A fundamental measure density functional for fluid and crystal phases of the Asakura-Oosawa model.

We investigate a density functional for the Asakura-Oosawa model of colloid-polymer mixtures, describing both fluid and crystal phases. It is derived by linearizing the two-component fundamental-measure hard sphere tensor functional in the second (polymer) component. We discuss the formulation of an effective density functional for colloids only. For small polymer-colloid size ratios the effective, polymer-induced potential between colloids is short-range attractive and of two-body form but we show that the effective density functional is not equivalent to standard mean-field approaches where attractions are taken into account by terms second order in the colloid density. We calculate numerically free energies and phase diagrams in good agreement with available simulations, furthermore we discuss the colloid and polymer distributions in the crystal and determine equilibrium vacancy concentrations. Numerical results reveal a fairly strong sensitivity to the specific type of underlying fundamental measure hard sphere functional which could aid further development of fundamental measure theory.

Fundamental measure theory for the inhomogeneous hard-sphere system based on Santos' consistent free energy.

Based on Santos' general solution for the scaled-particle differential equation [Phys. Rev. E 86, 040102(R) (2012)], we construct a free-energy functional for the hard-sphere system. The functional is obtained by a suitable generalization and extension of the set of scaled-particle variables using the weighted densities from Rosenfeld's fundamental measure theory for the hard-sphere mixture [Phys. Rev. Lett. 63, 980 (1989)]. While our general result applies to the hard-sphere mixture, we specify remaining degrees of freedom by requiring the functional to comply with known properties of the pure hard-sphere system. Both for mixtures and pure systems, the functional can be systematically extended following the lines of our derivation. We test the resulting functionals regarding their behavior upon dimensional reduction of the fluid as well as their ability to accurately describe the hard-sphere crystal and the liquid-solid transition.