Search Solid Membranes May Not Crumple

A membrane that is not rigid in the plane, or has zero in-plane shear modulus, is said to be fluid; one that does have a nonzero shear modulus in the plane is said to be solid-like. A fluid membrane shaped, say, like a rectangle will be easily deformed when antiparallel forces are applied along two of its parallel edges. In many cases the interesting excitations, or conformations, of a fluid membrane arise from out-of-plane bending. Wolfgang Helfrich (Freie Universitat, Berlin) argued in 1978 that out-ofplane fluctuations of fluid membranes may cause them to repel one another when they are brought close together, say, to form a stack, if the energy cost of bending the membrane is small (of order of kB T, where T is the temperature). The existence of this repulsion, as well as its inversesquare dependence on the distance between the membranes, was verified in 1986 in a synchrotron x-ray study by a team from Exxon Research and Engineering Company, the CNRS laboratories at Bordeaux and the University of Colorado at Boulder. That same year Reinhard Lipowsky (University of Munich) and Stanislas Leibler (CEA Saclay, France) predicted that because of the repulsive interaction a stack of fluid membranes might undergo a phase transition at which the mean separation between the membranes changes continuously from finite to infinite. Michael Mutz (Freie Universitat, Berlin) and Helfrich now report observing an "unbinding" phase transition in a stack of fluid membranes; they claim that the transition is similar to the one predicted by Lipowsky and Leibler. David Nelson (Harvard University) and Luca Peliti (University of Naples) predicted, in 1987, that solid-like membranes would be flat at low temperatures but would undergo a phase transition at some temperature to a crumpled phase in which a typical membrane configuration would be similar to that of a polymer. The flat phase has now been seen in extensive molecular dynamics simulations, by Farid Abraham, W. E. Lipid bilayers in an aqueous solution of NaCI at two different temperatures. The membranes appear as a thick fuzzy line at 22.8 °C (top) because they are unbound and undulate. They appear as a much sharper and darker line at 22.1 °C (bottom) because they are bound. The binding is not complete at 22.1 °C, hence the swollen part in the middle in the right panel. The lipid used was digalactosyldiacylglycerol. The bar represents 10 jam. (Courtesy of Wolfgang Helfrich.)