Modeling of micellar-catalyzed bimolecular ionic reactions by a nonlinear Poisson−Boltzmann equation and an electrostatic free energy model

The hydrolysis reactions of crystal violet (CV) and p-nitrophenyl acetate (PNPA) by sodium hydroxide in cetyltrimethylammonium bromide (CTAB) micellar solution were studied in this work. Combined with the Boltzmann probability of ionic species in an electrostatic potential field, a model with a numerical scheme was developed based on the nonlinear Poisson−Boltzmann equation in the micelle-cell consisting of the reactants and the surfactant. The numerical solution gives the ionic species distribution in the micelle phase and the radius of the micelle-phase. The dielectric constant of the micelle-phase varies in the range of 39.8−54.4. The second-order reaction rate constants in the micelle-phase were determined using the electrostatic and dipolar free energy models. For the basic hydrolysis of CV and PNPA, the overall second-order rate constants are three to five times and 1.4 times greater than the corresponding values in water, respectively. The rate enhancement occurs due to the distribution of the reactive ionic species in the cell region and the enhancement of the Coulombic and dipolar interactions among the ionic and polar reactants.