Smectic ordering in liquid-crystal–aerosil dispersions. II. Scaling analysis

Abstract

Liquid crystals offer many unique opportunities to study various phase transitions with continuous symmetry in the presence of quenched random disorder (QRD). The QRD arises from the presence of porous solids in the form of a random gel network. Experimental and theoretical work support the view that for fixed (static) inclusions, quasi-long-range smectic order is destroyed for arbitrarily small volume fractions of the solid. However, the presence of porous solids indicates that finite-size effects could play some role in limiting long-range order. In an earlier work, the nematic -smectic-A transition region of octylcyanobiphenyl (8CB) and silica aerosils was investigated calorimetrically. A detailed x-ray study of this system is presented in the preceding Paper I, which indicates that pseudo-critical scaling behavior is observed. In the present paper, the role of finite-size scaling and two-scale universality aspects of the 8CB+aerosil system are presented and the dependence of the QRD strength on the aerosil density is discussed.

Smectic liquid crystals in an anisotropic random environment

“…This analysis shows that the correlations, as characterized by effective critical exponents for the correlation lengths and susceptibility, differ from those of pure 8CB even when the correlation lengths are considerably smaller than the gel pore size, providing evidence that the presence of quenched disorder alters the coupling between nematic and smectic order and its influence over smectic critical behavior. When combined with similar results from smectics confined to isotropic gels for effective critical exponents for the specific heat and smectic order parameter [12,13,28], these findings provide a comprehensive picture of an evolution in the N-SmA critical fluctuations toward conventional 3D XY behavior with increasing quenched disorder.…”

High-resolution x-ray study of the nematic–smectic-Aand smectic-A–smectic-Ctransitions in liquid-crystal–aerosil gels

“…For 8CB-aerosil [2,3,4] and 8OCB-aerosil [5], the parameters extracted from the line shape compared favorably with the predictions of Ref. [19], giving the appearance that the gel applies a random field which pins the phase of the smectic density wave.…”

“…In a recent series of papers [2,3,4,5], it has been shown that the nematic to smectic-A (N -SmA) transition in liquid crystal-aerosil dispersions is well described as a continuous symmetry (XY) transition with quenched random fields. This facilitates studying this important class of transitions.…”

“…Early calorimetric studies have shown a systematic variation in the critical fluctuations as the aerosil concentration increases. These experiments and accompanying theory have focused on the isotropic to nematic (I -N) [6] and the N -SmA transitions [2,3,4,5,6]. Here we present results on a substantially different material at the NSmA transition and we present the first x-ray data for * Present Address: Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899 the smectic-A to smectic-C (SmA -SmC) transition for liquid crystal-aerosil dispersions.…”

Smectic-Aand smectic-Cphases and phase transitions in8¯SFreelon1, Ramazanoglu2, Chung3 et al. 2011Phys. Rev. E18170View full textAdd to dashboardCite

“…Thus, LC + aerosil gels provide an excellent experimental window through which to observe the manner in which QRD affects phase transitions. A key feature of LC + aerosil systems is that the degree of random field disorder is proportional [3] to the reduced aerosil mass density, in grams of SiO 2 per cm 3 of LC, S  . By changing S  , the random field disorder varies continuously from the dilute ( S  < 0.01 g/cm 3 ) to the soft (0.01< S  < 0.1 g/cm 3 ) and, at large S  , to the stiff ( S  > 0.1 g/cm 3 ) gel disorder limits.…”