An investigation of the SCOZA for narrow square-well potentials and in the sticky limit

TL;DR

This study examines the effectiveness of the SCOZA method for narrow square-well potentials and the sticky limit, revealing limitations in predicting critical behavior and suggesting the need for beyond Ornstein-Zernike approaches.

Contribution

It provides new insights into SCOZA's predictions for narrow potentials and highlights its failure in the sticky limit, proposing directions for improved theories.

Findings

SCOZA does not predict a finite B2(Tc) as delta approaches zero.

In the sticky limit, SCOZA fails to predict a liquid-vapor transition.

Limitations of SCOZA suggest the need for theories beyond the Ornstein-Zernike framework.

Abstract

We present a study of the self consistent Ornstein-Zernike approximation (SCOZA) for square-well (SW) potentials of narrow width delta. The main purpose of this investigation is to elucidate whether in the limit delta --> 0, the SCOZA predicts a finite value for the second virial coefficient at the critical temperature B2(Tc), and whether this theory can lead to an improvement of the approximate Percus-Yevick solution of the sticky hard-sphere (SHS) model due to Baxter [R. J. Baxter, J. Chem. Phys. 49, 2770 (1968)]. For SW of non vanishing delta, the difficulties due to the influence of the boundary condition at high density already encountered in an earlier investigation [E. Schoell-Paschinger, A. L. Benavides, and R. Castaneda-Priego, J. Chem. Phys. 123, 234513 (2005)] prevented us from obtaining reliable results for delta < 0.1. In the sticky limit this difficulty can be circumvented, but then the SCOZA fails to predict a liquid-vapor transition. The picture that emerges from this study is that for delta --> 0, the SCOZA does not fulfill the expected prediction of a constant B2(Tc) [M. G. Noro and D. Frenkel, J. Chem. Phys. 113, 2941 (2000)], and that for thermodynamic consistency to be usefully exploited in this regime, one should probably go beyond the Ornstein-Zernike ansatz.