Monte Carlo simulations of coupled diffusion and surface reactions during the aqueous corrosion of borosilicate glasses

Borosilicate nuclear waste glasses develop complex altered layers as a result of coupled processes such as hydrolysis of network species, condensation of Si species, and diffusion. However, diffusion has often been overlooked in Monte Carlo models of the aqueous corrosion of borosilicate glasses. Therefore, three different models for dissolved Si diffusion in the altered layer were implemented in a Monte Carlo model and evaluated for glasses in the compositional range (75 - x) mol% SiO₂ (12.5 + x/2) mol% B₂O₃ and (12.5 + x/2) mol% Na₂O, where 0 ≤ x ≤ 20%, and corroded in static conditions at a surface-area-to-volume ratio of 1000 m^{- 1}. The three models considered instantaneous homogenization (M1), linear concentration gradients (M2), and concentration profiles determined by solving Fick's 2nd law using a finite difference method (M3). Model M3 revealed that concentration profiles in the altered layer are not linear and show changes in shape and magnitude as corrosion progresses, unlike those assumed in model M2. Furthermore, model M3 showed that, for borosilicate glasses with a high forward dissolution rate compared to the diffusion rate, the gradual polymerization and densification of the altered layer is significantly delayed compared to models M1 and M2. Models M1 and M2 were found to be appropriate models only for glasses with high release rates such as simple borosilicate glasses with low ZrO₂ content.