ISSN 1061-933X, Colloid Journal, 2008, Vol. 70, No. 2, pp. 244–256. © Pleiades Publishing, Ltd., 2008. Original Russian Text © A.K. Shchekin, F.M. Kuni, K.S. Shakhnov, 2008, published in Kolloidnyi Zhurnal, 2008, Vol. 70, No. 2, pp. 270–283. 244 INTRODUCTION The concept of “slow” relaxation processes in micellar solutions as processes relevant to the establish- ment of complete equilibrium by the formation and dis- integration of micelles, which are accompanied by the forward and back fluxes of molecular aggregates through a potential barriers of micellization, was for- mulated for the first time in Aniansson’s and Wall’s works [1, 2] and is generally accepted today. Usually, when speaking of a slow relaxation time, they mean the characteristic time of the exponential decay of a distur- bance in monomer concentration or total micelle con- centration [3]. However, the exponential decay regime is only developed at the final stage of the relaxation pro- cess, when the deviations from the equilibrium concen- trations of surfactant monomers and micelles become very small [4–6]. The final stage of the slow relaxation occurring via the exponential decay of concentration disturbances with time is hereafter referred to as “expo- nent-law relaxation” for short. In the total relaxation process, a marked role is also played by the stage of power-law variations in the concentrations with time. This stage precedes the exponent-law relaxation. Accordingly, this initial stage of slow relaxation is hereafter referred to as a “power-law relaxation stage.” It is during the power-law stage that relaxing parame- ters of a solution undergo main nonlinear variations. An important peculiarity of the power-law stage is, in con- trast to the exponent-law stage, the dependence of the characteristic times and the duration of the power-law stage itself on whether the relaxing parameters of a micellar solution approach their equilibrium values from above or below. The relations between the relax- ation times of the exponent- and power-law relaxation processes were, in general, estimated in [4–6] for the situation in which, after an initial disturbance, the con- centrations of surfactant monomers and micelles decrease and increase, respectively. An opposite situa- tion when the surfactant monomer and micelle concen- trations rise and diminish, respectively, is also of exper- imental and theoretical interest. This situation will be considered in this paper. In this paper, analytical relations will be derived for the time dependences of surfactant monomer concen- tration at the power-law stage of slow relaxation in solutions at arbitrary initial conditions. The aforemen- tioned relations will be obtained on the basis of exact formulas describing the dependences of the positions and half-widths of the vicinities of extreme work values on surfactant monomer concentrations in dilute micel- lar solutions [7]. It will be shown that the derived rela- tions have a general form independent of the model, which is selected for surfactant molecular aggregates, and are applicable throughout the range of micellar solution concentrations from the first to the second crit- ical micellization concentration (CMC 1 and CMC 2 , Power-Law Stage of Slow Relaxation in Solutions with Spherical Micelles A. K. Shchekin, F. M. Kuni, and K. S. Shakhnov Fok Research Institute of Physics, St. Petersburg State University, ul. Ul’yanovskaya 1, Petrodvorets, St. Petersburg, 198504 Russia Received May 28, 2007 Abstract—General (independent of models selected for surfactant molecular aggregates) analytical relations are derived to describe the initial stage of slow relaxation in micellar solutions with spherical micelles. This stage precedes the final stage of the relaxation occurring via an exponential decay of disturbances with time. The relations obtained are applicable throughout the interval of micellar solution concentrations from the first to the second critical micellization concentration. It is shown that the initial stage is characterized by power laws of variations in the concentrations of monomers and micelles with time, these laws being different for the relax- ation processes proceeding from above and below toward equilibrium values of micellar solution parameters. Relations are derived for the duration of this stage, and the effect of initial conditions is studied. Characteristic times of the power-law stage are determined and compared with the characteristic time of the final exponent- law relaxation stage. The behavior of these times is investigated at surfactant solution concentrations in the vicinity of, and noticeably above, the first critical micellization concentration. On the basis of the droplet and quasi-droplet thermodynamic models of surfactant molecular aggregates, numerical solutions are found for nonlinearized equations of slow relaxation for the time dependence of surfactant monomer concentrations at all stages of the slow relaxation. Numerical results obtained from the models are compared with the results of a general analytical study. DOI: 10.1134/S1061933X0802018X