Extension of the robeson upper bound for target gas collection efficiency in membrane separations: Quantitative model of optimal separation factor and molecular design guidelines

Material design for gas separation membranes has long been constrained by the qualitative permeability-selectivity trade-off framework of the Robeson upper bound, which completely ignores the core industrial metric determining process economics—the net target gas collection efficiency per unit time. Herein, we establish a quantitative analytical framework centered on collection efficiency. We systematically derive the mathematical relationship between collection efficiency and separation factor, and obtain the analytical solution of the optimal separation factor (α_opt) for maximizing collection efficiency for the first time. We conduct a systematic study on 11 typical industrial gas pairs, and validate the model reliability using more than 100 sets of experimental data from high-performance polymeric materials. Our results reveal a significant linear correlation between the optimal separation factor and the square of the Stuart's high-temperature diameter ratio of gas pairs. The relative prediction errors for all 11 gas pairs are below 12.5%, with 9 pairs having errors less than 10%. Experimental results show that the actual separation factors of all current high-performance materials are higher than the theoretical optimal values, revealing the traditional “high selectivity first” design misconception and proposing a novel optimization direction of "high permeability-moderate selectivity". We further quantify the effects of key industrial parameters on actual collection efficiency, and demonstrate that material performance optimization and device engineering optimization are two independent and synergistic paths: reducing the selective layer thickness from 50 μm to 0.5 μm can increase the actual gas collection amount by 100 times, while the optimal separation factor remains unchanged.