Introduction

Integrating renewable energy, such as solar and wind power, is essential to reducing carbon emissions for sustainable development. However, large-scale utilization is hindered by the intermittence and uneven distribution of these power sources1,2,3. Implementation of grid-scale energy storage is essential to mitigate the mismatch between electricity production and consumption4. Different technologies are developed for this purpose, including supercapacitors, sodium–sulfur batteries, pump hydro, flywheels, and superconducting magnetic energy5. Redox flow battery (RFB) is considered one of the most attractive energy storage systems for large-scale applications due to the lower capital cost, higher energy conversion efficiency, and facile modularity6,7. The cores of flow cells are the circulating electrolytes that carry the redox-active materials for energy storage and release.

Currently, the all-vanadium RFB is the most researched and developed RFB chemistry; however, the market adoption of this system has been hampered by high-cost chemicals (material cost close to 60% of the overall system cost8 and low energy density. Although aqueous soluble organic redox species offer a potential option for low-cost materials9,10,11,12,13,14,15, the synthetic processes required to customize the molecular structure for high solubility and optimal potential will again limit the material cost and availability6,16,17,18. Also, they rely on the costly ion-permeable membranes to reduce cross-over, further increasing capital and maintenance costs19.

Recently, polymer redox couples were developed to circumvent ion-permeable membranes20, and the semi-solid Li-ion (suspensions of Li-ion battery active materials in nonaqueous electrolytes) systems have been explored for higher energy density and efficiency. However, high viscosity, lower peak power operation time, and high material cost emerged with these systems4,21,22.

To meet the needs of RFB chemistries with the naturally abundant and low-cost redox-active materials, we report a new RFB system that capitalizes the electrolysis of saltwater or aqueous NaCl electrolyte using the Cl2/Cl− redox couple as the active material for the positive electrode. The Cl2/Cl− has a theoretical capacity of 755 mAh/g, more than two times that of vanadium oxides (VO2+/VO2+, 226 mAh/g) used in current RFBs. Cl2/Cl− redox chemistry is a fast single-electron transferred reaction with an activation energy of 35.5 kJ/mol23,24, which is comparable to or even smaller than that of VO2+/VO2+25, thus is suitable for high power applications. In addition, sodium chloride is one of the cheapest commodities available due to the abundant source in seawater and large-scale production (~$40 per metric ton)26,27. These features enable Cl2/Cl− redox reaction to be a promising candidate for RFB.

Rarely heard in the battery history is that Cl2/Cl− redox couple was used in the RFB to power the first fully controlled airship La France in 188428. The Cl2/Cl− based batteries are often typified by low Coulombic efficiency (CE) of 40–70%29,30,31,32,33 due to Cl2 dissolution in the electrolytes and large voltage hysteresis (0.7 V at 32 mA/cm2) due to non-wettability between electrolytes and electrodes34,35, which limits the energy efficiency to around 60%. Graphite was reported as chlorine storage host via intercalation36. However, the instability of Cl2 intercalated graphite at room temperature results in low storage capacity (35–40 mAh/g) and limited cycle life. After that, no other materials with appropriate stability, storage capacity, and reaction kinetics have been reported to enable reversible Cl2 electrochemical reaction.

Our objective is to develop a new RFB with the highly reversible Cl2/Cl− redox species through electrolyzing the saturated NaCl aqueous electrolyte (NaCl/H2O) and storing the as-produced Cl2 in water-immiscible organic phases such as carbon tetrachloride (CCl4) or mineral spirits. These organic phases provide several desirable properties: (1) Cl2 in CCl4 (Cl2-CCl4) delivers a volumetric capacity of 97 Ah/L due to high solubility of Cl2 in CCl4 (0.184 mole/mole CCl437, which is a 2 to 4 times improvement over the current vanadium-based catholyte (22.6–43.1 Ah/L38; (2) The Cl2-CCl4 is immiscible to NaCl/H2O, thus requires no membrane to prevent cross-over, further reducing costs; (3) The Cl2-CCl4 has low and constant viscosity of 0.819 mPa.s, in contrast to high and varying viscosity of aqueous vanadium-based catholyte (1.4–3.2 mPa.s39, thus is easy to flow; (4) Cl2-CCl4 can wet carbon porous electrodes easily, which significantly enhances the surface area for Cl2 storage and reaction; (5) Cl2 has high diffusivity in CCl4, minimizing energy dissipation for mass transport.

Results

Storage and electrochemical performance of Cl2-CCl4

The Cl2/Cl− redox reaction in NaCl/H2O was evaluated in a concentric cell with RuO2-TiO2 coated porous carbon (RuO2-TiO2@C) as a working electrode, activated carbon as a counter electrode (Fig. S1), and Ag/AgCl as the reference electrode (Fig. 1A). The RuO2-TiO2 catalysts on porous carbon (Figs. S2, S3) are used to promote the oxidation kinetics of chloride40,41,42,43 (Fig. S4). CCl4 was pumped through the working electrode, and the NaCl/H2O through the interstitial space between the working and counter electrodes to ensure adequate Cl- supply. While CCl4 and NaCl/H2O entered the RuO2-TiO2@C electrode as separate flows, they both wet the carbon electrode, demonstrated by <90° contact angles (CAs) on a graphite plate electrode (Fig. 1B, C). And the two liquids take up 66.2% and 33.8% of the void volume in the RuO2-TiO2@C electrode, respectively (see the determination of percentage volume in Supplementary Note 1). The ion-permeable membrane used in traditional RFBs to prevent cross-contamination15,16,44,45,46 is not required here since the Cl2-CCl4 and NaCl/H2O are phase separated.

Fig. 1: Electrochemical performance and physical properties of Cl2-CCl4.
figure 1

A Schematic of the three-electrode cell. Inset shows the cylindrical structure of the cell from the top view, in which the inner diameter of the RuO2-TiO2@C working electrode is 2.0 mm, the thickness of the RuO2-TiO2@C electrode is 1.0 mm, the distance between the working and counter electrode is 3.0 mm and the thickness of the counter electrode is 3.0 mm. The height is 2.0 cm, and the volume capacity of the cell is around 2.0 mL. The total volumes of the CCl4 reservoir and the NaCl/H2O reservoir are 6.0 mL and 2.0 mL, respectively. B CA of CCl4 on graphite plate electrode. C CA of NaCl/H2O on graphite plate electrode. D Galvanostatic charge and discharge profiles of Cl2-CCl4 (red) and Cl2 without CCl4 (black) at the current density of 20 mA/cm2. Both cells ran with constant charge capacity of 600 mAh at Qaq (flow rate of NaCl/H2O) = 0.02 mL/s and Qorg (flow rate of CCl4) = 0.002 mL/s. The differences between discharge and charge capacity are labeled as percentage capacity loss. E The solubility of Cl2 in CCl4 and NaCl/H2O. F The viscosities of Cl2-CCl4 with different concentrations of Cl2 (100% refers to saturation).

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During charge, the Cl2 was generated from oxidizing the Cl− in the RuO2-TiO2@C electrode. The reaction shows a constant potential at 1.2 V versus Ag/AgCl reference electrode [1.36 V versus normal hydrogen electrode (NHE)]. During discharge, the Cl2 in CCl4 was reduced to Cl− in the working electrode and entered the NaCl/H2O (see the formulation for positive electrode reaction). The presence of CCl4 flow significantly enhances the coulombic efficiency (CE) from 8 to 97% (Fig. 1D). Because the solubility of Cl2 in CCl4 is three orders of magnitude higher than that in NaCl/H2O (0.184 mole/mole CCl4 versus 0.0005 mole/mole NaCl/H2O38) (Fig. 1E), the Cl2 generated during the charging process can be stored in CCl4, which prevents Cl2 diffusion into NaCl/H2O as supported by Raman spectroscopy (Fig. S5) and the positive Gibbs free energy to transfer Cl2 from CCl4 to NaCl/H2O (Fig. S6). When 6.0 mL CCl4 was used, a maximum reversible capacity for Cl2/Cl− conversion is 600 mAh (Fig. S7), rendering the capacity of 97 Ah/L for the Cl2-CCl4.

Positive electrode reaction

$$\begin{array}{cc}2{{{{{{\rm{Cl}}}}}}}^{-}\,-\,2{{{{{{\rm{e}}}}}}}^{-}\leftrightarrow {{{{{{\rm{Cl}}}}}}}_{2} & \quad{E}^{0}\,=\,1.36\,{{{{{\rm{V}}}}}}({{{{{\rm{versus}}}}}}\,{{{{{\rm{NHE}}}}}})\end{array}$$

The Cl2-CCl4 positive electrode has a low and almost consistent viscosity. When the concentration of Cl2 increases from 0 to 0.184 mole/mole CCl4 (saturation), the viscosity even slightly decreases from 0.894 to 0.819 mPa.s (Fig. 1F) in accord to Eyring’s absolute reaction rate theory for gas–liquid mixtures47,48. On the other hand, the viscosity of common catholyte could increase by several or even dozen times as the concentration of solute increases49. The low viscosity of Cl2-CCl4 reduces the pumping loss40, and the steady viscosity minimizes the volumetric transfer between catholyte and anolyte at different SOCs50,51.

Full chlorine flow battery (CFB)

To fabricate a full CFB, the activated carbon counter electrode was replaced by NaTi2(PO4)3 negative electrode (Fig. 2A). NaTi2(PO4)3 (Figs. S8, S9) was chosen as the negative electrode due to low potential (−0.5 V (versus NHE), rapid and reversible Na-ion insertion/extraction in NaCl/H2O demonstrated by the symmetric anodic and cathodic peaks with 60 mV separation in the cyclic voltammetry (negative electrode reaction and Fig. S10A)52. The NaTi2(PO4)3 shows a 65% capacity retention even at the C-rate of 315 C (1 C = fully discharge/charge within 1 hour, Fig. S10) and long cycle life of 1000 cycles (Fig. S11).

Fig. 2: Schematic and electrochemical performance of chlorine flow battery (CFB).
figure 2

A Schematic of the CFB, the inner diameter of the tube containing CCl4 and RuO2-TiO2@C electrode is 2.0 mm, the thickness of the RuO2-TiO2@C electrode is 1.0 mm, the distance between the working and counter electrode is 3.0 mm. The thickness of the counter electrode is 3.0 mm. The height of the cell is 2.0 cm, and the volume capacity of the cell is around 2.0 mL. The total volumes of the CCl4 reservoir and the NaCl/H2O reservoir are 6.0 mL and 2.0 mL, respectively. Qaq = 0.02 mL/s and Qorg = 0.002 mL/s. Galvanostatic charge B and discharge C profiles of the CFB at different current densities. The state of charge (SOC) of the battery is normalized to the maximum reversible capacity at 10 mA/cm2, in which 100% SOC represents charge to 600 mAh. D The voltage efficiencies of the CFB at different current densities. E The power densities of the CFB at different current densities.

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Negative electrode reaction

$$\begin{array}{cc}{{{{\rm{Na}}}}}_{3}{{{{\rm{Ti}}}}}_{2}{({{{{\rm{PO}}}}}_{4})}_{3}\,-\,2{{{{\rm{e}}}}}^{-}\,-\,2{{{{\rm{Na}}}}}^{+}\leftrightarrow{{{{\rm{NaTi}}}}}_{2}{({{{{\rm{PO}}}}}_{4})}_{3} & {{{{\rm{E}}}}}^{0}\,=\,-0.5\,{{{\rm{V}}}}({{{\rm{versus}}}}\,{{{\rm{NHE}}}})\end{array}$$

While the overpotentials enhanced (orange dash lines in Fig. 2B, C) as the current density increased, the discharge capacities did not vary (Fig. 2B, C), which could be attributed to the large reaction surface area endowed by the wetting between carbon electrode and Cl2-CCl4 (Fig. 1B, C). Fig. 2D demonstrates cell voltage efficiency (defined as the potential ratio of discharge to charge) of 93.6% at 10 mA/cm2 and ~77% at 100 mA/cm2. The multiplication of discharge capacity and voltage gives the cell power density that peaks at 325 mW/cm2 when operated at 350 mA/cm2 (Fig. 2E). It is worth noting that polarizations for discharge are more significant than those for discharge (Fig. 2B, C). In the CFB, overpotentials are caused by redox reactions and concentration gradient. Since the symmetric factors for Cl−/Cl2 redox reactions are equal17,25, the overpotentials needed to drive the reduction and oxidation reaction are the same, the different overpotentials for charge and discharge observed here could only be attributed to the concentration gradient.

A steady-state model was developed to understand the species distribution and controlling steps in the CFB. The Nernst-Plank equation was applied to the porous RuO2-TiO2@C electrode (cell width = 0–1.0 mm in Fig. 2A), and NaCl/H2O (cell width = 1.0–4.0 mm in Fig. 2A), Fick’s equation was applied to the Cl2-CCl4 phase (cell width = −2.0–0 mm in Fig. 2A). The negative electrode was involved implicitly at the boundary of the NaCl/H2O (cell width = 4.0 mm in Fig. 2A) (see model description and Tables S1–S4 in Supplementary Note 1). The model was validated by the agreement between the simulated and experimental cell voltages (black lines and dots in Fig. 3A, B, experimental potential retrieved from Fig. 2B, C) at the same flow rates and current densities.

Fig. 3: Simulation of the CFB.
figure 3

A Steady-state potentials of CFB charged at 50% SOC with different Qaq and Qorg = 0.002 mL/s, inset shows the whole current density range demonstrating steady charge potential. B Steady-state potentials of CFB discharged at 50% SOC with different Qorg and Qaq = 0.02 mL/s, inset shows the whole current density range demonstrating steady discharge potential. C Distribution of Cl− and Cl2 in the CFB charged at 50% SOC and 50 mA/cm2 with Qaq = 0.02 mL/s and Qorg = 0.002 mL/s. D Distribution of Cl− and Cl2 in the CFB discharged at 50% SOC and 50 mA/cm2 with Qaq = 0.02 mL/s and Qorg = 0.002 mL/s. The position of Cl2-CCl4, NaCl/H2O, porous RuO2-TiO2@C positive electrode and NaTi2(PO4)3 negative electrode are labeled in the legend.

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The model was then used to visualize the species distribution in the NaCl/H2O and in Cl2-CCl4. During charge, the Cl− in NaCl/H2O was consumed inside the porous carbon electrode (Fig. 3C) and limits the reaction kinetics; during discharge, Cl2 in CCl4 is consumed and limits the reaction kinetics. The Cl− concentration gradients are more significant than the Cl2 concentration gradient in the porous electrode for both charge and discharge (Fig. 3C, D), which is the result of a smaller diffusivity of Cl− (1.5 × 10−5 cm2/s for Cl−, 2.0 × 10−5 cm2/s for Cl2 in NaCl/H2O and 3 × 10−5 cm2/s for Cl2 in CCl453,54,55 and lower volume percentage of NaCl/H2O than CCl4 in the porous carbon electrode. The distinct species that control charge and discharge kinetics thus generate the asymmetric charge and discharge overpotentials (Fig. 2B, C). Since Cl− and Cl2 are in different phases, increasing the flow rate of NaCl/H2O during charge and that of the Cl2-CCl4 during discharge enhance the mass transport of the limiting species accordingly, in which not only the overpotentials reduce, but the current density range allowing steady cell voltage extends (inset of Fig. 3A, B). At the highest flow rate examined, the voltage efficiency could be postulated to >93% at 20 mA/cm2.

The high voltage efficiency of the cell is attributed not only to the fast reaction kinetics but also the membrane-free configuration. The potential gradient in the NaCl/H2O was determined by the model (Fig. 4A, B), and the potential difference across the cell at half-cell height was plotted. The potential drop of ~20 mV at 10 mA/cm2 and ~250 mV at 100 mA/cm2 (Fig. 4C) are equivalent to proton transport but over 5 times smaller than Na+ and K+ transport in Nafion ion-permeable membranes in aqueous flow batteries with similar cell dimensions56. Thus, removing the ion-selective membrane opens a range of chemistries to be investigated, as the charge carriers can be chosen arbitrarily.

Fig. 4: Potential gradient in the electrolyte of CFB.
figure 4

A Potential distribution during charge and B during discharge at 50% SOC and 50 mA/cm2. C The potential loss due to ion transport in the NaCl/H2O at different current densities. In all cases Qaq = 0.02 mL/s and Qorg = 0.002 mL/s. The positions of Cl2-CCl4, NaCl/H2O, porous RuO2-TiO2@C positive electrode, and NaTi2(PO4)3 negative electrode are labeled in the legend.

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The CFB demonstrates the round-trip energy efficiency of 91% (calculated by voltage efficiency × Coulombic efficiency) at 10 mA/cm2 and provides an energy density of 125.7 Wh/L (see Methods), which is among the highest of the flow battery systems reported in past 10 years (Table S5). It is worth noting that the Cl2-CCl4 is different from bromine used in flow batteries that faces the serious self-discharge due to the diffusion of Br2 to the negative electrodes in the form of polybromide. When ion-permeable membranes were used to decrease Br2 cross-over, voltage efficiency was significantly limited by the transport of ions in the membrane, resulting in <80% energy efficiency in overall performance57,58,59. Figure 5A, B show the measured cell voltage profile and stable round-trip cycling for this battery at 20 mA/cm2 with a charge storage capacity of 600 mAh and the stable capacity retention for 500 cycles.

Fig. 5: Charge and discharge behavior of CFB and comparisons of the performance matrices to redox flow batteries reported in the past 10 years.
figure 5

A Cell voltage profiles during constant-current cycling and B cycle performance of CFB at 20 mA/cm2, Qaq = 0.02 mL/s and Qorg = 0.002 mL/s, and the charge capacity was set to be 600 mAh. The amount of CCl4 is 6.0 mL, the size of the porous RuO2-TiO2@C electrode is 1.0 mm-thick and 2.0 cm2 area. C The comparison of performance matrices among CFB, organic redox flow battery (anthraquinones as the anode material and ferricyanide as cathode material, ref. S24), all-vanadium redox flow battery (refs. S28, 29), Zn-Bromine redox flow battery (ref. S33), and semi-solid redox flow battery (Li as the anode and LiFePO4 as cathode material ref. S34) (see details in Table S5).

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Discussion

In this study, CCl4 was used as a proof of concept, it can be replaced by other liquids with high Cl2 solubility and are immiscible with NaCl/H2O. The candidates include heptane (chlorine solubility = 0.173 mole fraction at ambient temperature), octane (chlorine solubility = 0.168 mole fraction at ambient temperature), tetradecane (chlorine solubility = 0.254 mole fraction at ambient temperature)29 and mineral spirit. Mineral spirit demonstrates good wettability (CA = 9.1°) with carbon current collector (Fig. S12A), low viscosity (1.24 mPa.s), low toxicity, and is cheaper than CCl460. When CCl4 was replaced by mineral spirit in the CFB, a volumetric capacity of 91.6 Ah/L was delivered at 20 °C (Fig. S12B).

The removal of the ion-permeable membrane also allows multivalent ions as charge carriers. When ZnCl2 is added to the electrolyte, NaTi2(PO4)3 can be replaced by zinc metal electrode, increasing the cell operating voltage to 1.9 V (Fig. S13).

Cost is one of the significant concerns to implementing flow batteries on a large scale for stationary energy storage. Considering that the ion-permeable membrane (mainly perfluorinated polymers) takes up more than 30% of the cost of flow batteries, significant cost reduction is expected with the membrane-free design20. The total material cost for energy storage with the proposed CFB is estimated to be ~$5/kWh, which is the cheapest among all the current flow battery systems (Fig. 5C and Table S5). In addition, the RuO2 catalyst for chlorine evolution reaction (CER) can also be replaced by tin, zinc, cobalt, and other cheap metal oxides partially30. Therefore, the proposed CFB design leaves significant space to meet the stringent target of ~$100/kWh for RFB applications61.

Cl2 is a reactive chemical commodity used in paper, plastic, dye, textile, medicine, antiseptics, insecticide, solvent, and paint industries. Administration and engineering controls for storage and transport are available to confine the incident rate to 0.019% of total chlorine shipments between 2007 and 201762. The Occupational Safety and Health Administration of the United States has set a permissible exposure limit at a time-weighted average of 0.1 ppm (0.68 mg/m3) for bromine, 0.05 mg/m3 for vanadium pentoxide dust, 0.1 ppm (0.4 mg/m3) for quinone, and 1.0 ppm (3 mg/m3) for chlorine63. Thus, there is no apparent increase in chemical exposure risk when changing to chlorine redox reaction.

However, protections and cautions are still crucial. The CFB proposed here is a closed system in which the leakage of Cl2 gas is minimized by the fluoropolymer gasket (see Supplementary Note 2 for evaluation of chlorine permeation). Strategies from the chloro-alkali industry can be applied to reduce the risk of exposure upon scaling up, such as external seal pipe, shutoff system, neutralization reagents (scrubber)64, and sensing systems65.

In summary, the CFB proposed has demonstrated several unique advantages over current flow battery systems, including higher energy density, higher round-trip energy efficiency, and significantly lower prices. The membrane-free design enables both anionic and cationic charge carriers for a RFB, thus expanding the material and chemistry space of the redox flow technologies.

Methods

Material synthesis

The activated carbon with RuO2/TiO2 particles was prepared by dissolving 0.69 mmol RuCl3 and 1.622 mmol C16H36O4Ti in 100 mL isopropanol, then adding 2.0 g activated carbon into the solution. The mixture was stirred for 2 hours, and then the isopropanol was evaporated at 90 °C. Finally, the products were annealed at 500 °C for 1 hour under ambient conditions.

The carbon-coated NaTi2(PO4)3 was synthesized from 0.002475 mol Na2CO3, 0.01485 mol NH4H2PO4, and 0.0099 mol TiO2 in 100 mL of a 2.0 wt% poly-vinyl-alcohol (PVA) aqueous solution. The mixture was stirred at 80 °C until the water evaporated and white solids formed. The white solids were placed in a porcelain boat and heated at 900 °C for 10 hours with an increasing rate of 5 °C/min under an N2 flow in a tube furnace. To improve the cycling stability and electronic conductivity, thermal vapor deposition (TVD) was employed to prepare carbon-coated NaTi2(PO4)3 after calcination. The as-prepared powder was transferred into a reaction tube to make a fluid-bed layer for the reaction at 700 °C for 2 hours where a toluene vapor was carried by N2 through the reaction tube at a flow rate of 1 L/min, followed by heat-treatment at 900 °C for 2 hours without toluene carrying gas to increase its electronic conductivity. The temperature increasing rate is 5.0 °C/min.

Electrode preparation and electrochemical measurements

The working electrode was fabricated by pressing a mixture of the active materials (porous carbon or carbon-coated NaTi2(PO4)3), carbon black, and PTFE (polytetrafluoroethylene) binder at the weight ratio of 7:2:1 onto a titanium grid with a pressure of 10 MPa. The cyclic voltammograms (CV) were obtained using a three-electrode cell with an active carbon counter electrode and Ag/AgCl reference electrode (0.197 V versus NHE). In the concentric cell, the inner diameter of the tube containing CCl4 and the RuO2-TiO2@C electrode is 2.0 mm, the thickness of the porous carbon electrode is 1.0 mm, the distance between the counter and working electrodes is 3.0 mm, and the thickness of the counter electrode is 3.0 mm. The height of the cell is 2.0 cm, and the volume capacity of the cell is around 2.0 mL. The total volume of the CCl4 reservoir is 6.0 mL, and the total volume of the NaCl/H2O reservoir is 2.0 mL. The CV measurements were carried out on a CHI660B electrochemical workstation. The galvanostatic charge and discharge profiles were obtained with an Arbin battery test station.

Material characterizations

Scanning electron microscopy (SEM) images were taken with Hitachi SU-70 analytical SEM (Japan). Powder X-ray diffraction (PXRD) data were collected on a Bruker D8 X-ray diffractometer using Cu Kα radiation (λ = 1.5418 Å). Raman spectroscopy was performed on a Horiba Jobin Yvon Labram Aramis using a 532 nm diode-pumped solid-state laser, attenuated to give ~900 μW power at the sample surface. Viscosity Measurements were carried out using a CANNON-FENSKE viscometer.

Energy density calculations

The energy density of CFB was calculated based on the 600 mAh cell used in this study with Eq. (1). The average operating potential is 1.8 V at 10 mA/cm2, the volume of CCl4 is 6.0 mL, the volume of NaCl/H2O is 2.0 mL and the volume of Na(Ti2(PO4)3) is 0.592 mL (weight = 5.0 g, density = 2.96 g/mL, volume = 2.96 g/mL ÷ 5.0 g = 0.592 mL). The total volume of active materials is 8.592 mL. Based on these configurations, the cell-level energy density (based on active materials) is 125.7 Wh/L.

$${{{{{\rm{Energy}}}}}}\,{{{{{\rm{density}}}}}}\,=\,\frac {{{{{{\rm{Cell}}}}}}\,{{{{{\rm{ capacity}}}}}}\,\times\, {{{{{\rm{average}}}}}}\,{{{{{\rm{potential}}}}}}}{{{{{{\rm{Total}}}}}}\ {{{{{\rm{volume}}}}}}\,{{{{{\rm{of}}}}}}\,{{{{{\rm{active}}}}}}\,{{{{{\rm{materials}}}}}}}$$
(1)