Siderius DW, Corti DS. Extension of scaled particle theory to inhomogeneous hard particle fluids. IV. Cavity growth at any distance relative to a planar hard wall.
PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011;
83:031126. [PMID:
21517473 DOI:
10.1103/physreve.83.031126]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2010] [Revised: 01/28/2011] [Indexed: 05/30/2023]
Abstract
A completely generalized version of an inhomogeneous scaled particle theory (I-SPT) for hard particle fluids confined by hard walls is presented, whereby the reversible work of cavity insertion can be determined for a cavity of any radius located at any distance from the hard wall. New exact and approximate conditions on the central function Ḡ of I-SPT are developed, where Ḡ is related to the average value of the anisotropic density of hard-sphere centers at the surface of the cavity. The predictions of the work of insertion and the form of Ḡ are quite accurate up to moderate bulk densities as compared to molecular simulation results. The accuracy of I-SPT begins to decline at high densities, due to limitations of certain needed approximations required for a complete description of Ḡ. Finally, interesting insights into the origin of depletion effects between a hard-sphere solute and the hard wall are generated via this version of I-SPT. The oscillatory nature of depletion forces, exhibiting both attractive and repulsive domains, is found to arise from the interplay between bulk SPT and I-SPT relations.
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