Critical behavior at the nematic–to–smectic-A transition in a nonpolar liquid crystal with wide nematic range

Abstract

High-resolution x-ray scattering experiments to study the critical smectic-^ fluctuations in the nematic phase have been performed on a mixture of two nonpolar, two-benzene-ring compounds. The ratio TNA/THI (-0.885) for this mixture is much smaller than for previously studied similar materials. The smectic correlation lengths parallel and perpendicular to the smectic-layer normal are found to diverge anisotropically with characteristic exponents v« =0.75 ±0.03, v± =0.65 ± 0.03, and the susceptibility with /=1.24 ±0.05. PACS numbers: 64.70.Md, 61.10.H, 6l.30.Eb, 64.60.Fr Since the pioneering work of McMillan [l], the nematic-to-smectic-/4 (NA) phase transition in thermotropic liquid crystals has been a subject of extensive theoretical and experimental studies. A convenient physical realization of the simplest freezing transition in nature, the NA transition is of fundamental scientific significance; however, the detailed nature of this apparently simple transition remains poorly understood. Theoretical attempts to understand the NA transition can be divided into two groups. The first group predicts isotropic divergence of the size of a correlated region of critical smectic-v4 fluctuations in the nematic phase. The values of the characteristic exponents v\\ and V_L, describing the divergence parallel and perpendicular to the smectic density wave, are predicted to be j by the mean-field theories [1,2], and y by de Gennes's analogy [3] to critical behavior of superfluid He. The second group includes theories based on the de Gennes model [4] and on the dislocation-mediated melting mechanism [5] which predict anisotropic divergence with v\\ =s 2v±. On the experimental front, this transition has been studied by several experimental techniques including x-ray diffraction [6,7], quasielastic light scattering [8,9], and heat capacity [10,11]. Anisotropic critical fluctuations at this transition are a common empirical feature among all materials. However, the values of critical exponents are material dependent and the ratio of the correlation-length exponents determined by x-ray scattering lies between 1.2 and 1.5 [8][9][10][11]. The value of the susceptibility exponent y lies between 1.10 and 1.53, and for several materials agrees with the predictions based on the He analogy within experimental uncertainties. Thus, some aspects of different models appear to be correct while none of them is right in its entirety. The situation is not hopeless. The hyperscaling relation, 2V_L + v\\ =2 -a, where a is the heat-capacity exponent, holds for most of the materials, suggesting some underlying universal behavior.This complex situation can, to some extent, be ascribed to a number of factors. Ideally, one would like to study systems in which only the smectic order parameter is important near the NA transition. Unfortunately, the coupling between the smectic and nematic order parameters is significant. In materials exhibiting a narrow nematic range, the nematic order parameter does not saturate before the NA transition occurs. As th...

“Bicellar” Lipid Mixtures as used in Biochemical and Biophysical Studies

“…In the case of thermotropic liquid crystal systems, a nematic-to-smectic transition is a common occurrence (Parmar and Clark 1989;Qiu and Ho 1990;Chen et al 1991;Safinya et al 1991;Lelidis and Durand 1994). However, the same cannot be said in the case of lyotropic systems.…”

Anisotropy of the Nematic–smectic a Phase Transition

“…28 Another difference between NA systems that has been investigated is the relative width of the nematic region. 21 This width has been historically characterized by the "McMillan ratio", TNA/TNI. 1 For McMillan ratios approaching 1, the nematic region is so small that fluctuations of both the nematic and smectic order parameters must be considered simultaneously and the critical behavior is tricritical in nature.…”

Smectic Liquid Crystals

“…During the last 25 years, many high resolution heat capacity and X-ray studies have been devoted to the S A N transition [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] . Most of the focus has been on the critical exponents in the hope of determining the universality class of this transition.…”