Capillary and winding transitions in a confined cholesteric liquid crystal

TL;DR

This study uses mean-field theory to analyze phase transitions in a confined cholesteric liquid crystal, revealing oscillatory and winding transitions driven solely by pore width changes, with complex phase diagrams including triple points.

Contribution

It predicts and analyzes winding transitions induced purely by geometric confinement without external fields, extending previous work to include phase diagrams in temperature and pore width.

Findings

Oscillatory isotropic-cholesteric transition with pore width

Infinite winding transitions due to geometry

Phase diagrams with triple points and coexistence regions

Abstract

We consider a Lebwohl-Lasher model of chiral particles confined in a planar cell (slit pore) with different boundary conditions, and solve it using mean-field theory. The phase behaviour of the system with respect to temperature and pore width is studied. Two phenomena are observed: (i) an isotropic-cholesteric transition which exhibits an oscillatory structure with respect to pore width, and (ii) an infinite set of winding transitions caused by commensuration effects between cholesteric pitch and pore width. The latter transitions have been predicted and analysed by other authors for cholesterics confined in a fixed pore and subject to an external field promoting the uniaxial nematic phase; here we induce winding transitions solely from geometry by changing the pore width at zero external field (a setup recently explored in Atomic-Force Microscopy experiments). In contrast with previous studies, we obtain the phase diagrams in the temperature vs pore width plane, including the isotropic-cholesteric transition, the winding transitions and their complex relationship. In particular, the structure of winding transitions terminates at the capillary isotropic-cholesteric transition via triple points where the confined isotropic phase coexists with two cholesterics with different helix indices. For symmetric and asymmetric monostable plate anchorings the phase diagram are qualitatively similar.