A test of generalized van der Waals theory for confined fluids of rigid particles

Abstract

The predictions of the generalized van der Waals (GvdW) theory for density profiles of hard rods and spheres confined between hard walls are considered as a function of chemical potential. The usual iterative solution of the stationarity condition of the functional becomes impractical at high μ and is replaced by a local steepest descent minimum search which is able to generate solutions with no apparent limit on μ. Further improvement can be achieved using the global method of simulated annealing to perform the combinatorial optimization and by consideration of the free-energy variation with the location of a test particle. The accuracy of the GvdW theory in one dimension is tested by comparison with exact results.