Nonlinear Dielectric Phenomena in Complex Liquids 1402027044, 9781402027048

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Nonlinear Dielectric Phenomena in Complex Liquids

NATO Science Series A Series presenting the results of scientific meetings supported under the NATO Science Programme. The Series is published by IOS Press, Amsterdam, and Kluwer Academic Publishers in conjunction with the NATO Scientific Affairs Division

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IOS Press Kluwer Academic Publishers IOS Press Kluwer Academic Publishers IOS Press

The NATO Science Series continues the series of books published formerly as the NATO ASI Series. The NATO Science Programme offers support for collaboration in civil science between scientists of countries of the Euro-Atlantic Partnership Council. The types of scientific meeting generally supported are “Advanced Study Institutes” and “Advanced Research Workshops”, although other types of meeting are supported from time to time. The NATO Science Series collects together the results of these meetings. The meetings are co-organized bij scientists from NATO countries and scientists from NATO’s Partner countries – countries of the CIS and Central and Eastern Europe. Advanced Study Institutes are high-level tutorial courses offering in-depth study of latest advances in a field. Advanced Research Workshops are expert meetings aimed at critical assessment of a field, and identification of directions for future action. As a consequence of the restructuring of the NATO Science Programme in 1999, the NATO Science Series has been re-organised and there are currently Five Sub-series as noted above. Please consult the following web sites for information on previous volumes published in the Series, as well as details of earlier Sub-series. http://www.nato.int/science http://www.wkap.nl http://www.iospress.nl http://www.wtv-books.de/nato-pco.htm

Series II: Mathematics, Physics and Chemistry – Vol. 157

Nonlinear Dielectric Phenomena in Complex Liquids edited by

Sylwester J. Rzoska Department of Biophysics and Molecular Physics, Institute of Physics, Silesian University, Katowice, Poland and

Vitaly P. Zhelezny Odessa State Academy of Refrigeration, Odessa, Ukraine

KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW

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1-4020-2704-4 1-4020-2259-X

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TABLE OF CONTENTS

Introduction

ix

Photograph of participants

xii

List of participants

xiii

Part I: Basics for nonlinear dielectric and related studies in liquids Anomalous expressions for the nonlinear harmonic components of the electric polarization. J.-L. Déjardin

1

Theory of anomalous dielectric relaxation W. T. Coffey

19

Rotational brownian motion and nonlinear dielectric relaxation of asymmetric top molecules in strong electric fields: the langevin equation approach Yu. P. Kalmykov

31

Experimental solutions for nonlinear dielectric studies in complex liquids M. Górny and S. J. Rzoska

45

Comments on nonlinear dielectric effect measurements in liquids S. J. Rzoska and A. Drozd-Rzoska

55

Effect of constraints on electrostriction C. M. Roland and J. T. Garrett

57

Douglas Kell comments on ‘methodology’ during the workshop D. B. Kell

61

A new technique of dielectric characterization of liquids N. T. Cherpak, A. A. Barannik, Yu. V. Prokopenko, T.A. Smirnova, and Yu.F. Filipov

63

v

vi Nonlinear dielectric losses and dynamics of intrinsic conductivity of dielectrics

77

Part II: Nonlinear dielectric and related problems in critical liquids Dielectric properties of critical conducting mixtures K. Orzechowski, M. Kosmowska

89

Nonlinear dielectric effect behavior in a critical and near-critical binary mixture. A. Drozd-Rzoska

101

Electric field effects near critical points A. Onuki

113

Critical phenomena in confined binary liquid mixtures A.V. Chalyi, K. A. Chalyi, L. M. Chernenko and A. N. Vasil’ev

143

Model of the critical behavior of real systems D. Yu. Ivanov

153

The methods of prediction of the properties for substances on the coexistence curve including vicinity of the critical point. Vitaly P. Zhelezny

163

Phase equilibrium in complex liquids under negative pressure A. R. Imre, A Drozd-Rzoska, T. Kraska, K Martinás, L. P. N. Rebelo, S. J. Rzoska, Z. P. Visak and L. V. Yelash

177

New approaches to the investigation of the metastable and reacting fluids P. V. Skripow, S.E. Puchinskis, A.A. Starostin, D. V. Volosnikov

191

Part III: Nonlinear dielectric results for liquid crystalline materials The discontinuity of the isotropic – mesophase transition in n-cyanobiphenyls homologous series from 4CB to 14CB. Nonlinear dielectric effect (NDE) studies. A. Drozd-Rzoska

201

Influence of pressure on the dielectric properties of liquid crystals S. Urban and A.

211

vii Frequency
domain nonlinear dielectric relaxation spectroscopy Y. Kimura

221

Phase behavior of perturbed liquid crystals S. Kralj, Z. Kutnjak, G. Lahajnar, M. Svetec

231

Edge dislocations in smectic
a liquid crystals M. Ambrožič , M. Slavinec, S. Kralj

241

Part IV: Nonlinear dielectric and related studies for supercooled/superpressed and polymeric liquids A schematic description of the dynamics of glass transition by the coupling model K. L. Ngai

247

Transient grating experiments in supercooled liquids. A. Taschin, M. Ricci, R. Torre, A. Azzimani, C. Dreyfus and R. M. Pick

259

Medium
range ordering in liquids appearing in nonlinear dielectric effect studies J. Zioo, S. J. Rzoska, A. DrozdRzoska,

269

The cooperative molecular dynamics and nonlinear phenomena C. A. Solunov

275

Annihilation response of ortho
positronium probe from positron annihilation lifetime spectroscopy and its relationships to the free volume and dynamics of glass
forming systems J. Bartoš, O. Šauša, J. Krištiak

289

Influence of molecular structure on dynamics of secondary relaxation in phthalates, S. HenselBielowka, M. Sekula, S. Pawlus, T. Psurek and Marian Paluch

307

Electrostriction and crystalline phase transformations in a vinylidene flouride terpolymer C. M. Roland, J.T. Garrett and S. B. Qadri

319

viii Part V: Nonlinear dielectric studies for biologically and environment relevant materials Self-assembly and the associated dynamics in PBLG-PEG-PBLG triblock copolymers P. Papadopoulos and G. Floudas

327

Nonlinear dielectric spectroscopy of biological systems: principles and applications D. B. Kell, A. M. Woodward, E. A. Davies, R. W. Todd, M. F. Evans and Jem J. Rowland

335

Measurement method of electric birefringence spectrum in frequency domain, T. Shimomura, Y. Kimura, K. Ito and R. Hayakawa

345

Melting/freezing in narrow pores; dielectric and EPR studies G. Dudziak, R. Radhakrishnan, F. Hung, K.E.Gubbins

357

Electrodilatometry of liquids, binary liquids, and surfactants M. Rappon, R. M.Johns, and Shih-Wei (Erwin) Lin

367

Influence of strong electric field on dielectric permittivity of polycrystalline ice doped by small amounts of NAOH A. Szala, K. Orzechowski

379

interaction in ACF: EPR study

387

ix INTRODUCTION In the last decade the new physics of complex liquids, associated with the search for universal patterns in such distinct systems as liquid crystals, polymer solutions, critical mixtures, bio-liquids etc, has emerged. Self-assembling, dominant role of mesoscale structures, complex dynamics, unusual phases and enormous sensitivity to perturbations are among the significant features of complex liquids. Extending the definition proposed by F. Yonezawa et al. [The Physics of Complex Liquids, World. Sci. Pub., Singapore, 1998], complex liquids may be classified into the following categories: 1 Complex liquids whose complexity originates from specific external conditions, for instance: a. “High density liquids ”, such as liquids under high pressure or supercooled b. “Low density liquids”, such as liquids under negative pressure (stretched liquids), liquids in a random surrounding (pores etc,..) or in the form of scattered clusters. c. Liquids under anisotropic external field, such as liquids under strong electric field or under shear flow. d. Liquids near a critical point, including spinodal, multicritical, etc. points. 2. Complex liquids whose complexity is associated with their structure, such as liquid crystals, polymeric liquids, bio-liquids, micellar solutions, etc..

A rich set of fluid mesophases associated with continuous or weakly discontinuous phase transitions is also a common feature of complex liquids. Hence, it may be expected that their properties are dominated by critical-like, pretransitional phenomena. Surprisingly, the application of the modern physics of critical phenomena may be puzzling. For instance, in the majority of monographs on the physics of liquid crystals the isotropic–nematic transition is presented as the best example of a simple mean-field description. However, recent studies point to a tricritical, “fluidlike” behavior associated with “glassy” dynamics. It is noteworthy, that the “glassy” dynamics, which is the basic feature of supercooled liquids is one of the most challenging fields in modern materials science. One may expect that the “glassy” dynamics may appear as model description for the whole category of complex liquids. In the last decades, an essentially new insight into the properties of complex liquids was possible due to the technical progress in broadband dielectric spectroscopy (BDS). The unique feature of BDS is associated with the possibility of testing relaxation processes extending in an extraordinary timescale range. Nowadays, BDS seems to have reached technical maturity. However, understanding properties of complex liquids remains far behind. It remains puzzling even for liquids so extensively studied as the supercooled ones. Hence, the application of novel research methods may be essential for progress in this field. Since mesoscale, bond-ordering structures are an inherent feature of complex liquids, research methods directly coupled to them seem to be of particular importance. One may include here the transient grating Kerr effect, dynamic light scattering, nonlinear dielectric effect, dielectric hole-burning spectroscopy and the novel state-of-the-art analysis of broad band dielectric spectra. An example worth stressing is the nonlinear dielectric effect

x (NDE), which may be treated as a natural extension of the BDS. NDE describes changes of dielectric permittivity due to the application of a strong electric field:

where respectively.

are dielectric permittivities in strong and weak electric field E, is the experimental measure of the non
linearity called

nonlinear dielectric effect (NDE). The relevant history of NDE began 80 years ago when Arkadiusz Piekara, at that time a school teacher in Poland, conducted the first ever measurement of static dielectric permittivity and NDE near the critical point in nitrobenzene
hexane mixture [A. Piekara, 1932, Phys. Rev. 42, 445
447 and A. Piekara, 1936, C. R. Acad. Sci. Paris, 203, pp. 1058
1059]. For NDE he noted “a very strong increase on approaching the critical consolute point” in the homogeneous phase. The explanation of this phenomenon was not possible until the nineties, when the physics of critical phenomena and the quasi
nematic ordering induced in the mixture by a strong electric field were taken into account [S. J. Rzoska et al.: Phys. Rev. E 50 (1993)]. At present there are several experimental techniques applied for NDE measurements. They give insight into the properties of critical binary liquids and homogeneous liquid crystals (Polish groups), polymeric films and ferroelectric liquid crystals (Japanese groups) and bio
liquids (UK groups). The main aim of the ARW NATO “Nonlinear dielectric phenomena in complex liquids” 10
14 May 2003, held in Katowice
Jaszowiec (Poland), was the first ever discussion
meeting of researchers interested in nonlinear dielectric phenomena in complex liquids. Particular attention was paid to the nonlinear dielectric spectroscopy (NDE). Its limited use so far is related to enormous technical problems encountered. Therefore the workshop was particularly well timed due to just emerging possibilities of constructing the first ever, user
friendly, nonlinear dielectric spectrometer, giving insight into time
scales relevant for complex liquids. Researchers from almost all existing groups associated with the nonlinear dielectric spectroscopy and its related methods took part in the meeting. Discussions were focused on the following items:

1. 2. 3. 4. 5.

Basics for nonlinear dielectric and related studies in liquids Nonlinear dielectric and related problems in critical liquids Nonlinear dielectric results for liquid crystalline (mesogenic) materials Nonlinear dielectric and related studies for supercooled/superpressed and polymeric liquids Nonlinear dielectric studies for biologically relevant materials

The workshop was organized in Jaszowiec Valley, in Hotel Jaskóka located in the heart of the Beskidy mountains, 80 km from Katowice, the capital of Upper Silesia, Poland. Lectures started at 9 am and finished at 6 pm, each lasting 35 minutes, with 45 minute coffee
breaks and party
meetings to boost discussions were held every evening. Participants had also the possibility to get acquainted with the still vivid culture of the Beskidy highlanders. This meeting would not have been such a success without the time devoted to its organization by a number of dedicated people. I would especially like to thank my wife

xi and the best co-worker Aleksandra Drozd-Rzoska, for her unwaving support and valuable advice. I am also very grateful to PhD students from our lab in Katowice, particularly to Sebastian Pawlus and Monika Sekula for their great organizational skills. I am also indebted to Prof. Vitaly Zhelezny, the co-director, who invited a superb staff of participants from Russia and Ukraine. I would like thank Takeo Furukawa for the photo. Further thanks to the Silesian University for the technical help, particularly to Mrs. Iwona Jarocka from the Financial Dept. of Silesian Univ. I also express the great gratitude to Kluwer for publication of these contributions. Organizers thank all contributing authors and acknowledge the generous and extensive support of the NATO Science Programme. Additional support was given by the Polish Chemical Society Society, branch Katowice. Sylwester J. Rzoska Katowice Poland

xii

Participants of NATO ARW Nonlinear Dielectric Phenomena in Complex Liquids Jaszowiec, Poland 10-14 May 2003

xiii

PARTICIPANTS Co-Directors Sylwester J. Rzoska Dept. Biophys. & Molecular Physics Institute of Physics Silesian University ul. Uniwersytecka 4, 40-007 Katowice Poland

Vitaly P. Zhelezny Dept. of Thermophysics Engn., Odessa State Academy of Refrigeration (OSAR), 65-026 Odessa, Ukraine

Organizing Committee Aleksandra Drozd-Rzoska Institute of Physics Silesian University ul. Uniwersytecka 4, 40-007 Katowice Poland Marian Paluch Institute of Physics Silesian University ul. Uniwersytecka 4, 40-007 Katowice Poland

Key Speakers Mikhail A. Anisimov Inst. of Physics and Techn. And Dept. Chem. Engn. , Univ. Maryland, College Park, USA A.V. Chalyi Phys. Dept., National Medical Univ., Shevchenko Blvd 13, 01601, Kiev, Ukraine Willam T. Coffey School of Engineering, Trinity College, Dublin 2, Ireland Jean-Louis, Dejardin Univ. de Perpignan, Perpignan, France Aleksandra Drozd-Rzoska Institute of Physics, Silesian University, ul. Uniwersytecka 4, 40-007 Katowice, Poland

xiv Takeo Furukawa Sci. Dept. Physics, Faculty of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku, Tokyo 162-8601, Japan Attila R. Imre KFKI Atomic. Res. Inst, H-1525, Budapest, Hungary Yasuyuki Kimura Dept. Appl. Phys. School Engn., Umiv. Tokyo, 7-3-1 Hongo, Bukyo-ku, Tokyo 113 – 8656, Japan Jerzy Institute of Molecular Physics, Polish Academy of Sciences, Smoluchowskiego 17, 60179 PL Poland Kia L. Ngai Naval Research Laborator, Washington, DC 20375-5320 USA, Laboratoire de Dynamique et Structure des Matériaux Moléculaires, U.M.R. CNRS 8024 Université des Sciences et Technologies de Lille, 59655 Villeneuve d’Ascq Cedex, France Akira Onuki Kyoto University, 606-8502 Kyoto, Japan Marian Paluch Institute of Physics, Silesian University, ul. Uniwersytecka 4, 40-007 Katowice, Poland Manit Rappon Dept. Chemistry, Lakehead Univ. Thunder Bay, Ontario, P7B 5E1, CANADA Mike C. Roland Naval Research Laboratory, Chemistry Division, Code 6120 Takeshi Shinomura Grad. School of Frontier Science, Univ. Tokyo, Kashiwanoha, Kashowa-shi, Chiba, 277-8562, JAPAN

Institute of Chemistry, Silesian University, ul. Szkolna 7, 40-007 Katowice, Poland Pavel, V. Skripov Inst. Thermal Physics, ul. Amundsena 106, 620016 Ekaterinburg, Russia

Institute of Physics, Silesian University, ul. Uniwersytecka 4, 40-007 Katowice, Poland

xv

Further Participants Christianne Alba
Simionesco Recherche Lab. de Chemie Physique, Univerite de Paris Sud, France Josef Bartos Polymer Institute of the Slovak Academy of Sciences, Dúbravská cesta 9, 842 36 Bratislava Roland Bohmer Exp. Physics III, Univ. Dortmund, Dortmund, Germany N. T. Cherpak Usikov Institute Eadiophys. & Electronics, Natl. Acad Sci., Kharkiv, Ukraine Catherine Dreyfus Laboratoire PMC and UFR 925, Université P. et M. Curie, Paris, France. Mike Evans Institute of Biological Sciences, University of Wales, Aberystwyth SY23 3DD, UK George Floudas Biomedical Res. Inst. (BRI
FORTH) and Univ. Ioannina, Ioannina, P.O. Box 1186, 451 10 Joannina, Greece Michał Górny Institute of Physics, Silesian University, ul. Uniwersytecka 4, 40
007 Katowice, Poland Yuri Ivanov St Petersburg State Univ of Refr. & Food, St. Petersburg, Russia Yuri Kalmykov Univ. de Perpignan, Av. Villeneuve 52, 66 860 Perpignan, FRANCE Douglas B. Kell Dept Chemistry, UMIST, Faraday Building, PO Box 88, Manchester M60 1QD, UK and Institute of Biological Sciences, University of Wales, Aberystwyth SY23 3DD, UK Antoni Kocot Institute of Physics, Silesian University, ul. Uniwersytecka 4, 40
007 Katowice, Poland

xvi Samo Kralj Laboratory of Physics of Complex Systems, Faculty of Education, University of Maribor, Koroška 160, 2000 Maribor, Slovenia Nicolai P. Malomuzh Dept. Theoretical Physics, Odessa Natl. University, Odessa , Ukraine Kazimierz Orzechowski Faculty of Chemistry, Poland

Joliot
Curie 14,

50
383

Ernst Roessler Insitute of Physics II, Univ. Bayreuth, Bayreuth, Germany Mitja Slavinec Regional development agency Mura, Lendavska 5a, 9000 Murska Sobota, Slovenia, Ma
gorzata ŚliwińskaBartkowiak Institute of Physics, A. Mickiewicz University., Umultowska 50, Poznań, Poland Hristo Solunov University of Plovdiv, 4000 Plovdiv, BULGARIA Laszlo Smeller Semmelweiss Medical Univ., Dep. Biophys. And Radiation Biology, Budapest, Puskin u. 9, H
1444. Hungary Urban Inst. Physics, Jagiellonian Univ., Reymonta 4, 30
059 Krakow, Poland

ANOMALOUS EXPRESSIONS FOR THE NONLINEAR COMPONENTS OF THE ELECTRIC POLARIZATION

HARMONIC

J.-L. DÉJARDIN Centre d’Etudes Fondamentales, Groupe de Physique Moléculaire, Université de Perpignan, 52 Avenue Paul Alduy, 66860 Perpignan Cedex, France.

Abstract: In view of having a better interpretation of experimental data of complex liquids which are not well described by usual Debye-like models, we propose to introduce a fractional approach applied to noninertial rotational diffusion of polar molecules. This leads to solve a fractional Smoluchowski equation (in configuration space only) characterized by an anomalous exponent varying in the interval ]0,1] corresponding to a slow relaxation process (subdiffusion). More precisely, we consider the problem of the nonlinear dielectric response due to the application of a strong electric field in the form of either a pure ac field or a strong dc bias field superimposed on a weak ac field. For both cases, we derive in the frequency domain analytical expressions for the electric susceptibilities valid up to the third order in the field strength. This yields harmonic components varying at the fundamental angular frequency and in To illustrate the results so obtained for the stationary regime, dispersion and absorption spectra are plotted for each harmonic component in order to show the significant departure from the classical Brownian behavior as Cole-Cole diagrams are also presented allowing one to see how the arcs become more and more flattened as which corresponds to a broadening of the absorption peaks as effectively observed in most of complex liquids. The theoretical model is in good enough agreement compared (i) with experimental data of the thirdorder nonlinear susceptibility of a ferroelectric liquid crystal and (ii) data of the third-order nonlinear relative dielectric permittivity of a polymer. The present work represents an extension of previous theories in nonlinear dielectric relaxation by Coffey and Paranjape, here applied to the harmonic dielectric responses in disordered media.

1. Introduction In the experimental study of complex fluids like liquid crystals, glass forming liquids, polymers, etc., one observes that the time evolution of the dielectric relaxation processes can no longer be described in the form of the exponential function as in the Debye model, but rather by the Kohlrausch-Williams-Watt law corresponding to a stretched exponential function [1-6]. As a consequence, in the frequency domain, when the systems are acted on by ac electric fields, the absorption spectra are characterized by broadened relaxation peaks [7]. For reproducing such typical patterns, three different empirical expressions are generally used for fitting the corresponding experimental data. Expressed in normalized forms, and considering, for instance, the responses provided with the complex electric susceptibilities being the angular frequency of the applied ac electric field, they are - the Cole-Cole equation [8]

1 S.J. Rzoska and V.P. Zhelezny (eds.), Nonlinear Dielectric Phenomena in Complex Liquids, © 2004 Kluwer Academic Publishers. Printed in the Netherlands.

1-18.

2

- the Davidson-Cole equation [9]

- and the combined Havriliak-Negami equation [10]

where and are characteristic relaxation times, and are said stretching exponents. For the well-known formulas corresponding to normal diffusion are recovered. As soon as (or becomes different from unity, anomalous diffusion takes place, which is what effectively occurs in disordered media. In order to account for the dielectric relaxation of such systems, it is possible to use a fractional FokkerPlanck equation, based on the continuous-time random walk as shown recently by many authors [11-13]. Moreover, the solution of fractional equations may be accomplished in the same manner as that well developed for usual partial differential equations [12]. In this paper, we shall restrict ourselves to the case where the fractal exponent ranges from 0 to 1, which corresponds to the subdiffusive regime characterized by a much slower decrease of the fractional relaxation function for long times than that observed with the exponential (superslow process) [14]. An attempt to give a demonstration of the Cole-Cole formula has been recently derived by Novikov and Privalko [2] who used a phenomenological relaxation function for describing the electric polarization. The same result has been also obtained by Coffey et al. [15] from the noninertial Fokker-Planck equation. Hence, we shall try to extend the usual theory (normal diffusion) of the nonlinear dielectric response to this context of the fractional dynamics. To accomplish this, we consider a dilute solution consisting of an assembly of noninteracting, rigid, polar, and symmetric-top molecules. With such assumptions, we can consider the rotational motion of a single molecule having a permanent dipole moment under the application of an external electric field E(t). In what follows, we shall seek the results obtained for two different electric fields, namely, either a pure alternating field, or a strong dc constant bias field on which is superimposed a weak ac field in the same direction, with