Demixing in a single-peak distributed polydisperse mixture of hard spheres

Grupo Interdisciplinar de Sistemas Complicados (GISC), Departamento de Matemáticas Universidad Carlos III de Madrid Avda. de la Universidad, 30, E-28911, Leganés, Madrid, Spain

Received: 30 November 1998
Accepted: 5 February 1999

Abstract

An analytic derivation of the spinodal of a polydisperse mixture is presented. It holds for fluids whose excess free energy can be accurately described by a function of a few moments of the size distribution. It is shown that one such mixture of hard spheres in the Percus-Yevick approximation never demixes, despite its size distribution. In the Boublík-Mansoori-Carnahan-Starling-Leland approximation, though, it demixes for a sufficiently wide log-normal size distribution. The importance of this result is twofold: first, this distribution is unimodal, and yet it phase separates; and second, log-normal size distributions appear in many experimental contexts. The same phenomenon is shown to occur for the fluid of parallel hard cubes.