Numerical solution of the RHNC theory for fluids of non-spherical particles near a uniform planar wall

Abstract

An efficient algorithm, a hybrid of the Picard-type and Newton-Raphson (NR) methods, is developed for solving the reference hypernetted-chain (RHNC) theory for non-spherical particles near a uniform planar wall. The basic idea of the algorithm is also applicable to non-spherical particles near a large macroparticle at infinite dilution. The problem of dipolar hard spheres near a hard wall is chosen here as an example system. A feature of the algorithm is that the Jacobian matrix is determined in the bulk calculation and serves as part of the input data for the wall calculation. Hence, the convergence is achieved in only a single iteration in the inner NR loop regardless of the initial values of the iteration variables. It is shown that the great advantage of the constant Jacobian matrix can be preserved even for general cases of other particle-particle and wall-particle interactions. In the course of the study, we encounter a singular behaviour of the RHNC theory for bulk dipolar hard spheres. Keeping the reduced density, we continue to increase the reduced dipole moment. Then, at a certain point the projections of the rotational invariant expansion of the total correlation function h ^mm0(r) (m ≠ 0; m = 1,2,3, …) become infinitely long ranged, which causes divergence of their Fourier transforms at zero wave-number, ħ ^mm0(0). The static dielectric constant and the heat capacity also diverge at that point. The singular behaviour implies the growth of the strong, long-ranged orientational order favouring parallel configuration, and represents a stability limit of the isotropic phase.