The Pseudophase Ion-Exchange PIE Model

The PIE model is essentially an extension of the PP model and therefore contains all the assumptions involved in the PP model and a few more, as clearly expressed in several excellent reviews. These additional assumptions may be summarized as follows  

The degree of counterion ionization remains constant (i.e., there is a strictly 1 1 ion exchange) irrespective of ion type or concentration or of surfactant concentration. 

The micellar surface region can be thought of as an ion-exchange resin in which ion exchange processes occur in the same way as for a resin. 

In view of the PIE model, the concentrations of a reactive anion, Y (anionic reactant), and an inert anion, X (counterion of cationic micelle), in the micellar and aqueous pseudophases are governed by an ion-exchange equilibrium process. Equation 3.18  

The values of my at different [D ] values can be calculated from Equation 3.24 for the given values of Kx and p, and these my values can be subsequently used to calculate kM and Kg from Equation 3.12 (with mR representing my), using the nonlinear least-squares technique. This is the general practice used in applying the PIE model for kinetic analysis of the rates of appropriate bimolec-ular reactions.  

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The combination of the pseudophase assumption with mass action binding constants of substrates and ion exchange of reactive and nonreactive counterions is called the pseudophase ion-exchange (PIE) model [10,48,66]. It successfully fits the kinetics of many bimolecular reactions and also shifts in apparent indicator equilibria in a variety of association colloids, especially reactions between organic substrates and inorganic ions in normal micelles over a range of surfactant and salt concentrations and types (up to about 0.2 M). It has also been successfully applied to cosurfactant-modified micelles [77,78], O/W microemulsions [79-81], and vesicles [82]. 

Second-order reactions and the pseudophase ion exchange (PIE) model... 

Khan, M.N., Ismail, E. An apparent weakness of the pseudophase ion-exchange (PIE) model for micellar catalysis by cationic surfactants with nomeactive counterions. J. Chem. Soc., Perkin Trans. 2. 2001, 1346-1350. 

The effects of micelles of cetyltrimethylammonium bromide (CTABr), tetradecyl-trimethylammonium bromide (TTABr) and sodium dodecyl sulfate (SDS) on the rates of alkaline hydrolysis of securinine (223) were studied at a constant [HO ] (0.05 m). An increase in the total concentrations of CTABr, TTABr and SDS from 0.0 to 0.2 M causes a decrease in the observed pseudo-first-order rate constants (kobs) by factors of ca 2.5, 3, and 7, respectively. The observed data are explained in terms of pseudophase and pseudophase ion-exchange (PIE) models of micelles. Cationic micelles of CTABr speed attack of hydroxide ion upon coumarin (224) twofold owing to a concentration effect. ... 

For the first case, one can use the so-called pseudophase ion exchange (PIE) model.The PIE model is based on the Menger-Portnoy model but additionally allows for ion exchange to occur in the micellar Stern region where a reactive counterion competes with nonreactive counterions (Scheme 5). 

Nearly 19- and 26-fold lower values of k than k for pH-independent hydrolysis of 2 in CTABr and SDS micelles, respectively, are explained in terms of high concentration of ionic head groups in Stem layer and electrostatic effect on partially anionic transition state. However, such an electrostatic effect cannot explain nearly 190- and 65-fold lower values of k, compared to k for pH-independent hydrolysis of 3. It has been suggested that the influence of hydro-phobic chains is more pronounced for 3 than for 2. But the nearly 3-fold larger value of k i for 3 in SDS micelles than in CTABr micelles remained unexplained. The deaease in kw for 2 from 4.8 x lO- to 2.4 x lO- seer with the increase in [NaCl] from 0.0 to 0.5 M in SDS micelles has been attributed to increased counterion binding (i.e., P value in pseudophase ion-exchange [PIE] model for-... 

Effects of cationic (cetylpyridinium chloride, CPC) and anionic (SDS) micelles on the rate of reaction of chromium(VI) oxidation of formaldehyde have been studied in the presence and absence of picolinic acid. Cationic micelles (CPC) inhibit whereas anionic micelles (SDS) catalyze the reaction rates that could be attributed to electrostatic interactions between reactants (cationic metal ions and catalyst H+) and ionic head groups of ionic micelles. Experimentally determined kinetic data on these metaUomicellar-mediated reactions have been explained by different kinetic models such as pseudophase ion-exchange (PIE) model, Monger s enzyme-kinetic-type model, and Piszkiewicz s cooperativity model (Chapter 3). The rate of oxidation of proline by vanadium(V) with water acting as nucleophile is catalyzed by aqueous micelles. Effects of anionic micelles (SDS) on the rate of A-bromobenzamide-catalyzed oxidation of ethanol, propanol, and n-butanol in acidic medium reveal the presence of premicellar catalysis that has been rationalized in light of the positive cooperativity model. ... 

The occurrence of ion exchange in ionic miceUar-mediated ionic or semiionic reactions has been unequivocally established (References 12, 13, 16, 23, 24, 36, 39 cited in Chapter 3). The expected kinetically effective ion exchange in the present reacting system is Br/HO. Pseudophase ion exchange (PIE) model can lead to Equation 7.81... 

Pseudo-first-order rate constants (kobs) for alkaline hydrolysis of 4-nitrophthal-imide (6), in the absence of micelles, obeyed Equation 3.27 with kon = 46.3 x 10- semonotonic decrease with the increase in [CTABrlj at a constant value of [NaOH] and [6]. These results could be explained in terms of both PP and PIE models with almost equal precision (i.e., with similar residual errors and least-squares values). Although the value of k /kw is nearly 25 Af, the value of k o is apparently so low that the increase in [HOm ] due to ion-exchange Br/HO has apparently no effect on the rate of alkaline hydrolysis of 6 in the micellar pseudophase. Thus, the use of PIE model in this and related reaction systems seems to be meaningless. 

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