Thermodynamics, mixed micelle

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

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. 

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... 

M Hong, BS Weekley, SJ Grieb, JP Foley. Electrokinetic chromatography using thermodynamically stable vesicles and mixed micelles formed from oppositely charged surfactants. Anal. Chem. 70 1394-1403 (1998). 

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... 

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. 

Medium-chain alcohols such as 2-butoxyethanol (BE) exist as microaggregates in water which in many respects resemble micellar systems. Mixed micelles can be formed between such alcohols and surfactants. The thermodynamics of the system BE-sodlum decanoate (Na-Dec)-water was studied through direct measurements of volumes (flow denslmetry), enthalpies and heat capacities (flow microcalorimetry). Data are reported as transfer functions. The observed trends are analyzed with a recently published chemical equilibrium model (J. Solution Chem. 13,1,1984). By adjusting the distribution constant and the thermodynamic property of the solute In the mixed micelle. It Is possible to fit nearly quantitatively the transfer of BE from water to aqueous NaDec. The model Is not as successful for the transfert of NaDec from water to aqueous BE at low BE concentrations Indicating self-association of NaDec Induced by BE. The model can be used to evaluate the thermodynamic properties of both components of the mixed micelle. 

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 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. 

The purpose of this paper will be to develop a generalized treatment extending the earlier mixed micelle model (I4) to nonideal mixed surfactant monolayers in micellar systems. In this work, a thermodynamic model for nonionic surfactant mixtures is developed which can also be applied empirically to mixtures containing ionic surfactants. The form of the model is designed to allow for future generalization to multiple components, other interfaces and the treatment of contact angles. The use of the pseudo-phase separation approach and regular solution approximation are dictated by the requirement that the model be sufficiently tractable to be applied in realistic situations of interest. 

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 surface tension of the aqueous solution of dode-cylaitunonium chloride (DAC) — decylairanonium chloride (DeAC) mixture was measured as a function of the total molality m of surfactants and the mole fraction X of DeAC in the total surfactant in the neighborhood of the critical micelle concentration (CMC). By use of the thermodynamic equations derived previously, the mole fraction in the mixed adsorbed film was evaluated from the y vs. X and m vs. X curves. Further, the mole fraction in the mixed micelle was evaluated from the CMC vs. X curve. By comparing these values at the CMC, it was concluded that the behavior of DAC and DeAC molecules in the mixed micelle is fairly similar to that in the mixed adsorbed film. 

On the other hand, we showed that the coii5>osition of surfactant in a mixed adsorbed film can be estimated thermodynamically from experimental results without introducing such a supposition (9-11). Further, the composition of a mixed micelle was calculated assuming that the micelle behaves thermodynamically like a macroscopic bulk phase whose thermodynamic quantities are given by the excess thermodynamic quantities similar to those used for the adsorbed film (i8). Therefore, we can now compare the composition of surfactant in the mixed adsorbed film with that in the mixed micelle at the critical micelle concentration (CMC). 

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... 

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. 

Surfactant Activity in Micellar Systems. The activities or concentrations of individual surfactant monomers in equilibrium with mixed micelles are the most important quantities predicted by micellar thermodynamic models. These variables often dictate practical performance of surfactant solutions. The monomer concentrations in mixed micellar systems have been measured by ultraf i Itration (I.), dialysis (2), a combination of conductivity and specific ion electrode measurements (3), a method using surface tension of mixtures at and above the CMC <4), gel filtration (5), conductivity (6), specific ion electrode measurements (7), NMR <8), chromatograph c separation of surfactants with a hydrophilic substrate (9> and by application of the Bibbs-Duhem equation to CMC data (iO). Surfactant specific electrodes have been used to measure anionic surfactant activities in single surfactant systems (11.12) and might be useful in mixed systems. ... 

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. 

To this point, only models based on the pseudo—phase separation model have been discussed. Mixed micelle models utilizing the mass action model may be necessary for micelles with small aggregation numbers, as demonstrated by Kamrath and Franses ( ). However, even for large micelles, the fundamental basis for the pseudophase separation model needs to be examined. In micelles, how much solvent or how many counterions (bound or in the electrical double layer) should be included in the micellar pseudo-phase is unclear. The difficulty is normally surmounted by assuming that the pseudo—phase consists of only the surfactant components i.e., solvent or counterions are ignored. The validity of treating the micelle on a surfactant—oniy basis has not been verified. Funasaki and Hada (22) have questioned the thermodynamic consistency of such an approach. 

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. 

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. 

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