A predictive model of separations in dead-end filtration with ultrathin membranes

Nanoporous Silicon Nitride (NPN) is a new ultrathin (50 nm thick) membrane with potential applications in laboratory and industrial preparations of nanoparticles, antibodies, and other therapeutic biotechnology products. Like prior ultrathin silicon-based membranes (nanomembranes), NPN is capable of high separation resolution (∼10 nm) despite polydisperse pore distributions. Here we present a mathematical model that is predictive of the sieving curves seen in dead-end filtration with NPN. Interestingly, the model requires the inclusion of concentration polarization to predict sieving curves. The model also reveals a pressure dependence on sieving curves that is highly sensitive to membrane thickness: Thicker membranes require higher, often impractical, pressures for the same separations while thinner membranes achieve sharp separations at lower pressures. The pressure sensitivity of sieving behavior is confirmed experimentally by comparing the performance of NPN with 10 μm thick nanoporous polycarbonate track etched membranes. The model illustrates that pore polydispersity limits the resolution of current silicon nanomembranes, suggesting that further manufacturing advancements are needed to realize the full potential of nanomembranes for size-based separations. Finally, the model further suggests that diffusion across ultrathin membranes aids separations, leading to higher resolutions.