The Stage of Ultrafast Relaxation in Micellar Surfactant Solutions

The Becker-Doring kinetic equations are employed to describe the stage of ultrafast relaxation in micellar surfactant solutions, which ends in the establishment of a quasi-equilibrium distribution in the premicellar region of aggregate sizes. This is performed by analyzing the spectrum of the eigenvalues of the matrix of kinetic coefficients of the linearized Becker-Doring difference equations, which describes the complete multistage relaxation in a micellar system. The first value of the spectrum ordered as an ascending series is equal to zero (infinite relaxation time), thereby corresponding to the law of conservation of the surfactant quantity. The second value is very small; it differs from the series of subsequent values by several orders of magnitude and determines the time of slow relaxation. The other eigenvalues describe the processes of fast relaxation and comprise the contributions from the relaxation processes in both micellar and premicellar regions of aggregate sizes. In the latter region of the spectrum, the contribution of the ultrafast relaxation can be numerically distinguished. The obtained result is confirmed by the analysis of the spectrum of relaxation times of premicellar aggregates, which are considered as a closed system. It is also shown that the spectrum of ultrafast relaxation times is mainly determined by the first diagonal elements of the matrix of the linearized Becker-Doring equations and can be described analytically.