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Gas separation membranes incorporating two-dimensional (2D) materials have received considerable attention in recent years, as these membranes have shown outstanding physical, structural, and thermal properties and high permeability- selectivity. The reduced thickness and diversity of the gas transport mechanisms through in-plane pores (intrinsic defects), in-plane slitlike pores, or plane-to-plane interlayer galleries provide the membranes with a significant sieving ability for energy-efficient gas separation. The discovery of 2D transition metal carbides/nitrides materials, MXenes, has provided new opportunities in the gas separation membrane area because of their hydrophilicity, rich chemistry, high flexibility, and mechanical strength. This Review puts into perspective recent advances in 2D-material-based gas separation membranes. It discusses research opportunities mainly in MXene-based gas membranes, highlights modification approaches for tuning the in-plane and plane-to-plane nanoslits, explains governing mechanisms of transport through these membranes, and compares their advantages and disadvantages with those of other 2D materials. It also discusses current challenges and provides prospects in this area. 

Many widely-used polymers are made via free-radical polymerization. Mathematical models of polymerization reactors have many applications such as reactor design, operation, and intensification. The method of moments has been utilized extensively for many decades to derive rate equations needed to predict polymer bulk properties. In this article, for a comprehensive list consisting of more than 40 different reactions that are most likely to occur in high-temperature free-radical homopolymerization, moment rate equations are derived methodically. Three types of radicals—secondary radicals, tertiary radicals formed through backbiting reactions, and tertiary radicals produced by intermolecular chain transfer to polymer reactions—are accounted for. The former tertiary radicals generate short-chain branches, while the latter ones produce long-chain branches. In addition, two types of dead polymer chains, saturated and unsaturated, are considered. Using a step-by-step approach based on the method of moments, this article guides the reader to determine the contributions of each reaction to the production or consumption of each species as well as to the zeroth, first and second moments of chain-length distributions of live and dead polymer chains, in order to derive the overall rate equation for each species, and to derive the rate equations for the leading moments of different chain-length distributions. The closure problems that arise are addressed by assuming chain-length distribution models. As a case study, β-scission and backbiting rate coefficients of methyl acrylate are estimated using the model, and the model is then applied to batch spontaneous thermal polymerization to predict polymer average molecular weights and monomer conversion. These predictions are compared with experimental measurements.