Chain model theory of lipid monolayer transitions

The extensive surface area A and the conjugate surface pressure Π are introduced into a cooperatively interacting hydrocarbon chain model. The exact statistical mechanical method of solution is extended to accommodate the new variables. The previously discussed 3/2 order transition becomes a critical point in phase diagrams involving Π and A. The values of the usual critical exponents are β=1, δ=2, γ=γ′=1, and α=0, and the 3/2 order exponents appear on the critical isobar, Π=Πc. The model shows Π-A phase behavior which is strikingly different from the P–V behavior, in agreement with the difference between the experimental Π-A monolayer behavior and the P–V bilayer behavior. This supports the theory that the bilayer is two weakly coupled monolayers.