Micelle formation entropy

Althogh, AG evaluated by Equation 9 takes into account the loss in translational entropy of counter ions upon micellar assoclatlon(3,4), it is doutfull that the term (m/n) RT ln[X], can Include all the effects of interionic interaction in micelle formation. 

This transition may j-.e. reducing the specific surface energy, f. The reduction of f to sufficiently small values was accounted for by Ruckenstein (15) in terms of the so called dilution effect". Accumulation of surfactant and cosurfactant at the interface not only causes significant reduction in the interfacial tension, but also results in reduction of the chemical potential of surfactant and cosurfactant in bulk solution. The latter reduction may exceed the positive free energy caused by the total interfacial tension and hence the overall Ag of the system may become negative. Further analysis by Ruckenstein and Krishnan (16) have showed that micelle formation encountered with water soluble surfactants reduces the dilution effect as a result of the association of the the surfactants molecules. However, if a cosurfactant is added, it can reduce the interfacial tension by further adsorption and introduces a dilution effect. The treatment of Ruckenstein and Krishnan (16) also highlighted the role of interfacial tension in the formation of microemulsions. When the contribution of surfactant and cosurfactant adsorption is taken into account, the entropy of the drops becomes negligible and the interfacial tension does not need to attain ultralow values before stable microemulsions form. 

FORMATION. Aqueous solutions of highly surface-active substances spontaneously tend to reduce interfacial energy of solute-solvent interactions by forming micelles. The critical micelle concentration (or, c.m.c.) is the threshold surfactant concentration, above which micelle formation (also known as micellization) is highly favorable. For sodium dodecyl sulfate, the c.m.c. is 5.6 mM at 0.01 M NaCl or about 3.1 mM at 0.03 M NaCl. The lower c.m.c. observed at higher salt concentration results from a reduction in repulsive forces among the ionic head groups on the surface of micelles made up of ionic surfactants. As would be expected for any entropy-driven process, micelle formation is less favorable as the temperature is lowered. 

Micelle formation is a nice example of self-organization under thermodynamic control. Following the addition of some liquid soap in water at a concentration higher than the cmc, spherical micellar aggregates spontaneously form. This process takes place with a negative free-energy change - actually the process is attended by an increase of entropy. 

We conclude this section with a brief discussion of the relatively large, positive values of AS°,C, which we have seen are primarily responsible for the spontaneous formation of micelles. At first glance it may be surprising that AS for Reaction (A) is positive after all, the number of independent kinetic units decreases in this representation of the micellization process. Since such a decrease results in a negative AS value, it is apparent that Reaction (A) is incomplete as a description of micelle formation. What is not shown in Reaction (A) is the aqueous medium and what happens to the water as micelles form. The water must experience an increase in entropy to account for the observed positive values for AS °,c. 

In spite of the fact that the concentration of surfactants in the outer solution is assumed to be smaller than the critical micelle concentration, inside the network, micelles are supposed to be formed. The reason for this assumption is, first of all, intensive adsorption of surfactants on the network as a result of the ion exchange reaction. Moreover, in Refs. [38, 39], it was shown that critical concentration of micelles formation c c" within a polyelectrolyte network is much less than that in the solution of surfactant c° . Indeed, when a micelle is formed in solution immobilization of counter ions of surfactant molecules takes place, because these counter ions tend to neutralize the charge of micelles (see Fig. 13), whereas there is no immobilization of counter ions when the micelles are formed in the network the charge of micelles is neutralized by initially immobilized network charges which do not contribute to the translational entropy (Fig. 13). 

Measurement of AH0 and AS0 showed that the former is small and positive and the second is large and positive. This implies that micelle formation is entropy driven and is described in terms of the hydrophobic effect (14). Then hydrophobic chains of the surfactant monomers tend to reduce their contact with water, whereby the latter form icebergs by hydrogen bonding. This results in reduction of the entropy of the whole system. Flowever, when the monomers associate to from micelles, these icebergs tend to melt (hydrogen bonds are broken), and this results in an increase in the entropy of the whole system. 

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 first reason lies in the fact that the interaction between solvent molecules (usually water) is stronger than the interaction between the solvent and the solute. This effect alone would lead to a precipitation of the solute. In the case of amphiphiles which form micelles, however, the head groups are strongly hydrated and repulse each other. The hydration forces and steric forces which are made responsible for this repulsion effect prevent crystallization above the Krafft point and also above the cmc. Where the formation of 3D crystals is impeded, the smallest possible droplet is formed, removing the alkyl chains from the solvent. The interactions between solvent molecules are therefore disturbed to a minimal extent, allowing the head groups to be solvated with a minimal entropy loss. It is irrelevant whether the solvent contains clusters or not. Micelle formation only occurs as a result of a solvation of head groups and non-solvation of a solvophobic core. ... 

The free energy change of a system is dependent on changes in both the entropy and enthalpy that is, AG = AH-T AS. For a micellar system at normal temperatures the entropy term is by far the most important in determining the free energy changes (T AS constitutes approximately 90-95% of the AG value). Micelle formation entails the transfer of a hydrocarbon chain from an aqueous to a nonaqueous environment (the interior of the micelle). To understand the changes in enthalpy and entropy that accompany this process, we must first consider the structure of water itself. 

However, as mentioned above, experimental results have shown clearly that micelle formation involves only a small enthalpy change, and is often endothermic. The negative free energy of micellisation is the result of a large positive entropy, and this led to the conclusion that micelle formation must be predominantly an entropy-driven process. 

A factor which has not been considered is the entropy change associated with the compression of a monolayer. In a manner analogous to micelle formation in solution, we would expect both Tift off and the association of oriented chains to involve a negative entropy change the removal of the alkyl chain from contact with water should contribute... 

In contrast to aqueous systems, micelle formation in non-polar media is driven by the benefit in energy rather than by an increase in entropy. The replacement of polar group - hydrocarbon interaction (as in the case of dissolution) with the interaction between polar groups upon their association into micellar core is thermodynamically beneficial. The benefit in energy upon association of polar groups is so large, that even at low concentrations true surfactant solutions contain small pre-micellar associates rather than individual surfactant molecules. 

Hydrophobic interactions which are enforced (entropy driven) by the nature of water are the principle forces behind protein folding (6). They facilitate the establishment of other stabilizing interactions (7,10). Hydrophobic interactions, being of fundamental importance to protein structure, are very relevant to the functional properties of many food proteins, especially caseins. These forces affect solubility, gelation, coagulation, micelle formation, film formation, surfactant properties and flavor binding (7,10). 

Micelle formation arises from the hydro-phobic effect [4,9-13]. This is the term used to describe the interaction between nonpolar solutes and water. It is well known that nonpolar solutes are almost insoluble in water, with the limited degree of solubility decreasing rapidly with increasing solute size. A thermodynamic analysis of the process shows that the introduction of a hydrocarbon into water at ambient temperature is always associated with a decrease of entropy. 

The notion of hydrophobic interaction was well developed by Tanford [9]. When a nonpolar solute is dissolved in water, some hydrogen bonds are disrupted. The solute tends to locally distort the water structure and to restrict the motion of water molecules. Thus, a large entropy increase in the water molecules is associated with the removal of the nonpolar solute from aqueous solution [9]. This entropy increase is responsible for the surface activity and micelle formation of surfactant molecules. 

The coalescence of hydrocarbon chains allows the ordered hydration layers to be expelled into the bulk phase, resulting in a considerable net gain in entropy. Indeed, micelle formation is primarily an entropy-driven process the enthalpy of hydrocarbon association is comparatively weak and can even be endothermic (opposing association). As an example, dimethyl-n-dodecylamine oxide (illustrated in Fig. 2) undergoes or free energy change of micellization of AG = —6.2 kcal/mol (a fairly typical value), of which the enthalpic contribution AH = 4-1.1 kcal/mol and the entropic contribution — T A S = -7.9 kcal/mol. 

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