Pathways to low-cost electrochemical energy storage : a comparison of aqueous and nonaqueous flow batteries

An energy storage system to support the electricity grid requires a power conditioning system, mainly an inverter and transformer, to connect the stack that produces DC power to a utility operator owned transformer. Power electronics are a significant cost component, with estimates in the range of $200-500 kW -1 for energy storage devices at rated power levels of 1-5 MW. 1, 2 The DOE Sunshot Program has a goal of reducing this number to $100 kW -1 for installed photovoltaic generating systems with low cost. 3 We use a power conditioning system cost of $250 kW -1 for current costs and $75-150 kW -1 for projections of high-volume future state costs.


Introduction
Energy storage is used to balance supply and demand on the electrical grid. The need to store energy is expected to increase as more electricity is generated from intermittent sources like wind and solar. [1][2][3][4] Pumped hydro installations currently account for greater than 95% of the stored energy in the United States, with a capacity equal to approximately 2.3% of generation. 5 Thermal storage, compressed air, ywheels, and batteries comprise the remaining 5% of storage capacity. 5 Other means of energy storage are also under investigation such as utilizing liquid fuels 6,7 (e.g., H 2 or CH 4 generation and consumption) as well as utilization of existing resources 8 if a large electric vehicle eet is established. The economics of storing grid energy is challenging. The Department of Energy's (DOE's) Advanced Research Projects Agency-Energy (ARPA-E) set a capital cost target of $100 per kW h for 1 hour of storage for widespread adoption. 9 The DOE Office of Electricity Delivery and Energy Reliability proposed cost targets of $250 per kW h by 2015, falling to $150 per kW h in the future for a fully integrated distributed energy storage system providing 4 h of storage. 10 The target cost of the energy storage device in the 2015 integrated system was $100 per kW h. These strict targets reect the cheap cost of electricity in the United States. Fortunately, compared with transportation applications, batteries for grid applications can tolerate higher temperature and lower energy density; this widens the scope of possible solutions to include, for example, sodium-sulfur and redox ow batteries. Yang et al. recently reviewed electrochemical storage technologies for grid electricity. 11 Comprehensive reviews of ow batteries include those of Weber et al., 12 Ponce de Leon et al., 13 and Skyllas-Kazacos et al. 14 The active species in most ow batteries are redox couples dissolved in liquid electrolytes that can be stored in inexpensive vessels, like plastic tanks. Fig. 1 schematically depicts a ow battery. The system includes electrochemical reactors, storage vessels, circulation pumps, a heat exchanger, and power conditioning equipment. The positive and negative electrolytes are fed to one or more electrochemical reactors, where the active species are oxidized or reduced to alternately charge or discharge the battery. Ideally, the redox reactions are facile, and the participation of solid components is limited to electron transfer, which is conducive to long cycle lives. Skyllas-Kazacos et al. report that durability generally exceeds 5000 deep cycles for ow batteries. 14 The energy densities of common aqueous ow systems, like vanadium redox (VRFB), are lower than those of enclosed batteries like lead-acid and lithium-ion (Li-ion). Fortunately, this deciency can be tolerated in many stationary applications. Flow battery systems require pumps to circulate the electrolytes, resulting in parasitic losses and complicating independent operation on the grid.
Flow batteries are suited to storing megawatt-hours of electrical energy that is meant to be discharged over the course of hours. A compelling feature of ow batteries is the distinct separation of power and energy characteristics. The reactors and ancillary equipment are sized for power, while the amount of active material and volume of storage vessels are determined by energy. The cost of the battery asymptotically approaches the cost of the redox solutions at long discharge times (see Fig. 8 (ref. 15) for example). This clean division between power and energy is absent from conventional enclosed batteries. This decoupling may offer advantages in large installations because it alters the scaling of cost with energy. The cost of an electrochemical device generally scales with active area, while the cost of conventional chemical process equipment varies with volume raised to a power like 0.5-0.6. 16 The architecture of ow batteries suggests a mixed scaling. Reactor cost should scale with area, while the cost of the other components should scale similarly to traditional chemical process equipment. This benet is somewhat muted at present by the high cost of the reactors relative to other major components.
The advent of modern redox ow batteries (RFBs) began with the development of the iron-chromium system at NASA in the 1970s. 12,17 Since then, a large number of aqueous RFBs have been developed including bromine-polysulde, vanadiumpolyhalide, and all-vanadium systems. In addition, several aqueous hybrid batteries have been pursued, where one or both electrode reactions are a deposition/dissolution process, such as zinc-bromine and soluble lead-acid systems. Though several of these technologies have been successfully demonstrated at large-scale, none have experienced widespread commercial success due to a number of technical and economic challenges. Though only sporadically investigated for the past 40 years, the renaissance of renewable electricity generators has spurred research and development in the eld and led to a number of important recent advances including high performance electroreactors, [18][19][20] new electrolyte formulations, 21 and new tailored redox molecules. [22][23][24] A recent area of research and development in the redox ow battery community is the identication, synthesis, and modication of novel redox active molecules. 6,12,23,[25][26][27][28][29][30][31][32][33][34][35][36][37] These tailored molecules may be composed of organic constituents or ligand modied inorganic species. Tailoring molecules to have the necessary properties required of active species in redox ow batteries leverages the dramatic advances in synthetic chemistry made since the pioneering work on ow batteries in the 1970s and 1980s. Demonstrations with synthetic molecules have shown attractive cell voltages, fast kinetics, and low cost. The challenge in front of developers is to capture all of the aforementioned benets in addition to high solubility, long cycle life, and low toxicity. While the majority of work to date has utilized aqueous electrolytes, nonaqueous electrolytes offer the attractive possibility of higher voltages.
As compared to their aqueous counterparts, non-aqueous redox ow batteries are in their infancy. In 1988, Matsuda et al. demonstrated the rst non-aqueous redox ow battery based on a ruthenium bypyridine complex with an open circuit potential of 2.6 V. 38 Over the next few decades, non-aqueous electrolytes were sporadically investigated for redox ow batteries with the focus on anion-exchange systems which employ single electrolytes composed of metal coordination complexes. 27,28,31,37,[39][40][41] Despite the promising cell potentials (>2 V), many of these systems have been hampered by limited solubility of the complexes, and low efficiencies. More recently, research efforts have broadened to include other redox materials most notably metal-centered ionic liquids 26 and tailored organic molecules 25,32 which have shown higher solubilities in non-aqueous electrolytes. A number of hybrid chemistries have also been investigated, using lithium metal as an anode and a owing positive electrolyte consisting of either polysuldes 42,43 or tailored molecules. 44 In general, most of these efforts have been exploratory with a focus on identifying new redox materials.
Transitioning from aqueous to nonaqueous electrolytes offers a wider window of electrochemical stability that enables operation at higher voltages. 25,45 Wang et al. illustrate the available voltage window and existing redox couples for aqueous electrolytes. 17 Depending on the salt, solvent, and electrode material, the stability window for nonaqueous electrolyte can span greater than 4 V. 46 High cell voltage leads to higher energy density, and typically to higher efficiency as well. These benets promise to reduce the cost of energy. In addition, a greater selection of redox materials may be available due to either the wider potential window or the variety of available nonaqueous solvents. 25,47 Higher energy density also leads to smaller system footprint, which may enable specic applications like storage in an urban environment. 42,43 However, this promise must be balanced with the challenges associated with nonaqueous electrolytes, namely, increased cost, reduced ionic conductivity, and other unfavorable physical properties including moisture sensitivity, ammability, and toxicity. Furthermore, as compared to their aqueous counterparts, nonaqueous ow batteries are in their infancy, and many unknowns still exist. Understanding and balancing these competing factors will be key to determining the true prospects for nonaqueous ow batteries.
Cost estimates of various sophistication have been reported previously for aqueous ow batteries. [48][49][50][51][52] We seek to build upon the knowledge disseminated in those works and examine the technological potential of aqueous, and for the rst time, nonaqueous ow batteries in achieving cost objectives. Our approach is to utilize the simplest model that maintains the essential performance and cost factors, enabling broad and meaningful discussions regarding material and system requirements. The analysis is intended to be exible enough to facilitate comparison of different systems. Sources for performance and cost parameters are provided within the analysis where pertinent. Through a comparative analysis, we examine trends as well as areas of strength and future research needs. The exact values of system price presented here, which can be challenged on various grounds, are of secondary importance to our goals.
The goal of this paper is to examine the relationships among the cost and performance of the components and the nal system price for ow batteries in a general way. This paper begins with a brief discussion of the economics of energy storage that provides an appreciation for the implications of price targets. This is followed by a mathematical description of the contributions to the price of a ow battery. The model is employed to determine sets of chemical and reactor costs, as well as area-specic resistance (ASR) and thermodynamic potential that yield a target battery price. These results are interpreted in the context of existing and conceptual aqueous and nonaqueous ow batteries. Solubility targets for the active species in nonaqueous batteries are derived from the chemical costs. Cost factors and ASR values for various battery systems are included to rationalize the range of parameters considered.
Examples are shown that demonstrate how costs are predicted to fall between now and a future state in which 1% of all energy generated is stored in the battery under study. The future-state costs of enclosed, hybrid, and ow batteries are compared, so that the different technologies can be judged on equal footing. Finally, prospects for achieving necessary ASR and solubility values for conceptual aqueous and nonaqueous ow batteries are discussed with the aid of theoretical models and experimental data.

Economics of energy storage
A variety of techniques are available to evaluate the economic prospects of an engineering project. These include evaluations of discounted cash ow, net present worth, capitalized costs, payback time, and rate of return on initial investment. The rst three methods account for the time value of money, while the last two do not, and are therefore less reliable. For the sake of simplicity, we assume continuous, uniform payments and continuous compounding in our analysis. Given these assumptions, the economics of the project can be described by a simple, rst-order differential equation relating the principle, the net revenue stream, and the internal rate of return. Newman et al. presented an analysis of energy-storage systems subject to the above constraints and we follow their approach in this work. 53 Newman et al. described the economics of energy storage with the equation: 53 where P 0 is the price of the installed energy storage system in dollars, N is the net revenue in $ per year, t L is the life of the battery in years, and r is an ination-adjusted rate of return in per year. The variable r is oen referred to as the "internal rate of return" (IRR). The ratio P 0 /N is a simple payback time in years, and the factor r/(1 À exp(Àrt L )), referred to as the capital recovery factor for continuous payments and compounding, accounts for the time value of money. An IRR of 30% per year, which yields a payback time of 3.3 years in the limit of large t L , is a reasonable benchmark for an industrial process with moderate technical risk. 16 An IRR of 10% per year is commonly used when establishing the economics of different energy storage scenarios. 1 Electric utilities oen work with longer time horizons than other industrial and commercial concerns. Both battery price and net revenue can be normalized by the discharge energy of the battery to create intrinsic values. The net revenue for a battery that stores energy purchased at a low price to be sold later at a higher price is given by: The variable N is the net revenue in $ per year, p is the price of electricity in $ kW h À1 (or $ J À1 ), E is energy in kW h (or J), and u is the frequency of deep cycling in per year. The subscript d denotes discharge, c denotes charge, and rt denotes round trip; 3 e,rt is the round trip energy efficiency of the battery system. Eqn (2) uses the energy discharged by the battery as a basis, while Newman et al. used charging energy. 53 This choice dictates where the energy efficiency appears in the equation, but is mathematically equivalent. The term in brackets on the right side of the equation indicates that the energy efficiency must exceed the ratio of electricity prices in order to achieve positive net revenue. Clearly, energy storage is most attractive when there is a large difference between peak and off-peak electricity prices. Excluded from our analysis are sources of revenue other than arbitrage, like managing demand charges, that may be available to batteries connected to the grid.
Eqn (1) and (2) may be combined to calculate how much storing energy in a battery adds to the cost of electricity: Casting the energy storage costs in this form was suggested by Poonpun and Jewell. 54 The cost added to the price of electricity, p d À p c , has the benet that it is easily understood by all consumers who receive electric bills. The rst term on the right shows that the price increase is proportional to the intrinsic capital cost of the battery, and inversely proportional to the cycling frequency. The second term on the right side of the equation shows how the cost and efficiency of charging affect the price increase. This term tends to be small because the factor in brackets tends to zero at high efficiency, and cheap electricity is typically used to charge the battery. For example, the nal term is just $0.0167 per kW h for p c ¼ $0.05 per kW h and 3 e,rt ¼ 75%. This analysis does not contemplate battery replacements because ow batteries should be able to achieve the required number of cycles and longevity, as cited in the Introduction. Fig. 2 shows the relationship between capital cost and the increase in electricity price for various internal rates of return. The electricity price increase at a particular capital cost rises with internal rate of return. For example, the electricity price increase at $100 per kW h and 30% per year is identical to the price increase at $200 per kW h and 10% per year. A storage device achieving a capital cost of $100 per kW h would add $0.08 per kW h to the electricity cost at an IRR of 10% per year. Average industrial and residential electricity rates in the United States were $0.070 per kW h and $0.118 per kW h in 2012, respectively. 55 Peak wholesale prices of approximately $0.25 per kW h were observed in the Northeast and Mid-Atlantic regions of the United States in January 2014. 56 Electricity rates in many European countries and Japan are considerably higher than those in the United States, 55 making energy storage potentially more valuable in these markets. For example, industrial and residential rates in Japan were $0.18 per kW h and $0.26 per kW h in 2012. 55 Fig. 2 was drawn for u ¼ 250 per year, roughly equal to one cycle per weekday. Cycling daily or more frequently moderates the increase in electricity price associated with storage.
The simplicity and transparency of the preceding analysis help to clarify the cost of storage in arbitrage applications. More comprehensive analyses of the markets for energy storage devices that include other applications and sources of revenue have been published. Sandia National Laboratories has reported discharge durations, addressable market sizes, and anticipated economic benets for nineteen segments of the energy storage market. 57 The benets are presented as present worths in units of $ kW À1 based on 10 years of life at a discount rate of 10% with 2.5% escalation. Present worth in $ kW À1 was converted to $ per kW h by dividing by average discharge time. Reported values include $245 per kW h for managing time-ofuse energy costs and $73 per kW h for managing demand charges. A ow battery could potentially accomplish both of these tasks for a building owner. Bundling services signicantly reduces the cost barrier to market entry.

Mathematical description of capital cost
The price of a ow battery system can be apportioned into terms that scale with reactor area and electrolyte mass, as well as system costs that scale with power. Thus, the system price may be expressed as: where P 0 is the initial system price in $, c a is the reactor cost per unit area in $ m À2 , A is the electrode area in m 2 , c bop is the cost for balance-of-plant components in $ kW À1 , c add is the addition to the capital cost to reach the system price in $ kW À1 , E d is the energy discharged by the battery system in kW h (or J), t d is the discharge time of the battery in h, c m,i is the cost per unit mass of electrolyte species i in $ kg À1 , and m i is the required mass of Energy & Environmental Science Analysis species i in kg. Power conditioning equipment, controls, sensors, pumps, pipes, fans, lters, valves, and heat exchangers are included in c bop . The cost of the electrolyte storage vessels is absorbed into the electrolyte mass term. The additional contribution to price, c add , includes factors such as depreciation, labor, overhead, and margin. The assumptions behind these two parameters are detailed in the ESI. † Installation costs, which tend to be site and project specic and highly variable, are excluded from the price. We do not anticipate large differences in installation costs amongst different kinds of ow batteries. Aqueous systems will tend to be larger, while nonaqueous systems may require additional environmental controls. Sandia provides example installation costs for various battery systems. 1 Estimation methods based on multipliers established from a ratio of installation and service costs to the costs of purchased equipment are commonly used in the chemical processing industries. A ow battery resembles a small, simple chemical plant in many respects. Our cost analysis is limited to the price of the electrochemical reactors, the mechanical and electrical balance of plant, and the chemicals leaving the factory. In our analysis, reactor area is determined by the discharging half cycle. The time available for charging is expected to exceed the discharge time in most applications, and thus discharging power density is the limiting attribute. Achieving high power density is typically easier on charge because the voltage is higher, even though the upper voltage is oen limited to avoid deleterious side reactions. The area is determined by dividing the output power by the power density of the electrochemical reactor. These quantities are assumed to be constant during discharge for the sake of simplicity. Practically, the power density of the reactor will decline as the battery discharges, and the active species are consumed. System losses associated with auxiliaries that include electrolyte pumps and power conversion equipment force the electrochemical reactor to discharge more energy than appears in the external circuit. Accounting for these losses, the area of the electrochemical reactor can be calculated from the formula: where 3 sys,d is an efficiency that accounts for losses associated with auxiliary equipment, including power conversion, electrolyte pumps, and heat exchanger fans, during discharge. The subscript d is needed because the efficiencies of the auxiliary equipment may differ on charge and discharge. The current density and voltage of the reactor are denoted i d and V d , respectively. Their product is the power density of the reactor in W cm À2 or kW m À2 . Pumping losses typically contribute less than 1% in a properly designed system. 18,51 However, the owing electrolyte also takes the role of cooling the reactor. Other architectures without pumps will then be required to take on the burden of blowing cooled air or pumping a coolant. We choose to not distinguish between these burdens as they are a small portion of the total. Shunt currents that reect the losses due to the required manifolds of ow batteries are reected in the coulombic efficiency as presented below.
A key factor that distinguishes enclosed battery designs from those based on ow architectures is the relationship between power and energy. For ow batteries, the reactors may be independently sized to meet power and efficiency requirements regardless of the energy requirements. By contrast, stationary electrodes in enclosed and hybrid cells are commonly limited by transport within the electrode or other phenomena that scale with current density. For example, in hybrid cells that utilize a metal electrodeposition and dissolution reaction at the negative electrode, the current density is constrained below a maximum on charge to ensure that the desired plating morphology is obtained (i.e., no dendrites). The reactor area is determined by either life or energy constraints rather than the target voltage efficiency. This typically results in larger reactors that are more expensive, albeit more efficient.
The round-trip energy efficiencies of the battery system and the electrochemical reactor are related by the equations: where E c and E d are the charge and discharge energies of the battery system observed at the connection to the external power grid, and E c,reactor and E d,reactor are those energies observed at the electrical connections to the reactor. The energy ratios are round-trip energy efficiencies. In general, 3 sys,d will depend on how the battery is operated. For example, pumping losses will increase with increasing ow through the system, and heat exchange losses will increase in proportion to ambient temperature in systems that require active cooling to maintain temperature below a prescribed maximum. Trading 3 sys with the efficiency of the reactor is an important aspect of design. For the simplied analysis presented in this paper, 3 sys,d is treated as a constant.
The amounts of the electrochemically active species needed can be found by application of Faraday's law. Conservatively, the amount of electrolyte that must be stored in the system is determined by the charging requirements, since coulombic inefficiency results in Q d < Q r < Q c , where Q is charge capacity in coulombs, and the subscripts d, r, and c denote discharge, reversible, and charge, respectively. The mass of the positive active material, for example, is given by: where m + is the mass of positive active species required to charge the battery, M + is the molecular weight, s + is the stoichiometry of the positive active species in the energy storage reaction, n e is the number of electrons, F is the Faraday constant, and c is the allowable state of charge (SOC) range. The SOC range is limited in order to avoid unwanted side reactions and disproportionately large ows in the system. With regard to ows, decreasing the minimum SOC from 20% to 10% requires a doubling of the pumping and plumbing capacities in order to maintain a constant stoichiometric excess. We replaced Q c with Q d in order to put all cost terms on the same basis. This change introduces the round-trip coulombic efficiency, 3 q,rt . Finally, the charge capacity was replaced with the ratio of energy to voltage.
This introduces the energy efficiency of the system, 3 sys,d , to account for losses associated with supporting equipment. Eqn (7) shows that the mass of electrolyte is inversely proportional to the discharge voltage. Thus, operating at low voltages is undesirable from the perspective of electrolyte cost. The electrolyte is expected to make a signicant contribution to the total cost of a nonaqueous ow battery. The electrolyte, in our terminology, includes a dissociated acid, base, or salt in a solvent, but excludes the active material. Explicitly accounting for the electrolytes and active species on the positive and negative sides yields: The subscripts + and À denote the positive and negative active species, and the subscripts e+ and eÀ refer to the positive and negative electrolytes. S + is the solubility of the positive active species per unit mass of electrolyte in kg kg À1 . The solubility of a redox species is typically a function of oxidation state. The minimum of the solubilities for the oxidized and reduced forms should be used with enough margin to ensure that concentration polarization does not lead to deposits in the electrodes that hinder performance. A conict between the solubilities of the salt and active species is likely to occur in practice. We chose not to distinguish the contributions of solvent and conductive species costs to limit the number of explicit parameters for ease of exposition. Expanding the expression for chemical costs to explicitly include the solvent and salt is straightforward, if justied.
A polarization equation relating i d and V d and relationships describing the system and coulombic efficiencies are needed to proceed with the analysis. A ow battery must operate efficiently, 3 e,rt > p c /p d , in arbitrage applications. It is, therefore, reasonable to expect a linear polarization response for a successful ow battery over the economically viable range of efficiencies: where the potential intercept, U, corresponds to the thermodynamically reversible or open-circuit potential, and R is the area-specic resistance (ASR) in U cm 2 . The ASR includes ohmic losses in the bipolar plates and separator, as well as kinetic, ohmic, and transport losses in the electrodes. The potential intercept and the ASR generally depend on SOC. For example, the variation in U for a redox pair separated by one oxidation state that follows the Nernst equation is 113 mV between 10% and 90% SOC at 25 C. The potential intercept and ASR are treated as constants in this work. Two important sources of coulombic inefficiency in ow batteries are crossover of active species through the membrane by diffusion and migration, and shunt currents in the manifolds connecting adjacent cells. The inefficiency caused by crossover decreases with increasing current density, while the inefficiency caused by shunt current decreases with decreasing voltage. Using thicker membranes will tend to reduce the crossover of active species at the expense of higher ASR. Using less conductive electrolytes will tend to reduce shunt currents. The effect on ASR is less straightforward in this case. The above mentioned effects are ignored in this work.
Combining expressions for reactor, electrolyte, and system costs and introducing the discharge voltage efficiency, 3 v,d ¼ V d /U, to simplify notation yields the following equation for the total system price for useable energy: The contribution of the reactor to the system cost is a minimum at 3 v,d ¼ 0.5 and monotonically increases as 3 v,d either increases or decreases according to eqn (10). Practically, the assumption of linear polarization will probably fail at low voltage efficiency as mass-transport effects become more important. The cost of the chemicals is a minimum at 3 v,d ¼ 1 and increases monotonically with decreasing 3 v,d . There is a voltage efficiency that yields a minimum total price for any set of component cost and performance parameters, according to eqn (10). In the limit of long discharge times, the total system price approaches the chemical cost.

Analysis of factors to achieve cost target
We are seeking to establish the performance and cost objectives necessary to achieve cost competitive energy storage for aqueous and nonaqueous ow batteries. While market opportunities currently exist at battery prices greater than $200 per kW h (see ref. 57 for example), we focus on aggressive targets that could enable dramatic penetration worldwide. First, we map a broad set of pathways to meet an aggressive metric of $120 per kW h for an energy storage system, not including installation costs. This value is in line with the rolled up installed capital cost target of $150 per kW h suggested by the U.S. DOE Office of Electricity Delivery and Energy Reliability. 5 Then we examine the likelihood of achieving the necessary technological and economic values. The areal costs for each ow battery include a ow eld plate, an electrically insulating frame, a separator, seals, and two electrodes for each cell, and balance of stack materials such as end plates and tie rods. Component costs vary widely and depend on the materials used and the production volume considered. Table 1 lists the costs used in the analysis for 2014 and a mature, high-volume future state. To establish a frame of reference for "future state" cases, we calculate the annual production volume for ow batteries if used to store 1% of the electricity produced worldwide for ve hours each day. In 2009, 20 000 TW h of electricity was produced worldwide. 4 Assuming daily use, 1% of electricity stored, and a 10 year battery life, $10 GW h of new energy storage systems is required annually. This equates to 2 GW of power and thus $10 6 m 2 of active area. For our calculations, values are taken from published literature on ow batteries and polymer electrolyte fuel cells where possible. Polymer electrolyte fuel cells and ow batteries share many design features and materials of construction. Fuel cells generally contain precious metal catalysts that are absent in ow batteries, conversely most fuel cells do not have insulating frames. The cost and performance characteristics of fuel cells have received considerable scrutiny because they are viewed as possible primary power sources for automobiles. When utilizing engineering estimates, we employed a comparison to similar high volume products and/or a bottom-up cost rationalization to determine long-run, high-volume costs.
The likelihood of achieving the low costs in the future state case is highly uncertain. We present the values here as one possible pathway to dramatically reduced energy storage costs that may be reached in the future. We note that both benets from manufacturing scale and engineering advancements will likely be required to reach the optimistic values. However, we also note that the cited studies estimate even lower material costs for items like ion-exchange membranes and carbon-paper electrodes than the values used in this study when annual production volumes exceeding those considered in this analysis are reached. [58][59][60] The analysis of the price of the battery system is presented in terms of the average chemical cost factor, c m , needed to reach a system price of $120 per kW h as a function of open-circuit potential, U, with the product c a R as a parameter. The appearance of the product c a R indicates that an expensive, high performance reactor and a cheap, low performance reactor may be equivalent in economic terms. The chemical cost factor is given by: The positive and negative active species are assumed to be identical in terms of cost, molecular weight, ratio of s/n e , and SOC range. The electrolyte cost factor, c m , can be interpreted as the cost of the active material in a free electrolyte solution, or the cost of the combination of active material and electrolyte in a nonaqueous battery. Aqueous acidic solutions approach the ideal free electrolyte. For nonaqueous electrolytes, the solubility required to reach a given value of c m can be calculated for prescribed values of c m,+ and c m,e+ from the equation: The subscripts + and À are interchangeable as we have assumed that the two electrolytes have identical properties. The contribution of the chemical costs was cast in the form of c m to enable comparison with commodity chemical prices. However, we note that the quantity sn e À1 Mc m which has units of $ per mol e À is a theoretically pleasing alternative that presents itself when examining eqn (10). The SOC range and coulombic efficiency could be included in this number to account for incomplete utilization of active material. Table 2 summarizes the parameters used in the simulations presented in Fig. 3, where P 0 /E d is the target system price, $120 per kW h, excluding installation. The discharge time of 5 h matches the average given by Sandia for time-of-use energy management. 57 The SOC range is typical of vanadium ow batteries. The coulombic efficiency, 3 q,rt , was set to 0.97 to capture both crossover and shunt current losses. The system efficiency was assumed to be 3 sys,d ¼ 3 sys,c ¼ 0.94. The voltage efficiency, 3 v,d ¼ 0.916, was calculated to give 3 e,rt ¼ 0.75, assuming that the magnitude of the discharging current density is twice that for charging. The corresponding voltage efficiency during charging is 0.96. The assumptions behind the balanceof-plant cost and additional contributions to price estimates are detailed in the supporting information. The oxidized and reduced forms of the active species were assumed to differ by one oxidation state. Species that can transfer more than one electron offer a considerable theoretical benet. The assumed molecular weight of 0.1 kg mol À1 is a compromise that is higher than metals like Fe and V and lower than organic molecules like benzoquinone. A rough optimistic limit for organics is 1 electron equivalent per benzene ring, which yields an equivalent weight of n e M i /s i ¼ 0.078 g (mol e À ) À1 . Fig. 3 illustrates lines of constant system price, $120 per kW h, for the parameters in Table 2, and the combinations of c a R listed in the gure. The abscissa is the open-circuit potential, U.

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Aqueous batteries should be possible for U < 1.5 V. This exceeds the thermodynamic stability window of water in recognition of the fact that oxygen and hydrogen evolution are sluggish on carbon. Higher voltages likely require nonaqueous, aprotic electrolytes like those used in Li-ion batteries. Lead-acid and zinc-bromine batteries, with U > 1.7 V, are notable exceptions to this heuristic. The aqueous region is marked with two triangles in the lower le of the gure. The nonaqueous region is iden-tied in a similar fashion, towards the upper right of the gure.
The darkly shaded triangles are considered to have a higher likelihood of achievement compared to the larger and lightly shaded triangles. The le ordinate is the chemical cost factor, c m , in $ kg À1 . This cost factor is an average of the positive and negative sides and includes the active material, salt, solvent, and storage vessel costs on a mass of active material basis. The electrolyte should be inexpensive in the aqueous region; thus, c m should correspond essentially to the sum of the active material and storage vessels only. A practical guideline for a minimum c m for aqueous systems is $2 kg À1 . Commodity prices will dictate the exact cost contribution, which will probably be higher (e.g., vanadium costs $23 kg À1 ). The vertical scales inset on the le side of the gure aid in the interpretation of c m for nonaqueous systems. The inner lemost scale shows the solubility in kg kg À1 required to achieve a given chemical cost factor if active material and electrolyte cost $5 kg À1 each. The rightmost scale converts the solubility to a concentration of active species, assuming specic volumes of 1 L kg À1 . The sloped, dashed lines represent different reactor costs, parameterized by the product c a R. Table 4, to be discussed later, contains c a R values that can be compared to the values in Fig. 3. The future cost of nonaqueous electrolytes and tailored molecules is difficult to forecast at the scale of a combined gigawatt hours of energy storage around the world. However, the commodity chemical industry provides some clues as to what a reasonable price for materials might be. 62,63 Annual production of a 3 V nonaqueous ow battery providing a combined 10 GW h of storage requires $10 4 metric tons per year of electrolyte and active material and $10 6 m 2 of membrane annually. Prices of commodities of similar or larger scale such as acetonitrile, propylene carbonate, triethylene glycol, and ethyl ether fall in the $1-5 kg À1 . 62,64 Based on the trends observed for these, we selected $5 kg À1 as a reasonable material price that could be achieved if volumes of electrolyte and active material on the order of 10 4 metric tons are demanded by the market. World-wide production of acetonitrile was near 10 5 metric tons in 2011, although only a portion of that amount was isolated and rened for resale. 62 An electrolyte includes both solvent and salt contributions, for which the salt is likely to be more expensive than the solvent, particularly if uorinated and only used in a few industrial applications. The assumption of $5 kg À1 for the electrolyte could be considered as $2 kg À1 for the solvent and $20 kg À1 for a salt at 1 M concentration; however, we lump the values together as a reection of the inherent uncertainty contained in this analysis.
In Fig. 3, the top line, c a R ¼ 0, corresponds to a free reactor and gives the maximum possible chemical cost that yields the system price target of $120 per kW h, subject to the parameters in Table 2, as a function of open-circuit voltage. This line prevails at long discharge times, as the contributions of the reactor and balance of plant diminish to zero. The lower lines correspond to higher reactor costs. The line at 5 $ mU is consistent with an ASR of 0.5 U cm 2 and a reactor cost of $100 m À2 . These values appear to be achievable with aqueous ow batteries having ion-exchange membranes and carbon bipolar plates for a high-volume, large-market future state. For the sake of comparison, ASR values as low 0.23 U cm 2 have been measured for H 2 /Br ow batteries with thin membranes. 15 Elimination of the ion-exchange membrane in favor of a nanoporous separator, if technically palatable, would certainly reduce costs at lower production volumes. Nanoporous is taken  Fig. 3 Allowable chemical cost factor on an active material basis (in $ kg À1 ) versus open-circuit voltage for a range of reactor costs (c a R in $ mU). All points on a line give a system price of $120 per kW h with the parameters given in Table 2. The region U < 1.5 V is considered to be available to aqueous systems. The dark shaded triangles are considered to have a higher likelihood of achievability compared to the larger lighter shaded triangles. The leftmost inset vertical scale shows the required solubility (in kg kg À1 ) of a nonaqueous active species when solvent and solute cost $5 kg À1 . The rightmost inset vertical scale on the right shows the molar concentration, assuming specific volumes of 1 L kg À1 .
here to mean pore sizes less than 100 nm. Thus, an aqueous system meeting the $120 per kW h target is possible with a chemistry that costs $5 kg À1 and operates at 1.5 V. The line drawn for c a R ¼ 50 $ mU represents a nonaqueous reactor cost of $100 m À2 and ASR of 5 U cm. 2 The ASR is expected to be higher in nonaqueous batteries compared to aqueous electrolytes because of a lower electrolyte conductivity in the separator and within the electrodes. High-power Li-ion cells have pulsepower ASR >5 U cm 2 with more common values near 20 U cm 2 . 65,66 Today's Li-ion batteries have area cost factors of approximately $6 m À2 and potentially lowering to $2-5 m À2 for higher volumes. This is at least a factor of 20 smaller than the optimistic future state area cost of ow batteries at $100 m À2 . The larger voltage window of nonaqueous electrolytes allows for a wider range of c a R values. As mentioned previously, power density scales with the square of voltage. In addition, stamped metal plates will likely replace the graphite ow elds, resulting in a net increase in c a R over aqueous that is less than a factor of 10. The dark shaded region bounds the most likely set of parameters yielding a nonaqueous ow battery with a system price of $120 per kW h. This region suggest U > 3 V and S > 0.8 kg kg À1 (a concentration of >4.4 mol L À1 with M ¼ 0.1 kg mol À1 and a specic volume of 1 L kg À1 ) with an active material that costs less than $12 kg À1 and is compatible with an electrolyte costing $5 kg À1 . These values are inexact, but they provide guidance regarding the combinations of potential, solubility, and performance that must be achieved in order to create a successful nonaqueous ow battery for storing grid energy. The quantities in Table 2 should be adjusted once a particular electrolyte and active material couple has been identied to improve accuracy. Fig. 3 indicates that nonaqueous electrolytes enable a potentially wider range of cell voltages compared to aqueous electrolytes. Nonetheless, one must also consider two additional factors that potentially counteract this perceived advantage. First, the lead-acid battery teaches us that while the thermodynamic stability window of water is 1.2 V, a 2.0 V aqueous cell is possible when the kinetics of water splitting is slow. The products of water decomposition, H 2 and O 2 , may be recombined advantageously to reform water. Energy storage systems based on enclosed architectures such as lead-acid and nickel-metal hydride are designed to promote this recombination. 67,68 An open architecture could also mitigate the loss of water by electrolysis with the addition of water to the reservoir, assuming that the gases escape from the system. Conversely, nonaqueous electrolytes generally undergo irreversible decomposition when pushed outside of their stability window, which results in various gas molecules, soluble compounds, and precipitants. 46,69 The precipitant is commonly associated with increased resistance to electron transport from the conducting surfaces (i.e., passivity). If passivity is not achieved, the irreversible reaction will continue to consume the electrolyte, thereby dramatically increasing the battery impedance and shortening the useable life. The second consideration is the higher cost of nonaqueous compared to aqueous electrolytes. Current Li-ion electrolytes are reported to cost $15-20 kg À1 , albeit at a relatively low production volume relative to commodity chemicals. 65,66 Conversely aqueous electrolytes cost signicantly less than $1 kg À1 . 70 Fig. 4 illustrates the sensitivity of the required solubility to the cost and equivalent weight of the active material for an electrolyte that costs $5 kg À1 and a battery price of $120 per kW h. For low molecular weights and low active material costs, the required solubility is below 0.5 kg kg À1 . However, a solubility at or above 1 kg kg À1 is required for the target active material cost of $5 kg À1 and a more reasonable equivalent weight of 100 g (mol e À ) À1 . The sensitivity to molecular weight raises an important issue related to the counter ion required by a tailored molecule. When a molecule undergoes a redox reaction, the newly formed charge is balanced with a cation or anion in the electrolyte. If a molecule is transformed to a net positive valence, then an anionic counter ion is needed. In nonaqueous electrolytes, PF 6 À or BF 4 À might be considered as counter ions.
Unfortunately, these uorine-based anions are expensive constituents of current electrolytes. Additionally, the anions have large molecular weights and will quickly shrink the available design space to nothing. In contrast, aqueous systems may utilize inexpensive salts such as sulfur (i.e., H 2 SO 4 ). For aqueous electrolytes, an anion-paired tailored molecule would likely be reasonable. A commodity counter ion such as sulfur may also be possible in a nonaqueous battery, assuming a high enough conductivity is reached. However, cation-associating molecules are most likely to achieve the cost target. Table 3 shows performance characteristics for various battery chemistries using enclosed, ow, or hybrid architectures. Mature conventional batteries, both aqueous and nonaqueous, are included together with various existing and conceptual ow batteries. These values are combined with the cost factors in Table 4 to estimate representative system prices for 2014 and prices for a potential future state, excluding installation. This future state is an example of one possible pathway to costeffective storage that may be reached through high-volume production, market competition, and engineering advances. Table 3 also includes reported prices for battery chemistries that are available for grid integration today. The performance and cost values are taken from the literature, private discussions with industry experts, and engineering estimates. The ESI † contains details regarding the calculation for each battery chemistry considered. The majority of the 2014 prices are taken from the EPRI/DOE handbook, 1 which compiled surveys for megawatt-scale energy storage devices from industrial suppliers. Examination of the power density, J A , reported in Table 3 illustrates that nonaqueous batteries can approach similar power densities to aqueous batteries. Greater differences are seen across different battery architectures than within a single class. The vanadium redox ow battery (VRFB), future-state tailored-molecule aqueous redox ow battery (AqRFB), and future-state tailored-molecule nonaqueous redox ow battery (NAqRFB) are projected to exhibit power densities on the order of >1 kW m À2 for a continuous 5 h discharge at 75% round-trip efficiency. While nonaqueous electrolytes commonly have lower conductivity and thus higher ASR, a nonaqueous electrolyte can support higher cell voltages. Reactor cost is proportional to c a , R, and U À2 . Thus, if the potential is increased from 1.5 to 3 V, the product c a R can increase by a factor of 4 without causing the cost of the reactor to increase. Recently, Aziz et al. demonstrated a tailored quinone in an aqueous electrolyte that had an ASR on par with VRFB and the values assumed for AqRFB. 23 A more detailed evaluation of ASR and power density is provided later in this paper.

Cost comparison of different battery technologies
The area of a ow reactor is sized specically for a target discharge efficiency. However, enclosed batteries are commonly limited by other factors such as mass transport or decay mechanisms that result in the comparatively low power densities for the graphite/LiFePO 4 (Gr/LFP) battery and carbon-based advanced lead-acid (C-PbAcid) battery. The electrode capacity densities used here are 2 mA h cm À2 for Gr/LFP and 60 mA h cm À2 for C-PbAcid. If Gr/LFP were not limited to a maximum electrode thickness of 100 mm, then a target discharge voltage efficiency of 91.6% would result in electrodes 3-fold thicker and power density a factor of 10 higher. The power density that is measured during a 5 h discharge is not representative of pulse power capability, which can be much higher. The power densities of enclosed batteries during pulses that are seconds in duration far exceed the values in Table 3. More discussion on the limitations of enclosed cells may be found in the ESI. † Hybrid architectures that utilize a metal negative electrode and a uid reactant at the positive electrode capture some of the benets of ow batteries, but are still constrained by a stationary electrode. The hybrid designs in Tables 3 and 4 are limited by the maximum allowable current density for the metal electrode considered. The current density constraint for metal electrodes is set by the need to control morphology during plating, when the battery is charging. 71,72 Assuming that the time available for charging is twice that for discharging, then the magnitude of the discharge current is approximately double the maximum charging current. The charge limitation is taken to be 20 mA cm À2 for zinc and 3 mA cm À2 for lithium. Lithium metal cycles poorly above 1.5 mA cm À2 as a result of poor lithium plating morphology control and irreversible capacity loss. 73 Crowther and West have visualized lithium dendrite growth at a current density of 2 mA cm À2 . 74 Thus, 3 mA cm À2 represents a dramatic advance in the ability to control lithium metal plating morphology, perhaps through a convection mediated approach. 72 A sensitivity analysis is presented in the ESI † highlighting the importance of improving charge acceptance if lithium metal is to be used in a hybrid battery. Fig. 5 illustrates the existing cost structure and potential future states for the Gr/LFP based Li-ion enclosed battery as well as the VRFB. The system price is separated into four contributions. The reduction in each of these factors between the reported 2014 minimum price and the projected future state price is shown in Fig. 5. Descriptions of these contributions, sources of information, and assumptions are documented in the ESI. † The energy and power costs are related to materials costs, with the quantities determined by the performance of the chemistry and the cell. The balance-of-plant cost, c bop , captures system complexity through purchased items such as heating and cooling equipment, state-of-charge management, power electronics, and pumps if required. The costs of the storage vessels are added to the electrolyte and active materials, because these three costs should scale together with energy. The additional contribution to price, c add , captures the manufacturing cost, sales, general costs, administration costs, research and development costs, and prot quantities necessary to mark up the materials cost to a system price. The 2014 c add estimates were found by subtracting the material and purchased items costs from battery prices reported in the literature, aer correcting for any installation costs.
The largest decrease in total system price for Li-ion batteries and VRFBs is the result of smaller c add values. The 10 GW h production scale considered in this analysis has the potential to enable this dramatic cost reduction. 65,75,76 Established largeformat Li-ion factories are commonly on the order of 1 GW h in annual production. 77 The C-PbAcid batteries are also projected to benet from a larger scale in recognition that current production levels are not at the volumes enjoyed by automotive starting lighting and ignition or forkli batteries. 78 The projected C-PbAcid battery prices approach those commonly reported for valve-regulated lead-acid batteries, but with Table 4 Cost factors for enclosed, flow, and hybrid architectures that are currently used and may be used in the future for energy storage. The cost factors for 2014 assumed in this analysis are detailed in the ESI. Additionally, the lower and upper 95% confidence intervals (L95% and U95%, respectively) for projected future states of each technology are also listed C-PbAcid PbC/PbO 2 Li-ion Gr/LFP VRFB V 2+ /V 5+  Table 4 and Fig. 5, the future values of c bop and c add are highly uncertain, but are included in an attempt to close the gap between material costs and the total equipment cost realized by the owner of the energy storage system. More importantly, these values demonstrate the dramatic lowering of price contributions that must occur to reach long-term goals. Competitive pressures, benets from scale, and benets from learning by doing will all be driving forces for these projected cost reductions. Whether or not the assumed values are reached depends on both the existence of a protable energy storage market that utilizes the chemistry in question and the quality of the engineering estimates.
For the high volume competitive market place projections, VRFB is shown to have signicantly smaller additional contributions to price than Li-ion or C-PbAcid. This projected future state is based on the assumption that ow batteries require a comparatively simpler assembly process than enclosed batteries. This is supported by the direct comparison of the US Department of Energy funded manufacturing cost models for Li-ion and fuel cells. 58,59,65 The future state manufacturing cost calculations made for the assembly of proton exchange fuel cells were examined to estimate values for the additional contributions to the price factor of ow batteries. 58,59 The 2 GW annual production volume based capital depreciation and labor costs for pressing, slitting, assembling, sealing, and conditioning the reactor were less than $6 kW À1 , aer the lower power density for the ow battery (i.e., 10 vs. 2 kW m À2 ) had been taken into consideration (details in ESI †). 44,45 We note the power density of an automotive fuel cell is rated at a considerably lower efficiency than a ow battery is. The report did not provide the required mark-up values on depreciation and labor necessary to reach a full system price and thus we estimated these multipliers here using the same framework as the BatPaC Li-ion model. Based on this minimal manufacturing cost contribution, we use a future-state value for additional contribution to price that ranges from $50 to $125 kW À1 (details in ESI †). Nonaqueous ow batteries are charged an additional $25 kW À1 in recognition of higher likelihood of complexity in the assembly process (e.g., need for a dry room). Future work will examine in greater detail the manufacturing cost and additional mark-up of a ow-battery assembly process. Fig. 6 illustrates the range of projected future-state battery prices compiled from the values in Tables 3 and 4. Uncertainty was calculated through a Monte-Carlo analysis to capture the upper and lower 95% condence interval for each battery chemistry. Uncertainty was only considered for cost inputs. The cost breakdown for the mean battery price value is shown to illustrate the relative contributions of each component. However, the range of uncertainty is most instructive when Here, balance of plant (BOP) is equivalent to c bop on an energy basis. In both cases, the largest decrease occurs in the additional contributions to price factor (ADD) that encompasses depreciation, overhead, labor, etc. comparing different batteries. Some batteries have signicant uncertainty owing to commodity uctuations, such as the vanadium in the VRFB. This projection does not take into account any resource recovery and recycling that may be possible. Other batteries, such as lithium polysulde (LiPS), exhibit signicant uncertainty as a result of calculated design and resulting sensitivity to a wide range in areal material cost factors. The LiPS battery has a modest average open circuit voltage of 2.25 V and is limited to relatively small charging current densities. In contrast, a battery design that combines a nonaqueous tailored molecule with lithium metal (NAqHyb) has nearly twice the voltage of LiPS and the same charging current limitation. The NAqHyb is much less sensitive to the wide range in area cost factors, and its higher power density results in a lower cost of power. The lithium metal batteries were both designed with a porous separator rather than a more costly ion-exchange membrane. However, the greater power density of the full ow architecture results in an overall lower cost of power.
As shown in Fig. 6, batteries utilizing closed architectures (C-PbAcid and Gr/LFP) are projected to be more expensive than those based on ow architectures. This difference in system price results from the lower reactor cost associated with the ow architecture, and from the lower additional contributions to price factor. The presumed simpler assembly process for a ow battery is projected to be a key distinguishing factor compared to enclosed cells. An additional discriminator, not captured in our economic analysis, is the reliance of ow batteries on facile reactions. These reactions are expected to be less susceptible to degradation than those that occur at stationary electrodes in enclosed cells like lead acid and involve more active participation of solid materials that can cause fatigue. Li-ion chemistries that undergo sizable volume expansion are also prone to cyclebased degradation. However, most Li-ion chemistries experience minimal volume expansion. The limiting factor for cells with graphite anodes is the growth of the solid-electrolyte interphase through electrolyte decomposition and, with it, the irreversible consumption of cyclable lithium. It is unknown at this time if nonaqueous ow batteries will age in a manner more similar to aqueous ow batteries or enclosed Li-ion cells. For nonaqueous hybrid approaches, signicant advances are required to enable lithium metal-based systems to reach life goals in excess of 5000 cycles with minimal capacity loss.
In the comparative analysis of Fig. 6, little difference is seen between AqRFB and NAqRFB. Nonaqueous approaches do not seem to provide a step change in opportunity beyond aqueous approaches. The differentiation between these two electrolyte platforms must fall to the chemists and engineers that will develop the tailored molecules and systems that store them. Nonaqueous electrolytes inherently offer a wider range of possibilities to explore beyond aqueous systems. However, the new constraints of solubility and electrolyte (solvent + salt) cost in the nonaqueous medium may be more constrictive than the promise of a larger design space.
The VRFB and AqRFB have nearly identical power, balance of plant, and additional costs. The energy cost is lower for the AqRFB, however the difference is much less than one might anticipate based on the prices of the active materials. While vanadium costs approximately 4Â more than the tailored organic molecule in $ kg À1 , the equivalent weight of the organic molecule in g (mol e À ) À1 is approximately 3Â more than vanadium. Achieving a low equivalent weight with an organic molecule is likely to be challenging.

Properties of aqueous and nonaqueous ow batteries
To assess the likelihood of achieving the estimated performances and costs, we compare key measured physical, transport, and kinetic properties of aqueous and nonaqueous electrolytes. Fig. 7 shows properties for a number of nonaqueous electrolytes. The properties have been normalized by dividing by the quantity appropriate for the VO 2+ /VO 2 + positive electrode couple of a VRFB; the separator is assumed to be a Naon ion-exchange membrane. The ESI † contains additional information about the electrolytes that is not included in the gure. The selected properties are pertinent to kinetic, ohmic, and mass transport losses in the electrochemical reactor as well as pumping losses and, indirectly, electrolyte cost. The arrows indicate better properties. Nonaqueous electrolytes have conductivities approximately two orders of magnitude lower than aqueous electrolytes. This difference drives comparatively higher ASR, although the additional losses may be less than proportional because, in cell designs without a gap, the ohmic losses associated with the electrolyte occur in a porous electrode that, in many designs, contains a highly conductive solid phase. This aspect will be discussed in more detail in the subsequent section on modeling. The second column in Fig. 7 shows the relative conductivity of the separator between the electrodes. The separators include Naon exposed to different organic electrolytes, which give conductivities differing by an order of Fig. 7 Physical properties of select nonaqueous electrolytes normalized by the quantity describing the VO 2+ /VO 2 + couple of a VRFB. A Nafion membrane is assumed for VRFB. The arrows indicate the direction of better nonaqueous properties. magnitude, and ceramic electrolytes. The ohmic loss through the separator makes a proportional contribution to ASR; therefore, this difference between aqueous and nonaqueous batteries is particularly important. Whether or not an ionexchange membrane is required in either an aqueous or nonaqueous system with two owing electrolytes is an open question. Clearly, minimizing transport of active species across the separator is desirable in order to maintain high coulombic efficiency and to eliminate the need for separation processes. However, a combination of tailored active species and membranes with low hydraulic conductivity may possibly satisfy these requirements for either aqueous or nonaqueous systems. For reference, a lithium battery electrolyte in a polypropylene separator has conductivity near the maximum shown in Fig. 7.
As shown in the third column of Fig. 7, nonaqueous viscosities range near aqueous values, indicating that it should be possible to achieve similar pumping losses. Nonaqueous active species tend to have lower diffusion coefficients than metal ions like vanadium. The higher mass transport losses may not be important because nonaqueous cells will tend to operate at lower current densities than aqueous cells because of ohmic losses. Transport losses can usually be addressed by increasing intra-electrode velocity, at the expense of higher pumping losses. The solubility of a nonaqueous active species must be high because the supporting electrolyte is relatively expensive. The data in column 5 indicate that high solubility is possible in some nonaqueous systems. The nal column indicates that high rate constants can be achieved in nonaqueous systems. The importance of this result is shown in the subsequent modeling section.

Modeling of ASR
The probability of future nonaqueous and aqueous ow batteries attaining low reactor cost is a direct function of the range of achievable ASR values. We employed a mathematical model based on porous-electrode theory to determine physically realistic ASR values. The model treats polarization losses in the direction perpendicular to the plane of the membrane. The electrode thickness is optimized to achieve the smallest ASR while maintaining the target discharge voltage efficiency of 91.6%. Liquid electrolyte is continuously forced through the electrodes in a primary ow direction that is parallel to the membrane. The electrodes are assumed to be inert, porous carbon felts or papers. This is a common electrode structure for aqueous ow batteries.
The cell potential may be expressed as: The rst and second terms in the nal equality signify the potential drops across the positive and negative electrodes. The nal term captures ohmic losses in the membrane, current collectors, and contact resistances. The subscripts 1 and 2 denote the solid and electrolyte phases; the subscripts + and À denote the positive and negative electrodes. Analytical solutions are available for the potential drop across a porous electrode when either linear or Tafel kinetics applies, in the absence of mass-transport limitations. [79][80][81] The linear solution was used for i < ai 0 L; the Tafel expression was used otherwise. The ASR was calculated by dividing (U À V d ) by i d . By this denition, ASR is not necessarily a local tangent to the polarization curve. The ASR is independent of current density when the linear approximation applies to the electrodes.
Properties that affect the voltage drop across a porous electrode include thickness L, electrolyte conductivity k, solid conductivity s, interfacial area per unit volume a, exchange current density i 0 , anodic transfer coefficient a a , and cathodic transfer coefficient a c . The conductivities are corrected for the porosity and tortuosity of the electrode. Interfacial area per unit volume can be calculated from the ber diameter (assuming high aspect ratio) and porosity. The exchange current density is related to the rate constant by Faraday's law. Both transfer coefficients were assumed to be 0.5 following convention in the absence of more detailed information. 82 The reader is referred to the aforementioned literature for complete descriptions of the potential drops across porous electrodes in the linear and Tafel regimes. Given the wide range of reaction rate constants in the literature, we have chosen to present results in terms of ASR versus rate constant, with optimistic values for other parameters. Table 5 contains parameters, aside from rate constants, used in the simulations. Simulations were conducted for aqueous and nonaqueous cells with either Naon or an inert nanoporous separator. The properties of the solid matrix were identical for all simulations. The electrode porosity, ber diameter, solid conductivity, and contact resistance were measured for a moderately compressed carbon paper. 18 Bulk electrolyte conductivities include 229 mS cm À1 for an aqueous solution of 1.5 M VO 2+ in 4.0 M total sulfate, 83 52 mS cm À1 for Naon in contact with the same solution, 84 and 5 mS cm À1 for 1 M LiPF 6 in propylene carbonate, 69 and less than 1 mS cm À1 for Naon in contact with lithium salts dissolved in aprotic solvents. 85,86 Conductivity in the nanoporous separators is the bulk electrolyte conductivity corrected with the Bruggeman correlation for a porosity of 50%, raised to power of 1.5. The solid conductivity is considerably higher than either the aqueous or nonaqueous electrolyte conductivity. Fig. 8 shows the calculated ASR as a function of kinetic rate constant for hypothetical aqueous and nonaqueous cells. The ASR is calculated at a discharge voltage efficiency of 91.6%. The electrode thickness is optimized to give the minimum ASR at the target efficiency for each rate constant, subject to a minimum of 50 mm and a maximum of 5000 mm, respectively. A more conservative minimum is 100 mm when pressure drop from convective ow is considered. The ratio of nonaqueous-toaqueous power densities is shown in Fig. S3 in the ESI † assuming 3 V and 1.5 V, respectively. The resistance is between 0.5 and 30 times higher for the nonaqueous cell in the range of rate constants examined, with the largest differences occurring for large kinetic rate constants. The difference in limiting ASR at high rate constants is driven by the membrane resistivity for nonaqueous compared to aqueous conditions. While this is not a direct function of the bulk electrolyte conductivity, the chemical physics driving the differences is likely similar.
Cation mobility in an electrolyte is related to multiple phenomena, but the most important in this comparison are likely the mode of conduction, solvated radius, and the solvent viscosity. 69 Aqueous electrolytes that conduct protons or hydroxide ions as the primary charge carrier benet from the Grotthuss hopping mechanism, which utilizes the hydrogen bonding network present in water. The transport of other ions in aqueous and nonaqueous electrolytes is governed by diffusion in an electric eld, a markedly slower process. Examination of the Stokes-Einstein equation shows that the diffusivity is inversely proportional to solvent viscosity and solvated ion radius. 69 In general, the solvated radius of aqueous electrolytes is smaller than nonaqueous electrolytes, leading to expectations of faster conduction in aqueous electrolytes in line with experimental observations. Ion transport in nanoporous separators is expected to be directly proportional to the bulk electrolyte. In the case of cation-selective membranes, such as Naon, while the Grotthuss mechanism still enables proton hopping, the transport of other ions is impacted by the cation type, the solvent choice, and the dissociation of the cation from the xed anion site (anion basicity). 85, 86 Doyle and co-workers showed that ionic conductivities for the N117 (Li + ) membrane exceed 10 À3 S cm À1 at room temperature for a number of nonaqueous solvents. 86 Solid lines in Fig. 8 represent the improvement in ASR if a 50 mm-thick nanoporous separator replaces Naon. The nonaqueous ASR is signicantly reduced by this change. Conversely, a separator of 100 mm thickness would result in the same ASR and perhaps a more acceptable crossover contribution to the coulombic inefficiency. The higher voltage that is achievable in nonaqueous electrolytes can counterbalance a higher ASR, resulting in acceptable reactor power density (power density is proportional to U 2 R À1 ). The key factors in determining the relative comparison are the rate constant and the conductivity of the membrane. Fig. 8 and S5 † support the selection of ASR values used in Table 3 and demonstrates that nonaqueous chemistries should be able to achieve adequate power densities. While this analysis was completed for room temperature, operating at higher temperatures is an alternative pathway to reducing the ASR and thus system cost.

Membrane vs. porous separator
Recently, the development of aqueous redox ow batteries has benetted tremendously from parallel efforts in fuel cells. In comparison, nonaqueous redox ow batteries are still in their infancy, and the extent to which the acquired knowledge from fuel cell and Li-ion battery development can be applied remains to be seen.
Presently, although Naon is expensive, it is the preferred membrane for most aqueous redox ow batteries due to its high proton conductivity and chemical stability. Dramatic reductions in cost can be expected with increased manufacturing volumes (i.e., over an order of magnitude [58][59][60] ). Recent research efforts have primarily focused on optimizing existing Naon membranes, through chemical and physical modications, for specic redox ow battery chemistries or exploring potentially less expensive alternative membranes. Schwenzer et al. comprehensively reviewed the current state of membrane development for vanadium redox ow batteries, highlighting efforts in cation-exchange uorocarbon, cation-exchange hydrocarbon, anion-exchange and amphoteric polymers, and nonionic separators. 87,88 The key challenge for these alternative membranes is maintaining or improving upon the ionic conductivity, selectivity, and chemical stability of Naon without increasing the manufacturing costs. Replacing ionconducting membranes with porous separators could lead to immediate cost reductions, provided the reactor design could be modied to account for the likely increase in crossover of active species.
Signicantly less is known about the development needs of nonaqueous membranes beyond ionic conductivity. Of particular interest for ow batteries is the chemical stability to redox electrolytes, physical stability in large format cell, and species selectivity. The present state of membrane development for nonaqueous redox ow batteries was recently reviewed by Shin et al. 34 Their report highlighted that anion-exchange membranes are employed in the majority of nonaqueous cells primarily due to the chemistries under investigation (i.e., metalcentered coordination complexes). While few cell chemistries employ cation-exchange membranes, this number is expected to increase due to the diversity of potential redox materials and the need to increase energy density. A body of literature exists for cation-exchange polymeric and ceramic solid electrolytes for rechargeable Li-ion and Li-metal batteries. 85,86,89 Indeed, several materials deemed unsuccessful for these applications (e.g., unstable against Li metal) may nd utility for nonaqueous redox ow batteries. Under nonaqueous conditions, replacing ionselective membranes with porous separators could lead to cost reductions and appreciable improvements in ASR, provided the reactor design is modied to account for the likely increase in crossover. Although signicant improvement is possible in the science and engineering of nonaqueous ion conductors, they will not surpass aqueous proton (or hydroxide)-based conductors with regard to conductivity.

Conclusions and path forward
Materials-level performance and cost requirements are presented in Table 6. Both aqueous and nonaqueous electrolyte platforms would benet from tailored molecules with low equivalent weights, fast kinetics, and cell voltages that stretch the electrolyte stability window. The active material and electrolytes must both be inexpensive. Nonaqueous electrolytes should be no greater than $5 kg À1 , and aqueous electrolytes must be almost free. Targets for the concentrations of active materials are 5 mol L À1 and 2 mol L À1 for nonaqueous and aqueous systems, respectively. Finally, the sensitivity of the nonaqueous system to salt cost and the equivalent weight of the active material suggests that successfully tailored molecules will utilize cation-based counter ions.
Nonaqueous ow batteries are far from a commercial reality at the time of this publication. This analysis provides the rst quantitative guidance for researchers to consider in their exploration of chemical systems that, through maturation, may provide cost-effective energy storage. Unlike aqueous ow batteries, an archetype nonaqueous redox couple is not yet established. Examples of intriguing pathways for nonaqueous redox electrolytes that are aligned with the above goals could follow disparate routes. Reducing the unneeded molecular complexity of known redox structures to minimize equivalent weight (e.g., modifying Li-ion overcharge protection molecules) can reduce cost and may lead to increased charge carrier concentration. Conversely, suspensions of electroactive polymers with multiple redox moieties can be created to achieve required charge carrier concentration and potentially obviate the need for an ion exchange membrane.
Both aqueous and nonaqueous ow batteries have pathways to reach long-term objectives for cost-effective energy storage. The design space for nonaqueous appears to be broader than that of aqueous systems. However, the constraints for nonaqueous systems of active material solubility and electrolyte cost create additional hurdles that must be overcome before a system of technological interest can be developed. Additionally, lower risk existing technologies that require less development like C-PbAcid, Li-ion, and VRFB will reach cost effective system price levels for many applications if large enough production volumes are demanded by the marketplace.