**Size-sieving separation of hard-sphere gases at low concentrations
through cylindrically porous membranes**

Y Yu and K Zhang, SOFT MATTER, 17, 10025-10031 (2021).

DOI: 10.1039/d1sm01158h

Membranes are compelling devices for many industrial separation processes, which are all subject to the intrinsic permeability- selectivity tradeoff. A general strategy to enhance separation performance is to reduce the pore size distribution and, ideally, make the membrane isoporous. In this study, we focus on a minimal model for regularly porous membranes, which consists of hard spheres moving through cylindrical pores. The collision dynamics is solved exactly and implemented in nonequilibrium event-driven molecular dynamics simulations. For such size-sieving porous membranes, we show that the permeability P of hard spheres of size sigma through cylindrical pores of size d follows the hindered diffusion mechanism due to size exclusion as P proportional to (1 - sigma/d)(2). According to this law, the separation of binary mixtures of large and small particles exhibits a linear relationship between alpha(-1/2) and P-1/2, where alpha and P are the selectivity and permeability of the smaller particle, respectively. The mean permeability through polydisperse pores is the average of the permeabilities of individual pores, weighted by the fraction of the single pore area over the total pore area.

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