A short review of literature and the authors' experimental results for the pretransitional behavior in the isotropic phase of nematogens is given. The paper also presents new results of non-linear dielectric effect and dielectric
permittivity measurements in the broad temperature range. Results obtained show significant advantages of non-linear dielectric effect and dielectric permittivity for studying pretransitional properties in liquid crystalline
materials. The paper contains a comprehensive comparison of the experiment with predictions of the mean-field model and the fluid-like description. The presented analysis strongly supports the image of the isotropic phase as
a complex liquid resulting from vicinity of the fluid-like, "nematic-isotropic", critical point

Drozd-Rzoska, Aleksandra

Rzoska, Sylwester

Zioło, Jerzy

Acta Physica Polonica A

English

A short review of literature and the authors' experimental results for the pretransitional behavior in the isotropic phase of nematogens is given. The paper also presents new results of non-linear dielectric effect and dielectric permittivity measurements in the broad temperature range. Results obtained show significant advantages of non-linear dielectric effect and dielectric permittivity for studying pretransitional properties in liquid crystalline materials. The paper contains a comprehensive comparison of the experiment with predictions of the mean-field model and the fluid-like description. The presented analysis strongly supports the image of the isotropic phase as a complex liquid resulting from vicinity of the fluid-like, "nematic-isotropic", critical point

Drozd-Rzoska, A.

Rzoska, S. J.

Zioło, J.

Biblioteka Nauki - repozytorium artykuÅÃ³w

The Fluid-Like and Critical Behavior of the Isotropic-Nematic Transition Appearing in Linear and Non-linear Dielectric Studies

Repozytorium Uniwersytetu Śląskiego RE-BUŚ

             Title: The fluid-like and critical behavior of the isotropic-nematic transition appearing in linear and non-linear dielectric studies  Author: Aleksandra Drozd-Rzoska, Sylwester J. Rzoska, Jerzy Zioło  Citation style: Drozd-Rzoska Aleksandra,. Rzoska Sylwester J, Zioło Jerzy. (2000). The fluid-like and critical behavior of the isotropic-nematic transition appearing in linear and non-linear dielectric studies. "Acta Physica Polonica A" (Vol. 98, nr 5 (2000), s. 637-643).  Vol. 98 (2000)	 ACTA PHYSICA POLONICA A	 No. 5Proceedings of the International Conference "Condensed Matter Physics", Jaszowiec 2000THE FLUID-LIKE AND CRITICAL BEHAVIOROF THE ISOTROPIC-NEMATIC TRANSITIONAPPEARING IN LINEAR AND NON-LINEARDIELECTRIC STUDIESA. DROZD-RZOSKA, S.J. RZOSKA AND J. ZIOŁOAugust Chełkowski Institute of Physics, Silesian UniversityUniwersytecka 4, 40-007 Katowice, PolandA short review of literature and the authors' experimental results forthe pretransitional behavior in the isotropic phase of nematogens is given.The paper also presents new results of non-linear dielectric effect and di-electric permittivity measurements in the broad temperature range. Resultsobtained show significant advantages of non-linear dielectric effect and dielec-tric permittivity for studying pretransitional properties in liquid crystallinematerials. The paper contains a comprehensive comparison of the experi-ment with predictions of the mean-field model and the fluid-like description.The presented analysis strongly supports the image of the isotropic phase asa complex liquid resulting from vicinity of the fluid-like, "nematic-isotropic",critical point.PACS numbers: 64.70.Md, 64.30.+t, 77.22.Ch1. IntroductionOn approaching the nematic clearing temperature (T1-N) a series of physicalproperties exhibit a strong pretransitional increase, proportional to (T — T*) -1 ,where T > TI-N and T* = TI_N -+ ΔT: the temperature T* denotes the ex-trapolated temperature of a hypothetical continuous phase transition and ΔTis the measure of the discontinuity of the transition [1-7]. These properties in-clude: the intensity of the scattered light (IL) [8-10] , the Cotton-Mouton effect(CME) [11-13], the optical Kerr effect (OKE) [14-16], the electrooptic Kerr ef-fect (EKE) [17-19], the turbidity (t) [20], the non-linear dielectric effect (NDE)[21-25], relaxation time of pretransitional processes (τ) [15, 16, 26], the square ofNMR linewidth [27], thermal expansion coefficient and compressibility (α p , X) [28].The parametrization of these anomalies made the application of mean field basedmOdels possible, such as the Maier-Saupe model [29] or the Landau-de Gennes(LdG) model [1]. Particularly the latter has been broadly explored in the isotropic(637)638 A. Drozd-Rzoska et al.phase due to its simplicity (see Refs. above). However, there is long-standing ev-idence of a limited consistency between mean-field based models and the exper-iment [1, 2, 30, 31]. The most puzzling fact is the discrepancy between the the-oretically predicted values of transition discontinuity and the experimental ones[1, 31]. Experiments mentioned above showed a weakly discontinuous character ofthe I—N transition with ΔTEXp . = 0.5-2 K. Significant efforts led to the reductionof the calculated value of ΔTTheor. from about 40 K to 7 K [1-7, 31-34]. Thefirst to mention the problem of the mean-field approximation was probably deGennes in his monograph in 1974 [1]. He also wondered what the reason was forsuch a different behavior of the intensity of scattered light in the isotropic phase(IL α (T —T*)-γ,γ = 1) and for the gas—liquid critical point or critical consolutepoint (IL α (T — TC) -γ , γ = 1.23) [1]. It is noteworthy that a similar problemarises for EKE and NDE: in the isotropic phase NDE, EKE α (T —T*)-γ , γ = 1whereas in critical mixtures EKE α (T — TC)- EKE, ΨEKE = 0.59-0.85 and NDEα (T — TC)—ΨNDE ΨNDE 0.4 or ΨNDE Pe, 0.59 [35-37].When discussing problems of mean-field models in the isotropic phase ofnematogens it is worthy pointing to the significant inconsistencies between predic-tions of the Maier—Saupe and Landau—de Gennes models.Within the mean-field approximation there is no anomaly of physical prop-erties associated with the exponent α in the high temperature phase: the exponent= 0. However, experiments clearly show the pretransitional anomaly of physicalproperties associated with the critical exponent α [4, 38-46]where p(T) and cp(T) are the density and the specific heat respectively. Coefficientsdi, αi, D, and A denote amplitudes.Unfortunately, there are no conclusive results for the value of exponent αso far. For instance, a reasonable fit could be reached for α = 0.5-0.11, witha flat minimum around 0.4 for a specific heat [4, 42, 43]. This uncertainty canbe related to the minute scale of anomalies, their limited range of appearance(T — TI_N < 4 K) and the discontinuity of the I—N transition. However, recentlyan agreement between the theory and the experiment has been reached due tothe concept of fluid-like, critical behavior in the isotropic phase of nematogens[22, 24, 31, 47, 48]. The theoretical model proposed by Mukherjee et al. [31, 47, 48]did not only give reasonable values of ΔT, but also predicted a non-zero value ofthe critical exponent α = 0.5 in the isotropic phase. Recent linear (dielectricpermittivity) and non-linear dielectric studies led to significant new experimentalresults supporting the fluid- lke hypothesis [22-25]. The application of the LdGmodel for NDE gave [22, 25, 491:where Δε/ is the anisotropy of dielectric permittivity for a given frequency of aweak measuring field, the coefficient α denotes the constant amplitude containingin the second rank term in the LdG series the free energy density.The Fluid-Like and Critical Behavior ...	 639In the static, low-frequency limit (f --> 0) this relation is simplified toIn leading monographs the I—N transition is presented as an example of the validityof the mean-field behavior despite the problems mentioned above. This statementis often supported by results already obtained in the seventies for It„ CME, KE[7—l0]. The reciprocal of these properties is a linear function of temperature usu-ally up to 5-10 K from TI-N . In the immediate vicinity of the clearing temper-ature weak distortion from such dependence appears. Some problems introducethe necessity of considering the additional, non-pretransitional, background term[4, 8-10, 13, 14]. The behavior of low frequency (LF) NDE is unique particularlybearing in mind that the same behavior is observed both for the I—N and isotropicto smectic A and smectic E transitions [50, 51]. The latter feature definitivelydoes not take place for KE, CME, IL [4, 8-10, 13, 14]. The reciprocal of NDEis linear functions of temperature up to Tx TI-N + 40 K from the clearingpoint. This temperature may be considered as the place where fluctuations shrinkto about 3 molecules [25, 52, 53]. Additionally, there is no background term andthere are no discrepancies near TI-N from linearity of the NDE reciprocal [25].All this significantly increases the reliability of the determined values of ΔT. Thepretransitional behavior is also observed for the static dielectric permittivity ifthe permanent dipole moment lies along the long axis of the molecule. This takesplace, for instance, in n-cyanobiphenyls. Hence ε(T) registers the changes of dielec-tric permittivity due to the cancellation of the prenematically ordered permanentdipole moments. The obtained dependencies are parameterized by [24, 25, 50, 51]:Figure 1 shows the behavior in the isotropic phase for the static NDE and dielectricpermittivity for 4-cyano-4-pentyl-alkoxybiphenyls (5CB) in a broad temperaturerange up to TI-N + 80 K. The descriptions of experimental setups are given indetail in our previous papers [50, 51]. It is noteworthy that ε(T) is parameterizedin the whole temperature range. Figure 2 shows the derivative of experimentaldata from Fig. 1.This very sensitive analysis shows that relation (3) for NDE is valid onlyup to about Tx P.1 T* + 40 K. The inset made it possible to claim that thereis definitively no discrepancies from relation (5) in the whole tested range, alsoabove Tx. However, above Tx the prenematic ordering may take place in group ofmolecules which effectively contain less than 2 molecules and hence are too smallto be recognized as a fluctuation by the fluctuation-sensitive method (for instance:NDE). Figures 1 and 2 made possible a reliable estimation of critical exponents:γ=1 and α=0.5±0.02.It is noteworthy that Eqs. (3), (4) can also be derived beyond the LdGapproximation, basing on relations for critical mixtures [23-25]:640 	 A. Drozd-Rzoska et al.where (OM 2 ) v denotes the mean square of the order parameters. The presentedapproximation is possible because prenematic fluctuations are naturally elongatedand almost non-interacting.Fig. 1. Results of NDE and dielectric permittivity measurements in the isotropic phaseof 5CB. The measurement frequency of NDE was 62 kHz and the frequency of dielectricpermittivity was 10 kHz.Fig. 2. Results of differential analysis of experimental dielectric permittivity and NDEin 5CB from Fig. 1.The Fluid-Like and Critical Behavior ...	 641It should be mentioned here that differences in the behavior of EKE andNDE in critical mixtures is associated with the classical-nonclassical properties offluctuations elongated in the strong electric field which have a different influenceon NDE and EKE [36, 37].The above analysis answers the mentioned "de Gennes problem" ([1], 1974).It also shows that the pretransitional amplitude of NDE is associated with fluc-tuations of the order parameters. This fact is significant when analyzing NDE(T)for frequencies coinciding with the relaxation time of pretransitional processes asshown in Fig. 2. The strong discrepancies near TI-N can be treated as the con-sequence of the relation between the timescale introduced by the measurementfrequency and the relaxation time. Additional distortion in the immediate vicinity642 	 A. Drozd-Rzoska et al.of TI-N may be related to the consequence of the sensitivity to the intensity ofthe weak measuring field. Such sensitivity agrees with the complex liquid natureof the isotropic phase. It is noteworthy that remotely from T*, where f- 1 » τ,the presented effect follows the LF NDE pattern.The mentioned three-decades success of the mean-field description was dueto the lack of alternative proposals. In the opinion of the authors the idea of afluid-like, critical description may be treated as such an alternative proposal. Inthis case temperature T* can be identified as the pseudospinodal, critical Gaussianpoint or the pseudospinodal tricritical point [25, 54]. To support the fluid-like ideawe present the first comprehensive comparison between theory and experiment(Table). Concluding, it is also noteworthy that linear and non-linear dielectricinvestigation deliver a set of new experimental data, which were not available byother experimental methods mentioned above [22-25, 50, 51].AcknowledgmentsThe authors would like to acknowledge the support of the Committee forScientific Research grant no. 2P03B 020 15.References[1] P.G. de Gennes, The Physics of Liquid Crystals, Clarendon Press, Oxford 1974;P.G. de Gennes, J. Prost, The Physics of Liquid Crystals, Clarendon Press, Oxford1993.[2] F.H. Gramsbergen, L. Longa, W.H. de Jeu, Phys. Rep. 135, 195 (1986).[3] G. Vertogen, W.H. de Jeu, Thermotropic Liquid Crystals, Fundamentals, SpringerSeries in Chemical Physics, Springer-Verlag, Berlin 1988.[4] M.A. Anisimov, Critical Phenomena in Liquid and Liquid Crystals, Gordon andBreach, Philadelphia 1993.[5] S. 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The fluid-like and critical behavior of the isotropic-nematic transition appearing in linear and non-linear dielectric studies

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The fluid-like and critical behavior of the isotropic-nematic transition appearing in linear and non-linear dielectric studies

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The fluid-like and critical behavior of the isotropic-nematic transition appearing in linear and non-linear dielectric studies

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