On the role of defects in modelling approaches for thin film gas barrier coatings on polymer substrates: I. Model development

We present a method to model the gas permeation through silicon-oxide thin film coatings that are afflicted with nanoscale defects. With it, we are able to give an estimation of the diffusion coefficient in bulk by subtracting the influence of the defects. The model is based on data obtained from positron annihilation spectroscopy, which is processed to yield possible defect allocation patterns of the coatings. For a systematic evaluation of these patterns, a path through the coating is calculated and then subjected to in-depth analysis to evaluate the used approach as well as to interpret the results for insights on the permeation mechanisms. The model appears to function as intended and no unexpected behaviour is observed. The defect volume share is overestimated, which can be retraced to the underlying algorithm, and a correction method is applied to the resulting bulk diffusion coefficient. The model gives reasonable results both for oxygen and water vapor permeation. These results can be used in following works that build on the presented model.