Gibbs energy of micellization

Abbreviations A H Huggins coefficient M, molar mass R, radius of gyration RD, core radius p, association number AmcH°, standard enthalpy of micellization, AmlcG°, standard Gibbs energy of micellization A2, second virial coefficient. Ru, hydrodynamic radius. 

The molar Gibbs energy of micelle formation is the Gibbs energy difference between a mole of monomers in micelles and the standard chemical potential in dilute solution ... 

Calculate the standard Gibbs energy of micellization per mole of surfactant. What is the main driving force for micellization Is it of enthalpic or entropic nature ... 

Blandamer Ml, Cullis PM, Soldi LG et al (1995) Thermodynamics of micellar systems comparison of mass action and phase equilibrium models for the calculation of standard Gibbs energies of micelle formation. Adv Colloid Interface Sci 58 171-209. doi I0.I0I6/... 

The transition between molecules and micelles upon increasing am-phiphile concentration becomes sharper for larger association numbers. In the limit of very large association numbers, the amphiphile solution above the CMC can be modelled as a pseudo-phase-separated system of micelles and unimers. The CMC then corresponds to the saturation concentration of surfactant in the unimer state. In equilibrium, the molar chemical potentials of unimer in the aqueous phase and of associated amphiphile in the micellar phase are equal. Erom this, it can be shown that (Q. 4.10) the molar Gibbs energy of micellization is given by Eq. (4.40). 

There are several approaches to derive the Gibbs free energy of micellization. We only discuss one of them which is called the phase separation model. Even this approach only leads to approximate expressions for nonionic surfactants. More detailed discussions of the thermodynamics of micellization can be found in Refs. [3,528,529],... 

For nonionic surfactants we can use this equation to calculate the change in Gibbs free energy of micellization. For ionic surfactants the change of dissociation of charges from the head groups effects the result. 

To quantify the effect of additives in the mixture on the micellization process, the standard Gibbs free energy change of micellization, dmicG , and the standard Gibbs energy of adsorption, dadsC , were calculated by using equations (5) and (6),... 

As the clouding components above CP release their solvated water and separate out from the solution, the CP of an amphiphile can be considered as the limit of its solubility. Hence, the standard Gibbs energy of solubilization (AG ) of the drug micelles can be evaluated from the relation... 

The surface properties, Gibbs energies of an amphiphilic drug IMP in water are evaluated in absence and presence of additive (TX-lOO), and the micellization and clouding behavior of IMP in absence and presence of KCl have studied and the results obtained are as ... 

A lesser degree of the variation of Ep with n when n > 9 (Fig. 4b), where the desorption accompanies the phase transition of the monolayer, is likely to be attributable to the formation of micelles or aggregates of alkanethiolates formed in the vicinity of the electrode surface after the desorption [12, 25, 71]. When the desorbed species is in the form of such aggregates on the electrode surface, the value of the transfer Gibbs energy of the thiolates from the electrode surface to the aggregates would be much smaller than that into the bulk aqueous phase, giving rise to the smaller shift of the Ep with n. 

Below the cmc, the molar Gibbs energy of a surfactant monomer in solution is lower than in a micelle. At increasing monomer concentration in solution, the molar configuration entropy of the monomers decreases and hence the molar... 

Gibbs energy increases until it equals the Gibbs energy of the monomer in a micelle at the cmc. Hence, the equilibrium concentration of the monomer in solution equals the cmc. 

A thermodynamic description of the process of micelle formation will include a description of both electrostatic and hydrophobic contributions to the overall Gibbs energy of the system. Hydrocarbons (e.g., dodecane) and water are not miscible the limited solubihty of hydrophobic species in water can be attributed to the hydrophobic effect. The hydrophobic Gibbs energy (or the transfer Gibbs energy) can be defined as the difference between the standard chemical potential of the hydrocarbon solute in water and a hydrocarbon solvent at infinite dilution [36-40]... 

A number of parameters are introduced in the standard Gibbs free energy of micellization (that is, Eq, (5.64b)) and the total Gibbs free energy expression (that is, Eq. (5.84)). These parameters can be estimated from the chemical structure of the species and other measurements. In the folio ing, numerical values for these peirameters will be discussed. 

Example 5.6 Show that the standard Gibbs free energy of micellization can... 

Solution Since amphiphiles have a polar head, they arc expected to coadsorb with resins onto the micellar-core surface. Therefore, one needs to modify both AG and the Gibbs free energy of the liquid phase L. In the following, we will briefly present the modifications to The standard Gibbs free energy of micellization, including the co-adsorption of the amphiphiles, can be expressed as,... 

Above the CMC we cannot ignore the correlation between the solute a and the micelles. For simplicity, assume that we have only one kind of micelle, say with fixed n = , and suppose that the system is osmotic, i.e., open with respect to the solvent. In such a system, the first-order deviation of the solvation Gibbs energy of a is given by... 

The argument above can be repeated for aggregates of any size or shape. Thus the main reason for the solubilization phenomenon is the loss of the large positive solvation Gibbs energy of the solute a upon penetrating into the micelle. 

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