A beta-coupled gauche kink description of the lipid bilayer phase transition

A statistical-mechanical model for a lipid bilayer was built around the assumption that beta-coupled gauche kinks are the only nonstraight hydrocarbon chain configurations allowed. Packing of these chains was considered and expressions for the energy and entropy are developed based on those considerations. A solution was obtained which was not exact but was still accurate enough to be useful. In addition, an intermolecular potential was formulated which includes the attractive and repulsive forces between the hydrocarbon chains, the polar group repulsions, and hydrophobic forces. Combining the solution to the kinking model and the intermolecular potential, we obtain the total free energy of the lipid bilayer, which exhibits a first-order phase transition at a characteristic temperature. The theoretical heat of transition indicates that kinks alone can provide enough disorder for the transition to occur. Other physical quantities can be calculated, including order parameters. The order parameters calculated here give a picture of chains which are rigid near the polar group and more fluid near the methyl group.