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Even though the study of interfacial phenomena dates back to Laplace and wasformalised by Gibbs, it appears that some concepts and relations among them arestill causing some confusion and debates in the literature, particularly forinterfaces involving solids. Moreover, ever since the Molecular Dynamics (MD)simulations have started to be widely used in the study of surface properties,these debates only intensified. In this work, we present a systematicdescription of the interfacial properties from the thermodynamic andstatistical mechanics points of view. In particular, we link our derivations toMD simulations, describing precisely what different quantities represent andhow they can be calculated. We do not follow the usual way that consists ofdescribing the thermodynamics of the surfaces in general and then consideringspecific cases (e.g. liquid-liquid interface, liquid-solid interface). Instead,we present our analysis of various properties of surfaces in a hierarchicalway, starting with the simplest case that we have identified: a singlecomponent liquid-vacuum interface, and then adding more and more complicationswhen we progress to more complex interfaces involving solids. We propose thatthe term "surface tension" should not be used in the description of surfacesand interfaces involving solids, since its meaning is ambiguous. Only "SurfaceFree Energy" and "Surface Stress" are well defined and represent distinct, butrelated, properties of the interfaces. We demonstrate that these quantities, asdefined in thermodynamics and measured in MD simulations, satisfy theShuttleworth equation.

A unified description of Surface Free Energy and Surface Stress