Modeling of Structure and Transport in Mixed-Matrix Membranes for Gas Separation

Mixed matrix membranes combine the superior separation efficiency of inorganic fillers with the processability of polymeric materials and appear to be quite promising in the field of demanding separation problems. However, the resulting performance regarding selectivity is usually far less than the expected one, attributed among other factors to limited affinity between polymer and inorganic materials and the concomitant reduction of adherence of the two phases. This allows the formation of non-selective voids around the fillers, which can destroy the selectivity of the membrane, allowing the gases to follow pathways through these voids. The problem can be addressed by either filling the empty space with a suitable interphase material or eliminate it  using appropriate functionalization at the interface. In both cases, the design and preparation of such composite materials relies heavily on the understanding and quantifying the relationship between the effective transport coefficient and the configuration of the material.

In this work, a numerical model is developed that allows the prediction of the effective diffusivity in composite membranes, taking into account the different diffusion and solubility constants in each phase. The algorithm involves computer-aided stochastic reconstruction of the membrane in two and three dimensions by randomly placing non-overlapping inclusions within the working domain, yet allowing free overlapping of the interphase layers. The size of the inclusions can be uniform or sampled from a given distribution, while their shape can be varied in two and three dimensions (spherical, elliptic, or circular). The width of the interphase layer can vary according to the physicochemical affinity between the inclusions and the polymer.

The permeability and selectivity of this composite membrane is numerically computed using a method that is adapted to the particular reconstructed material. Specifically, the resistor network approach is used following a suitable mapping of the composite material onto a regular network. It is found that the permeability of a composite membrane is a strong function of the filler-loading of the composite, the width of the interphase layer, and the diffusivities and solubilities in the three phases. The shape of the inclusions as well as their orientation in the case of elliptical particles are found to affect strongly the membrane permeability. Moreover, different spatial organizations of the particles in the polymer phase have been examined and it was found that the type of particle agglomeration can also have a significant effect on the membrane permeability. These results elucidate the utilization of the inclusions, which is evidently the key factor in the design and eventual performance of mixed matrix membranes.