  Even though the study of interfacial phenomena dates back to Laplace and was
formalised by Gibbs, it appears that some concepts and relations among them are
still causing some confusion and debates in the literature, particularly for
interfaces 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 systematic
description of the interfacial properties from the thermodynamic and
statistical mechanics points of view. In particular, we link our derivations to
MD simulations, describing precisely what different quantities represent and
how they can be calculated. We do not follow the usual way that consists of
describing the thermodynamics of the surfaces in general and then considering
specific cases (e.g. liquid-liquid interface, liquid-solid interface). Instead,
we present our analysis of various properties of surfaces in a hierarchical
way, starting with the simplest case that we have identified: a single
component liquid-vacuum interface, and then adding more and more complications
when we progress to more complex interfaces involving solids. We propose that
the term "surface tension" should not be used in the description of surfaces
and interfaces involving solids, since its meaning is ambiguous. Only "Surface
Free Energy" and "Surface Stress" are well defined and represent distinct, but
related, properties of the interfaces. We demonstrate that these quantities, as
defined in thermodynamics and measured in MD simulations, satisfy the
Shuttleworth equation.
