Quasicritical behavior of the low-frequency dielectric permittivity in the isotropic phase of liquid
Aleksandra Drozd-Rzoska,1Sylwester J. Rzoska,1Jerzy Zioło,1and Jan Jadz ˙yn2
1‘‘August Chełkowski’’ Institute of Physics, Silesian University, ul. Uniwersytecka 4, 40-007 Katowice, Poland
2Institute of Molecular Physics, Polish Academy of Sciences, ul. Smoluchowskiego 17, 60-179 Poznan ´, Poland
?Received 18 October 2000; published 13 April 2001?
Results presented give evidence of the existence of quasicritical, fluidlike behavior in the isotropic phase of
4-cyano-4-pentyl-biphenyl ?5CB? for frequencies ranging from the static to the ionic-dominated ?low-
frequency ?LF?? region. Despite the boost of dielectric permittivity on lowering the frequency below 1 kHz,
values of the isotropic-nematic transition discontinuity ??1.1 K? and the critical exponent ? ??0.5? remain
constant. It is shown that the contribution from residual ionic impurities is a linear function of temperature in
the critical, prenematic fluctuation-dominated region. The validity of the fluidlike and critical behavior for LF
dielectric permittivity confirmed results of a derivative analysis of the experimental data:
?T*)??, originally proposed for critical mixtures. Results of a preliminary test in the isotropic phase of
4-decyl-4?-isothiocyanatobiphenyl ?10BT?, on approaching the smectic-E phase, may indicate a general valid-
ity of results obtained.
DOI: 10.1103/PhysRevE.63.052701PACS number?s?: 64.70.Md, 64.30.?t, 77.22.Ch
In recent years the complex liquid ?1–18?, fluidlike and
critical ?1–8? nature of the isotropic phase ?I? of nematic
liquid crystals was shown owing to the application of experi-
mental techniques. These included the transient grating Kerr
effect ?9–12?, dynamic light scattering ?13–16?, ultrasonic
birefringence ?17,18?, and ‘‘linear’’ and ‘‘nonlinear’’ dielec-
tric permittivity studies ?4–8?. The mentioned fluidlike de-
scription ?1–8? is a point of view on the isotropic phase of
nematogens whose picture was for several decades domi-
nated by the simple mean-field description within the
Landau–de Gennes ?19,21? or Maier-Saupe ?19–23? models.
The unique feature appearing in linear and nonlinear dielec-
tric studies is the fact that in the static case, when relaxation
processes can be neglected, the same dependences are valid
on approaching the nematic ?N?, smectic-A (SmA), and
smectic-E (SmE) phases ?4–8,24,25?:
where ENDE?(?E??)/E2is the measure of the nonlinear
dielectric effect ?NDE? ? denotes dielectric permittivity in a
weak, measuring radio frequency electric field, ?Eis dielec-
tric permittivity under additional strong, steady electric field,
T* is the virtual critical temperature, TCis the clearing tem-
perature, ?T is the discontinuity of the isotropic-mesophase
transition, ??0denotes the molecular anisotropy of dielectric
permittivity in the zero-frequency limit, and a?1is the sus-
When discussing these dependences it is noteworthy that
they can also be derived from relations for the homogeneous
phase of critical mixtures, in agreement with the fluidlike
and critical description ?4,6–8?. Particularly noteworthy is
the fact that the reciprocal of the static NDE is a linear func-
tion from Tx?TC?40K up to TC, without any distortions
?6,8?. The temperature Txcan be recognized as a point where
fluctuations shrink to two or three molecules ?6,9–12?. This
allowed for a precise estimation of ?T ?4,6,8,24,25?. Re-
garding dielectric permittivity, relation ?1b? describes experi-
mental data even 100 K away from TC?6,8,24,25?. This
behavior may be associated with the fact that the static di-
electric permittivity is not directly coupled to pretransitional
fluctuations. It originates from cancellation of permanent di-
pole moments due the prenematic arrangement. This occurs
only if the permanent dipole moments are predominantly
parallel to the long axis of the rodlike molecule ?20,21?. The
behavior of the static dielectric permittivity suggests that
prenematic ordering may occur also for T?Tx, but the num-
ber of arranged molecules is too small to be recognized as a
fluctuation by fluctuation-sensitive methods ?6?. It has to be
stressed that ?(T) studies in the static region ?1–100 kHz?
allowed for an unequivocal estimation of the exponent ?
?0.5?0.02 ?4,7,8,24,25?. Such a reliable estimation was dif-
ficult in density or heat capacity measurements previously
applied. Pretransitional anomalies of these properties are
weak, limited only to a few degrees from ?26–32?.
Decreasing the frequency below f?1 kHz dielectric per-
mittivity boosts the value as a result of the influence of re-
sidual ionic impurities ?20,21?. The behavior of the dielectric
permittivity in the low-frequency ?LF? region is still a puz-
zling problem. There have been several phenomenological
attempts to parametrize dielectric permittivity at lower fre-
quencies mainly in terms of space charge polarization ?33–
43?. The majority of those studies were conducted for
n-pentylcyanobiphenyl ?5CB? which is considered as a
model material. They concentrated on parametrization of the
frequency or time evolution of the dielectric permittivity for
a few temperatures in the isotropic or nematic phase.
To the best of the authors’ knowledge, there have been no
studies taking into account the possible influence of complex
liquid structures on results and there have been no attempts
to portray the temperature evolution of dielectric permittivity
at lower frequencies.
PHYSICAL REVIEW E, VOLUME 63, 052701
1063-651X/2001/63?5?/052701?4?/$20.00©2001 The American Physical Society
Results discussing both these factors are presented in this
paper. They show the essential influence of premesomorfic
fluctuations on the behavior of dielectric permittivity even
remote from TC. Studies were conducted in the isotropic
phase of 4-cyano-4-pentyl-alkylbiphenyl ?5CB?, especially
purified to reduce residual ionic impurities ?21?. In LF di-
electric studies 5CB is used as the classical, basic material.
The I-N transition in 5CB characterizes the smallest value of
?T in the n-cyanobiphenyl series ?8,25?, and hence it exhib-
its particularly pronounced pretransitional effects ?5,8,25?.
To test the range of the general validity of the results ob-
tained, preliminary investigations were also conducted for
the I-SmE transition in 4-decyl-4?-isothiocyanatobiphenyl
?10BT?, the material with the smallest discontinuity ?T
?5.6K in the nBT homologous series ?25?.
The sample of 5CB (TI-N?308.4K) was synthesized in
the Technical Military Academy in Warsaw ?Poland? and
obtained due to the courtesy of Krzysztof Czupryn ´ski and
Roman Da ¸browski. Prior to measurements, the sample was
carefully degassed. The sample was placed in a measurement
capacitor made from Invar:
d?0.5mm, diameter 2r?20mm, and hence C0?7.55pF.
A quartz ring was used as the spacer so that the sample was
only in contact with the Invar, quartz, and Teflon. The ca-
pacitor was placed in a specially designed thermostatted
jacket fed from the Julabo FP45 HD thermostat with external
circulation. It made changes of temperature with resolution
?0.01 K possible. Temperature was measured by means of a
miniature platinum resistor ?DIN 43 260? placed in one of
the covers of the capacitor and a Keithley 195A multimeter.
Additionally, the temperature gradient between the covers of
the capacitor was scanned by a copper-Constantan thermo-
couple. Dielectric permittivity was measured using a Solar-
tron 1260A impedance analyzer with voltage U?1 V and
averaging over 100–1000 periods, which gave a permanent
5-digit resolution. Data were analyzed by means of Origin
3.5 and 5.0 software.
the gap of the capacitor was
III. RESULTS AND DISCUSSION
The temperature dependences of dielectric permittivity for
a series of tested frequencies are shown in Fig. 1. On de-
creasing the frequency below f?1 kHz, the influence of
ionic impurities boosts the value of the dielectric permittiv-
ity. Despite this fact, Eq. ?1b? remains valid even for f
?20Hz ?see Table I and solid lines in Fig. 1?. It is particu-
larly noteworthy that for all frequencies the critical exponent
??0.5 and the discontinuity ?T are the same, within the
limit of experimental error. The fact that the fluidlike, critical
equation ?1b? remains valid also in the ionic-dominated re-
gion confirms the distortion-sensitive derivative analysis of
experimental data ?Fig. 2?:
Such a dependence was originally proposed by Mistura ?44?
for critical mixtures to show the relationship between the
anomaly of dielectric permittivity with that of the specific
heat. Only recently were its first successful experimental
tests made:in critical ?7,45? and isotropic phases of me-
sogens ?6–8,25?. The latter finding additionally supported
the mentioned fluidlike hypothesis ?3,6?.
However, in correlation length units ??? the distance ?l? at
which mobile ions are moved by the electric field is
?l(f )/?(T)?T→T*→0. Figure 3 presents an analysis aimed at
resolving the boost of the value of ?(T) on decreasing the
frequency. There are shown temperature dependences of
FIG. 1. Results of dielectric permittivity measurements in the
isotropic phase of 5 CB. The dashed arrow indicates the nematic
clearing temperature. Solid curves are parametrized by relation ?1b?
with the parameters given in Table I.
TABLE I. Results of fitting temperature dependences of dielec-
tric permittivity in the isotropic phase of 5CB compounds by means
of relation ?1b?. An asterisk denotes that the value of the exponent
BRIEF REPORTSPHYSICAL REVIEW E 63 052701
taken as a ‘‘static’’ and ‘‘nonionic’’ reference background. It
is visible that ??(T) can be well portrayed by linear func-
tions, with an increasing slope on frequency decrease. The
extent of the linearity shrinks on lowering the frequency, but
even for f?20Hz it is still as large as T?TC?15K. This
behavior may suggest that the pretransitional ‘‘bending
down’’ associated with the term A?(T?T*)1??in Eq. ?1b?
is extracted. It is only possible if for T→T* the amplitude
A?has a constant value, which may suggest also the results
in Table I. Hence one may conclude that the ionic LF con-
tribution of mobile ionic dopants seems to contribute only to
the linear term in Eq. ?1b?. It was mentioned that in the static
domain equation ?1b? portrays experimental data also for T
?TX. However, it is apparent that the LF dielectric permit-
tivity region of Eq. ?1b? follows experimental data only for
the data for f?100kHz are
temperatures lower than Tx, which suggests that it becomes
directly coupled to prenematic fluctuations as in the case of
the NDE. One may put forward a hypothesis that on ap-
proaching the clearing point ionic impurities are caught in
quasicritical, prenematic fluctuations and next polarize them.
At a given frequency the ability of mobile ions to polarize
fluctuations disappears at T* where the correlation length is
infinite. Based on the linear dependence visible in Fig. 3 and
on the fact that Eq. ?1b? remains valid in the ionic region, the
linear term in relation ?1b? may be presented as the sum of
two linear terms as is shown in Fig. 4. It is noteworthy that
neither the power term A?(T?T*)1??nor the linear term
?*?a?(T?T*) does not describe the experimental data
FIG. 4. The analysis of the ?(T) pretransitional behavior in the
isotropic phase for f?100kHz ?static region? and f?20Hz ?ionic
region?. The parameters describing solid curves ?Eq. ?1a?? are given
in Table I. The lower dashed, ‘‘static’’ line is parametrized by:
?(T)?11.217?0.0204(T?T*). The upper dotted, ‘‘ionic’’ line
describes equation ?(T)?12.167?0.020(T?T*) and the bottom
dot-dashed curve ?(T)?0.113(T?T*)0.5.
FIG. 5. Results of measurements in the isotropic phase of 10BT
?I-SmE transition? for ‘‘static’’ and ‘‘ionic’’ frequencies. Insets
show the behavior in the immediate vicinity of the I-SmE transition
and results of the ‘‘difference’’ analysis, as in Fig. 3 for 5CB.
FIG. 2. The derivative of ?(T) experimental data from Fig. 2 for
several chosen frequencies in the static and ionic regions. The inset
presents the same data in a way showing the value of the critical
??(100kHz) for experimental data taken from Fig. 2. The fre-
quencies f are shown in the figure.
BRIEF REPORTSPHYSICAL REVIEW E 63 052701
separately at any distance from T*. Consequently, the linear Download full-text
term in Eq. ?1b? cannot be treated as a background effect,
describing data remote from TI-N.
Concluding, the results obtained show that the appearance
of prenematic fluctuations in the isotropic phase may have a
dominant influence on the behavior of the low-frequency di-
electric permittivity also in the low-frequency region. Re-
sults presented in Fig. 5 for 10BT on approaching the ‘‘soft
crystal’’ smectic-E phase ?20? may suggest that the discussed
behavior may be general. The fluidlike and critical descrip-
tion ?1–8? remains valid in the static domain ?4–8,24,25?
and in the ionic region, with the same value of the critical
exponent ??0.5 and the discontinuity ?T of the isotropic-
The authors wish to thank the Polish State Committee for
Scientific Research ?KBN? for financial support under Grant
No. 2P03B 020 15. The authors are also very grateful to
Professor Takeo Furukawa for significant discussions and a
kind invitation to the Science University of Tokyo where the
majority of the paper was prepared. A.D.R. would like to
thank strongly the Matsumae International Foundation, sup-
porting her stay in Japan.
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