Interaction energies in paranematic colloids

TL;DR

This paper analyzes weak interactions between colloidal particles in a paranematic phase, developing asymptotic models, verifying their accuracy, and exploring the statistical behavior through simulations.

Contribution

It introduces rigorous asymptotics for the linearized model of paranematic colloids and compares nonlinear and linear solutions to understand interaction decay.

Findings

Decay rates of nonlinear and linear solutions are similar.

Interactions depend on particle distance similarly in both models.

Monte-Carlo simulations reveal statistical properties of colloidal suspensions.

Abstract

We consider a system of colloidal particles embedded in a paranematic -- an isotropic phase of a nematogenic medium above the temperature of the nematic-to-isotropic transition. In this state, the nematic order is induced by the boundary conditions in a narrow band around each particle and it decays exponentially in the bulk. We develop rigorous asymptotics of the linearization of the appropriate variational model that allow us to describe weak far-field interactions between the colloidal particles in two dimensional paranematic suspensions. We demonstrate analytically that decay rates of solutions to the full nonlinear and linear problems are similar and verify numerically that the interactions between the particles in these problems have similar dependence on the distance between the particles. Finally, we perform Monte-Carlo simulations for a system of colloidal particles in a paranematic and describe the statistical properties of this system.