Over the past three decades, mixed-matrix membranes (MMMs), comprising an inorganic filler phase embedded in a polymer matrix, have emerged as a promising alternative to overcome limitations of conventional polymer and inorganic membranes. However, while much effort has been devoted to MMMs in practice, their modeling is largely based on early theories for transport in composites. These theories consider uniform transport properties and driving force, and thus models for the permeability in MMMs often perform unsatisfactorily when compared to experimental permeation data. In this work, we review existing theories for permeation in MMMs and discuss their fundamental assumptions and limitations with the aim of providing future directions permitting new models to consider realistic MMM operating conditions. Furthermore, we compare predictions of popular permeation models against available experimental and simulation-based permeation data, and discuss the suitability of these models for predicting MMM permeability under typical operating conditions.

This work introduces a comprehensive approach to assess the sensitivity of model outputs to changes in parameter values, constrained by the combination of prior beliefs and data. This approach identifies stiff parameter combinations strongly affecting the quality of the model-data fit while simultaneously revealing which of these key parameter combinations are informed primarily by the data or are also substantively influenced by the priors. We focus on the very common context in complex systems where the amount and quality of data are low compared to the number of model parameters to be collectively estimated, and showcase the benefits of this technique for applications in biochemistry, ecology, and cardiac electrophysiology. We also show how stiff parameter combinations, once identified, uncover controlling mechanisms underlying the system being modeled and inform which of the model parameters need to be prioritized in future experiments for improved parameter inference from collective model-data fitting.

Nanodiamonds (ND) have recently emerged as excellent candidates for various applications including membrane technology due to their nanoscale size, non-toxic nature, excellent mechanical and thermal properties, high surface areas and tuneable surface structures with functional groups. However, their non-porous structure and strong tendency to aggregate are hindering their potential in gas separation membrane applications. To overcome those issues, this study proposes an efficient approach by decorating the ND surface with polyethyleneimine (PEI) before embedding it into the polymer matrix to fabricate MMMs for CO₂/N₂ separation. Acting as both interfacial binder and gas carrier agent, the PEI layer enhances the polymer/filler interfacial interaction, minimising the agglomeration of ND in the polymer matrix, which is evidenced by the focus ion beam scanning electron microscopy (FIB-SEM). The incorporation of PEI into the membrane matrix effectively improves the CO₂/N₂ selectivity compared to the pristine polymer membranes. The improvement in CO₂/N₂ selectivity is also modelled by calculating the interfacial permeabilities with the Felske model using the gas permeabilities in the MMM. This study proposes a simple and effective modification method to address both the interface and gas selectivity in the application of nanoscale and non-porous fillers in gas separation membranes.