Thermodynamic derivation of mechanical expressions for interfacial parameters

Abstract

We derive mechanical expressions for interfacial parameters from their thermodynamic definition. The ‘classical’ thermodynamics of curved interfaces as first derived by Gibbs and elaborated later by Tolman and contemporaries gives the well-known interfacial tension of an interface, γ_G. A more recent approach by Boruvka and Neumann gives complementary interfacial parameters: the interfacial tension according to Boruvka and Neumann γ_BN the bending stress C₁, and the torsion stress C₂. In the literature both approaches are matched with the classical mechanical expression for the interfacial tension in order to arrive at mechanical expressions for the aforementioned interfacial parameters. We discuss whether this matching can be done unambiguously. Following a thermodynamically consistent formalism, we arrive at mechanical expressions for interfacial parameters which differ significantly from the ones given in the literature which were found with the matching procedure. We prove the consistency of our expressions by showing its accordance with the generalized Laplace equation of capillarity. Moreover, we show by means of a lattice gas model that our expressions give, unlike those in the literature, unambiguous results. The consequences of the new mechanical expressions for the surface of tension and Tolman length are discussed.