Molecular diffusion in a living network

We report on the diffusion of a surfactant confined in a branched cylindrical "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 detailed investigation on the microstructure of the micellar network. Our results 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 studied the lecithin diffusion along two different oil dilution lines, corresponding 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 observation times investigated. Furthermore, the selfdiffusion coefficient was found to be independent of the concentration in the micellar volume fraction 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 coefficient, D-c. At the second dilution line, W-0 = 2, the situation is markedly different. At lower concentrations (Phi < 0.11), we found at shorter times a mean square displacement <z(2)> scaling as t(1/2) consistent with curvilinear diffusion. For longer times, there was a crossover to a Gaussian diffusion with <z(2)> proportional to t. The observation time where there is a crossover from curvilinear to a Gaussian diffusion shifts to shorter times 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 at W-0 = 3 clearly indicate that the structure is a branched micellar network 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 much smaller density of branch points. The branching density increases with increasing Phi. Finally, the measured water diffusion along the two oil dilution lines was found to be Gaussian with a time-independent, single diffusion coefficient. The dominating mechanism for the water diffusion was found to be the motion inside the giant wormlike reverse micelles mediated by an interaggregate exchange with a characteristic time of the order of microseconds.