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

Davide Pini (1) , Alberto Parola (2) , Jader Colombo (2) , Luciano Reatto (1)

1 Dipartimento di Fisica [Milano]
2 Dipartimento di Fisica e Matematica

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 $\delta\to 0$, 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 [R. J. Baxter, J. Chem. Phys. {\bf 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. Scholl-Paschinger, A. L. Benavides, and R. Castaneda-Priego, J. Chem. Phys. {\bf 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 $\delta\to 0$, the SCOZA does not fulfill the expected prediction of a constant $B_{2}(T_{c})$ [M. G. Noro and D. Frenkel, J. Chem. Phys. {\bf 113}, 2941 (2000)], and that for thermodynamic consistency to be usefully exploited in this regime, one should probably go beyond the Ornstein-Zernike ansatz.

Mots clés: Physical Sciences

Domaines: Matière Condensée [cond-mat]

Davide Pini, Alberto Parola, Jader Colombo, Luciano Reatto. An investigation of the SCOZA for narrow square-well potentials and in the sticky limit. Molecular Physics, 2011, 109 (07-10), pp.1343-1361. ⟨10.1080/00268976.2011.558028⟩. ⟨hal-00692123⟩