CHAPTER 5
TEMPERATURE STUDIES OF ”NONLINEAR”
CHANGES OF DIELECTRIC PERMITTIVITY IN A
STRONG ELECTRIC FIELD IN
NITROBENZENE-DODECANE CRITICAL
MIXTURE
It is possible (Fig. 5.1) to compare the anomaly of dielectric permittivity presented in
Chapter 4 to the anomaly of its nonlinear changes in a strong steady electric field (NDE).
Fig. 5.1.
The NDE on approaching the critical consolute temperature. The solid line shows
the non-critical background effect. The arrow denotes the critical temperature.
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The inset shows the critical effect of NDE vs. the logarithm of temperature
distance from the critical point of fm = 250 kHz.
It is visible that the pretransitional effect is much stronger. Their form is characterised by two
different critical exponents, as was mentioned in papers [101,102].
NDE = 0.390.01,
for T - TC < 2 K,
NDE = 0.610.02,
for T - TC > 1 K.
In the analysis of the NDE the critical effect has to be extracted from the total measured effect by
taking into account the non-critical background effect, marked as NDEB. NDEB was determined
from measurements in a reference solution of unlimited miscibility nitrobenzene - benzene [103].
The value of dTC/dE2 was determined in the nitrobenzene-dodecane critical mixture. The
method proposed by Orzechowski was applied [110] (Chapter 2.2 p. 30, 31).
Fig. 5.2.
Electric field dependencies of the NDE increment at different temperatures for
nitrobenzene-dodecane critical solution. The inset shows /E2 vs. E2.
The inset in Fig. 5.2 proves that NDE depends on E2 and on E4 too. Therefore, the average value
of dTC/dE2 = -2.2  10-14 Km2/V2. The negative value of the derivative proves the downward
shift of the critical temperature in the presence of an electric field. The results presented in this
thesis are consistent with Debye and Kleboth [89]and Orzechowski [110]. However these results
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are not consistent with the predictions of Beaglehole [90].
According to Beaglehole the
equations derived by Beaglehole and Kleboth seem to be applicable case of constant current only.
In the case of constant potential (the case presented in this thesis), the sign of the dTC/dE2 value
predicted by Debye and Kleboth theory, should be reversed, and consequently the upward shift of
TC is expected. The upward shift of the critical temperature (when  2  x 2 > 0) was also
predicted by Onuki [104]. Taking into account the above, the obtained downward shift of
critical temperature after applying electric field seems to be inconsistent with the expected
behaviour. Orzechowski [110] pointed to a possible reason for such a discrepancy namely, to the
influence of electrostriction, not included in theoretical expectations. Electric field changes the
volume of liquid, resulting in a change of pressure between electrodes. Because the critical
temperature is very sensitive to pressure [33], electrostriction should influence TC too. However,
the change of TC due to electrostriction is difficult to predict. Volume could both increase and
decrease in the presence of electric field [8] and depends on quantities having anomalous
behaviour in critical region (i.e. dielectric permittivity) [100]. It seems that electrostriction
should be taken into account when predicting the critical temperature shift caused by electric
field. However, the lack of experimental data required for estimation of electrostriction in the
critical region is required for a quantitative estimations of this effect.
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