Defect-Aware Transport Descriptors for Electrospun PBI Membranes: A Resource-Efficient Structural Screening Approach for Clean-Technology Applications

In heterogeneous fibrous networks, the void fraction measured by displacement porosimetry does not coincide with the fraction accessible to through-plane flow, and classical capillary-based permeability models, which take a single nominal porosity as input, cannot resolve this discrepancy. In the present work, a defect-aware structural framework is developed and applied to a set of 17 electrospun polybenzimidazole (PBI) membranes produced in triplicate across a broad processing window, covering fiber diameters from 83 to 174 nm, total porosities from 68 to 85%, and defect fractions from 0 to 52.2% as quantified by Scanning Electron Microscopy (SEM) image analysis. A defect-corrected effective porosity is introduced as a transport-oriented structural descriptor, defined as the fraction of nominal pore volume remaining accessible to through-plane flow after accounting for the obstruction imposed by morphological irregularities. Starting from this quantity, tortuosity is estimated through three complementary analytical models, Tomadakis, Bruggeman, and Koponen, and the corresponding Kozeny–Carman structural resistance constants are derived. All three models consistently show increasing tortuosity and amplified flow resistance as defect content increases, with model divergence becoming most pronounced below an effective porosity of approximately 65%, identifying a structural threshold beyond which heterogeneous fibrous networks deviate significantly from idealized pore-path descriptions. Experimental Darcy permeability, derived from Gurley air-flow measurements, does not exhibit a statistically significant bivariate correlation with the defect fraction alone (rs = −0.38, p = 0.13), consistent with the multi-factorial nature of macroscopic transport in morphologically complex fibrous media. Kozeny–Carman-derived permeability, computed from the corrected effective porosity, still diverges from the Darcy reference by up to 2.7 orders of magnitude, but the deviation is not random: it varies monotonically with effective porosity and crosses unity at 0.81. This discrepancy is therefore interpreted not as a framework limitation but as a quantitative diagnostic of the structural conditions under which classical capillary-based permeability models become unreliable for heterogeneous electrospun mats. The framework is thus diagnostic rather than predictive: from routine SEM micrographs alone, it delimits the structural regime in which capillary-bundle descriptions lose validity, enabling resource-efficient screening of fibrous membranes for clean-technology applications.