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

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