Some Properties of the Gibbs-Guggenheim Relations

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Abstract
The Gibbs adsorption formula for a binary mixture of liquids, γ2 = γ1(x/(1 - x)) - (x/RT)δγ/δx, and Guggenheim's formula, A 1γ1 + A 2γ2 = 1, are examined in a practical case, the surface of a liquid mixture of adiponitrile and tris(dioxa-3,6-heptyl)amine (γ1 and γ2 are the surface concentrations of the two components, x is the bulk mole fraction of component 2, R is the gas constant, T is the temperature, A 1 and A 2 are the area of the components per monolayer of unit surface area and γ is the surface tension). Loci of constant values of E = (γ2/γ1)/(x/(1 - x)) are plotted in the plane A 1, A 2. Such loci (1) are linear (2) pass through the point A 1∗, A 2∗ = RT/(δγ/δx(1 - x)), -RT/(x(δγ/δx)) and (3) possess a linear scale parallel to the A 1 axis. Measurements of γ1 and γ2 carried out by He(I) photoelectron spectroscopy support the above better if it is assumed that not one but N monolayers are sampled by the technique, with A 1γ1 + A 2γ2 = N. The value of N is found to be between 1 and 2.

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