Читать книгу Non-equilibrium Thermodynamics of Heterogeneous Systems - Signe Kjelstrup - Страница 19

Consider three phases of a multi-component system in equilibrium with each other. The three surfaces separating these phases come together in a contact line. For simplicity, we assume that the contact line is not polarizable. In Sec. 3.1, we have seen that the thermodynamic relations for an autonomous surface has the same form as for homogeneous phases. The same is true for the autonomous three-phase contact line. The Gibbs equation for the contact line is as follows:

(3.19)

Superscript c indicates a contribution of the contact line, γ^c is the line tension and L is the length of the line. The curvature of the line is assumed to be negligible, so that there are no contributions to dU^c from changes in the curvature. By integration for constant line tension, temperature and composition, we obtain

(3.20)

The line energy and therefore also the line entropy and the line mole numbers have here been defined as the total values minus the bulk and the surface values.

Gibbs–Duhem’s equation for the line follows by differentiating this equation and subtracting Eq. (3.19):

(3.21)

When the contact line is part of a heterogeneous system in global equilibrium, the chemical potentials and the temperature are constant throughout the system. For the contact line, we therefore also have

(3.22)

More direct definitions of thermodynamic properties of the line can be obtained following the procedure for the surface in the following section.