BOUNDARY EFFECTS IN THE ONE-DIMENSIONAL COULOMB GAS

We use the functional integral technique of Edwards and Lenard to solv e the statistical mechanics of a one-dimensional Coulomb gas with boun dary interactions leading to surface charging. The theory examined is a one-dimensional model for a soap him. Finite-size effects and the ph enomenon of charge regulation are studied. We also discuss the disjoin ing pressure for such a film. Even in the absence of boundary potentia ls we find that the presence of a surface affects the physics in finit e systems. In general we find that in the presence of a boundary poten tial the long-distance disjoining pressure is positive, but may become negative at closer interplane separations. This is in accordance with the attractive forces seen at close separations in colloidal and soap film experiments and with three dimensional calculations beyond mean held. Finally, our exact results are compared with the predictions of the corresponding Poisson-Boltzmann theory which is often used in the context of colloidal and thin liquid film systems.