Molecular diffusion in a living network

We report on the diffusion of a surfactant confined in a branched cylindric al "micellar" network, formed by lecithin and small amounts of water in the solvent isooctane. By means of the pulsed field gradient H-1 NMR technique , the measured surfactant mean square displacement, <z(2)>, allows for a de tailed investigation on the microstructure of the micellar network. Our res ults show that the structure depends weakly on the micellar volume fraction , Phi, and strongly on the water-to-lecithin molar ratio, W-0. We have stud ied the lecithin diffusion along two different oil dilution lines, correspo nding to different water-to-lecithin molar ratios, 2 and 3. The time window in the diffusion experiments was varied in the range from 50 ms to 1 s. At W-0 = 3, a Gaussian diffusion, characterized by a mean square displacement varying linearly with time, was observed for all concentrations and all ob servation times investigated. Furthermore, the selfdiffusion coefficient wa s found to be independent of the concentration in the micellar volume fract ion range studied from Phi = 0.1 to Phi = 0.38. The value of the diffusion coefficient is approximately 1/3 of the value of the lateral diffusion coef ficient, D-c. At the second dilution line, W-0 = 2, the situation is marked ly different. At lower concentrations (Phi < 0.11), we found at shorter tim es a mean square displacement <z(2)> scaling as t(1/2) consistent with curv ilinear diffusion. For longer times, there was a crossover to a Gaussian di ffusion with <z(2)> proportional to t. The observation time where there is a crossover from curvilinear to a Gaussian diffusion shifts to shorter time s with increasing Phi. At higher concentrations, only a Gaussian diffusion was observed within the experimental time window. The diffusion coefficient evaluated from the Gaussian regime increases linearly with Phi, the value varying from D-c/100 to D-c/20. The high diffusion coefficients evaluated a t W-0 = 3 clearly indicate that the structure is a branched micellar networ k where the curvilinear distance along the cylindrical micelles between two branch points is smaller than the persistence length. At W-0 = 2, the data can also be interpreted in terms of a branched network, however with a muc h smaller density of branch points. The branching density increases with in creasing Phi. Finally, the measured water diffusion along the two oil dilut ion lines was found to be Gaussian with a time-independent, single diffusio n coefficient. The dominating mechanism for the water diffusion was found t o be the motion inside the giant wormlike reverse micelles mediated by an i nteraggregate exchange with a characteristic time of the order of microseco nds.