The isotropic and nematic liquid crystal phase of colloidal rods

Abstract

The density-dependent distribution function of the orientation of the long axis of rod-like colloidal particles in the liquid crystalline nematic phase is numerically calculated as the solution of a nonlinear integral equation. From this solution, which is obtained by an iterative method that is explained in detail, the free energy, the pressure and the chemical potential can be computed, as well as the nematic order parameter. Moreover, the first-order phase transition from the disordered isotropic fluid phase to the nematic phase is analysed numerically. This study, presented at the level of advanced undergraduates or starting graduate students, not only illustrates the existence of liquid crystalline ordering for nonspherical particles, but also shows explicitly how thermodynamics, structure and symmetry are related.