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

TL;DR

This study uses molecular dynamics to calculate the interfacial free energy between a hard-sphere fluid and curved surfaces, confirming theoretical predictions at moderate densities and identifying deviations at higher densities.

Contribution

It verifies Hadwiger's theorem for interfacial free energy in hard-sphere fluids up to a certain packing fraction and compares simulation results with classical density functional theory.

Findings

Hadwiger's theorem holds for luid surfaces up to luid packing fraction 0.42

Simulation results agree with classical DFT calculations within valid range

Deviations occur at higher packing fractions, indicating limitations of the theorem

Abstract

Using molecular-dynamics simulation, we have calculated the interfacial free energy, \gamma, between a hard-sphere fluid and hard spherical and cylindrical colloidal particles, as functions of the particle radius R and the fluid packing fraction \eta= \rho\sigma^3/6, where \rho and \sigma are the number density and hard-sphere diameter, respectively. These results verify that Hadwiger's theorem from integral geometry, which predicts that \gamma 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 \eta about 0.42. In addition, earlier results for \gamma 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 \eta about 0.42, \gamma(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 $\gamma$ for any sufficiently smooth surface immersed in a hard-sphere fluid.