Thermodynamics of mixed micellization

Calorimetric measurements can be used to obtain heats of mixing between different surfactant components in nonideal mixed micelles and assess the effects of surfactant structure on the thermodynamics of mixed micellization. Calorimetry can also be successfully applied in measuring the erne s of nonideal mixed surfactant systems. The results of such measurements show that alkyl ethoxylate sulfate surfactants exhibit smaller deviations from ideality and interact significantly less strongly with alkyl ethoxylate nonionics than alkyl sulfates. 

HOLLAND Thermodynamics of Mixed Micellization Legend of Symbols... 

Except for some anionic/cationic surfactant mixtures which form ion pairs, in a typical surfactant solution, the concentration of the surfactant components as monomeric species is so dilute that no significant interactions between surfactant monomers occur. Therefore, the monomer—mi celle equilibria is dictated by the tendency of the surfactant components to form micelles and the interaction between surfactants in the micelle. Prediction of monomer—micelle equilibria reduces to modeling of the thermodynamics of mixed micelle formation. 

A brief accounting of the thermodynamics of mixed micelle formation is given here primarily to clarify certain important issues which appear to have been previously overlooked. The necessity for measuring the monomer and micellar composition will be demonstrated. 

Critical Micelle Concentration. In order to demonstrate the analogy between our treatment of mixed adsorption and earlier treatments of mixed micellization, we will briefly review the thermodynamics of mixed micelles. The thermodynamics of formation of ideal mixed micelles by two surfactants has been treated by Lange and Beck (9 ) and Cling (10). Rubingh ( ) extended the treatment to account for interactions between the surfactants, essentially by writing the cmc in the mixed surfactant solution as. 

Model Development. There is vast opportunity for development of fundamentally based models to describe the thermodynamics of mixed micelle formation. As discussed in Chapter 1, regular solution theory has yielded useful relations to describe monomer—mi cel 1e equilibrium. 

A.P. Graeiaa, J. Lachaise and R.S. Schechter, The thermodynamics of mixed micelle formation, in Mixed Surfactant Systems, Eds. K. Ogino and M. Abe Surfactant science series, V. 46, Marcel Dekker, NY 1993, pp. 63-97. 

The thermodynamics of mixed micelle formation has been recently reported (56). 

A study of the solubilization of decanol in solutions of sodium octanoate showed that at low surfactant concentrations the solubilization of the additive increased rapidly after the cmc was exceeded, and continued to do so for some time as the concentration of sodium chloride was increased. At higher surfactant concentrations, however, it was found that there was an initial increase in decanol incorporation, which reached a maximum and then began to decrease as the salt level continued to increase. When the octanoate concentration well exceeded the cmc, the addition of salt resulted in an immediate decrease in the ability of the system to incorporate the additive. Such complex interactions have been attributed to alterations in the thermodynamics of mixed micelle formation for the decanol and carboxylate salt. Similar results may be seen in systems where the increased electrolyte content produces a change in the character of the micellar system a sphere-to-rod micellar transformation or the development of a mesophase, for example. 

The finding that the assumptions of the regular solution approximation do not hold for the mixed micellar systems investigated here suggests a re-examination of how the thermodynamics of mixing enter the nonideal mixed micelle model. 

The structure and thermodynamics of formation of mixed micelles is of great theoretical interest. Micelles are also present and often integrally involved in practical processes. For example, in a small pore volume surfactant flooding process (sometimes called micellar flooding), the solution injected into an oil field generally contains 5-12 weight X surfactant (i) and the surfactant is predominately in micellar form in the reservoir water. In detergency, solubilization can be... 

For a binary system of surfactants A and B, the mixed micelle formation can be modeled by assuming that the thermodynamics of mixing in the micelle obeys ideal solution theory. When monomer and micelles are in equilibrium in the system, this results in ... 

Most of the studies on thermodynamics of mixed micellar systems are based on the variation of the critical micellar concentration (CMC) with the relative concentration of both components of the mixed micelles (1-4). Through this approach It Is possible to obtain the free energies of formation of mixed micelles. However, at best, the sign and magnitude of the enthalpies and entropies can be obtained from the temperature dependences of the CMC. An Investigation of the thermodynamic properties of transfer of one surfactant from water to a solution of another surfactant offers a promising alternative approach ( ), and, recently, mathematical models have been developed to Interpret such properties (6-9). 

In such studies. It Is preferable to use two surfactants with widely different CMC s so as to explore the possibility of coexistence of two types of mixed micelles, 2 In 3 and 3 In 2. In this respect, the system cetyltrlmethylammonlum bromide (CTAB)-2-butoxyetha-nol (BE)-water Is being Investigated (14). Unfortunately, with CTAB, the CMC Is too low to allow thermodynamic measurements below the CMC. Still, this study shows unambiguously that BE dissolves In the CTAB micelles and also that CTAB can distribute Itself In the BE microaggregates. 

The chemical equilibrium model of Roux et al (6) is a powerful tool for the study of the thermodynamics of mixed micellar solutions. It can estimate the distribution constant of the surfactant 3 between water and micelles of the surfactant 2 and the thermodynamic properties of the surfactant 3 in the mixed micelles. For this it is necessary to obtain reliable data over a large concentration range of solute 2. 

The thermodynamics of mixing upon formation of the bilayered surface aggregates (admicelles) was studied as well as that associated with mixed micelle formation for the system. Ideal solution theory was obeyed upon formation of mixed micelles, but positive deviation from ideal solution theory was found at all mixture... 

Others have studied the volumetric changes occurring in mixed micelles of anionic-anionic and nonionic-nonionic surfactants as a determinant of intermolecular interactions and a measure of the thermodynamic ideality of mixing. In particular, Funasaki et al. (1986) have studied the volumetric behavior of mixed micelles of ionic and nonionic surfactants and analyzed their results in terms of regular solution theory. They found that in water, anionic surfactants such as SDS bind to PEG,... 

In the molecular-thermodynamic theory of mixed micellization, the size and shape of the mixed micelles can also be predicted by calculating the size and composition distribution. This distribution can be expressed as a function of two fundamental parameters that control the size of the mixed micelles. The Lrst parameter, is deLned as (Puwada and Blankschtein, 1992a,b) to be... 

An amine oxide surfactant solution can be modeled as a binary mixture of cationic and nonionic surfactants, the composition of which is varied by adjusting the pH. The cationic and nonionic moieties form thermodynamically nonideal mixed micelles, and a model has been developed which quantitatively describes the variation of monomer and micelle compositions and concentrations with pH and... 

Another approach has been intensively developed recently by Puvvada and Blankschtein, who considered also the formation of mixed micelles in surfactant mixtures [20-22]. For example, the free energy of formation of binary mixed surfactant micelle, containing Ha molecules of the surfactant A, ns molecules of the surfactant B and, n water moleeules in thermodynamic equilibrium was expressed as... 

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. 

Advances in the theory of mixed-micelle formation have made it possible to calculate the composition of mixed micelles formed by two or more surfactants. A thermodynamic treatment of micellar solutions of mixed surfactants is usually based on the pseudophase separation theory [61,71-74]. The pseudophase models developed for binary surfactant solutions assume ideal mixing of the surfactants in the micelle. 

Calorimetric measurements represent a promising way of gaining thermodynamic information about mixed micellization. 

The adsorption of mixed surfactants at the air—water interface (monolayer formation) is mechanistically very similar to mixed micelle formation. The mixed monolayer is oriented so that the surfactant hydrophilic groups are adjacent to each other. The hydrophobic groups are removed from the aqueous environment and are in contact with other hydrophobic groups or air. Therefore, the forces tending to cause monolayers to form are similar to those causing micelles to form and the thermodynamics and interactions between surfactants are similar in the two aggregation processes. 

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