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

TL;DR

This paper investigates how random surface pinning affects smectic liquid crystals, revealing a transition from a weakly pinned state to a smectic glass, with implications for experimental observations.

Contribution

It introduces a minimal elastic model showing the instability of the smectic state under random pinning and predicts a temperature-driven phase transition to a smectic glass.

Findings

Weak disorder leads to a smectic glass state.

A temperature-controlled phase transition exists between weakly and strongly pinned states.

Predicted phenomena align with experimental microscopy and scattering results.

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.