Dislocations in lamellar phases confined in wedges

Abstract

A mesoscopic model for a binary water–amphiphile mixture in contact with external walls is developed from a microscopic description. The grand potential is a functional of the amphiphile concentration and a vector field representing average orientation of amphiphiles in mesoscopic regions. For parameters corresponding to the stability of lamellar phases of different periods λ, deformations occurring in caped wedges with different angles are determined. For 4l < λ < 7l, where l is the thickness of the monolayer, we find a strong dependence of the kinds of defects in the stable configurations on the period of the lamellar phase, on the angle of the wedge, and on the type of surfaces. For small λ/l the bilayers are just terminated, whereas for larger λ/l the bilayer branches and at the defect from one bilayer, two bilayers emerge. The defects in stable or metastable structures occur either near the mid plane of the wedge and near the cap when the lamellas are parallel to the wedge walls, or near the wedge walls when the lamellas are parallel to the wedge cap. In some cases a transition between the first structure, stable for small wedge angles, and the second structure, stable for large angles, is found.

Keywords:

• lyotropic liquid crystals
• confinement
• lamellar phase
• defects

Acknowledgements

Partial support by the Polish Ministry of Science and Higher Education, grants Nos NN 202 006034 and NN 204 240534 is acknowledged.