J. Phys. II France
Volume 3, Numéro 4, April 1993
Page(s) 531 - 546
DOI: 10.1051/jp2:1993149
J. Phys. II France 3 (1993) 531-546

2D crystalline order and defects in a stack of membranes

David C. Morse1 and T.C. Lubensky2

1  Corporate Research Science Laboratories, Exxon Research and Engineering Co., Annandale, NJ 08801, U.S.A.
2  Department of Physics, University of Pennsylvania, Philadelphia PA 19104, U.S.A.

(Received 18 November 1992, accepted 23 December 1992)

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 $T_{\rm m}$ 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 $T_{\rm m}$, which is predicted to vanish continuously in the limit of large d. We discuss implications for recent experiments on biological membranes.

87.20E, 61.30J, 64.70M

© Les Editions de Physique 1993