J. Phys. Chem. 1985,89, 2695-2705
2695
Equlilbrlum and Kinetic Propertles of Mixed Micelles Staffan Wall* and Christer Elvingson Department of Physical Chemistry, University of Goteborg and Chalmers University of Technology, S-412 96 Goteborg, Sweden (Received: December 27, 1984)
The mass action law has been applied to a general two-componentmicelle distribution. Formulas for the concentrationdependence of aggregation numbers and central moments of the micelle distribution are given in the form of differential equations. The concentrations of the monomers are calculated as a function of various concentration variables as for example the total concentration of one of the components. One-component ionic micelles considered as two-component systems are also discussed. The two components are then the monomer and the counterion. The kinetics of the micellization is treated, and relaxation times and corresponding amplitudes are given. The kinetic theory is illustrated by numerical examples. A treatment of the narrow passage is done when it has a double-Gaussian saddle-shaped form and either the disintegration constants are equal or one of them is much larger than the other.
I. Introduction Micelle kinetics has been treated both experimentally and theoretically in numerous papers. The more important contributions are given in ref 1-5. The first successful interpretation of experimental data2 was based on the assumption that the micellar aggregates were formed by a stepwise process AI
+ AI ~t A2
A2 4- Ai
i=?
A3
As denotes an aggregate with s monomers and A, the corresponding concentration. With the additional assumption that k;As, considered as a function of s, has a deep minimum between the oligomers and the region of proper micelles, the equilibration process after a disturbance can be split into two processes with time constants, 71 and 7*, differing by several orders of magnitude ( T ~
