Equilibrium constant 502 micellation

The solubilization of diverse solutes in micelles is most often examined in tenns of partitioning equilibria, where an equilibrium constant K defines the ratio of the mole fraction of solute in the micelle (X and the mole fraction of solute in the aqueous pseudophase. This ratio serves to define the free energy of solubilization -RT In K). 

The rate of attack of water upon the tri-/>-anisylmethyl cation is unaffected by binding of this cation to anionic micelles of sodium dodecyl sulfate (SDS) (Bunton and Huang, 1972) and equilibrium constants for aldehyde hydration are only slightly reduced by binding to micelles (Albrizzio and Cordes, 1979). These observations are also consistent with substrate binding at a wet micellar surface rather than in the interior of the micelle. 

As n increases, so the value of Wmiceiiatioru changes quite dramatically with concentration. Being an equilibrium constant, the value of (micellation) is fixed (at constant temperature), so there is effectively no micelle at low concentration but, at a sharply defined concentration limit, just about all of the monomer M becomes bound up within the micelle. 

Although anation and aquation rates of vitamin B12 are not affected appreciably by aqueous micelles, the solubilized water in reversed micelles, in contrast, influences the rate and equilibrium constants for the formation and decomposition of glycine, imidazole, and sodium azide adducts of vitamin Bl2 (Fendler et al., 1974). A vitamin B12 molecule is conceivably shielded from the apolar solvent (benzene) by some 300 surfactant molecules. 

Micelles are extremely dynamic aggregates. Ultrasonic, temperature and pressure jump techniques have been employed to study various equilibrium constants. Rates of uptake of monomers into micellar aggregates are close to diffusion-controlled306. The residence times of the individual surfactant molecules in the aggregate are typically in the order of 1-10 microseconds307, whereas the lifetime of the micellar entity is about 1-100 miliseconds307. Factors that lower the critical micelle concentration usually increase the lifetimes of the micelles as well as the residence times of the surfactant molecules in the micelle. Due to these dynamics, the size and shape of micelles are subject to appreciable structural fluctuations. 

MICELLAR CATALYSIS. Chemical reactions can be accelerated by concentrating reactants on a micelle surface or by creating a favorable interfacial electrostatic environment that increases reactivity. This phenomenon is generally referred to as micellar catalysis. As pointed out by Bunton, the term micellar catalysis is used loosely because enhancement of reactivity may actually result from a change in the equilibrium constant for a reversible reaction. Because catalysis is strictly viewed as an enhancement of rate without change in a reaction s thermodynamic parameters, one must exercise special care to distinguish between kinetic and equilibrium effects. This is particularly warranted when there is evidence of differential interactions of substrate and product with the micelle. Micelles composed of optically active detergent molecules can also display stereochemical action on substrates. ... 

Secondary chemical equilibria, 230,280 see also Secondary equilibria with diprotic acids and zwitterions, equilibrium constants and retention. 241 with micelle ftmtiation, 236... 

The Menger-Portnoy model is closely related to the Berezin model employing partition coefficients instead of equilibrium constants.For the case where only two pseudophases (bulk water and micelle) are considered, the partitioning of the reactant is given by the partition coefficient P. This leads to Equation (4) describing observed rate constants as a function of surfactant concentration. 

In the mass action approach we use Reaction (B) as a prototype for the process of micellization. The equilibrium constant for this reaction is given by... 

Having looked at an example of micellar catalysis, let us next consider how such results are analyzed quantitatively. By analogy with Reaction (E), we visualize the micelle M and the substrate A entering a solubilization equilibrium characterized by an equilibrium constant K ... 

Since k0 is known, Equation (29) allows km to be evaluated. Likewise, the equilibrium constant for the binding of the substrate to the micelle can be evaluated from Equation (31) if n is known from a separate experiment. This method of analysis of catalyzed reactions is called a Lineweaver-Burke plot after the corresponding technique in biochemistry. Example 8.5 illustrates the use of these relationships. 

Equilibrium constants for the binding between substrates and micelles — Reaction (G) — generally range from 103 to 106 for hydrophobic organic substrates. Furthermore, they are expected to increase as the hydrophobic character of the substrate increases. Figure 8.10b shows that this effect sometimes overshoots optimum solubilization. The figure shows, on a... 

Micelles are formed by association of molecules in a selective solvent above a critical micelle concentration (one). Since micelles are a thermodynamically stable system at equilibrium, it has been suggested (Chu and Zhou 1996) that association is a more appropriate term than aggregation, which usually refers to the non-equilibrium growth of colloidal particles into clusters. There are two possible models for the association of molecules into micelles (Elias 1972,1973 Tuzar and Kratochvil 1976). In the first, termed open association, there is a continuous distribution of micelles containing 1,2,3,..., n molecules, with an associated continuous series of equilibrium constants. However, the model of open association does not lead to a cmc. Since a cmc is observed for block copolymer micelles, the model of closed association is applicable. However, as pointed out by Elias (1973), the cmc does not correspond to a thermodynamic property of the system, it can simply be defined phenomenologically as the concentration at which a sufficient number of micelles is formed to be detected by a given method. Thermodynamically, closed association corresponds to an equilibrium between molecules (unimers), A, and micelles, Ap, containingp molecules ... 

Here M is a large number. Writing the equilibrium constant for 1 mol of micelles... 

Keto-enol equilibrium constants for simple /i-dicarbonyl compounds, RCOCH2COX (R = X = Me R = Me, Ph for X = OEt) have been measured in water1423 by a micelle perturbation method previously reported for benzoylacetone142b (R = Ph, X = Me). The results have been combined with kinetic data for nitrosation by NO+, C1NO, BrNO, and SCNNO in all cases, reaction with the enol was found to be rate limiting. 

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... 

Fig. 21. The micelle formation equilibrium constant K = —- of PIOP-n as function of the num-...

The most straightforward approach to the micelle formation is through equilibrium constants. For an ionic amphiphile the association can be described through a number of equilibria... 

Summarizing the statements of these three most commonly used models, it appears that the so-called mass action and phase-separation models simulate a third condition which must be fulfilled with respect to the formation of micelles a size limiting process. The latter is independent of the cooperativity and has to be interpreted by a molecular model. The limitation of the aggregate size in the mass action model is determined by the aggregation number. This is, essentially, the reason that this model has been preferred in the description of micelle forming systems. The multiple equilibrium model as comprised by the Eqs. (10—13) contains no such size limiting features. An improvement in this respect requires a functional relationship between the equilibrium constants and the association number n, i.e.,... 

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