Computer Simulation of Uphill Diffusion in Ternary Ionic System

Abstract

In multi-component ionic diffusion systems, uphill diffusion is frequently observed. The conditions for the development of uphill diffusion were investigated by computer simulation of ion exchange between a glass containing two cations (A, B) and a molten salt containing the third cation (C). The following conclusions are obtained. (1) The uphill diffusion of B ion is observed when DA>DB>DC or DA>DC>DB, if all diffusion coefficients D's are independent of concentration. (2) This uphill diffusion behavior is affected by the molar ratio of A to B in a mother glass. In the simulated ion exchange systems that were investigated, the uphill diffusion was prominent when the molar fraction of B ion is around 0.25. (3) The concentration dependence of D does influence the distribution of ions, however, the relationship between three diffusion coefficients is more important condition for the development of the uphill diffusion. Ion exchange experiments in (Na, Rb) glass/(K) salt and (Na, K) glass/(Tl) salt systems were carried out to confirm the results of simulation. The uphill diffusion of Rb ion and K ion was observed as predicted by the simulation. The diffusion behavior of ions in glass during the ion exchange process for the fabrication of gradient index lens was also investigated by the computer simulation. The progression of ion concentration profiles during this ion exchange process, especially the development of the uphill diffusion of Tl ion in the initial stage of this process, was well reproduced in this simulation study.