  We investigate the effect of the metallic character of solid substrates on
solid-liquid interfacial thermodynamics using molecular simulations. Building
on the recent development of a semi-classical Thomas-Fermi model to tune the
metallicity in classical molecular dynamics simulations, we introduce a new
thermodynamic integration framework to compute the evolution of the interfacial
free energy as a function of the Thomas-Fermi screening length. We validate
this approach against analytical results for empty capacitors and by comparing
the predictions in the presence of an electrolyte with values determined from
the contact angle of droplets on the surface. The general expression derived in
this work highlights the role of the charge distribution within the metal. We
further propose a simple model to interpret the evolution of the interfacial
free energy with voltage and Thomas-Fermi length, which allows us to identify
the charge correlations within the metal as the microscopic origin of the
evolution of the interfacial free energy with the metallic character of the
substrate. This new methodology opens the door to the molecular-scale study of
the effect of the metallic character of the substrate on confinement-induced
transitions in ionic systems, as reported in recent Atomic Force Microscopy and
Surface Force Apparatus experiments.
