We present a study of the self-consistent Ornstein-Zernike approximation (SCOZA) for square-well (SW) potentials of narrow width . The main purpose of this investigation is to elucidate whether, in the limit 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 [J. Chem. Phys. 49, 2770 (1968)]. For the SW of non-vanishing , the difficulties due to the influence of the boundary condition at high density, already encountered in an earlier investigation by Scholl-Paschinger et al. [J. Chem. Phys. 123, 234513 (2005)], prevented us from obtaining reliable results for 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 0, the SCOZA does not fulfill the expected prediction of a constant B2(Tc) [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.
An investigation of SCOZA for narrow square-well potentials and in the sticky limit
PAROLA, ALBERTO;COLOMBO, JADER;
2011-01-01
Abstract
We present a study of the self-consistent Ornstein-Zernike approximation (SCOZA) for square-well (SW) potentials of narrow width . The main purpose of this investigation is to elucidate whether, in the limit 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 [J. Chem. Phys. 49, 2770 (1968)]. For the SW of non-vanishing , the difficulties due to the influence of the boundary condition at high density, already encountered in an earlier investigation by Scholl-Paschinger et al. [J. Chem. Phys. 123, 234513 (2005)], prevented us from obtaining reliable results for 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 0, the SCOZA does not fulfill the expected prediction of a constant B2(Tc) [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.
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