€r World Scientific Series in Contemporary Chemical Physics - Vol. 8

DIELECTRIC RELAXATION AND DYNAMICS OF POLAR MOLECULES

Vladimir I Gaiduk Institute of Radio Engineering & Electronics

Russian Academy of Sciences Moscow

\\P * * World Scientific Singapore • New Jersey • London • Hong Kong

CONTENTS

List of Symbols xv

Part One INTRODUCTION TO THE DIELECTRIC SPECTROSCOPY 1

1 Basic Terms, Processes and Models 3 1.1 Displacement and polarization vectors

for a constant external field 5 1.2 Relative complex permittivity and susceptibility 6 1.3 Complex refractive index and absoiption coefficient 9 1.4 Debye model of rotational diffusion 12 1.5 About the dynamic method 19 1.6 Classification of semi-microscopic molecular modeis 30

2 Rotational and Dielectric Spectra 37 2.1 Gaseous and gas-like states 37 2.2 Diluted Solutions 46 2.3 Individual nonassociated liquids 47 2.4 H-bonded network 52 2.5 Water bounded by a macromolecule 59 2.6 Aqueous Solutions 66

Part Two THE DYNAMIC METHOD 73

3 Basic Equations and Theorems 75 3.1 Maxwell's equations and wave equation

for a plane electromagnetic wave 75 3.2 The to theorem 77 3.3 The average perturbation (AP) theorem 82

CONTENTS

3.4 Rotation of a polar molecule in an axisymmetric potential 87

3.5 Libration of a polar molecule in a parabolic potential well 107

Relation of Susceptibility to Complex Power 117 4.1 The dispersion equation 117 4.2 The steady State and induced distributions 121 4.3 The effective susceptibility 122 4.4 Susceptibility / permittivity relation

for the case of isotropy 124

The Spectral Function 129 5.1 Representation in terms of perturbed motion

of a dipole in radiation field 129 5.2 Representation in terms of undamped motion

for thermal equilibrium 132 5.3 Relation to the direction of alternating external field 139 5.4 The spectral functions in the case

of an isotropic medium 142 5.5 Fourier series for the spectral function: planar motion 147 5.6 Fourier series for the spectral function: motion in Space 155 5.7 Integrated absorption 169 5.8 The Kramers-Kronig rule 175 5.9 Landau damping in polar medium 176

Collision Models 183 6.1 The effective susceptibility at an arbitrary

non-equilibrium induced distribution F 183 6.2 The Boltzmann induced distribution F# 186 6.3 The Debye induced distribution jFrj 186 6.4 The self-consistent induced distributions FQ, F&, Fj 187 6.5 The spectral function K(z). The summary table

for the susceptibility 192 6.6 The low-frequency approximation 194 6.7 The resonance phenomena

(The Poley absorption region) 204 6.8 The extension of the theoryto multicomponent media 210

CONTENTS

6.9 Models of collisions for an isotropic medium (continuation) 215

Addendum I About the Evolution of the Dynamic Method 219

Part Three MODELS OF FREE ROTATION / LIBRATION 223

7 The Extended Rotational Diffusion (ED) Model of Symmetrie Top Molecules 225 7.1 Ensemble of linear molecules 225 7.2 Ensemble of Symmetrie top molecules 239

8 The Confined Rotator (CR) Models 255 8.1 The planar CR model 255 8.2 The simplified spatial CR model 264 8.3 Dielectric spectra of an isotropic medium

for the DWP configuration 266 8.4 The peak absorption and Debye relaxation

time as funetions of the lifetime 270 8.5 • The cone confined rotator (CCR) model 279 8.6 The cone confined rotator model with a Single

Potential well: dielectric behavior 304

9 The Hybrid Confined Rotator / Extended Diffusion Model (HM) 305 9.1 The mean molecular parameters at equilibrium 308 9.2 The spectral funetions K(z) and L(z) 317 9.3 Evolution of dielectric spectra

with the rise of the reetangular potential 320 9.4 The hybrid model 2 (HM2) 326

PartFour FIELD MODELS 359

10 The Elastic Bond (EB) Approximation 363 10.1 The spectral funetion of the planar ensemble 364 10.2 The spectral funetion of the spatial ensemble 365 10.3 The complex suseeptibility of linear molecules

subjeeted to the influence of the parabolic potential 369 10.4 The Poley absorption 376

CONTENTS

11

12

13

10.5 The loss frequency dependence for the Single well potential 377

10.6 The loss frequency dependence for the double well potential

The Constant Field (CF) Model 11.1 11.2 11.3 11.4 11.5 11.6 11.7

The steady State law of motion Distribution functions The field dependence of the steady State parameters Rigorous expressions for the spectral functions The quasi-harmonic approximation (QUA) Dielectric behavior The stratified approximation

The Cosine Squared (CS) Model 12.1 12.2 12.3 12.4

12.5 12.6 12.7

The law of motion The steady State The spectral function: rigorous theory The Spectral Function: the quasi-harmonic approximation Limiting lines Influence of the field parameter on dielectric spectra The stratified approximation

The Hat Model (HM) 13.1 13.2 13.3 13.4 13.5 13.6

13.7 13.8

The law of motion The steady-state distribution W— Cexp(-A) Fourier amplitudes of librating molecules The spectral function of librators The spectral function of free rotating molecules The effect of the potential well steepness on loss / absorption spectra Statistical parameters The curved-brim hat model

378

381 381 388 396 407 415 418 428

431 431 436 446

451 453 455 462

465 467 467 469 471 478

480 480 486

Xll

CONTENTS

Part Five APPLICATIONS OF THE THEORY 495 14 Individual Nonassociated Polar Liquids 497

14.1 Liquid fiuoromethane CH3F 498 14.2 The rotational ceU model (RCM) 503 14.3 Liquid trifluoromethane CHF3 508 14.4 Prediction of the critical temperature 510 14.5 Molecular Interpretation of the «rotational» lifetime x

in the light of the Debye rotational diffusion theory 512 14.6 Relation of the potential welldepth to dielectric spectra 514 14.7 The Polarizability A"(v) Spectra 515 14.8 Distortion of the Cole-Cole diagram

due to micro heterogeneity 518 14.9 Isotropie potential and the self-diffusion coefficient 526

15 Liquid Water and Aqueous Systems 531

15.1 Liquid water 531 15.2 Electrolytes in aqueous Solution 553 15.3 Water in a bound State 567 15.4 Nonelectrolyte in aqueous Solution 581

16 Quantum Effects in Polar Gases and Gas-Iike Liquids 589 16.1 The quasi-classical approach 589 16.2 Resonance phenomena in biatomic gases 593 16.3 Classical theory of collisions 602 16.4 Gas-Iike liquids 612

The Afterword 619

Addendum II. On the Evolution of Molecular Models of Orientational Relaxation 623

References 627

Subject Index 633