PHYSICAL CHEMISTRY IN BRIEF

CHAP. 13: PHYSICAL CHEMISTRY OF SURFACES [CONTENTS] 437

The value of interfacial tension depends on temperature, pressure and the composition of
both phases in contact. The temperature dependence is described in section (13.1.8). In a
one-component system, the interfacial tension thus depends only on temperature and pressure
is equal to the equilibrium pressure. The composition dependence in multicomponent systems
is described in section (13.1.9). The pressure dependence is relatively low and usually can be
neglected.

13.1.2 Generalized Gibbs equations

By including surface work in the Gibbs equations (see3.4.1), which represent combined for-
mulations of the first and second laws of thermodynamics in a closed system, we obtain

dU=TdS−pdV+γffdA , (13.2)

dH=TdS+Vdp+γffdA , (13.3)

dF=−SdT−pdV+γffdA , (13.4)

dG=−SdT+Vdp+γffdA. (13.5)

From these relations we may define interfacial tension by

γff=

(

∂U

∂A

)

S,V

=

(

∂H

∂A

)

S,p

=

(

∂F

∂A

)

T,V

=

(

∂G

∂A

)

T,p

. (13.6)

13.1.3 Interfacial energy

The energy of an interfaceσff is comprised of the work needed for its creation and the heat
connected with the change of the surface area. It is given by the relation

σff=

(

∂U

∂A

)

T,V

. (13.7)

By applying the Maxwell relations (see3.4.3) to the Gibbs equations we obtain

σff=γff−T

(

∂γff

∂T

)

V,A

. (13.8)