J. Phys. II France
Volume 3, Number 7, July 1993
Page(s) 971 - 997
DOI: 10.1051/jp2:1993177
J. Phys. II France 3 (1993) 971-997

Phase transitions and shapes of two component membranes and vesicles I: strong segregation limit

Toshihiro Kawakatsu1, 2, David Andelman1, 3, Kyozi Kawasaki1, 2 and Takashi Taniguchi1

1  Department of Physics, Kyushu University 33, Fukuoka 812, Japan
2  IFF Theorie III, Forschungszentrum Jülich, 5170 Jülich, Germany
3  School of Physics and Astronomy, Tel-Aviv University, Ramat Aviv 69978, Tel Aviv, Israel

(Received 17 February 1993, accepted 13 April 1993)

We investigate unilamellar membranes and vesicles composed of an A/B mixture of partially miscible amphiphiles. Assuming a simple bilinear coupling between relative composition and local curvature, and in the strong segregation limit of the A/B mixture, we show for unilamellar open-shape membranes that the competition between surface tension and curvature results in a phase with a selected periodicity (modulated phase) both in the shape and in the A/B composition. The limits of large and small surface tension are discussed separately. These findings extend previous results obtained close to the A/B critical point (shallow quench). For the same limit of strong segregation, we also investigate the coupling between the separation of the system into A and B domains, and the overall shape of closed-shape vesicles. For cylindrical vesicles of fixed overall area (or equivalently vesicles embedded in a two-dimensional space), equilibrium shapes and phase diagrams are obtained. We also consider the effect of an added pressure difference (osmotic pressure) across the vesicle. The results are extended to axial symmetric vesicles embedded in a three-dimensional space.

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