The use of analytic continuation to increase the accuracy in modelling fluid-surface interactions in cylindrical nanopores

In this paper, the mathematical formulation of a rigid/smooth-walled semi-empirical fluid¿surface interaction potential is discussed. Potentials of this type may be used to model the adsorption of simple fluids in cylindrical nanopores, for example, cavities in a solid material or free standing single- or multi-wall nanotubes. Analysis of the properties of the hypergeometric series functions used to evaluate these potentials indicates that modelling of the fluid surface interactions for particles very near to the surface is improved with analytically continuous series. The derivation and implementation of a potential representing a cylindrical cavity within a continuous solid material are also presented.