Potential of mean force between a spherical particle suspended in a nematic liquid crystal and a substrate: sphere size effects.

The expanded ensemble density of states method (ExEDOS) is used to investigate the effective interaction of a spherical colloidal particle suspended in a confined liquid crystal (LC) with a substrate. The potential of mean force (PMF) is determined as a function of the normal distance between the particle and the substrate's surface. The presence of the substrate induces a layered structure of the LC, which in turn greatly influences the PMF. We analyze the structure of the Saturn ring defect that accompanies the colloidal sphere, and find that the ring is displaced slightly towards the surface when the sphere is within the first LC surface layer. A transition occurs from an overall attraction of the colloid to the substrate to a global repulsion when the sphere's radius is roughly twice the length of the LC molecules.