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ABSTRACT
We theoretically investigate the coexistences of lamellar phases both in binary and in ternary surfactant solutions. The previous free energy of a lamellar stack is extended to take into account the translational entropy of membrane segments. The obtained phase diagram for binary surfactant solutions (surfactant/water mixtures) shows a phase separation between two lamellar phases and also exhibits a critical point. For lamellar phases in ternary surfactant solutions (surfactant/surfactant/water mixtures), we explore the possible phase behaviors and show that the phase diagrams exhibit various three-phase regions as well as two-phase regions in which different lamellar phases coexist. We also find that finite surface tension suppresses the undulation fluctuations of membranes and leads to a wider three-phase and two-phase coexistence regions.
Acknowledgments
We thank T. Kato and Y. Kawabata for useful discussions.
Funding
S.K. and R.O. acknowledge the support from the Grant-in-Aid for Scientific Research on Innovative Areas “Fluctuation and Structure” (Grant No. 25103010) from the Ministry of Education, Culture, Sports, Science, and Technology of Japan, and the Grant-in-Aid for Scientific Research (C) (Grant No. 15K05250) from the Japan Society for the Promotion of Science (JSPS). J.W. acknowledges the support from the C.N.R.S. (Centre National de la Recherche Scientifique), the French ORT association, and ORT school of Strasbourg.