Polydispersity and surface energy strength in nematic colloids

TL;DR

This paper models a polydisperse suspension of colloids in a nematic liquid crystal, deriving an effective free energy that accounts for surface energy effects and their influence on the composite's behavior.

Contribution

It introduces a homogenized Landau-de Gennes model for polydisperse colloids with surface anchoring, revealing how inclusions induce an effective field and dominate free energy in strong anchoring regimes.

Findings

Effective free energy includes a linear term due to inclusions.

In the strong anchoring limit, surface effects dominate the free energy.

The model accounts for polydispersity and inhomogeneity in colloidal suspensions.

Abstract

We consider a Landau-de Gennes model for a polydisperse, inhomogeneous suspension of colloidal inclusions in a nematic host, in the dilute regime. We study the homogenised limit and compute the effective free energy of the composite material. By suitably choosing the shape of the inclusions and imposing a quadratic, Rapini-Papoular type surface anchoring energy density, we obtain an effective free energy functional with an additional linear term, which may be interpreted as an "effective field" induced by the inclusions. Moreover, we compute the effective free energy in a regime of "very strong anchoring", that is, when the surface energy effects dominate over the volume free energy.