Surface equation of state for insoluble surfactant monolayers at the air/water interface

A surface equation of state is derived and used to interpret the liquid-expanded (LE)-liquid-condensed (LC) phase transition. The monolayer is treated as a two-dimensional mixture consisting of LC domains, disordered molecules in the LE state, and free sites. The free sites are assumed to have two-dimensional size only and to be located at the internal surface between the headgroups and the tails of the surfactant. They are introduced to account for the translational freedom of the domains and of the disordered molecules on the surface. The model can explain the nonhorizontal LE/LC phase transition and its dependence on temperature. In addition, the equilibrium radius and equilibrium area fraction of the domains are calculated as a function of the average molecular surface area (A). In the absence of domains, the surface equation of state reduces to a modified two-dimensional van der Waals equation. The dependence of the surface cohesion pressure on the molecular surface area A is calculated by including three contributions: the dipole-dipole interactions, the chain van der Waals interactions, and the chain conformation. The theoretical model is compared with the experimental pi-A isotherms for six phospholipid surfactants, and good agreement is obtained.