Excess chemical potential and surface free energy of a hard-sphere fluid at curved walls

Title: Excess chemical potential and surface free energy of a hard-sphere fluid at curved walls: deviations from Morphometric Thermodynamics

Abstract: Excess chemical potential (or solvation free energy) is an important thermodynamic quantity that characterises properties of fluids in contact with surfaces and the behaviour of fluid mixtures.   General theoretical analysis of this quantity is rather complicated and available only for simple systems (like hard-sphere fluids) in various approximations (Percus-Yevick integral equations, Scaled Particle Theory, density-functional theory).  A significant simplification can be obtained under the assumptions of the so-called Morphometric Thermodynamics (MT), which is based on Hadwiger's theorem from integral geometry.   We use Gibbs-Cahn integration, Widom's particle insertion, and the inclusion-exclusion principle to obtain high-precision measurements of the excess chemical potential and surface free energy.  With these results, we are able to observe deviations from the MT expressions and thus test the extent of applicability of the MT assumptions in hard-sphere fluids.