Rigorous Models for Vapor Diffusion in Polymers with\nImmobilization and Chemical Potential Gradients

Two key phenomenaimmobilization\nand concentration-dependent\nmixing free energiessimultaneously alter the sorption thermodynamics\nand diffusion of vapors in materials. This interrelation is leveraged\nto fit a unified model simultaneously capturing both sorption dynamics\nand the equilibrium isotherms. This transport model incorporates quasi-equilibrated\nimmobilization reactions and considers Fick’s law rigorously\nin terms of chemical potential gradients rather than concentration\ngradients. Five material case studies are discussed with varying characteristics,\nincluding fillers that provide sites for surface sorption, pores for\ncapillary condensation, and apparent clustering or pooling at high\nvapor concentrations. Each case study illustrates that intrinsic diffusivity\nis constant, while the effective diffusivity changes predictably because\nof immobilization or changing free energies of mixing.