Nematic van der Waals Free-energy

Abstract

We develop the calculation of free energy in a nematic phase for a model of spherical particles with the long-range anisotropic interaction from the van der Waals theory. We map the gas-liquid equilibrium, which is coupled to a first-order isotropic-nematic transition. We discus how the topology of the phase diagrams changes upon varying the strengths of the isotropic and nematic interactions.

Phase Transitions in Nematic Fluids

“…The N' branch is the unphysical branch because ηf is a concave function of η . The N branch, however, is the physical branch because ηf is a convex function of η (see [32] for more details). In our previous study [32], we have shown that the nematic phase can only occur for q larger than 1.51 or 2 t φ γ γ * = larger than 2.24.…”

“…The N branch, however, is the physical branch because ηf is a convex function of η (see [32] for more details). In our previous study [32], we have shown that the nematic phase can only occur for q larger than 1.51 or 2 t φ γ γ * = larger than 2.24. In other words, the isotropic-nematic transition is always of the first-order type because the order parameter q has to jump from q=0 to 1.51. q ≥ In the following we will give the phase diagram for the fluid phases (both isotropic and nematic), solid phases, and finally we present the complete phase diagram where both fluid and solid phases are present.…”

“…From Eqs. (8) and (23) the pressure of the fluid phase can be written as According to the value of Γ* = γ (n 1 -3)/(n 2 -3) there are two topologically distinct types of phase diagrams (see [32]…”

“…In our early extensive study of the phase behavior of the Heisenberg model [15,16] we have generalized the van der Waals (vdW) theory for anisotropic interactions to study the phase behavior of a system of particles with magnetic exchange interactions. By using this vdW theory we have recently developed the calculation of free energy in a nematic fluid phase [32]. We have shown that there is no difficulty in stabilizing the nematic liquid phase over a large domain of the temperature-density plane.…”

“…In the present investigation we perform a similar study. We will use the nematic Maier-Saupe interactions [17,32] and the generalized vdW theory to calculate the free energy functional for the nematic phases (including the solid phases) and examine the thermodynamic stability of nematic liquids when the solid phases are taken into account. The value order parameter has been found by minimization of the reduced Helmholtz free energy functional in terms of order parameter.…”