Monomer-micelle equilibrium species

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. 

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. 

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. 

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 ... 

In this type of extraction, micellar structures are retained by correctly selecting the ultrafiltration (UF) membrane (Scamehorn et al., 1988). Hydrophobic species are solubilized within the micelles, but surfactant monomers in equilibrium with the micelles can penetrate the membrane along with the free solutes in equilibrium with those solubilized in the micelles. Whereas several uses for this technique have been suggested, such as the collection of radioactive uranium and plutonium present in acid wastes during nuclear plant decommissioning, from our point of view its principal use is in enantiomeric separation (Overdevest et al., 1998). 

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. 

At a speci-fic adsorption level, we can view the sur-f actant monomers as being in equilibrium with admicelles on speci-fic sur-face patches, just as the monomer is in equilibrium with the micelles at a monomeric concentration o-f the CMC. There-fore, CAC is... 

The Pseudo-Phase Model Consider a process in which surfactant is added to water that is acting as a solvent. Initially the surfactant dissolves as monomer species, either as molecules for a non-ionic surfactant or as monomeric ions for an ionic surfactant. When the concentration of surfactant reaches the CMC, a micelle separates from solution. In the pseudo-phase model,20 the assumption is made that this micelle is a separate pure phase that is in equilibrium with the dissolved monomeric surfactant. To maintain equilibrium, continued addition of surfactant causes the micellar phase to grow, with the concentration of the monomer staying constant at the CMC value. This relationship is shown in Figure 18.14 in which we plot m, the stoichiometric molality,y against mj, the molality of the monomer in the solution. Below the CMC, m = m2, while above the CMC, m2 = CMC and the fraction a of the surfactant present as monomer... 

The Mass Action Model The mass action model represents a very different approach to the interpretation of the thermodynamic properties of a surfactant solution than does the pseudo-phase model presented in the previous section. A chemical equilibrium is assumed to exist between the monomer and the micelle. For this reaction an equilibrium constant can be written to relate the activity (concentrations) of monomer and micelle present. The most comprehensive treatment of this process is due to Burchfield and Woolley.22 We will now describe the procedure followed, although we will not attempt to fill in all the steps of the derivation. The aggregation of an anionic surfactant MA is approximated by a simple equilibrium in which the monomeric anion and cation combine to form one aggregate species (micelle) having an aggregation number n, with a fraction of bound counterions, f3. The reaction isdd... 

Monomer Solutions. At surfactant concentrations less than the critical micelle concentration (cmc), all the surfactant is in monomeric form and the equilibrium between the protonated and neutral species of an alkyldimethyl amine oxide can be described by a classical dissociation constant, Ka ... 

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. 

On the basis of surface and bulk interaction with water. Small [85] classified bile acids as insoluble amphiphiles and bile salts as soluble amphiphiles. On account of the undissociated carboxylic acid group, the aqueous solubility of bile acids is limited [35] in contrast, many bile salts have high aqueous solubilities as monomers [33] and, in addition, their aqueous solubilities are greatly enhanced by the formation of micelles [5,6]. Because many bile salts are weak electrolytes, their ionization and solubility properties are more complicated than those of simple inorganic or organic electrolytes [5,35]. For example, the p/Tj, values of bile acids in water vary markedly as functions of bile salt concentration and, because micelles formed by the A (anionic) species can solubilize the HA (acid) species [5,35], the equilibrium precipitation pH values of bile acids also vary as functions of bile salt concentration. Finally, certain bile salts are characterized by insolubility at ambient temperatures [2,5,6,86,87], only becoming soluble as micelles at elevated temperatures (the critical micellar temperature) [6]. 

The problem of calculating the distribution of micelle sizes reduces to that of establishing the dependence of ACe(i) on i. Since there is good evidence that the equilibrium mixture at and above the c.m.c. contains only a low concentration of species other than those of a size close to the mean micelle size, we must seek a form of AG°(i) which leads to this result. Some early theories assumed that the standard free energy is a linear function of i. This would mean Lhal AG (i, i + 1), which is equal to AG"(i + 1) — AGe(i), is constant. However, wc saw in Chapter 9 that, if this is so, above a certain concentration aggregates will grow to macroscopic size, contrary to the limiting sizes associated with miccllisation. Other theories have set AG (i) equal to zero for all values of i except lor a particular value of i at the c.m.c. This implies that miccllisation occurs by the. simultaneous association of i monomer molecules, which is physically unrealistic. 

Figure 3.10 Preparation of latex (nanoparticles) through emulsion polymerisation. Insert in the absence of initiator, equilibrium between monomer droplets, monomer in solution, and micelles of surfactant with or without monomer. Main figure after initiation by the active species (star), distribution of monomer between the different forms, either solution, or micelles or particles.

The molecular species at the interface are in equilibrium with those in the aqueous and oil phases. If we consider the addition of a fresh oil drop in a micellar solution (Figure 4), the surfactant monomers should move to the interface first and then to the inside of the oil drop. As monomers get depleted in the vicinity of the interface due to adsorption, the micelles break down and produce additional monomers. From the interface, the oil-soluble species preferentially migrate towards the inside of the oil droplet. 

To sum up, the following mechanism is proposed to account for the observed effects in IFT and oil droplet flattening phenomenon. As shown in Figure 4, mixed micelles in equilibrium with surfactant monomers are formed by the water-soluble and oil-soluble species in the bulk aqueous solutions. During equilibration, the surfactant monomers transfer to the water/oil interface and then to the interior of the oil drop resulting in a reduction of IFT. 

Surfactant solutions above the cmc may be considered as made up of two species in equilibrium, i.e. monomers and micelles. Chromatographic methods may indicate how the monomer concentration, C., varies with the total concentration above the cmc. The concentration of monomers, C, above cmc is often assumed to be constant, as indicated surface tension [54] or from equilibrium dialysis [55]. This question was recently investigated by the use of chromatography [47]. In Fig. 14 the equilibria between the various species are depicted. Before elution the surfactant solution above cmc consists of micelles and monomers. These investigations were carried out where the eluant contained only monomers, C, somewhat lower than cmc. In order to calculate the magnitude of the monomer concentration, C, in equilibrium with micelles, when the total surfactant concentration, C, is larger than cmc, the following analytical procedure was carried out. The situation of the elution process is shown in Fig. 14b. 

Table XV shows that the two methods used (equilibrium/ultracentrifugation and sedimentation/diffusion) give comparable results. The sodium taurocholate micelle is swollen appreciably by the presence of even small amounts of potassium oleate. As the weight ratio increases the micelle increases in size. It is not possible to say whether there are two different species of micelle present, although this seems unlikely since the schlieren sedimentation curve was symmetrical and showed no shoulders or second bumps that would suggest polydispersity. It is probable that sodium taurocholate and potassium oleate form a mixed micelle that increases in size as more oleate is added. Since both these compounds are soluble amphiphiles (42) they will be present in both the micelle and as monomers. At present it is impossible to know how the species are partitioned. If one assumes that the micelle composition is similar to that of the whole solution (a valid assumption at high micelle concentrations) then the number of molecules of each...

As mentioned earlier, the aggregation number of micelles is not monodisperse but polydisperse. Therefore, their distribution is a matter of some concern. Let us take the model of micelle formation expressed by Eq. (4-1), where n is not definite but diffuse. Then, if /jl and fii are the chemical potentials of the micellar species composed of n monomers and the monomer, respectively, we have for the equilibrium between the monomers and any micellar species ... 

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