Anomalous Kinetics of Ion Exchange in Heterogenous Systems — A Computer Simulation

Abstract

The kinetics of ion exchange in heterogenous mixtures in a well stirred batch system, where film diffusion is the rate determining step was investigated by a computer simulation. Heterogeneity of the different ion exchanger particles in the mixture with respect to their diameters, their ion exchange capacities and their separation factors was considered. The distribution of these properties was assumed to be given by a normal frequency distribution. If sufficient ion exchanger is added to the solution to remove a given counter ion species almost completely, each type of the above heterogeneities will produce an anomalous kinetic behaviour of the system. The faster reacting particles overshoot their equilibrium values initially considerably and have to release subsequently part of these ions in favor of the slower reacting particles. This redistribution of the counterions between the particles via the solution phase, is however, extremely slow and balanced in such a way that the concentration of the counterions in solution remains during this time period constant and exhibits already its final equilibrium value. The kinetic behaviour of such systems can, therefore, not be characterized completely by monitoring only the solution concentration as a function of time. The implications of this effect for sorption measurements involving soils are discussed.counterfoil species almost completely [11]. In this case the smaller and thus faster reaction particles will take up initially an excess of ions at the expense of the large particles. After a relatively short time, however, the smaller particles have to release this excess in favor of the larger particles (redistribution phase), because in equilibrium the equivalent fraction of the ions has to be the same in all size fractions of the otherwise homogenous ion exchanger. During this redistribution phase, however, which lasts orders of magnitude longer than the initial phase, the concentrations of the ions in solution remains all the time constant and corresponds almost exactly to the equilibrium concentration.The purpose of the present investigation was to apply the theory of the kinetics of ion exchangers given earlier [11] also to systems involving particles which exhibit a distribution of their diameters, their ion exchange capacities or their separation factors. In the following we will solve the corresponding rate equations numerically, explain the effect of various parameters on the presence of an anomalous kinetic behaviour, and discuss possible implications on the sorption kinetics in soil systems.