Smectic order, pinning, and phase transition in a smectic-liquid-crystal cell with a random substrate

摘要

We study smectic-liquid-crystal order in a cell with a heterogeneous substrate imposing surface randomnpositional and orientational pinnings. Proposing a minimal random elastic model, we demonstrate that, for anthick cell, the smectic state without a rubbed substrate is always unstable at long scales and, for weak randomnpinning, is replaced by a smectic glass state. We compute the statistics of the associated substrate-drivenndistortions and the characteristic smectic domain size on the heterogeneous substrate and in the bulk. We findnthat for weak disorder, the system exhibits a three-dimensional temperature-controlled phase transition betweenna weakly and strongly pinned smectic glass states akin to the Cardy-Ostlund phase transition. We explorenexperimental implications of the predicted phenomenology and suggest that it provides a plausible explanationnfor the experimental observations on polarized light microscopy and x-ray scattering.