Virial series for inhomogeneous fluids applied to the Lennard-Jones wall-fluid surface tension at planar and curved walls

摘要

We formulate a straightforward scheme of statistical mechanics forinhomogeneous systems that includes the virial series in powers of the activityfor the grand free energy and density distributions. There, cluster integralsformulated for inhomogeneous systems play a main role. We center on secondorder terms that were analyzed in the case of hard-wall confinement, focusingin planar, spherical and cylindrical walls. Further analysis was devoted to theLennard-Jones system and its generalization the 2k-k potential. For thisinteraction potentials the second cluster integral was evaluated analytically.We obtained the fluid-substrate surface tension at second order for the planar,spherical and cylindrical confinement. Spherical and cylindrical cases wereanalyzed using a series expansion in the radius including higher order terms.We detected a $\ln R^{-1}/R^{2}$ dependence of the surface tension for thestandard Lennard-Jones system confined by spherical and cylindrical walls, nomatter if particles are inside or outside of the hard-walls. The analysis wasextended to bending and Gaussian curvatures, where exact expressions were alsoobtained.