Thermodynamics, mixed micelle formation

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. 

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 ... 

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. 

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. 

The evaluation of the Interaction parameters is based upon equations (1 and 2), derived by Rubingh (7) for mixed micelle formation from the thermodynamics of the system ... 

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... 

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. 

The same thermodynamic quantities needed for mixed micelle formation (already discussed) are also needed for mixed admicelle formation. Luckily, the monomer-admicelle equilibrium data can be fairly easily and unambiguously obtained (e.g., see Chapter 15). This should be combined with calorimetric data for a more complete thermodynamic picture of the mixed admicelle. As with micelles, counterion bindings on mixed admicelles also need to be obtained in order to account for electrostatic forces properly. Only one study has measured counterion binding on single-component admicelles (3 .), with none reported for mixed admicelles. 

The two fundamental properties of surfactants are monolayer formation at interfaces and micelle formation in solution for surfactant mixtures, the characteristic phenomena are mixed monolayer formation at interfaces (Chapter 2, Section RIG) and mixed micelle formation in solution (Chapter 3, Section VIII). The molecular interaction parameters for mixed monolayer formation by two different surfactants at an interface can be evaluated using equations 11.1 and 11.2 which are based upon the application of nonideal solution theory to the thermodynamics of the system (Rosen, 1982) ... 

Thus the theory of regular solutions turns out to be a useful tool to describe mixed micelle formation. However, some of the assumptions of this theory are inconsistent with a strict thermodynamic treatment. Scamehorn [43] and later Nishikido [34] presented experimental evidences of its inapplicability. Their arguments can be summarised as follows ... 

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). 

There is some disagreement within the surfactant literature as to the exact definition of solubilization, particularly as the ratio of surfactant to additive decreases, and one approaches the nebulous frontier between swollen micellar systems and the micro- and macroemulsion regions. For present purposes, solubilization will be defined as the preparation of a thermodynamically stable, isotropic solution of a substance (the additive ) normally insoluble or only slightly soluble in a given solvent by the addition of one or more amphiphilic compounds at or above their critical micelle concentration. By the use of such a definition, a broad area can be covered that includes both dilute and concentrated surfactant solutions, aqueous and nonaqueous solvents, all classes of surfactants and additives, and the effects of complex interactions such as mixed micelle formation and hydrotropes. It does not, however, limit the phenomenon to any single mechanism of action. 

The thermodynamic equilibria of amphiphilic molecules in solution involve four fundamental processes (1) dissolution of amphiphiles into solution (2) aggregation of dissolved amphiphiles (3) adsorption of dissolved amphiphiles at an interface and (4) spreading of amphiphiles from their bulk phase directly to the interface (Fig. 1.1). All but the last of these processes are presented and discussed throughout this book from the thermodynamic standpoint (especially from that of Gibbs s phase rule), and the type of thermodynamic treatment that should be adopted for each is clarified. These discussions are conducted from a theoretical point of view centered on dilute aqueous solutions the solutions dealt with are mostly those of the ionic surfactants with which the author s studies have been concerned. The theoretical treatment of ionic surfactants can easily be adapted to nonionic surfactants. The author has also concentrated on recent applications of micelles, such as solubilization into micelles, mixed micelle formation, micellar catalysis, the protochemical mechanisms of the micellar systems, and the interaction between amphiphiles and polymers. Fortunately, almost all of these subjects have been his primary research interests, and therefore this book covers, in many respects, the fundamental treatment of colloidal systems. 

The two-phase (phase separation) model [24,41-43] regards the micelle as a separate phase, albeit a small entity of microscopic dimensions. The cmc is considered to correspond to the maximum solubility of the monomeric surfactant. If the saturation concentration is exceeded, a new phase, the micelle, appears. The micelle is thermodynamically stable and reversible. The phase-separation model assumes that the activity of the surfactant molecule [44-51] and/or the surface tension [50,52] of the surfactant solution remains constant above its cmc. This assumption is not correct, however [29]. Furthermore, the phase-separation model is not consistent with the number of degrees of freedom given by the Gibbs phase rule [29]. In spite of these difficulties, the two-phase model has explained solubilization and mixed-micelle formation reasonably well and is therefore widely used. 

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. 

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 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... 

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). 

The magnitude and sign of the distribution constants and of the thermodynamic functions of the transfered solute to the mixed micelle, when compared with those predicted from the binary systems, indicate that the formation of a mixed micelle between BE and NaDec is a highly favorable event. 

Thermodynamic Study of the Surface Adsorption and Micelle Formation of Mixed Surfactants... 

Scamehorn et. al. (20) also presented a simple, semi—empirical method based on ideal solution theory and the concept of reduced adsorption isotherms to predict the mixed adsorption isotherm and admicellar composition from the pure component isotherms. In this work, we present a more general theory, based only on ideal solution theory, and present detailed mixed system data for a binary mixed surfactant system (two members of a homologous series) and use it to test this model. The thermodynamics of admicelle formation is also compared to that of micelle formation for this same system. 

The mixed admicelle is very analogous to mixed micelles, the thermodynamics of formation of which has been widely studied. If the surfactant mixing in the micelle can be described by ideal solution theory, the Critical Micelle Concentration (CMC) or minimum concentration at which micelles first form can be described by (21) ... 

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. 

In. my opinion, the study o-f monolayer -formation has less practical importance than the study o-f micelles. Yet, the thermodynamics of monolayer formation has seen substantial study. I think that this is largely due to the fact that the monomer—monolayer equilibrium can be unambiguously and relatively easily measured using the Hutchinson method (25), as exploited by Rosen and Hua ( ), while this cannot be said for monomer—micelle equilibrium. Therefore, mixed monolayer formation will be a more fruitful field for model development in the near future than mixed micelles because of the availability of a method of obtaining experimental data for comparison. 

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... 

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