Free energy of micellisation

In the presence of excess added electrolyte, with mole fraction x, the free energy of micellisation is given by the expression ... 

However, as mentioned above, experimental results have shown clearly that micelle formation involves only a small enthalpy change, and is often endothermic. The negative free energy of micellisation is the result of a large positive entropy, and this led to the conclusion that micelle formation must be predominantly an entropy-driven process. 

It was shown in Chapter 2 that the standard free energy of adsorption AG" can be calculated from the standard free energy of micellisation AG" via the relationship (2.179),... 

Equation (5.108) together with the geometric peculiarities of the micelles and with the expressions for the different contributions to the free energy of micellisation allows us to calculate all properties of a micellar system. Note that many of the above-mentioned contributions to the free energy of micellisation contain parameters related to the molecular structure of the surfactant. They can be estimated from the geometrical characteristics of molecules and molecular structure, and from experimental data on the bulk properties of individual substances. 

The total free energy of micellisation can be then composed of these contributions... 

Beyond the CMC the addition of surfactant leads mainly to the increase of the number of micelles and the total monomer concentration is practically constant. Furthermore, the first forming micelles will have a composition close to the optimum value yA because the free energy of micellisation has a minimum at this composition. As it follows from Eq. (5.110) the mole fraction of these micelles x i at yA is finite and becomes small only when xi expfgm/kuT). Further approximation of the CMC at this concentration and application of Eq. (5.124) for the optimum composition yA allows us to get finally the relation for the CMC of the mixture as... 

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

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... 

Numerous theories, models and mathematical approaches have been developed over the years in order to describe the micellisation process and the dependence of fundamental structural parameters of the micelles, like cmc, aggregation number (Nagg), overall size (Rm), core radius (Rc) and corona thickness (L), on the molecular characteristics of the block copolymer, with respect to the degrees of polymerisation of the constituent blocks (Na and N ), as well as the Flory-Huggins interaction parameters x between the blocks and between the blocks and the solvent. Some of these approaches use the minimisation of the total free energy of the micellar system so as to extract relations between the copolymer and micelle features, while others are based on the scaling concept of Alexander-de Gennes and... 

Since the equilibrium constant, 07C, in equation (4.23) and the standard free energy change, AG°, for the micellisation of 1 mole of surfactant are related by... 

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