J. Phys. II France
Volume 1, Numéro 3, March 1991
Page(s) 375 - 380
DOI: 10.1051/jp2:1991174
J. Phys. II France 1 (1991) 375-380

Theory of the ripple phase coexistance

M. L. Belaya1, M. V. Feigel'man2 and V. G. Levadny3

1  Institut of Plant Physiology, Botanicheskaya 35, 127276, Moscow, U.S.S.R.
2  Landau Institute for Theoretical Physics, Kosygina 2, 117940 Moscow, U.S.S.R.
3  Institute of Cybernetics, U.S.S.R. Academy of Sciences, Vavilov str. 34, Moscow, U.S.S.R.

(Received 18 September 1990, accepted 13 December 1990)

The macroscopic theory of the competition between two different modifications ( $\Lambda$- and $\Lambda$/2-phases) of P $_{\beta'}$ (ripple) phase in lipid bilayers is presented. It is shown that the increase of the membrane curvature should lead to the phase transition from the $\Lambda$/2-phase to the $\Lambda$-phase; the critical value of the curvature $R^{-1}_{\rm c}$ is obtained as a function of the geometrical parameters of the $\Lambda$/2-phase and the free energy difference $\Delta F^0$ between both phases in the case of planar membranes. The observed [3] splitting of disclinations in the $\Lambda$/2-phase into well-separated half-integer parts connected by linear defects (of the lenght $\ell_d \ll \lambda$) is shown to be related with the smallness of $\Delta F^0$. the relation between $R_{\rm c},~\ell_{\rm d}$ and geometrical and thermodynamic parameters of the $\Lambda$/2-phase alone is obtained.

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