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

Abstract

We present a study of the self-consistent Ornstein–Zernike approximation (SCOZA) for square-well (SW) potentials of narrow width δ. The main purpose of this investigation is to elucidate whether, in the limit δ → 0, the SCOZA predicts a finite value for the second virial coefficient at the critical temperature B 2(T c), 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 [J. Chem. Phys. 49, 2770 (1968)]. For the SW of non-vanishing δ, the difficulties due to the influence of the boundary condition at high density, already encountered in an earlier investigation by Schöll-Paschinger et al. [J. Chem. Phys. 123, 234513 (2005)], prevented us from obtaining reliable results for δ <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 δ → 0, the SCOZA does not fulfill the expected prediction of a constant B 2(T c) [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.