Entropy Production During Ion Exchange of Glass

The thermodynamics and kinetics of interdiffusion are analyzed for the case of glass ion exchange, a process by which alkali ions from a glass inter-diffuse with different, usually larger, alkali ions from a surrounding salt bath. The spontaneity of the ion exchange reaction is driven by entropy production. This paper details the first derivation and quantification of the entropy produced during this process. We present models for the evolution of the ion concentration profile for both common and extreme conditions, validate against experimental literature, and derive the entropy produced due to ion exchange as a function of time, temperature, composition, diffusivity, and glass and salt bath dimensions. Results reveal that when considering typical industrial parameter sets, the entropy produced in the glass accounts for <10% of the total entropy production, with the entropy produced in the salt bath being the dominant factor driving reaction spontaneity. Using the equations derived in this work, one can calculate concentration profile and entropy production for a two-ion interdiffusion process between a low-viscosity liquid and materials including, by not limited to, glass-forming systems.