Micelles free energy change

ENERGETICS. The standard free energy change for micelle formation from 1.0 mole surfactant is given by the relationship,... 

The simplest way in which a process occurs by itself is when it is under thermodynamic control. The folding of a protein, or the self-assembly of micelles at the critical micelle concentration (cmc) are examples of spontaneous processes the latter are characterized by a negative free-energy change, as the self-orgaiuzed product has a lower energy than the single components. ... 

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. 

Although there are some aspects of micellization that we have not taken into account in this analysis —the fact that n actually has a distribution of values rather than a single value, for example —the above discussion shows that CMC values expressed as mole fractions provide an experimentally accessible way to determine the free energy change accompanying the aggregation of surfactant molecules in water. For computational purposes, remember Equation (3.24), which states that x2 n2/n, for dilute solutions. This means that CMC values expressed in molarity units, [CMC], can be converted to mole fractions by dividing [CMC] by the molar concentration of the solvent, [solvent] x2 [CMC]/[solvent] for water, [solvent] = 55.5 mole liter... 

Fig. 1.2. Dependence of free-energy changes (AG° mic) of micellization of surfactants in high, intermediate, and low-polar solvents. Normal micelle (M) to reverse micelle (RM) transition as function of polarity (e) of the medium. Surfactants in a medium of optimum dielectric constants 38 to 41 do not aggregate but remain in the monomeric state (n)...

The standard state of free energy change of micellization, AGT, is the standard free energy change per one mole of surfactant. 

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. 

A standard free energy change upon micellization for ionic gemini surfactants with two hydrophilic groups and monovalent counterions can be calculated (Zana, 1996) by taking into account the degree of binding (1 a) of the counterions to the micelle,... 

Equations relating CMC to the free energy change, AG, of the aggregation of the individual surfactant molecules that form micelles can be derived on the basis of the theoretical considerations of Shinoda (1963). When no salt is added to the surfactant solution, Ci = CMC, and Eq. (2.93) becomes ... 

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. 

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),... 

The excess free energy change of micellization,, calculated by the equation (15)... 

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