title: Smectic order, pinning, and phase transition in a smectic-liquid-crystal cell with a random substrate.
abstract: We study smectic-liquid-crystal order in a cell with a heterogeneous substrate imposing surface random positional and orientational pinnings. Proposing a minimal random elastic model, we demonstrate that, for a thick cell, the smectic state without a rubbed substrate is always unstable at long scales and, for weak random pinning, is replaced by a smectic glass state. We compute the statistics of the associated substrate-driven distortions and the characteristic smectic domain size on the heterogeneous substrate and in the bulk. We find that for weak disorder, the system exhibits a three-dimensional temperature-controlled phase transition between a weakly and strongly pinned smectic glass states akin to the Cardy-Ostlund phase transition. We explore experimental implications of the predicted phenomenology and suggest that it provides a plausible explanation for the experimental observations on polarized light microscopy and x-ray scattering.
authors.affiliation: Department of Physics, University of Colorado, Boulder, Colorado 80309, USA.
authors.forename: Quan
authors.initials: Q
authors.lastname: Zhang
authors.forename: Leo
authors.initials: L
authors.lastname: Radzihovsky
mesh_terms: D003198:Computer Simulation; D050866:Liquid Crystals / Q000737:chemistry*; D008956:Models, Chemical; D008958:Models, Molecular; D015233:Models, Statistical; D012031:Refractometry / Q000379:methods*