Thermodynamics and Kinetics of Silicate Glasses submitted to Binary Ion Exchange: Equilibrium Conditions and Interdiffusion Kinetics

Abstract: Ion exchange processes between an ion reservoir and a solid matrix are modeled under the assumption that near interface volumes reach equilibrium in a much faster time than the overall ion exchange process time while, in the bulk of the solid matrix, ions are transported by an interdiffusion kinetic process. Ion exchange equilibrium conditions are initially established according to classical thermodynamics. The result is defined in terms of the chemical potentials of exchanging ionic species. The proposed original derivation is performed making use of the thermodynamics of subsystems to determine near-surface equilibrium concentrations and ion exchange isotherms. Interaction energies of the exchanging ions in the glass are determined through the thermodynamic factor n, which is a parameter of the ion exchange isotherm. The kinetics of the ion exchange process in silicate glass is discussed to find connections with the near-surface equilibrium condition. The flux equation for the incoming ions in the glass is written in the form of a Fick equation with a concentration-dependent interdiffusion coefficient incorporating the thermodynamic factor n. It has been found that the thermodynamic factor of the interdiffusion coefficient is related to the interaction energy of the exchanging ions in the glass allowing a new approach to the interpretation of past experimental results. Surface concentration has been found substantially connected to the second parameter of the ion-exchange isotherm which is the equilibrium constant K and significatively influenced by the chemical composition of the ion reservoir (the molten salt bath). Further treatment of kinetics of ion-exchange within the framework of non-equilibrium thermodynamics allows the interpretation of the thermodynamic factor as a function of incoming ions concentration in the glass matrix.