFF, a thermal field is applied perpendicular to the flow direction by forming a temperature gradient across the FFF channeL The temperature difference induces thermal diffusion in which the velocity of movement is related to the thermal diffusion coefficient of the species. Thermal FFF is particularly well suited for the separation of synthetic polymers with molecular masses in the range of 103 to 107 The technique has significant advantages over size-exclusion chromatography for high-molecular-mass polymers. On the other hand,

low-molecular-mass polymers appear to be beller separated by size-exclusion methods. In addition to polymers, particles and colloids have been separated by thermal FFE 24 FlowFFF

Perhaps the most versatile of all the FFF subtechniques is flow FFF, in which the external field is replaced by a slow cross flow of the carrier liquid. The perpendicular tlow transports material to the accumulation wall in a nonselective manner. However, steadystate layer thicknesses are differcnt for various components because they depend not only on the transport rate but also on molecular diffusion. Exponential distributions of differing thicknesses are formed as in normal FFE Flow FFF has been applied to the separation of proteins, synthetic polymers, and a variety of colloidal particles. Figure 30-24 illustrates the separation of three proteins by flow FFE The reproducibility is illustrated by the fractograms for the three injections.

30E-3 Advantages Chromatographic

of FFF over Methods

FFF appears to have several advantages over ordinary chromatographic methods for some applications. First, no packing material or stationary phase is needed for separation to occur. In some chromatographic systems, there may be undesirable interactions between the packing material or stationary phase and the sample constituents. Some solvents or sample materials adsorb or react with the stationary phase or its support. Macromolecules and particles are particularly prone to such adverse interactions. The geometry and flow profiles involved in FFF are well characterized. Likewise, the effects of most external fields can be readily modeled. As a result, fairly exact theoretical predictions of retention and plate

height can be made in FFF. Chromatographic predictions are still rather inexact in comparison. Finally, the external field governs FFF retention. With electrical, sedimentation, and flow FFF, the per. pendicular forces can be varied rapidly and in a time. programmed fashion. This gives FFF a certain versatil. ity in adapting to different types of samples. Methods can also be readily optimized for resolution and sepa. ration speed. Although FFF is a fairly recent addition to the repertoire of analytical separation methods, it has been shown to be highly complementary to chromatography. The FFF methods are best suited for macromolecules and particles that are for the most part beyond the mo· lecular mass range of chromatographic methods. On the other hand, chromatographic methods are clearly superior for low-molecular-mass substances.

30-9 Three large proteins are ionized at the pH at which an electrical FFF separation is carried out. If the ions are designated A", B +, and C J+, predict the order of elution. 30-10 What determines the elution order in sedimentation

C hallenge

~

P roblem

3O-U Doxorubicin (DOX) is a widely used anthracycline that has been effective in treatments of leukemia and breast cancer in humans (A. B. Anderson, C. M. Ciriaks, K. M. Fuller, and E. A. Ariaga, An a l. C h er n ., 2003, 75,8). Unfortunately, side effects, such as liver toxicity and drug resistance, have been reported. In a recent study, Anderson et al. used laser-induced fluorescence (LIF) as a detection mode for CE to investigate metabolites of DOX in single cells and subcellular fractions. The following are results similar to those obtained by Anderson et al. for quantifying doxorubicin by LIF. The CE peak areas were measured as a function of the DOX concentration to construct a calibration curve.

0.10 1.00 5.00

*Answers are provided at the end of the book for problems marked with an asterisk. ~

Problems with this icon are best solved using spreadsheets.

30-2 Suggest how electroosmotic flow might be suppressed. 30-3 Why does pH affect separation of amino acids by electrophoresis? 30-4 What is the principle of separation by CZE? *30-5 A certain inorganic cation has an electrophoretic mobility of 4.31 x 10'4 em 2 s' 1 V'I. This same ion has a diffusion coefficient of9.8 X 10.6 cm' s'I.If this ion is separated from other cations by CZE with a 50.0-cm capillary, what is the expected plate count N at applied voltages of (a) 5.0 kV? (b) 10.0 kV? (c) 30.0 kV? *30-6 The cationic analyte of Problem 30-5 was separated by CZE in a 50.0-cm capillary at 10.0 kV Under the separation conditions, the electroosmotic flow rate was 0.85 mm S·l toward the cathode. If the detector were placed 40.0 em from the injection end of the capillary, how long would it take in minutes for the analyte cation to reach the detector after the field is applied? 30-7 What is the principle of micellar electrokinetic docs it differ from CZE?

capillary chromatography?

30-8 Describe a major advantage of micellar electrokinetic over conventional liquid chromatography.

10.00

How

capillary chromatography

0.10 0.80 4.52 8.32

20.00

15.7

30.00

26.2 41.5

50.00

30-1 What is electroosmotic flow? Why does it occur?

FFF?

30-11 List the major advantages and limitations of FFF compared to chromatographic methods.

(a) Find the equation for the calibration curve and the standard deviations of the slope and intercept. Find the R' value. (b) Rearrange the equation found in part (a) to express concentration in terms of the measured area. (c) The limit of detection (LOD) for DOX was found to be 3 X \0-11 M. If the injection volume was 100 pL, what was the LOD in moles? (d) Two samples of unknown DOX concentration were injected and peak areas of 11.3 and 6.97 obtained. What were the concentrations and their standard deviations? (e) Under certain conditions, the DOX peak required 300 s to reach the LlF detector. What time would be required if the applied voltage were doubled? What time would be required if the capillary length were doubled at the same applied voltage? (f) The capillary used in part (e) under normal conditions had a plate count of 100,000. What would N be if the capillary length were doubled at the same applied voltage? What would N be if the applied voltage were doubled at the original capillary length'! (g) For a 40.6-cm-long capillary of inside diameter 50 flm, what would the plate height be for a capillary with N = !OO,OOO'! (h) For the same capillary as in part (g), what is the variance a ' of a typical peak')

Instrumental Analysis in Action "t'''"

~

;::'

100

In 1997 in southwestern

bromination

landsas ridge began finding dead rain how trout in nearh:' streams and paralyzed cows in grasslands

in their extremities.

cal-ionization

tingling and numbness

The problem was soon traced to chem-

grasses prompted Acrylamide

and the grazing

used industrial polymer. [n ZOOZ acrylamide

of acrylamide

discovered

foods, such as potato

have been

laboratory Analytical

has been found to cause cancer in

animals. The chemical has been classified as a

group ZA carcinogen

("possibly carcinogenic

methods to determine

quite important

in establishing

acrylamide

than other m~th-

g -g

60

.g

50

~ ~ ~ ;j1 >

FIGURE IA5-1 A typical matogram

to humans").' are clearly

are measured in the selective-ion moni-

M S/M S

or GCcoupled

40 30

MS instrument.

20

Im-

with high-resolution

f\

A

MS. Detection

limits are less than 10 ~g/kg.

Most LC/MS methods use solid-phase extraction sample cleanup and analyte preconcentration.

sure to its effects.

released into the headspace monitored

cies. Often, tandem MS is used following the extraction

the treatment

to

released correlated

Ethyl acetate extractions

levels of matrix interferences,

particularly

Early methods used GC or HPLC in the determination.

Al-

though these methods were successful in water, agricultural samples, and environmental

sufficient for samples of cooked foods where the matrices

mass spectrometers

samples in complex matrices.5

from are

Heel

dilution, LC, and electrospray

Acrylamide

and

decrease the analysis time. Typical LC I MS chromatograms and an acrylamide-spiked

extract are shown in Figure IA5~2. Elcctrospray monitoring

potato chip

With analytical methods based on G C /M S

Ionization

P. Karlsson,

$,

Eriksson.

and M. Tornqvist.

}

were used. A completely aque-

Ag r ic. F o o d C h er n ,. 2002, 5 0 , 4 9 9 8 .

clnternalional

Agency for Research on Cancer, M o n o g r a p h s

cio n a /C a r cin o g en ic

Risk o f C h emica ls

CO

H u ma n s,

o n E va lu a '

foods and the environment.

reversed-

arises from agricultural,

.V II[{ ..

and industrial polyacrylamide

used in water purification

suspended

in irrigation

to aggregate

in

acrylamide

sources. Among its many applications, compounds,

(!'TRIMS)

In the environment,

water~treatmcnt,

it

originates

is

organic

water to improve soil texture, in

has been used for on-line monitoring of acrylarnide without any sample pretreatmenl.--l The formation

of acrylamidc FIGURE IA5-2 A chromatogram

1 9 9 4 ,6 0 ,4 3 5 .

3D. Taeymans, 1. Wood. P. Ashby, I. Blank. el al. C r it. Rn . F o u d Sci. 2004. 44, 323.

mass spectrometry

or LC /M S,

has been possible to discover how acrylamide

phase LC column.

Proton-transfer-reaction P. Rydberg.

powders,

O~NH'

the IO-~g/kg level.

O n-Line M onitoring

E. Tareke,

M S/M S-'

on chocolate

cocoa, and coffee.

tion methods.

1

that uses isotope

ionization

Excellent results were obtained

of LC methods is that derivatiza-

tion is not necessary, which can simplify the procedure

in analytical methodology

MS method was recently reported

limits by both

ous mobile phase was employed with a fluorinated

samples have involved MS coupled with GC or LC separa-

for

Even with relatively simple

samples, the range of results was too wide to be accept~

have been more

systems. Detection

advantage

and selected-ion

are quite complex. The most successful methods for food

comparison

are certainly in order. A fully validated improved LC /M SI

of a control standard

samples, the selectivity was not

progress has been made in detera recent interlaboratory

able. Thus, more improvements

An important

in starchy foods.

mining acrylamide,

ars, starches, and amino acids. Such cleanup procedures

single-stage and tandem MS approach

samples presents a special challenge because of the high

S tudies

substantial

an aqueous phase have also been used to remove salts, sug-

successful than M S/M S

The analysis of food

positively with

resolution and freedom from interfer-

sample, single-stage of acrylamide.'

Although

showed that many current methods are not satisfactory

lates, and cocoa powders. With extensive cleanup of the

for the determination

The

temperature.

often necessary with difficult matrices such as coffee, choco~

have been proposed

Interlaboratory

above a potato sample was

in real-time during thermal treatment.

amount of acrylamidc

ences due to coextractants.

health risks, and in finding means to reduce human expo-

(SPE) for

A major ad-

vantage of SPE is the retention of the many interfering speprovide additional

its origins, in studying its

Several different analytical approaches

chro-

G C /C I/M S

of standards.

LC IM S M ethods

chips, coffee, breakfast cereals, peanut butter, and pastries. In high doses, acrylamide

methods

""

proved results have been obtained for acrylamide by G C I

Since that

time, relatively high concentrations in a variety of processed

a Carbowax capillary column was used

toring mode using a basic quadrupole

was identified

I

In these experiments,

and (CH 2=CHBr)'

a widely

and the University of Stockholm

70

A typical G C I

rect methods. Usually, the ions (CH2-CHBr~CONH2)'

in human foods by workers at the Swedish National Food Administration

(CliMS).

of standards is shown in Figure IAS-!.

analyte is more volatil~, and they are more sensitive than di-

a shutdown of the tunnel construction.

is the monomer of polyacrylamide,

mass spectrometry

ods, have several advantages. They are more selective, the

and possible ca r -

cin o g en , in the streams, the groundwater,

80

CI IM S chromatogram

although more tedious and time-consuming

The discovery of high levels of acrylamid~ a n eu r o to xin

3. Acrylamidc

In the direct method, the extract is sepa-

with positive-ion CI /MS detection. Bromination

firm up the soft rock layers being bored near the tunnd (CH 2=CH-CO-NH 2),

, Buty;arnide

90

by a direct method after liquid-

rated by capillary GC, and the eluent is monitored by chemi-

icals that had leached from a grouting agent injected to entrance.

or determined

liquid extraction.

used for grazing.

In addition, workers building a tunnel through the ridge for the Swedish railway experienced

!\-Icth\-'Iacf\'lamide

In these methods, the analyte has either been derivatized by

Sweden. residents near the Hal-

an acrylamide-spiked

potato

of control standards

chip.

and

'T Wenzl. B, de la Calle, R. Gatennann. K. Hoenicke, F. Ulbcrlh. and E. Anklam. An a l. Bio a n a l. C h em .. 2004, 379. 4~9 ~T Delalour. A. Perisset, T Goldmann. S. Riediker. and R. H. Stadler. } Ag r ic. F o o d C h er n ,. 2004.52.4625

pesticide formulations

to limit spray drifting, and in biology

and chemistry to prepare gels used in electrophoresis Section 30C~2). Although

polyacrylamide

(see

An arbitrary

limit of 500 ppm acrylamide

polyacrylamide

preparations

has been set for agricultural

used in irrigation

uses. The polyacrylamide

and water treatment

in

preparation

is often an acrylic

acid copolymer, which can also release acrylates known to foods cooked at high tem~

peratures and under low-moisture found to contain acrylamide.7

conditions

The compound

found in raw and boiled foods. Researchers lished that acrylamide

incidences of cancer. although animal studies ha'le suggested such a link. The study also called for additional search hy the international

It was also

cooking foods excessively, hy lowering consumption

has not been

and fatty foods, and by eating a balanced diet.

of fried A modern

have estab~

reaction responanalytical methodology

of an amino acid and

the case of foods, the amino acid has

been found to be asparagine.

A complex series of steps

has been proposed.

Heating time

are crucial. The role of water and the

influence of side reactions are less well understood.

research is aimed at further improvements

to help elucidate

in the

modeling methods

the kinetics of its formation: understand-

foods. Once the formation ter understood,

reduction

kinetics and mechanism are bet-

in potato products by storing raw potatoes temperatures

and by modifying the condi-

tions used in potato processing. Enzymatic treatments

of

tem in humans and animals. A joint study of the UN Food

potato products with asparaginase

and Agriculture

gested. Clearly, more scientific research must be done in this

Organization

(WHO) reported

(FAO) and the World Health in 2002 on the health impli~

analyzer.

The instrument

ha:; a

entire system is under computer control with software dcslgned fur specific techniques and analytical method~. (Courtesy of TA In.-;trument:'i, New Castle, DE.)

of acrylamide levels can be pur-

methods have been suggested for reducing lev-

under controlled

Organization

thermogravimetrie

temperature-controlled thennoLalallc.e and operates ulHin conditions of controlled humidity. It has a muhiposition autosampler capable of automated analysis of up to twenty-finsamples. Olle version of this system features an infrared furnarc for heating from arnhif:llt temperature to 1200°C. Thl'

sued on a sound basis. For example, on the basis of current els of acrylamide

is known to cause damage to the nervous sys-

for acrylamide,

ing its health risks; and methods for reducin"'g i.ts levels in

knowledge,

Acrylamide

on acrylamide.

have been

Current

leading to acrylamide

re~

community and for betlt:r shar-

suggested that the public try to minimize exposure by not

action involves the initial combination

and temperature

that the evidence from human

studies did not show a link between acrylamide levels and

sible for the brown color of cooked foods. The Maillard re~ In

g~netic damage that may lead to

cancer. the study concluded

in foods arises from reactions related

to the Maillard reaction, a nonenzymatic

a reducing sugar.

was estimated

to be below the level that could be expected to cause neuro-

ing of scientific information

cause birth defects (a ter a togen). In foods. carbohydratc~rich

in foods.s The average daily food in-

in the general population

toxic effects. Regarding

with the

toxic monomer.

and water· treatment

take of acrylamide

is generally classi~

fied as a nontoxic additi\'e, it can be contaminated

cations of acrylarnide

area. and analytical chemistry

have also been sug~

will playa leading role.

S

ection6 consists offour cha pter s devoted to mis~

cella neous instr umenta l

methods.

metr ic a na l)'sis, differ entia l

differ entia l sCflltr ling ca lor imetr y,

Ther mo:;r a vi~

themwl

a na l)'sis.

a nd micr ot!",r ma l

a na !) "is a r e discussed in Cha pter 31. The theor )'a w] pr a ctice o( r a diochemica l

methods, including neutr on

a Clica lion a na ll·sis a nd isotope dilution

techniques,

are

disCllssed in Cha pler 32. In Cha pter 33 the pr inciples, instr ur r wnta tion,

a nd a ppliea lions

of a utoma led

a na l~

yzer s a r e descr ibed. F low injection a na ~\"Zer s, micr ojluidic sptems,

a nd discr ete a na l)"Zer s a r e included.

Cha pter 34,

the jina l cha pter in this section a nd in the book, e.nuoines a na !)tica l

melhods to deler mine pa r licle

ods include low~a ngle huer li:;hl

light sca lter ;ng, a nd pholosedimenta lion. la lAr uz!) ·sis ;n Act;on fea lur e pr esenls ca se, the fi'r st mur der inr estiga tion ca tion

Gnu(l ·si.)' u'a s used.

size. The meth~

sca lter ;ng,

({I ""wn;e The [ nstr umeo~

the J ohn I"llmnn

in ll'hich fleutr ofl a cti-

1,;1

----_

T h e n n a l M :e th 6 d s

Thermal methods differ in the properties measured and the temperature programs applied'! The four methods discussed here find widespread use for both quality control and research applications on polymers, pharmaceutical preparations, clays, minerals, metals, and alloys. &

60.0

.c

'"

~

In a thermogravimetric analysis (TGA) the mass of a sample in a controllcd atmosphere is recorded continuously as a function of temperature or time as the temperature of the sample is increased (usually linearly with time). A plot of mass or mass percentage as a function of time is called a ther mogr a m or a ther ma l decomposition cur ve.

T

her ma l a nqlysis techniques

··which

a r e th,ose in

a physica l pr oper ly of a s~g$ta nce or

its r ea ction pr oducts

tion of temper a tur e.

Usua lly,

is mea sur e~~

a func~

the substa '!~Gis sub-

jected to, a contr oUed temper a tJ ,tr e pr og(O;ir ldur ing

Commercial instruments for TGA consL~tof (1) a sensitive microbalance, called a thermob~lance; (2) a furnace; (3) a purge-gas system for providing an inert, or sometimes reactive, atmosphere; and (4) a computer system for instrument control, data acquisition, and data processing. A purge-gas switching system is a common option for applications in which the purge gas must be changed during an experiment.

the a na lysis. AltlwiJ .gh ther e a te mor e th'& !q dozen ther ma l a na lysis teqhniques'lf;e sia n in this cha pter fo

conjine? Ur discus-

four mft,hods tha tJ i5< J J J idep r i~

ma r ily chemica l r a tl] er tha n physica l

infoljna tion

a bout sa mples of ma tter . 7'h~emethodSir lelude ther mol5r a Vimetr !ca na lysi~,~iffer entiffr ther ma l a na lysis,

differ entifll

mier other ma l

sca nning

ca lor imetr y,

a nd

a na lysis.

of thermal methoos, see P r inciples of Ther ma l P. 1. Haines, ed., Cambridge, UK: Royal Society or Chemistry, 2002: P. 1. Haines, Ther ma l Methods of Ana lysis, London: Blackie, 1995; B. Wunderlich, Ther ma l Ana lysis, Boston: Academic Press, 1990; W. W. Wendlandt, Ther ma l Ana lysis. 3rd ed., New York: Wiley, 1985. For recent re .•iews. see S. Vyazovkin. Ana l. Cher n., 2006, 78. 3875; Ana l Chem., 2 0 0 4 ,7 6 ,3 2 ' 1 ' ) ; Ana l. Cher n., 2002, -4,2749. For a description of thermal analysis instruments, see B. E. Erickson, Ana l. Chem., 1999. 71. 689A. 1

For a detailed description

An.a lysis a nd Ca lor imetr y,

fd"

Throughout this chapter, this logo indicates

IQ.J an opportunity for online self-study at www .thomsooedu.com/cbemistry/skoog, linkingy< '" OIl

e-A("O mio!

60

X

20

10- 3 min-!

10

In 2

=

I

A (11~ 5) 140

40

285 cpm) In ( 453 cpm

Half-lives of radioactive species range from small fractions of a second to many billions of years. The activity A of a radionuclide is defined as its disintegration rate. Thus, from Equation 32-2, we may wnte dN

160

4

u

tV2~A= -A-

= -

200

180

= -At

ln~

A

the use of the decay rate

t V2

AN

= A

0.693 1.10 x 10 3 mini

=

Deviation

=

from {rue average

count,

15

(Xi - Ji)

630 min

dt

Activity is given in units of reciprocal seconds. The becquer e! (Bq) corresponds to one decay per second. That is, 1 Bq = 1 S-I. An older, but still widely used, unit of activity is the cur ie (Ci), which was originally defined as the activity of 1 g of radium-226. One curie is exactly equal to 3.7 X 1010 Bq. In analytical radiochemistrv activities of analytes typically range from a nanocuri~ or less to a few microcuries. In the laboratory, absolute activities are seldom measured because detection efficiencies are seldom 100%. Instead, the counting r a te R is used, where R = cA. Substituting this relationship into Equation 32-6 yields

Here, c is a. constant called the a bsolute detection effiCIency, which depends on the nature of the detector the geometric arrangement of sample and detector, and other factors. The dccay law given by Equation 32-4 can then be written in the form

32A-4

Counting

Statistics

As will be shown in Section 32B, radioactivity is measured by means of a detector that produces an electronic pulse, or count, each time radiation strikcs the detector. Quantitative information about decay rates is obtained by counting these pulses for a sp'ccified

Minute

Counts

1 2 3

7 8

180

4

187 166 173

5 6

164

Total counts

Minute

9

10 11 12

170

=0

168 170

173 132 154 167

For a more complete discussion, see G. Friedlander, 1. W. Kennedv, E. S. Macias, and 1. M. Miller, l\'uclea r a nd Ra diochemistr y, 3rd ed .. Chap. 9.

4

2004.

Average counts/min

Connts

period.' Table 32-2 shows typical dccay data obtained by successive I-minute measurements of a radioactive source. Because the decay process is random, considerable variation among the data is observed. Thus, in Table 32-2, the rates range from a low of 132 to a high of 187 counts per minute (cpm). Although radioactive decay is random, the data, particularly for low number of counts, are not distributed according to Equation a1-14 (Appendix 1), because the decay process does not follow Gaussian behavior. The reason that decay data are not normally distributed is that radioactivity consists of a series of discrete events that cannot vary continuously as can the indeterminate errors for which the Gaussian distribution applies. Furthermore, negative numbers of counts are not possible. Therefore, the data cannot be distributed symmetrically about the mean. To describe accurately the behavior of a radioactive source, it is necessary to assume a P oisson distr ibution, which is given by the equation

=

i

=

167.

New York: Wiley. 1981.

where y is the frequency of occurrence of a given count Xi and J1 is the mean for a large set of counting data.' The data plotted in Figure 32-1 were obtained with the aid of Equation 32-9. These curves show the deviation (Xi - J1) from the true average value that would be expected if WOO replicate observations were made on the same sample. Curve A gives the distribution for a substance for which the true average count J1 for a selected period is 5; curves Band C correspond to samples having true means of 15 and 35. Note that the a bsolute deviations become greater with increases in J1, but the r ela tive deviations become smaller. Note also the lack of symmetry about the mean for the two smaller count numbers. .;In the derivation of Equation 32-9, it is assumed that the counting period is short with respect to the half-life so that no significant change in the number of radioactive atoms occurs. Further restrictions include a detector that responds to the decay of a single radionuclide only and an invariant counting geometry so that the detector responds to a constant fraction of the decay events that occur.

Standard Deviation

of Counting

Data

In contrast to Equation al-14 (Appendix 1) for a Gaussian distribution, Equation 32-9 for a Poisson distribution contains no corresponding standard deviation term. It can be shown that the breadth of curves such as those in Figure 32-1 depend only on the total number of counts for any given period.' That is,

(a) Applying Equation

O'R

= VM = v180= I min

-1-

=

L

13.4 cpm

13.4 cpm 180cpm x 100%

O 'R

R

32-12 gives

=

7.4%

(b) For the entire set. where M is the number of counts for any given period and 0' M is the standard deviation for a Poisson distribution. The relative standard deviation O'MIM is given by O 'M

=

M

O 'R

R

=

3.7 cpm

=

167 x

100%

=

YO'~ + (aa~YO';

Generally, time can be measured with such high precision that a? = O. The partial derivative of R with respect to Mis 111.Thus, 2~ fIR =

(2

Background

Interval

for Counts

In Section alB-2 (Appendix 1), the confidence interval for a measurement is defincd as the limits around a measured quantity within which the true mean can be expected to fall with a stated probability. When the measured standard deviation is believed to 'be a good approximation of the true standard deviation (s --> 0'), the confidence interval CI is given by Equation a 1-20: CI for

JL =

x

:t ZO'

For counting rates, this equation takes the form CI for R = R

:t

ZO 'R

(32-14)

where z depends on the desired level of confidence. Some values for z are given in Table al-3. Example 32-3 illustratcs the ealculation of confidence intervals.

Taking the square root of this equation and substituting Equation 32-10 gives O'R

= VM = v'Ri = -Vif1l I

I

:;=V:=ff Example 32-2 illustrates the usc of these equations for counting statistics.

Calculate the 95% confidence interval for (a) the first entry in Table 32-2 and (b) the mean of all the data in the table.

(a) In Example 32-2, we found that O 'R = 13.4 cpm. Table al-3 (Appendix 3) reveals that z = 1.96 at the 95 % confidence level. Thus, for R 95% CI

Calculate the absolute and relative standard deviations in the counting rate for (a) the first entry in Table 32-2 and (b) the mean of all of the data in the table.

Figure 32-2 illustrates the relationship between total counts and tolerable levels of uncertainty as calculated from Equation 32-14. Note that the horizontal axis is logarithmic. Thus, a decrease in the relative uncertainty by a factor of 10 requires that the number of counts be increased by a faetor of 100.

=

=

(b) In this instance 95% CI for R

180 cpm :t (1.96 x 13.4 cpm) 180 :t 26 cpm O 'R

= =

where R, is the corrected counting rate and Rx and Rb are the rates for the sample and the background, respectively. The standard deviation of the corrected counting rate can be obtained by application of Equation (1) in Table al-6 (Appendix 1). Thus,

Substituting leads to

Equation

32-12 into this equation

2.2%

VM

M

(;~

3.73 cpm

3.73

O'R

Confidence

O'k =

V2OO4 = u=

Vii!.. = _1_

Thus, although the standard deviation increases with the number of counts, the relative standard deviation decreases. The counting rate R is equal to Mil. To obtain the standard deviation in R, we apply Equation al-29 (Appendix 1), which gives

ThUS,there are 95 chances in 100 that the true rate for (for the average of 12 min of counting) lies bctween 160 and 174 counts/min. For the single count in part (a), 95 out of 100 times, the truc rate will lie between 154 and 206 counts/min.

R

was found to be 3.73 cpm and 167 cpm :t (1.96 x 3.73 cpm) 167 :t 7 cpm

Corrections

The number of counts recorded in a radiochemical analysis includes a contribution from sources other than the sample. Background activity can be traced to the presence of minute quantities of radon radionuc1ides in the atmosphere, to the materials used in construction of the laboratory, to accidental contamination within the laboratory, to cosmic radiation, and to the release of radioactive materials into the Earth's atmosphere. To obtain an accurate determination, then, it is necessary to correct the measured counting rate for background contributions. The counting period required to establish the background correction frequently differs from the counting period for the sample. As a result, it is more convenient to employ counting rates as shown in Equation 32-15.

A sample yielded 1800 counts in a lO-min period. Background was found to be 80 counts in 4 min. Calculate the absolute uncertainty in the corrected counting rate at the 95% confidence level. Solution

1800

Rx =

10 =

Rb

="4 =

80

O'R,

=

180

180cpm 20cpm

80

10 +"4 =

6.2cpm

32B-1

CL for R, = (180 - 20) :!: 1.96 x 6.2 = 160:!: 12cpm Here, the chances are 95 in 1()()that the true count lies between 148 and 172 cpm. Note that the inclusion of background contributions invariably leads to an increase in the reported uncertalllty of the determination.

Radiation from radioactive sources can be detected and measured in essentially the same way as X-radiation (Sections 12B-4 and 12B-5). Gas-filled chambers scintillation counters, and semiconductor detecto:s are all sensitive to alpha and beta particles and to gamma rays because absorption of these particles produces 101llzallon or photoelectrons, which can in turn produce thousands of ion pairs. A detectable electrical pulse is thus produced for each particle reaching the transducer.

Measurement

of Alpha Particles

To minimize self-absorption, alpha-emitting samples are generally counted as thin deposits prepared by electrodeposillon or by vaporization. Often, these deposits are then sealed with thin layers of material and counted III wllldowiess gas-flow proportional counters or ionizatlOn chambers. Alternatively, they are placed immediately adjacent to a solid-state detector, often in a vacuum for counting. Liquid scintillation counting (see next secllon) IS becoming increasingly important for counting alpha emitters because of the ease of sample preparation and the higher sensitivity for alpha-particle detecllon. Because alpha-particle spectra consist of characteristic, discrete energy peaks, they are quite useful for identification. Pulse-height analyzers (Section 12B-5) permIt the recording of alpha-particle spectra.

32B-2

Measurement

1.2

x 10"

1.0

x to'

1---._-

"':

-

L

----

~

---

._--- --

---

!

~

,

! , i

I

-b,

~

~I

-~--

!

!

I

" 'lilo l


(J'- AN*

Ncf>(J' N* = -A-[I

If we substitute term, we obtain N*

Equation

= Ncf>(J'[l _ A

- exp(-At)] 32-5 into the exponential

exp(-

0.693t)] tll2

The last equation can be rearranged to give the product AN*, which is the activity A (see Equation 32-6), Thus, A = AN* = Ncf>(J'[ I - exp( - 0,~:3t)

] "': Ncf>(J'S

F I G U R E 32-7 The effect of neutron flux density and time on the activity induced in a sample,

(32'17)

ijNa(n, y)iiNa

where S is the saturation factor, which is equal to 1 minus the exponential term, Equation 32-17 can be written in terms of experimental rate measurements by substituting Equation 32-7 to give

mass of analyte is directly proportional to the counting rate, If we use the subscripts x and s to represent sample and standard, respectively, we can write (32-19) (32-20)

R

When exposed to neutrons, the rate of formation of radioactive nuclei from a single isotope is given by dN* ----;;t=Ncf>(J'

where dN*ldt is the reaction rate (S'I), N is the number of stable target atoms, cf> is the average flux density (n cm -I S·I), and (J' is the capture cross section (cm'). The capture cross section is a measure of the probability of the nuclei reacting with a neutron at the neutron energy employed, Tables of reaction cross sections for thermal neutrons list values for (J' in ba r ns b, where I b = 10.24 cm'. Once formed, the radioactive nuclei decay at a rate given by Equation 32-2, That is,

-dN*ldt

-

dN*

--

dt

=

AN*

=

cNcf>(J'[ I - exp( - 0,~:3t)

]

=

Ncf>(J'cS

Figure 32-7 is a plot of this relationship at three levels of neutron flux density, The abscissa is the ratio of the irradiation time to the half-life of the isotope (tlt ll2). In each case, the counting rate approaches a constant value where the rates of formation and disintegration of the radionuclide approach one another. Clearly, irradiation for periods beyond four or five half-lives for an isotope will result in little improvement in sensitivity. In many analyses, irradiation of the samples and standards is carried out for a long enough period to reach saturation so that S approaches unity. Under this circumstance, all of the terms except N on the right side of Equation 32-18 are constant, and the number of analyte radionuclides is directly proportional to the counting rate, If the parent, or target, nuclide is naturally occurring, the mass of the analyte m can be obtained from N by multiplying it by Avogadro's number, the natural abundance of the analyte nuclide, and the atomic mass. Because all of these are constants, the

E x p e r im e n ta l

in A c tiv a tio n

Integrating this equation from time 0 to t, gives

Usually, equations of this type are written in the abbreviated form

The prompt gamma rays formed by capture reactions are of analytical interest in some cases, but the radionuclide produced (24Na) and its decay radiations are more often used in NAA.

3 2 C -4

Thus, during irradiation with a uniform flux of neutrons, the net rate of formation of active particles is

where k is a proportionality constant. Dividing one equation by the other and rearranging leads to the basic equation for computing the mass of analyte in an unknown:

s a m p le s

of and

sta n d a r d s

Figure 32-8 is a block diagram showing the flow of sample and standards in the two most common types of activation mcthods, destr uctive and nondestr uctive, In both procedures the sample and one or more standards are irradiated simultaneously with neutrons (or other types of radiation), The samples may be solids, liquids, or gases, although the first two are more common. The standards should physically and chemically approximate the sample as closely as possible. Generally, the samples and standards are contained in small polyethylene vials; heat-scaled quartz vials are also used on occasion. Care must be taken to ensure that the samples and standards are exposed to the same neutron flux. The time of irradiation depends on a variety of factors and often is determined empirically. Frequently, an exposure time of roughly three to five times the half-life of the analyte product is used (see Figure 32-7). Irradiation times generally vary from a few minutes to several hours. After irradiation is terminated, the samples and standards are often allowed to decay (or "cool") for a period that again varies from a few minutes to several hours or more, During cooling, short-lived interferences decay so that they do not affect the outcome of the analysis. Another reason for allowing an irradiated sample to cool is to reduce the health hazard associated with higher levels of radioactivity. Nondestructive

M ethods

As shown in Figure 32-8, in the nondestructive method the sample and standards are counted directly after cooling. Here, the ability of a gamma-ray spec-

D a ta

S im u lta n e o u s ir r a d ia tio n

C o n s id e r a tio n s

M e th o d s

C o o lin g p e r io d

p r o c e s s in g

and display

trometer to discriminate among the radiations of different energies provides selectivity. Equation 32-21 is then used to calculate the amount of analyte in the unknown as shown in Example 32-5.

Two 5.oo-mL aliquots of river water were taken for NAA. Exactly 1.00 mL of a standard solution containing 1.00 Ilg of Al J+ was added to one aliquot, and 1.00 mL of deionized water was introduced into the other. The two samples were then irradiated simultaneously in a homogeneous neutron flux. After a brief cooling period, the gamma radiation from the decay of 28 Al was counted for each sample. The solution diluted with water gave a counting rate of 2315 cpm, whereas the solution containing the added Al J+ gave 4197 cpm. Calculate the mass of Al in the 5.00-mL sample.

Here, we are dealing with a simple standard-addition problem that can be solved by substituting into Equations 32-19 and 32-20. Thus, 2315 = km x 4197 = k(m x + m,) = k(m x + 1.00) Solving these two equations leads to m x = 1.23 1lg

Destructive

u.,

I

I

-

-

-

.,

M ethods

As shown in the lower pathway in Figure 32-8, a destructive method requires that the analyte be separated from the other components of the sample prior to counting. If a chemical separation method is used, this technique is called r a diochemica l neutr on a ctiva tion. In this case a known amount of the irradiated sample is dissolved and the analyte separated by precipitation, extraction, ion exchange, or chromatography. The isolated material or a known fraction thereof is then counted for its gamma - or beta - activity. As in the nondestructive method, standards may be irradiated simultaneously and treated in an identical way. Equation 32-21 is then used to calculate the results of the analysis.

-

0

-

en

N

~.

~ ,;;:

-

~. xN or."

I

0

~

-~

x

, i:O -

E

I

""

x

x

~.

"2

-

-

.D

"-

x x ~, v;

I

- '7 -x 0 -:::x x - bx sx - ~. ~. -

"1 ~

1

"1

o ~

0

:t

X

X

or,

-

b

~-

N

x

N

1eo

""

U x

x

x v;

eo

'"

I

:t

x

- - .r. "1 , - 1 -.: -

X

X

,

V;

Z

X

or,

S ~ S bX

V;

x

"2

e

"'::: S

;;:

b

1 1

::l:=: S Ul

I

V;

;> :::

x or,

0

-

U

N

X

"I

or,

~,

eo

"1

S

"2

- X

X

, , S S

"

-0

or,

Scope

Success of the nondestructive method requires that the spectrometer be able to isolate the gamma-ray signal produced by the analyte from signals arising from the other components. Whether adequate resolution is possible depends on the complexity of the sample, the presence or absence of elements that produce gamma rays of about the same energy as that of the element of interest, and the resolving power of the spectrometer. Improvements in resolving power, which have been made in the past several decades because of the development of high-purity germanium detectors (Section 12B-4), have greatly broadened the scope of the nondestructive method. The great advantage of the nondestructive approach is its simplicity in terms of sample handling and the minimal time required to complete an analysis. In fact, modern activation analysis equipment is largely automated. The nondestructive purely instrumental technique is often termed instr umenta l neutr on a ctiva tion a na lysis, or INAA.

0

0

"2

~

.r ,

eo eo

:;;: -

~

or.

x

x

>-

~. - ~

eo

a-

.D

~.

-x

.D

or.

,.

-

0

x x

X

X

~.

Vi x ~.

"-b

0

-


c .~

Organic to detection system

~ =8 1!.

-;

~L (a) Flow diagram of a flow injection system containing an extraction module (A B C ). (b) Details of A , the organic injector system. (c) Details of C, the separator. (Adapted from J. Ruzicka and E. H. Hansen, F lo w In je c tio n A n a ly s is , 2nd ed., New York:Wiley,1988. With permission of John Wiley & Sons.) FIGURE

_

33-5

plementary channels have been cut to accommodate the two streams on opposite sides of the membrane. The transfer of smaller species through the membrane is usually incomplete (often less than 50%). Thus, successful quantitative analysis requires close control of temperature and flow rates for both samples and standards. Such control is easily accomplished in automated flow injection systems. Gas diffusion from a donor stream containing a gaseous analyte to an acceptor stream containing a reagent that permits its determination is a highly selective technique that is often used in flow injection analysis. The separations are carried out in a module similar to that shown in Figure 33-4. In this application, however, the membrane is usually a hydrophobic microporous material, such as Teflon or isotactic polypropylene. The determination of total carbonate in an aqueous solution is an example of this type of separation technique. Here, the sample is injected into a carrier stream of dilute sulfuric acid, which is then directed into a gas-diffusion module, where the liberated carbon dioxide diffuses into an acceptor stream containing an acid-base indicator. This stream then passes through a photometric detector that yields a signal proportional to the carbonate content of the sample. Solvent Extraction. Solvent extraction is another common separation technique that can be easily adapted to continuous flow methods. Figure 33-5a shows a flow diagram for a system for the colorimetric determination of an inorganic cation by extracting an aqueous solution of the sample with chloroform containing a complexing agent, such as 8-hydroxyquinoline. At

point A , the organic solution is injected into the samplecontaining carrier stream. Figure 33-5b shows \hat the stream becomes segmented at this point anClis madc up of successive bubbles of the aqueous solution and the organic solvent. Extraction of the metal complex occurs in the reactor coil. Separation of the immiscible liquids takes place in the T-shape separator shown in Figure 33-5c. The separator contains a Teflon strip or fiber that guides the heavier organic layer out of the lower arm of the T, where it then flows through the detector labeled Fe in Figure 33-5a. This type of separator can be used for low-density liquids by inverting the separator. It is important to reiterate that none of the separation procedures in FIA methods are complete. Bccause unknowns and standards are treated identically, incomplete separation is unimportant. Reproducible timing in FIA ensures that, even though separations are incomplete, there is no loss of precision and accuracy as would occur with manual operations.

FIGURE 33-6 Effect of convection and diffusion on concentration profiles of analytes at the detector: (a) no dispersion, (b) dispersion by convection, (c) dispersion by convection and radial diffusion, and (d) dispersion by diffusion. (Reprinted with permission from D. Betteridge, A n a l. Chern., 1 9 7 8 ,5 0 , 836A. Copyright 1978 American Chemical Society.)

the fluid moves more rapidly than the liquid adjacent to the walls, creating the parabolic front and the skewed zone profile shown in Figure 33-6b. Diffusion also causes broadening. Two types of diffusion can, in principle, occur: radial, which is perpendicular to the flow direction, and longitudinal, which is parallel to the flow. It has been shown that longitudinal diffusion is insignificant in narrow tubing, and radial diffusion is much more important. In fact, at low flow rates, radial diffusion is the major source of dispersion. Under such conditions, the symmetrical distribution shown in Figure 33-6d is approached. In fact, flow injection analyses are usually performed under conditions in which dispersion by both convection and radial diffusion occurs; peaks like that in Figure 33-6c are then obtained. Here, the radial dispersion from the walls toward the center essentially frees the walls of analyte and nearly eliminates cross-contamination between samples. D is p e r s io n

Immediately after injection with a sampling valve, the sample zone in a flow-injection apparatus has the rectangular concentration profile shown in Figure 33-6a. As it moves through the tubing, band broadening, or disper sion. takes place. The shape of the resulting zone is determined by two phenomena. The first is convection arising from laminar flow in which the center of Anima tion: Learn mOre about

analysis.

flo w

in je c tio n

Dispersion D is defined by the equation

where Co is the analyte concentration of the injected sample and c is the peak concentration at the detcctor (see Figure 33-6a and c). Dispersion is measured by injecting a dye solution of known concentration Co and then recording the absorbance in a flow-through cell. After calibration. c is calculated-from Beer's law.

Dispersion is influenced by three interrelated and controllable variables: sample volume, tubing length, and flow rate. The effect of sample volume on dispersion is shown in Figure 33-7a, where tubing length and flow rate are constant. Note that at large sample volumes, the dispersion becomes unity. Under these circumstances, no appreciable mixing of sample and carrier takes place, and thus no sample dilution has occurred. Most flow injection analyses, however, involve interaction of the sample with the carrier or an injected rcagent. Here, a dispersion value greater than unity is necessary. For example, a dispersion value of 2 is required to mix sample and carrier in a 1: 1 ratio. The dramatic effect of sample volume on peak height shown in Figure 33-7a emphasizes the need for highly reproducible injection volumes when D values of 2 and greater are used. Other conditions also must be closely controlled for good precision. Figure 33-7b demonstrates the effect of tubing length on dispersion when sample size and now rate are constant. Here, the number above each peak gives the length of sample travel in centimeters.

33B-3 Applications of

F IA

Flow injection applications tend to fall into three categories: low disper sion, medium disper sion, and la r ge d; sper sion.

11 .20-

A

j\ \/ "

V

50 em

= 2.0

"E

~

;5

u

=" .2

B

~L sample

II \

~ Bypass

~iPh~otometer

V

100 em

= 4.0

0.25

~

• To waste

I

Recorder

.~

~

:;:

5

~ 0.3

~

1:

'?

. 0.2

< (b)

Effect of sample volume and length of tubing on dispersion. (a)Tube length: 20 cm; flow rate: 1.5 mLimin; indicatec volumes are in ~L. (b) Sample volume: 60 ~L;flow rate; 1.5 mLimin. (From J. Ruzicka and E. H. Hansen, A n a l. C h im . A c ta , 1980, 114,21. With permission.)

FIGURE

33-7

2345678 --Time,

m in

---

33-8 (a) Flowinjection apparatus for determining calcium in water by formation of a colorec complex with o-cresolphthalein complexone at pH 10. Alltubing had an inside diameter of 0.5 mm. A and B are reaction coils having the indicated lengths. (b) Recorded output. Three sets of curves at left are for triplicate injections of three samples. Four sets of peaks on the right are for duplicate injections of standards containing 5,10,15, and 20 ppm calcium. (From E. H. Hansen, J. Ruzicka, and A. K.Ghose, A n a l. C h im . Acta, 1978, 1 0 0 , 151. With permission.)

FIGURE L o w - a n d M e d iu m - D is p e r s io n

A p p lic a tio n s

Low-dispersion flow injection techniques (dispersion values of 1~3) have been used for high-speed sample introduction to such detector systems as inductively coupled plasma atomic emission, flame atomic absorption, and specific-ion electrodes. The justification for using flow injection methods for electrodes such as pH and pea is the small sample size required (-25 flL) and the short measurement timc (-10 s). That is, measurements are made well before steady-state equilibria are established, which for many specific-ion electrodes may require a minute or more. With flow injection measurements, transient signals for sample and standards provide excellent accuracy and precision. For example, it has been reported that pH measurements on blood serum can be accomplished at a rate of 2 4 0 /h with a precision of :+:0.002pH. In general, limited-dispersion conditions are realized by reducing as much as possible the distance between injector and detector, slowing the flow rate, and increasing the sample volume. Thus, for the pH measurements just described, the length of 0.5-mm tubing was only 10 cm and the sample size was 30 flL.

Medium dispersion corresponds to D values of 3 -10. Figure 33-8a illustrates a medium-dispersion system for the colorimetric determination of calcium in serum milk, and drinking water. A borax buffer and a colo~ reagent are combined in a 50-cm mixing coil A prior to sample injection. The output for three samples in triplicate and four standards in duplicate is shown in Figure 33-8b. Figure 33-9 illustrates a more complicated flow injection system designed for the automatic spectrophotometric determination of caffeine in acetylsalicylic acid drug preparations aftcr extraction of the caffeine into chloroform. The chloroform solvent, after cooling in an ice bath to minimize evaporation, is mixed with the alkaline sample stream in a T-tube (see lower insert). After passing through the 2-m extraction coil L, the mixture enters a T-tube separator, which is differentially pumped so that about 35% of the organic phase containing the caffeine passes into the flow cell, and the other 65 % accompanying the aqueous solution containing the rest of the sample flows to waste. To avoid contaminating the flow cell with water, Teflon fibers, which are not wetted by water, are twisted into

a thread and inserted in the inlet to the T-tube in such a way as to form a smooth downward bend. The chloroform flow then follows this bend to the photometer cell where the caffeine concentration is determined on the basis of its absorption at 275 nm. S to p p e d - F lo w

M e th o d s

As discussed earlier, dispersion in small-diameter tubing decreases with decreasing flow rate. In fact, it has been found that dispersion ceases almost entirely when the flow is stopped. This phenomenon has been exploited to increase the sensitivity of measurements by allowing time for reactions to go further toward completion without dilution of the sample zone by dispersion. In this type of application, a timing device is required to turn the pump off at precisely regular intervals.

A second application of the stopped-flow technique is for kinetic measurements. In this application, the flow is stopped with the reaction mixture in the flow cell where the changes in the concentration of reactants or products can be monitored as a function of time. The stopped-flow technique has been used for the enzymatic determination of glucose, urea, galactose, and many other substances of interest in clinical chemistry. F lo w

In je c tio n

T itr a tio n s

Titrations can also be performed continuously in a flow injection apparatus. In these methods, the injected sample is combined with a carrier in a mixing chamber that promotes large dispersion. The mixture is then transported to a confluence fitting, where it is mixed with the reagent containing an indicator. If the

Phase

/

NaOH

/

samples

\

, !''' \

C~~~J.:.' .• " \

+

'9).

1Aqueous

~_:_'i.

\\

I

Ie

/1 I

\ ,~HCI3~/ \

--

pump

I

\

0.16MNaOH

Waste

I

\

~ 2~/min ~ 0.8 mm

/

I

\

Peristaltic

height. Titrations of this kind can be performed at a rate of sixty samples/h in a conventional FIA system.

separation

/---

I \

I \

• L

I \

I

Photometer Chloroform

2.0mLlmin -... 0.8 mm

•

\ \ \ \ 0.7 mUmin

~

//1-..... ,\\ /

NaOH

\

~'l\ " ----

Waste

/

/ / Phase

mixing

FIGURE33-9 Flow injection apparatus for the determination of caffeine in acetylsalicylic acid preparations. With the valve rotated 90 the flow in the bypass is essentially zero because of its small diameter. Rand L are Tefloncoils with 0.8-mm inside diameters; L is 2 m, and the distance from the injection point through R to the mixingpoint is 0.15 m. (Adapted from 8. Karlberg and S. Thelander, A n a l. C h im . A c ta , 1978, 98, 2. With permission.) 0

detection is set to respond to the color of the indicator in the presence of excess analyte, peaks such as those shown in Figure 33-10 are obtained. In this example, an acid is being titrated with a standard solution of sodium hydroxide, which contains bromo thymol blue

Zones

indicator. With injection of samples, the solution changes from blue to yellow and remains yellow until the acid is consumcd and the solution again becomes blue. As shown in the figure, the concentration of anaIyte is determined from the widths of the peaks at half

338-4

Variants

of

F IA

Since the introduction of FIA in the mid-1970s, several variations have appeared on normal FIA, which employs continuous unidirectional pumping. F lo w

R e v e rs a l

F1A

One variation on normal FIA, termed flow r ever sa l F lA, was introduced by Betteridge and coworkers" Reversing the direction of flow allows the effectivc reaction coil length to be varied without a physical change in the FlA apparatus. Multiple pumps can be used or the direction of flow can be reversed by means of valves as shown in Figure 33-11a. Flow recycling can also be accomplished by switching two valves as shown in Figure 33-lIb. Reversing the flow or recycling the sample plug can allow automated optimization ofFIA methods using a variety of different software approaches. Alternatively, kinetics data can be obtained without stopping the flow. S e q u e n tia l

FIGURE33-10 Flow injection titration of HCIwith 0.001 M NaOH. The molarities of the HCIsolutions are shown at the top of the figure. The indicator was bromothymol blue. The time interval between the points is a measure of the acid concentration. (From J. Ruzicka, E. H. Hansen, and M. Mosback, A n a l. C h im . A c ta , 1980,114,29. With permission.)

F IA

-,

-"',

5'

v' :::)t

~: 8

"' ~,

,£,

.iil

':::1

~:, I I

L

_

(\)

I I

~ .•.. ,. CHCI]I~""'Y I \

\t~"~ ,

275 nm

M e r g in g

The merging zones principle was first inlroduced to economize on the use of expensive reagents. When a sample is injected into a carrier stream of reagent, the reagent is usually pumped continuously even when the sample zone is not present In merging zones FIA, the sample and the reagent arc injected into two carrier streams, which arc then allowed to merge downstream. Because the carrier streams contain only water or an inert buffer, the expensive reagent is conserved and only a limited quantity injected. By choosing different lengths of the reagent zone and letting it overlap in different ways with the sample zone, differing concentrations of the sample and reagent can be brought together to produce data to construct calibration curves or to study concentration effects.

In je c tio n

,., 5

"

I g

C;

~ ~

FIGURE33-11 Configurations for flow reversals (a) and fiow recycles (bl. In both cases, six-port valves are used. The initialvalve positions are shown in diagram I, and diagram IIshows the valve configuration during the reversal or recycle. In the recycle configuration (b), both valves turn, but in the reversal configuration, valve B is stationary. Allarrows exiting valves go to waste. (From E. 8. Townsend and S. R. Crouch, T re n d s A n a l. C h e rn ., 1992, 11,90. With pennission.)

A n a ly s is

In 1990 Ruzicka and Marshall6 introduced a variation of flow injection called sequentia l injection a na lysis (SIA), which can overcome some of the reagent waste of FIA. Instead of the continuous, unidirectional flow typical of FlA, SIA uses discontinuous, bidirectional 50. Betteridge. P. B. Oates. and A. P. Wade. Ana l. C hem., 1987. 59.1236 "1. Ruzicka and G. Marshall. Ana l. C him. Acra.,J-990. 2.17. 329

________________________ ..1

flow. A typical apparatus is illustrated in Figure 33- 12. The SIA system offers precise, low-volume delivery of reagents and reproducible flow reversals because of the syringe pump. The volumes introduced (usually microliters or less) are controlled by the time the port TU ior ia l:

Learn more about sequential injection

a n a ly s is .

_

consumption parallel

and

waste

procedures,

analyses

production,

pcr day. There

to implementing successful

the lah-on-a-chip

formi~g

concept.

electronic

and reaction

chemical devices

scientists

and engineers

The

is an active

circuits.

the valves, propul-

chambers

analyses.

crotluidic

The most technologv

integrated

is used to produce

of

approaches

photolithography

as is used for preparing This technology

the numhcrs

have heen several

use the same

sion sYstems,

by automating

and by incrcasing

needed

for per-

development

research

of mi-

involving

area

from academic

and industrial

laboratories.'! At lirs!. microfluidic

FIGURE 33-12 Sequential injection apparatus based on a bidirectional syringe pump and a six-port selection valve. The valve is equipped with a central communication channel (CG), which can address any 01 the ports, and a communication line (CL) connected to a holding coil (HG) and the syringe pump. When the communication channel is directed to the various ports, sample and reagent zones are sequentially drawn into the holding coil and stacked one after another. Switching the communication channel to position 5 causes tbe segments to flow into the reactor toward the detector (D). During this Ilow, the segments undergo dispersion, partial mixing, and chemical reaction.

with traditional

systems

and valves.

channels

showed

low reagent

propulsion

systems

systems,

pump

flow rate. Dispersion

the sample coil. The travcl

and

reagents

aids the

into the reaction

compared reagent

gram.

With F[1\, the entire

tire

to another

which

allows

Sequential

injection

useful for a variety such

applied

solid-phase In addition

amperometry,

chemiluminescence, used as detection

and methods

proven

LaY

idea

technology

croconduit needed

is designed

tors,

mixers,

mierofluidic

within

and membranes

the LaY

flow systems

descrihed

Mixing points

reactors, system.

are used

bead

reac-

can all be

In some cases,

in ways similar

can

to

pump,

reactor.

to analytieal

as membrane extraction, to colorimetry, fluorescence, conductimetry

lematic.

operations

especially procedures

are

circuit,

of microlluidic miniaturized

has enahled

or

la bor lltor y-oll-a -chip

(I'TAS)-'

Miniaturization

chip scale can reduce

to the scale the fabrication

micr o

{ola l

of an inte-

for many

of a complete llna lysis

of lahoratory

analysis

of laminar

syster n

operations

costs hy lowering

to a

reagent

ion-selective [R absorption. have

been

"1. RUlicka. Ana lvst, 2000, Ll"'. ]()".' "For rt'views uf thes..: s\"

E~ U

30 20

This equation can bc solved in matrix form or by iterative methods. In most modern instruments, the measurement is performed by an array of N detectors. Also, Mie scattering theory is used in many instrumcnts instead of Fraunhofer diffraction theory. In one popular approach the particles are divided into size intervals and each interval is assumed to generate an intensity distribution according to the average sizc. In this case, the preceding equation becomes N

giN)

=

:L K(N,di)f(d,)!l.d i= l

where giN) is the output of the Nth detector, K(N, d,) is the response coefficient of the Nth detector, d i is the ith diameter, and !l.d is the particle size inter~a~ number. The particle size distribution f(d,) is calculated from the relationship between the output of the dctector and its response function. The distrihution is usually calculated on the basis of volume. Figure 34-5 shows a plot of the cumula tive under size distr ibution. The value at each particle diameter represents the percentage of particles having diameters less than or equal to the expressed value. A frequency distribution showing the percentage of particles having a particular particle diameter or range of diameters is also com-

10 0 0.1

manly given. These can be plotted either as histograms or as continuous distributions. D yna mic light sca tter ing (DLS), also known as photon cor r ela tion spectr oscopy (peS)

Since the initial introduction of laser diffraction instrumentation in the 1970s, many different applications to particle size analysis have been reported.3 These have included measurements of size distributions of radioactive tracer particles, ink particles used in photocopy machines, zirconia fibers, alumina particles, droplets from electronic fuel injectors, crystal growth particles, coal powders, cosmetics, soils, resins, pharmaceuticals, metal catalysts, electronic materials, photographic emulsions, organic pigments, and ceramics. About a dozen instrument companies now produce LALLS instruments. Some LALLS instruments have become popular as detectors for size-exclusion chromatography.

and qua si-ela stic light

sca tter ing (QELS), is a powerful technique for probing

solution dynamics and for measuring particle sizes.' The DLS technique can obtain size information in a few minutes for particles with diameters ranging from a few nanometers to about 5 f1m. Thc DLS technique involves measurement of the Doppler broadening of the Rayleigh-scattered light as a result of Brownian motion (translational diffusion) of the particles. This thermal motion causes time fluctuations in the scattering intensity and a broadening of the Rayleigh line. The Rayleigh line has a Lorentzian line shape. In macromolecular solutions, concentration -1For additional

information. see 1. D. Ingle Jr. and S. R Crouch. Spectr oUpper Saddle RIver. NJ: Prentice-Hall, 1988. Chap. 16;

chemica l Ana lysis.

N. C. Ford.

in

Mea sur ements

Sca tter ing, B. E. Dahenke.

·'See. for example.

B. B. Weiner, in Moder n

Method,

of P a nicle

Size

Ana lysis. H. G. Barth, ed .. New York: Wiley, 1984, Chap. 5; P. E. Plantz,

ibilL Ch~p. 6

of Suspended

P a r tides by Q ua si·ela stic

Light

ed .. New York: \\/iley. 1983; M. L. McConnelL Ana l. C her n., 1 9 8 1 , 53. 1007:\: B. 1. Berne and R. Pecora, D .\'na mic Light Sca tter ing with Applica tions to C hemistr y. Blulogy a nd P hysics, Nc:w York: Wiley. IY76, reprinted by Dover Publications. fne .. N.::w 'York.

averaged product is obtained at various delay times and plotted against the delay time. The autocorrelation function is the Fourier transform of the power spectrum. Because the scattered radiation has a Lorentzian line shape. its Fourier transform should be an exponential decal', as illustrated in Figure 34-6b. According to the thco~v of DLS, the time constant of the exponential decav T i; directly related to the translational diffusion coefficient of the isotropic. spherical particles in Brownian motion.

fiuctuations arc usually dominant. Under these conditions, the width of the Rayleigh line is directly proportional to the translational diffusion coetJicient D r . The DLS method uses optical mixing techniques and correlation analysis to obtain these diffusion coefficients. The line widths (1 Hz to I MHz) are too small to be measured bv conventional spectrometers and even interferometers.

=

S (w )

A(Elsin'WII"

+ E,E,[ cos(w,

Eisin'w21

- WI)I - COS(W2 + WI)IJ}

(34-6)

wherc A is a proportionality constant. The PMT cannot respond directly to frequencies and or the sum term because these are greater than 10" Hz for visible radiation. The PMT can respond, however, to the difference frequency term (w, - WI)'which can be as small as a few Hz. When multiple frequencies are present, a difference spectrum is generated that is centered at o Hz. The time dependence of the intensity fluctuations is then used to obtain the particle size information. Optical mixing is accomplished by beating thc scattered light against a small portion of the source bcam (hetcro-

w,

It]

w,

Tutor ia l: Learn more about particle size anal)'sis

__

L_a,_, 'i

1000 Alfred Nobel Dr.. Hercules, CA 94547 ~For a more detailed treatment of statisticS, see J. L. DCqlTe, P r oba bilin and S ratl.H ic\ for E fll.;inrerin).; and thl' S ciences, 6th ed .. Pacific Gru\'(::, CA Duxburv Pn:ss at Brooks 'Cole. 2004: D. A. Skoog, D. M. West. F. 1. Holler and S. R'. Crouch, F unda mt:nwls (If Anul ..•. lin.il Cher n/SIn, Kth ed .. Belmont CA: Bruoks;Cole, 2004, Chaps. 5--::: S. R. Crouch and F. 1. Holler. A ppll' ca tions of .\ficr owfl:;' E.tcel ifl Ana lvticu/ Chem/sr r L Belmont. C:\ Bwuk.s 'Cok. 2004

Because N in this case is a finite number, x often differs somewhat from the population mean /l, and thus the true value, of the quantity being measured. The use of a different symbol for the sample mean emphasizes this important distinction. Population Standard Deviation (..,.) and Population Variance (..,.'), The population standard dC\'latlon and the population \'ariance provide statisticallY' SIgnificant

measures of the precision of a population of data. The population standard deviation is given by the equation ,r ----,,,,-,

!

2; (x, -

\ I lim c.~ __

._

where x, is again the value of the ith measurement. Note that the population standard deviation is the root mean square of the individual devia tions fr om the mea n for the population. The precision of data is often expressed in terms of the va r ia nce (IT '), which is the square of the standard deviation. For independent sources of random error in a system, variances are often additive. That is, if there are n independent sources, the total variance IT; IS given by

where IT ;, IT ), error sources.

...

=

, IT ~

,r;

+

IT )

+.

+

IT ~

(al-9)

are the individual variances of the

Note that the standard deviation has the same units as the data, whereas the variance has the units of the data squared. Scientists tend to use standard deviation rather than variance as a measure of precision. It is easier to relate a measurement and its precision if they both have the same units. Sa,mple Standard Deviation (sl and Sample Variance The sta nda r d devia tion of a sample of data that is of limited size is given by the equation (s-).

When z = 2, the relative standard deviation is given as a percent; when it is 3, the deviation is reported in parts per thousand. The relative standard deviation expressed as a percent is also known as the coefficient of va r ia tIOn (CV) for the data. That is,

CV

x

3.771

Xi

= -N = 5 =

=

x,)'

N

(3.771)2

0.7542

=

=

2.844t45

0.754 ppm Pb

14.2~0441

= 2.8440882

T he N orm al E rror Law

In Gaussian statistics, the results of replicate meaSUrements arising from indeterminate errors are assumed to be distributed according to the normal error law, which states that the fraction of a population of observations, dNIN, whose values lie in the region x to (x + dx) is given by

5

2.844145 - 2.8440882 5-1

s= =

Other Ways to Calculate Standard Deviations, Scientific calculators usually have the standard deviation function built in. Many can find the population standard deviation IT as well as the sample standard rdevia_ tion s. For any small set of data, the sample standard deviation should be used. To find s with a calculator that does not have a standard deviation key, the following rearrangement of Equation al-IO is easier to use than Equation al-1O Itself:

'"

( Xi

2

-

2; N

X i )' -

,~I

--N ---

N -1

'By definition. the number of degrees of freedom is the numher of values thar remain indcpel~dent when s is calculated. \\-'hen the sample mean x is ~ed In the calcul.allOn, only .v ~ I values are independent. because one \alue can be obtamed from the mean and the other values.

2;

L xi ~

3.77t

=

calculations, these programs can be used to carry out least-squares analysis, nonlinear regression, and many advanced functions.

Substituting into Equation al-13 leads to

i~

Relative Standard Deviation (RSD) and Coefficient of Variation (CVI. Relative standard deviations are often more informative than are absolute standard

x

In dealing with a population of data, IT and JL are used In place of s and x in Equations al-11 and al-12.

N

Note that the sample standard deviation differs in three ways from the population standard deviation as defined by Equation al-8. First, IT is replaced by s in order to emphasize the difference between the two terms. Second, the true mean JL is replaced by:t, the sample mean. FInally, (N - I). which is defined as the number of degr ees of fr eedom, appears in the denominator rather thanN7

LX,

(2;

100%

= ~ X

0.565504 0.57t536 0.565504 0.564001 0.577600

0.752 0.756 0.752 0.75t 0.760

JL)'

N

V.\'-+"

IT ;

deviations ..The relative standard deviation of a data sample ISgIven by

----

Example al-2 illustrates the use of Equation a 1-13 to finds.

The following results were obtained in the replicate determination of the lead content of a blood sample: 0.752,0.756,0.752,0.751, and 0.760 ppm Pb. Calculate the mean, the standard deviation, and the coefficient of variation for the data. S olution

To apply Equation (Lx,)'IN.

al-l3,

we calculate

LX! and

0.00377

s

CV

=:f

X

]00%

=

(D.()()()()4

568

\j-

0.004 ppm Pb

=

0.00377

0.7542

X

100%

= 0.5%

Note in Example a 1-2 that the difference between LX; and (Lx,)'1 N is very small. If we had rounded

these numbers before subtracting them, a serious error would have appeared in the computed value of s. To avoid this source of error, never r ound a sta nda r d devia tion ca lcula tion until the ver y end. Furthermore, and for the same reason, never use Equation al-13 to calculate the standard deviation of numbers containing five or more digils. Use Equation al-IO instead.' Many calculators and computers with a standard deviation function use a version of Equation al-13 internally in the calculation. You should always be alert for roundoff errors when calculating the standard deviation of values that have five or more significant ligures. In addition to calculators, computer software is widely used for statistical calculations. Spreadsheet software, such as Microsoft'· Excel, can readily obtain a variety of statistical quantities9 Some popular dedicated statistics programs include MINITAB, SAS, SYSTAT, Origin, STATISTICA, SigmaStat, SPSS, and STATGRAPHICS Plus. In addition to normal statistics most cases, the first two or three digits in a set of data arc identical to each other. As an alternative, then, to using Equation a 1-10, these identical digits can be dropped and the remaining digits used with Equation a 1-13 For example. the standard deviation for the data in Example al-2 could he based on 0.052, 0.056, 0.052. and so forth (or even 52, 56, 52. etc.). ~S_R. Crouch and E 1- Holler, Applicmions {If Micr osoft] ; Excel in Ana htica l Chemistr y. Belmont. CA: Brooks/Cole. 2004 1I10

Here, JL and IT are the population mean and the standard deviation, and N is the number of observations. The two curves shown in Figure al-3a are plots of Equation al-14. The standard deviation for the data in curve B is twice that for the data in curve A . Note that (x - JL) in Equation al-14 is the a bsolute devia tion ofr he individua l va lues ofx fr om the mea n in whatever units are used in the measurement. Often, however, it is more convenient to express the deviations from the mean in units of the variable z, where x -I-'

z= -IT

Note that z is the deviation of a data point from the mean relative to one standard deviation. That is, when x - JL = ,

"" 0

~

r 0.2 j

samples, each containing N results, is taken randomly from a population of data, the means of samples will show less and less scatter as N increases. The standard deviation of the means of the samples is known as the sta nda r d er r or of the mea n and is denoted by a It can be shown that the standard error is inversely proportional to the square root of the number of data points N used to calculate the means. That is, m'

IT

:i! 0.1

AN N

0-----_ Deviation

from mean, x -

-

f

a

~

-,'/2

dz = erf

(aV2) -

--/::"N =

"" ~

N

0

cr'

0.2

>

~ ~ 01

a1-3 Normal error Curves.The standard deviation (a)The abscissa of B is twice that of A ; that is, is the deviation from the mean in the units of the measurement. (b)The abscissa is the deviation from the mean relative to fI. Thus, A and B produce identical curves when the abscissa is z = (x - iL)/ ~

2 fI

k

s

= -m

N

Relative error in the sample standard deviation s as a function of the number of measurements N . FIG URE

a1-4

s

VN

1.J

0.3

fIB

\/Fi

For data in which the sample standard deviation s is calculated, Equation al-18 can be written as

2

=

2

Iov7T b

-

,

e-r dx

The fraction of the population between any Specified limits is given by the area under the curve between these limits. For example, the area under the curve between z = -1 and z = + 1 is given by the definite integral

FIG URE

m

where erf(b) is the er r or function given by

0>,

0

1

\/2 ; e

erf(b)

~

= --

IT

Areas under Regions of the Normal Error Curve. The area under the curve in Figure al-3b is the integral of EquatIOn al-17 and is determined as follows:

fl 1 _, --= e

_1V27T

,(2dz = erf

(V2) -

= 0683

2'

Thus, A N IN = 0.683, which means that 68.3% of a populahon of data lie within ±llT of the mean value. For similar calculations with z = 2 and z = 3, we find that 95.4% lie within ±2lT and 99.7% within ±3lT. Valucs for (x - iL) corresponding to ±llT, ±2lT, and ±3lT are indicated by blue vertical lines in Figure al-3. The properties of the normal error curve are useful bccause they permit statements to be made about the probable magnitude of the net random error in a given measurement or set of measurements pr ovided the sta nda r d devia tion is known. Thus, one can sav that it is 68.3 % probable that the random error asso~iated with any single measurement is within ± IlT, that it is 95.4% probable that the error is within ±2lT, and so forth. The standard deviation is clearly a useful quantitv for estimating and reporting the probable net rando~ error of an analytical method.

fI

Standard Error of the Mean. The probability figures for thc Gaussian distribution just cited refer to the probable error of a single measurement. If a set of

where .I'm is the sample standard deviation of the mean. The mean and the standard deviation ofa set of data are statistics of primary importance in all types of science and engineering. The mean is important because it usually provides the best estimate of the variable of interest. The standard deviation of the mean is equally important because it provides information about the precision and thus the random error associated with the measurement. M ethods

to

O btain

a

G ood E stim ate

of

IT

To apply a statistical relationship directly to finite samples of data, it is nccessary to know that the sample standard deviation s for the data is a good approximation of the population standard deviation IT . Otherwise, statistical inferences must be modified to take into account thc uncertainty in s. In this section, we consider methods for obtaining reliable estimates of a from small samples of data.

Performing Preliminary Experiments. Uncertainty in the calculated value for s decreases as the number of measurements N in Equation al-IO increases. Figure al-4 shows the relative error in s as a function of N . Note that when N is greater than about 20, sa nd IT can be assumed. for most purposes. to be identical. Thus, when a method of measurement is not excessively timeconsuming and when an adcquate supply of sample is available, it is sometimes feasiblc and economical to carry out preliminary experiments whose sole

purpose is to obtain a reliable standard deviation for the method. For example, if the pH of numerous solutions is to be measured in the course of an investigation, it is useful to evaluate 5 in a series of preliminary experiments. This measurement isstraigbtforward, requiring only that a pair of rinsed and dried electrodes be immersed in the test solution and the pH read from a scale or a display. To determine 5, 20 to 30 portions of a buffer solution of fixed pH Can be measured with all steps of the procedure being followed exactly. Normally, it is safe to assume that the random error in this test is the same as that in subsequent measurements. Tbe value of .I' calculated from Equation al-lO is then a good estimator of the population value, a .

Pooling Data. lfwe have sevcral subsets of data, we can get a better estimate of tbe population standard deviation by pooling (combining) the data than by using only a single data set. Again, we must assume the same sources of random error in all the measurements. This assumption is usually valid if the samples have similar compositions and have been analyzed in exactly the same way. We must also assume that the samples are randomly drawn from the same population and thus have a common value of IT . The pooled estimate of a , which we call Spoolod, is a weighted average of the individual estimatcs. To calculate Spookd' deviations from the mean for each subset are squared: the squares of the deviations of all subsets are then summed and divided by the appropriate number of degrees of freedom. The pooled S is obtained by

taking the square root of the resulting number. One degree of freedom is lost for each subset. Thus, the number of degrees of freedom for the pooled S is equal to the total number of measurements minus the number of subsets n t:

For the first month. the sum of the squares in the next to last column was calculated as follows: Sum of squares ~ (1108 - 1100.3)' + (1122 -1100.3)' + (1075 - 1100.3)' + (1099 - 1100.3)' + (1115 - 1100.3)' + (1083 - 1100.3)' + (1100 -- 1100.3)' = 1687.43 The other sums of squares were obtained similarly. The pooled standard deviation is then _

Here, the indices i, j, and k refer to the data in each subset, N" N" N3, ••. , Nn , are the numbers of results in each subset. Example al-3 illustrates the calculation and application of the pooled standard deviation.

Glucose levels are routinely monitored in patients suffering from diabetes. The glucose concentrations in a patient with mildly elevated glucose levels were determined in different months by a spectrophotometric analytical method. The patient was placed on a low-sugar diet to reduce the glucose levels. The following results were obtained during a study to determine the effectiveness of the diet. Calculate a pooled estimate of the standard deviation for the method. Glucose Concentration, Time

Month I

Month2

Month3

Month4

Sumor Mean Glucose,

Squares of Deviations

mg/L

mg/L

from Mean

1108,1122, 1075,1099, 1115,1083, 1100 992.975, 1022,1001. 991 788,805. 779,822, 800 799,745, 750,774, 777.800. 758

1100.3

1687.43

16.8

996.2

1182.80

17.2

798.S

1086.80

16.5

771.9

295086

22.2

Note: Total number of measurements squares = 6907.89.

Standard Deviation

Spooled

-

!69078'!.

-3

=

19m9/L

-2

-I

0 ;:=~ (J

In most of the situations encountered in chemical analysis, the true value of the mean JL cannot be determined because a huge number of measurements (approaching infinity) would be required. With statistics, however, we can establish an interval surrounding an experimentally determined mean x within which the population mean JL is expected to lie with a certain degree of probability. This interval is known as the confidence inter va l. For example, we might say that it is 99% probable that the true population mean for a set of potassium measurements lies in the interval 7.25 :!: 0.15% K. Thus, the mean should lie in the interval from 7.10 to 7.40% K with 99% probability. The size of the confidence interval, which is computed from the sample standard deviation, depends on how well the sample standard deviation s estimates the population standard deviation iT. If s is a good approximation of iT, the confidence interval can be significantly narrower than if the estimate of < I is based on only a few measurement values. C onfidence

2-k 10(al sum of

_

Note this pooled value is a better estimate of iT than any of the individual S values in the last column. Note also that one degree of freedom is lost for each of the four data sets. Because 20 degrees of freedom remain, however, the calculated value of s can be considered a good estimate of < I.

Interval

W hen

or s Is a G ood E stim ator

=

_

V 24 _ 4 - 18.)8

of

iT

Is K now n

iT

Figure al-5 shows a scries of five normal error curves. In each, the relative frequency is plotted as a function of the quantity z (Equation a I-IS), which is the deviation

FIGUREa1-5 Areas under a Gaussian curve for various values of :':z. (a) z ~ :':0.67; (b) z = :':1.29; (c) z ~ :':1.64; (d) z ~ :': 1.96; (e) z ~ :':2.58.

from the mean nor ma lized to the popula tion sta nda r d devia tion. The shaded areas in each plot lie between the values of - z and + z that are indicated to the left and right of the curves. The numbers within the shaded areas are the percentage of the total area under each curve that is included within these values of z. For example, as shown in curve a, 50% of the area under any Gaussian curve is located between ~0,67iT and + 0,67iT. In curves band c, we see that 80% of the total area lies between -1.28iT and + 1.28iT, and 90% lies between - 1.64i

I ~,

*al-24 The following are relative peak areas for chromatograms of methyl vinyl ketone (MVK):

0.5011 1.50

000 500 10.00

2.50 350 4.50 5.50

15.0 20.0

Assume that there is a linear relationship between the instrument reading and the concentration. (a) Plot the data and draw a straight line through the points by eye. (b) Compute the least-squares slope and intercept for the best straight line among the points. (c) Compare the straight line from the relationship determined in (b) with that in (a). (d) Calculate the standard deviation for the slope and intercept of the leastsquares line. . (e) Obtain the concentration of sulfate in a sample yielding a turbidimeter reading of 3.67. Find the absolute standard deviation and the coeffi~ient of variation. (f) Repeat the calculations in (e) assuming that the 3.67 was the mean of six turbidimeter readings.

al-23

' .

0.6

.~

0.4

K-

"G

The relationship between the a c t i v i t y a x of a species and its molar concentration [Xl is given by the expression

a2A

P R O P E R T IE S

O F A C T IV IT Y

C O E F F IC IE N T S

Ca 2-'-

=

::;"

0.2

A IJ+

Fe(CN)6 4 ' 0 0.1

0

where Yx is a dimensionless quantity called the a c t i v i t y c o e ffi c i e n t . The activity coefficient, and thus the activity of X, varies with the i o n i c s t r e n g t h of a solution such that the use of a x instead of [XI in an electrode potential calculation, or in equilibrium calculations, renders the numerical value obtained independent of the ionic strength. Here, the ionic strength J.1. is defined by the equation

where Cb C " c ], ... represent the molar concentration of the various ions in the solution and Z b Z 2 ' 2 ], ... are their respective charges. Note that an ionic strength calculation requires taking account of a l l ionic species in a solution, not just the reactive ones.

Calculate the ionic strength of a solution that is 0.0100 M in NaNO] and 0.0200 M in Mg(NO]),. S o lu tio n

Here, we will neglect the contribution of H and OH to the ionic strength because their concentrations are so low compared with those of the two salts. The molarities of Na', NO] -, and Mg" are 0.0100, 0.0500, and 0.0200, respectively. Then t

=

CN,+X (I)' CNO,- x (1)2 CMg" x (2)'

I

J.1.

= "2

0.0100 x I

=

=

0.0500 x I

=

0.0100 0.0500

=

0.0200 x 2'

=

0.0800

Sum

=

0.14(Xl

x 0.1400

=

00700

0.2

0.3

0.4

J.i

1. The activity coefficient of a species can be thought of as a measure of the effectiveness with which that species influences an equilibrium in which it is a participant. In very dilute solutions, where the ionic strength is minimal, ions are sufficiently far apart that they do not influence one another's behavior. Here, the effectiveness of a common ion on the position of equilibrium becomes dependent ollly on its molar concentration and independent of,other ions. Undcr these circumstances, the activity 'e~efficient becomes equal to unity and [Xl and a in Equation a2-1 are identical. As the ionic strength becomes greater, the behavior of an individual ion is influenced by its nearby neighbors. Thc result is a decrease in effectiveness of the ion in altering the position of chemical equilibria. Its activity coefficient then becomes less than unity. We may summarize this behavior in terms of Equation a2-1. At moderate ionic strengths, Yx < I; as the solution approaches infinite dilution (J.1. ....• 0), Yx ....•1 and thus a x " '"

[X].

At high ionic strengths, the activity coefficients for some species increase and may even become greater than 1. The behavior of such solutions is difficult to interpret; we shall confine our discussion to regions of low to moderate ionic strengths (i.e., where J.1. < 0.1). The variation of typical activity coefficients as a function of ionic strength is shown in Figure a2-1. 2. In dilute solutions, the activity coefficient for a given species is independent of the specific nature of the electrolyte and depends only on the ionic strength. 3. For a given ionic strength, the activity coefficient of an ion departs further from unity as the charge carried by the species increases. This effect is shown in Figure a2-1. Thc activity coefficient of an uncharged molecule is approximately I, regardless of ionic strength.

F IG U R E

where YAand YB....•I), we could obtain K ; p - A second solubility measurement at some ionic strength, J .1 .,. would give values for [A] and [BJ. These data would then permit the calculation of YAYB= y': " .n , for ionic strength J.1.l'It is important to understand that there are insufficient experimental data to permit the calculation of the i n d i v i d u a l quantities YAand YR.h owever. and that there appears to be no additional experimental information that would permit evaluation of these quantities. This situation is general; the e x p e r i m e n t a l determination of individual activity coefficients appears to be impossible.

a2-1 Effect of ionic strength on activity

coefficients.

4. Activity coeflicients for ions of the same charge are approximately the same at any given ionic strength. The small variations that do exist can be correlated with the effective diameter of the hydrated ions. 5. The product of the activity coefficient and molar concentration of a given ion describes its effective behavior in all equilibria in which it participates.

a2B

E X P E R IM E N T A L O F A C T IV IT Y

E V A LU A T IO N

C O E F F IC IE N T S

In 1923, P. Debye and E. Hiiekel derived the following theoretical expression. which permits the calculation of activity coefficients of ions:l 0 .5 0 9 Z ~

-logYA

=

Vj" . r

1 + 3.28 v_by 26 flY for + limit and

for -limit

0.08 :'c:0.01 (d) 4.87 :'c:0.09 mM

at lOO~Cand is difl:lcult to dry to constant weigh!.

v

for -limit (e) v+>v_8.7flVfor+limitandv

0.070 :'c:0.002 95% CI for

Should be ignited just before use.

h Loses both waters at 110°C, molar mass

(b)

1

9.00 x 10-' M

1-10 (a) m ~ 0.0701; b ~ 0.0083 (b) S m = 0.0007; S , ~ 0.OO4{) 0.0701:'c: (el 95% CI for m

primary standard quality

b Highly toxic. c Loses ~ H 20

C h a p te r

C h a p te r 2

2-1

(a)

R, ~

500

n; R , = 2.0 kll;

(b) 5.0 V

R]

~

2.5 kll

(e) 0.002 A (2.0 mAl

3-21

(a )

Vo

~

(b)

Vo

~

R:R: VI

+

v 1 R f lR n

V )R fl

+ R ,R - ; - -

4 v, -

£ I]

40'1

34.0 em from common end

(d) 0.02 W 2-2

(a )

4.4 V

4

C h a p te r

(c) 30% 4 -1

2-3

(a) -15% (c) -0.17% 4-2

2-4

(a) 74 kll

2-5

(a) VI = 1.21 V; V , = V 3 = 1.73 V; V , ~ 12.1 V (b) /1 = /, ~ 1.21 X 10-' A; /, ~ 3.5 X 10-3 A; /, = /,

(b) 740 kll

~ 8.6 X 10-' A (e) P=1.5XIO-'W 2-6

2-7

4-4

(d) 13.8 V

4-5

(a) 0010 I()()()

(b) lOOI()()()l

(e) ()()()10011 0101

(d) 0011 HXJl 0110 (b) 21 (d) 859

5

(a)

(d) 5.3 V

(b) 89 (d) 968

(a) 4 (e) 347

4-7

(a) 1111, ~ 15 10 (c) 111111,=63 10

0.535 V

4-8

(a) 0.039 V (e) 0.()()()15V

4-U

(a) 1 Hz

4-12

62.5 kHz

2-10 (a) 20 kll I, S

i,,,A

0.00

2.40

0.010

2.39

0.10

2.28

2-13

(b) 1011011 (d) 11()()()1100

1 1 ()()()

(e) 117 (b) 8.0 X 10-3 A (8.0 mAl

(a) 0.085 W (c) 8.0V (e) J6V

(c) 1()()()()111

(a )

I, S

1.0 10

i,,,A 1.46

(b) 101110010, ~ 370 10 (d) 11()()(), = 24 10 (b) 0.0024 V

0.0162 C h a p te r

2-14 (a) 0.69 s (c) 6.9 X 10-5 s

5-7

5

(a) S IN = 358

(b )

n ~

(b)

tl

5-8

(a)

5 -1 0

n =

5-U

( S IN I," ~ 7 .1 ( S IN h ; ( S IN h " ,

5 -1 2

( S IN ) o

S IN ~

5.3

18

= 29

2-15 (a) 0.15 s (e) 1.5 X 10-5 s C h a p te r

3-1

3

100

(a) v.>v_by65flVfor+iimitandv_>v.by75flY for~

limit

= 3.9(S/NIA

~

14.I(SINl,

6

C h a p te r

-1.80 10" eV

6 -3

v

v ~

A ~

6~5

Vs~ci~s Asp " a u ld be smaller.

=

32-8

\476

2.0

loss occurs be-

30

C h a p te r

32-4

25

(a) N ,

table, the largest percentage

30-5

31-2

R,

25-10

5.42

(e) 24.1 mUg; 55.5 mUg; 109.6 mUg (d) K 1 ~ 33.8; K 2 = 77.8; K j ~ 154

g /c q u iv

V

C h a p te r

1.90

(a) k l ~ 26.7 (h) 71 % CHClj and 29% n-hexane

C h a p te r

27-22

27-23

7.17 3.76

tween 1.0 and 1.5 h.

6.1

16.52%

=

20.29

2.86 2.43 10'

x

27

C h a p te r

(b) 6.55 min

-0.367

~0.644 V

=

(d) (R,hl

(a) 19.6 min

22-10

0.24 V

100

(a) 0.432 V

-0.90 V

22-17

5.62 3.34

=

(e) 2.61 min

as written

not spontaneous as written spontaneous as written spontaneous as written

(h) s

3653 27.85

5'i8

24

(a) ~ 1.342 V

22-9

22-16

6

(e) -0.101 V

spontaneous as written not spontaneous as written

7.79

27-21

(e) -0.043 V

24-6

~

estriol

C h a p te r

(e)

24-5

12.61

(b) L ~ 2.0 em

61.7 or 62 min

l.l

(a )

% Change/OoS h

12.28

=

0015

=

of

mg/mL

14.05

= \.OS

= 14.99%; estradiol ~ dehydroepiandrosterone 18.10%: estrone ~ 27.40%; testosterone = 22.99%:

4.28 x 10-'%

C h a p te r

24-1

10)

X

aCB

(b) K 1 = 14; K , = 15; K , ~ 19 (e) "2.1 = LlI; a , . 2 = 1.28

(e) for (a). 5.19-5.23; for (b). 4.05-4.09

23-26

(bl)

(e) 0.571 V

6.22

(bl 3.64 x 10-'-4.97 x 10 (e) -23.3% and 16.7%

(b) -0.685 V (e) ~0.867 V - 22-8

26-17

(a) 0.366 V

Ihuprofen,

30

~ 50

(d) (t.),

(e) pBr = (£"11 + 0.213)/0.0592 (d) 1.99

23-16

Ko

(b)

(a) R , ~ 072 (e) L=i08cm

(d) 6.33

(a) 165.4 eV

22-3

Br-(xM)iCu

C o n c e n tr a tio n

= 27

KB

Kc ~

3.5 k o ~ 6.0

kc . =

(b) S C E IIA g ,A s O ,( s a l'd ) , AsO,' (xM)IAg (E 'd l - 0.122) x 3 (e) pAsO, ~ -0.0592~~

0.106

21-4

C h a p te r

(b) - 1.085 V (d) 0.482 V

(a) 0.031 V (b) SCEIICuBr(sat'd),

(b) K, ~ 6.2

(a) k , ~ 0.74 k B ~ 3.3

23

(a) 0.540 V (e) -0.583 V

34-11

%

(h) 5.79 cpm 443 :': 11 cpm (h) 379 counts

34

11.4 nm; the diameter

of a hypothetical

the same translational

diffusion coefficient

1.22 x lO~IO em 'Is

34-12

1.92 x 10-10 cmls; 5.2 x 10" s

34-13

70.4 min; 8952 G

34-14

1~5 nm

sphere with

1008

An:;wers to Selected

A p p e n d ix

Prubll'ms

al-24

al-10

1

al-1 B

C

D

(a)

0.030

-2%

1.44(2:0.03)

6143

3.25

12.10

2.65

(b)

0.089

0 .4 2 ° /0

21.26( 2:0.09)

0.0482 (CV ~ 4.8%). For four replicate measurements,

df

3

6

2

4

(c)

0.14 x 10-16

1.8%

7.5(2:0.1) X 10-16

RSD = 0.308 (CY

(d)

750

0.58%

1.290( 2:0.008) x 10'

0.005 1.1 x 10-'

6.9% 1.34%

7.6( 2:0.5) x 10-'

(b)

0.11

0.02

0.06

0.21

df

2

(e)

CY

0.17%

0.60%

1 0.47%

3

(c)

7.9%

(f)

(d)

Sm

0.061

0.008

0.040

0.10

8.1(2:0.1) x 10-'

al-11 Sy

al-2 A

(a) (b)

Absolute error

~0.28

Relative

~0.45%

B

D

C

-0.03

-0.13

-0.10

-1.1%

-0.82%

-3.8%

e rro r

(a) -2.0% (c) '-0.2%

(b) ~0.5% (d) ~0.1%

al-4

(a) 10 g (e) 1.3 g

(b) 2.1 g (d) 0.87 g

al-s

N=lx1O'

al-6

N

al-7

-25 ppt

lO-

(a)

3

(b)

0.1

(c)

3

(d)

6.8

(e)

25 1.5 x 10-5

(f) al-3

al-8

X

lU

CV

y

-4% 8.4%

6.7(2:0.3) x 10-'

25% 4.3%

12(2:3)

50%

50(2:25)

2.4%

6.0(2:0.2) X 10-'

1.2( 2:0.1) 158(2:7)

al-U A

= 13.5 (14 replicates)

D

E

x

3.1

70.19

0.82

2.86

70.53

0.494

0.37 2:0.46

0.08 2:0.20

0.05

0.24

0.22

0.016

CI

2:0.08

2:0.30

2:0.34

2:0.020

B

C

\

F

(a) Sample

Mean

Standard

The 95% confidence interval establishes the range about the mean that the true value should lie 95 % of the time if the errors are random.

Deviation

1

5.12

0.08

2

7.11

0.12

3

3.99

0.12

4

4.74

0.10

5

5.96

0.11

at-l3

al-14 (b)

= 0.11 % is a weighted average of the individual estimates of 0 " . It uses all the data from the five samples. The reliability of s improves with the

Set A, 95% CI = 2:0.18; set B, 95% CI = 2:0.079; set C, 95% Cl = 2:0.009; set D, 95% CI = 2:0.26; set E, 95% CI = 2:0.15; set F, 95% CI = 2:0.013 (a)

x 2: 0.029

(h) N = 11.9 or 12 measurements

Spool""

( c ) Spooled

at-IS

(a) x 2: 0.76 (h) N = 6.9 or 7 measurements

number of results. al-9

(a) slope = 5.57. intercept = 0.90 (e) 1.69 mmollL (d) For one measurement, S"VK = 0.080; RSD

x

A

(a)

y

CV

Sy

(a) al-17 Bottle

(a) Systematic error is suggested. (h) No systematic error is demonstrated.

0.096

al-18

0.077

For C, no systematic error is suggested, systematic error is indicated.

but for H. a

0.084 0.090 0.104

al-20

0.083

At pH = 2.0. S for [HJO-j for [H p 'j = 2.3 x 10-"

S

al-21

S

= 7.5 X 10-5 g/mL

=

2.3 x 10-" at pH 12.0.

=

3.1 %).

SMYK

=

(el C"VI( ~ 3.93 mmol/1. For one measurement,s"VK =

0.052;

2.03%). For four measurements. 0.0126 (CY = 1.26%). (C Y

= 0.08; RSD

=

0.0203

=

SMVK

=

0.05; RSD

=

Ablation, 227, 292, 604 Absorbance corrected, 242-244. 385. 386 definition of, 158 detection. indirect. 873 flame absorption profiles, 232 measurements, 238, 336-341, 346,375,376,455, 467-469 plot of, 153,379,386 range,360,376 Absorbing species, 153-158,367, 374, .177 Absorption analysis electrothermal atomic, 247 flame atomic, 248 bands, 155,241,346,347, 368-402.408.437,438. 464,473,476 electronic, 368, 493, 494 overlapping, 468, 469, 474 charge-transfer, 371 detectors, 824, 872 edge, 307-309, 311, 597 of electromagnetic radiation, 132,133,141,148,151-156 filters, 176, 180,413 frequencies, 476, 499, 504, 511 in s tr u m e n ts

electrothermal atomic. 2·lJ UV -visible, 350, 351 lines, 237, 242, 243, 368 maximum, 356. 367, 369. 375. 467 measurements, 204, 351,374,474, 8 2 3 ( s e e a /s o Absorbance measurements) methods, 157,273,325,872 peaks, overlapping. 378 process. 146, 170.243,307.498. 499,501,503 secondary. 408

spectra. 153,245,307.370,371. 376,469.473 spectroscopy, 148,241. 309, 374, 431 electrothermal atomic, 296 molecular, 336, 368 spectrum. 237. 243. 307, 341, 346. 350,356,368,369,373,375 transitions. 402 of ultraviolet radiation, 367, 368, 823 Absorptivity. 158.339.342,367, S e e a /s o Molar absorptivity ac circuits, 34 -36 source, sinusoidal. 37-39 Accelerating voltage, 304. 310, 567, 568.576 Acceleration, 434, 567. 612 due to gravity, 959 Accelerator mass spectrometry, 301 Accelerators, 919 Accuracy, 967 Acid dissociation constant, 339, 407, 880 error, 247, 644, 645, 671 ( s e e a /s o Glass electrode) Acrylamide,890·892 Actinide transition series, 370 Activation analyses, 909, 918. 924 instrumental neutron. 7, 922 Activity coefficients, 634, 641, 642, 644, 687,688,766,994-996 effects on electrode potentials. 634,639,640,687,688 of radionuclides. 912-915 ADC. 81,87-90,95, S e e a /s o Analog-to-digital c o n v e rte rs

Address bus. computer, 93

Adjusted retention time, 768. 781 Adsorption chromatography. 817, 829,837.839,841,852 AFMs (atomic force microscopes), 613, 617-619 Ag electrode, 639 Ag-AgCl reference electrodes. 062. 670,673,704 Agent, chiral resolving, 837, 883 Airy patterns, 953, 954, 962 Algorithms. 91, 323 Alizarin garnet R as f1uorometric reagent, 420 Alkaline error, glass electrode, 670--671,689 Alkanes, retention index of, 806. 807 Alpha particles, 603, 604, 910, 916, 917 Alphanumeric display, 54 Alternating-current circuits. 32 Amorphous phases, 327, 328 Amperometric titrations, 59. 62. 63, 65,114,734-736 Amperometry, 716, 718, 720, 826. 874,940 Amperostats, 71, 707 Ampholytes, 881 Amplification. 47, 48, 65, 67,114, 115,239,314,317,524 Amplifier difference. 69, 70, 114 lock-in. 116, 117.241, 757 noise, 116, 317, 344 operational,59-74 transistor, 46-49 Analog. 25, 81 computers. 59 domains, 5. 6. 74, 88 filtering, 115 instruments, 344. 378. 608 oscilloscopes. 51

Analog ( c o n tin u e d ) pulses, 81 quantities, 6, 7 scanning system. SEM, 608 signal processing circuits, 52 threshold, 7 signals, 6, 74, 81, 88, 197, 202 Analog-to-digital converters, 30, 81, 88, 197, 524, 706. S e e a ls o ADC Analysis systems, total micro, 929, 940 Analyte, 1, 2, 9 atoms, 221, 239, 245 bands, capillary electrophoresis, 873,880 concentration standard, 12 unknown, 11 deposition, 749 emission, 250 fluorescence, 419 fluorescent in capillary electrophoresis, 873 half-reaction, 702 ( s e e a ls o Halfreaction) ions chromatography, 841 electrochemistry, 662, 665, 671, 677 mass spectrometry, 283, 294, 300,301,562,564 migration, 880 negative in mass spectrometry, 562 positive in mass spectrometry, 300 lines, 260, 267, 268 nucleus, 509, 920 particles, 826 preconcentration by solid-phase extraction, 890 recovery of in separations, 862, 863 signal, 17, 235 species, polarizable in gas chromatography, 802 target in immunosensors, 733, 734

unstable in supercritical fluid chromatography, 856, 863 Analytical columns chromatography, 822, 844 ordinary packed, 791 concentration, 385-387 errors, positive, 241 instruments, 3, 9, 88, 90, 95, 103 multiplex, 204 laboratories, electronic, 127, 128 methods, 1,11,17,21,22 problems, I, 17, 18 procedures, 11 sensitivity, 19, 20 signal, 20, 115, 1l7, 119 Analyzers automated, 930-948 computer-based clinical, 681 discrete, 929, 930, 945 electron energy, 594 microprobe, 608 electrostatic, 290, 568, 603 energy-dispersive, 612 filter correlation, 448 i-STAT, 682 mass, 291, 557, 560, 566, 570, 574, 588,594 photosedimentation, 958 pulse-height, 315-317, 916, 917 time-of-f1ight, 603 Anatase, 624, 625 Angle of incidence, 179, 185, 186, 471,472,607 Angstroms, 217 Aniline, 373, 374, 407 Anions in chromatography, 839-843 in electrochemistry, 630, 635, 659, 663-665,686,688 Anisotropy, chemical-shift, 532, 533 Anode electrochemical cell, 630-632, 639,647,650,748 reaction, 709 Anodic currents, anodic waves, 729, 738, 739, 744, 749

stripping, 748-750 ( s e e a ls o Stripping analysis) Anomalous dispersion, 141. S e e a ls o Dispersion ANOYA (analysis of variance), 985 Anthracene, 316, 410, 412 IO-Anthraquinone,780 Antibodies, 679, 733, 734, 740, 741, 848,925 Anti-Stokes, 149,483,484 Applications passive with computers, 103, 104 quantitative, 300, 324, 465, 493, 583,597,746,904 Arc source spectrometers, 273 sources, emission spectroscopy, 227,254,269-274 Area-normalization method, chromatography, 783, 784 Argon flows, 225, 226, 257, 292 ions, 227, 255, 269, 600 Argon-ion laser, 482, 483, 488 Arithmetic logic unit, 91, 92 Array detectors, 286, 353, 354, 360, 415, 474,481,491,492,568 coulometric, 706, 707 segments, 265 transducers, 285-287 Array detector spectrometric systems, 388 systems, 354 Ashing, 234, 235, 247 Asymmetry potential, glass electrode, 669, 670 Atomic absorption, 153,220, 222, 223, 230 analyses, 236, 241, 248 electrothermal, 248, 257 instrumentation, 237-244 lines, 237,250 measurements, 247-249 e m is s io n

detectors, 797 sources, 254 spectrometry, 254 - 276

flu o r e s c e n c e

dctection system for mercury, 333 spectroscopy, 222. 230, 234, 249, 250, 333 lines, 219, no m ass

number. 296 spectrometers, 284 spectrometric analysis, 281 spectrometry, 281-284, 291, 294 units, 281. 282 masses, 229, 281, 282, 298, 603, 604,920 numbers, 303-306, 318, 325, 593, 599,909,910,920 resolution, 617 spectra, optical, 215 spectroscopy, 215, 219, 223, 224, 300 Atomic emission spectrometry, 254-276 Atomic X-ray spectrometry, 303 Atomization, 215, 230, 231, 234-236,258,281,283, 292 devices, 116, 224, 226, 300 electrothermal, 230, 233-235, 242,248 Atomizer, 221, 223, 224, 226, 227, 230,235 Atoms concentration of, 140, 246 energetic in mass spectrometry, 562 heavy in phosphorimetry, 404, 407,420,421 unexcited in atomic spectroscopy, 222,238 ATR (attenuated total reflectance) crystal, 472, 478 measurements, 471 spectroscopy, 472, 478 Auger electron spectroscopy, 592, 598-600 electrons, 596, 598, 600, 608, 610 Automated analytical systems, 929. 930,947

Automatic systems, discrete, 931, 942 Automation, 90, 816, 929-931, 940 Babington nebulizer. 225-226 Background, 150, 152,206,250, 264,915,916 corrections, 242-244 Baekscattered ions, 603 Band separation in chromatography, 765 spectra in spectroscopy, 150, 152, 223 Bands chromatographic, 764, 765, 768-771,773-775,778, 780,818,833,847 conduction, 173, 174, 191, 193 filter rejection, 179,180 focused in electrophoresis, 881 methylene in NMR, 515, 518, 519 molecular, 223, 245, 294, 341 spectroscopic, 150 -153, 223, 341, 342,368 .. 370,373,374, 473 -476, 485, 486, 493, 494,518-520,764,765, 768-771,773-775,817, 818,867-870,880,881 valence, 173, 174 Bandwidth of electronics, 65, 112, 115 of filters, 177, 179, 180 of lasers, 173 of monochromators, 188, 189 spectral, 184,347,373 unity-gain, 65 Barrier-layer photovoltaic cells, 192 Base peak in mass spectrometry, 551,555,558,576,577 Baseline method, quantitative 1R spectrometry, 467 Battery. 26, 27,30,35,357,721 BCD (binary coded decimal), 82. 83 Beam detected in surface analysis, 590,

604 double-beam 356

instrume nt, 351,

monochromatic. 134, 143, 311, 326, 482, 592 plane-polarized, 143 primary, 303, 317, 590-592, 599, 604 secondary, 303, 590,602 Beamsplitter, 208, 351, 353, 443 Beat period, 136, 156, 206 Beer's law, 158,308,336 -338 application to mixtures, 338, 376, 377 limitations of, 338-342, 348, 375, 466 titrations and, 380 Bending vibrations, 433, 884 Benzene ethyl, mass spectrum, 551, 555 vapor, UY spectrum, 155, 189. 190,346,347,373 Bernoulli effect, 202, 256, 917 Beta particles, 910, 916, 919 Beta-particle energies, 911 Bias forward, 45, 47, 54 in measurements, 970, 984, 985 voltage, 612, 615, 683. 757 Binary numbers, 8, 81-84, 88 Binary-coded decimal, 83 Binding energies, 175, 314, 593-596,911 Biochemical species IR absorption, 455 luminescence, 420 Biological molecules, 494, 534, 535, 550,579 Bioluminescence, 422, 757-760 Biosensors, 10, 203, 605, 679, 680, 733, 734, 740, 753 Biotin, 741 Bits (binary digits), 8, 84, 88, 90, 91, 93 BJTs,46-49 Blackbody radiation. 152 Blank, 13, 17, 19-22,241,343,358 Bode diagram, 41,64, 65, 115 Boiling points in G c . 791. 792, 803 Bolometer, 67, 201, 452 Boltzmann equation, 221 Bond axis, 437, 438, 514. 515

Bonded-phase chromatography, 828,829 Bonds, force constants of chemical, 435,436 Boundary conditions in counting, 81, 85 potential, 635,667-670 Boxcar averaging, 118-120 Bragg's law, 309 Brain electrochemistry of, 745, 746 MR[ of, 542 Breakdown conditions, diodes, 50, 51 Bremsstrahlung, 257,303 Bromine, electrogenerated, 710, 711 Buffer capillary electrophoresis, 867, 868,871,872,875 isotachophoresis, 880 pH, 666, 685, 689, 690 radiation, 242 Bus, computer, 93, 105 Bytes, 91 Cable modem, 106, 107 Calibration curve uncertainty, 14 curves, 11, 17, 19-21,246-248, 267, 268, 278, 291, 292, 298,342,366, 375, 376, 688,746,846,889, 985-988 atomic absorption, 11-13, 17, 19-21,246-248,267,268, 278,291,292,298,342, 366,375,376,688,746, 846,889 emission, 258, 267, 268 chromatography, 783 [CPMS, 29[, 292, 298 luminescence spectroscopy, 419 potentiometry,688 UV -visible spectroscopy, 375, 376 voltammetry, 746, 752 function, 13

multivariate, 13 sensitivity, 20, 21, 191 Californium-252 as neutron source, 918 Calomel electrodes, 660, 662, 668, 6 8 9 . S e e a ls o SCE Cantilever tip, AFM, 617, 618 Capacitance, in electrical circuits, 34-42,50,64 Capacitive reactance, 38-39 Capillary cells, Raman spectroscopy, 489 columns, GC, 791, 795, 798,800, 801 electrochromatograph y, 867 electrophoresis, 582, 583, 867-883 instrumentation, 868 gel clectrophoresis, 867, 869, 877 isoelectric focusing, 880, 881 zone electrophoresis, 875 Carbon dioxide gas sensing probe for, 677-679 laser as IR source, 450 Carbon monoxide, determination of, 448 Carbon-13 NMR, 529-531 Carrier gas, GC, 790, 795 Carriers, majority, 26, 44, 45, 47 Catalysts, determination of, 382 Cathode, electrochemical cell, 630-632,637,639,647, 650, 698 - 700 Cathode-ray tubes, 51 Cathodic current, 738, 744 stripping methods, 748, 749 Cation exchangers, chromatography, 839, 842-844 CCD detectors, 196, 198, 199,261, 264,265,335,353,361, 4 1 3 ,4 1 5 ,4 9 1 ,6 0 6 ,8 7 9 . a ls o

Array detectors

Cell barrier-layer, 193 collision in mass spectrometry, 574-576 compartments, optical

Se e

spectroscopy, 358, 383, 413,445,470 constant, DSC, 903 coulometric, 698-700, 703, 704, 708.709 electrochemical, 628, 630, 631 detector, 826 electrolytic, 630, 697-700 electrothermal atomization, 249 galvanic, 630, 631 glass, 336, 337 interaction in mass spectrometry, 573-575 [R absorption, 447-449, 456 -458, 467,474 luminescence, 414 photoconductive, 68, 69 photovoltaic, 191-193, 351 potentials, 633, 646, 684, 687 calculations of, 645, 652 . measuring, 684 ., standard, 644 ( s e e a ls o Standard electrode potentials) Raman spectroscopy, 489 reaction, 630, 631, 633-635, 639, 640 resistance, electrochemistry, 684, 698, 705, 706, 723 single biological, 422, 675, 872 spectrophotometry, 351, 352, 375, 380 three-electrode, 718, 724 trapped-ion analyzer, 572 Cells, matched, spectrophotometry, 342,351,375,467 Centrifugal sedimentation, 960, 961 Channel electron multiplier, 286 of MOSFET device, 49 number, 320, 322 of pulse height analyzer, 317 Characteristic frequency, quartz crystal, 9 group frequencies, [R absorption, 460. 476 Charge separation. 635 Charge-coupled devices, 196, 198, 2 6 1 ,4 1 3 ,4 9 1 .

S e e a ls o

Array detectors

reversed-phase, 832, 836 size-exclusion, 845-847 suppressor, 841-844 Array detectors temperature, 779, 783. 789, 790, Chemical 792,822 Circuit analysis, 17, 25, 26 tunable, 808 components, 26. 43, 90 composition, surface analysis, variables, 806, 807 model, electrochemical cell. 722, 589, 590, 597 wall-coated, 801 723, 746 deviations from Beer's law, 339, Combination bands, [R Circuits 340 spectroscopy, 437 ac, 34-36, 42 equivalence, 11,707 Common mode rejection ratio dc, 26, 27, 30-32 interferences, atomic (CMRR),70 digital, 80. 81,114 mass spectrometry, 295 CAJmmunication channel, operational amplifier, 59-64, spectroscopy, 241, 269 sequential injection, 940 67-74 ionization sources, mass Comparators, 62, 74, 84, 88, 89, 202 R e , 36, 37, 39-42 spectrometry, 557, 558, Complex ions, spectrophotomctric Clark oxygen sensor, 732 587 studies, 384, 385, 387 Clinical analysis, 681 shifts Complexes, charge-transfer, 371 CMRR,70 NMR, 511-515, 517, 519, 520, Complex-formation coulometric Coefficient 536 titrations,709 selectivity, 21, 22 XPS,596 Component waves, 136 of variation, 19, 24, 972 Chemiluminescence, 149, 399, Components Coefficients, activity, 688, 994-996 422-425 high-frequency, 41,115 Coherence, of electromagnetic methods, 424 low-frequency, 40, 41 radiation, 139-140, 168, photometers, 424 nonreversing in DSC, 901 170 signals, 424 reversing heat flow in DSC, 901, Cold vapor atomic fluorescence Chiral separations, 837, 883 902 spectrometry, 333 Chloride ions Compositional analysis, 604, 896, Collector determination of, 663, 710, 735, 897 electrode, mass spectrometry, 736,932 Compound nucleus, excited, 918, 285,566 quenching by, 408 919 transistor, 47, 48 Chopper, optical spectroscopy, Compton effect, 911, 917 Collimators, X-ray analysis, 312, 115-117,201,239,240, Computer 318 242, 359, 446 applications, 91 Collisional qucnching, 408 Chromatic aberrations, 141 control, 103, 104,260,265,523, Collisions, optical spectroscopy, Chromatograms, 765, 766, 768, 769, 595,616,824,893 152, 155, 169,220,221,274 771,775,779 memory, 92, 94 Colorimeter, 204 Chromatographic networks, 104, 105, 107 Column column, 765, 768, 769, 772, 774, software, 95, 97, 99,101 bonded-phase, 804, 805, 828 800,831,840,944,947 system, 94, 107 chromatography, 763, 849, 850 gas-liquid, 803 terminology, 90, 91 diameter, 774, 775 separations, 762, 775, 831 Computer-based efficiency, 768 -772, 775. 783, 800, Chromatography, 762 spectrophotometers,431 816,817,883 affinity, 848 Computerized frequency-analysis ion-exchange, 835, 836, 841, 843 applications of, 781 instrumentation, 723 length, 770, 778, 808, 859 bonded-phase, 828 Computerized instruments, 90, 91 packings, 778. 792, 802, 803. 806. gas, 788-810 Computerized mass spectrometers, 807,818,821-823. 831, ion-exchange, 817, 836, 839-841, 576,577 844.854.883 843,873 Computers, 25, 26, 54, 80 - 82. preparation, 789 ion-exclusion, 843, 844 90-108 resolution, 775 ign-pair, 836, 838

Charge-injection

devices, 196, 198,

2 6 2 ,2 6 3 ,4 9 1 .

S e e a ls o

liquid, 816-848 rate theory of. 768 CID (charge-injection device), 196. 198,199.261,264,491

Concentration bulk in electrochemistry, 381, 724 concomitant, 296 constant electron in ICP, 258 critical micelle, 882 difference,635,651, 724, 774 errors, spcctrophotometry, 344-346 estimates, X-ray analysis, 320, 323 gradients, electrochemistry, 633, 699,725,726,751 levels, safe of mercury, 332 limit, 19 particle in sedimentation. 960 polarization, 649-651, 697-700, 703.706,707.716 profiles chromatography, 765, 935 electrochemistry, 724, 725, 727, 728.741 rectangular, 934 quencher,408 uncertain ty in spectrophotometry, 343, 345 units of in spectrophotometry, 337,338 Conductance, electrical, 29, 44, 45, 67-69.194 Conduction in electrochemical cells, 630, 632 in membranes, 665, 668, 671, 672 in semiconductors, 44-47, 49, 173 Conductivity detectors, 796, 841 - Confidence intervals. 976-980 level, 19,20,110,914,977-980, 984.985 Constant current electrolysis, 697, 699 potential electrolysis, 700 Constantan thermocouple, 70. 201 Constant-current coulometry. 735 ( s e e a ls o Coulometry) sources, 71 Constant-voltage sources, 70

Constructive interference, 136, 138, 140,176,183,208. 310, 458 C o n tin u o u s

flow analyzers, 930-932 variations, method of, 385 Continuum radiation, 150, 152.221, 223, 237, 242, 257, 294, 303, 304, 306, 3l1, 326, 351. 413, 449, 450 Continuum-source background correction systems, 242 spectrometers, 237 Control bus, computer, 93 Convection in electrochemistry, 633, 651, 724, 726 -728,878 in flow analysis, 934, 935 Conversion external in luminescence, 403, 404,406,408 internal in luminescence, 402-406,420 Converters frequency-to-voltage.7 voltage-to-frequency, 7, 706 Copper deposition of, 699, 700, 703 electrode, 630, 631, 638, 663 Core electrons, 596. 598 Correlation charts, 460, 464 Coulometric methods, 11,697,701-703, 707-712,714 tit rations, applications of, 709, 711 Coulometry,697-703 controlled-potential, 702, 703 Count data, 8 Counler electrode, 700, 701, 705, 718, 719, 722 electronic, 81, 83-85, 87. 89, 317, 318 proportional, 314, 315, 916 Counting, 81. 83-86, 317,602. 910-912,916,924 gate, 85 -87 rate, 599, 912, 914, 915, 920, 921,

924

Coupling constants, NMR, 515, 517-519 CPU, 90-94 Cross dispersion, of echelle grating. 186 Cross-linking of stationary phases, 804,805,810,840,845 Crossover of electron beam, 599. 600 CRT, 51, 52, 608, 610. 612 Crystal oscillalor, 87 Crystalline membrane electrodes. 671,672 Crystallinity, 327, 328, 904 Crystallization, 490, 665, 899,903, 904 Crystals, diffraction of X-rays by, 309,312 . erDs

(charge-transfer devices), 196, 198. 204. S e e a ls o . Array detectors Curie point, 202, 451, 895 Current density, 651, 652 follower, 62-64, 66, 67 Currents alternating, 42 ( s e e a ls o ac circuits) anodic, 649, 721 direct, 26, 30 ( s e e a ls o dc circuits) Current-splitting equations, 29 Current-voltage relationships diodes, 45, 51 electrochemistry, 648, 649, 697, 699, 728, 729 CV (cyclic voltammetry), 737-742, 746, 753 CW NMR instruments, 498, 499 Cyclic voltammetry excitation signal, 737 voltammograms, 738-742, 745, 754 CZE (capillary zone electrophoresis). 875-877 DAC, 87-90, 95. S e e a ls o Digitalto-analog converters Daly detector, 287

Data analysis, 80. 90, 95. 99,102.323 chemomctric, 59.'; domains. 3-5 system, 127, 130, 595, 798 dB (decihel), 41, 65 dc

circuits, basic, 26. 27 power source, 70 signal,34, 62, lIO. ll5, 117. 118 voltages, 49, 50, 68.202 DCr (direct-current plasma), 255, 258, 259, 266 DCU (decade counting unit), 85-87 Deactivation of excited states, 399. 402-406,419-421 Dead time chromatographic. 766 of counters, 315, 924 . of Geiger tuhe, 315 Debye-Huckel eq ualion, 995 - 996 theory, 641, 995 -996 Debye-Scherrer powder camera, 326.327 Decays, radioactive, 910, 911,913. S e e a ls o Radioactivity Decimal numbers, 54, 81-83 Decoupling in NMR, 520, 521, 529 -533,536 Degrees of freedom, 437, 922, 975, 976,979 Dendrimer, 740, 741 Densitometer. for TLC, 851 Density of supercritical fluids, 856 - 858, 860 Depletion layer, semiconductors. 45,194 Depolarization of an electrode, 699, 735 ratio, Raman spectroscopy, 486-487 Deposition electrolytic, 652. 697-699, 749 step. stripping analysis_ 748 time, stripping analysis, 750 Derivative spectra, 378, 599 Oeshielding, NMR, 514. 515 Deliolvation, in !lames. 230

Desorption in electrochemistry. 649 in MALD!. 560 Destructive interference, 136. 140-142, \76,208,309 Detection electrochemical in CEo 874 limits, 20 a to m ic

Diamagnetic shielding, NMR. 514 Diameters. hydrodynamic. 957,962 Dielectric materials, 177.201. 202, 45\

Difference amplitier, 69, 70, 1\4,201 gain, 70 Difference IR spectrum. computercalculated, 456, 457

mass spectromelrv, 28\, 286, 290. 292,294. 296, 297 spectroscopy, 237, 248 250, 264,2/m,267,269. 273. 274 luminescence spectrometry, 399,419,424 radiochemistry, 918 separations, 782, 826, 872, 890 UV-visible absorption, 374 voltammetry, 732, 734. 741. 742,744,750 X-ray fluorescence, 324, 333 mass spectrometric, 294, 297, 874,875,883 volumes, separations, 871, 872 Detector, 9,157 electrochemical for separations, 826,874 ideal for GC and HPLC, 793, 823 lithium-drifted, 3\6,317 noise, 205, 206 obscuration, 951 photoionization for GC, 797, 809 semiconductor, 317, 318, 612, 916 voltammetric. 730, 73\ Determinate errors. S e e Systematic e rro rs

Deuterium lamp, 349. 350 Deviations from Beer's law, 338-343, 466 chemical. 338-340 measurement, 972 -976,980,986, 987 absolute, 973 standard. 969, 971-976, 978, 980 -984,986-988 Diagnostic applications of oscilloscopes. 52 Diagram, energy level, 147, 171. 215-217,219, no, 305. 606 Dialysis, with flA. 933

Differential scanning calorimetry, 893, 894. 896,900,901. 903, 904 ( s e e a ls o DSC) thermal analysis, 897 ( s e e a ls o DTA) thermogram, 896, 898-900 Differential-pulse voltammetry, 742-743 Differentiation, operational amplitler, 73, \22 Diffraction angle, 138, 183,185,326

o f e le c tr o m a g n e tic

r a d ia tio n ,

137-139.181, \83, 185. 186 order, 183, 185, 186 patterns, 139, 140, 326, 951, 953 of X-rays, 303, 309, 326 Diffusion coefficient, 699, 725, 728, 739, 773-775,778,818,854, 869,884 translational,957 eddy, 772, 773 and FIA, 935 longitudinal, 774, 775, 869, 935 mass transport by, 651, 724 Digital data, 8, 9, 95, 104 Digital electronics, 25, 80. 82, 84. 86, 88. 90, 92, 94, 98, 100, 102,104,106,108 Digital-to-analog converters, 10,87. S e e a ls o DAC Diode lasers, 173-175 Diode-array detectors. S e e Array detectors Diodes. 44 -46, 50.174.175,197. 350. 353 D ip o la r

in k r a c tio n s

chromatographv.833 NMR, 5.,2, 537

Dipole moment changes in IR absorption, 431, 432, 435-438 Direct-current circuits, 26, 27 Direct-current plasma source, 258-259 Discharge lamps, electrodeless, 239 Discrete automated systems, 931, 942 Disk electrode, 719, 720, 736, 737 Dispersion angular, 181, 185 anomalous, 141, 159 of electromagnetic radiation, 141 in FIA, 934-937, 940, 941 by monochromators, 182, 185, 186, 189 values, F1A, 935, 936 Dispersive instruments, atomic fluorescence, 250 Dissociation reactions, 244, 245, 339 Dissociative interactions, mass spectrometry, 574 Distribution constants, separations, 766-769,777-779,789, 803,810,844, 846, 882 DLS (dynamic light scattering), 955-958 DMMs (digital multimeters), 30-32,42,43,52 Doppler broadening, 221, 237, 238, 955, 957 shift, 220, 221 Double layer, 632,633, 723, 746, 870 reciprocal plot, 388, 389 Double beam, 241, 352, 359, 444, 445 Double-focusing mass spectrometers, 283, 290, 299,300,567-569,578 Dropping mercury electrode, 716-717 DSC, 900, 901, 904. S e e a ls o Differential scanning calorimetry DSL (digital subscriber line), 106, 107

DTA (differential thermal analysis), 897-900, 906, 907 DVM (digital voltmeter), 30, 31 Dye lasers, 168, 173 Dynamic concentration limit, 19 Dynodes, 194, 195, 284, 285 ECD (electron capture detector), 795,796 Echellc grating, 186, 262, 265 monochromator, 186, 187 spectrometer, 198,260,262-264 Echellette grating, 183 Eddy diffusion, zone broadening by, 772-773 ED Ls (electrodeless discharge lamps), 239, 250 EDTA in electrochemistry, 663, 664 as protective agent, 245 as titrant, 380, 381, 735 EELS (electron energy-loss spectrometry), 602 Efficiency of chromatographic column, 769, 772 current, 703, 707, 712 Electric field oscillations, 133 Electrical circuits, 26 -28, 34 domains, 3-5, 9, 10,26,81 double layer, 632 signal, 3, 5-7, 71,164,165,191 Electroactive species, 707, 735, 737, 739,743,746,753 Electroanalytical cells, 633 Electroanalytical methods, 628, 633,647,648,651,653,659 Electrocardiographic instrumentation, 115 Electrochemical cell potentials, 636 cells, 628, 630, 633, 634, 636, 638-640,647,653,659, 677,705,716,717,722,723 disposable, 683 galvanic, 629 stirred, 726

deposition, 734 detectors CE,874 HPLC,823 devices, gas-sensing, 677 methods, 628 preconcentration, 748 reactions, 737, 751 Electrochromatography, 867, 883, 884 Electrode, 664 area, 633, 651, 683, 699, 725, 739 calibration methods, 687, 688 enzyme, 680-682 half-reaction, 638 materials for coulometry, 706, 719,732 potentials, 635, 636, 638-641, 643,645,646 table of standard, 644, 997-1000 • reaction, 630, 635, 638, 649, 650, 663,697,700,703,724, 729, 737, 739 direct in coulometry, 707 response, 686, 687 surface, 630, 632, 633, 637, 649, 651,698-700,724-727 modified,716 systems amperometric, 735 glass-calomel, 684 Electrodeposition, 652, 699, 700, 720, 749 step, stripping analysis, 749 Electrodes auxiliary, 708 classical,751 graphite for spectroscopy, 259, 271, 272, 721 ion-selective, 664 ( s e e a ls o lonselective electrodes) left-hand, 638, 639, 659, 660, 697 metallic, 636, 662, 665, 720, 735 modified, 720, 721, 739, 740 reference, 637-638 right-hand, 638-640, 686, 697 ring for mass spectrometry, 570 ring-disk, 736, 737 solid-state, 672, 735

specific-ion, 677 ( s e e a ls o lonselective electrodes) spherical, 751, 755 zinc, 633, 638 Electrogravimetry, 697 Electrokinetic chromatography, micellar, 867, 882,883 injection, capillary electrophoresis, 871-872 Electrolysis, 697-701,721,724,725, 728, 748 cells, coulometry, 704 constant current, 699 potential, 700, 701, 703, 706, 707

stripping analysis, 748 Electrolyte concentrations, electrochemistry, 645, 688, 746 solutions, 628, 630, 635, 636, 641, 689,709,732,880 concentrated, 635 supporting, 718 ( s e e a ls o Supporting electrolyte) Electrolytic cells, 629-632, 647, 6 4 9 -6 5 1 .

S e e a ls o

Electrochemical cells Electrolytic conductivity detectors, for GC, 796 Electromagnet, NMR spectrometers, 521, 523, 566,567 Electromagnetic field, 134, 140, 175 radiation, 2, 9,132-137,139-141, 143-145,147,149 absorption of, 148, 368, 498 ( s e e a ls o Absorption) dispersed, 285 ( s e e a ls o Dispersion) emission of ( s e e Emission) plane-polarized, 133, 143 properties of, 132 short-wavelength,303 sources of. 140 spectrum, 134, 135 Electron acceptors, 371

beam apertures, SEM, 613 CRT tube, 51, 52, 612 mass spectrometry, 557, 572, 581 source, of X-rays, 303, 304 surface analysis, 592, 594, 598, 600,607-611 capture, 306-307, 910-911 density, NMR, 511, 514, 596 detector, SEM, 608, 609, 613 energy, electrochemistry, 636, 638 energy-loss spectrometry, 602 guns, surface analysis, 591, 595, 599,600,608,609,613 microprobe, 328, 607, 610-612, 624 microscopy, 602, 608, 611, 613, 614 multipliers continuous-dynode, 284, 285 discrete-dynode, 284 mass spectrometry, 284 - 286, 290, 292, 299, 570, 603 signals, secondary, 611, 613 spectrometers, 593, 594 spectroscopy, 591-595, 597, 599, 601,602 instrumentation for, 594, 595 spectrum, 595, 600 spins, 215, 399, 400 transfer, 631, 649, 650, 735, 740 Electron-beam interactions, SEM, 610 Electron-capture detectors, 795-796 Electronic devices, molecular, 721 energy levels, 152-154, 169,242, 400,402,403 integrators, 703, 704, 789 ( s e e a ls o Operational amplifier) laboratory notebooks, 127-130 signatures, for electronic laboratory notebooks, 127, 128 states atoms, 254 lasers, 169 lower, 169,403

metastable excited, 156 molecules, 152, 155, 400 - 402 properties, 147, 152, 154, 155 transitions atomic spectroscopy, 153,219, 242,243 IR spectroscopy, 431 properties, 151-153, 155 UV -visible spectroscopy, 368, 369,402,405 X-ray analysis, 303, 305,307, 309 Electronics, 2, 43, 59, 80,136,319, 354,411,412,449,947 Electrons backscattered,610-613 beam of, 591, 592, 598, 600, 602, 608,610 emission of in radiation transducers, 144, 191, 193, 344 emitted in surface analysis, 591-594,599 energetic in mass spectrometry, 551,552 ground-state, 220, 400 scattering in EELS, 602 Electron-transfer kinetics, slow, 739, 745 process, 649, 664, 703, 737, 742, 746,751 reactions, 632, 641, 723, 739, 741 Electroosmotic flow, 869-871, 875, 882,883 Electropherogram, 873, 876 Electrophoresis capillary, 867-870, 875, 876 array, 878, 879 principles, 867, 868 slab, 868, 869 Electrophoretic mobility, 868 Electrospray ionization, mass spectrometry, 552, 560 Electrostatic mass filters, 301 Electrothermal atomizers for atomic spectroscopy, 234, 235, 257 background correction with, 242, 243,250 principles, 224, 233-235

Elemental 'lOalysis bv atomic srectroscory, 26'1, 270, 272 by mass srectrometrv, 2'11, 30f by NMR, 529 bv surface techniques, 301. 5'15. 600 - 602, 604, 624, 626 bv X-ray methods, 3IH, 324, 325, 32S, 330 Ellirsometry,606 Eluent column chromatograrhy, 76-1 ion chromatograrhy, S41-H44 strength, 764, 774, 785, 7'12, 7'17, ROO,803, 823 -H25, 8.1'1, 841-H44, H5H,890 Elution, 763, 764, 76'1, 78S, HI'I, H30 Emission bands, 18'1,210,223,238 bonding electrons, 115 of electromagnetic radiation. 135,147,148,157,255. 26'1,272 intensity, 272, 280 lines, 21'1, 220, 23H, 241, 244, 25'1, 265,267 measurements, 222 m o n o c h ro m a to r, flu o re s c e n c e ,

415,416,4IH sou rces,

fo r a to m ic

e m is s io n

spectrometry. 273

254. 266.

srectra atomic, 227, 234, 254, 258, 269, 273 fluorescence, 403, 411. 414-416,418 srectroscory, 148, 165, 168, 254-276 srectrum, 150, 151 srontaneous, 169, 170, 172 stimulated, 168-171 wavelength selector, fluorescence, 41 I, 412, 414 Emitter, transistors, 47, 48 Emulsions, rhotograrhic, 1'14. 1lJ6.

27) E n a n tio m e r s .

s e p a r a tio n

838.860.861

o f. ~17.

Endothermic rrocess, thermal analysis, 8'19 E nergy

band-gar, 173, 174 changes, scattering, 483, 484, 494 differences between states. 147, 148,153-155,211>,220, 222, 305, 405, 411, 431. 432,503 disrersive instrument, X-ray analysis, 320, 321 electrical. )47, 148, 151, 152, 193. 283,349,1>30,632 excess, 148, 149, 152, 169,920 free in electrochemistry, 634, 63'1 levels in NMR, 4'18-500 in 0rt ical spectroscopy, 153, 154,210,221,243,400, 401,433,435-437,482 rotational, 155,432 srlitting of electronic, 242, 400 in X-ray spectrometry, 305, 306, 308, 309 pass, XPS, 594 photon, 146 resolution, 3 I 7,596,603 states of atoms and molecules, 146, 147,153,154,173 excited electronic, 368, 488 rotational, 173, 368, 431 transfer. molecules, 403, 408, 409. 484 Energy-dispersive systems, 318, 31'I, 3 2 ')

Energy-level diagrams, I'll, 152, 483 Enhancement, ICPMS, 296 Enhancement effects, X-ray fluorescence. 322, 323 Ensemble averaging, 117-119 Entrance slit. monochromator. 180. ISI. IK\ 187-1H'I. 197,21>1 Environment. chemical in NMR, 509. ') 10.532,596 Emironmental noise. 81, III. 111, 204 Enzyme electrodes. 080

Enzymes. 3H2. 383, 42'i in biosensors. 1>7'1.680 immohilized. 679. 680,733 EPA.

in m e rc u ry d e te r m in a tio n s ,

332,333 Equation solver software. '1K '19 Equilibrium ahsorbance. in kinetic methods. 384.385 rosition. molecular vihrations, 433.434.484. 48') Equivalence point. tit rations. 37'1. 380,691,709,712,714. 734-736 Error roundoff, '173 standard of estimate, 987 of mean, 974, 975, '178 Error propagation, 982 Errors acid in pH measurements. 671, 689 alkaline in p H measurements, 670,671,68'1 indeterminate, II, 11, 1'1 loading, 31 in measurement, 12, 13, 17, 19, 31,967,969,973, 974 random, 13, 1'1,20,907-'169, 971-975 systematic, 13, 1'1,967,96'1-971. 984 ESCA. S e e X-ray rhotoelectron spectroscopy ESEM (environmental SEM). 613 Evaporative light-scattering detector, 826 Everhart-Thornley secondary electron detector, 612 Exchange, chemical in NMR, 51'1. 520.535,536 Excimer laser, 172 Excitation of atoms and molecules, 147-151 srectrum. fiuorescence. 410--412 wavelength luminescence, 410-41.1. 416. 4111

Fiher ortics. 202. 203. 286. Raman, 481. 4S2. 48H 354 -356.361.417 selector. luminescence. 41 I. F ID 412.41S (name ionization detector), 7'13. Excited 794. S59 ( s e e a ls o Flame molecules, 11>'1,171. 231. 34'1. ionization detector) 402 - 405. -107( s a a ls o (free induction decay) in NMR. Electronic transitions) 505.508-510.521. 522. nuclei, NMR, ')03-505 535. 538, 540. S4 I. 543 states. 147, 1-18.152-1')4, 156 Field Exclusion limit. size-exclusion centrifugal, 884. 959, '161 chromatograrhy, H46, 847 desorption sources, 552. 55'1, 5S5 Exit slit. monochromator, 181. 184. g ra d ie n t. m a g n e tic re s o n a n c e 187-18'1.203,204,21>0. imaging, 538-')40 261,285 gravitational, 959-961 Exothermic process, thermal ionization sources. 558, 559 analysis, 898-'104 secondary in NMR, 51.1-51') Expression, mass-balance, 246, 381>, Field-effect transistors, 40 -48 387,390 Field-flow fractionation. 88-1-888 Extracellular acidification, 757. 758 Field-frequency lock. NMR, 525 Extracolumn band hroadening, LC, Filter 81S instruments, fR. 447, 474 Extraction rhotometers. UV -visible, 204, cell, 863, 864 354. 380. 824 solid-rhase. 8'10. '140 Filtering, digital, 120. 121 solvent. 930, 934, 936 Filters supercritical fiuid. 850. 8')7. absorption. 180 862-806 correlation analyzers, 448 for electrical signals, 40. 41, SO, Fabry-Perot etalon, 176 -I 77 73.113,115,117.122 Factor, retardation, in thin-layer interference, 176,177,180 chromatography, 849, 850 for luminescence spectroscopy, Faradaic 411-413,424 currents, 632, 633, 742, 743, 7')1 for X-rays, 311, 326-328 impedance. 722, 723 First-order spectra, NMR, 517. ') 18 Faraday cur, for mass Flame spectrometry, 285-287 ahsorrtion profiles, 232 Far-IR sreetroscory, 470 atomization. 230, 232. 233. 241, Fast 248 atom hombardment, sources for chemiluminescence, 425 MS,562-563 neutrons. 918. 922 Fellgett advantage, 206 Ferrocene in electrochemistry, 740.741,745 FFF (field-fiow fractionation), 884-888 FlA. 247. 933-935. 939-941. a /s o Flow injection analysis

e m is s io n

721.

Se e

srectroscopy. 230-233, 246, 248.273 spectrum.21H ionization detector. 7'13. 794. 7'10. 797.800.85'1,861 rhotometers.273 photometric detectors in chromatograrhy. 7'17.859

Flicker noise. 112. 113.115,206 Flight times. time-of-flight mass sreetrometry. 290. 569 F1ir-fiops.85 F lo w

injection analysis, 225, 247. 383. 931- )35.937, '138 ( s e e a ls o 1

HA)

meter for G c , 78'1, 7'10 rates e1ectroosmotic. 870, 875 FIA, 932, '134-931> flame. 231. 233 mobile phase. 77 I -774.778. 78'1.790. S19, H21 volumetric, 761>,767.7'10. 846 turbulent in electrochemistry. 726 Flow cells FlA. '132, '136. '137 LC, S23 voltammetry,731 Flow FFI'~ 887 Fluorescence,S. 6, 148. 156 atomic ( s e e Atomic fiuorescence spect roseopy ) bands,402,403,411 detection, LC, 414, 421,825. H73 emission,S, 402, 405, 407, 408, 411,412,414,417.419, 422,494 instrumentation, 411, 413, 414 intensity, 407, 409, 410, 412 lifetime measurements, 421 molecular, 150. 157,399,400, 483 quantum efficiency of, 406-408, 428 radiation. 155, 156, 169 resonance, 219, -100 spectroscopy, 168,399,422 srectrum, 219, 311, 410. 415. 425 theory of, 40()- 409 Fluoride determination of, 688, 689. 746 electrode. 672 Fluorometers. 5. 6. 204, 411-415 F-numher, 185

Focal length of monochromator. 185, 186 of optical element, 185 plane mass spectrometer, 285, 286, 291,568 optical spectrometer, 181, 182, 185, 187, 188, 194, 196, 203,260,261,270,353,361 Follower current, 63, 64, 66, 67, 75 voltage, 62, 63, 65, 67, 71, 114, 684 Force constant, 434-436 Formal potential, 645, 997-1000 Formation constant, of complexes, 384-390 Forward biasing, of semiconductor diodes, 45-46 Fourier transform instruments, UV-visible, 259, 265,266 IR spectrometers, 438, 439, 474, 476,824 mass spectrometers, 571-573, 584,604,800 measurements, 206, 499, 572 NMR, 521, 529 Raman spectrometers, 491 spectroscopy, principles, 204-207,209,211 Four-level system, lasers, 171-173 Fragmentation, mass spectrometry, 551,552,554,555, 557-560,562,574,576, 578,580 Frame of reference, rotating in NMR, 505, 508 Frequency of absorbed radiation, 153 bandwidth, electronics, 112, 115 carrier in NMR, 524, 525 chopping, 115, 116 components, 120,524,745,759 cyclotron, 571 domain, 7, 207, 209, 508 - 510 exchange NMR, 520 fundamental vibrational, 436, 437 lock system, NMR, 543

meter, 9, 85, 86 natural, 434 precession in NMR, 539, 540 proton, 521, 523, 532 range, 65,207,211, 524, 722 resonant of crystal, 10,87 response, electrical circuits, 41, 64,65,120 spectrum, 210, 211, 759 sum, 606 sweep signal, 571 synthesizers, NMR, 522, 524 Frequency distribution, of data, 968-970 Frequency-domain spectrum, 121, 207, 209, 522, 525 Frequency-doubling system for laser, 175 Fronting of chromatographic peaks, 769 FT voltammetry, 745 FTIR spectrometers, 439-443, 451, 453,454,466,467,470, 4 7 1 ,4 7 3 ,4 7 4 ,4 7 7 .

S e e a ls o

Fourier transform, IR spectrometers FT-NMR spectrometers, 498, 522, S e e a ls o Fourier transform, NMR FT-Raman instrument, 488, 491, 4 9 2 . S e e a ls o Fourier transform, Raman spectrometers Fuel, combustion flames, 221, 230, 231,233,241 Function autocorrelation in dynamic lightscattering, 956, 957 work, 145, 146,593 Functional group detection IR, 438, 459, 460, 464, 474, 493 mass spectrometry, 552, 578 NMR, 512, 513, 515, 516, 526, 529,533 Raman, 493 surface analysis, 596, 602, 620, 621 UV-visible, 369, 373, 374

groups, and fluorescence, 405, 420,425 Furnaces atomic spectrometry, 234, 235, 243,245,247,256,257 thermal analysis, 894, 895, 898 GaAs photovoltaic cell, 192 Gain of amplifier, 41,60,63-65,67,70 bandwidth product, operational amplifier, 65 of

BJT, 47

of PMT or electron multiplier, 285 Galvanic cell, 629-631, 638-640, 645,647 Gamma radiation, 303, 306, 612, 910, 911, 916-918,922 rays, prompt, 918-920 , Gamma-ray spectrometers, 9[6, 917 Gas chromatographic columns, 8tll-805 chromatography, 582, 788-804, 806-810,890,891 chromatography/mass spectrometry, 582, 761 sensor, electrochemistry, 677, 681 Gases dissolved, 677-679, 818 in electrochemistry, 677-679 in HPLC, 818, 819 purge in thermal analysis, 894, 895,903 Gas-filled detectors, X-ray analysis, 314,315 Gas-permeable membranes, 677, 678 Gas-sensing probes, 677-680 Gas-solid chromatography, 788, 810 Gaussian distributions chromatograms, 768, 770, 771 random errors, 768, 968, 969, 977, 978 Gaussian statistics, 973, 989 GC,788-81O

GDOES,

S e e Glow discharge optical emission spectroscopy Geiger tubes, 314, 315 Gel filtration, 817, 845, 847 Gels electrophoresis, 877, 878, 892 size-exclusion chromatography, 844,845,847 General elution problem, chromatography, 780 - 781 Generation, sum frequency, 591, 604 Generator electrode, coulomctry, 707 Glass electrode acid error, 671, 689 alkaline error, 670, 671, 689 asymmetry potential, 669 hygroscopicity, 668 membranes, 665-670 transition, 899, 901, 904 GLC S e e Gas chromatography Globar,450 Glow discharge optical emission spectroscopy, 273, 274 Gold electrode, cyclic voltammetry, 740,741 Goniometer, X-ray analysis, 312 Gradient elution, chromatography, 781,819-820 Graphite furnace, atomic spectroscopy, 234 Grating, 179-181, 184-187, 189 concave, 184,261,262,359 echelle,186 echellette, 183, 184, 186 instruments, 358, 440, 474, 476, 477 master, 182, 183 monochromators, 181, 182, 184, 185, 188, 189,260,359, 360,413,415,438,476,825 Gravitational sedimentation, 960 Ground state, 147, 148, 151-156 vibrational states, 149,401 Ground-state analyte atoms, 274 Group frequencies. 459-461, 464

GSC

Gas-solid chromatography Guard columns, HPLC, 822 Se e

Hair, analysis of. 584, 964. 965 Half cycle, 116, 117,243,271.272 Half-celL 630, 635 -640,645,649, 659,660 potentials, 639, 642, 644, 646. 659 reactions, 630, 631, 635, 640, 641, 648, 649 ( s e e a ls o Halfreaction) Half-life, 307, 912, 919-921 Half-reaction, 635 -646 Half-wave potential, 722, 727-730, 746, 749 rectifier, 50 Hall electrolytic conductivity detector, 796 Hanging mercu£y drop electrodc, 7 1 9 - 7 2 0 . S e e a ls o HMDE Harmonic oscillator, 433-435 Heat capacity component, modulated DSC, 901,903 determinations, 903 thermal analysis, 901-904 transducers, 201, 451 flow, differential scanning calorimetry, 900-904 flow signal, reversing, 901 Heavy-atom effect, 404-405 Helium-neon laser, 172,483 Hertz (Hz), 33 Heteronuclear decoupling, NMR, 529 Hexacyanoferrate, 371, 636, 738, 745 High-pass filter, 40, 41,115 mass filter, 288, 289 High-performance liquid chromatography, 816-848 High-pressure gas flow, Bernoulli effect, 225, 226 High-purity germanium detector, 916,917,922

High-resolution mass spectrometers, 282 High-resolution NMR, 509-510 spectrometers, 498, 515, 521 High-resolution TGA, 896 High-speed voltammetry, 745 HMDE (hanging mcrcury drop electrodc), 719, 720, 742, 744, 749 Holes, in semiconductors, 44-46, 48,191,193,194,198,316 Hollow-cathodc lamps, 238-244, 250 Holographic grating, 184 Homonuclear decoupling, NMR, 520 Hooke's law, 434 HPLC,816-848 HPLC detectors, 823-828 Human Genome Project, 867, 878 Hydride generation tcchniques, atomic spectroscopy, 226 Hydrodynamic voltammetry, 722-737 Hydrogen electrode, 636-638, 641, 659, 660 io n

activities, glass electrode, 641, 668. 669 concentration, 684, 688 ions, generation of, 708-709 peroxide, 375, 399, 425, 679, 730, 733,737 Hydroxide ions, generation of, 708, 709 Hyper Raman effect, 495 Hyphenated methods, 283, 582, 800 Hypothesis testing, 983~985 ICP emission spectrometry, 255-258, 266-269 sources, 255-259, 263, 266-269, 276,291-294 ICPMS, 282, 291-299 Image current, ion-cyclotron resonance, 571,572 Immobilized enzyme, 679-680, 733 Immunosensors.733

Impedance, 39-42, 63, 71, 72 measurements, 42 Incandescent wire source, IR spectroscopy, 450 Incident electron beam, surface analysis, 611,612 frequencies, sum-frequency generation, 605 Incoherence, of electromagnetic radiation, 140 Indeterminate errors. S e e Random errors Indicator electrode, 659, 660, 662, 664,665,686,687,691 Indicators, Beer's law deviations of, 339,340 Inductively coupled plasma mass spectrometry ( s e e ICPMS) S e e ICP Inductors, 34, 35 Inert electrodes, 664, 749 Information digital, 5, 7, 8, 80 flow of, 3, 5, II5 sampling-interval interferometry, 440 spectral, multichannel instruments, 199, 204 Infrared absorption spectrometry, 430-452,454,455-477 detectors, LC, 824 radiation, 134, 149, 155, 172, 174, 180,182,191,201-203, 209,213,364 Initial rate, 382, 383 - Injection in chromatography, 783, 791, 801. 821 electrokinetic in capillary electrophoresis, 871, 872 in FlA, 864, 871,872,877,887, 931,933,934 Inlet on-column for capillary GC, 791 system, mass spectrometry, 283, 563-565 Inorganic species absorption by, 370, 371. 419

chemiluminescence of, 419, 424, 425 far-IR applications to, 476 fluorometric determination of, 419-420 Raman spectra of, 419, 492 Input difference voltage, 59, 62 frequency, digital circuits, 85-87 transducer, 5, 81, 111 ( s e e a ls o Detector) Input-output systems, for computers, 95 Instructions, for computers, 91, 92, 94 Instrument components, 3, 4 control mass spectrometry, 318, 576, 577 software for, 99 thermal analysis, 894 response, 6, 11, 15, 16,248 standardization, luminescence, 418 Instrumental deviations, from Beer's law, 338, 340 -342, 466 limitations, in IR spectrometry, 464,465 methods, 1-3 calibration of, 11- I 7 noise, 111 effects on spectrophotometric analysis, 343-345 precision, 344 procedures, 2, 3 Instrumentation amplifiers, 114, 115,201 voltammetric,718-721 Instruments automated, 127,326,736,929, 930,945 calibration of, 11-17 cold-vapor atomic fluorescence, 333 commercial CE, 874, 875 components of optical, 164,249, 310,411 computerized coulometric. 706

double-beam, 241, 346, 351-353, 358-360, 441, 444 energy-dispersive X-ray, 310. 318-320,322 Fourier transform, 265, 266, 430, 443 gas chromatographic, 789 multinuclear NMR, 534 nondispersive atomic fluorescence, 250 IR, 431, 447, 448 portable, 193, 315, 354, 415, 809 pulsed NMR, 499 sector for mass spectrometry, 566,575 sequential for atomic spectrometry, 259-261 single-channel X-ray, 318 tandem-in-spaee mass spectrometers, 575, 5 :J 6 virtual, 102, 103 wavelength-dispersive for X:;'ay analysis, 310,318 Integration, operational amplifiers for, 71-73 Integrators boxcar, 120 for eoulometry, 706 Intensity distribution, light scattering, 952-954 of electromagnetic radiation, 134 t1uctuations, light scattering, 956 reflected, 142, 470, 605 Interaction volume, SEM, 611, 612 Interactions, analyte-ligand in affinity chromatography, 848 Intercept, of calibration curve, 12-17 Interfaces electrode-solution, 632, 703, 723, 727 liquid-liquid, 605, 606, 774 Interfacial methods, 652, 653 Interference filters, 176, 177, 179,350,355, 41-\,430 fringes, 458 pattern, 178, 179, 184,209,210

Interferences atomic spectroscopy, 219, 239, 2-\1-247,250,266,267, 269 chemical, 2-\4, 248. 254, 258, 269 general, 2, 13,21,22 ICPMS,294-296 isobaric, mass spectrometry, 294, 300 plasma emission spectroscopy, 269 spectral, 241. 242, 248, 269 Interferograms, 209-2II, 439, 440, 442,443,466, 467 Interferometer, 208-210, 440-443, 492 Internal c o n v e r s io n

luminescence, 402- 404 nuclear, 911 resistance of glass electrode, 30, 31, 55, 57,62,66,67,71,124,649, 655,684 loading and, 30, 31, 62, 66, 67 solution indicator electrodes, 668, 669, 675,677-679 reference electrode, 662 standard method, 17, 18,98 for chromatography, 783, 807 for emission spectroscopy, 98, 272 Intersystem crossing, 404, 405, 407, 409,421 Inverse Raman spectroscopy, 495 Inverting input, operational amplifier, 61-63,67,71,74,705 voltage amplifier, 64 Ion chromatography, 839-844, 852, 875 applications of, 841, 842 single-column, 843 cyclotron resonance, 571-572 detector elcctrooptical, 285, 286 mass spectrometry, 574, 828 microprobe, 603, 624

sources, mass spectrometry, 283, 288, 290, 294, 551. 552-563,564 spectroscopic techniques, 602-604 trap analyzers, 569-571 Ion-exclusion chromatography, 843-844 Ionic strength, 641, 642, 646, 647, 687, 688, 848, 994 - 996 Ionization chemical, 552, 553, 557, 558 degrees of in atomic spectroscopy, 246 electron-impact, 554-557,558, 559,563,581 electrospray, 552, 560, 562 region, mass spectrometry, 557, 565 source, 565, 566, 570, 573, 583 hard, 552, 553 soft, 552, 553, 574, 575 suppressor, atomic spectroscopy, 246 lon-molecule collisions, 555 Ionophores, 674, 675 Ion-pair chromatography, 836, 838 Ions alkali-metal, effect on glass electrodes, 689 energetic mass spectrometry, 285, 287 Rutherford backscattering, 603 excited, 276, 305, 307, 309, 593, 598 nitrate, reduction of, 698,- 700 organic solute in HPLC, 836 primary in ion spectroscopic methods, 603 product in tandem mass spectrometry, 573-576 protonated matrix in MALDI, 560 reagent in mass spectrometry, 558 separation of by CE,875 ion chromatography, 569, 839-844.875 mass spectrometry, 566 -577

simultaneous detection of in mass spectrometry, 286. 287 trapped, 570, 572 Ion-selective electrodes, 664-675, 680, 683 field effect transistor (ISFET), 675-677 membrane electrodes, 286,576, 664-675 Ion-trap mass spectrometer, 570 IR absorption spectrometry, 4 3 1 - 4 5 2 ,4 5 5 - 4 6 9

(se e

Infrared absorption spectrometry) active transitions. mutual exclusion principle, 486 detectors, 440, 477, 825 ( s e e a ls o Infrared detectors) filter correlation analyzer, 449 photometers, 447, 469 instrumentation, 438-449 instruments, dispersive, 445, 446, 465 liquid cells, 457 radiation, 166, 167,430-432 ( s e e a ls o Infrared radiation) sources, 449 - 451, 477 spectra, 432, 437, 438, 446, 459, 464,466,467,481,482,485 spectral regions, 455 spectrometry, applications of, 455-477 transducers, 451-452 Irradiation, neutron activation analysis, 909, 918, 920, 921,924 ISFETs (ion-selective field effect transistors), 675-677 Isobaric profile, SFC, 294, 858 Isoelcctric focusing, capillary. 880-882 point, 876, 880, 881 Isotope dilution, 924 -925 a ls o

r a tio

m e a s u r e m e n ts ,

m ass

spectrometry, 299, 578, 580

ISS (ion-scattering spectroscopy), 591.603.604.622 IUPAC sign convention. cell potentials, 31, 639-640 Johnson noise, 111-112.344-345 Joule heating. capillary electrophoresis. 144, 146, 160,640.869 Junction p n , 44, 45, 47 potential, 630, 635, 665, 667, 668, 686-689 thermal, 201,452 Kinetic energy, photoelectron in photoelectric effect, 144-146 methods, 381-385 polarization, 697 Kirchhoff current law, 26-30 voltage law, 26-27,30,36,62 Lab-on-a-chip analyzers, 941 Laboratory electronic, 127-130 operations, in microfluidics, 940 paperless, 127 recorders, 52-53 LabVIEW, 99,102-103,745 LALLS (low-angle laser light scattering), 951-955 Laminar-flow burners, 233 LAN (local area network), !O5, 107 LAPS (light-addressable potentiometric sensor), 683-684,757-760 Larmor frequency, NMR, 502-509, 533 Laser ablation, 227, 292-294 beam detector, in AFM, 617 diodes, 173-175 Laser-fringe reference systems, 440, 441 Lasers, 168-175 carbon dioxide, 450

for desorption of sample in MALDI,560 in holographic grating fabrication, 184 microprobe, 274 as reference in FTIR spectrometer, 440 sou rce

for atomic fluorescence, 250 in DLS, 957 in ellipsometry, 606 for excitation in on-column CE,879 in low-angle light scattering, 951 in nonlinear Raman spectroscopy, 495 in photoluminescence measurements, 413 for Raman spectroscopy, 488 LC detectors, 823, 828 LC instrumentation, 821-827 LC (liquid chromatography), 816-856 LCD (liquid crystal display), 54 Least-squares analysis, 15, 20 weighted, 12,279-280,331 method,985-988 polynomial smoothing, 120 -123 LEOs (light-emitting diodes), 54, 174,350,413,757,758,960 Level detector, operational amplifier, 74 L1BS (laser-induced breakdown spectroscopy),274-276 Lifetime measurements, fluorescence, 421-422 Light amplification, in lasers, 168-171, 174 scattering dynamic, 955, 957, 958 low-angle laser, 893, 950, 951, 953 Limiting current, 722 LlMS (laboratory information management systems), !O7, 127-130,692,930

Line sources, 168,237 spectrum, 150, 151,254.303,304, 311 X-ray, 304 -305 voltage, 49-50 widths, natural, 220, 221 Linear dispersion, of monochromator, 181, 185 -186 Linearity, 21 calibration curves, 248 departures from in absorption measurements, 341 from in fluorescence measurements, 408 from in ICP, 268 from in pH measurements, 671 Liquid chromatography, 816-848 junctions, 630-631, 635, 659, 690 cells without, 631- 632 mobile phases, chromatography, 774 -779,828-830,859 stationary phases, chromatography, 773-775, 801-S03,884 Liquid-membrane electrodes, 672-675 Liquid-solid chromatography, 837, 839 Lithium, salts as supporting electrolyte in organic voltammetry,747 Lithium-drifted silicon detectors for X-rays, 316 Loading errors, 30-32, 62, 66, 684 LOD (limit of detection), 20 conductivity detector, 796 fluorimetry, 420 nitrogen-specific chemiluminescence GC detector, 800 piezoelectric sensor, 10 sulfur chemiluminescence GC detector. 800

Logic level, S4 state, 84, 88, 94 LOL (limit of linearity), 21 Loop in electrical circuits. 26, 27, 29, 821 sampling for FlA, 933 for LC, 821 Low-pass filter, 40-41,115-117, 123

Luminescence methods, 399-419 Luminol, as chemiluminescent reagent, 425 Magic angle spinning, 533 Magnetic field absorption in, 155 electronic, relation to chemical shift, 511 energy levels in, NMR, 499 locking, NMR, 523 precession in, NMR, 502 strength, 499, 501, 567-568, 576 moment, 499-500, 502, 505-506 quantum numbers, 499, 501, 504, 542 Magnetic resonance imaging, 537-541 Magnetic sector analyzers, 566, 568 Magnetogyric ratios, 499-501,504, 529,534 Magnets, NMR, 522 Map, data-domain, 3-4, 7-8 Martian surfaces, 476, 917 Mass absorption coefficients, 308 analyzers, 283 double-focusing, 291 ion-trap, 570 secondary-ion, 602, 603 time-of-flight. 290, 798 change, in TGA, 896, 897 chromatograms, 799. 800 exact, 282, 566, 578 fraction, 308, 320

numbers, 281 reduced, 434 -436 spectra in GC/MS, 798 molecular mass from, 578 spectral data, presentation, 551, 580 libraries, 552, 577, 581 spectrometers atomic, 283, 290 molecular, 563 -577 spectrometry, 281-302, 550 -588, 798-874 accelerator, 301 applications, 583, 798 of molecular, 577-581 of tandem, 582 atomic, 281-302 detection limits, ICPMS, 297 detectors GC, 798, 809 LC,825 laser-microprobe, 604 molecular, 550-588 quantitative applications of, 583-584 secondary-ion, 602 spark source, 299 transfer in chromatography, 774, 830 in electrochemical cells, 633, 649 rate of in electrochemical cells, 628,774 transport, mechanisms of, 651 Mass-analyzed ion kinetic energy spectrometer (MIKES), 576 Mass-to-charge ratios in atomic mass spectrometry, 282 in mass spectrum, 551 in quadrupole MS, 289 Matrix effects, 325 in AA,241 in calibration, 13 enhancement in XRF, 322 in ICPMS, 296 in the internal-standard method, 17

minimizing in standard-addition methods, 13 in plasma sources, 269 in UV-visible spectrometry, 376 in XRF, 321 Mattauch-Herzog geometry, mass spectrometer, 291 Mean population, 971 sample, 967-969, 971,976 value, 967-969 Medium, lasing, 168-169, 172 Membrane electrode systems, types, 677 electrodes, 664 -665, 66S-671, 675-677,680,686, 692-695 ion-selective, 659, 665 ion-selective, 665, 683 properties of, 665 Memory, computer. 92-94 Mercury electrodes, 663-664, 719, 720 dropping, 716, 717, 737 film electrode, 720-721, 737, 740, 749 Metal sample plate, 560 Metallic indicator electrode, 662-663 Meter, DMM, 31 Meter, loading error, 31 Method of least squares, 985-988 Methods continuous flow, 3S3, 931, 933, 934 kinetic, 381-383, 385 Methyl protons, in NMR. 511-518 Micelles in MEKC, 882-883 in room-temperature phosphorescence, 421 Michelson interferometer. 208-210, 213,214,439,454, 491-492 Microchannel plates, 285-286 Microcomputers, 80, 90-92 Microelectrodes applications o[ 753 voltammelric, 751- 753

croprobe. electron. 328. 607. 610-612.624 icroscope. 1R. 477 icroscope. scanning electrochemical. 613. 753 probe. 613-621, 623. 753 tunneling, 613-616 1icrothermal analysis, 904-906 rlicrowave-induced plasma, 255, 797 Mid·J R absorption spectrometry, 457-467 Mie theory,.951-952 Migration of anions and cations in electrolytic conduction, 630 of cations in Geiger tube, 315 cessation of at isoelectric point in CE,881 in chromatography, rate theory, 768 in concentration polarization, 651 drifting of Li ions in SiLi detectors, 316 holes and electrons in p n junction, 44 in ion-selective membranes, 665 of majority carriers in a BIT, 47 mass transfer mechanism, 633, 651 minimizing in voltammetry with supporting electrolyte, 724 of mobile phase measured by dead time. 766 rate of in chromatography, 763 in electrophoresis, 868, 869 relation to concentration difference and diffusion coefficient, 774 to distribution constant, 767 varying to optimize column performance, 775 retardation of in CGE. 878 Mirrors, movable, in Michelson

interferometer. 208. 439-441,443,492 Mixers in microtluidics. 941 stopped-flow, 384 Mixtures, two-component, 377, 729, 767.787 l\lobile phase. in chromatography. 762 Mobile-phase veiocity, 772, 773. 775 Mooilities, ionic. 635 Modem, 9,106 Modes, normal. 437-438 Modulation, 115-116 refractive-index, 179, 214 Molar absorptivity, 158. 367, 375 Molecular absorption, 153. 155. 157,223, 237,431 ions, 282, 555 luminescence spectrometry, 399-429 mass spectrometry, 550-588 masses, 281 average, or chemical. 282 high-precision. 568 mass numocr, 282 from mass spectra, 578 in size-exclusion chromatography, 845 -848 Molecular-mass calibration standards, in sizeexclusion chromatography, 847 Molecular-selective electrode systems, 677- 683 Molyodenum target, X-ray, 304, 311 Momentum, angular, in NMR, 499 Monochromatic radiation Beer's law, 158 diode lasers, 173 incoherent, 169 Monochromator,18o-J89 dispersion. 185 echelle spectrograph, 21>I effect of slit width on resolution, 188 in tluorescence spectrometry, 411.413 in IR spectrometry. 444

light-gathering power. 185 performance characteristics, 181> in Raman spectrometry. 490 resolving power. 185 slits. 187 Monochromator. Spectronic 20, 357 Monochromator. X-ray. 311-312, 325 MOSFET.48 Moving average. 120. 125 MRI (magnetic resonance imaging), 537-542 MS (mass spectrometry). 281-302, 550-588 Mull, in IR spectroscopy. 459 Multichannel analyzer. 317, 319, 595. 603 electrode array detector, 707 emission spectrometers. 26(;-262 instruments, UV-visible. \ 353-354.30-361 photoelectric spectrometers, 271 Multidimensional NMR, 535-536 Multiplct peaks in NMR, 515-519 Multiplicity, 518 in internal conversion. 402 in intersystem crossing. 404 in NMR, 517-519 NAA.

Neutron activation analysis Nanoneedle electrode. 752 Natural line width. 220-221 Near-IR region. 455 Near·IR spectroscopy, 473-476 Nebulizer in atomic spectrometry, 224 -225. 256 in evaporative light-scattering detector, 826 Nernst diffusion layer. 726-727, 751 equation. 634, 640. 642. 644 calculation of half-cell potentials. 642, 643 effect of substituting Se e

c o n c e n tr a tio n

fo r a c tiv ity ,

644 with formal potentials. 645

in voltammetric concentration protiles,724 glower. 449 - 450 Network, computer. 103 -107 Neutralization titrations, hy coulometry. 709 N e u tr o n

a c tiv a tio n

a n a ly s is ,

918-924 in the John Vollman case, %4-965 Nichrome wire sources. 450 NfR spectrometry, 473-474 NIST standard-reference pH solutions. 691 Nitrogen-specific chemiluminescence detector, 800 NMR (nuclear magnetic resonance spectroscopy). 498-549 applications of. 528-537 sample cell. 523 spectrometers. 521. 526 theory of, 499-509 Noise. 126 chemical. Ill. 582 effect on spectrophotometric analyses, 343 -346 electrical. 1>,1>62 shot.III-Il2, U5, 191.206.344 signals and, UO s~urces of in instrumental analysis, III Noise-power spectrum, 115 Nondestructive methods. NAA. 921-922 Nonelectrical domains. 3-4.6.8-9, 81 Nonfaradaic current. 633, 742-743 Noninverting input. operational amplifier. 61-63. 1>9.74, 114.706 Nonlinear regression, 388 semiconductor devices. 43 - 44 Nonpolarizcd electrodes, ideal. 641-;-649 N o n r a d ia li\'c

t'\c ita tio n

147 Normal error curve, 976

9 1 > 1 '1 ,

p r o c e s s e -;.

973, 974.

N o r m a l-p h a s e

s c p a ra lH ..H 1 3 . ~ ,.. _ .

835.839 Notch filter. holographic, 179-180. 491-49~ Notehook, electronic laooratorY, 127-130 n p n transistors. 46 - , n n-type Si, 191>,199.311> Nuclear magnetic resonance spectroscopy. S e e NMR Nuclear Overhauser effect, 520,531 Nuclear quantum numhers, 499 Nuclei properties in NMR. 499-504 target. in NAA, 918-919 Null hypothesis. 984, 985 Nyquist frequency, 118-119.525 sampling theorem, 118-119,524 Off-resonance dccoupling. in NMR, 529-531 Ohmic potential drop, electrochemical cell, 647 Ohm's law,S. 26-27, 30, 31>.38. 39, 1>3.69.73 On-column laser fluorescence detection system. 879 One-tailed tests. 984 On,line operations. data collection. 92 pre-concentration. in MEKC, 883 Open tubular columns G c.

801

SFC, 859 Open-loop gain, 59. 1>4-1>5 Operational amplifier applications of. 74 to mathematical operations, 71. 73 to voltage and current control. 70

circuits, 62-1>3. 67. 1>9,73, 378.

706 difference amplifier. 69 functions, 71 output voltage. 706 properties of. 59-61 yoltage follower. 62 l.c n )-c r o s s in g

d e te c to r.

a to m iC

SrtX':Uq".,,~ .. ,.

in s tr u m e n ts .

c o m p o n e n ts

Oroitals in atomic spectra, 215 in charge-transfer complexes, 371 in K capture, 911 in molecular aosorption. 369, 370 splitting, 211> in valence band of semiconductors, 173 in X-ray spectra, 593, 598 Order of diffraction, 186 of interference, 139. 177 Organic solvents. effect on AA, 248 voltammctric analysis. 747-748 Oscillator anharmonic. 436 harmonic. 433 - 436 Output impedances, operational amplifier. 59 - 63 transducers, 6 Overtones, 436. 473-474,481> Overvoltage, 649 -652,697-700 Oxygen concentration. automated determination of. ' 1 4 k dissolved, 409. 730 determination of with Clar! electrode, 732 effect on fluorescence. 407

409 reduction of voltammetric wave. 730 voltammogram. 737 Ozone in chemiluminescence dete' of sulfur. 800 determination of. 424 Packed c o lu m n

7 -1 -

o f.

11>4-214 Optimization of column performance, 775-779

e k c tr o c h r o m a to g SK3

Packed

( ( o w illl/e d )

difference,

c o lu m n s in c o lu m n c h ro m a to g ra p h y .

810

methods, theory

Packings sizes of in Le, 817-818

reversed-phase,

829, 8 3 h

chromatography, circuits,

Partial

848

energy-level

Particle

Photocathode,

diagrams,

152,

distribution

analysis,

height

in G e ,

number,

954 828--836

measurements,

Photometers,

337

law, 158 209

IR from interference (photodiode

458

arrays),

196-197 33-34

voltage,

33, 39, 40

counting,

195,202,313,491,957

emission,

148-149

Photosedimentation

surface

methods,

590 computer,

Se e

Isoelectric

92-93 247, 760, 9_,2, 937,

Pixel,

663, 665

Planar

electrodes,

angle,

Planck's

constant,

143-144

Polychromatic

radiation,

146. 156,

976, 978

in lasers,

171 ~l72

971 deviation,

variance,

971, 981

clinical

971

analyzer,

iSTAT,

681-6S2

407

radiant, Beer's

in DSe,

- Raman

Ouantum Ouantulll

134

emission,

background

Radiationless

transitions, sou rces.

Radius,

methods, source~,

909-928 com m on.

9lO. 925

analytical.

in

activc

transitions.

functional 418

spectra, uf

group

microprobe. scattering.

Se e

e l1 ic ic n c )

properties

32:i

959, 962

Raman

absolutc.

144 -157

219, 404

fo r X -r a y

909

Radionuclides.

372 -374

Q u a n tu m

radiation.

148. 165, 17h

307

of lIV-

vield. 4114, 408. 423.

Ouantum-mechanical

191-201

transmitted.

575 -577

4lJ4-4118,

237

transducers,

Radiochemical

absorption

467

303, :i94

R a d iO is o to p ic

tripk,

efficiency.

absorption.

synchrotron.

methods.

828

486

4K6

115, 16:i, 166 -175

in atomic

Radioactivity.

MS. ';75

analysis.

lllso

law, 337

s p e c tr o s c o p y ,

in Zeeman

MS. 3(Xl

291 -2'12

applications

Quantitative

502

in R a m a n

R a d io a c tiv e

RBS.604

IR measurcment, 35

569, 575, 576

spectroscopy.

X-ray, 308

of radiation.

capacitor,

2112,

798

visihle

monochromator,

900 836

287-290,

spectrometers, Qualitative

plot of vs. temperature

reaction,

201

mass

in tandem

184-IS6

910-911

a charged

emission.

light -gathering,

Potential

ICp)

in XI'S, 592

1 7 S, 191 .. ,48, ,,50

correction. 243

transducers,

in lCP-MS.

m a lte r.

143, 486, 502

source,6g,

170-172

in GC/MS.

3 S6 ,

147-149

170, 172

analyzers.

146, I:iS

of. 132,204,315,

in NMR,

168-169,

178

of, 149 -152 of, units,

near-infrared.

317 -318

in LC/MS. beam

energy

393

742 -743,748

in glow discharge clement,

gain, 63

difference (s e e

699, 70l, 704,

Power, 63

electron

164, 310, 9lO

in te ra c tio n s o f w ith

726

c o n d iti()fis ,

917

selectors,

Quadrupole

in a resistive

139-140,

detector,

470,475

451

705, 730, 731. 757-759 dissipated

coherent,

polarized,

Pyroelectric

688

of. 152 -1:i5

of. 1.'2. 167,402,450

intensity

for, I h 6

P s e u d o -fIrs t-o rd e r

laser,

691-692 70-71,

absorption

emission IX 7

Pumping

curves,

of fluorescence

standard

182, 186

686 - 690

Potentiostat, 356

-lO X

2 3 1 -2 3 2

pH, 690

deviations

deviation,

zone.

energy,

titrations,

across

spectrometry

28

27

postcolumn

Plasma

53

659

calibration of

737

due to, 340-342, standard

Positron.

499 emission

716-719

716-717,

724 - 726, 728,

divider,

direct,

Polarography,

Portable

161-163.169,304.435,

685 - 690 33

of radiation,

175

flu o r e s c e n c e .

c o m h u s tio ll

analysis, recorders,

measurements, effects,

a h s o r p tio n .

157

132 -133

bands

Pulse voltammetry.

Potentiometric optical

mean, sample,

752

pH, 636, 670 Phase

voltage

in nonlinear

c h ira l s e p a ra tio n s . X () I

Primary

Prisms,

power.

Radiation,

v o lta m m e tr y ,

electrode,

67

648, 649, 651

697

Radiant

in flu u re s c e n c e .

Pulse-height

laboratory,

inNMR,533

P rc d is s o c ia tio n ,

P re p a ra tiv e

409

P ro lilL 's . c o n c e n tra tio n -d is ta n c e ,

997-](J(J()

140

static,

748

in ('c h e lle m o n o c h ro rn a ln rs .

Potentiometer

or molecules,

inversion,

198-199

932-933

697

- 486

dynamic.408-40tj

materials

of standard

Population

point

transducer,

a ls o

in electrolysis,

electrochemical,

Pooled

(s < 'C

electrode of, 641

in laboratory

958

618

941

meters,

analyzers, 5, 9, 81, 41 I

cell, 192-193

Piezoelectric

143,484

instrumental

66, 67,144,191-194

photovoltaic pI.

devices,

p-funetion,

146

184, 683, 733

pholotubes,

in spectroscopic

pump,

effect,

6hl

determination tables

839

144,652

in voltammetry,

in photoelectric

Phototransducer,

in ATR,472

Peristaltic

194

668

64 J, 645

649, 651

Photosedimentation,958-961

depth

Peripheral

(PMTs),

700

electrodes,

charge-transfer, kinetic,

tubes

Photoresist,

current,

curves,

132, 144

Photons,

Peak

in FlA,

titration

cells, h 3 3

417. 421

408. 421. 428

P re c o l1 c e n tra tio n

s te p . in s trip p in g

428

3 1 ::;

407-409,

collisional.

S O I -S 0 2

4m.404

potential)

index, 831-832,

of atoms

6h8

tu h e .

Ouenching,

l)O ()

o f n u c le u s .

408-409,

in G e ig e r

D S ('

2. tj·IO

P re c is io n c lo c k . X 5

660

at constant,

Standard

44 -45,48,50,54,·197,

Polarization,

354, 355

electrodes.

standard,

810

Polarizability,

of, 418-421

379-381 Photon,

fringes,

methods,

oscillator,

in glass electrode,

of reference

316

354-355

Photomultiplier

interferometer,

junction,

P r e c e s s io n .

10, gi

9. 87

Ouencher.

49-:i0

analysis.

in glass electrode,

52, 54

Polarity

Photometric

Penetration

pn

385. 397

386

columns,

supplies,

in s tru m e n ts ,

303

in e1ectroanalytical

rate, 382

146,194,597-598,

double-beam,

Path length in absorption

PLOT

194, 197,354,355

applications

of, 835 -837

735

oscillatur.

P o w e r -c o m p e n s a te d

633--647

of calomel

mole-ratio, -354,

4 -4

26

of a harmonic

electrolysis

initial

d io d e .

crystal.

microbalance,

m easu re-

ments.336

c ir c u its ,

tube,

boundary

698, 704. 709

continuous-variations,

384,

196,353

Photoluminescence

950, 958, 961

chromatography,

applications

PDAs

rotating,

635

Quartz

and

ah sorb an cL '

434

Plot

916

measurement,

energy,

in CY, 740

Plotters,

Photoelectrorts,

636,

in X-ray

Potentials,

in coulometrv,

488

351-352.

Photodiodes,

775,802

Beer's

194-195

491

953 -955

t.

in CE, 871

in Raman

spectroscopy,

950-963

effect of on plate

Partition

473

200, 451

arrays,

63

770

642-644,664,703

144, 191, 193,268

photodiode

determination,

electrodes,

in r e s is tiv e

in lr a n s m itta lll:e

thermoeouple,201

of chromatography,

Platinum

957-958

950

interval

414. 421

144 -145,

Photodetector,

850,

668

phase

a s e m ic o n d u c to r

8h9. 889

816-818,

859 - 860, 869 theory,

Photodecomposition,

size

analysis,

414, 417

spectra,

Photocurrent,

154,401

769-778,

of. 400 - 409

Photoconductors,

28-29

769, 771, 850.

height,

420-421

Photoacoustic

liquid-junction boundary,

count,

room-temperature, in, 773

a glass membrane,

259

[CP)

(s e e

Plale

409, 417, 421

low-temperature, sieves,

zone broadening

Parallel

411.

fo r m e a s u r in g .

measurements,

in LC, 821

spectrometers.

sources

417

8(K)-801

with molecular in SFC, 859

particle

source 15h

in s tr u m e n ts

7h3 in Gc,

Paper

33

Phosphorescence,

486 frequencies.

490, 493 484 - 4 8 S . 4 ,~ K

4g 1- 482. 485-- 486, 489 - 495

s p e c tr o m e te r s .

49 I

493

Raman spectroscopy, 143, 149, 481-498 biological applications of, 493 Random errors, 967-969, 971-975, 979,981,984,985 Rate constants for deactivation, 404 standard heterogencous, 742 equation, 383 theory, chromatography, 768 -772 Ratio depolarization, 486-487 mole, 385 - 386 Rayleigh lines, 482, 955, 956 scattering, 143, 482-491, 952-953 RBS (Rutherford backscattering), 603-604 R C circuits, 35-41 RDE (rotating disk electrode), 736 -737,749 Reactance capacitive, 34-38, 40, 723 inductive, 34 Reaction rates, 2, 382-383, 645, 650, 920 reversible, 722, 742, 744, 753, 754 Readout devices, 10,51,54 Reagent chemicals, 372 Reciprocal linear dispersion, 185-186,188-189 Reciprocating pumps, 820 Rectifiers, 44, 50, 446 Reduction, two-electron, 729-730 Reference beam, 241, 444, 446, 448, 458, 467,824 electrode external, 666 ideal, 660 internal, 666, 683 non polarizable, 697 potentials, 668 saturated calomel, 665 SHE, 636 silver chloride, 666, 674, 678, 689,731 junction, thermocouple, 201,452

material, standard, 19 spectrum, 418, 443 Rcflectance, 470, 475 Reflection gratings, 173, 181-184,309,358, 444 of radiation, 142 spectra in IR, 431, 470, 471, 477 total internal in optical fibers, 203 of surface plasmon waves, 604 Refraction of radiation, 141, 181, 182,185,186,458,471,478 Refractive index, 140-142, 177,179, 180,203,339,458,472, 604-606,823,825,885, 951,957,958 Refractive-index detectors, in LC, 825,826 Regression analysis, 11, 323 Regulators, 49, 51 Relative abundance, 581 areas, 519, 528, 597 standard deviations, 19, 110 of concentration, 343, 345 in counting, 914 Relaxation, 152,494 in Auger spectroscopy, 598 in fluorescence, 403 in lasers, 171 in MS, 551, 552, 554 in NMR, 503, 504, 506, 508 nonradiative, 155 processes, 155,368,503, 504, 506, 598 nonradiative, NMR, 503 in Raman spectroscopy, 485, 494 in UV -visible absorption, 368 Replicate analyses, 19 measurements, 967,970,973,979 Residual current 743 Residuals, in least-squares analysis, 12,99, 100,388 Resistance, 26 parallel, 29 series, 27 voltage divider, 28 Resistors, standard, 31, 32, 706

Resolution clements, in FT spectroscopy, 205

spectral, 188, 360 Resolving power chromatographic column, 768, 775 double-focusing mass spectrometer, 300 electrophoresis, 867 grating, 185 monochromator, 185, 218 Resonance lines, 219, 238, 240 Resonances, surface plasmon, 590, 604,605,733 Response current, 724, 744 in CV, 737 to step excitation, 725 voltammetry,717 time, 112,313 " Restrictor, 821, 857,858,863,804 in LC column, 821 in SFC, 857 Restrictor, SFC, 858 Restrictor, in SFE, 863 Retardation factor, TLC, 849-850 zero, interferometer, 211, 440, 441 Retention factors, 767, 768, 776, 779, 808, 832 effect on column resolution, 778 of solvent strength in partition chromatography, 831 and retardation factor in TLC, 850 in SFC, 858 indexes, 806, 807 times, 766. 781, 808, 846 and distribution constant, 767, 803 and resolution, 777 volumes, 788, 789 Reverse bias, 45. 46, 50,194,197 Reversed-phase chromatography, 829.830,833.836

Reversible reactions, currentvoltage relationships, 728 Ring current, 514 Ripple, 50 Rise time, 65, 74,112 Robotics, 943, 945 ROM (read-only memory). 91, 94 Rotational transitions, 432 Rowland circle, 261, 262, 265, 266, 595 RSD (relative standard deviation), 19, 1l0, 286, 706-708, 711, 715 Salt bridge, 630 SAM (self-assembled monolayer), 721,741 Sample atomization techniques, atomic spectroscopy, 230, 235 beam, IR, 446 injection systems, GC, 791 inlet systems, in MS, 564 introduction, continuous, in plasmas and flames, 224 photodecomposition of, minimizing, 362, 491 probe, 523 in NMR, 523 scanners, in STM, 616 s iz e s

in FIA, 933 reproducibility in GC, 791 standard deviation, 972 variance, 972 volume, effect on dispersion in FIA,936 zone, FlA, 934, 937, 939 Sample-illumination system, Raman spectroscopy, 488 Sample-injection systems, HPLC, 821 Sample-insertion technique, direct, 227 Sample-introduction methods, atomic spectroscopy, 223, 225, 227, 228 Sampling cone, ICP-MS. 291

frequencies, 118,745 loops, 821,933 picoliter, 872 rate, 102, 525 Sampling, NMR signal, 524 Sampling surfaces, 590 Sampling valve, 933, 934 Saturation of energy states, NMR, 503-504, 520 factor, neutron activation analysis, 920 Sawtooth wave, 42 Scalers, 86, 87, 317, 318 Scan coil, SEM, 608, 609 rate, 260, 576, 612, 737, 739, 746, 754 Scanning electron microscopy, 608, 613 probe microscopc (SPM), 613, 619,621, 753 tunneling microscope (STM), 614,615,617 Scattered radiation, 142 Scattering, 143 centers Mie,952 X-ray, 309 in LALLS, 951 of radiation, 142, 143 Raman, 481, 485 in spectroscopic surface experiments, 590 stray radiation, 341 X-ray, 309 SCE (saturated calomel electrode), 638,660-662,666,737, 738 Scintillator, 315, 611-613 SECM (scanning electrochemical microscopy), 753 Secondary absorption, fluorescence, 408 electrons, 195, 285, 315, 608, 610-612 fluorescent sources, X-ray. 311

Sedimentation FFF, 885, 886 Selection rules. 436,437, 4R5

Selectivity coefficients, 21, 22, 670, 671, 674. 680 factor. 768, 775, 776, 779, 806. 831 Self-absorption, 258, 268 SEM (scanning electron microscope),608-610, 612,613 Scmiconductor devices, 43, 48 Semiconductor diodes, 44, 45, 50, 174 Semiconductors, 26, 3 L 43 - 47, 168,173,174,191-193, 198-201,276,451,452, 592,597,604,607,683, 719 Semiquantitative analysis, 272, 292, 296,300, 320 Sensor array in i-STAT analyzer, 682 in vivo, 6R3 head, Mars rover, 319, 324 Sensors, 9, 10, 417, 683 fiber optic, 203 gas, 679 glucose, 733 immuno-, 734 LAPS, 760 in vivo, 683 Separation of anions, 871, 875, 880 chiral, R60, 883 ( s e e a ls o Chiral separations) electrochromatographic, 884 ion-exchange, 839, 875 ( s e e a ls o Ion chromatography) methods, 762 electrophoresis, 867 reversed-phase, 829, R33, 835 Separator, in FIA, 934 Separator, MS, 798 Sequential injection analysis (SIA), 939 Series circuit. 26, 27 Series R C circuit, 35. 37. 39, 40. 57 Server, network, 105 SFC (supercritical fluid chromatographv),857-862

I

SFE (supercritical fluid extraction), 862-865 SFG (sum frequency generation), 605,606 Shielding for noise reduction, 114 of nuclei, NMR spectroscopy, 514 Shutter, 158, 159,241,351,353,354 SIA (sequential injection analysis), 939,940 Sieves, molecular, 790, 810 Sign convention, electrode, 639, 640,686 Signal analog-domain, 6, 7 background, 84, 89 dark, 365 digital, 81, 87, 93, 95 frequency-domain, 120,207,499, 505,508,521,541,572 integration, in NMR, 525 interferogram, 209, 210 laser, in interferometer, 440 logic-level, 7 low-frequency, 85 measuring, 85 modulated, 115,208,240,448 power, in time-domain spectroscopy, 206, 208, 209 processors, 348 in optical instruments, 202 in X-ray instruments, 313, 317 radio-frequency, in FTMS, 572 sampling, in FTIR, 440 shaper, 84, 87 sinusoidal, 74,116,117 source, in voltammetry, 718 staircase, 742, 744 Signal-to-noisc ratio, 110, III enhancement, 113, 123 Silicon photodiode transducers, 194 Silver chloride electrode, 637, 661, 662, 666,689,718 electrode, 628, 630, 639, 643, 644, 662,663,703 SIMS (secondary-ion mass spectrometry), 602, 603

Simultaneous multicomponent determinations, 361 Sine waves, 33, 34, 5ms, 956 mathematical description, 135 superposition, 137 Single-beam computerized spectrophotometers, 358 grating instruments, 357 instruments, 240, 241, 351 for atomic spectroscopy, 240 effect of mismatched cells, 343 for molecular absorption measurements, 351 advantages, 358 Singlet state, 216, 400-402, 411 excited, 216, 400, 401, 405 Size distributions, measuring, 951, 955,961 Size-exclusion chromatography, 844-847 applications of, 847, 848 Slew rate, 65, 76 Slit, 137 widths in array spectrometer, 197 choice of in monochromator, 189 effect on resolution, 188 Slope, 12, 14, 19,20,986-988,992, 993 least-squares, 992 Slurry, 224 Smith-Hieftje background correction, 244 Smoothing of data, 92, 102, 117, 120,122,123,414 Snell's law, 141-142 Solid samples, 227 direct analysis of with electrothermal atomizers, 235 of in glow discharge MS, 300 introduction in atomic spectroscopy, 224, 226 in glow discharge MS, 3(K) in LlBS, 276 in IR spectroscopy, 458

in mid-IR spectroscopy, 469 in NJR spectroscopy, 475, 476 NMR spectroscopy, 526 in Raman spectroscopy, 489 in SEM, 608 in surlace spectroscopic methods, 590 in X-ray spectrometry, 326 Solid-state crystalline electrodes, 673 Solution absorbing, 158 resistance, 746, 869 Solvent strength, 831, 833, 835, 841, 863 effect on retention factors, 831 Source flicker noise, 279, 346, 365, 419 intensity fluctuations, compensation, 348, .4IS radiant power, 413, 418, 419· radiation, monochromatic, Beer's law, 340 temperature, 237, 576 Sources constant-voltage, 59, 70 continuum, 167, 168,211,242, 249,349,413 current, 31, 63, 64, 708, 712 desorption, 558, 560 deuterium, 349, 36J electron, SEM, 608 electron-impact, 552, 557, 558 excitation, 247, 250, 413, 488, 495, 496 glow-discharge, 228, 273, 300 spectroscopic, 167 Spark ablation, 227, 266 SOurce mass spectrometry (SSMS), 299, 300 Sparks high-voltage, in emission spectroscopy, 269, 272 radio-lrequency, in MS, 299, 300, 583 Spatial resolution of analytical techniques, 625

high in Auger spectroscopy, 599 laser microprobe MS, 604 in MS, 294 inSEM,611 Species, unretained, 766, 777, 833 Spectra alpha-particle, 916 atomic absorption, 153 emission, 150 derivative, 378 electron-impact, 554, 555, 557, 581 high-resoluiion in electron spectroscopy, 594 NMR, 509, 526 in Jep, 291 in JR, 431 in MS, 281, 300 plasma, 257 from plasma sources, 266 product-ion in MS, 574 proton NMR, 510, 524, 529, 532 soft-source in MS, 552 inXRF,323 Spectral lines, 269 Doppler broadening, 221 folding due to undersampling, 525 widths, 220 Spectrochemical measurements, quantitative aspects, 157 Spectrofluorometers, 204, 411-413, 415,417,825 components, 413 Spectrograph, 204, 261, 270, 271, 353,361,491 Spectrometer, 196, 197,204,260, 261,264-266,271,272, 318,319,324,325,361, 487-490,522,523, 562-566,576,590,603, 604,622,623 energy-dispersive X-ray, 317, 324, 328,607 high-resolution gamma ray, 917 NMR,521 tandem-in-time mass, 576

Spectrometric methods, 132, 162 optical, 215, 281 Spectrometry, 132 Spectronic 20, 357, 358 Spectrophotometers, 73, 182,204, 213,235,240,310,344, 348,349,351-354,356 array, 353, 378 computer-controlled, 351 designs, 352 detector in F1A, 933 dispersive 1R, 438, 439, 444, 445 double-beam, 240, 351, 359 near-JR, 344,430 single-beam, 351 single-beam computerized, 358 typical, 354 Spectrophotometers, X-ray, 310 Spectrophotometric analyses cleaning and handling of cells, 375 effects of instrumental noise on, 343, 345,347 quantitative by absorption measurement, 375 standard additions, 376 kinetic methods, 381, 383 observation cell, stopped-flow, 384 studies of complex ions, 384, 385, 387,389 Spectrophotometry derivative, 378 dual-wavelength, 378, 379 Spectroscopic data analysis, software, 99 instruments, 168 construction materials and wavelength selectors, 166 detection systems, 792 sources and detectors, 167 transducers for. 191 types, 351 surface methods, 589, 590 Spectroscopy electrochemical impedance, 723 electron energy-loss (EELS), 591,592

frequency-domain, 206 high-resolution with lasers, 168 laser-induced breakdown, 274, 276 mid-lR, 459, 474 molecular, 131, 132,166,335,477 photoelectron, 592 vibrational sum-frequency, 605 Spectrum Auger, 600 band, 152 computer search system, 464 continuum, 168,257,304,349 derivative, 378, 379 deuterium lamp, 349 diode array, 361 electromagnetic, 134 electron, 597 electron-impact, 557, 558, 581, 587 emission, 150 energy-dispersive, XRF, 317 far JR, 450 fingerprint region of fR, 464 fluorescence, 412 hard-source, MS, 552 JR, 430, 431 of water, 456 mass, 551 of a mixture, 376 near-JR,473 NMR, 499, 505 carbon-13, 529 fluorine-19,534 product-ion, 574 Raman, 481, 490 spark source, 299 synchronous, luminescence, 410 TOF-MS,560 tungsten lamp, 350 X-ray ahsorption, 325 photoelectron, 592 XRF. 309 atomic mass, 294 X-ray, 304 Spin decoupling, 520, 5,12

I

Spin ( c o n lin u e d ) quantum number, 499, 500, 502, 529,534,542 Splitting patterns NMR, 519, 526 Zeeman effect, 243 Spreadsheet applications, 95 Square-wave voltammetry, 717, 742-744,753 excitation signal, 744 Standard deviation 967, 969, 971-976,978,980-984, 986-988 of counting data in radiochemical analysis, 914 as measure of column efficiency, 770 pooled, 976, 978 population, 971-972 sample, 972 of transmittance, 343 Standard electrode potentials, 640, 641,644,645,686 Standard-addition method, 13-15, 248,375,376,427,688,746 Standard less analysis, 323 Standards, in calibration, 11, 17 States, virtual, 495, 606 in laser media, 171 in Raman spectroscopy, 482, 484 Stationary phase, 762 chiral, 806, 837 Statistical treatment of random errors, 971- 983 Stator, motor, 53 Stern- Volmer equation, 408, 409 - Stokes diameter, 959, 960 equations, 959 shift, in Raman spectroscopy, 484 Stopped-flow methods in FIA, 937 in kinetic methods. 384 Stray radiation, 341, 348, 443 effects of, 348, 469 Stretching vibrations, 432 mechanical model of. 433 Stripping analysis. 748, 749, 754 Substrate, 178,425,677

biosensor, 733 concentration, 382 enzyme, 382. 425, 681 in holographic fitters, 179 for microfabricated columns, 809 in SEM, 753 semiconductor, 48,199 Cm.198 ISFET, 676 Sulfur chemiluminescence detector, 798,800 Sum of squares of residuals (SSR), 99,100,390 Sum-frequency generation, 605, 606 Summing points, 64. 71. 72 Supercritical fluid chromatography and extraction, 763. 856 -864, 866 fluids, 763, 856, 857, 961 Superposition, 136-138, 156, 173, 443 of vibrational transitions. 369, 373 Supporting electrolyte, 704, 718, 720, 722, 724, 746, 747 Surface analysis, special techniques, 604 characterization by spectroscopy and microscopy, 589, 590, 592, 594, 596, 598, 600, 602,604,606,608,610, 612,614,616,622,623 composition, 274, 301,590,598 concentration, 650, 727, 728, 738, 741 electromagnetic waves, 604 functionalized, 721 photocathode, 146. 194 photoemissive, 191, 193 photon spectroscopic methods, 605,606 spectroscopic techniques, 591 techniques, ion spectroscopic, 604 Surface-enhanced Raman spectroscopy (SERS), 495 Surfactants, in micellar electrokinetic chromatography. 882

Switching potentials, in CV, 738, 739 Synchronous demodulator, 117 Systematic errors, 13, 17, 19,967, 969-971,984,985 Table, circular rotating sample, 943 Tailing of chromatographic peaks, 769,788,829,849 Tandem mass spectrometry, 573, 575,576,582,584,800, 828,947 Tapping mode, AFM, 618 Tartar relation, 624, 625 TCD (thermal conductivity detector), 794, 795 Temperature absolute, 221, 222, 501, 957 compensation, automatic in ion meters, 685 critical, in SFC, 856 glass transition, 904 measurement, with operational amplifier, 69 profiles flame, 232 graphite furnace, 234 programming GC, 791, 792 SFC,858 TGA (thermogravimetric analysis), 894-897,906 applications of, 897, 907 Theoretical plates, 769 Theory of IR absorption spectrometry, 431, 433, 435,437,438 Thermal analysis, 894, 904, 907, 908 differential, 897, 899 methods, 900, 907 techniques, 894, 908 conductivity detectors, 794, 823, 825 detectors, 201, 344, 451 methods, 894, 896, 898, 900, 904, 906.908 neutrons. 918, 919. 922, 927, 928 noise, Ill, 112,191,201,451,452, 795

transitions. in TGA. 899 Thermionic detectors, in GC, 796 Thermocouple detector circuits. 201 Thermocouples, 67, 167, 20l as lR transducer, 452 as radiation transducer, 201 as transducer in thermal methods, 896 Thermogram, 894, 896, 899-901 Thin-layer chromatography (TLC). 848-851 applications of, 848, 850 Three-level systems, 171. 172 Time constant, 36 Time-domain signals, 7 high-frequency, 209 spectra, 206, 207 Time-of-flight, mass spectrometer, 283,290,560,569,576,828 Titration curves coulomctric, 708, 714 photometric, 379, 380 voltammetric, 736 Titrations, 11 ampcrometric, 734, 735 photometric, 380 spectrophotometric, 379, 380 TMS (tetramethylsilane), 512-514 Torch, lCP, 255-257 Tracers, 299, 909, 924 Transducer elements, in array detectors, 196 -198, 262, 263, 265, 287 signals, amplification and measurement of, 65. 67, 69,70,73 Transducers. 5, 9, 10,291 electrochemical in biosensors. 679 gas-tilled, 313-315, 607 ideal, 191, 20l infrared, 201, 209 multichannel, 196. 594 photoconducting for [R. 451 photodiodc, 354 photoelectric. 158. 191, 192. 204 ph_oton. 191, 192, 287

piezoelectric. 616 semiconductor for X-rays, 313. 316 voltammet ric, 7.11 Transistors, 46, 48 Transition energies, electronic. 237 metal ions absorption hy, 374 spectra, 370 probability, 367, 404, 405 Transmission, 140, 177 of electromagnetic radiation, 132 Transmittance, 157 measurement of. 158,205,336, 441 reading, 358 Triplet state, 216, 400, 409. 411 in phosphorescence, 156 Triton X-I00. nonionic surfactant, 862 Tunneling current, in STM, 615, 617 quantum mechanical, 600 Two-dimensional multichannel electron detectors, 595 spectrum from echelle spectrometer, 186, 198 NMR, 535, 536 Two-tailed test, 984 Ultraviolet, 164 detector, 9 electronic excitation, 368 grating, 182 photoelectron spectroscopy (UPS), 592 radiation, spectrophotometric measurements with, 372 species that absorb, 367 spectra, 372, 373, 526 Ultraviolet-visihle molecular absorption spectrometry applications of. 367, 398 introduction to. 336, 366 Uncertainties. 344, 583. 975. 980. 982,983,985,986 in analyzing mixtures, 377, 378

in chromatographic measurements. concentration. 346 in coulometry, 697 counting, 85

70S)

in c u rre n t. v o lta g e , a n d rc s is ta n c c

measurements, 30 electrode calibration. h 8 7 in frequency of radiation, no in high-resolution mass spectrometry. 578 in junction potentials, hhO.687 least-squares, 12. 13,924 in pH measurements, 684 sample positioning, 346 spectrophotometric. 343 - 345 wavelength, 375 in X-ray analysis, 320 Uncertainty principle, 156, no Unit operations, 929, 931, 940, 942, 943 U rea nitrogen, determination. 681, 947 UV absorption detectors, in liquid chromatography, 824 UV -visible absorption detectors, in liquid chromatography, 823 molecular absorption spectrometry, 367 region, 185, 341 Vacuum phototuhes, 144, 193, 194 ultraviolet region, 369 Valence electrons, 43, 44, 173, 175, 368,596 Valinomycin, ionophore, 674, 675 van der Waals interactions, 863 van't Hoff equation. 908 Variance, 967, 972, 981, 982, 985 Variation, coefficient of, 972 Vectors electric field, 133, 143 impedance, 39 magnetic moment. 505 in NMR. 502 rotating, 33 Velocity electrophoretic migration, 870

I

Velocity ( c o n t i n u e d ) linear in LC,850 mobile phase, 766, 771, 772, 774,850 in SFC, 860 solute, 771 of radiation, 134, 141 Vibrational energy, 403, 437, 492 levels, 154,402,432, 435 in lasers, 169 frequency, 434, 435, 482, 485 molecular, 431 natural, 432, 434 interactions, 433 levels, 152, 155, 156, 169,368, 402-405 excited state, 152 ground state, 152 lowest, 152, 402, 405, 494 in Raman spectroscopy, 484, 494 modes, 437,438,486 IR and Raman activity, 485, 486 in resonance Raman bands, 494 quantum number, 433, 435, 436 relaxation, 156,401-403,426 states, 149, 152, 154, 155 transitions, 149,369,373,605 Vibrational-rotational transitions, 432 Vibrations bending, 433, 437, 438, 460, 476 low-frequency, effect on fluorescence intensity, 406 molecular, 432, 433, 435, 436 Vinland map, 493, 624-626 Visible radiation, absorption, 367, 368 Voltage breakdown, 46, 50, 51 divider, 27,28, 43, 701 in OMM, 31 follower, 62, 63, 65, 67, 71, 75 in instrumentation amplifier, 114 step response of, 65 use in pH meters, 684 instantaneous, 33, 36, 40

radio-frequency, 289, 570 regulators, 50, 51 signal, 83 sinusoidal ac, 37 source, 30, 31,62 loading, 62 standard, 70, 71 stable reference, 51, 53 ( s e e a ls o Zener diode) stopping, 144, 145 Voltage-measuring device high-impedance, 67 in potentiometry, 687 Voltammetric electrodes, commercial, 719 measurements of hydrogen peroxide, 733 linear-scan, 718 techniques, classical, 716 Voltammetry, 716-720, 722, 724, 726,728-730,732,734, 736,738,740,742, 744-748,750-754,756 adsorptive stripping, 750 applications of, 746-748 cyclic, 737-739, 741, 742 differential-pulse, 742, 743, 753 organic, 747 square-wave, 717, 742-744 Voltammograms, 721, 722, 728-730 FT,745 cyclic, 745 differential pulse, 743 effect of pH on, 747 equation for, 728 with microelectrode, 753 for mixtures, 729 for revcrsible systems, 736 ring-disk, 737 square-wave, 743 stripping, 748 Voltmeter, 30, 32 Volume fractions, method of continuous variations, 385 transmission hologram, 179 Walls, accumulation, 884-887 Wave properties of electromagnetic radiation, 133, 135, 137, 139.141,143

Wavelength calibration in absorption spectrometry, 350 maximum, LED. 350 range dye laser, 173 edgewidth,180 laser diode, 174 spectrophotometers, 357 X-ray crystal, 312 X-rays, 303 reproducibility in FT, 205, 474 resolution in FT, 205 selection, 351, 357, 411 with filters. 176 in fluorescence spectrometry, 413 mters,879 X-ray, 325 selectors, 164-166,175-177,179, 181,183,185,187, i89, 487 in AA, 237 . in molecular luminescence, 418 in Raman, 487 in UV-visible, 348 separation in grating monochromators, 181 Wavelength-dispersive systems, XRF,319 Wavelengths function of, absorption spectra, 153 of, derivative spectrometry, 378 of, ellipsometry, 607 of light Oebye scattering, 952 in microscopy, 608 of maximum absorption, 220, 341,356 multiple in multivariate calibration, 13, 389 Wavenumber, 134, 457 range in IR, 430 relationship to frequency of an interferogram,209 shift, 482, 483 Waves amplitude, 133 electromagnetic double-slit diffraction, 139 interaction with matter. 132

nonlinear effects, 175 polarization, 143 superposition, 136 mathematical description, 135 particle behavior, 132 superposition of, 136 surface plasmon, 604, 605 voltammetric, 722, 747 WCOT columns, 801 Wedge, interference, 177 Weston cell, 56, 78 White noise, 112 Wide-line spectra, 509 Wien displacement law, 160 Windows, examination, 263 Wire anode, 193, 314 Witness, 129,964,965 Word, in computers, 91 Work function for electron spectrometer, 593 photoelectric effect, 146 Working curves ( s e e Calibration curves) electrode, 716 block, 731, 732 fixed, 723 platinum, 704 Workstation, 105 Xenon arc lamp, 152,351,413,415, 417 X-nucleus coil, 524

XPS (X-ray photoclectron spectroscopy) electron, 622 instruments, 594, 595 spectra, 596, 597, 599 X-radiation, 305-309, 312-316, 325,916,917 emission of, 149,309 monochromatic, 592 X-ray, 303 absorption analysis, 312 applications, 325 measurements, 329 peaks, 325 spectra, 307, 308 total sample, 323 detector, 313, 319, 608, 609 diffraction, 309, 310, 325, 626, 904 emission, 303, 319, 324, 325, 328, 607,610,911 results, 911 spectrum, 150, 151,317 fluorescence, 303, 317-319, 322, 324,325,590,598,599, 608,611 detection system, 624 energy-dispersive instrument, 318 measurement, 321 methods, 317, 319, 321, 323-325

wave len gth -dispersive spectrometer, 318 line spectra, 151, 304, 305 monochromators,312 photoelectron spectroscopy, 592 spectrum, 593, 597 sources, 303, 310, 316, 318, 594, 596 monochromatic, 595 spectrometers, 311, 313 energy-dispersive, 607 spectroscopy, energy-dispersive, 317 transducers, 313, 314, 317 tube, 303, 304, 306, 309-312, 317-319,326-328,594, 599 XRF (X-ray fluorescence), 318, 323 Zeeman effect, 220 background correction, 244 instruments, 243 Zener breakdown voltages, 46 diodes, 50, 51 Zone electrophoresis, 880 profile, FlA, 935 Zwitterion, 880

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