Role of constraints in the thermodynamics of heterogeneous condensation on solid soluble particles: Failure of the capillarity approximation

The Debenedetti-Reiss method of using constraints in the derivation of the reversible work of nucleus formation is extended to the case of heterogeneous formation of multicomponent liquid droplets on solid (soluble or insoluble) particles. It is shown that not only does the capillarity approximation fail to predict the complete, true free energy of formation of a drop of arbitrary (i.e., nonequilibrium) size, but it may also fail to provide a well behaved "surrogate" free energy which would not depend on the path of formation of the drop. This failure is illustrated by calculating the free energy of formation of a liquid film on a NaCl-like particle.