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Flowable suspension-based electrodes (FSEs) have gained attention in recent years, as the integration of solid materials into electrochemical flow cells can offer improved performance and flexible operation. However, under conditions that engender favorable electrochemical properties (e.g., high particle loading, high conductivity, high surface area), FSEs can exhibit non-Newtonian characteristics that impose large pumping losses and flow-dependent transport rates. These multifaceted trade-offs motivate the use of models to broadly explore scaling relationships and better understand design rules for electrochemical devices. To this end, we present a one-dimensional model, integrating porous electrode theory with FSE rheology as well as flow-dependent electron and mass transport under pressure-driven flow. We study FSE behavior as a function of material properties and operating conditions, identifying key dimensionless groups that describe the underlying physical processes. We assess flow cell performance by quantifying electrode polarization and relative pumping losses, establishing generalized property-performance relationships for FSEs. Importantly, we expound relevant operating regimes—based on a subset of dimensionless groups—that inform practical operating envelopes, ultimately helping to guide FSE and cell engineering for electrochemical systems.

 

Redox flow batteries (RFBs) are hindered by complex failure modes, particularly crossover through the membrane, resulting in capacity fade and reduced cycling efficiencies. Redox‐active oligomers (RAOs) have recently been proposed for mitigating this phenomenon while maintaining sufficient transport properties; however, to date, few studies have quantified how the chemical and electrochemical properties of RAOs influence their performance in redox flow cells. Here, we demonstrate that oligomeric derivatives of 2,2,6,6‐tetramethylpiperidine 1‐oxyl (TEMPO) exhibit lower diffusivities than the monomeric species but retain facile charge transfer characteristics. The size‐dependent variations in mass transport rates directly translate to differences in flow cell polarization and symmetric cycling performance. Post‐mortem analyses reveal that oligomerization does not meaningfully alter decay processes as evinced by similar capacity fade across all species. Broadly, these findings corroborate and extend upon previously developed relationships between molecular size, electrochemical properties, and flow cell performance.

 

Engineering redox-active compounds to support stable multi-electron transfer is an emerging strategy for enhancing the energy density and reducing the cost of redox flow batteries (RFBs). However, when sequential electron transfers occur at disparate redox potentials, increases in electrolyte capacity are accompanied by decreases in voltaic efficiency, restricting the viable design space. To understand these performance tradeoffs for two-electron compounds specifically, we apply theoretical models to investigate the influence of the electron transfer mechanism and redox-active species properties on galvanostatic processes. First, we model chronopotentiometry at a planar electrode to understand how the electrochemical response and associated concentration distributions depend on thermodynamic and mass transport factors. Second, using a zero-dimensional galvanostatic charge/discharge model, we assess the effects of these key descriptors on performance (i.e., electrode polarization and voltaic efficiency) for a single half-cell. Finally, we extend the galvanostatic model to include two-electron compounds in both half-cells, demonstrating compounding voltage losses for a full cell. These results fundamentally show why multi-electron compounds with disparate redox potentials are less attractive than those with concerted electron transfer. As such, we suggest new directions for molecular and systems engineering to improve the prospects of these materials for RFBs. 

We use the C2-equivariant Adams spectral sequence to compute part of the C2-equivariant stable homotopy groups π^{C2}_{n,n}. This allows us to recover results of Bredon and Landweber on the image of the geometric fixed-points map π^{C2}_{n,n}→π_0. We also recover results of Mahowald and Ravenel on the Mahowald root invariants of the elements 2^k.