Micelle-water distribution

Table 6.13 Micelle/water distribution coefficients, P, for the solubilisation of benzoic acid by r>olkyl polyoxyethylene surfactants C E , (where n = alkyl (C) chain length and m = polyoxyethylene (E) chain length) os a function of temperature°...

An alternative treatment of the micelle-water distribution equilibrium in terms of the thermodynamics of small systems (see Section 3.6) has been proposed by Mukerjee [76, 77]. The chemical potential of a solubilizate molecule (component 3) in the aqueous phase, may be written as... 

The extent of solubilization of benzoic acid by several n-hexadecylpolyoxy-ethylene surfactants of varying ethylene oxide chain length showed an apparent increase with increasing temperature [163]. However, benzoic acid has an appreciable water solubility which also increases with temperature and this is, of course, a contributing factor towards the overall increase in the amount of benzoic acid taken into solution. Allowance for this effect was made by expressing the solubilization data in terms of the micelle/water distribution coefficient, P ,. Table 5.21 shows a minimum in at about 300 K. The decrease in below this... 

Table 5.21 Micelle/water distribution coefficient, P, , for the solubilization of benzoic acid by n-alkyl-polyoxyethylene surfactants as a function of temperature [163].

Herein Pa and Pb are the micelle - water partition coefficients of A and B, respectively, defined as ratios of the concentrations in the micellar and aqueous phase [S] is the concentration of surfactant V. ai,s is fhe molar volume of the micellised surfactant and k and k , are the second-order rate constants for the reaction in the micellar pseudophase and in the aqueous phase, respectively. The appearance of the molar volume of the surfactant in this equation is somewhat alarming. It is difficult to identify the volume of the micellar pseudophase that can be regarded as the potential reaction volume. Moreover, the reactants are often not homogeneously distributed throughout the micelle and... 

Similar considerations apply to situations in which substrate and micelle carry like charges. If the ionic substrate carries highly apolar groups, it should be bound at the micellar surface, but if it is hydrophilic so that it does not bind in the Stern layer, it may, nonetheless, be distributed in the diffuse Gouy-Chapman layer close to the micellar surface. In this case the distinction between sharply defined reaction regions would be lost, and there would be some probability of reactions across the micelle-water interface. 

The kinetic complexity seen in oriented micelles persists in inverse micelles. The distribution of electron transfer quenchers within the water pool follows Poisson statistics and enables the kinetic data to describe migration rates to and from the aqueous subphase [65]. These orientation effects also make possible topological control of non-electron transfer photoreactions occurring within AOT micelles [66]. 

Extensive studies in reverse micelles revealed a similar water distribution [127-130], which is consistent with the distinct water model proposed by Finer [150]. For example, when the molar ratio (wo) of water to the surfactant is 6.8 in lecithin reverse micelles with a corresponding diameter of 37 A, three solvation time scales of 0.57 (13%), 14 (25%), and 320 ps (62%) were observed using coumarin 343 as the molecular probe. At w0 = 4.8 with a 30-A water core diameter, only a single solvation dynamic was observed at 217 ps, which indicates that all water molecules are well ordered inside the aqueous pool. The lecithin in these reverse micelles have charged headgroups, which have much stronger interactions with water than the neutral headgroups of monoolein in the... 

Quantitative approaches to describing reactions in micelles differ markedly from treatments of reactions in homogeneous solution primarily because discrete statistical distributions of reactants among the micelles must be used in place of conventional concentrations [74], Further, the kinetic approach for bimolecular reactions will depend on how the reactants partition between micelles and bulk solution, and where they are located within the microphase region. Distinct microphase environments have been sensed by NMR spectrometry for hydrophobic molecules such as pyrene, cyclohexane and isopropylbenzene, which are thought to lie within a hydrophobic core , and less hydrophobic molecules such as nitrobenzene and N,N-dimethylaniline, which are preferentially located at the micelle-water interface [75]. Despite these complexities, relatively simple kinetic equations for electron-transfer reactions can be derived for cases where both donors and acceptors are uniformly distributed inside the micelle or on its surface. 

The structure of the AOT micellar system, as well as the state of water entrapped inside swollen micelles, have been characterized using different techniques, such as photon correlation spectroscopy (25), positron annihilation (26), NMR (27, 28), fluorescence (29-32) and more recently small angle neutron scattering (33). The existence of reversed micelles has been demonstrated in the domain of concentrations explored by protein extraction experiments. Their size (proportional to the molar ratio of water to surfactant known as wo), shape and aggregation number have been determined. Furthermore, the micelle size distribution is believed to be relatively monodisperse. 

The situation is more complicated for nonspontaneous bimolecular reactions involving a second reactant, whose distribution between the two pseudophases has to be considered. The simplest situation is that for reaction of a hydrophobic species whose solubility in water is sufficiently low that it is incorporated essentially quantitatively in the association colloid. For example, for reactions of nucleophilic amines in aqueous micelles, second-order rate constants in the micellar pseudophase calculated in terms of local concentrations are lower than in water [103,104], because these reactions are inhibited by a decrease in medium polarity and micelle/water interfaces are less polar than bulk water [59,60,99101]. Nonetheless, these bimolecular reactions are generally faster in micellar solutions than in water because the nucleophile is concentrated within the small volume of the micelles. Similar results were obtained for the reaction of 2,4-dinitrochlorobenzene (5) with the cosurfactant -hexylamine in O/W microemulsions with CTABr and w-octane [99], again consistent with the postulated similarities in the interfacial regions of aqueous micelles and O/W microemulsions. 

Aqueous micellar solutions provide some interesting theoretical problems, such as the prediction of the micelle size distribution, the most stable shapes of the micelles and the elucidation of their behavior at the CMC. From the practical point of view, the most important aspect of micellar solutions is their capability to solubilize solutes that are very sparingly soluble in pure water. This phenomenon occurs naturally in biological systems and has been exploited in many applications, as for example in the pharmaceutical and detergent industries. 

Returning to the micelle size distribution, we can estimate how this distribution changes upon the addition of solute a. Suppose again that the two-component system of surfactant and water behaves as an associated ideal dilute solution for which (8.9.11) and (8.9.13) are valid. By adding the solute a we can define the new species A(k, n), i.e., an aggregate with n monomers and k solute molecules a. Since the strong correlations between a and An are within the species A k, n), the assumption of associate ideality can be retained for all the species A k, n). Hence the analogue of (8.9.11) is now... 

We have demonstrated that due to inhomogeneous distribution of both reaction partners in the micelles, the pseudophase model leads to erroneous estimates of the second-order rate Constantin the micellar pseudophase, so that conclusions regarding the medium of the reaction cannot be derived through this model. However, analysis of substituent effects and endo-exo ratios of the Diels-Alder adducts indicate that the reaction experiences a water-like medium. 

The surfactant is initially distributed through three different locations dissolved as individual molecules or ions in the aqueous phase, at the surface of the monomer drops, and as micelles. The latter category holds most of the surfactant. Likewise, the monomer is located in three places. Some monomer is present as individual molecules dissolved in the water. Some monomer diffuses into the oily interior of the micelle, where its concentration is much greater than in the aqueous phase. This process is called solubilization. The third site of monomer is in the dispersed droplets themselves. Most of the monomer is located in the latter, since these drops are much larger, although far less abundant, than the micelles. Figure 6.10 is a schematic illustration of this state of affairs during emulsion polymerization. 

Chain-Growth Associative Thickeners. Preparation of hydrophobically modified, water-soluble polymer in aqueous media by a chain-growth mechanism presents a unique challenge in that the hydrophobically modified monomers are surface active and form micelles (50). Although the initiation and propagation occurs primarily in the aqueous phase, when the propagating radical enters the micelle the hydrophobically modified monomers then polymerize in blocks. In addition, the hydrophobically modified monomer possesses a different reactivity ratio (42) than the unmodified monomer, and the composition of the polymer chain therefore varies considerably with conversion (57). The most extensively studied monomer of this class has been acrylamide, but there have been others such as the modification of PVAlc. Pyridine (58) was one of the first chain-growth polymers to be hydrophobically modified. This modification is a post-polymerization alkylation reaction and produces a random distribution of hydrophobic units. 

The potential of reversed micelles needs to be evaluated by theoretical analysis of the metal ion distribution within micelles, by evaluation of the free energy of the solvated ions in the reversed micelle organic solution and the bulk aqueous water, and by the experimental characterization of reversed micelles by small-angle neutron and x-ray scattering. 

The different location of polar and amphiphilic molecules within water-containing reversed micelles is depicted in Figure 6. Polar solutes, by increasing the micellar core matter of spherical micelles, induce an increase in the micellar radius, while amphiphilic molecules, being preferentially solubihzed in the water/surfactant interface and consequently increasing the interfacial surface, lead to a decrease in the miceUar radius [49,136,137], These effects can easily be embodied in Eqs. (3) and (4), aUowing a quantitative evaluation of the mean micellar radius and number density of reversed miceUes in the presence of polar and amphiphilic solubilizates. Moreover it must be pointed out that, as a function of the specific distribution law of the solubihzate molecules and on a time scale shorter than that of the material exchange process, the system appears polydisperse and composed of empty and differently occupied reversed miceUes [136],... 

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