Insoluble mixed monolayers. I. Phase equilibria at the collapse of binary monolayers at gas/liquid interfaces

Abstract

Based on the two-dimensional phase rule, 13 fundamental types of phase diagrams are given for binary systems of surfactants spread at the gas-liquid interface, by taking into account the possibility of total miscibility, partial miscibility, or immiscibility of the components both in the monolayer and in the collapsed bulk phase (4 of them are known in the literature and 9 are new ones). A thermodynamic model of the monolayer is proposed, by considering the molecules of the two surfactants together with their solvation shell, the “free” subphase liquid molecules to be the third component of the monolayer and by presuming the molar fraction of the latter to become practically equal to zero at the equilibrium collapse surface pressure. The definition of the surface chemical potentials and the physical meaning of the standard state are discussed. The equations of the equilibrium curves are derived. The approximations of perfect solutions and of the regular ones are applied to the systems with total miscibility. The conditions necessary for the appearance of surface azeotropes are discussed. The state parameters of surface azeotropes are derived from the surface characteristics of the surfactants and of the interaction parameters. Several relations, reported by other authors, are obtained as particular cases. Experimental collapse pressure versus composition curves are reported and discussed by using the relations derived. Examples are given for the applicability of the approximation of perfect solutions and of regular solutions, as well as for a system with nonregular behavior. Some results are discussed in terms of the molecular structure.