Defects and the sol-gel transition in lamellar fluid membranes

Phase transitions of a multilamellar system Lα composed of water, lipids and PEG-lipids are investigated. Increasing the water fraction or the PEG-lipids concentration of such a system, the fluid multilamellar phase changes to a gel phase and then returns to a fluid phase. Since flat layers with a sufficient concentration of PEG-lipids are unstable with respect to undulation fluctuations, we assume that undulations of large amplitude create certain kinds of defects, which are composed of folded membranes and multilayer spherical or cylindrical vesicles. The concentration of these defects changes the viscosity of the system. We calculate the concentration of defects using an ideal gas approximation and show that the transition point from the fluid to gel phase is inversely proportional to the membrane separation, under the assumption that the energetically favorable defect size is independent of the separation. We predict three types of sol-gel transitions, which qualitatively explain the phase diagram obtained by experiments.