On the limitation of the time-lag method for characterizing mixed-matrix membranes embedding filler particles of different permeability

Abstract

The effective diffusivity, permeability, and solubility coefficients of the materials for gas separation membranes are usually determined by the time-lag method in a single dynamic gas permeation experiment. The term “effective properties” implies that they are independent of the thickness of the film used to determine these properties. However, this may not always be the case. In this paper, we modelled time-lag experiments by numerically solving the governing partial differential equation for ideal mixed matrix membranes (MMMs) consisting of uniformly dispersed cuboid particles of the same shape, orientation, and size in a continuous polymer phase. An ideal MMM is comprised of a large number of identical, repeatable elementary units where each elementary unit consists of a centrally-located filler particle embedded in a polymer matrix. Contrary to a neat polymer membrane, the simulated time lag of an ideal MMM is not directly proportional to the square of the membrane thickness, expressed by the number of repeatable layers in the main diffusion direction. The effective diffusivity of MMM from the simulated time lag can be greater or smaller than the constant ratio of MMM’s effective permeability and solubility. The difference depends on the relative transport coefficients of the dispersed particles compared to those of the continuous polymer phase. It decreases with the number of repeatable layers and becomes negligible for five or more layers.