Reaction-Diffusion Transport Model To Predict Precursor Uptake And Spatial Distribution In Vapor-Phase Infiltration Processes

Vapor-phase infiltration (VPI) has emerged as a scalable process for transforming polymer products into a variety of organic-inorganic hybrid materials with potential applications to a number of commercial industries. However, the fundamental transport kinetics of VPI are still not well understood. Most explorations to date have relied on simple Fickian diffusion models for VPI transport. However, these Fickian diffusion models often fail to entirely capture the physical phenomena of VPI because of the complex convolution of diffusion and reaction processes. In this work, a reaction-diffusion model is developed that provides additional insight into how the presence of reactions between polymers and metal-organic precursors modifies the transport behavior of the metal-organic VPI precursor through the infiltrated polymer. From this model, parameters such as the second-order rate constant for the reaction between the precursor and polymer and a diffusive hindering factor can be extracted. The model is shown to both fit well to physical measurements and, more critically, predict experimental outcomes. Additionally, nondimensionalization is employed to create domain maps based on a wide variety of VPI parameters. The resulting domain maps showcase the breadth of behaviors captured by this reaction-diffusion model for VPI.