Defect-Dominated Gas Permeation through High-Barrier Coatings Modeled with Fractional Diffusion Equations

Thin-film encapsulation is critical in many important engineering applications. Accurate theoretical models of gas permeation through high-barrier films are needed for the prediction of steady-state permeation rate and extraction of characteristic mass transport parameters. On the other hand, microscopic defects within the barrier coating usually cause anomalous dynamics in mass transport, which deviates from existing permeation models based on Fick’s law. Utilizing fractional diffusion equations, an improved model with higher accuracy was developed. The model was tested with gas permeation data from various barrier structures with different permeants, confirming its advantages in data fitting as well as steady-state forecasting. Furthermore, through a comparative modeling analysis of H2O vs CO2 permeation through the alumina barrier film, the space-fractional order was revealed as a possible indicator of the uniformity of defect distribution during permeation, thereby suggesting a new way of looking at the degradation of alumina due to water vapor permeation.