Statistical Mechanics of Biomembrane Phase Transition. I. Excluded Volume Effects of Lipid Chains in Their Conformation Change

Abstract

The main phase transition of a membrane is attributed to conformation changes of the hydrocarbon chains constituting the lipid bilayers. The excluded volume effect, which is crucial for cooperative nature of the conformation changes, is taken into consideration by a modified dimer model. Statistical mechanics of the model is investigated rigorously by means of the transfer matrix formalism without introducing any extra simplification such as the continuum approximation. The model is found to exhibit a new type of second order phase transition which does not contain critical fluctuation: Specific heat is zero for T<T_c and is bounded by a finite value for T≥T_c. A variational evaluation of the maximum eigen-value of the transfer matrix is given for the purpose of quantitative (though approximate) analysis of the phase transition.