Interfacial free energy of a hard-sphere fluid in contact with curved hard surfaces.

Using molecular-dynamics simulation, we have calculated the interfacial free energy γ between a hard-sphere fluid and hard spherical and cylindrical colloidal particles, as functions of the particle radius R and the fluid packing fraction η=ρσ(3)/6, where ρ and σ are the number density and hard-sphere diameter, respectively. These results verify that Hadwiger's theorem from integral geometry, which predicts that γ for a fluid at a surface, with certain restrictions, should be a linear combination of the average mean and Gaussian surface curvatures, is valid within the precision of the calculation for spherical and cylindrical surfaces up to η ≈ 0.42. In addition, earlier results for γ for this system [Bryk et al., Phys. Rev. E 68, 031602 (2003)] using a geometrically based classical density functional theory are in excellent agreement with the current simulation results for packing fractions in the range where Hadwiger's theorem is valid. However, above η ≈ 0.42, γ(R) shows significant deviations from the Hadwiger form indicating limitations to its use for high-density hard-sphere fluids. Using the results of this study together with Hadwiger's theorem allows one, in principle, to determine γ for any sufficiently smooth surface immersed in a hard-sphere fluid.