Measurement of the compressibility modulus in a lyotropic lamellar phase stabilized by undulation forces

Lamellar mesophases of the anionic double-chain surfactant AOT in brine were oriented homeotropically between two smooth silica surfaces of a surface force apparatus (SFA). The force-distance profile was measured at different membrane volume fractions (Phi = 0.09-0.18) all close to the sponge/lamellar phase boundary in the phase diagram. Oscillatory profiles were consistently observed with the same characteristic features. The periodicity of the oscillations was twice the reticular spacing of the bulk lamellar phase, indicating that the lamellar stack responds to the applied strains by creating edge dislocations of Burgers vector 2. Such a defect is topologically equivalent to a handle joining two membranes and arises naturally from the topology of the neighboring sponge phase. The compressibility modulus at constant chemical potential, (B) over bar, was extracted from the parabolic shape of the force oscillations and was found to be consistent with an intermembrane interaction dominated by undulation forces.