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

Variable shape telescopic mirror

A telescope mirror 10 comprises a substrate 11 with a reflecting surface 12 and having a network of electrical conductors 14 located in a magnetic field. By supplying respective adjustable electrical current to the individual conductors, the mirror is constrained to adopt a desired shape. The mirror may comprise a plurality of discrete segments 20 e.g. concentric annuli separated by magnetic poles

Integral equations and the pressure at the liquid solid interface

The relationship between the pressure in a fluid and the density-functional which controls the density profile of a fluid confined between two walls is examined. As a result, the conditions which must be fulfilled by an approximate density functional to yield a bulk pressure P, a normal pressure, P W at the interface between a hard wall and the fluid, and a fluid density, ρW, adjacent to the wall which satisfy the exact relations P W=P=k B T ρW, are established. The density-functional which yields the HNC closure for a hard-sphere fluid near a hard wall is modified so that the modified functional yields the Carnahan-Starling bulk pressure and hence fulfils the necessary conditions. The density profile to which this gives rise is compared with the results of computer simulation for various bulk densities when the fluid is bounded by two hard walls separated by a distance equal to 8 diameters of the hard sphere. The agreement is found to be very good even at a bulk reduced density of 0·91

Solvation forces in a model mixture of ions and dipoles

The forces between two charged thick plates immersed in a model fluid are investigated using the density-functional method. The model fluid comprises oppositely charged spherical ions together with neutral spherical particles with fixed dipoles µ at their centres. The thermodynamic potential is obtained as a quadratic functional of the local density, local electric charge and polarisation of the fluid with kernels which depend on the direct correlation functions of the bulk liquid. The latter are approximated by the functions obtained by means of the mean spherical approximation. The equilibrium densities which minimise the thermodynamic potential are computed and from these the forces between the plates are derived. When the dielectric constant of the bulk fluid is large, the liquid structure has a significant effect on these forces and differences from the results obtained using Debye–Hückel theory are apparent. It is suggested that these results have implications for the theory of colloidal stability