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.

30 pages, 11 figures, Published in PRE, with minor typos corrected

References in corpus (5)

• Driven particle in a random landscape: disorder correlator, avalanche distribution and extreme value statistics of records
• Liquid crystal cells with "dirty" substrates
• Stability and distortions of liquid crystal order in a cell with a heterogeneous substrate
• Smectic-glass transition in a liquid crystal cell with a "dirty" substrate
• The Smectic $A$-$C$ Phase Transition in Biaxial Disordered Environments

Cited by in corpus (5)

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• Transverse Quantum Fluids
• Exact form of the exponential correlation function in the glassy super-rough phase