Thick Li-ion battery electrodes with high ion transport rates could enable batteries that cost less and that have higher gravimetric and volumetric energy density, because they require fewer inactive cell-components. Finding ways to increase ion transport rates in thick electrodes would be especially valuable for electrodes made with graphite platelets, which have been shown to have tortuosities in the thru-plane direction about 3 times higher than in the in-plane direction. Here, we predict that bi-tortuous electrode structures (containing electrolyte-filled macro-pores embedded in micro-porous graphite) can enhance ion transport and can achieve double the discharge capacity compared to an unstructured electrode at the same average porosity. We introduce a new two-dimensional version of porous-electrode theory with anisotropic ion transport to investigate these effects and to interpret the mechanisms by which performance enhancements arise. From this analysis we determine criteria for the design of bi-tortuous graphite anodes, including the particular volume fraction of macro-pores that maximizes discharge capacity (approximately 20 vol.%) and a threshold spacing interval (half the electrode's thickness) below which only marginal enhancement in discharge capacity is obtained. We also report the sensitivity of performance with respect to cycling rate, electrode thickness, and average porosity/electroactive-material loading. Present-day oil demand and supply statistics show a clear need for alternatives in energy production, management, and storage. Amongst the various energy-storage devices available, Li-ion batteries have benefits of high gravimetric and volumetric energy-density.1-3 Modern Li-ion battery electrodes are porous composites of solid-state activematerial particles bound together by a conductive carbon-binder mixture, with an ion-conducting liquid electrolyte filling the pores. When a battery operates, electrons and ions are simultaneously transported to the surfaces of active-material particles, where electrochemical reactions take place. The rates at which ions are transported depend on the microscopic structure of the composite electrodes through a parameter called tortuosity. The microstructure in an electrode results from the particular choice of material constituents and processes that are used to fabricate the electrodes. To maximize the energy density of a battery, we would like to have electrodes with low porosity (maximizing the density of active material) and high thickness, reducing the number of inactive components (separators, current collectors) that are required for a given amount of active material, saving considerable cost. Unfortunately, electrodes with low porosity generally have high tortuosity, 4 making ion transport slow, an effect whose importance is magnified when electrodes are thick. Thus, techniques that produce thick, dense electrodes with enhanced ion transport could enable the development of batteries with high energy-density and high power density at a lower cost than...
Redox flow batteries (RFBs) are potential solutions for grid-scale energy storage, and deeper understanding of the effect of flow rate on RFB performance is needed to develop efficient, lowcost designs. In this study we highlight the importance of modeling tanks, which can limit the charge/discharge capacity of redox-active polymer (RAP) based RFBs. The losses due to tank mixing dominate over the polarization-induced capacity losses that arise due to resistive processes in the reactor. A porous electrode model is used to separate these effects by predicting the time variation of active species concentration in electrodes and tanks. A simple transient model based on species conservation laws developed in this study reveals that charge utilization and polarization are affected by two dimensionless numbers quantifying (1) flow rate relative to stoichiometric flow and (2) size of flow battery tanks relative to the reactor. The RFB's utilization is shown to increase monotonically with flow rate, reaching 90% of the theoretical value only when flow rate exceeds twenty-fold of the stoichiometric value. We also identify polarization due to irreversibilities inherent to RFB architecture as a result of tank mixing and current distribution internal to the reactor, and this polarization dominates over that resulting from ohmic resistances particularly when cycling RFBs at low flow rates and currents. These findings are summarized in a map of utilization and polarization that can be used to select adequate flow rate for a given tank size.
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