ON OSMOTIC-TYPE EQUATIONS OF STATE FOR LIQUID-EXPANDED MONOLAYERS OF LIPIDS AT THE AIR-WATER-INTERFACE

Wolfe and Brockman (Proc. Natl. Acad. Sci. U.S.A. 1988, 85, 4285-4289) derived a quasi-two-dimensional equation of state for liquid-expanded monolayers, which reproduces experimental data particularly well in comparison to other forms and can reveal mixing nonidealities in single phase, mixed-lipid monolayers (Smaby, J. M.; Brockman, H. L. Langmuir 1991, 7, 1031, and 1992, 8, 563). To describe the surface pressure-area properties of monolayers, it utilizes three constant parameters: a lipid geometric parameter, a water activity parameter, and an osmotic coefficient-type parameter. In this report, errors in the derivation of this equation of state are identified and corrected. It is shown that the simultaneous introduction of both constant activity and osmotic parameters, although necessary to accurately describe experimental data, leads to the loss of their original physical significance. Additionally, the true water activity and osmotic coefficients are calculated from the corresponding best-fit parameters and are shown to depend on the mole fraction of water in the interface and, hence, on lipid molecular area. In particular, the apparent water activity coefficient parameter of the Wolfe-Brockman equation is shown to be equal to the particular value of the true, area-dependent water activity coefficient evaluated at the lipid area at which the surface pressure extrapolates to zero. The lipid area dependence of the true water activity and osmotic coefficients was investigated for monolayers of oleic acid, 1-palmitoyl-2-oleoylphosphatidylcholine, and 1-palmitoyl-2-oleoylphosphatidylethanolamine; the quasi-two-dimensional mole fraction of water in the monolayer changes by as much as 110% over the area range of the lipid expanded state and for these three lipids, and this produces changes in the water activity coefficient of up to 21, 43, and 106%, respectively. It is shown that although the two-dimensional osmotic pressure due to the nonideal mixing entropy of the water and lipid head groups is a major factor in surface pressure, it cannot be the only one and that, contrary to earlier predictions of the asymptotic value of the surface water activity coefficient, the difference between predictions of simple osmotic theory and experimental data for dilute lipid-water interface cannot be completely attributed to nonideal interactions of the type that are directly proportional to frequency of intermolecular contact.