Theory of micellisation

The classical theories of micellisation can be divided into two classes. One approach is based on the mass action law and assumes that micelles are chemical species ( quasichemical or chemical approach). Then the theoretical apparatus of chemical thermodynamics is applied to the whole system containing monomers and micelles. 

Another approach is the so-called pseudophase treatment. It uses the similarity of the first order phase transition and the micellisation process. Subsequent modifications of this approach are focused mainly on the properties of a micelle, which is considered to be a phase particle. Different theoretical models taking into account geometrical, mechanical and thermodynamic peculiarities of micelles were developed. 

Both of these approaches are not free from some disadvantages related to the restrictions of the corresponding concepts. Most of the recently developed theories combine both concepts. Therefore, their predictions are in a better agreement with experimental data although some discrepancies still remain. 

A micellar solution at constant temperature T and pressure p can be described by the following fundamental equations [12]  

When micelles and monomers are considered to be individual components and no other aggregates are present in the solution, equations (5.8) and (5.9) can be rewritten as follows 

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It is obvious that the kinetic theory of micellisation outlined above, cannot be applied to living polymers. For wormlike micelles one has to distinguish between several processes leading to disintegration and formation of micelles and to determine the corresponding characteristic times [141 - 145] ... 

The first attempt to take into account the two-step kinetic theory of micellisation was made by Fainerman [147]. With that end in view two pairs of diffusion equations (for micelles and monomers) were written down for two situations eorresponding to the fast and slow proeesses. Approximate solutions of the boundary problems for these equations were used subsequently in the course of analysis of experimental data on the adsorption kinetics from micellar solutions [77, 85, 87, 88]. However, as it has been shown by Dushkin et al. [137], this approaeh is equivalent to the PFOR model for the slow proeess and probably eannot be applied to the description of the adsorption kinetics for the fast process. 

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