Design Ultrathin Polyamide Membranes against Funnel Effect: A Novel Zone-of-Influence-Based Approach

Ultrathin polyamide membranes have gained significant attention due to their potential to achieve high water permeance. Nevertheless, their water permeance is constrained by the substrate-induced funnel effect. For years, researchers have been investigating how substrates impact membrane water permeance. However, these studies generally rely on a trial-and-error approach to find the optimal substrate porosity, which is often time-consuming and offers limited insights. To establish a more intuitive framework for membrane design, we introduced a novel zone-of-influence (ZOI)-based approach for the first time. We first analyze the distinctively different funnel behaviors for thin and thick films through numerical simulations. Thin films, characterized by small ratios of film thickness over substrate pore size (i.e., aspect ratio θ ≤ 0.5), show a highly localized influence of substrate pores and present a more severe funnel effect than thick films with θ ≫ 1. This analysis leads to the concept of ZOI-a region of polyamide over a single substrate pore with water permeation efficiency exceeding a predefined threshold value. A linear relationship between ZOI and θ was observed, which enables an intuitive design to achieve a target water permeance by simply overlapping ZOIs of multiple pores, making it far more efficient than the traditional trial-and-error approach. We further developed an analytical model based on the superposition principle to unravel the fundamental structure-performance relationship between water permeation efficiency, aspect ratio and substrate porosity. This study provides convenient design tools for optimizing ultrathin membrane structure, offering critical guidance and deep insights for the advancement of high-performance membranes.