Effects of chain unsaturation on the equation of state for lipid monolayers at the air-water interface

An equation of state for lipid monolayers at the air-water interface is presented, which takes into account the effects of the conformation and the number and position of double bonds of the hydrocarbon chains. The total Hamiltonian of the monolayer is assumed to consist of three terms. Two of them are calculated exactly within the limitations of the formulation. These are the two-dimensional entropy of mixing of the lipid and water molecules at the surface and the conformational entropy of the chains using a model available from the literature. These two terms give rise to positive surface pressure. The third term, which includes all energies that are not amenable to calculation, was obtained as the difference between the sum of the two calculated terms and experimental data and is found to represent an approximately area-independent tension. The effects of chain unsaturation on the equation of state were modeled in the present theory in two ways; the chain bend caused by cis double bonds increases the minimal molecular area, and the double bond linkage on a chain decreases the degrees of freedom of the chain. Calculations revealed that the former is highly significant whereas the latter is negligible. The deduced equation of state reproduces experimental data with appropriate values for three parameters, which represent the collapse area, the overlap of adjacent chains, and the combined effects of the intra- and intermolecular interactions other than the surface mixing entropy and the chain conformational energy.