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

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 supports 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, which indicates that pseudocritical 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.