2D crystalline order and defects in a stack of membranes

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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 Tm 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 Tm, which is predicted to vanish continuously in the limit of large d. We discuss implications for recent experiments on biological membranes

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