Phase transitions and phase equilibria in spherical confinement

Phase transitions in finite systems are rounded and shifted and affected by boundary effects due to the surface of the system. This interplay of finite size and surface effects for fluids confined inside of a sphere of radius $R$ is studied by a phenomenological theory and Monte Carlo simulations of a model for colloid-polymer mixtures. For this system the phase separation in a colloid-rich phase and a polymer-rich phase has been previously studied extensively in the bulk. It is shown that spherical confinement can strongly enhance the miscibility of the mixture. Depending on the wall potentials at the confining surface, the wetting properties of the wall can be controlled, and this interplay between preferential adsorption of one species to the confining surface and bulk unmixing leads to very special shapes of the loops observed for the chemical potential of the colloids as a function of their packing fraction. We also discuss the extent to which concepts used for phase transitions in macroscopic systems, such as critical exponents of the order parameter distinguishing the phases, or the Kelvin equation describing the shift of the chemical potential at phase coexistence with the radius $R$, are applicable.