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

Abstract
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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