A model for diffusive transport in microporous mixed matrix membranes is given which utilizes the Maxwell-Stefan formulation. The multicomponent adsorption of nitrogen and methane is predicted by Henry's law, the extended Langmuir model, and ideal adsorbed solution theory. The transport model in the limit of facile exchange and weak confinement of the adsorbates is applied to the case of a mixed matrix membrane containing clinoptilolite selective flakes dispersed in a microporous silica matrix and is solved for each adsorption model by the method of finite elements. The extended Langmuir model is then used along with loading-dependent Maxwell-Stefan diffusivities to predict the performance of the same mixed matrix membrane under these assumptions. Finally, a calculation is done to predict the performance of a microporous silica/silicalite mixed matrix membrane for the separation of para- and ortho-xylene under the assumption of Henry's law. The results are compared with an existing model for transport through such membranes. It is found that membrane permselectivity is a function of operating pressure for mixed matrix membranes obeying the extended Langmuir and ideal adsorbed solution theory models with facile exchange and weak confinement. Likewise, the performance is pressure-dependent for membranes obeying the extended Langmuir model with loading-dependent Maxwell-Stefan diffusivities. The causes of this pressure dependence are explored in terms of adsorption selectivity and the permeability balancing between matrix and flake which is important for mixed matrix membranes. It is shown that inclusion of the more realistic models for adsorption can result in predictions for membrane performance that vary considerably from those given by models that rely only on Henry's law and constant diffusivity.
Bibliographical noteFunding Information:
JAS gratefully acknowledges that this material is based upon work supported under a National Science Foundation Graduate Research Fellowship. This work was also supported by NSF NIRT Grant NSF/CTS-0403574.
- Maxwell-Stefan diffusion
- Mixed matrix membrane
- Selective flake