The pressure in interfaces having cylindrical geometry

While much work has been reported on the statistical mechanics and molecular simulation of interfaces of planar and spherical geometries, very little has been published on the interfaces of cylindrical geometry. The cylindrical geometry is important for the study of cylindrical micelles and particularly for nano-phases confined within cylindrical pores since the most well-defined porous materials (e.g., carbon and silicon nanotubes, SBA-15 and KIT-6 silicas) that are presently available are of this geometry. In this work, we derive the statistical mechanical equations for the pressure tensor for an interfacial region of cylindrical geometry via the virial route and for the condition of mechanical (hydrostatic) equilibrium. We also report the equation for the surface tension via the mechanical route. Monte Carlo and molecular dynamics simulation results are obtained for two example systems involving a fluid nano-phase of Lennard-Jones argon: a gas-liquid interface of cylindrical geometry and a confined nano-phase within a cylindrical carbon pore. All three diagonal elements of the pressure tensor are reported in each case, the component normal to the interface, PN = Pρρ, and the two tangential components PTϕ = Pϕϕ and PTz = Pzz, where (ρ, z, ϕ) are the usual cylindrical polar coordinates. For the cylindrical pore, the tangential pressures, Pϕϕ and Pzz, show strong compression in the adsorbed layers, as has been found in slit-shaped and spherical pores.