Gas Membrane Characterization Via the Time-Lag Method for Neat and Mixed-Matrix Membranes

Abstract

Separation technologies with polymeric membranes are widely studied and have a wide range of applications. The membrane's heart is a dense selective layer whose permeability should strongly depend on the permeating species' properties. In turn, permeability depends on the diffusivity and solubility of the permeating species in the selective layer, which are considered intrinsic properties of the polymer forming the selective layer. When developing new membrane materials, the ultimate objective is to exceed the famous "upper bound" limit by achieving simultaneously higher selectivity and higher permeability. This objective is impossible without a reliable and accurate characterization method to determine the selective layer's intrinsic transport properties. The time-lag method is the most common membrane characterization technique, initially developed for polymeric membranes. However, as the membrane technology and material science advance, the selective layer structure becomes more complex and not limited to organic polymers. As a result, the time-lag method needs to be reviewed and adapted to these more complicated cases, which was the main objective of this thesis. Numerical simulation of dynamic gas permeation experiments is a powerful tool to examine different aspects of the time-lag method. Therefore, we have established a comprehensive variable-mesh finite-difference scheme, which was used throughout the thesis. It allowed us to investigate the effect of different random and resolution errors and an extrapolation error on the resulting time lag of an ideal membrane. We then considered more complex systems, particularly those of glassy polymers and mixed matrix membranes, to investigate the effect of different transport mechanisms on the results of dynamic and steady-state gas permeation experiments. In parallel, we also focused on developing a novel gas permeation system that would monitor dynamic gas permeation experiments based on pressure decay at the feed side. All the existing constant-volume gas permeation systems rely on monitoring pressure to rise at the membrane's permeate side. Although this work is still ongoing, we have made considerable progress. Among the numerous contributions made through this thesis, there are three of particular significance. We have developed an analytical model to predict mixed matrix membranes' relative permeability with the uniformly dispersed non-permeable fillers of different shapes. The model requires three structural parameters arising from the filler's shape and size, and it is superior to all existing analytical models, including the famous Maxwell model. We have also demonstrated that the diffusivity of mixed matrix membranes determined by the time-lag method depends on the number of layers of dispersed particles. In the limiting case of a single layer of uniformly impermeable fillers, it is possible for the diffusivity determined by the time-lag method to be greater than that of the host polymer, which might appear as counterintuitive in the absence of defects at the polymer-particle interface. In the case of glassy polymers, it is possible to observe an upward deviation from the steady-state flux, resulting from a non-instantaneous equilibrium between permeating species in Henry's and Langmuir adsorption sites.