Study of a model for the main phase transition of lipid bilayers using the Kikuchi cluster method

The statistical mechanics of Doniach's two-state lattice model for the main gel – liquid crystal phase transition of phospholipid bilayers is treated in a similar manner to order–disorder transformations in binary alloys and magnetic systems, using the cluster variation method developed by Kikuchi. Indeed, the analogy holds better for the latter system, since the entropy difference between the two states gives rise to an effective temperature-dependent field. This effective field vanishes at the first-order phase transition, whose latent heat is associated with the discontinuity in the order parameter.We use Kikuchi's approximation with the inclusion of triangle bond correlations, and pair and site probabilities in the expression for free energy. We assume that the lipid chains only interact through nearest neighbour pair potentials and that triangle correlations are important for approximate counting of allowed states. Two long-range order parameters and a short-range order parameter are introduced in th...