Young and Young--Laplace equations for a static ridge of nematic liquid crystal, and transitions between equilibrium states

TL;DR

This paper develops a comprehensive theoretical framework for a static nematic liquid crystal ridge on a substrate, revealing complex wetting transitions, contact-angle hysteresis, and multiple partial wetting states beyond classical isotropic liquids.

Contribution

It provides the first complete theoretical description of nematic ridges, including Young and Young--Laplace equations, and analyzes transitions between different wetting states with anchoring breaking.

Findings

Identification of continuous and discontinuous wetting transitions.

Discovery of contact-angle hysteresis in nematic systems.

Existence of multiple partial wetting states not seen in classical liquids.

Abstract

Motivated by the need for greater understanding of systems that involve interfaces between a nematic liquid crystal, a solid substrate, and a passive gas that includes nematic--substrate--gas three-phase contact lines, we analyse a two-dimensional static ridge of nematic resting on a solid substrate in an atmosphere of passive gas. Specifically, we obtain the first complete theoretical description for this system, including nematic Young and Young--Laplace equations, and then, under the assumption that anchoring breaking occurs in regions adjacent to the contact lines, we use the nematic Young equations to determine the continuous and discontinuous transitions that occur between the equilibrium states of complete wetting, partial wetting, and complete dewetting. In particular, in addition to continuous transitions analogous to those that occur in the classical case of an isotropic liquid, we find a variety of discontinuous transitions, as well as contact-angle hysteresis, and regions of parameter space in which there exist multiple partial wetting states that do not occur in the classical case.