Free energy of solubilization

The solubilization of diverse solutes in micelles is most often examined in tenns of partitioning equilibria, where an equilibrium constant K defines the ratio of the mole fraction of solute in the micelle (X and the mole fraction of solute in the aqueous pseudophase. This ratio serves to define the free energy of solubilization -RT In K). 

The partition coefficients yield the standard free energy of solubilization... 

The cleaning process proceeds by one of three primary mechanisms solubilization, emulsification, and roll-up [229]. In solubilization the oily phase partitions into surfactant micelles that desorb from the solid surface and diffuse into the bulk. As mentioned above, there is a body of theoretical work on solubilization [146, 147] and numerous experimental studies by a variety of spectroscopic techniques [143-145,230]. Emulsification involves the formation and removal of an emulsion at the oil-water interface the removal step may involve hydrodynamic as well as surface chemical forces. Emulsion formation is covered in Chapter XIV. In roll-up the surfactant reduces the contact angle of the liquid soil or the surface free energy of a solid particle aiding its detachment and subsequent removal by hydrodynamic forces. Adam and Stevenson s beautiful photographs illustrate roll-up of lanoline on wood fibers [231]. In order to achieve roll-up, one requires the surface free energies for soil detachment illustrated in Fig. XIII-14 to obey... 

Other molecular thermodynamic models for protein-reverse micelle complexes have also emerged. Bratko et al. [171] presented a model for phase transfer of proteins in RMs. The shell and core model was combined with the Poisson-Boltzmann approximation for the protein-RM complex and for the protein-free RM. The increase in entropy of counterions released from RMs on solubilization of a protein was the main contribution to the decrease in free energy of com-plexation. Good agreement was found with SANS results of Sheu et al. [151] for cytochrome C solubilization and the effect of electrolytes on it. However, this model assumes that filled and empty RMs are of the same size, independent of salt strength and pH, which is not true according to experimental evidence available since then. 

Why denaturants such as urea and GdmCl cause proteins to denature may be considered empirically. Those denaturants solubilize all the constituent parts of a protein, from its polypeptide backbone to its hydrophobic side chains. To a first approximation, the free energy of transfer of the side chains and polypeptide backbone from water to solutions of denaturant is linearly proportional to the concentration of denaturant.7,8 Because the denatured state is more exposed to solvent than the native state, the denatured state is preferentially stabilized by denaturant. Thus, the free energy of denaturation at any particular concentration of denaturant is given by... 

It is clear from Equations (9.1) to (9.4) that the free energy of formation of a nucleus and the critical radius r, above which the cluster formation grows spontaneously, depend on two main parameters, namely a and (S/S ), both of which are influenced by the presence of surfactants, a is influenced in a direct way by the adsorption of surfactant onto the surface of the nucleus this adsorption lowers y and this in turn reduces r and AG in other words, spontaneous cluster formation will occur at a smaller critical radius. In addition, surfactant adsorption stabilises the nuclei against any flocculation. The presence of micelles in solution also affects the processes ofnucleation and growth, both directly and indirectly. For example, the micelles can act as nuclei on which growth may occur, and may also solubilize the molecules of the material this can affect the relative supersaturation and, in turn, may have an effect on nucleation and growth. 

As noted above, MeC trimerizes and MeLC does not self-associate in CHCI3. Under these conditions, Foster et al. [202] used vapor pressure osmometry to show that solubilized cholesterol (which dimerizes in CHCI3 [203]) heteroassociated with MeC but not with MeLC. The result was a 1 1 mixed dimer complex of cholesterol and MeC with a molar free energy of formation which was 33% that for the trimerization of MeC in the same solvent [202]. The bonding is presumably via the 3-hydroxyl functions in both steroids this interaction may be of potential importance in the binding of cholesterol to bile acids and salts within membranes and mixed micelles. 

In the presence of a polymer, the surfactant chemical potential is lowered with respect to the situation without polymer (Figure 20.6). There are several interactions which can be responsible for surfactant binding or a polymer-induced micellization. We note that in many respects (variation with surfactant alkyl chain length, solubilization, micelle structure and dynamics) there is a close similarity to the micellization of the surfactant alone. The normal hydrophobic interaction between the alkyl chains must therefore still be a dominating contribution to the free energy of association. However, it is modified by mainly one of the following two factors. 

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 free energy of transfer of alkylphenols and alkylphenoxides to cationic micelles has been measured. For the neutral parent compound SAGq = -5.680 kcal mol and for its anion 8AGo =-6.870 kcal moP. Incremental methyl substitution changes this value by —0.300 kcal moP in both cases and it was concluded that the environment of solubilized molecule and anion are very similar. The size of micelles can be quite subtly dependent on counterion however, since sodium p-toluenesulphonate and sodium p-toluate increase the viscosity of cetyltrimethylammonium bromide solutions sharply but sodium benzenesulphonate and disodium phenylphosphate do not. The anthra-quinone sulphonate (9) is absorbed very slowly ki = 0.37s by cationic micelles, the process being accelerated by added KBr. ... 

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