General features of micellisation kinetics

The kinetics of formation and disintegration of micelles has been studied for about thirty years [106-130] mainly by means of special experimental methods, which have been proposed for investigation of fast chemical reaction in liquids [131]. Most of the experimental methods for micellar solutions study the relaxation of small perturbations of the aggregation equilibrium in the system. Small perturbations of the micellar concentration can be generated by either fast mixing of two solutions when one of them does not contain micelles (method of stopped flow [112]), or by a sudden shift of the equilibrium by instantaneous changes of the temperature (temperature jump method [108, 124, 129, 130]) or pressure (pressure jump method [1, 107, 116, 122, 126]). The shift of the equilibrium can be induced also by periodic compressions or expansions of a liquid element caused by ultrasound (methods of ultrasound spectrometry [109-111, 121, 125, 127]). All experimental techniques can be described by the term relaxation spectrometry [132] and are characterised by small deviations from equilibrium. Therefore, linearised equations can be used to describe various processes in the system. 

If micelles (Xn) consist only of one kind of species (Xi - mononers), the chemical equilibrium in the system (5.16) can be represented in the following form 

The reaction given by Eq. (5.146) corresponds to the following mass action law 

The kinetic model, which can explain the origin of these two relaxation processes and can describe the dependence of the corresponding relaxation times on the concentration, has been proposed by Aniansson and Wall [114, 115, 119]. This model allows to explain the main experimental facts and is generally accepted nowadays. At the same time, subsequent studies allowed for the determination of the application limits of this theory [116-118, 128]. Because the model of Aniansson and Wall is frequently used also for the analysis of dynamic surface properties of micellar solutions [93, 96-103, 133-138], it will be considered below in details. 

Let us assume that changes of the aggregation number of different particles in the solution can take place only as result of a step by step joining or discharging of monomers. This means that instead of (5.146) the following kinetic model is considered 

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