# Coexistences of lamellar phases in ternary surfactant solutions

## TL;DR

This paper theoretically explores the phase coexistences in binary and ternary lamellar surfactant solutions, revealing complex phase diagrams with multiple coexistence regions influenced by surface tension effects.

## Contribution

It extends the free energy model to include membrane segment entropy and analyzes the resulting complex phase behaviors in surfactant solutions.

## Key findings

- Binary solutions show phase separation and a critical point.
- Ternary solutions exhibit various three-phase and two-phase coexistence regions.
- Finite surface tension broadens coexistence regions.

## Abstract

We theoretically investigate the coexistences of lamellar phases both in binary and 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 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 undulation fluctuations of membranes and leads to a wider three-phase and two-phase coexistence regions.