Micellar hexagonal phases in lyotropic liquid crystals

Abstract

The hexagonal cell parameter a of the system sodium dodecyl lauryl sulfate and water as a function of volume concentration ${\mathit{c}}_{\mathit{v}}$ in phase ${\mathit{H}}_{\mathrm{\alpha }}$ shows the functional behavior expected for micelles of finite length: a∝${\mathit{c}}_{\mathit{v}}^{\mathrm{-}1/3}$. The interpretation of x-ray data based on finite micelles leads to an alternative description of the hexagonal phase ${\mathit{H}}_{\mathrm{\alpha }}$: spherocylindrical micelles of constant radius with length that may grow along the range of the ${\mathit{H}}_{\mathrm{\alpha }}$ phase. Results are compared with recent statistical-mechanical calculations for the isotropic I-${\mathit{H}}_{\mathrm{\alpha }}$ transition. The absence of diffraction in the direction perpendicular to the hexagonal plane is ascribed to polydispersity of micellar length, which also is a necessary condition for the occurrence of direct I-${\mathit{H}}_{\mathrm{\alpha }}$ transitions.