Spatiotemporal Patterns and Nonclassical Kinetics of Competing Elementary Reactions:  Chromium Complex Formation with Xylenol Orange in a Capillary

Abstract

An experimental investigation of chemical reaction fronts, created by an initial separation of reactants, is reported for a system of two competing reactions. Spatiotemporal patterns are observed experimentally for the competing reaction front and are accounted for quantitatively by a reaction-diffusion model. We use the reaction of xylenol orange with Cr3+ in aqueous solution. Different oligomers of Cr3+ provide the two kinetically different species that react competitively with xylenol orange. The parameters that determine whether pattern formation is observable at the front are the ratios of (1) the microscopic reaction constants of the competing reactions and (2) the concentrations of the competing species. Under the parameter values studied, which allowed clear spatiotemporal separation of the two competing reactions, we find that the behavior of the reaction front at early times follows a perturbation theory developed for a simple elementary A + B → C reaction with initially separated reactants. The global reaction rate, observed over the entire time scale of the experiments, is highly non-monotonic. Overall, with no free parameters, our theoretical model is quantitatively consistent with the experimental observations of the spatiotemporal patterns, the unusual scaling laws, and the crossover behaviors. The geometrical constraints and nonclassical behavior of the reaction rate allow a quantitative determination of the reaction probability of the chromium ion monomer relative to that of the higher order oligomers.

Front Dynamics during Diffusion-Limited Corrosion of Ramified Electrodeposits

“…as t → ∞, with |η| < ∞ fixed (38) and by matching we conclude A ′ (∞) = A 1 , where A 1 (ν) ≡ A ′ (0)/2 can be expressed in terms of ν(q) using Eq. (27). In light of Eq.…”

“…Reaction−diffusion processes have been the subject of intense and continuous interest since the work of Smoluchowski. − A crucial feature of many such processes controlling pattern formation and reaction efficiency is the “reaction front”, a dynamic but localized region where reactions are most actively occurring and which separates regions rich in the individual reactants. The simplest theoretical model of a reaction front, introduced more than a decade ago by Gálfi and Rácz, is the “mean-field” model for two initially separated species A and B reacting to produce an inert species C. Since then, the case of two diffusing reactants A and B has been thoroughly studied analytically − and numerically, − and some predictions of the mean-field model have been checked in the experiments. − …”

Nonlinear phenomena and qualitative evaluation of risk of clogging in a capillary microreactor under imposed electric field

“…The authors explained the observed splitting of the reaction zone as an effect of the immobile component. Taitelbaum et al [4] and Yen et al [5] theoretically and experimentally studied the competing reactions of Cr 3+ ions with xylenol orange and the corresponding pH dependences of the distribution of the reaction product. Reaction front splitting and temporary nonmonotonic behavior of the global reaction rate was observed.…”