The Enthalpy of Micelle Formation

The enthalpy changes involved in a micelle formation process can be obtained experimentally using several different techniques. From the temperature dependence of the CMC, the enthalpy is obtained through a van t Hoff type relation 

Enthalpy changes can also be measured directly in a calorimeter. The temperature dependence of kinetic parameters can be interpreted in terms of AH values. In analyzing the enthalpies it is essential to recognize the chemical processes that actually contribute to the particular AH-value. 

Experimentally the CMC is usually weakly temperature dependent12) (cf. Fig. 2.5) indicating that AHn is close to zero. For the cases141-147) where calorimetric determinations have been performed this conclusion has been confirmed. 

In calorimetric studies of micelle formation it is often difficult to relate the measured enthalpy changes to specified steps in the aggregation process. Instead one perferably determines the partial molar enthalpy hA of the amphiphile as a function of concentration12). The ideal case of the phase separation model predicts that hA is constant up to the CMC where it discontinuously jumps to another constant value. 

The behavior of hA in real micellar systems is more complex as seen in Fig. 2.12. Similar data have been obtained for several other amphiphiles148,149). The deviations in hA from the standard value at infinite dilution appear clearly below the CMC, but at these concentrations one has a compensating change in the partial molar entropy. This effect might be due to a repulsive interaction between the hydrophobically hydrated alkyl chains leading to a breakdown of the water structure with a concomitant increase in entropy. 

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The enthalpy of micelle formation of various mixed sodium dodecylsulfate (NaDDS) and sodium deoxycholate (NaDOC) systems was measured by calorimeter In aqueous systems. The heat of micelle formation, AH, showed a maximum around NaDDS NaDOC molar ratio 1. These data are analyzed In comparison to the aggregation number of mixed micelles and the second virial coefficient, Bg. 

The mixed NaDDS-NaDOC systems gave the enthalpy of micelle formation,AH C, which varies with composition as shown in Figure... 

If the aggregation number, m, is assumed to be independent of temperature, then the enthalpy of micelle formation, aH, can be estimated by using the Clausius-Clapeyron relationship ... 

This study is a continuation of our previous investigations, in which the aggregation phenomena of surfactant molecules (amphiphiles) in aqueous media to form micelles above the critical micelle concentration (c.m.c.) has been described based on different physical methods (11-15). In the current literature, the number of studies where mixed micelles have been investigated is scarcer than for pure micelles (i.e., mono-component). Further, in this study we report various themodynamlc data on the mixed micelle system, e.g., ci H25soi4Na (NaDDS) and sodium deoxycholate (NaDOC), enthalpy of micelle formation (by calorimetry), and aggregation number and second virial coefficient (by membrane osmometry) (1 6). 

The present study reports the variation of enthalpy of micelle formation of mixed NaDDS-NaDOC systems. Our current enthalpy... 

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... 

The enthalpy of micellization of many surfactants in aqueous solution has been determined in the past, using mostly cell type and flow microcalorimeters [6-8]. These determinations were based on measurements of the excess heat associated with dilution of a surfactant from a concentration above the cmc to a concentration below the cmc, which results in demicellization of the preexisting micelles. One diffleulty with these determinations relates to the dependence of the heat evolution (AQ) on the initial and final concentrations, probably due to secondary self-aggregations of the surfactants at high concentrations and/or pre-micellar dimer formation at low surfactant concentrations [6,9], These difficulties are at least partially responsible for the lack of consistent data on the thermodynamics of micelle formation [6]. 

The value of the partition coefficient increases with decreasing surfactant concentration. Furthermore, similar to the heat of micelle formation, transfer of OG molecules into the bilayers is endothermic at room temperature but exothermic at high temperature (Table 9). The enthalpy at any given temperature depends on the composition and size of the vesicle bilayers (Table 9). Thus, at room temperature, the introduction of OG into POPC bilayers appears to become more endothermic as the size of the vesicles increases as well as when either POPG or cholesterol is included in the POPC vesicles. However, even when the bilayers contain relatively high cholesterol concentrations, is only a factor of up... 

The enthalpies of micellization, AH, , can be calculated indirectly by use of the van t Hoff treatment or directly by isothermal titration calorimetry (ITC). Except for few cases (e.g., some nonionic surfactants), the results of these methods do not agree [38]. The main reason is that there is no provision in van t Hoff equation for factors that are important for micelle formation of ionic surfactants, in particular, the dependence of micellar geometry, surface-charge density, and extent of hydration on temperature T) [38]. On the other hand, the effects of (T) on the aforementioned micellar parameters are included in the direct (i.e., calorimetric) determination of AH, . From Gibbs free energy relationship, any uncertainty introduced in the calculation of Ai7, j will be carried over to so that A5 rK > AS, Where available, therefore, we compare the thermodynamic quantities of micellization, based on experimental data of the same technique. 

Considering again the case of a nonionic surfactant, the standard molar enthalpy of micelle formation is then... 

The enthalpy change associated with formation of a thermodynamically ideal solution is equal to zero. Therefore any heat change measured in a mixing calorimetry experiment is a direct indicator of the interactions in the system (Prigogine and Defay, 1954). For a simple biopolymer solution, calorimetric measurements can be conveniently made using titra-tion/flow calorimeter equipment. For example, from isothermal titration calorimetry of solutions of bovine P-casein, Portnaya et al. (2006) have determined the association behaviour, the critical micelle concentration (CMC), and the enthalpy of (de)micellization. 

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 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. 

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. 

The real breakthrough in terms of kinetic theory was published in 1973 by Aniansson and Wall [80, 81], who provided much more applicable kinetic equations for stepwise micelle formation using a polydisperse model. In a substantial paper two years later they were able to predict the first-order rate constants for the dis-sociation/association of surfactant ions to and from micelles (and hence residence times/lifetimes of surfactant monomers within micelles) [82]. They found values for the association and dissociation of surfactants into/from micelles (Ar and k , respectively) for sodium dodecyl sulfate (SDS) as 1 x 10 s and 1.2 x 10 mok s". Their kinetic model still remains essentially unchanged as a basis for the kinetics of micellar formation and breakdown. Modifications made to existing theory also allowed them to offer a significant thermodynamic explanation for the low enthalpy change upon micellization. 

Typical behavior is shown in Fig. 9, where the enthalpy of formation of AgCl nanoparticles in AOT reversed micelles is reported as a function of the molar ratio R at various salt concentrations. As can be seen, the enthalpies become more exothermic as R increases. The small AH values at lower R, corresponding to... 

S.2.2.3 Thermodynamic Parameters The CMC value dependence on temperature is used for the determination of thermodynamic parameters applying models [60]. The mass action model, apparent and partial model, and phase separation model [14,59,60] are apphed to estimate the thermodynamic parameters Gibbs energy, enthalpy, and entropy of micelle formation. The enthalpy and entropy change for the miceUization can be determined using the Gibbs-Helmholtz equation [55]. 

As mentioned above, the process of micellization is one of the most important characteristics of surfactant solution and hence it is essential to understand its mechanism (the driving force for micelle formation). This requires analysis of the dynamics of the process (i.e. the kinetic aspects) as well as the equilibrium aspects whereby the laws of thermodynamics may be applied to obtain the free energy, enthalpy and entropy of micellization. Below a brief description of both aspects will be given and this will be followed by a picture of the driving force for micelle formation. 

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