2D crystalline order and defects in a stack of membranes

(Received 18 November 1992, accepted 23 December 1992)

Abstract
We consider the stability of two-dimensional (2D) crystalline order within the membranes of a lyotropic lamellar phase, concentrating on the effects of 2D crystal dislocations and thermal undulations. At lamellar spacings d less than a critical value, the 2D melting transition is found to be essentially unaffected by the flexibility of the membranes, and thus occurs at a melting temperature near that of a single membrane on a rigid substrate. At larger spacings the interactions between membranes become weak enough to allow buckling of the membrane in a finite region around each thermally excited dislocation. This leads to a partial screening of the elastic interaction between dislocations, and acts to depress, but not destroy, the melting tranistion. Thermal undulations act to soften the membrane and thus further depress , which is predicted to vanish continuously in the limit of large d. We discuss implications for recent experiments on biological membranes.