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

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

2003-04-02

arxiv.org/abs/cond-mat/0304053v1

Physics

Condensed Matter

Statistical Mechanics

21 pages, 1 figure, accepted in Molecular Physics (2003)

Scientific paper

10.1080/0026897031000122379

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.

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