On the compressibility equation of state for multicomponent adhesive hard sphere fluids

TL;DR

This paper investigates the limitations of the compressibility equation of state for multicomponent adhesive hard sphere fluids within the mean spherical approximation, revealing non-existence issues and proposing a potential solution.

Contribution

It identifies the non-existence of the compressibility EOS in certain multicomponent models and offers a method to obtain a consistent pressure in specific cases.

Findings

Compressibility EOS does not exist for some multicomponent models.

Inadequacy of MSA causes non-reciprocity in derivatives of pressure.

A specific example yields a consistent compressibility pressure.

Abstract

The compressibility equation of state for a multicomponent fluid of particles interacting via an infinitely narrow and deep potential, is considered within the mean spherical approximation (MSA). It is shown that for a class of models leading to a particular form of the Baxter functions $q_{ij}(r)$ containing density-independent stickiness coefficient, the compressibility EOS does not exist, unlike the one-component case. The reason for this is that a direct integration of the compressibility at fixed composition, cannot be carried out due to the lack of a reciprocity relation on the second order partial derivatives of the pressure with respect to two different densities. This is, in turn, related to the inadequacy of the MSA. A way out to this drawback is presented in a particular example, leading to a consistent compressibility pressure, and a possible generalization of this result is discussed.