Thermodynamics of interfaces extended to nanoscales by introducing integral and differential surface tensions

Publication of Laboratoire de chimie in  PNAS on January 19, 2021. As a system shrinks down in size, more and more molecules are found in its surface region, so surface contribution becomes a large or even a dominant part of its thermodynamic potentials. Surface tension is a venerable scientific concept; Gibbs defined it as the excess of grand potential of an inhomogeneous system with respect to its bulk value per interface area [J. W. Gibbs, "The Collected Works" in Thermodynamics (1928), Vol. The mechanical definition expresses it in terms of pressure tensor. So far, it has been believed the two definitions always give the same result. We show that the equivalence can break down for fluids confined in narrow pores.