Synchrotron x-ray study of the modulated lamellar phasePβ’in the lecithin-water system

Abstract

The results of a high-resolution, synchrotron x-ray powder diffraction study of lattice constants in the $P_{\beta \mathcal{’}}$ (‘‘rippled’’) phase of lecithin-water multilamellar mixtures are given. The variation with water volume fraction ${\phi }_w$ and hydrocarbon chain length $N_c$ of the modulation wave vector $Q_r$ suggests that membrane curvature and hydration interactions between membranes play a significant role in the modulation. The dependence of the membrane thickness and area per head group on $N_c$ indicates that the conformation of hydrocarbon chains is predominantly solidlike. The appearance of significant intensity in higher harmonics of the modulation wave vector rules out simple (e.g., sinusoidal or triangular) membrane density modulations. The results are consistent with a Lifshitz phenomenological model for lamellar phases of interacting membranes proposed by Goldstein and Liebler [Phys. Rev. Lett. 61, 2213 (1988)]. The phase behavior predicted by the model includes a multicritical point called the Lifshitz point where the wavelength of the modulation diverges. The experimental results indicate that this multicritical point lies in the vicinity of $N_c$=9 and ${\phi }_w$=0.18.