Normal and tangential components of pressure tensor in spherical cavities; an investigation of certain well-known bulk fluid regularities

Abstract

Using statistical thermodynamics and the DFT approach, local normal and tangential pressures are determined for LJ fluids in spherical cavities. Both pressure components are observed to exhibit an oscillatory behavior in the sense that their amplitudes increase with increasing density and decreasing cavity size. It is found that normal pressure oscillations have lower amplitudes than tangential ones because the positions of maximum peaks in the kinetic contribution to pN correspond to minimum peaks of the configurational contribution. For large enough cavities, the oscillations of tangential pressure remain at a distance of only a few molecules from the wall while normal pressure maintains a constant value for all positions in the pore. One aspect of the study involves an investigation of the validity of certain well-known bulk regularities for LJ fluids in spherical cavities. These regularities include common compression point, linear relation between pressure and temperature for each isochore, common bulk modulus point, and the Tait–Murnaghan equation. These regularities are studied for both pressure components and their relevant properties. All the four regularities mentioned are found valid for LJ fluids in spherical cavities of sizes greater than 3σ. In addition, the densities of the common compression and common bulk modulus point are found not only to depend on but also to increase with nanopore size, while they near the corresponding values for bulk LJ fluids for large cavities.