Lamellar phase separation in a centrifugal field. A method for measuring interbilayer forces
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We present a novel method for measuring interbilayer forces in lamellar liquid crystals of amphiphile-water systems. In a centrifuge the gravitational effect is easily strong enough to produce clearly observable concentration gradients. During the experiment the concentration profile in the test-tube is monitored using NMR imaging of the deuterium quadrupole splitting in the lamellar phase, by temporarily transferring the sample into a NMR spectrometer. We also present a theoretical analysis of the experiment, where interactions dominate over entropy of mixing effects. For a system at sedimentation equilibrium one obtains a direct measurement of the interbilayer force, or equivalently chemical potential of the components over a substantial concentration range. It requires long times to obtain equilibrium in the centrifuge but very useful information about equilibrium and dynamic parameters is also obtained through an analysis of the sedimentation process. Experiments were performed on samples of a dilute lamellar phase of the non-ionic surfactant C10E3. After a few days of centrifugation a consistent concentration pattern was observed. At the bottom of the sample there appears a pure water-phase. The concentration profiles stabilize after a long centrifugation time. If they are related to the phase boundary the different profiles superimpose. This observation is consistent with the theory and the observation allows for a determination of how the chemical potentials vary with composition. The observed profiles are consistent with a dominating undulation force with a bilayer bending rigidity of 4.8-5.1 kT.