Nanomaterials Theory Problems and Solutions [2 ed.]

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( CONTENTS) c hapter 1: Introdu ction

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1 Introduction ............................. ............................................................. l 2 Importont d iscoveries in na nom a terlals ................................................. 4 3 Basic physical principles a nd quantum effec ts ................................... ... .7 4 Synthesis ......................... .....................................................................8 s Characterization .......... ......................... .................................................8 6 Effect of size on various physica l properties ....................... ... .................9 7 Applications of the nanomaterials .. .... .......................... ............. ........... 12 8 About the book ............................ ......................................... ............... 14 Chapter 2 : Nanoscale Systems

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1 Introduction .... ... ..... ... ................................. ..... ....... ............................ 18 2 Length scales in physics ... ................................... ......... ....................... 20 2.1 Plan ck 's scales in physics .... .. ................................ ..... ...................22 3 Nanostructures ..................... .. .. ...... ............................... ... .................. 23 3.1 Zero dimens ional nanostruc tures ... ......... ......................................25 3.2 One dimen s ional nanostructures .... ....... ........... ..... ........................26 3.3 Two dimension al nanostruct ures......... ............... ........................... 27 3.4 Three Dimen sional Nanostructure Materials ...... ............. ...............29 3.5 Nanodots............. .... .... .... ... ...................... ...... ...... ......... ................ 30 3.6 Thin Films.................... ........................................ ............. ..... .......3 1 3.6 .1 Applications of thin films .......................................... ............ 32 3.7 Nanowires ............................................................................ .. .... ... 33 3 . 7 . 1 Nanowire Size ............ ............... .............................. ........ ..... 3 4 3 .7.2 Quantum mechanical effects......... ............ ............................34

3. 7.3 Nanowire conductivity.............. ....... ..... .. .... .. .. ....................... 34 3.7.4 Applications of nanowire .............................. .. ... .................... 35 3 .8 Nanorod s ........................... . .............................................. ... ...... ... 37 4 Band Structure of m aterials at nanoscale ......... .... ................ ............ .. .42 4.1 Single crystal, polycrystal a n d amorphou s materials ......... ... ........ .43 4 .2 Band structu re of single crystal m aterials .. .................................. .44 4 .3 Band structure of a one dimensional ch ain of atoms .....................45 4 .4 Band gap of n anomaterials .. .......... ......... ............. ... .......................48 5 Density of States of materials at nanoscale ......................... .................49

S. l Density of Stntt's in H :in uniform solid material.. .......................... 50 5.2 Dens ity of Stuks in a 20 uniform solid material ............................ 53 5.3 Dt'nsity of Stulo 0 8 big ns t ho original proton.

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Nanoma.terials: Theory Problems and Solutions

Nanoscale Systems

The Mesoscopic sea.le is the length at which quantum mechanical behaviors in Uquids or solids can be describxist in various historical ac10"4m Olametet ol red blood eel tivities of human society. Some 10'4m of the evidences are the discov_ _ _.,.. VlsJble light wavelengths ery of multiwalled carbon nanJ()-'m otubes (MWCNT) within swords Intel's newest transistor fabricated with Damascus steel in IO"'m around AD 500, their presence witlliu stained glass paints, an