The dynamics of colloidal intrusions in liquid crystals: a simulation perspective

Dispersing colloidal particles into liquid crystals provides a promising avenue to build a novel class of materials, with potential applications, among others, as photonic crystals, biosensors, metamaterials and new generation liquid crystal devices. Understanding the physics and dynamical properties of such composite materials is then of high-technological relevance; it also provides a remarkable challenge from a fundamental science point of view due to the intricacies of the hydrodynamic equations governing their dynamical evolution. Here, we provide an overview of our current theoretical understanding of the dynamical and hydrodynamic properties of colloid–liquid crystal composites, focussing on the results obtained from computer simulations; no or very limited previous knowledge of the field of liquid crystals is assumed. While our main emphasis is on the dynamics, we also review a selection of equilibrium results and simulations to provide the necessary background. We start by describing what we know about the simplest possible problem: that of a single particle in a nematic, or cholesteric, liquid crystal. We then consider two particles, and review the conditions which lead to the formation of a dimer; we then again focus on dynamical problems. Finally, we turn to the more complicated case of a dispersion, reviewing here simulations motivated by optical tweezer and rheological experiments. We close by making a list of some of the many open problems in this rapidly developing research field.