No abstract

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.

Derivation of dynamical density functional theory using the projection operator technique J. Chem. Phys. 131, 244101 (2009) We present an alternative derivation of the dynamical density functional theory for the one-body density profile of a classical fluid developed by Marconi and Tarazona ͓J. Chem. Phys. 110, 8032 ͑1999͔͒. Our derivation elucidates further some of the physical assumptions inherent in the theory and shows that it is not restricted to fluids composed of particles interacting solely via pair potentials; rather it applies to general, multibody interactions. The starting point for our derivation is the Smoluchowski equation and the theory is therefore one for Brownian particles and as such is applicable to colloidal fluids. In the second part of this paper we use the dynamical density functional theory to derive a theory for spinodal decomposition that is applicable at both early and intermediate times. For early stages of spinodal decomposition our nonlinear theory is equivalent to the ͑generalized͒ linear Cahn-Hilliard theory, but for later times it incorporates coupling between different Fourier components of the density fluctuations ͑modes͒ and therefore goes beyond CahnHilliard theory. We describe the results of calculations for a model ͑Yukawa͒ fluid which show that the coupling leads to the growth of a second maximum in the density fluctuations, at a wave number larger than that of the main peak.

When gases or liquids are adsorbed in narrow pores or capillaries their properties aresignificantlydifferentfrom thoseinabulkphase. Thisarticle reviewsrecentdevelopments in the statistical theory and computer simulation of simple fluids confined in model pores, emphasizing the microscopic structure and phase equilibria. The structure reflects the packing of atoms or molecules in confining geometries while the phase behaviour reflects the presence of surface and bulk contributions to the fluid's free energy. Confinement shifts first-order transitions, such as condensation or freezing, away from their location in bulk; it also alters the location and nature of the bulk critical point reducing the effective dimensionality. Sometimes surface phase transitions such as layering and prewetting compete with shifted bulk transitions giving rise to rich phase diagrams. The extent to which the theorists' results for fluids in single idealized pores might be relevant for solvation force studies probing liquids between crossed mica cylinders and for gas adsorption studies in real mesoporous solids such as VYCOR is mentioned briefly.

We study the phase behavior and structure of highly asymmetric binary hard-sphere mixtures. By first integrating out the degrees of freedom of the small spheres in the partition function we derive a formal expression for the effective Hamiltonian of the large spheres. Then using an explicit pairwise (depletion) potential approximation to this effective Hamiltonian in computer simulations, we determine fluid-solid coexistence for size ratios q=0.033, 0.05, 0.1, 0.2, and 1.0. The resulting two-phase region becomes very broad in packing fractions of the large spheres as q becomes very small. We find a stable, isostructural solid-solid transition for q< or =0.05 and a fluid-fluid transition for q< or =0.10. However, the latter remains metastable with respect to the fluid-solid transition for all size ratios we investigate. In the limit q-->0 the phase diagram mimics that of the sticky-sphere system. As expected, the radial distribution function g(r) and the structure factor S(k) of the effective one-component system show no sharp signature of the onset of the freezing transition and we find that at most points on the fluid-solid boundary the value of S(k) at its first peak is much lower than the value given by the Hansen-Verlet freezing criterion. Direct simulations of the true binary mixture of hard spheres were performed for q > or =0.05 in order to test the predictions from the effective Hamiltonian. For those packing fractions of the small spheres where direct simulations are possible, we find remarkably good agreement between the phase boundaries calculated from the two approaches-even up to the symmetric limit q=1 and for very high packings of the large spheres, where the solid-solid transition occurs. In both limits one might expect that an approximation which neglects higher-body terms should fail, but our results support the notion that the main features of the phase equilibria of asymmetric binary hard-sphere mixtures are accounted for by the effective pairwise depletion potential description. We also compare our results with those of other theoretical treatments and experiments on colloidal hard-sphere mixtures.

Abstract. We study the phase behaviour and structure of model colloid-polymer mixtures. By integrating out the degrees of freedom of the non-adsorbing ideal polymer coils, we derive a formal expression for the effective one-component Hamiltonian of the colloids. Using the twobody (Asakura-Oosawa pair potential) approximation to this effective Hamiltonian in computer simulations, we determine the phase behaviour for size ratios q = σ p /σ c = 0.1, 0.4, 0.6, and 0.8, where σ c and σ p denote the diameters of the colloids and the polymer coils, respectively. For large q, we find both a fluid-solid and a stable fluid-fluid transition. However, the latter becomes metastable with respect to a broad fluid-solid transition for q 0.4. For q = 0.1 there is a metastable isostructural solid-solid transition which is likely to become stable for smaller values of q. We compare the phase diagrams obtained from simulation with those of perturbation theory using the same effective one-component Hamiltonian and with the results of the free-volume approach. Although both theories capture the main features of the topologies of the phase diagrams, neither provides an accurate description of the simulation results. Using simulation and the Percus-Yevick approximation we determine the radial distribution function g(r) and the structure factor S(k) of the effective one-component system along the fluid-solid and fluid-fluid phase boundaries. At state-points on the fluid-solid boundary corresponding to high colloid packing fractions (packing fractions equal to or larger than that at the triple point), the value of S(k) at its first maximum is close to the value 2.85 given by the Hansen-Verlet freezing criterion. However, at lower colloid packing fractions freezing occurs when the maximum value is much lower than 2.85. Close to the critical point of the fluid-fluid transition we find Ornstein-Zernike behaviour and at very dilute colloid concentrations S(k) exhibits pronounced small-angle scattering which reflects the growth of clusters of the colloids. We compare the phase behaviour of this model with that found in studies of additive binary hard-sphere mixtures.

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

Phase transitions at fluid interfaces and in fluids confined in pores have been investigated by means of a density functional approach that treats attractive forces between fluid molecules in mean-field approximation and models repulsive forces by hard-spheres. Two types of approximation were employed for the hard-sphere free energy functional: (a)tile well-known local density approximation (LDA) that omits short-ranged correlations and (b) a non-local smoothed density approximation (SDA) that includes such correlations and therefore accounts for the oscillations of the density profile near walls. Three different kinds of phase transition were considered: (i) wetting transition. The transition from partial to complete wetting at a single adsorbing wall is shifted to lower temperatures and tends to become first-order when the more-realistic SDA is employed. Comparison of the results suggests that the LDA overestimates the contact angle 0 in a partial wetting situation. (ii) capillary evaporation of a fluid confined between two parallel hard walls. This transition, from dense 'liquid' to dilute 'gas', occurs in a supersaturated fluid (p > Psat)" The lines of capillary coexistence calculated in the LDA and SDA are rather close, suggesting that non-local effects are not especially important in this case. (iii) capillary condensation of fluids confined between two adsorbing walls or in a single cylindrical pore. For a partial wetting situation the condensation pressures p(