The penetrable square-well model: extensive versus non-extensive phases

Abstract

The phase diagram of the penetrable square-well fluid is investigated through Monte Carlo simulations of various nature. This model was proposed as the simplest possibility of combining bounded repulsions at short scale and short-range attractions. We prove that the model is thermodynamically stable for sufficiently low values of the penetrability parameter, and in this case the system behaves similarly to the square-well model. For larger penetration, there exists an intermediate region where the system is metastable, with well-defined fluid–fluid and fluid–solid transitions, at finite size, but eventually it becomes unstable in the thermodynamic limit. We characterize the unstable non-extensive phase appearing at high penetrability, where the system collapses into an isolated blob of a few clusters of many overlapping particles each.

Keywords:

• penetrable square-well model
• thermodynamic stability
• phase diagram
• Monte Carlo simulations
• Gibbs ensemble

Acknowledgements

R.F. would like to thank Giorgio Pastore for useful discussions on the problem. We thank Tatyana Zykova-Timan and Bianca M. Mladek for enlightening discussions and useful suggestions. The support of PRIN-COFIN 2007B58EAB (A.G.), FIS2010-16587 (A.S), and GAAS IAA400720710 (A.M.) is acknowledged. Monte Carlo simulations where carried out at the Center for High Performance Computing (CHPC), CSIR Campus, 15 Lower Hope St., Rosebank, Cape Town, South Africa.

Notes

Note added in proofs. After manuscript acceptance, we became aware that the issue of non-extensivity for effective potentials was also studied in the framework of polymers in solution (See V. Krakoviack, J.-P. Hansen, and A. A. Louis, Phys. Rev. E 67, 041801 (2003)).