A generalized model for the prediction of the permeability of mixed-matrix membranes using impermeable fillers of diverse geometry

Abstract

In this paper, we propose a model to predict the relative permeability of ideal MMMs, which requires the specification of only two geometrical parameters: the relative projected area available for permeation and the relative thickness of the nanofiller. The model, which was initially developed for MMMs with impermeable nano cuboids, provides excellent predictions for nanofillers with a constant relative thickness (i.e., vertical cylindrical and elliptical rods and vertical tubes) with the average prediction error not exceeding 2.1%. For nanofillers with a variable relative thickness (i.e., spheres, horizontal cylindrical and elliptical rods, horizontal tubes), the model is still excellent using the average relative thickness, which is the ratio of the volume fraction and the projected area of the nanofiller. The corresponding average prediction error does not exceed 8%. Except for spherical nanofillers, the model is superior to seven theoretical models commonly used in the literature. After introducing a simple correction factor, the prediction error decreases to 2.3% or less for spheres and horizontal cylindrical and elliptical rods.