Micellar kinetic model

Kinetic study has been one of the best mechanistic (reaction) tools to establish the most refined reaction mechanisms. In an attempt to establish such a reaction mechanism, kinetic experimental data on the reaction rate are obtained under a set of reaction conditions that could be explained by a kinetic equation derived on the basis of a proposed reaction mechanism. The study is repeated to obtain kinetic data under slightly or totally dilferent reaction conditions, and if these kinetic data fail to fit the kinetic equation derived on the basis of the earlier reaction mechanism, a further refinement in the mechanism is suggested so that the present and earlier kinetic data could be explained mechanistically. A similar approach has been used to provide quantitative or semiquantitative explanations for the micellar effects on reaction rates. Let us now examine the micellar kinetic models developed so far for apparent quantitative explanations of the effects of micelles on reaction rates. 

The validity of most of the assumptions involved in this model has not been tested rigorously. Furthermore, as with other micellar kinetic models, the success of this model is basically claimed on the basis of fairly low residual errors between experimentally determined rate constants (ko,s) and calculated rate constants (kcaicd) in terms of this model. Such a satisfactory statistical fit of observed data to such a micellar kinetic model is necessary for the apparent success of the model but is not sufficient to guarantee the reliability of the values of the calculated parameters from this model. Such a problem has been encountered in both PIE and MA-SB models. ... 

OTHER MICELLAR KINETIC MODELS 3.6.1 PiszKiEwicz s Kinetic Model... 

PP model of micelle. This model generally gives a satisfactory fit of observed data in terms of residual errors (= kobs i - kcaicd where kobs i and i are, at the i-th independent reaction variables such as [D ], experimentally determined and calculated [in terms of micellar kinetic model] rate constants, respectively). The model also provides plausible values of kinetic parameters such as micellar binding constants of reactant molecules and rate constants for the reactions in the micellar pseudophase. The deviations of observed data points from reasonably good fit to a kinetic equation derived in terms of PP model for a specific bimo-lecular reaction under a specific reaction condition are generally understandable in view of the known limitations of the model. Such deviations provide indirect information regarding the fine, detailed structural features of micelles. 

The rate of cleavage of 1 has been studied in the absence and presence of metallomicelles of surfactant with tridentate ligand head groups (10 and 11) at a constant pH, but the observed kinetic data are not snfficient to provide a quantitative explanation of these data in terms of a micellar kinetic model. However, these kinetic data may provide a qualitative assessment of catalytic factor (Y) due to aqueous metal ion catalysis (Y" ), metal ion-tridentate Ugand complex catalysis (Y ), and metal ion-tridentate ligand surfactant complex catalysis (Y ls), xhns, Y = (k b kg)/k, = (k m - - ko)/ko, and Y ls =... 

Various kinetic models on particle formation were proposed by different researchers. These may be classified as follows (1) radical absorption mechanisms by Gardon [28-34] and Fisch and Tsai [13], (2) micellar nucleation newer models by Nomura et al. [35,36] and by Hansen and Ugelstad [37], (3) homogeneous nucleation by Fistch and coworkers [13,38,39]. 

The catalytic activities of Cu(II), Co(II) and Mn(II) are considerably enhanced by sodium dodecyl sulfate (SDS) in the autoxidation of H2DTBC (51). The maximum catalytic activity was found in the CMC region. It was assumed that the micelles incorporate the catalysts and the short metal-metal distances increase the activity in accordance with the kinetic model discussed above. The concentration of the micelles increases at higher SDS concentrations. Thus, the concentrations of the catalyst and the substrate decrease in the micellar region and, as a consequence, the catalytic reaction becomes slower again. 

Despite the abovementioned difficulties, kinetic models reproducing typical micellar kinetics have found widespread use and typically reproduce micellar reactivity well. Whereas these models are described here in terms of micellar kinetics, they can equally be adopted for the analysis of most vesicular rate effects, as long as bilayer permeation is either slow or fast compared to the rate of reaction. The issue of bilayer permeation-dependent rates of reaction has been addressed in detail by Moss et and will not be discussed here. A brief overview of the basic kinetic... 

The most straightforward of the various models describing micellar kinetics is the Menger-Portnoy model for (pseudo) unimolecular reactions.The Menger-Portnoy model assumes rapid equilibration of the reactant of interest over bulk water and the micellar pseudophase with equilibrium constant K. The reaction then proceeds in both pseudophases with rate constants and in bulk water and the micellar pseudophase, respectively (Scheme 4). 

Photoinduced electron transfer from eosin and ethyl eosin to Fe(CN)g in AOT/heptane-RMs was studied and the Hfe time of the redox products in reverse micellar system was found to increase by about 300-fold compared to conventional photosystem [335]. The authors have presented a kinetic model for overall photochemical process. Kang et al. [336] reported photoinduced electron transfer from (alkoxyphenyl) triphenylporphyrines to water pool in RMs. Sarkar et al. [337] demonstrated the intramolecular excited state proton transfer and dual luminescence behavior of 3-hydroxyflavone in RMs. In combination with chemiluminescence, RMs were employed to determine gold in aqueous solutions of industrial samples containing silver alloy [338, 339]. Xie et al. [340] studied the a-naphthyl acetic acid sensitized room temperature phosphorescence of biacetyl in AOT-RMs. The intensity of phosphorescence was observed to be about 13 times higher than that seen in aqueous SDS micelles. 

Among the practical consequences of micellar-contained electron transfer systems are the photocatalytic evolution of hydrogen [56], the containment of photoactive semiconductors within the protective micellar core [57], and the use of such systems as kinetic models for mechanistic characterization of light-responsive redox herbicides [58]. 

Unzueta et al. [18] derived a kinetic model for the emulsion copolymerization of methyl methacrylate (MMA) and butyl acrylate (BA) employing both the micellar and homogeneous nucleation mechanisms and introducing the radical absorption efficiency factor for micelles, F, and that for particles, Fp. They compared experimental results with model predictions, where they employed the values of Fp=10 and Fn,=10", respectively, as adjustable parameters. However, they did not explain the reason why the value of Fp, is an order of magnitude smaller than the value of Fp. Sayer et al. [19] proposed a kinetic model for continuous vinyl acetate (VAc) emulsion polymerization in a pulsed... 

Piskiewicz [119] has developed a kinetic model of micellar catalysis, based on the Hill equation of enzyme kinetics, which assumes a cooperative interaction between reactants and surfactant to form reactive substrate-micelle complexes. This model is probably not applicable to systems in which the surfactant is in large excess over substrate, as in most micellar mediated reactions, but it gives a very reasonable explanation of the rate effects of very dilute surfactants. 

A quantitative model must consider the diffusion of monomers and micelles, and the micellar kinetics mechanisms as it was reviewed in the paper by Dushkin [94] or in the book by Joos [16]. As example the transport equations for a continuously expanding surface can be given in the following form... 

These equations can serve to estimate the influence of micellar kinetics on the adsorption process. Much more details will be given in Chapter 5 where the various micelle kinetics models and their practical relevance for interfacial studies are discussed. 

The kinetic model, which can explain the origin of these two relaxation processes and can describe the dependence of the corresponding relaxation times on the concentration, has been proposed by Aniansson and Wall [114, 115, 119]. This model allows to explain the main experimental facts and is generally accepted nowadays. At the same time, subsequent studies allowed for the determination of the application limits of this theory [116-118, 128]. Because the model of Aniansson and Wall is frequently used also for the analysis of dynamic surface properties of micellar solutions [93, 96-103, 133-138], it will be considered below in details. 

Kinetic Modeling of Micellar Reactions (Without Transport Limitations)... 

The coupling of the diffusion of monomers and micelles is given by the micellar kinetics, which consists of different physical processes a fast process in the range of microseconds (exchange of monomers between the micellar and the aqueous solution phase), and a second in the range of milliseconds (total disintegration of micelles into monomers). The entire variety of micellar kinetics was discussed by Aniansson et al. (1976), and a quantitative model, considering the diffusion of monomers and micelles, and the micellar kinetics mechanisms, was reviewed in the paper by Dushkin (1998) or in the book by Joos (1999). 

The pseudophase kinetic models for speeded or inhibited bimolecular, second-order, reactions are more complex. Here the focus is on reaction between a neutral organic substrate and a reactive counterion in micellar solutions in the absence of oil (d>o = 0, Scheme 4). Micellar effects on reactions of substrates with reactive counterions are important because they illustrate the general differences of micellar effects on spontaneous and bimolecular reactions and also how specific counterion effects influence the results. Pseudophase models also work for bimolecular reactions between two uncharged organic substrates and third-order reactions, reactions in vesicles and microemulsions, which may include partitioning into and reaction in the oil region, reactions of substrates with an ionizable (e.g., deprotonatable) second reactant, and the effect of association colloids on indicator equilibria. ... 

This equation states that the interfacial molarity of counterion is eqnal to the initial molarity in the absence of added salt, first term, plus the molarity of the stoichiometric concentration of the counterion added as salt, second term. This inteipietation qualitatively fits both kinetic and chemical trapping results above about 0.2 M of added salt and indicates that the micellar interfaces (and by implication other association colloid interfaces) do not saturate with counterions as originally assumed in pseudophase kinetic models. ... 

Alkaline hydrolysis of ethyl caprylate (itself insoluble in water) yields sodium caprylate, initially at a very slow rate bnt as soon as sufficient caprylate was formed for aggregation into micelles to take place, the authors observed an exponential increase in reaction rate owing to micellar catalysis. These self-assembling surfactant strucmres may consequently provide a model system for studies of pre-biotic chemistry. The possible relevance of this process to prebiotic chemistry was emphasized by their observation that the micelles can be converted into more robust vesicles by a pH change induced by dissolved CO2, and latter on, Luisi extended this approach to vesicular systems (see Section 3.3). Kinetic models for this kind of autocatalytic dynamic systems were also developed in the literature." ... 

Here we have undertaken a study of the effects of SDS micellar systems and added organic solvents on the electrochemical behaviour of relevant antioxidants. In the last years we have taken great interest in determining the distribution of antioxidants in the emulsified systems, and for that purpose we have developed a novel kinetic method based on the reaction between a hydrophobic arenediazonium ion and the antioxidants which allows to determine the partition constants of the antioxidant between the oU, water and interfacial regions of the emulsified system [10-12]. The kinetic results are interpreted using the pseudophase kinetic model based on the hypothesis that the rates of chemical reactions are not limited by transport of reactants, i.e., that all reactants are in the dynamic equilibrium throughout the reaction. This hypothesis was experimentally proved by fitting the kinetic data to the equations derived from the pseudophase model, but determination of the diffusion coefficients of the reactants in the studied system will be very useful from the conceptual point of view to confirm or discard the mentioned idea. 

A novel kinetic model for micellar catalysis has been developed based on the assumption that the Stem layer is always saturated with respect to counterions. This means that the ground state for ions is the ion bound to the micellar surface and not the free-ion in the bulk phase. An analogy between micellar reactions and reactions catalysed by regulatory enzymes has led to the application of the Hill model to the dependence rate constants of micellar catalysed reactions upon the detergent concentration. The decrease in rate at high concentrations of detergent is interpreted in terms of substrate inhibition. ... 

The real breakthrough in terms of kinetic theory was published in 1973 by Aniansson and Wall [80, 81], who provided much more applicable kinetic equations for stepwise micelle formation using a polydisperse model. In a substantial paper two years later they were able to predict the first-order rate constants for the dis-sociation/association of surfactant ions to and from micelles (and hence residence times/lifetimes of surfactant monomers within micelles) [82]. They found values for the association and dissociation of surfactants into/from micelles (Ar and k , respectively) for sodium dodecyl sulfate (SDS) as 1 x 10 s and 1.2 x 10 mok s". Their kinetic model still remains essentially unchanged as a basis for the kinetics of micellar formation and breakdown. Modifications made to existing theory also allowed them to offer a significant thermodynamic explanation for the low enthalpy change upon micellization. 

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