Monomer-micelle equilibrium

Monomer/Micelle Equilibrium Mixtures of surfactants, like any surfactant species in an aqueous solution, give rise to monomer or micelle aggregates provided that the concentration reaches a minimum value, called the critical micellar concentration (CMC). The micelles thus formed are mixed, i.e. made up of the different surfactant species in solution. 

CMC will change if the additive has an effect on the monomer-micelle equilibrium, and also if the additive changes detergent solubility. The CMC of all ionic surfactants will decrease if coions are added. However, nonionic surfactants show very little change in CMC on the addition of salts, which is to be expected from theoretical considerations. The change of CMC with NaCl for SDS is as follows (Figure 3.10) ... 

Ideal Mixed Micelles. The Critical Micelle Concentration (CMC) is the lowest surfactant concentration at which micelles form the lower the CMC, the greater the tendency of a system to form micelles. When the total surfactant concentration equals the CMC, an infintesimal fraction of surfactant is present as micelles therefore, the CMC is equal to the total monomer concentration in equilibrium with the micellar pseudo—phase. The CMC for monomer—micelle equilibrium is analogous to the dew point in vapor—liquid equilibrium. 

As also seen in Table I, the micellar composition can be a-f-fected substantially by nonideality. In -fact, azeotropic behavior in the monomer—micelle equilibrium is possible -for these nonideal systems i.e., as the monomer composition varies -from pure A to pure B, the micelle can vary -from Xn > y to Xn = y (azeotrope) to Xa < yA. This azeotrope -formation is illustrated -for the cationic/nonionic system in Figure 2, where an azeotrope -forms at Xa = yA = 0.3. The minimum CMC -for a mixture corresponds to the azeotropic composition i-f an azeotrope is present (32.37). For an ideal system, azeotropic behavior is not observed. 

Equations 3 and 4 are derived from Equation 5 (31) which has been Found to be invalid For the systems oF interest. However, Equations 3 and 4 have been shown to accurately describe mixture CMC values and monomer-micelle equilibrium. The resolution is that Equations 3 and 4 should be considered as valuable empirical equations to describe these nonideal systems. The Fact that they were originally derived From regular solution theory is a historical coincidence. 

Solubilization o-f dissolved organic molecules into micelles is important in detergency (2), emulsion polymerization (65). and micellar—enhanced ultra-fiItration (3), Just to name a -few applications. Solubilization also indirectly a-f-fects many other operations because it o-ften a-f-fects monomer—micelle equilibrium, in-fluencing sur-factant adsorption, wetting, etc. when solubi 1 izable, non—sur-factant species are present in solution. 

The equilibrium in these systems above the cloud point then involves monomer-micelle equilibrium in the dilute phase and monomer in the dilute phase in equilibrium with the coacervate phase. Prediction o-f the distribution of surfactant component between phases involves modeling of both of these equilibrium processes (98). It should be kept in mind that the region under discussion here involves only a small fraction of the total phase space in the nonionic surfactant—water system (105). Other compositions may involve more than two equilibrium phases, liquid crystals, or other structures. As the temperature or surfactant composition or concentration is varied, these regions may be encroached upon, something that the surfactant technologist must be wary of when working with nonionic surfactant systems. 

Micelles are often present in surfactant systems. In some processes, such as solubilization, they are directly involved. Micelles indirectly affect many other processes because monomer concentrations or activities of the surfactant components are dictated by the monomer— micelle equilibrium at total surfactant concentrations above the CMC. Therefore, interest in mixed micelle formation will continue to grow. 

As already discussed in Chapter 1, the relative tendency of a surfactant component to adsorb on a given surface or to form micelles can vary greatly with surfactant structure. The adsorption of each component could be measured below the CMC at various concentrations of each surfactant in a mixture. A matrix could be constructed to tabulate the (hopefully unique) monomer concentration of each component in the mixture corresponding to any combination of adsorption levels for the various components present. For example, for a binary system of surfactants A and B, when adsorption of A is 0.5 mmole/g and that of B is 0.3 mmole/g, there should be only one unique combination of monomer concentrations of surfactant A and of surfactant B which would result in this adsorption (e.g., 1 mM of A and 1.5 mM of B). Uell above the CMC, where most of the surfactant in solution is present as micelles, micellar composition is approximately equal to solution composition and is, therefore, known. If individual surfactant component adsorption is also measured here, it would allow computation of each surfactant monomer concentration (from the aforementioned matrix) in equilibrium with the mixed micelles. Other processes dependent on monomer concentration or surfactant component activities only could also be used in a similar fashion to determine monomer—micelle equilibrium. 

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. 

In aqueous surfactant solutions, either by circumstance or design, non—surface active organic species may be present. Examples are oil recovery, where crude oil is present, or micellar—enhanced ultrafiltration, where micelles are being used to effect a separation of dissolved organic pollutants from water. The ability of mixed micelles to solubilize organic solutes has received relatively little study. In addition, the solubilization of these compounds by micelles may change the monomer—micelle equilibrium compositions. 

As our understanding and ability to model monomer-micelle equilibrium in the absence o-f added solutes evolves, research into the more complex systems will... 

Except at concentrations near the CAC, the amount of surfactant adsorbed in the Henry s law region is small in comparison to the amount of surfactant present in the admicelles. This implies that nearly all of the adsorbed surfactant molecules are associated on the mineral surface in the form of admicelles. It is important to keep in mind that Equation 8 is valid only between the CAC and the CMC. Above the CMC, equations could be included to account for the formation of micelles, by including monomer-micelle equilibrium equations (1 1). ... 

Effluent profiles obtained from a core-flood performed with a mixture of two surface-active components (C12 and C18) separated from a commercially available sulfobetaine are shown in Figure 24 (115). The points represent experimental data, and the lines were obtained by simulating the core-flood with a convection—dispersion—adsorption model that is based on the surface excess concept and takes into account monomer—micelle equilibrium (115). Because the mixture contains different homologues of the same surfactant, the ideal mixed micelle model... 

The first example illustrates that in micellar systems, the adsorption process may be dominated by monomer—micelle equilibrium. The second example provides experimental evidence that it is possible to lower adsorption by mixing surfactants. 

The exclusion chromatography of surfactant solutions is a problematic method for analyses, since the micelles are only stable when in equilibrium with monomers of concentration equal to the cmc. The monomer-micelle equilibrium thus can be subjected to chromatographic investigations, under various conditions, e.g. dynamic or equilibrium. In the former case, if one applies a micellar solution with concentration greater than cmc, the surfactant front would move down the column at a speed relative to the size of micelles. However, if the dilution factor in the column is too large, such that only monomers are present, then the front moves at the same speed as the monomer. In these systems the eluant is supposed to be pure solvent. However, if concentration of the surfactant in the eluant is close to the cmc, then the micellar solution moves down the column with little perturbation of the monomer-micelle equilibrium. The surfactant front under these conditions then moves... 

The monomer-micelle equilibrium, present when the surfactant concentration is >cmc, has been subjected to chromatographic analyses by various investigators [4,28,43,44,45,46,47,48,49,50,51,52]. Below the cmc, micelles break down to form monomers. The rate of mi-... 

On the other hand, if the eluant contains surfactant at concentration ca. cmc, the monomer-micelle equilibrium will not be perturbated appreciably during elution. This process we shall designate as "equilibrium" analysis. 

If a surfactant solution with concentration >cmc is applied to the chromatography column in an eluant as pure solvent (without any added surfactant), the monomer-micelle equilibrium is driven towards monomer due to dilution during the chromatography process. This system under dynamic conditions has been investigated by various investigators [45,48,52]. 

Studies on micellar solutions began in the first half of the 20th century, and a summary of the results obtained was presented in Hartley s book [59] published in 1936, which describes many currently used terms. Further research focused primarily on micelle structures and properties, monomer-micelle equilibrium, and solubilization by micelles [60]. The research turned out to be extremely interesting, and the results were used in a number of applications. 

Scamehom [64] has emphasized, however, that although these equations have accurately predicted mixture cmc values and monomer-micelle equilibrium, they do not validate the regular solution theory for nonideal surfactant mixtures. Ample evidence contradicts the validity of the regular solution theory in describing the nonideal surfactant mixtures. 

In the mass action model, it is assumed that equilibrium exists between the monomeric surfactant and the micelles. For the case of nonionic (or un-ionized) surfactants, the monomer-micelle equilibrium can be written... 

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