Pathologies in the sticky limit of hard-sphere-Yukawa models for colloidal fluids. A possible correction

TL;DR

The paper identifies a fundamental flaw in a commonly used sticky-hard-sphere model for colloidal fluids, proposes a corrected model and closure, and provides an analytical solution to address the divergence issue.

Contribution

It introduces a new, well-defined model (SHS3) and a modified closure (modified MSA) to fix the divergence problem in the original SHS2 model, enabling accurate analytical results.

Findings

SHS2 model's second virial coefficient diverges.

Modified MSA and SHS3 restore a well-defined model.

Analytical solutions are obtained for the corrected model.

Abstract

A known `sticky-hard-sphere' model, defined starting from a hard-sphere-Yukawa potential and taking the limit of infinite amplitude and vanishing range with their product remaining constant, is shown to be ill-defined. This is because its Hamiltonian (which we call SHS2) leads to an {\it exact}second virial coefficient which {\it diverges}, unlike that of Baxter's original model (SHS1). This deficiency has never been observed so far, since the linearization implicit in the `mean spherical approximation' (MSA), within which the model is analytically solvable, partly {\it masks} such a pathology. To overcome this drawback and retain some useful features of SHS2, we propose both a new model (SHS3) and a new closure (`modified MSA'), whose combination yields an analytic solution formally identical with the SHS2-MSA one. This mapping allows to recover many results derived from SHS2, after a re-interpretation within a correct framework. Possible developments are finally indicated.