Fractional order phase transition in lipid bilayer: dipalmitoyllecithin

Dipalmitoyllecithin (DPL) shows an order ← → disorder pressure transition which is neither of first order nor of second order but can be treated as a fractional order (3/2 order) transition. The Ising model formalism is adopted for the study of such a system. A suitable equilibrium constant is defined which generates a 3/2 order transition. Transition curves are obtained and compared with the experimental curves of Liu and Kay. Reverse transition curves are also obtained and the system exhibits hysteresis effect. An approximate expression connecting transition pressures at different temperatures is obtained and the calculated and the experimental values are in good agreement.