(170d) Modeling Of Diffusion Processes—Implementation Of Infinite Series Solutions

Polyesters, including poly(ethylene terephthalate) (PET), comprise the main materials used in CO₂ packaging applications. More advanced polyester resins are currently under consideration to expand beyond PET’s performance. While transport evaluation and screening of polyester resins can be performed through a rapid pressure decay method, evaluation of applicable model parameters is challenging. Penetrant uptake can be described through solutions of the time-dependent diffusion equation. This talk illustrates the technique of fitting infinite series solutions containing a constant effective diffusion coefficient to experimental kinetic sorption data using a widely available non-linear least squares fitting program in MATLAB^®. Various sorption kinetic curves will be considered for modeling cases ranging from simple Fickian diffusion in an infinite sheet with constant boundary conditions to more complex diffusion problems involving Bessel functions and non-repeating roots of transcendental equations. Applications for fitting complex CO₂ kinetic sorption data in a polyester will also be explored. For such data, the Berens-Hopfenberg model coupled with a variable surface concentration is needed to accurately describe the non-Fickian long-term relaxations induced by CO₂ conditioning. The diffusion coefficient determined from the model will be combined with equilibrium sorption data and compared to actual steady-state permeation results. The analysis and illustrated procedure provides researchers with a powerful tool for extracting diffusion coefficient information from experimental data.