Free energy of micellization

From Equation (15.3), the standard free energy for micelle formation per mole of micelles is given by 

As shown above, at (or near) the cmc, S 5n, so that the first term on the right side of Equation (15.9) can be neglected, and an approximate expression for the free energy of micellization per mole of surfactant will be 

The situation is complicated somewhat in the case of ionized surfactants because the presence of the counterion and its degree of association with the monomer and micelle must be taken into consideration. For an ionic surfactant the mass-action equation is 

When the ionic micelle is in a solution of high electrolyte content, the situation described by Equation (15.14) reverts to the simple nonionic case given by Equation (15.11). 

In general, but not always, micelle formation is found to be an exothermic process, favored by a decrease in temperature. The enthalpy of micellization, given by 

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Free energy of micellization, 24 130 Free enzyme-catalyzed reactions ionic liquids in, 26 897-898 Free fatty acids, 70 802-804, 825-826 removal of, 70 807 as soap bar additives, 22 742-743 Free-flow agents, in sodium chloride (salt), 22 808... 

For pure nonionic EO adducts, increase in the number of oxyethylene groups in the molecule results in a decrease in the tendency to form micelles and an increase in the surface tension of the solution at the critical micelle concentration (1 ) (l. ) This change in surface activity is due to the greater surface area of the molecules in the adsorption layer and at the micellar surface as a result of the presence there of the highly hydrated polyoxyethylene chain. The reduction in the tendency to form micelles is due to the increase in the free energy of micelle formation as a result of partial dehydration of the polyoxyethylene chain during incorporation into the micelle ( 1 6) (17). 

Standard Thermodynamic Parameters of Micellization. Standard free energies of micellization were calculated by the relationship ... 

From the standard free energy of micellization of the N-alkyl-glycines, the per methylene group at 25 C is -2.80 kJ. This... 

Effect of Structure on Activity at the Critical Micelle Concentration and on the Free Energy of Micelle Formation... 

In this work, the critical micelle activity, cma, which is the activity of the surfactant at the cmc, is introduced and used Instead of the cmc to Investigate the free energy of micelle formation. It is found that upon the addition of an extra methylene group into the hydrocarbon chain, an approximately 3-fold reduction in cma is observed, irrespective of the hydrophilic head group. The effect of added electrolyte on cmc is also examined by the use of cma. 

Here fM and fL are the activity coefficients of micelle and monomer. The free energy of micelle formation is, therefore,... 

On the other hand, micelle formation has sometimes been considered to be a phase separation of the surfactant-rich phase from the dilute aqueous solution of surfactant. The micellar phase and the monomer in solution are regarded to be in phase equilibrium and cmc can be considered to be the solubility of the surfactant. When the activity coefficient of the monomer is assumed to be unity, the free energy of micelle formation, Ag, is calculated by an equation... 

The free energy of micelle formation of a methylene group, (CH2), is... 

In contrast to Equations 7 and 8, based on the binding of counter ion to micelle, an equation including a form for the electrostatic part of free energy of micelle formation, Fgi, evaluated from double... 

Application of Activity at cmc. The above consideration suggested us to propose a new treatment for ionic micelle formation. According to thermodynamics, the micelle-monomer equilibrium is achieved when the chemical potential of surfactant in the micelle is equal to that in the bulk solution. The free energy of micelle formation can be represented by the use of the critical micelle activity, cma, which is the activity of surfactant at the cmc, as... 

This may be caused by two factors. First of all, in the case of pyridinium salts there may be a contribution from the hydrophobic interactions between neighbouring bound headgroups (an effect which would not contribute to the free energy of micelle formation). Secondly, a steric hindrance effect may prevent the positive chrge on the trlmethylammonium head group from approaching close to the polylon charge. 

RT ln x is the free energy of micellization and is independent of the interaction with the surface it is determined by the hydrophobic interactions between hydrocarbon chains and the repulsion between end groups. 

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. 

Values ofKm determine the extent of aggregation, in thaKa increases, so does the amount of aggregation. The standard free energy of micellization at the critical micellization concentration (CMC) is... 

Model Calculations of the Free Energy of Micelle Formation. 

The standard free energy of micellization, AG°, is then given by... 

The free energy of micelle formation has been found to be more dependent on entropy than on enthalpy factors (Kavanau, 1965 Elworthy, 1968). Micelle formation has been treated theoretically either... 

Gorg(A, P) results from the van der Waals forces and conformational energy of the hydrocarbon chains and the van der Waals and electrostatic interactions of the head-groups within the organic subphase. It is related, but different, to the free energy of micellization for ionic surfactants defined by Evans et al.[79]... 

The amphiphilicity of a compound is defined as the difference between the free energy of transfer of a compound from the aqueous phase to the air-water interface and the free energy of micelle formation and is quantified by means of surface tension measurements. 

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