Depletion potential in hard-sphere mixtures: theory and applications

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 {\em 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. By investigating the depletion potential for high size asymmetries we assess the regime of validity of the well-known Derjaguin approximation for hard-sphere mixtures and argue that this fails. 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

Thermodynamic fluctuation relation for temperature and energy

The present work extends the well-known thermodynamic relation $C=\beta ^{2}< \delta {E^{2}}>$ for the canonical ensemble. We start from the general situation of the thermodynamic equilibrium between a large but finite system of interest and a generalized thermostat, which we define in the course of the paper. The resulting identity $=1+< \delta {E^{2}}> \partial ^{2}S(E) /\partial {E^{2}}$ can account for thermodynamic states with a negative heat capacity $C<0$; at the same time, it represents a thermodynamic fluctuation relation that imposes some restrictions on the determination of the microcanonical caloric curve $\beta (E) =\partial S(E) /\partial E$. Finally, we comment briefly on the implications of the present result for the development of new Monte Carlo methods and an apparent analogy with quantum mechanics.Comment: Version accepted for publication in J. Phys. A: Math and The

Optical extinction, refractive index, and multiple scattering for suspensions of interacting colloidal particles

We provide a general microscopic theory of the scattering cross-section and of the refractive index for a system of interacting colloidal particles, exact at second order in the molecular polarizabilities. In particular: a) we show that the structural features of the suspension are encoded into the forward scattered field by multiple scattering effects, whose contribution is essential for the so-called "optical theorem" to hold in the presence of interactions; b) we investigate the role of radiation reaction on light extinction; c) we discuss our results in the framework of effective medium theories, presenting a general result for the effective refractive index valid, whatever the structural properties of the suspension, in the limit of particles much larger than the wavelength; d) by discussing strongly-interacting suspensions, we unravel subtle anomalous dispersion effects for the suspension refractive index.Comment: Submitted to Journal of Chemical Physics 37 pages, 4 figure

Hard-Sphere Fluids in Contact with Curved Substrates

The properties of a hard-sphere fluid in contact with hard spherical and cylindrical walls are studied. Rosenfeld's density functional theory (DFT) is applied to determine the density profile and surface tension $\gamma$ for wide ranges of radii of the curved walls and densities of the hard-sphere fluid. Particular attention is paid to investigate the curvature dependence and the possible existence of a contribution to $\gamma$ that is proportional to the logarithm of the radius of curvature. Moreover, by treating the curved wall as a second component at infinite dilution we provide an analytical expression for the surface tension of a hard-sphere fluid close to arbitrary hard convex walls. The agreement between the analytical expression and DFT is good. Our results show no signs for the existence of a logarithmic term in the curvature dependence of $\gamma$.Comment: 15 pages, 6 figure

Monte Carlo simulations of the screening potential of the Yukawa one-component plasma

A Monte Carlo scheme to sample the screening potential H(r) of Yukawa plasmas notably at short distances is presented. This scheme is based on an importance sampling technique. Comparisons with former results for the Coulombic one-component plasma are given. Our Monte Carlo simulations yield an accurate estimate of H(r) as well for short range and long range interparticle distances.Comment: to be published in Journal of Physics A: Mathematical and Genera

Lattice density-functional theory of surface melting: the effect of a square-gradient correction

I use the method of classical density-functional theory in the weighted-density approximation of Tarazona to investigate the phase diagram and the interface structure of a two-dimensional lattice-gas model with three phases -- vapour, liquid, and triangular solid. While a straightforward mean-field treatment of the interparticle attraction is unable to give a stable liquid phase, the correct phase diagram is obtained when including a suitably chosen square-gradient term in the system grand potential. Taken this theory for granted, I further examine the structure of the solid-vapour interface as the triple point is approached from low temperature. Surprisingly, a novel phase (rather than the liquid) is found to grow at the interface, exhibiting an unusually long modulation along the interface normal. The conventional surface-melting behaviour is recovered only by artificially restricting the symmetries being available to the density field.Comment: 16 pages, 6 figure