Effect of charge and anisotropic diffusivity on ion exchange kinetics in nuclear waste form materials

Motifs of radionuclide absorption particles (absorbers or fillers) for the nuclear waste treatment usually have crystal structures with nano-sized tunnels for fast ion diffusion. On the other hand, the accumulation of ions generates an electric field which affects the ion diffusion. Therefore, the strong anisotropic kinetic properties and the electric field affect ion exchange kinetics, especially in an assembly of these particles which may block the fast diffusion tunnels for each other. In this work, we developed a mesoscale model to describe the effect of anisotropic kinetic properties and electric field on ion exchange kinetics. With the model we simulated the effect of anisotropic diffusivity, electrochemical potential, particle morphology, size and aggregation on ion exchange kinetics during batch experiments. It is found that (1) ion exchange results in charge accumulation inside the particle because different ions have different diffusivities and different diffusion driving forces. The electric neutrality is not preserved; (2) the electric field speeds up the slower diffusion ions (either uptake or release) and slows down the faster diffusion ions to reduce charge accumulation and maintains charge neutrality; (3) the ion exchange becomes very slow at the later stages because (a) diffusion driving force (electrochemical gradient, Cs+ concentration in the solution and Na+ inside the particle) continuously decreases, as observed in batch experiments; and (b) the diffusivity decreases due to the Cs+ concentration dependence of ion diffusivity. This can explain the observed experimental phenomena that the radionuclide capacity usually cannot be reached; (4) for needle-like particle and their clusters, both surface area and diffusion distance along the direction with the fastest diffusivities have significant impact on the ion exchange kinetics.