Effective potentials for polymers and colloids: beyond the van der Waals picture of fluids?

This paper briefly reviews some recent work demonstrating the partial breakdown of the colloidal fluid ↔ atomic fluid analogy. The success of liquid state theory for atomic fluids stems in part from the van der Waals picture, where steric interactions dominate the structure, and attractive interactions can be added as a perturbation. For complex fluids described by effective potentials, this picture may break down. In the first example discussed, depletion potentials in non–additive hard–sphere mixtures are shown to be surprisingly complex, leading to fluid structure and fluid–solid transitions dominated by properties of the attractive potentials instead of by the hard–cores. Many colloidal suspensions, and possibly globular proteins, fall into this energetic fluid category. In the second example, the coarse–graining of polymers leads to soft–core effective potentials and associated mean–field fluid behaviour distinguished by a breakdown of the virial expansion, an equation of state that is nevertheless nearly linear in density, and correlation functions well described by the random phase approximation.