Thermodynamic Parameters of Micellization

The value of AGmic( CH2 -) obtained in this fashion falls in the range —(2.8-3.3) kJ[—(708-777)cal]/mol for all types of surfactants (nonionics, zwitterionics, uni- and divalent ionics), irrespective of the presence or amount of added electrolyte. 

For ionic surfactants AG(—W), the electrical energy Eel involved in transferring the ionic hydrophilic group from an aqueous environment to the micelle is given, when the aggregation number is not too small, by (Shinoda, 1977) 

Equation 3.15 predicts the effect of electrolyte on the CMC of ionic surfactants, indicating that the log of the CMC will decrease linearly with log C which is in accordance with experimental findings (equation 3.3). It also indicates that the CMC of ionic surfactants will decrease with increase in the extent of binding of the counterion to the micelle since that decreases the charge density on the micellar surface. Organic additives that decrease the dielectric constant of the solvent will increase the CMC of the surfactant, both of which are consistent with the experimental results discussed previously. The effect of temperature on the CMC of ionic surfactants is difficult to predict from equation 3.15. An increase in the temperature should cause a direct decrease in the CMC, but since an increase in temperature causes a decrease in the dielectric constant er of the solvent and may also affect a, the overall effect of an increase in temperature is not readily determinable from the equation alone. 

As is evident from the previous discussion, a clear understanding of the process of micellization is necessary for rational explanation of the effects of structural and environmental factors on the value of the CMC and for predicting the effects on it of new structural and environmental variations. The determination of thermodynamic parameters of micellization AG c, A//mio and A,S mic has played an important role in developing such an understanding. 

A standard free energy of micellization AG C may be calculated by choosing (Molyneux, 1965) for the standard initial state of the nonmicellar surfactant species a hypothetical state at unit mole fraction x, but with the individual ions or molecules behaving as at infinite dilution, and for the standard final state, the micelle itself. For nonionic surfactants, the standard free energy of micellization is given by 

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They have studied also the N dependence of the thermodynamic parameters of micellization, calculated from the cmc values and their temperature dependence, as shown in Figure 1, where AGm is... 

Table II. Thermodynamic Parameters of Micellization for Nonionic of n-C j2H250(EO)jj H at 25°C, data from Rosen et at.(3 ) ...

Table IX shows the thermodynamic parameters of micellization, calculated from the cmcs and their temperature dependence, for two homologues of each of these types of nonionics. It can be seen that AHm and ASm progressively decrease in the order usual-type > S > L-A > G type for both homologous series. This suggests that the high polarity of the amido linkage causes either less dehydration or exothermic association of the hydrophilic part on micelle formation.

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

Table III. Standard Thermodynamic Parameters of Micellization for R-N+(CH2C6Hs)(CH3)CH2C00-...

Kinetic investigations of the effects of urea and similar denaturing agents on rates and thermodynamic parameters of micelle catalyzed reactions have been suggested to be more sensitive probes for the nature and extent of hydrophobic interactions than CMC determinations. Thus, Monger and Portnoy (1968) have taken advantage of the base catalyzed hydrolysis of micellar -nitrophenyl dodecanoate. The rate constant for the hydrolysis of -nitrophenyl dodecanoate decreases rapidly with increasing initial concentration of the ester (10 to 10 m), and the second-order rate constant for the base-catalyzed hydrolysis of this ester... 

Table 3 Thermodynamic parameters of micellization in aqueous solution for some representative surfactants under various conditions.

Attempt of correlating the molecular structures and experimental data, for example, cmc, and the thermodynamic parameters of micellization (enthalpy, entropy, and free energy), rests on the assumption that they have been calculated by a consistent procedure this point needs further consideration. At the outset, it should be noticed that there are systematic differences between the results, for example, the cmc, obtained by using distinct experimental techniques. The reason is that the function plotted (absorbance of micelle-solubilized dye, conductivity, surface tension, light scattering intensity, etc.) versus [surfactant] measures different averages of the various species in solution. Examples are surface tension that primarily depends on monomer concentration and solubilization of (water-insoluble) dye that depends mainly on the total amount of micelles present. The consequence is that cmc measured from surface tension will always be lower than cmc measured by dye solubilization [28]. In fact, values of the cmc of the same surfactant, determined by different groups, by the same technique show differences. For example, fifty-four erne s determined by the same technique for Cj NMe Br (measurements at 25°C) differ by 22% [29]. 

Pestman et al. [64] synthesized eight homologous series V-acetyl- and N-propionyl-A-alkylglucosyl/lactosylamines XXIII R a/XXVn R a,b and N-acetyl- and A-propionyl-A-alkyl-1-amino-1-deoxyglucitols/lactitols XXIV/ XXVIII R a,b (Fig. 8) with high yields of the final acyl derivatives. They determined the CMC values and the thermodynamic parameters of micel-lization by titration microcalorimetry. The results can be summarized as follows ... 

TABLE 20.3. Change of Thermodynamic Parameters of Micellization of Alkyl Sulfoxide with... 

Table 6.6 Area/Molecule, cmc Values, and Thermodynamic Parameters of Micellization for Monflor 51...

In contrast to this, there is little information available (11) on the thermodynamics of adsorption of alkyl betaines and no data on the thermodynamic parameters of adsorption or micellization for sulfobetaines. 

Lin and Yang (1987) also calculated the thermodynamic parameters of diazepam for micellar solubilization in Pluronic surfactant solutions at different temperatures (Table 13.4). For all systems, AG was negative, indicating micellar solubilization was spontaneous. The sign of entropy has been associated with the location of solubilized molecules within the micelles. Positive values have been observed for molecules embedded in the micelle center and negative values for adsorption of the molecules on the micelle surface. The results in this paper indicate that in the F-108 and F-88 Pluronics, diazepam molecules can penetrate into the micelle interior, whereas for F-68 and lower concentrations of F-88, diazepam is adsorbed on the micelle surface without penetration into the micellar core. 

The variations of the cmc with temperature have been used to estimate the thermodynamic parameters for micellization, and more rigorous direct measurements from heats of solution have also been made [1,2,7-9,34], Tanford [18] estimates a contribution of ca. 700 cal/mole per methylene group to the free energy of micellization, which is consistent with hydrophobic interactions of hydrocarbons in water. 

The study of thermodynamic parameters of mixing showed that the oligomer—siufactant system is thermodynamically stable even when the surfactant concentration is considerably above CCMF. This is a surprise and seems to be related to the fact that the surfactant molecules aggregate into the micelles in such a way that those parts of the surfactant molecules are directed at the oligomeric solvent that have maximum affinity to it. 

Determinations of the thermodynamic parameters for micellization in the vicinity of room temperature support the above interpretation. The major contributor to the free energy of micellization, AG per unimer, is from the entropy of micellization, AS, Table Note that... 

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. 

Table 4 Typical Values of Thermodynamic Parameters of Surfactant Micellization in Water...

Surface activity in 1,4-polyisoprene-polyacetylene, AB, block copolymer solutions was to be expected from the amphiphilic properties of such a diblock system with one moiety so insoluble because of the strong polyacetylene-polyacetylene attractive interactions. The present experiments allow access, for the first time, to some of the thermodynamic parameters of these interactions and give a structural model for the surface excess above and below the critical micelle concentration. This has been identified as about 10" moles/L for the lelated polymer 1,4-polyisoprene-polyacetylene (MW 8000 520) in toluene at 20 C using the drop weight method to determine surface tension. From ca. 10" molar to molar the surface tension drops by about 3.5% to a constant value of ca. 28.4 dyne cm at concentrations above 10 3 molar (ca. 1% w/w). Referring to Figure 3 we see that it is above ca 1% that a broad peak develops in the solution/solvent reflectivity ratio for 0.15 < k / < 0.25. The area per... 

The differences in thermodynamic parameters of solubilization between flu-orinated surfactants and their hydrocarbon counterparts have been reviewed [124,214]. Fisicaro et al. [124] pointed out the large discrepancies between partition coefficient values obtained by different techniques pointed out (compare the P values for alkanols in sodium perfluorooctanoate given in Tables 6.15 and 6.16). The limited reproducibility appeared to be related to the nature of the micellar systems studied The equilibrium between different kinds of mixed micelles can easily be perturbed by the procedure used for the determination of partition coefficients and the equilibrium is slowly restored. 

Oremusova, J., Greksakova, O. Micellization parameters of cationic surfactants consisting of the [l-(ethoxycarbonyl)-pentadecyl]-trimethylammonium ion and various anions. 1. Effect of temperature and type of anion on the critical micelle concentration and thermodynamic functions of micellization. Tenside Surfactants Deterg. 2003, 40(1), 35-39. 

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