文档介绍：2 Thermodynamics of Interfaces
Two-phase Systems
Thermodynamic Approach
As we have discussed, the stability of a disperse system depends on surface con-
ditions of the particles. The surface always appears between two different bulk
phases in contact, so that it may also be called an interface but is quite obscure in
its structure. (The word, ªinterfaceº, may be reserved for the boundary between
two condensed phases. However, we ignore the difference between the words,
ªinterfaceº and ªsurfaceº, in the following.) In order to theoretically treat the ther-
modynamic behavior of the interface in any change of the environments, Gibbs
(1931, 1961) introduced a concept of a dividing surface, mathematically con-
structed between the two phases (see also Chattoraj and Birdi, 1984).
Consider, for instance, a two-phase system of ponent, where a liquid is
in equilibrium with its vapor (the boundary may be planar or curved). The two
bulk phases, ' and '', in reality do not change their states sharply when crossing
the interface, but have a region, as shown in Fig. , over which the density con-
tinuously varies (for theoretical thickness, see Lekner and Henderson, 1977 and
1978). However, for convenience, we arbitrarily introduce a sharp dividing sur-
face somewhere around the region.
The extensive (additive) thermodynamic variables, such as the volume, number
of moles, internal energy, entropy, etc., of each phase, ' or '' , are assumed to con-
Fig. Gibbs' dividing surface.
10 2 Thermodynamics of Interfaces
tinue unchanged up to the hypothetical dividing surface. Thus, if we denote the
extended volumes of the two phases by V' and V'', respectively, the numbers of
moles, n' and n'',inV' and V'' are n'=c'V' and n''=c''V'', respectively, where c'
and c'' are concentrations of the two phases. If the actual total number of moles
of the system is n, n will in general differ from the sum of them, n'+n'', by an ex-
cess or deficiency. Thi