Monomer-micelle equilibrium surfactant systems

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. 

MONOMER MOLE FRACTION OF SURFACTANT A Monomei—micelle equilibrium -for systems in... 

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. 

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... 

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]. 

Taking Simultaneous Micellizadon and Adsorption Phenomena into Consideration In the presence of an adsorbent in contact with the surfactant solution, monomers of each species will be adsorbed at the solid/ liquid interface until the dual monomer/micelle, monomer/adsorbed-phase equilibrium is reached. A simplified model for calculating these equilibria has been built for the pseudo-binary systems investigated, based on the RST theory and the following assumptions ... 

Equation 1 has proved to be a better predictor of the equilibrium which exists between monomer and micelles for mixed surfactant systems than is the regular solution theory model. It also predicts well the mixture CMC and shows the heat of mixing to be smaller than that predicted by the regular solution theory in agreement with the experiment (13). The purpose of this paper is to further explore... 

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. ... 

In sufficiently dilute aqueous solutions surfactants are present as monomeric particles or ions. Above critical micellization concentration CMC, monomers are in equilibrium with micelles. In this chapter the term micelle is used to denote spherical aggregates, each containing a few dozens of monomeric units, whose structure is illustrated in Fig. 4.64. The CMC of common surfactants are on the order of 10 " -10 mol dm . The CMC is not sharply defined and different methods (e.g. breakpoints in the curves expressing the conductivity, surface tension, viscosity and turbidity of surfactant solutions as the function of concentration) lead to somewhat different values. Moreover, CMC depends on the experimental conditions (temperature, presence of other solutes), thus the CMC relevant for the expierimental system of interest is not necessarily readily available from the literature. For example, the CMC is depressed in the presence of inert electrolytes and in the presence of apolar solutes, and it increases when the temperature increases. These shifts in the CMC reflect the effect of cosolutes on the activity of monomer species in surfactant solution, and consequently the factors affecting the CMC (e.g. salinity) affect also the surfactant adsorption. 

Both of the above effects are probably related to changes in the relative abundances of various surfactant species present as monomer in the solution, arising from micelle-monomer equilibrium. In a single surfactant system, the monomer is always 100 of a particular species and hence no n. changes are observed. 

The equilibrium and dynamics of adsorption processes from micellar surfactant solutions are considered in Chapter 5. Different approaches (quasichemical and pseudophase) used to describe the micelle formation in equilibrium conditions are analysed. From this analysis relations are derived for the description of the micelle characteristics and equilibrium surface and interfacial tension of micellar solutions. Large attention is paid to the complicated problem, the micellation in surfactant mixtures. It is shown that in the transcritical concentration region the behaviour of surface tension can be quite diverse. The adsorption process in micellar systems is accompanied by the dissolution or formation of micelles. Therefore the kinetics of micelle formation and dissociation is analysed in detail. The considered models assume a fast process of monomer exchange and a slow variation of the micelle size. Examples of experimental dynamic surface tension and interface elasticity studies of micellar solutions are presented. It is shown that from these results one can conclude about the kinetics of dissociation of micelles. The problems and goals of capillary wave spectroscopy of micellar solutions are extensively discussed. This method is very efficient in the analysis of micellar systems, because the characteristic micellisation frequency is quite close to the frequency of capillary waves. 

This relation holds for nonionic surfactants, but will be modified in the case of ionic surfactants (as shown in the following text). This equilibrium shows that, if we dilute the system, micelles will break down to monomers to achieve equilibrium. This is a simple equilibrium for a nonionic surfactant. In the case of ionic surfactants, there will be charged species. 

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 ... 

Systems in which surfactant precipitate is present in substantial quantities in equilibrium with micelles and monomer are of interest. For example, in a technique for improving mobility control in oil reservoirs, surfactant is purposely precipitated in the permeable region of a reservoir to plug it (44). When substantial precipitate is present, crystals of different composition can be in simultaneous equilibrium. Experimental study and modeling of these systems where several Ksr- relationships are simultaneously satisfied will be a challenging task. 

Once a micelle is stung, polymerization proceeds very rapidly. The particle can accommodate more monomer as its polymer content increases and the water-polymer interfacial surface increases concuirently. Tlie new surface adsorbs emulsifier molecules from the aqueous phase. This disturbs the equilibrium between micellar and dissolved soap, and micelles will begin to disintegrate as the concentration of molecularly dissolved emulsifier is restored to its equilibrium value. Thus the formation of one polymer particle leads to the disappearance of many micelles. The initial latex will usually contain about 10 micelles per milliliter water, but there will be only about 10 particles of polymer in the same volume of the final emulsion. When all the micelles have disappeared, the surface tension of the system increases because there is little surfactant left in solution. Any tendency for the mixture to foam while it is being stirred decreases at this time. 

Aggregation of surfactants in apolar solvents, e.g., aliphatic or aromatic hydrocarbons, occurs provided that small amounts of water are present [1,126,127], These aggregates are often called reverse micelles, although the solutions do not always appear to have a critical micelle concentration, and surfactant association is often governed by a multiple equilibrium, mass action, model vith a large spread of aggregate sizes [130,131], It has recently been suggested that the existence of a monomer f -mer equilibrium should be used as a criterion of micellization, and that this term should not be applied to self-associated systems which involve multiple equilibria [132],... 

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