We studied the free fluid-fluid interface in a phase-separated colloid-polymer dispersion with laser scanning confocal microscopy and directly observed thermally induced capillary waves at the interface in real space. Experimental results for static and dynamic correlation functions validate the capillary wave model down to almost the particle level. The ultralow interfacial tension, the capillary length, and the capillary time are found to be in agreement with independent measurements. Furthermore, we show that capillary waves induce the spontaneous breakup of thin liquid films and thus are of key importance in the process of droplet coalescence.

A geometrically based fundamental-measure free-energy density functional unified the scaled-particle and Percus-Yevick theories for the hard-sphere fluid mixture. It has been successfully applied to the description of simple (``atomic'') three-dimensional (3D) fluids in the bulk and in slitlike pores, and has been extended to molecular fluids. However, this functional was unsuitable for fluids in narrow cylindrical pores, and was inadequate for describing the solid. In this work we analyze the reason for these deficiencies, and show that, in fact, the fundamental-measure geometrically based theory provides a free-energy functional for 3D hard spheres with the correct properties of dimensional crossover and freezing. After a simple modification of the functional, as we propose, it retains all the favorable D=3 properties of the original functional, yet gives reliable results even for situations of extreme confinements that reduce the effective dimensionality D drastically. The modified functional is accurate for hard spheres between narrow plates (D=2), and inside narrow cylindrical pores (D=1), and it gives the exact excess free energy in the D=0 limit (a cavity that cannot hold more than one particle). It predicts the (vanishingly small) vacancy concentration of the solid, provides the fcc hard-sphere solid equation of state from closest packing to melting, and predicts the hard-sphere fluid-solid transition, all in excellent agreement with the simulations.

A hard sphere system confined between two parallel hard plates is investigated theoretically. Using extensive Monte Carlo computer simulations, the phase diagram is calculated for the whole range of densities and plate separations ranging from one to two particle diameters. There occurs a strong first-order fluid freezing transition and both very weak and strong discontinuous phase transitions between different crystal structures, namely, layered, buckled, and rhombic crystals. The results are compared with predictions from free volume theory, and a semiquantitative agreement is found. All predicted transitions should be experimentally observable in confined suspensions of sterically stabilized or highly salted charged colloidal particles.

The freezing transition of hard spheres confined between two parallel hard plates is studied for different plate separations interpolating between two and three spatial dimensions. Using Monte Carlo simulations and free volume theory, the full phase diagram is obtained exhibiting solid-to-solid transitions between buckled, layered, and rhombic crystals. While the fluid-solid transition is always strongly first order, both strong and very weak transitions occur between different crystalline structures. All predicted transitions should be experimentally observable in confined colloids.

Classical density functional theory (DFT) provides an exact variational framework for determining the equilibrium properties of inhomogeneous fluids. We report a generalization of DFT to treat the non-equilibrium dynamics of classical many-body systems subject to Brownian dynamics. Our approach is based upon a dynamical functional consisting of reversible free energy changes and irreversible power dissipation. Minimization of this “free power” functional with respect to the microscopic one-body current yields a closed equation of motion. In the equilibrium limit the theory recovers the standard variational principle of DFT. The adiabatic dynamical density functional theory is obtained when approximating the power dissipation functional by that of an ideal gas. Approximations to the excess (over ideal) power dissipation yield numerically tractable equations of motion beyond the adiabatic approximation, opening the door to the systematic study of systems far from equilibrium.

We present a density functional theory for mixtures of (hard sphere) colloidal particles and ideal polymers. For this extreme nonadditive system we employ a fundamental measures approach to construct a functional which incorporates the correct dimensional crossover and the exact low density limit. In bulk fluid mixtures the functional yields the same free energy and, therefore, the same gas-liquid (demixing) transition as given by free-volume theory. It generates consistent pair correlation functions; the partial structure factors $S^{\mathrm{ij}}\left(k\right)$ diverge, as $k\to 0$, at the critical point obtained from the free energy. Our results for the structure agree well with those from simulation and Percus-Yevick theory.