Confocal micro-Raman measurements on Nafion® under a through-plane water-permeation flux showed that the local water content inside the membrane is not in equilibrium with the gas-phase water activity, and that an interfacial water-transport resistance at the membrane/gas interface, attributed to a non-equilibrium membrane structure at the interface, cannot be neglected. Fifteen years of subsequent work has confirmed that this resistance can dominate the total resistance to water transport, especially in thin membranes, but has not settled its physical origin: competing pictures (a slowly relaxing surface layer, a hydrophobic fluorine-rich blocking skin, a dehydration-induced water-depletion layer, or dynamic sorption/desorption kinetics) remain in play, its magnitude has not been quantified directly inside a fully operating fuel cell, and no predictive constitutive relation linking membrane mechanics and swelling dynamics to the interfacial resistance exists. The problem is to establish the origin, operating-condition behavior, and predictive modeling of this interfacial resistance for perfluorosulfonic-acid (PFSA) ionomer membranes such as Nafion®.

Background

A proton exchange membrane fuel cell (PEMFC) converts hydrogen and oxygen to electricity across a polymer electrolyte membrane, most commonly Nafion®, a perfluorosulfonic-acid (PFSA) ionomer: a hydrophobic fluorocarbon backbone with pendant side chains terminated by sulfonic acid groups. The membrane conducts protons well only when hydrated; the water content is usually denoted λ\lambda, the average number of water molecules per sulfonic acid group. Water moves through the membrane by diffusion down concentration/activity gradients (back-diffusion) and by electro-osmotic drag, the convective transport of water molecules complexed to migrating protons under current. Balancing these fluxes — cell water management — is a central constraint on PEMFC performance and durability.

A long-standing body of permeation and sorption experiments has shown that water transport through Nafion is not limited by internal diffusion alone. Majsztrik, Bocarsly and Benziger (2008) measured water permeation through 51–254 µm membranes and found that as feed-side water activity approaches 1 the limiting resistance shifts from diffusion inside the membrane to interfacial mass transport at the gas/membrane interface. Satterfield and Benziger (2008) found water-vapor sorption/desorption kinetics to be strongly non-Fickian: desorption is about ten times faster than absorption, and absorption proceeds in two stages — early uptake limited by interfacial mass transport, later uptake limited by polymer swelling and relaxation. Adachi and co-workers (2010) showed that vapor–vapor and liquid–vapor permeation fluxes stop increasing below roughly 56 µm membrane thickness because the interfacial resistance, which is independent of thickness, then exceeds the internal resistance; the interfacial contribution was more than half of the total even for a 201 µm membrane. Kientiz, Yamada, Nonoyama and Weber (2010) extracted an interfacial mass-transfer coefficient from permeation experiments, found it to depend exponentially on relative humidity, showed that it flattens the water-content profile across the membrane during operation, and found no analogous resistance at liquid/membrane or membrane/membrane interfaces. This cluster of results is closely tied to Schroeder's paradox — the observation that Nafion equilibrated with liquid water takes up more water than Nafion equilibrated with saturated vapor at the same water activity — because a vapor-exposed surface layer that resists uptake naturally suppresses vapor-equilibrated hydration; Kusoglu, Modestino, Hexemer, Segalman and Weber (2011) showed by in situ small-angle X-ray scattering (SAXS, which resolves nanometer-scale ionic-domain morphology) that morphological changes on vapor uptake are four orders of magnitude slower than on liquid-water uptake, consistent with interfacially limited penetration.

Tabuchi, Ito, Tsushima and Hirai (2011) measured the through-thickness water distribution of Nafion during a water permeation test using confocal micro-Raman spectroscopy, in which a Raman spectrum (vibrational scattering sensitive to the O–H stretching band of water) is collected from a confined focal spot of 2–3 µm resolution scanned across the membrane cross-section. They observed that under a steady water flux the internal water-content profile is flattened relative to what pure diffusion would produce and concluded that an interfacial water-transport resistance, arising from a non-equilibrium (slowly relaxing) membrane structure at the interface, cannot be neglected; the resistance depends on temperature and relative humidity. Related quantifications followed: Zhao, Majsztrik and Benziger (2011) separated interfacial from internal resistances using pulsed-gradient spin-echo NMR diffusivities; Kongkanand (2011) measured sorption of 0.03–3 µm Nafion films on a quartz-crystal microbalance (QCM, a resonant mass sensor) and fit both an interfacial mass-transfer coefficient and a mechanical relaxation coefficient; Cheah, Kevrekidis and Benziger (2011) showed in a membrane–electrode assembly under applied potential that net water flux under electro-osmotic drag is controlled by interfacial transport.

What is missing is threefold. First, the mechanism: structural probes give partial, model-dependent evidence for an interfacial layer — neutron reflectometry (a technique that measures nanometer-scale depth profiles of scattering-length density) required a bilayer model with a less-hydrated outer layer for liquid-water-exposed films (Murthi et al., 2008), and time-resolved small-angle neutron scattering by Fumagalli et al. (2015) showed the ionic domains keep reorganizing logarithmically in time over years after fast diffusive swelling — but competing mechanistic interpretations persist: Luo and Holdcroft (2016) speculated a dehydration-induced water-depletion layer; Soniat and Houle (2022) argued from reaction–diffusion simulations matched to time-dependent infrared data that the resistance is not slow diffusion through a hydrophobic fluorine-rich skin but a dynamic competition between dehydration and rehydration; Dura, Kim, Page and Soles (2025) showed the interfacial morphology can be deliberately controlled by substrate chemistry, establishing a structure/impedance methodology without settling the mechanism for bulk membranes. Second, operating-condition validity: the resistance has been quantified in ex situ permeation cells and modeled in simplified membrane–electrode assemblies, but operando water-content measurements in running fuel cells (e.g. the µ-Raman study of Tran et al., 2021) do not extract an interfacial resistance, and 2024 water-transport models of operating electrolyzers still assume electro-osmosis plus diffusion only. Third, no predictive constitutive relation connects membrane mechanical properties (elastic modulus, swelling stress), swelling-rate dynamics, and interfacial sorption/desorption kinetics to the magnitude of the interfacial resistance, although industrial practice already needs it: for the ~10 µm reinforced membranes used commercially, the interfacial effect is expected to dominate total water-transport resistance (Redmond, Hansen and Berg, 2019).

Problem Statement

Establish a predictive, experimentally validated physical description of the interfacial water-transport resistance at the gas/membrane interface of Nafion® and other perfluorosulfonic-acid (PFSA) ionomer membranes — the resistance that Tabuchi et al. (2011) attributed to a non-equilibrium membrane structure at the interface. Concretely, this description should address three linked open questions that together form this single objective: (1) Mechanism — determine the molecular/morphological origin of the resistance, discriminating between the competing pictures in the literature (a slowly relaxing, non-equilibrium surface layer; a hydrophobic fluorine-rich blocking skin; a dehydration-induced water-depletion layer; dynamic sorption/desorption kinetics at the interface), which are the leading hypotheses rather than an exhaustive menu, so that establishing a different or combined origin also resolves this part, at the length and time scales relevant to the interfacial region; (2) Operating conditions — quantify the interfacial resistance and its parametric dependences (temperature, water activity, membrane thickness, current density) inside an operating PEMFC, where electro-osmotic drag, current-driven water production, multicomponent gas streams, and pressure gradients act simultaneously, establishing whether the ex situ measured resistances and their dependences carry over; and (3) Predictive coupling — derive and validate a constitutive/model relation that connects membrane mechanical properties (elastic modulus, swelling stress/strain), swelling-rate dynamics, and interfacial sorption/desorption kinetics to the magnitude of the interfacial resistance, in a form usable for membrane-material and fuel-cell operating-strategy design. The common objective is a predictive description that converts the reported ex situ observations into design rules. All three parts are jointly required — a result that resolves only one of them does not resolve the task, though a single result may resolve more than one — and each part is resolved by a demonstrated result rather than by a specified method; part (2), in particular, may be met either by a new direct operando measurement of the interfacial resistance or by a validated model-based inference of it from existing operando water-content data, provided the operating-condition dependences are established. Extension to non-PFSA ionomer chemistries, catalyst-layer interfaces, and cyclic or transient operation is a desirable generalization axis rather than part of the core objective.

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