Surface Free Energy of a Hard-Disk Fluid at Curved Hard Walls: Theory and Simulation

In this work, we examine the surface thermodynamics of a hard-disk fluid at curved hard walls using Monte Carlo (MC) simulation and a generalized scaled particle theory (gSPT). The curved walls are modeled as hard disks of varying radii, R. The surface free energy, γ, and excess surface volume, v_ex, for this system are calculated as functions of both the fluid packing fraction and the wall radius. The simulation results are used to test, for this system, the assumptions of morphometric thermodynamics (MT), which predicts that both γ and v_ex are linear functions of the surface curvature, 1/R, for a two-dimensional system. In addition, we compare the simulation results to the gSPT developed in this work, as well as with virial expansions derived from the known virial coefficients of the binary hard-sphere fluid. At low to intermediate packing fractions, the non-MT terms (terms of higher order than 1/R in a expansion of γ and v_ex) of γ are zero within the simulation error; however, at the highest densities, deviations from MT become significant, similar to what was seen in our earlier simulation work on the three-dimensional hard-sphere/hard-wall system. In addition, the new gSPT gives improved results for both γ and v_ex over standard scaled particle theory (SPT) but underestimates the deviations from MT at high density.