Density functional theories and the structure of fluids near walls

The structure of fluids near walls is examined using density functional techniques. A brief introduction to the subject is given, followed by a mathematical derivation of some important basic results. A linear (Chap.3) and non-linear (Chap.4) density functional approximation for the thermodynamic potential is used to treat a model fluid comprised of hard spheres with embedded point ions or dipoles confined between two hard infinite planar walls. Results are obtained and compared for the charge and polarisation densities. Both theories produce oscillatory charge and polarisation density profiles, in agreement with results at a single wall from other workers. These results differ qualitatively with those given by earlier, continuum theories of the electrical double layer such as Debye-Huckel and Poisson-Boltzmann. A modified functional is introduced (Chap.5), and is used to treat a simple fluid of hard spheres. A single variable parameter of the theory is chosen to ensure thermodynamic consistency, and results for the number density are obtained. These results are in excellent agreement with results from Monte Carlo computer experiments, even up to unrealistically high fluid densities. The modified functional is further applied to a hard sphere fluid with attractive long-range interactions. This leads to wetting of the walls by vapour, a result also observed previously at a single wall. Finally,. a perturbation treatment is applied to experimental scattering data to give a potential of mean force for an aqueous dispersion of polystyrene spheres.