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D I E L E C T R IC P R O P E R T I ES
OF
B I N A RY S O L U T I O NS
by
Y. Y. Akhadov
PERGAMON PRESS
OXFORD · NEW YORK · TORONTO · SYDNEY · PARIS · FRANKFURT
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Copyright © 1980 'Nauka' and Pergamon Press Ltd.
All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system or transmitted
in any form or by any means: electronic, electrostatic,
magnetic tape, mechanical, photocopying, recording or
otherwise, without permission in writing from the
copyright holders
This Pergamon Press edition 1981
British Library Cataloguing in Publication Data
Akhadov, Y. Y.
Dielectric properties of binary solutions.
1. Solution (Chemistry)
2. Dielectrics
I. Title
541'.341 QD541 80-40366
ISBN 0-08-023600-6
Printed in Great Britain by A. Wheaton Et Co. Ltd., Exeter
PREFACE
Investigation of dielectric properties of liquids can lead to information con-
cerning molecular interactions and the mechanism of molecular processes which
go on in liquids.
The results of such investigations are of great significance both theoretically
and practically.
Without a deep understanding of the mechanism of molecular movements
and interactions there can be no successful solutions of problems such as the
effective direction of chemico-technological processes, the discovery of the
nature of physico-chemical processes in the biological sphere, synthesis of new
materials satisfying specific requirements, and the contriving of rapid methods of
analysis and control in chemical processes.
Dielectric radiospectroscopy is one of the most sensitive means for the
physico-chemical investigation of materials.
Knowledge of the dielectric parameters of liquids is indispensable for the
operation of a number of contemporary electrochemical and radiochemical
enterprises, for the construction of various appliances for automatic control of
chemical processes in the organic synthesis industry, and for the operation of
equipment for metering costs of fuel, oil, etc.
Dielectric data for liquids are indispensable for a wide circle of scientific
workers specializing in various fields in physics, chemicstry, biology and
medicine. This is clear from the great number of published works which provide
information on the permittivity, dielectric loss, and relaxation phenomena in
particular liquids and solutions over a wide range of frequencies and tempera-
tures.
Despite this wide field of applicability there has not been, until now, either
at home or abroad, any reference book in which the numerous experimental
investigations on the dielectric properties of liquids have been collected and
systematized.
The general reference books [1—4] contain selective collections of dielectric
parameters for liquids outside the dispersion region.
In reference [5] an attempt was made by the author to systematize di-
electric data for pure liquids.
None of the reference books deals with dispersion data for solutions such as
Preface
permittivity, dielectric loss, relaxation times and the distribution of relaxation
times, and thermodynamic functions of dielectric relaxation.
The present book aims to fill this gap and to make data on the dielectric
parameters of binary solutions accessible to readers. It collects and systematizes
numerous experimental results from 1892 to 1973 on the dielectric parameters
of solutions. Critical analysis forms the basis of recommendations of the most
reliable values for binary solutions taken from the original works.
The book consists of four chapters. Chapter I gives the basic formulae which
describe the dielectric properties of substances and relate the experimentally
observed quantities to the parameters characteristic of the substance. Chapters II
and III consist of tables giving the result of measurements of static permittivity,
limiting high-frequency permittivity, permittivity and dielectric loss, relaxation
time, coefficient of distribution of relaxation times, and also thermodynamic
functions of dielectric relaxation over a wide range of temperatures and an
extensive frequency variation for non-aqueous and aqueous solutions of in-
organic and organic compounds. Chapter IV presents dielectric data in graphical
form.
At the end of each chapter section there are additional references to figures
at the end of the book and to literature sources of experimental data which are
not included elsewhere in the book.
The author expresses his deep gratitude to Y. I. Gerasimov, corresponding
member of the Academy of Sciences of the U.S.S.R., for his great interest in the
present work and Professor M.I. Shakhparonov for valuable critical observations
and useful advice.
USE OF THE TABLES
In certain cases several values are given for the dielectric quantities measured
at the same temperatures and frequencies. This indicates that it is not possible to
give preference to one or other of the sources.
The tables for binary solutions of organic compounds are arranged accord-
ing to the summary formulae of the components. In the summary formulae the
symbols for the elements are placed in the order C, Η, Ν, Ο and thereafter in
alphabetic order. The precedence of compounds is decided according to the
number of atoms of carbon and thereafter the number of atoms of hydrogen and
so on. For any binary mixture the first component is that which precedes the
other according to the above rule. The various binary mixtures are then arranged
according to the precedence of the first components. Under a given first com-
ponent, the second components are similarly arranged according to their pre-
cedence.
Concentrations of solutions are expressed in the same units as in the original
works. When a concentration refers to the first component the concentration
symbol has the index 1 (0ι, Χγ, ννχ), and when it refers to the second com-
ponent it has the index 2. Concentrations are expressed as percentages.
In order to avoid repetition, values of permittivity which are shown in the
tables of dielectric dispersion parameters § § 3, 4 chapter II and § § 3, 4 chapter
III are not included in the tables of permittivity §§1,2 chapter II and §§1,2
chapter III. To obtain full details concerning the permittivity of systems it is
essential to consult the tables accordingly.
The first literature citation indicates the source of the values given in the
table.
SYMBOLS
e — limiting low-frequency permittivity.
e', e" — real and imaginary parts of the permittivity.
€1, € , €3 — limiting low-frequency permittivity for the first, second and
2
third absorption regions.
e'i> €2, €3 — real part of the permittivity in the first, second and third absorp-
tion regions.
e"i> e'3 — dielectric loss (loss factor) in the first, second and third absorp-
tion regions.
tan δ — tangent of the loss angle.
— limiting high-frequency permittivity.
eooi > eoo2 > Coo3 — limiting high-frequency permittivity for the first, second
and third absorption regions.
λ — wave length.
X — limiting wave length corresponding to the maximum of the dielectric
m
loss.
ν — limiting frequency corresponding to the absorption maximum,
"mi' vm2' pm3 ~ n m^nS frequencies corresponding to the first, second
and third absorption regions.
r — the macroscopic relaxation time.
f\, τ, r — relaxation time in the first, second and third absorption regions.
2 3
C\, C — contribution of the first and second relaxation processes to the
2
dielectric relaxation.
g — Kirkwood's structure factor.
a — coefficient of distribution of relaxation times.
β — parameter of distribution of relaxation times according to Cole-
Davidson.
AF — change in free energy of activation of dielectric relaxation.
AFi, AF, AF — change in free energy of activation of dielectric relax-
2 3
ation for the first, second and third absorption regions.
AH — heat of activation of the dielectric relaxation.
AH χ, AH, AH — heat of activation of dielectric relaxation for the first,
2 3
second and third absorption regions.
Χι — concentration of the first component of the solution expressed as
molar percentage.
Symbols
x — concentration of the second component of the solution expressed as
2
molar percentage.
Wi — concentration of the first component of the solution expressed as
weight percentage.
w — concentration of the second component of the solution expressed as
2
weight percentage.
φι — concentration of the first component of the solution expressed as
volume percentage.
02 — concentration of the second component of the solution expressed as
volume percentage.
η — concentration of the solution expressed in gram-equivalents per litre
of solution.
Ν — concentration of the solution expressed in moles per litre of solution,
σ — conductivity.
CHAPTER I
FUNDAMENTAL FORMULAE DESCRIBING THE
DIELECTRIC PROPERTIES OF LIQUIDS
Results of theoretical and experimental investigations devoted to the pro-
perties of dielectrics in static and alternating electric fields have been published
in various books and monographs [5—16].
For information on the methods of calculating the experimental values
given in the book and of establishing relationships between them we give the
fundamental equations which describe the dielectric properties of liquids. Fora
closer acquaintance with matters relating to these equations and to the experi-
mental results reference may be made to the works cited in the text.
The polarization of a dielectric is represented as the sum of the electronic
Ρ , atomic P and orientational P polarization
Q 0
P=P+P*+P. (i)
E 0
The times for completion of polarization have the orders of magnitude Ρ
ΙΟ"14 - 10Λ\Ρ 10'11 - ΙΟ"14 andP 10'10 seconds.
Α 0
The Clausius-Mosotti equation for the molecular polarization P is
M
ε—1 M 4nN
7+2T =~3~a = = Pt m ) ( 2
where M = molecular weight, ρ = density, Ν = Avogadro's number, a = deform-
ation polarizability, equal to the sum of the electronic and atomic polariz-
abilities.
The molecular refraction Ρ :
Η.
1 M 4nN
~n* + 2 ρ -ä-ae, (3)
where a is the electronic polarizability.
e
The temperature coefficient of the permittivity
J_ de _(ε— 1)(ε + 2) 1 dp
ε dt 3ε ρ dt ' ) ( 4
10 Fundamental formulae
The permittivity of binary solutions of non-polar liquids is given by the
formula
where e is permittivity, pi is density and Pi is molecular polarization of the
x 2 2 2
solution, x, x are mole fractions, M M molecular weights and P P
x 2 lr 2 lt 2
molecular polarizations of the components,
Ρ ±ηΝα P = jJiNa, (6)
1 = ΐ9 % t
where a a are the deformation polarizabilities of the components.
u 2
Since
*i = 1 - *„ Pi%=Pi-(Pi—Pà x - (7)
2
Debye's equation [5]
ε—1 M 4JIN ( , μ2 \
P = Λ / $
where μ is the dipole moment of the molecule, k is Boltzman's constant, Τ is
temperature. We define
A=^nNa, B = Ä° (9)
and obtain
PT = AT + B.
The numerical formula for calculating the dipole moment has the form
μ = 0,0127·(10~8)5. (10)
The effect of solvent is given in the equations [17—23]
±_=1 0,43Λ(ε-1), (U)
μο +
or
μ 3β[1-(β.-1Μ]
) ( i 2
μ ( + 2)[β + (β.-Β)Λ] '
0 β
Where β is the dipole moment of the molecule in the rarefied gas, A = 1/3 for
α
a spherical molecule, is the limiting high-frequency permittivity.
Onsager's equation [24]
(e-ej(2e+ej _4πΛΓμ 2
(13)
e(e + 2)2 9kT •
œ
