^{1,a)}, N. Shimokawa

^{1}and T. Kato

^{1}

### Abstract

We propose models for the first-order unbinding transition of lyotropic lamellae in surfactant solutions. The coupling between the surfactant volume fraction and the elastic degree of freedom is considered so that the net attractive interaction between the surfactant molecules is enhanced. The elastic degree of freedom can be either (i) a membrane elastic degree of freedom or (ii) a bulk elastic degree of freedom. The phase behaviors of these two models are analyzed. For both cases, the unbinding transition becomes first order when the coupling is strong enough. We determine the associated preunbinding line which separates two lamellar phases having different repeat distances.

This research was partly supported by the Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science under Grant No. 15540395.

I. INTRODUCTION

II. UNBINDING TRANSITION

III. MODEL A

A. Free energy

B. Phase behavior

IV. MODEL B

A. Free energy

B. Phase behavior

V. DISCUSSION

### Key Topics

- Surfactants
- 27.0
- Elasticity
- 17.0
- Mean field theory
- 14.0
- Free energy
- 10.0
- Elasticity theory
- 9.0

## Figures

Phase diagram of the system, redrawn from Fig. 1 in Ref. 9. , lamellar phase; , isotropic micellar phase; , cubic phase; , hexagonal phase; and , nematic phase.

Phase diagram of the system, redrawn from Fig. 1 in Ref. 9. , lamellar phase; , isotropic micellar phase; , cubic phase; , hexagonal phase; and , nematic phase.

The phase diagrams of the Milner and Roux model as a function of (a) surfactant volume fraction and virial coefficient , and (b) surfactant chemical-potential and virial coefficient . The solid line is a first-order line, whereas the dashed line is a second-order one. The horizontal lines and the dot-dashed line in (a) are tielines and the spinodal line, respectively. The filled circle denotes the tricritical point (tcp).

The phase diagrams of the Milner and Roux model as a function of (a) surfactant volume fraction and virial coefficient , and (b) surfactant chemical-potential and virial coefficient . The solid line is a first-order line, whereas the dashed line is a second-order one. The horizontal lines and the dot-dashed line in (a) are tielines and the spinodal line, respectively. The filled circle denotes the tricritical point (tcp).

The phase diagrams for in model A as a function of (a) surfactant volume fraction and virial coefficient , and (b) surfactant chemical-potential and virial coefficient . The same notation of different lines is used as in Fig. 2. The filled circle denotes the tricritical point (tcp).

The phase diagrams for in model A as a function of (a) surfactant volume fraction and virial coefficient , and (b) surfactant chemical-potential and virial coefficient . The same notation of different lines is used as in Fig. 2. The filled circle denotes the tricritical point (tcp).

The phase diagrams for in model A. The same notation of different lines is used as in Fig. 2. The filled square and diamond indicate the critical end point (cep) and critical point (cp), respectively.

The phase diagrams for in model A. The same notation of different lines is used as in Fig. 2. The filled square and diamond indicate the critical end point (cep) and critical point (cp), respectively.

The values of at the critical point (solid line) and the unbinding transition point (dashed line) as a function of the coupling strength for model A.

The values of at the critical point (solid line) and the unbinding transition point (dashed line) as a function of the coupling strength for model A.

The phase diagrams for in model B. The same notation of different lines is used as in Fig. 2. The filled circle, triangle, diamond indicate the tricritical point (tcp), triple point (tr), critical point (cp), respectively.

The phase diagrams for in model B. The same notation of different lines is used as in Fig. 2. The filled circle, triangle, diamond indicate the tricritical point (tcp), triple point (tr), critical point (cp), respectively.

The values of at the critical point (solid line) and the unbinding transition point (dashed line) as a function of the coupling strength for model B.

The values of at the critical point (solid line) and the unbinding transition point (dashed line) as a function of the coupling strength for model B.

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