Micellar rate constant

The question then becomes that of the significance of the ion-exchange and mass-law equations which successfully account for the dependence of micellar rate constants upon the concentrations of surfactant and reactive and inert counterions. It seems reasonable to continue to use these descriptions at the present time, despite uncertainties as to the location of hydrophilic counterions at the micellar surface. 

Here, k is the rate constant for hydrolysis in the Stern region, Fstem and Fmic are the volumes of the Stern region and of the micelle, respectively, AvS and Pm are the water-to-Stern region and water-to-micelle partition coefficients, respectively. Equation (6) shows that, for the assumptions described above, the micellar rate constant is given by the rate constant for the reaction in the Stern region, multiplied by a factor representing the distribution of the reactant within the micelle. Further subdivision of the micellar pseudophase is (mathematically) possible " " " but may not be warranted. 

Considering the number of factors influencing micellar rate constants, it is no wonder that not even the order of reactivity in micellar aggregates can be reliably predicted, and a separation of the micellar medium effect into its component parts would be advantageous. 

However, it was noted that the discrepancy between the micellar rate constant and the rate constant in the model compound solution was largest for 4, which was known to be more sensitive toward hydrophobic interactions than 5. In addition, the solvatochromic Ex30 probe indicated a much more hydrophobic environment and other authors similarly found systems for which a model solution only mimicking the surfactant headgroups was insufficient to reproduce properties of the micellar pseudophase. The Hammett p-value for hydrolysis of substituted 1-benzoyl-1,2,4-triazoles 6a-f could similarly not be reproduced using a model solution mimicking ionic interactions only. " ... 

To correct for nonideal behavior of the 1-propanol and tetramethylammonium at these high concentrations, a further optimization of the mimicking solution was required. A second-order solution for CTAB was elaborated using the first-order solution as a starting point. This second-order solution was found to reproduce not only the micellar rate constants for the hydrolysis of the substituted 1-benzoyl-1,2,4-triazoles 6a-f but the hydrolysis rate constant for 5 and the Ex30 value with good accuracy as well. " ... 

Despite the sometimes impressive reaction rate enhancements, second-order rate constants for most bimolecular reactions involving counterions actually decrease,with just a few remaining virtually constant or increas-ing. As discussed (vide supra), micellar rate constants for (pseudo) unimole-cular reactions are frequently lower than rate constants in water. Many of the... 

The two micellar rate constants are related in terms of the molar volume, of the... 

The effect of surfactants (cetyltrimethylammonium bromide [CTAB], sodium dodecyl sulfate [SDS]) at their critical micellar concentration significantly influences the yield and diastereoselectivity of Diels-Alder reactions of acrylates with cyclopentadiene performed in water at room temperature. A recent contribution on the effects of micelle on the Diels-Alder reaction was reported by Engberts who observed that in the cycloadditions of N-substituted maleimides with cyclopentadiene, sorbyl alcohol, and sorbyl trimethyl ammonium bromide, a micellar catalysis seems to be active, but if one considers the micellar rate constant, the neat effect on the rate constant of the reaction is remarkably small. 

The values of bimolecular rate constants (kw ) for Diels-Alder reactions of cyclopentadiene, sorbyl alcohol (20), and sorbyltrimethylammonium bromide (21) with a series of TV-substituted maleimides are 20 to 40 times lower in SDS micelles than the corresponding rate constants (k ) in aqueous phase." The low micellar rate constants (k ) have been ascribed to the relatively apolar region of micelle, in which the reactions take place. The observed apparent second-order rate constants (k pp) for the reactions of 18 with 19a to 19c are significantly increased, up to a factor of 17 (for 18 + 19c /CTABr)." These observed data have been explained in terms of PP model (i.e., Equation 3.61, Chapter 3). However, the values of k /k remain constant at 0.23 and 0.45 for the reactions of 18 with 19a to 19c in SDS and CTABr micelles, respectively. Nearly 4-fold and 2-fold lower values of k compared to k in respective SDS and CTABr micelles are largely attributed to ionic micellar reaction environment." ... 

The kinetic data are essentially always treated using the pseudophase model, regarding the micellar solution as consisting of two separate phases. The simplest case of micellar catalysis applies to unimolecTilar reactions where the catalytic effect depends on the efficiency of bindirg of the reactant to the micelle (quantified by the partition coefficient, P) and the rate constant of the reaction in the micellar pseudophase (k ) and in the aqueous phase (k ). Menger and Portnoy have developed a model, treating micelles as enzyme-like particles, that allows the evaluation of all three parameters from the dependence of the observed rate constant on the concentration of surfactant". ... 

Herein k js is the observed pseudo-first-order rate constant. In the presence of micelles, analogous treatment of the experimental data will only provide an apparent second-order rate constant, which is a weighed average of the second-order rate constants in the micellar pseudophase and in the aqueous phase (Equation 5.2). 

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... 

Studies of micellar catalysis of himolecular reactions of uncharged substrates have not been frequent" ". Dougherty and Berg performed a detailed analysis of the kinetics of the reaction of 1-fluoro-2,4-dinitrobenzene with aniline in the presence of anionic and nonionic surfactants. Micelles induce increases in the apparent rate constant of this reaction. In contrast, the second-order rate constant for reaction in the micellar pseudophase was observed to be roughly equal to, or even lower than the rate constant in water. 

Unfortunately, more detailed kinetic studies aimed at the determination of the second-order rate constants in the micellar pseudophase have not been published. 

Herein [5.2]i is the total number of moles of 5.2 present in the reaction mixture, divided by the total reaction volume V is the observed pseudo-first-order rate constant Vmrji,s is an estimate of the molar volume of micellised surfactant S 1 and k , are the second-order rate constants in the aqueous phase and in the micellar pseudophase, respectively (see Figure 5.2) V is the volume of the aqueous phase and Psj is the partition coefficient of 5.2 over the micellar pseudophase and water, expressed as a ratio of concentrations. From the dependence of [5.2]j/lq,fe on the concentration of surfactant, Pj... 

Table 5.2 shows that the partition coefficients of 5.2 over SDS or CTAB micelles and water are similar. Comparison of the rate constants in the micellar pseudophase calculated using the... 

Table 5.4. Apparent second-order rate constants (ycjfp) for the reaction of 5.1c with 5.2 in micellar solutions of Co(DS)2, Ni(DS)2, Cu(DS)2 and Zn(DS)2 compared to the second-order...

Further evidence for an increased efficiency of complexation in the presence of micellar aggregates with bivalent metal counterions is presented in Table 5.4. The apparent rate constants of the reaction of 5.1c with 5.2 in the presence of micelles of Co(DS)2, Ni(DS)2, Cu(DS)2 and Zn(DS)2 are compared to the rate constants for the corresponding bivalent metal ion - dienophile complexes in the absence of micelles. The latter data are not dependent on the efficiency of the formation of the catalyst - dienophile complex whereas possible incomplete binding will certainly be reflected in the former. The good correlations between 1 and and the absence of a correlation between and... 

Calculations usirig this value afford a partition coefficient for 5.2 of 96 and a micellar second-order rate constant of 0.21 M" s" . This partition coefficient is higher than the corresponding values for SDS micelles and CTAB micelles given in Table 5.2. This trend is in agreement with literature data, that indicate that Cu(DS)2 micelles are able to solubilize 1.5 times as much benzene as SDS micelles . Most likely this enhanced solubilisation is a result of the higher counterion binding of Cu(DS)2... 

Comparison of the micellar second-order rate constant of 0.21 M" s with the rate constants for the... 

In order to obtain more insight into the local environment for the catalysed reaction, we investigated the influence of substituents on the rate of this process in micellar solution and compared this influence to the correspondirg effect in different aqueous and organic solvents. Plots of the logarithms of the rate constants versus the Hammett -value show good linear dependences for all... 

Assuming complete binding of the dienophile to the micelle and making use of the pseudophase model, an expression can be derived relating the observed pseudo-first-order rate constant koi . to the concentration of surfactant, [S]. Assumirg a negligible contribution of the reaction in the aqueous phase to the overall rate, the second-order rate constant in the micellar pseudophase lq is given by ... 

Figure 4 indicates the effect of the CTAB concentration on the rate constant of the complexes of 29 and 32. The CMC of CTAB is near 1 x 10 3 M. Below CMC, the rates cannot be measured because of insolubility of the ligands. Although unmeasured, the rates of the 29 and 32 complexes must be greatly enhanced in the presence of CTAB micelles up to CMC, but further increase of the micelle concentration above CMC cause a rate decrease. This type of micellar effect can be seen in many micellar reactions 27). Hence, it should be noted that the rate constants in Table 3 would be several times larger if they are measured by using a lower concentration of CTAB than 5 x 10-3 M. 

Figure 5a indicates the effect of the CTAB concentration on the rate constants of the complexes of 38b and 38c. In the case of the water soluble 38b ligand, the rate increases with increasing CTAB concentration up to a saturation level. This type of saturation kinetics is usually interpreted to show the incorporation of a ligand-metal ion complex into a micellar phase from a bulk aqueous phase, and the catalytic activity of the complex is higher in the micellar phase than in the aqueous phase. In the case of lipophilic 38c, a very similar curve as in Fig. 4 is obtained. At a first glance, there appears to be a big difference between these two curves. However, they are rather common in micellar reactions and obey the same reaction mechanism 27). 

Table 4.16 Micellar catalysis of Diels-Alder reactions of cyclopentadiene (1) with 3-(p-substituted phenyl)- -(2-propen-1-one (113) in water at 25 °C. Relative rate constants ( rei) to the reactions performed in sole water...

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