Pseudophase approach to micellisation

Primarily, this approach was based on the formal analogy between a first order phase transition and the micellisation. When a new phase of a pure substance is formed the chemical potential of this substance and its concentration in the initial phase do not change with the total content of this substance in the system. A similar situation is observed above the CMC, where the adsorption and the surface tension become approximately constant. In reality variations of these properties are relatively small to be observed by conventional experimental methods. The application of the Gibbs adsorption equation shows that the constancy of the surfactant activity above the CMC follows from the constancy of the surfactant adsorption T2 [13] 

The calculated standard thermodynamic functions according to this equation are in a reasonable agreement with experimental data. Moreover, the authors [14] used the quasichemical approach 

Some theories developed in the framework of the pseudophase approach attempt to obtain the thermodynamic properties of the whole micellar system from a detailed description of a single micelle. This is the main content of the book by Tanford [16] and this approach was developed further by Israelachvili and co-workers [11]. Let us discuss briefly some general principles of these theories. It is assumed that micelles are in equilibrium with the surrounding solution. Then the chemical potentials of both pseudophases are equal and one can write 

If we assume that the surfactant solution is a binary system (surfactant + water), the total mole fraction of particles containing surfactant S becomes 

The main characteristics of the size distribution of micelles are the mean aggregation number Nm and the standard deviation  

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