Long-range forces and aggregation of colloid particles in a nematic liquid crystal

Abstract

We calculate the long-range pair potential between spherical colloid particles suspended in a uniform liquid crystal. At weak director anchoring on the particle surface the director distortions decay as \ensuremath{\delta}n\ensuremath{\sim}${\mathrm{r}}^{\mathrm{\ensuremath{-}}3}$sin 2\ensuremath{\theta} away from its center. This leads to an anisotropic interaction potential of the form U\ensuremath{\sim}${\mathrm{d}}^{\mathrm{\ensuremath{-}}5}$ with d the distance between two colloid particles. This interaction also depends on the particle position with respect to the nematic director, giving strong repulsion for particles along the director axis and for particles located in the perpendicular plane, and attraction at oblique angles. We also analyze the system behavior in an external field, when the director decays exponentially away from the particle and, hence, interaction forces are short range.