We develop a density functional for hard-sphere mixtures which keeps the structure of Rosenfeld's fundamental measure theory (FMT) whilst inputting the Mansoori-Carnahan-Starling-Leland bulk equation of state. Density profiles for the pure hard-sphere fluid and for some binary mixtures adsorbed at a planar hard wall obtained from the present functional exhibit some improvement over those from the original FMT. The pair direct correlation function c (2) (r ) of the pure hard-sphere fluid, obtained from functional differentiation, is also improved. When a tensor weight function is incorporated for the pure system our functional yields a good description of fluid-solid coexistence and of the properties of the solid phase.

Hard-sphere systems are one of the fundamental model systems of statistical physics and represent an important reference system for molecular or colloidal systems with soft repulsive or attractive interactions in addition to hard-core repulsion at short distances. Density functional theory for classical systems, as one of the core theoretical approaches of statistical physics of fluids and solids, has to be able to treat such an important system successfully and accurately. Fundamental measure theory is up to date the most successful and most accurate density functional theory for hard-sphere mixtures. Since its introduction fundamental measure theory has been applied to many problems, tested against computer simulations, and further developed in many respects. The literature on fundamental measure theory is already large and is growing fast. This review aims to provide a starting point for readers new to fundamental measure theory and an overview of important developments.

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We present a versatile density functional approach (DFT) for calculating the depletion potential in general fluid mixtures. In contrast to brute force DFT, our approach requires only the equilibrium density profile of the small particles before the big (test) particle is inserted. For a big particle near a planar wall or a cylinder or another fixed big particle the relevant density profiles are functions of a single variable, which avoids the numerical complications inherent in brute force DFT. We implement our approach for additive hard-sphere mixtures, comparing our results with computer simulations for the depletion potential of a big sphere of radius R b in a sea of small spheres of radius R s near i) a planar hard wall and ii) another big sphere. In both cases our results are accurate for size ratios s = R s /R b as small as 0.1 and for packing fractions of the small spheres η s as large as 0.3; these are the most extreme situations for which reliable simulation data are currently available. Our approach satisfies several consistency requirements and the resulting depletion potentials incorporate the correct damped oscillatory decay at large separations of the big particles or of the big particle and the wall. By investigating the depletion potential for high size asymmetries we assess the regime of validity of 1 the well-known Derjaguin approximation for hard-sphere mixtures and argue that this fails, even for very small size ratios s, for all but the smallest values of η s where it reduces to the Asakura-Oosawa potential. We provide an accurate parametrization of the depletion potential in hard-sphere fluids which should be useful for effective Hamiltonian studies of phase behavior and colloid structure. Our results for the depletion potential in a binary hard-sphere mixture, with size ratio s = 0.0755 chosen to mimic a recent experiment on a colloid-colloid mixture, are compared with the experimental data. There is good overall agreement, in particular for the form of the oscillations, except at η s = 0.42, the highest value of packing fraction considered.82.70.Dd, 61.20.Gy

We examine the dependence of a thermodynamic potential of a fluid on the geometry of its container. If motion invariance, continuity, and additivity of the potential are satisfied, only four morphometric measures are needed to describe fully the influence of an arbitrarily shaped container on the fluid. These three constraints can be understood as a more precise definition for the conventional term extensive and have as a consequence that the surface tension and other thermodynamic quantities contain, aside from a constant term, only contributions linear in the mean and Gaussian curvature of the container and not an infinite number of curvatures as generally assumed before. We verify this numerically in the entropic system of hard spheres bounded by a curved wall.