Simulation of internal diffusion for a selective ternary exchange of equally charged counterionsстатья
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Дата последнего поиска статьи во внешних источниках: 10 августа 2018 г.
Местоположение издательства:Road Town, United Kingdom
Первая страница:1361
Последняя страница:1367
Аннотация:Variants of the exchange of three equally charged counterions [(B + E)/ℛA (sorption)] at different values of the diffusion coefficients and selectivity of the counterions were considered in terms of a model previously developed by the authors for the kinetic process in a selective ternary system. The basic assumption of the model is that, during the exchange process in grains of a selective ionite [accompanied by chemical reactions of B, E, and A counterions with fixed groups ℛ: ℛA + (B + E) ⇄ (ℛB + ℛE) + A], these counterions can exist in fixed and free states. Counterions i are immobile in the bound state (ℛi) and diffuse in the free state. The model involves mass balance equations for all ions, including the coion Y; the ionic fluxes involved in the equations are presented by the Nernst-Planck relations. The influence of the association constants (KRA, KRB, and KRE) and the diffusion coefficients (DA, DB, and DE) of the counterions on the character of the concentration waves of the diffusing components B, E, A, and Y and on the rate of the internal diffusion selective kinetic process in grains was considered on the basis of a theoretical analysis of computer simulation results. The effects of the main factors on the concentration waves in the kinetic process were represented in the concentration-radius-time pseudo-three-dimensional space. It was found that the distinctions observed in the profiles of the concentration waves of the counterions and the differences in the rates of the kinetic processes are due to different combinations of the diffusion coefficients and selectivity constants. It was shown that these factors have an influence on the height of the maximum in the sorption-intermittent desorption kinetic curve, an anomalous effect that is occurred only in the exchange-sorption regime and for only one of the two entering counterions (B or E). In this case, early in the process, the displaced counterion diffuses counter to the concentration gradient of the more mobile selectively entering counterion (the concentration front is displaced toward the grain center). This effect is due to the action of the electric field arising during the process.