The relationships between gas permeability and free volume fraction, intersegmental distance, and glass transition temperature, are investigated. They are analyzed for He, CO₂, O₂, CH₄, and N₂ gases and for five similar polyimides with a wide range of permeabilities, from very low to extremely high ones. It has been established here that there is an exponential relationship between permeability and the free volume fraction, and between permeability and the most probable intersegmental distance as measured by WAXS; in both cases, with an exponential coefficient that depends on the kinetic gas diameter as a quadratic polynomial and with a preexponential positive constant. Moreover, it has been proven that the intersegmental distance increases linearly with the free volume fraction. Finally, it has been established that the free volume fraction increases with the glass transition temperature for the polymers tested, and that they depend on each other in an approximate linear way.

Swine farming produces large quantities of nutrient-rich wastewater, which often contains metals such as Cu and Zn, used as feed additives for pigs. These metals must be removed from the wastewater before discharge but their retention in the biomass can limit its subsequent utilization. Photobioreactors are a very promising alternative for swine wastewater treatment, as the consortium of microalgae and bacteria growing symbiotically in these reactors allows high nutrient and metal removal efficiency at moderate costs. This work studies the mechanisms of removal of Cu(II) and Zn(II) by the two types of microorganisms growing in these photobioreactors. A microalga commonly used in wastewater treatment (Scenedesmus almeriensis) and an activated sludge were kept in contact with synthetic wastewater containing 100 mg/L of Cu and Zn. After 72 h, Scenedesmus almeriensis removed 43% of Cu and 45% of Zn, while activated sludge removed 78% of Cu and 96% of Zn. Single and sequential extractions of the biomasses using different extracting reagents revealed that biosorption on protonable groups is the dominant removal mechanisms. Mild reagents solubilized 69% of Cu and 94% of Zn from the microalgae and 76% of Cu and 93% of Zn from the activated sludge. Low metal concentrations in the oxidizable and residual fractions evidenced minimal bioaccumulation inside the cells. FTIR and ESEM-EDX analysis confirmed biosorption by ion exchange and complexation as the main metal remediation mechanisms. The weak bonds of the biosorbed Cu and Zn ions are beneficial for the valorization of biomass and the obtaining of safe bioproducts.

Mixed-matrix membranes (MMMs) incorporating porous organic fillers into high-performance polyimides were developed to investigate the influence of free volume and molecular architecture on gas transport. Four structurally rigid, intrinsically porous fillers (TFAP-Trp, Is-Trp, TFAP-TPB, and Is-TPB) were incorporated into a range of polymer matrices (P84^®, Matrimid^®, Pi-DAPOH, Pi-DAROH, Pi-HABAc, Pi-DAM, and PIM-1), enabling the development of a matrix-independent methodology for estimating intrinsic filler permeabilities for five gases (He, O₂, N₂, CH₄, and CO₂). This comprehensive multi-matrix, multi-gas study reveals a strong correlation between filler fractional free volume (FFV), BET surface area, and gas permeability, with isatin-based fillers exhibiting particularly high CO₂ permeability. Filler incorporation generally resulted in substantial permeability enhancements (100–350%) while maintaining selectivity, often with only minor losses or even favorable improvements in CO₂/CH₄ and He/CH₄ separation performance. Several MMMs, particularly those based on Pi-DAPOH and Pi-DAROH polyimides, approached or exceeded the Robeson upper bound. Analysis of permeability as a function of gas kinetic diameter further elucidated clear structure–property relationships, confirming that filler-induced disruption of polymer chain packing and the creation of additional transport pathways are the primary factors governing separation performance. Overall, these findings demonstrate that rationally designed porous organic fillers provide a robust and broadly applicable strategy for mitigating the permeability–selectivity trade-off in polymer membranes and enhancing gas separation efficiency.