Analytical models for concentration profiles after single and double reversals of the electric field during K⁺-Na⁺ field assisted ion exchanges in glass

Analytical models are developed which describe the K⁺ ion concentration profiles after single and double reversals of the electric field during K⁺-Na⁺ field assisted ion exchanges in glass. The models assume that drift transport is the dominant transport process and that, to first order, diffusion effects can be ignored. Concentration dependent, mobility ratio effects are included in the model. The expressions are compared with computer simulations based on the full drift-diffusion equation with nonlinear self-diffusion coefficients. The work provides a greater understanding of certain experimental results that were recently obtained by the same authors.