Perfluorosulfonic acid (PFSA) membranes such as Nafion conduct protons through hydrated ionic nanochannels and are the electrolyte of hydrogen fuel cells. Time-resolved Raman spectroscopy of H2O/D2O exchange has shown that the weakly hydrogen-bonded, interfacial ('nonbulk-like') water population diffuses consistently faster than bulk-like water across five different PFSA membranes, and that its apparent diffusivity correlates directly with proton conductivity. What is open is the causal mechanism behind this correlation: whether fast interfacial-water motion reflects a less tortuous channel network or an intrinsically altered transport mechanism under nanoconfinement; how vehicular and Grotthuss (proton-hopping) motions partition within the interfacial population; and how sulfonic-acid head-group density and channel width separately control the water populations and conductivity. Resolving this would convert an empirical correlation into predictive design rules for high-conductivity proton-exchange membranes.

Background

Perfluorosulfonic acid (PFSA) ionomers — ion-containing polymers, of which Nafion and Aquivion are the canonical examples — are the workhorse proton-conducting membranes of hydrogen fuel cells. They combine a hydrophobic perfluorinated backbone with pendant side chains terminated by sulfonic acid groups; upon hydration the polymer segregates into hydrophilic ionic domains (channels and clusters with characteristic dimensions from subnanometer to a few nanometers) containing water and protons, through which all membrane transport occurs. The polymer's equivalent weight (mass per sulfonic-acid group) sets the sulfonic-acid head-group density, while hydration and processing set the width and connectivity of the aqueous channels. Proton conductivity, the key functional property, depends on all of these in a way that remains mechanistically unexplained.

The Raman OH-stretching band of water in PFSAs decomposes into two spectral components: a bulk-like population (bulkW), whose strong hydrogen bonding resembles liquid water, and a weakly hydrogen-bonded, under-coordinated population (nonbulkW) associated with water at the ionic/polymer interface and in narrow channels. Ling, Bonn, Domke and Parekh (2019) used broadband coherent anti-Stokes Raman scattering (BCARS) microscopy — a nonlinear optical technique that records full vibrational spectra from a femtoliter volume with millisecond time resolution — to follow H2_2O/D2_2O isotope exchange through the thickness of five PFSA membranes (Nafion 117, 212, 1035 and Aquivion E87, E98). Fitting the time evolution of the subspecies bands with a one-dimensional diffusion model yielded apparent diffusion coefficients ADC(bulkW) and ADC(nonbulkW). Three findings resulted: (i) the interfacial (nonbulkW) subspecies consistently diffuses faster than bulkW in every membrane examined; (ii) the total water diffusivity is a fraction-weighted linear combination of the two subspecies diffusivities, indicating that the two populations transit the membrane as physically separated, weakly exchanging entities; and (iii) across the five membranes, ADC(nonbulkW) correlates directly with proton conductivity.

Proton transport in hydrated PFSAs proceeds by two canonical mechanisms: vehicular diffusion, in which the proton travels as a hydronium ion whose motion is coupled to water diffusion, and Grotthuss (structural) diffusion, in which the proton hops along the hydrogen-bond network by sequential proton-transfer steps. Reactive multistate empirical valence bond (MS-EVB) simulations — a technique that treats the excess proton as a delocalized defect spread over many water configurations — indicate that in the confined PFSA geometry the two mechanisms are anticorrelated, so their contributions are difficult to separate, and that proton transfer mediated by sulfonate head groups (sulfonate-to-sulfonate passing of the hydrated proton) dominates (Savage, Tse and Voth, 2014). Molecular dynamics work has long shown that head-group placement (monomeric sequence) controls nanophase segregation and water diffusion (Jang, Molinero, Çağın and Goddard, 2004), and precisely sulfonated polyethylene has demonstrated that controlled acid-group spacing produces ordered, efficient proton-transporting layers (Trigg et al., 2018) — but no comparable control exists for PFSAs themselves.

The 2019 measurements thus established a correlation between interfacial water transport and proton conductivity, but not its cause, and they were performed only on fully hydrated (saturating) membranes at room temperature outside an operating cell. The unresolved question is what mechanism produces the correlation — an answer that determines whether membrane design should optimize the geometry of the channel network or the chemistry governing the interfacial water itself.

Problem Statement

Determine, with experimental evidence and/or validated molecular simulation, whether and by what mechanism interfacial (nonbulk-like) water transport controls proton conductivity in perfluorosulfonic acid (PFSA) membranes — converting the correlation reported by Ling et al. (2019) into an established mechanism and predictive membrane-design rules. Here ADC(nonbulkW) denotes the apparent diffusion coefficient of the interfacial, weakly hydrogen-bonded water population, obtained by fitting the time evolution of its Raman spectral signature during H2O/D2O isotope exchange with a one-dimensional diffusion model, and ADC(bulkW) is the corresponding quantity for the bulk-like population. This requires answering three linked questions:

  1. Origin of fast interfacial-water transport. Determine whether the systematically larger ADC(nonbulkW) — the interfacial population diffuses faster than the bulk-like population in every membrane tested — arises because the channels hosting the nonbulk-like population are less tortuous and better connected than those hosting bulk-like water, or because nanoconfinement itself alters the microscopic transport mechanism (for example, water-wire transport with reduced hydrogen-bond-breaking barriers), or both.

  2. Proton-transport mechanism in the interfacial population. Determine the relative contributions of vehicular (hydronium-ion) diffusion and Grotthuss (structural, proton-hopping) transport within the interfacial water population — in particular, whether the correlation between ADC(nonbulkW) and proton conductivity reflects enhanced vehicular proton diffusion, enhanced structural-transfer efficiency, or a combination.

  3. Chemical versus geometric control. Vary sulfonic-acid head-group density and ionic-channel width/connectivity independently, and determine their separate effects on the subspecies fractions, the subspecies diffusivities, and proton transport.

The problem is complete when a causal account that answers the three questions above identifies which parameters (head-group density, channel width and connectivity, water-population fractions) govern interfacial-water mobility and proton conductivity and states the resulting relation between those parameters and conductivity concretely enough to yield predictive design rules for higher-conductivity PFSA membranes — or when it is demonstrated that the reported correlation does not survive tests that independently vary head-group density and channel width.

References

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