Thermodynamic of micellisation

Both problems, changes of the equilibrium adsorption with micellar concentration and the influence of micelles on the adsorption rate, are the subjects of this review. Various definitions of the CMC are represented at the outset. Nowadays the thermodynamics of micellisation is the most developed part of modem theories of micellar systems. Two main approaches ("quasichemical and "pseudophase") are discussed in the second section of this chapter. In section 3 the thermodynamic equations for the Gibbs adsorption of surfactants in the micellar region are considered together with corresponding experimental data. The subsequent sections are devoted to non-equilibrium micellar systems. First, section 4 delineates briefly the theory of... 

All the definitions of the CMC discussed above reflect a general feature of surfactant solutions, namely, a qualitative change in the concentration dependencies of their properties at the CMC. This means that the thermodynamic state of such systems must also differ from the state below the CMC and cannot be described by conventional theories proposed for non-micellar solutions. A brief review of the thermodynamics of micellisation is presented in the following section. 

Table 3.3 Change of thermodynamic parameters of micellisation of alkyl sulphoxide with...

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. 

Note that all these abovementioned expressions for the standard affinity and the standard thermodynamic functions of micellisation were based on the definition of the CMC as an inflection point in the dependence ai(ctoti) given by Eqs. (5.53) and (5.54). If we use other definitions of the CMC, the corresponding relations will be different. 

Motomura et al. proposed a method of evaluation of various thermodynamic properties of micellar solutions from the surface tension data in the framework of the pseudophase treatment of micellisation [50, 52-55]. According to these authors, the micellar composition at the CMC can be found from the functional dependence of the CMC on the overall surfactant mole fraction using an analogy to the method proposed by Nguyen et al. [49], The approach of Motomura et al. [50] gives also a possibility to determine the relation between the composition of the surface layer and the micelles. Application of the Gibbs-Duhem equation to the whole... 

Concluding the discussion of micellisation kinetics it is necessary to note that a new theory based on the ideas of nucleation kinetics have been proposed recently by Kuni et al. [174,175]. The nucleation theory allows to study in detail the size distribution of aggregates on the basis of a thermodynamic analysis and to obtain more general kinetic equations. 

The free energy of micellisation is large and negative, indicating that micelle formation is spontaneous and that micelles are thermodynamically stable. 

The importance of thermodynamics in the pharmaceutical sciences is apparent when it is realised that such processes as the partitioning of solutes between immiscible solvents, the solubility of dmgs, micellisation and dmg-receptor interaction can all be treated in thermodynamic terms. This brief section merely introduces some of the concepts of thermodynamics which are referred to throughout the book. Readers requiring a greater depth of treatment should consult standard texts on this subject. ... 

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. 

The so-called thermodynamic-molecular models [18, 20-22] form another separate group of theories. For example, Puvvada and Blankschtein showed that the expression for the total free energy of mixed micellisation could be presented for binary surfactant mixture as follows... 

It is well established that when an amphiphilic block copolymer is dissolved in a selective solvent at a fixed temperature, above a specific concentration called the critical micelle concentration (cmc), micellisation occurs. Below the cmc, only molecularly dissolved copolymer chains (unimers) are present in the solution, while above the cmc multimolecular micelles are in thermodynamic equilibrium with the unimers. This process is in analogy to classical low molecular weight surfactants, differing in that the cmc is much lower in the case of block copolymers macrosurfactants. The self-assembly arises from the need of the copolymer chains to minimise energetically unfavourable solvophobic interactions. Therefore, micelle formation is dictated by two opposite forces, the attractive force between the insoluble blocks, which leads to aggregation, and the repulsive one between the soluble blocks preventing unlimited growth of the micelle. At the same time, the interaction of the soluble blocks and the solvent is responsible for the stabilisation of the micelles [1, 10]. 

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