Standard free energy of micelle formation

The standard free energy of micelle formation will be... 

One can easily see that Eq. (2.179) follows from Eqs. (2.9) and (2.177), in consideration that at the CMC the relations Xj = 1 and Yi =Ycmc valid. Therefore, the standard free energy of adsorption can also be calculated from the standard free energy of micelle formation [185,... 

At very high concentration the micelles probably dissociate in the subsurface layer [13]. The dose distance to the surface could influence the free energy of micelle formation and kinetics of dissociation of micelles. To calculate the standard free energy of micelle formation for non-ionic surfactants, the expression ... 

In accord with this model, the standard free energy of micelle formation per monomer unit, AG,° is given by... 

The data on the temperature dependence of surface tension of surfactant solutions are often used to estimate the thermodynamic characteristics of adsorption and micelle formation. One of such characteristics is the standard free energy of adsorption AG [83, 160, 178-191]. To derive the expression for AG , one can use the relations for the chemical potential in the surface layer and in the solution bulk. The chemical potentials p] depend on the composition of the surface layer and its surface tension y and are given by the relation (2.2), the potentials... 

According to various experimental information the hydrocarbon core of the "aqueous micelle has a liquid-like structure (3,4). This has been confirmed, in particular, by spectroscopic probing techniques (5,6). Hence the micelle in aqueous surfactant solutions presents itself to the surfactant monomer as an equivalent with respect to the (macroscopical) oil/water interface. It might be not unreasonable, therefore, to consider this type of micelle formation an "auto-solubilization" to stress the close resemblance between adsorption and homoassociation processes. The hydrocarbon core of a micelle in aqueous surfactant solutions is characterized by its excellent solvent power for crystalline non-polar compounds (7). This latter feature appears remarkable and could serve as a more fundamental distinction between "normal" and inverted micelles than the generally cited apparently more obvious differences. The free energy of micellization is customarily (8) referred to the standard free energy of a monomer in a micelle, i.e. AG° represents the free energy of transfer of a monomer from the aqueous solution to a micelle of size n. 

The left hand side of this equation is the standard free energy of forming a micelle of size n, AG° is made up of two contributions corresponding to the above discussed main factors which control formation and size of micelles in aqueous surfactant solutions. 

Thus, one can write the standard free energy of a micelle formation, AG ce, as follows ... 

Molecules containing both hydrophobic and hydrophilic parts, amphiphile molecules, under the influence of the hydrophobic interactions in aqueous media form aggregates, micelles, when the concentration is greater than the critical micelle concentration (CMC). In this aggregation process, the hydrocarbon chains are located inside the micelle core such that this behaves as liquid-like alkane, while the hydrophilic groups maintain contact with the continuous solvent phase (water) at the micelle-water interface. In order to be able to describe the standard free energy of formation of micelles, many theories have been proposed by various investigators in the current literature. 

Because of the mutual orientation of membrane-making compounds during bilayer membrane formation, decrease in the bifacial energy takes place. This means that the micelle is more stable than separate constituent molecules. The corresponding entropy change AS is given by AS = d AFi)/dT, where F, is the standard free energy, and T is the absolute temperature. 

The micelle sketched in Fig. 5.10 contains an asphaltene core with asphaltene molecules 2 resin molecules are adsorbed onto the surface of the core. In addition to resins that are part of the solvation shell surrounding the core, asphalt-free oil species are also present in the shell. The formation of the solvation shell around the asphaltene core lowers the Gibbs free energy. The standard Gibbs free energy of micelli-zation, AG , represents the standaird Gibbs free energy difference between (1) asphaltene molecules in the core, resin molecules in the shell, and (2) those and ri2 molecules in an infinite-dilution petroleum mixture ... 

Now that the mass-action model has been supported by a number of observations, we move to the thermodynamics of micelle formation based on this model. As would be predicted from the above discussion, micelle formation can be well expressed by a single association constant, even though the process strictly involves multiple association equilibria. The error is less than 5%, for example, for micelles having an aggregation number more than 50. For nonionic surfactants, the standard free energy change AG° per mole of surfactant molecules follows directly from the equilibrium constant and is given from (4.21) and [S] = Q by... 

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