A general theory of free energies of inhomogeneous spatially dispersive media. I

A general formalism is developed to calculate free energies of inhomogeneous spatially dispersive media in terms of bulk dielectric properties. To illustrate the application, two semi-infinite half spaces separated by a vacuum are considered. All previously known results for surface energies and interaction energies for dielectrics and electrolytes derived using continuum theories emerge as special cases. The result for the interaction free energy of two like media across a vacuum reduces to a form which is identical to that obtained by Lushnikov and Malov (see abstr. A82652 of 1974) using diagrammatic methods. In addition it is demonstrated that, subject to certain reasonable assumptions about the dielectric permittivity, it is equivalent to the results obtained using the method of surface modes.