Kinetic modeling of self-aggregation in solutions with coexisting spherical and cylindrical micelles at arbitrary initial conditions

We have numerically studied the nonlinear dynamics of aggregation of surfactant monomers in a micellar solution. The study has been done on the basis of a discrete form of the Becker–Doring kinetic equations for aggregate concentrations. The attachment–detachment coefficients for these equations were determined from the extended Smoluchowski diffusion model. Three typical situations at arbitrary large initial deviations from the final aggregative equilibrium with coexisting premicellar aggregates, spherical and cylindrical micelles have been considered. The first situation corresponds to micellization in the solution where initially only surfactant monomers were present. The other two situations refer to nonlinear relaxation in the cases of substantial initial excess and deficit of surfactant monomers in solution over their equilibrium concentration in the presence of spherical and cylindrical aggregates. The interplay between non-equilibrium time-dependent concentrations of premicellar aggregates, spherical and cylindrical micelles in relaxation far from equilibrium has been found. The existence of ultrafast relaxation and the possibility of nonmonotonic behavior of the monomer concentration has been confirmed. Comparison with predictions of analytical kinetic theory of relaxation and micellization for the concentration of monomers and total concentrations for spherical and cylindrical micelles has been given. It has been shown that the analytical theory is in fine agreement with the results of the difference Becker–Doring kinetic equations both for fast and slow nonlinear relaxation.