Abstract
A coupled diffusion model based on continuum thermodynamics is developed to quantitatively describe the transport properties of glassy thin films during physical aging. The coupled field equations are then embodied and applied to simulate the transport behaviors of O2 and CO2 within aging polymeric membranes to validate the model and demonstrate the coupling phenomenon, respectively. It is found that due to the introduction of the concentration gradient, the proposed direct calculating method on permeability can produce relatively better consistency with the experimental results for various film thicknesses. In addition, by assuming that the free volume induced by lattice contraction is renewed upon CO2 exposure, the experimental permeability of O2 within Matrimid® thin film after short-time exposure to CO2 is well reproduced in this work. Remarkably, with the help of the validated straightforward permeability calculation method and free volume recovery mechanism, the permeability behavior of CO2 is also well elucidated, with the results implying that the transport process of CO2 and the variation of free volume are strongly coupled.
Highlights
The transport property of thin films is one of the most concerning issues for many engineering applications, such as packaging, painting, sensor development, and membrane separation for separating the different components of gaseous streams [1]
McCaig and Paul et al [20,21] have shown that the experimental oxygen permeability data for thin BPA–BnzDCA films (0.25–33 μm) are remarkable. They have proved that the free volume reduction associated with physical aging behind these data occurs by two distinct simultaneous mechanisms, i.e., one is thickness-dependent, which is expected for a vacancy diffusion process, while the other is independent of thickness which is hard to describe by the diffusion mechanism
Since the flux of gas concentration is analyzed, the permeability is expressed as an integral function of the concentration gradient, free volume, and free volume gradient, which differs from the existing free volume-based method
Summary
The transport property of thin films is one of the most concerning issues for many engineering applications, such as packaging, painting, sensor development, and membrane separation for separating the different components of gaseous streams [1]. As amorphous glassy solids, these membranes are in a non-equilibrium state after the materials fabrication, during which they were cooled from above to below their glass transition temperature (Tg ). The process is known as physical aging. This gradual approach to equilibrium affects many properties of amorphous polymers, such as specific volume, permeability, and mechanical response, as well as microstructural or molecular scale properties [3,4,5,6]. How to elucidate the effect of physical aging and properly evaluate the behavior of gas separation membranes is essential to ensure satisfactory performance of the films over long service periods for the membrane separation industry
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