Free energy of micelle formation

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). 

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. 

Model Calculations of the Free Energy of Micelle Formation. 

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... 

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. 

To calculate the standard free energy of micelle formation for non-ionic surfactants, the expression... 

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,... 

The minimum free energy of micelle formation is positive when compared with the corresponding mechanical mixtures, i.e., the block copolymers are more compatible than the corresponding blends. This is a direct consequence of the existence of A-B junction points. (See Section 4.7.1.)... 

Figure 4.10. Relationship between the relative minimum free energy of micelle formation (A dispersed in B) and the weight fraction of A blocks, with the following assumed values (Tb/(Ta = l,flA = = ,and...

Hence, the slope of the logioCe versus n plot is ( )/2.3 kT, and from the data a value of of 1.1 kT was obtained, somewhat higher than the value for the free energy of micelle formation of this type of surfactant, but close to the value for hemimicelle formation on oppositely charged mineral solids (179). 

The data for various ionic and nonionic (Triton-X-100) micelles are given in table 1 as examples. It is conclusively observed that ionic micelles (e.g. n-CgHi7S04Na, rt-CjoHaiSO Na, -CuH23S04Na and -Ci2H25S04Na) are all spherical in H2O as solvent, without any added constraints on the free energy of micelle formation, AG , [25] ... 

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 ... 

The critical micelle concentrations of mixtures of POE nonionic surfactants are of particular interest, since the synthesis of such materials on a commercial basis will always produce a rather broad range of POE chain lengths. Because they contain no electrostatic contribution to the free energy of micelle formation, they can be treated theoretically with a simpler relationship between composition and cmc. In a mixture of nonionic surfactants in which the average POE chain lengths are approximately the same and the hydrocarbon chains different, there was a smooth decrease in the cmc of the mixture as the mole fraction of the more hydrophobic material (lower cmc) was increased, reminiscent of the surface tension-mole fraction curves found for miscible organic materials mixed with water. 

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