On elliptical soft colloids in smectic-C films

TL;DR

This paper provides an analytical and numerical study of how the shape of elliptical soft colloids in smectic C films depends on elastic and surface parameters, revealing the influence of defects and elastic energy.

Contribution

It introduces a combined analytical and numerical approach to determine equilibrium shapes of elliptical colloids considering defect formation and elastic effects in smectic C films.

Findings

Shape diagram derived analytically for small eccentricities

Numerical methods extend results to arbitrary eccentricities

Elastic constants and anchoring strength significantly influence colloid shape

Abstract

We investigate theoretically the elliptical shapes of soft colloids in freely standing smectic C films, that have been reported recently. The colloids favour parallel alignment of the liquid crystal molecules at their surfaces and, for sufficiently strong anchoring, will generate a pair of defects at the poles of the colloidal particles. The elastic free energy of the liquid crystal matrix will, in turn, affect the shape of the colloids. In this study we will focus on elliptical soft colloids and determine how their equilibrium shapes depend on the elastic constants of the liquid crystal, the anchoring strength, the surface tension and the size of the colloids. A shape diagram is obtained analytically, by minimizing the Frank elastic free energy, in the limit of small eccentricities. The analytical results are verified, and generalized to arbitrary eccentricities, by numerical minimization of an appropriate Landau free energy. The latter is required for an adequate description of the topological defects when the liquid crystal correlation length is comparable to the size of the colloidal particles.