Balanced-state electrolytes overcome crossover in vanadium redox flow batteries

Domain: chemistry
Published: 2026-03-24
Editorial outcome: major_revision

Abstract
Flow batteries are a leading large-scale energy storage technology, valued for inherent safety and scalability. However, active species cross over the membrane—beyond intended charge carriers—resulting in rapid capacity decay and hindering further development. Traditional approaches to mitigate capacity decay focus on increasing membrane ion selectivity, but this typically compromises power density. Here, we introduce a balanced-state electrolyte strategy that departs from traditional symmetric electrolyte designs by independently tuning both concentration and valence. This approach enables precise control over transmembrane ion flux, thereby maintaining the dynamic equilibrium of active species and effectively reducing capacity decay. Vanadium flow battery tests demonstrate that this approach overcomes the traditional trade-off between proton conductivity and ion selectivity: a battery employing a 15 μm-thick Nafion membrane with balanced-state electrolytes achieves a 75.4% reduction in capacity decay rate— from 0.061% to 0.015% per cycle over 1,000 cycles —compared to a system using a 183 μm-thick Nafion membrane with traditional electrolytes. This method shows the potential to lower the capital cost of a 1 MW/4 MWh flow battery system by over 41.7%. Crucially, the balanced-state electrolyte approach circumvents existing membrane-related constraints in redox flow battery development and establishes a framework for advanced electrolyte design.

Introduction
Redox flow batteries (RFBs) are the most promising solutions for large-scale energy storage, particularly for applications such as peak shaving and valley filling in grid systems.1 The cation exchange membrane (CEM) is a critical component in aqueous RFBs with acidic electrolytes,2 ideally conducting protons while preventing the crossover of active species.3 However, the trade-off between the proton conductivity and ion selectivity of CEMs significantly restricts the power density, capacity retention rate, and electrolyte utilization ratio of RFBs.4 To obtain an ideal CEM, tremendous efforts have been made in membrane design, such as precisely regulating the pore size of membranes,5,6 introducing porous structures,7,8 building composite structures,3,9 and developing new materials.10,11 Despite these advances, challenges persist in the applicability of these membranes in aqueous RFBs operating acidic electrolytes, including low proton conductivity, scalability issues, escalated costs, and long-term stability concerns.2 Consequently, almost all the commercially available membranes for such RFBs are Nafion-based membranes due to their good mechanical/chemical stability and high proton conductivity.3 Nafion-based membranes still face challenges of poor ion selectivity resulting from the large water channels12,13 and heavy water migration,14 seriously restricting the further improvement of RFBs.15 Although strategies similar to those applied to CEMs, such as blocking water channels,16,17 confining Nafion’s swelling behavior18,19 or introducing resistant layers,20,21 have been attempted in Nafion-based membranes, their poor ion selectivity remains a major challenge for RFB applications.22

This poor ion selectivity leads to the transport of active species across the membrane between the positive and negative sides, resulting in crossover phenomena that significantly reduce the coulombic efficiency (CE) and capacity retention rate of RFBs. However, according to Fick’s law ( J = − D \nabla C , where J is the diffusion flux, D is the diffusion coefficient, and \nabla C is the concentration gradient on the two sides of membranes), the crossover of ions is dominated by two parameters. The first one is the diffusion rate, which is largely determined by membrane characteristics and has attracted almost all the attention of researchers when addressing the crossover issue. The second factor is the concentration gradient of electrolytes, which exerts a similar influence on crossover phenomena yet rarely captures researchers' attention.

Compared with membrane design, electrolyte regulation is more tractable for industrial applications and has the potential to overcome the limitations imposed by membrane science. Therefore, we studied the variation of electrolytes induced by crossover during cycling and theoretically analyzed the variation of different vanadium ions’ concentration effects on the performance of vanadium redox flow batteries (VRFBs) based on their diffusion rate across Nafion-based membranes (V2+ > VO2+ >VO+ > V3+).23 Results indicate that crossover leads to the net flux of vanadium ions transporting from the negative to the positive sides, increasing the volume and concentration of the positive electrolyte while depleting the negative electrolyte over cycling. The net flux of electrolytes between the two sides during cycling results in poor CE and rapid capacity decay.24 Consequently, if the electrolyte net flux is eliminated by precisely regulating electrolytes, the capacity can be maintained at a consistent level. However, the net flux of electrolytes significantly changes during the charge and discharge process, suggesting that the capacity decay caused by crossover is a dynamic accumulation process. It is impractical to calculate the gradient concentration ratio between the positive and negative electrolytes mathematically, as it involves numerous parameters, many of which remain unknown.25

Herein, we treat the VRFB as a dynamic diffusion system during cycling, introducing the concept of balanced-state electrolytes (BSEs). Ideally, the balanced-state electrolyte in a VRFB is defined by a crossover flux of vanadium ions from the negative to the positive side that is counterbalanced by an equivalent flux in the opposite direction. This approach allows the parameterization of the balanced-state electrolyte by leveraging the system's inherent self-balancing characteristic. Traditional electrolytes exhibit the same initial concentrations and symmetric valences on the positive and negative sides. However, cyclic operation causes the electrolyte concentration to increase gradually on the positive side while decreasing on the negative side due to transmembrane crossover. Simultaneously, the average vanadium valence of the electrolytes is elevated due to the side reactions, collectively accelerating capacity decay. Traditional strategies have focused on maintaining the same concentrations and symmetric vanadium valences on the positive and negative sides to suppress capacity decay. By contrast, we amplify the concentration gradient across the membrane by increasing the positive electrolyte concentration while decreasing that on the negative side. Meanwhile, we depart from the valence symmetry of conventional electrolytes by precisely elevating the average vanadium valence of the positive electrolyte.

The balanced-state electrolytes successfully overcome the trade-off between proton conductivity and ion selectivity of Nafion-based membranes, enabling a VRFB employing a 51 μm-thick Nafion 212 to achieve a higher CE of 97.79% at 50 mA cm-2, surpassing the 95.90% CE obtained with a 183-μm-thick Nafion 117 and traditional electrolytes. Moreover, the VRFB with N212 presents a significantly lower capacity decay rate (0.025% per cycle) than the Nafion 117 system (0.061%) over 1000 cycles. This approach was extended to thinner membranes, Nafion 211 (25 μm) and the reinforced membrane NC700 (15 μm), both exhibiting substantially lower capacity decay rates (0.017% and 0.015% per cycle, respectively) over 1000 cycles compared to the Nafion 117 system. The combined effects of enhanced battery performance and reduced membrane costs lowered the capital cost of a 1 MW/4 MWh VRFB system by over 41.7%. To further demonstrate the effectiveness and applicability of our proposed BSE method, we have extended it to iron-vanadium flow batteries (IVFBs), which suffer from severe crossover issues and successfully suppressed crossover therein.

Results
Capacity decay of VRFBs with cycling
Fig. 1a shows that the discharge capacity of the VRFB with Nafion 212 first increases for a short period and then rapidly decays between about 10 and 200 cycles. Finally, it enters a relatively stable stage, which is consistent with the previous report.24 The capacity decay is up to 67.9% after 400 cycles, attributed to the deterioration of electrolytes’ symmetry caused by crossover (Fig. 1b). This mechanistic interpretation was corroborated by the complete restoration of both discharge capacity and voltage efficiency upon electrolyte refreshment (Fig. 1c-d). The crossover of vanadium ions induces the imbalance of electrolytes between the two sides, manifesting as asymmetries in volume and valency.24 Specifically, it results in a deficiency of VO+ on the positive side caused by crossover (Detailed in the Supplementary Information), thereby diminishing discharge capacity and voltage efficiency during VRFB cycling (Fig. 1a).Although increasing membrane thickness effectively mitigates vanadium ion crossover and capacity decay (Fig. 1e), it simultaneously greatly increases the resistance of VRFBs (Fig. 1f). Consequently, merely thickening membranes to curb crossover is suboptimal, as it substantially impairs voltage efficiency (Fig. S1a) and electrolyte utilization ratio (Fig. S1b). Similarly, although high-selectivity resistive layers on Nafion-based membranes effectively suppress crossover,26 they invariably elevate membrane resistance.

Regulating vanadium ion transport across the membrane via electrolyte design
In VRFBs, the crossover is caused by the poor ion selectivity of membranes, which conduct protons but fail to prevent vanadium ions from crossing. However, the inherent trade-off between ion selectivity and permeability in membranes2 is challenging to overcome directly. Unlike proton conductivity, the transport of vanadium ions across Nafion-based membranes can be approximated by Fick’s law.27 This suggests that besides decreasing the diffusion coefficient of vanadium ions across membranes, regulating the concentration of electrolytes can also directly influence crossover flux. Therefore, we propose an electrolyte design strategy to equilibrate vanadium-ion transport across the membrane, thereby suppressing capacity decay during cycling, rather than struggling with membrane design.

In the VRFBs assembled with Nafion-based membranes, the net flux of electrolyte travels from the negative to the positive sides (Fig. 1b) after cycling due to the very different diffusion rates of vanadium ions (V2+ > VO2+ >VO+ > V3+) across the membrane.23 Thus, appropriate regulation of vanadium ion transport from the positive to the negative side during cycling enables maintenance of a high stoichiometric balance between the positive and negative electrolytes. Specifically, reducing the negative electrolyte concentration while increasing that of the positive concentration mitigates vanadium ion crossover from the negative to positive and promotes its reverse transport (Fig. S2). Consequently, these opposing fluxes counter each other, resulting in minimal net crossover and stable cell balance. Based on Fick’s law, adjusting the concentration of vanadium ions can effectively control the amount of crossover, as demonstrated by the calculation results (Fig. 2a). Experimental results (Fig. 2b) further confirm that enhancing the electrolyte transfer from the positive to the negative side by increasing the positive electrolyte concentration significantly alters capacity decay. However, precisely quantifying the electrolyte concentrations needed to offset crossover-induced flux imbalances between the positive and negative sides during long-term cycling remains highly challenging. The complex ion transport model in VRFBs, combined with the dynamic evolution of electrolytes over extended cycling, complicates this task. Moreover, the state of charge (SOC) of electrolytes profoundly impacts the net flux of electrolytes (Fig. S3), which varies during charging and discharging. Additionally, the SOC range is also significantly influenced by the working current density (Fig. 2c) and varies with cycling.

Inspired by the trend of capacity decay in VRFBs, where the capacity decay rate gradually decreases to near zero with test time (Fig. 2d), we regard the VRFBs during cycling as a dynamic diffusion system. Combined with the self-balancing capability of a diffusion system, we propose using the electrolytes situated within the ‘horizontal region’ in the discharge capacity–test time curve (Fig. 2d) as the balanced-state electrolyte. The introduction of balanced-state electrolytes establishes a dynamic equilibrium of electrolyte net flux between the positive and negative sides during charge and discharge cycling. Nevertheless, there are three ‘horizontal regions’ as depicted in Fig. 2d that are caused by the variation of voltage efficiency with temperature (Fig. S4). Hence, we selected the electrolyte concentrations corresponding to the first ‘horizontal region’ after 107 hours of cycling as those of the balanced-state electrolytes. Compared to traditional electrolytes with the same concentration (1.70 M), the concentration on the positive side is significantly increased, whereas that on the negative side is substantially decreased in the balanced state (Fig. 2e). This concentration gradient forces more vanadium ions to transport from the positive to the negative side, consuming the surplus V2+ and generating V3+, which is in short supply. This process balances both the contents and valences of electrolytes between the positive and negative sides, improving the discharge capacity and CE of VRFBs. Results (Fig. 2f) show that the capacity decay is markedly suppressed when adopting the concentrations at the balanced state compared to that using traditional electrolytes with the same concentration on the positive and negative sides. The suppression of capacity decay is attributed to the ion rebalancing driven by a concentration gradient. Although adjusting electrolyte concentrations to achieve the balanced state increases the pressure drop difference between the positive and negative sides owing to viscosity changes (Fig. S5a), this exerts only a negligible effect on mitigating capacity decay, as evidenced by the lack of discernible differences in Fig. 2g. In this experiment, we constructed an equivalent pressure drop difference to that caused by the different viscosities of electrolytes by increasing the positive electrolyte flow rate from 51 to 96 rpm (Detailed calculations are provided in Supplementary Information, section 4). The slightly larger discharge capacity of the VRFB at 96 rpm can be attributed to improved voltage efficiency (Fig. S5b). The results (Figs. 2g and S6) demonstrate that the presence of an asymmetric pressure drop has no significant impact on capacity decay.

Although the capacity decay of the VRFB is significantly suppressed (Fig. 2f), it still experiences a notable decline over 150 cycles. In addition to concentration variations, the average vanadium valence in electrolytes is elevated by side reactions (hydrogen evolution and air-induced oxidation of V²⁺; Eqs. S8 and S9) 28 before the system reaches its balanced state (Fig. 2d). Merely regulating electrolyte concentrations is insufficient for achieving optimal suppression of capacity decay. Therefore, we introduced a surplus of VO+ into the positive electrolytes to elevate the average vanadium valence of electrolytes, which significantly reduced the capacity decay rate (Fig. 2h), consistent with previous reports.24 The working principle is shown in Fig. S7. Considering the difficulty in accurately measuring the valence of the electrolytes at the ‘horizontal regions’ in Fig. 2d, we adopted the amount of 2 mL of VO+ to regulate electrolyte valence, according to the results of Fig. 2h. To simplify the preparation of the balanced-state electrolytes (BSEs), we diluted 40 mL of 1.70 M V3.5+ electrolyte with 18.12 mL of 3 M sulfuric acid to obtain a 1.17 M negative electrolyte. Additionally, we added 1.81 g VOSO ·5H O into 35.60 mL of 1.70 M V3.5+ electrolyte to obtain a 1.91 M V3.55+ positive electrolyte. This composition corresponds to an excess vanadium equivalent to that provided by an additional 2.19 mL of the stock electrolyte (calculation details in Sections 3). Conventional strategies enforce symmetry in the concentration and valence between the positive and negative sides to suppress capacity decay. By contrast, we intentionally amplify the concentration gradient between the positive and negative electrolytes while precisely elevating the average vanadium valence of positive electrolytes.

Suppressing the crossover of VRFBs with the balanced-state electrolytes
A VRFB employing an N212 membrane with the BSEs (P 1.91 M V3.55+; N 1.170 M V3.50+) exhibit an 86.3% reduction in capacity decay rate—from 0.182% to 0.025% per cycle—and a 71.0% increase in accumulated discharge capacity (from 256.97 to 439.35 Ah) over 400 cycles, compared to that using traditional electrolytes (P 1.70 M V3.50+; N 1.70 M V3.50+) (Fig. 3a). The periodic fluctuation in the discharge capacity curve is caused by temperature variation24 which is also reflected in the discharge capacity versus test time curves (Fig. 3b and Figs. S8a-c) and the variation of voltage efficiency (Fig. S9). Notably, the CE of VRFB with BSEs is significantly improved compared to that using traditional electrolytes (TEs), especially at low current densities (Fig. 3c). As illustrated in Figs. 3d and S10, the CE is improved with the increase of positive electrolyte (VO2+) concentration. However, decreasing the negative electrolyte concentration from 1.70 to 1.17 M does not obviously improve its CE but markedly increases the voltage efficiency (Fig. 3e) via a reduction in the resistance of VRFBs (Fig. 3f). The effects of reducing the negative electrolyte’s concentration on the CE become prominent below 1.1 M (Fig. S11). The improvement in CE observed in the VRFB using the BSEs is also evident in the prolonged self-discharge duration (Fig. 3g), and diffusion simulation results (Figs. S12-14). Furthermore, the power density of the VRFB does not decrease when using BSEs; rather, it improves markedly compared with that of the system using TEs (Fig. 3h) due to the enhanced voltage efficiency (Fig. S9). To elucidate the underlying reasons for this improvement in CE, molecular dynamics (MD) simulations were conducted. Results show that the diffusion rates of V2+ and VO+ across Nafion membranes become similar after replacing TEs with BSEs (Fig. 3i). Additionally, the diffusion rate of V3+ across Nafion membranes is markedly reduced in the presence of BSEs, whereas the diffusion rate of VO2+ remains relatively unaffected (Fig. S15). The effects of varying electrolyte concentration on the crossover flux and diffusion coefficients of vanadium ions across the Nafion membrane were confirmed by diffusion experiments (Fig. S16). These alterations in the diffusion rates of vanadium ions across Nafion membranes can be attributed to variations in the interactions between vanadium ions and sulfonic acid groups, as demonstrated in Figs. 3j and S17-18. The solvent structures of hydrated vanadium ions within Nafion membranes immersed in TEs and BSEs do not exhibit obvious differences (Fig. 3k, Fig. S19).

Stability of VRFBs with the balanced-state electrolytes
To evaluate the stability of the BSEs in VRFBs, long-term cycling tests were conducted using N212 (51 μm), and the results were compared with those obtained using a significantly thicker N117 membrane (183 μm) with TEs (P 1.70 M V3.50+; N 1.70 M V3.50+). Results show that the BSEs enable the VRFB with N212 to exhibit a much lower discharge capacity decay rate of 0.025% per cycle, in contrast to 0.061% for N117 over 1000 cycles (Fig. S20). This advantage is particularly pronounced (reduced from 0.214% to 0.038% per hour) in the timescale (Fig. 4a). The VRFB with less than one-third thickness membrane N212 exhibits a capacity decay rate approximately one-sixth of that with N117 over the same testing duration. Furthermore, the accumulated discharge capacity of the VRFB with N212 and BSEs was enhanced by 159.5% compared to that with N117 (Fig. S20) due to the higher capacity retention rate and the smaller ohmic resistance (Fig. 4b). The CE of the VRFB with N212 and BSEs reached 97.79% at 50 mA cm-2, significantly outperforming the N117-based system (95.90%), yet both systems converged to similar CE values at 200 mA cm⁻² (Fig. 4c). Therefore, the ability of the BSEs to balance the net flux of electrolytes enables the VRFB with N212 to exhibit a significantly higher discharge capacity retention rate. Conversely, increasing the membrane thickness from 51 μm (N212) to 183 μm (N117) extends the transport distance for all vanadium ions across the membrane. This modification uniformly affects all vanadium ions, meaning that increasing the thickness of Nafion membranes does not alter the diffusion rate order of vanadium ions across the membrane nor reverse the net flux direction of electrolytes during cycling. Therefore, simply increasing the difficulty for vanadium ions to cross the membrane merely extends the time it takes to reach the same level of capacity decay. It fails to fundamentally address the capacity decay problem unless vanadium ions are completely prevented from crossing the membrane. In contrast, the proposed method utilizing BSEs effectively regulates the amounts of vanadium ions across the membrane, which can change the net flux direction and offer the potential for a fundamental solution to the crossover problem. However, in addition to crossover, the fade of electrodes in long-term cycling also profoundly influences the capacity decay of VRFBs.29 As illustrated in Fig. 4d, the voltage efficiency decreases by 3.40% after 1000 cycles compared to the initial 50 cycles, and this decline cannot be recovered after refreshing electrolytes, suggesting that it does not arise from electrolyte variations. The decrease in voltage efficiency is mainly attributed to electrode fading due to increased oxygen content30 and reduced degree of graphitization, as evidenced by XPS (Figs. S21a-b), XRD, and Raman spectra (Figs. S21c-d). The deterioration of electrodes is also reflected in the increased ohmic and charge transfer resistances after cycling (Fig. 4e). The fading of electrodes not only leads to the discharge capacity decay in VRFB (Fig. 4a) but also marginally affects the range of electrolyte SOC during the charge and discharge process and impacts the electrolyte net flux (Fig. 2a). Consequently, following 675.72 hours of operation (1000 cycles) in the VRFB employing the BSEs, a 4.59% of active materials (quantified by net flux) traveled from the negative to the positive sides, markedly lower than the 38.94% observed in the VRFB utilizing TEs over approximately one-quarter of the testing duration (175.67 hours) (Figs. S22-23).

Applicability of BSEs
Unlike membrane optimizations that face the inherent trade-off between ion selectivity and proton conductivity, the proposed BSEs achieve high capacity retention without increasing membrane resistance. This advancement renders membranes with low resistance yet poor ion selectivity viable for use in VRFBs. Therefore, the effectiveness of the proposed BSEs in suppressing crossover is also examined in the Nafion series membranes of smaller thicknesses Nafion 211 (N211, 25 μm) and NC700 (15 μm), as shown in Fig. 5.

Decreasing the Nafion membrane thickness from 51 μm (N212) to 25 μm (N211) greatly reduces membrane resistance and improves voltage efficiency (Figs. S24a-b). However, it leads to more severe capacity decay than N212 in the first 50 cycles (Fig. S24c). The concentrations of electrolytes in the VRFB with N211 at the balanced-state (Figs. S25-26) were obtained as those with N212 (Figs. 2d-e). Then, the BSEs (P 1.83 M V3.54+; N 1.15 M V3.50+) were obtained after elevating the average vanadium valence of the electrolyte on the positive side by directly adding vanadyl sulfate into the commercial electrolyte V3.50+. Fig. 5a shows that the accumulated discharge capacity of the VRFB utilizing the BSEs significantly increases by 85.1% over 400 cycles compared to that using the TEs (P 1.70 M V3.50+; N 1.70 M V3.50+). Furthermore, the CE of the VRFB with the BSEs exhibits a marked improvement compared to that using the TEs (Fig. S27). The high capacity retention rate and CE of the VRFB with BSEs were also validated by extended self-discharge tests (Fig. S28). The incorporation of BSEs substantially improved capacity retention in VRFBs with the N211 membrane, exhibiting a discharge capacity decay rate of 0.05% per hour. This rate represents a 72% reduction in comparison to the significantly thicker N117 membrane (0.19% per hour) over the same testing duration (Fig. 5b). Benefiting from the much smaller resistance (Fig. S29a) and a more stable capacity retention (Fig. 5b), the VRFB utilizing N211 achieved an accumulated discharge capacity 177.9% higher than that of the N117 system over 1000 cycles (Fig. S29b). The capacity decay in the VRFB with N211 during long-term cycling is also accompanied by electrode fading, including variations in oxygen contents (Fig. S30a-c) and graphitization degree (Fig. S30d-e), which raise charge transfer resistance (Fig. S30f) and reduce voltage efficiency (Fig. S31). We also extended the application of the BSEs strategy to the VRFB using a reinforced Nafion NC700 membrane with reduced thickness 15 μm. Results indicate that the VRFB with NC700 presents a smaller resistance than that with N212 (Fig. S32a) but experiences more severe capacity decay in the initial stage due to its much smaller thickness (Fig. S32b). Similarly, the electrolyte concentrations of the VRFB with NC700 at the balanced-state were obtained (Figs. S33a-c), which displays a very close concentration to that of N211. Thus, we selected the same electrolytes (P 1.83 M V3.54+; N 1.15 M V3.50+) as the BSEs for the VRFB with NC700, which also demonstrated an extended duration in the self-discharge test (Fig. S32d). As illustrated in Fig. 5c, the accumulated discharge capacity of the VRFB with NC700 improves by 84.8% after adopting the BSEs (P 1.83 M V3.54+; N 1.15 M V3.50+) compared to that using TEs (P 1.70 M V3.50+; N 1.70 M V3.50+) over 400 cycles. The CE of the VRFB with NC700 is also greatly improved (96.15% at 50 mA cm-2) after using the BSEs, reaching a level comparable to that of N117 (95.90% at 50 mA cm-2) (Fig. S34). Moreover, the capacity decay rate of the VRFB with NC700 (0.04% per hour) represents a 77.6% reduction compared with that of N117 (0.19% per hour) under the same test duration (Fig. 5d). Superimposing the smaller resistance advantage of the VRFB with NC700 compared to that with N117 (Figs. S35a-b), the accumulated discharge capacity of the former increases by 172.2% compared to that with the latter over 1000 cycles (Fig. S35c). The capacity decay rate reduction is 75.4% from 0.061% to 0.015% per cycle over 1,000 cycles (Fig. S35c). The battery also suffers from electrode degradation after prolonged cycling, as reflected by changes in oxygen content (Figs. S36a–c) and the degree of graphitization (Figs. S36d–e), as well as an increased charge-transfer resistance (Fig. S36f) and a reduced voltage efficiency (Fig. S37).

Currently, Nafion 212 is widely used in advanced VRFBs.31 Hence, we compared the performance of VRFB employing NC700 with the BSEs to that of the system using N212 with TEs. Results show that the accumulated discharge capacity of the former increased by 116.0% compared to the latter (Fig. S38), resulting in a 53.7% reduction in electrolyte costs at equivalent discharge capacity. Consequently, in an advanced 1 MW/4 MWh system,32 the capital cost of the VRFB system can be reduced by over 41.7% (Fig. 5e) by substituting N212 and TEs with the much cheaper reinforced copolymer membrane NC700 (perfluorosulfonic acid (PFSA)/polytetrafluoroethylene (PTFE)) 33 and BSEs (Tables S2-3). This significant reduction enables the Unit capital cost (CAPEX per unit energy) [€ kWh−1] of the VRFB to become competitive with that of Li-ion batteries,34 which could facilitate the broader adoption of VRFB technology and profoundly influence the energy storage market. Compared with prior reports utilizing commercial or custom-designed membranes, this work demonstrates competitive energy efficiency and stable capacity retention over extended cycling (Fig. 5f), even when employing as-received commercial membranes of minimal thickness (Table S4). To further demonstrate the effectiveness and applicability of our proposed BSEs method, we have extended it to iron-vanadium flow batteries (IVFBs), which suffer from severe crossover issues (Fig. S39).35 The accumulated discharge capacity improved 56.36% from 388.37 to 607.25 Ah over 400 cycles when traditional electrolytes (P 1.70 M V2+; N 1.70 M Fe3+) were replaced with the BSEs (P 1.072 M V2+ + 0.876 M Fe2+; N 1.324 M Fe3+ + 0.914 M VO2+), indicating successful suppression of the crossover, as shown in Fig. 5g. Moreover, this method also has the potential to be applied to the VRFBs with nanoporous membranes36 and offers a valuable reference for other flow battery technologies, such as polysulfide-based,19,37 and organic-based redox flow batteries,38,39 which have faced significant challenges due to crossover effects.

Methods
Materials
In this work, graphite felt with a thickness of 2.5 and 1.75 mm and carbon cloth with a thickness of 0.7 mm were used as the electrodes provided by Liaoning Jingu Carbon Material Co., Ltd. Membranes included Nafion 211 (25 μm), 212 (51 μm), 115 (127 μm), 117 (183 μm), and NC700 (15 μm) (noted as N211, N212, N115, N117, and NC700), all purchased from DuPont. The commercial electrolyte 1.70 M V3.50+ /3.00 M H SO was supplied by Sichuan Xingming Energy Material Co., Ltd. The vanadyl sulfate (VOSO ·5H O) was purchased from Shenyang Haizhongtian Fine Chemical Factory. Iron (II) sulfate heptahydrate (FeSO ‧7H O CAS Number: 7782-63-0) and Iron (III) chloride hexahydrate FeCl ‧6H O (CAS Number: 7447-40-7) were purchased from Sigma-Aldrich. In addition, both the electrode and Nafion membranes were employed as received. A single membrane was used in each battery cell.

Electrolyte preparation
The 1.70 M V2+/3.00 M H SO , 1.70 M V3+/3.00 M H SO , and 1.70 M VO2+/3.00 M H SO were obtained by charging the commercial (1.70 M V3.50+/3.00 M H SO ) electrolytes. The electrolytes of 1.17 M V3+/3.00 M, 1.17 M V3.5+/3.00 M H SO and 1.15 M V3.5+/3.00 M H SO were prepared by diluting 1.70 M V3+/3.00 M H SO and 1.70 M V3.50+/3.00 M H SO with 3.00 M H SO , respectively. Higher-concentration positive electrolytes (1.80, 1.90, and 2.00 M) were obtained by adding 0.96, 1.81, and 2.58 g of VOSO₄·5H₂O to 37.78, 35.79, and 34.00 mL of 1.70 M VO2+ stock electrolytes, respectively. Similarly, the electrolytes with 1.81, 1.91, and 2.01 M VO2+ were obtained by adding 0.99, 1.89, and 2.65 g VOSO ·5H O into 37.57, 35.60, and 33.83 mL of 1.70 M VO2+ electrolytes, respectively. The electrolyte with 1.83, 1.93, and 2.03 M V>3.50+ can be obtained by adding 1.22, 2.05, and 2.80g VOSO ·5H O into 37.16, 35.23, and 33.50 ml of 1.70 M V3.5+ electrolytes, respectively. 1.70 M Fe3+/3.00 M H SO electrolyte was prepared by dissolving FeCl ‧6H O in 3.00 M H SO solution.

The BSEs for IVFBs were prepared as follows. For the positive side, 11.62 g VOSO ·5H O was added to 40 mL of 1.70 M Fe3+/3.00 M H SO solution and then diluted with 11.36 mL of 3.00 M H SO , serving as the positive electrolyte. For the negative side, 11.45 g FeSO ‧7H O was added to 40 mL 1.70 M V2+/3.00 M H SO solution and then diluted with 23.43 mL of 3.00 M H SO , serving as the negative electrolyte.

Characterization techniques
The concentration and viscosity of electrolytes were determined using Lambda 365 UV-Visible Spectrophotometer (PerkinElmer, USA) and an 1834 Ubbelohde viscometer in an HS0100 thermostat (Lorderan, China). A further discharge process for VRFBs under a constant voltage mode (0.9 V) was conducted prior to measuring the concentration and viscosity of electrolytes. Ion concentrations in the positive and negative electrolytes of IVRFs were measured using an Inductively Coupled Plasma –Optical Emission Spectrometer (Avio-200, PerkinElmer) following a 7500-fold dilution with deionized water.

The ohmic resistances of VRFBs were measured by electrochemical impedance spectroscopy (EIS) on BioLogic SP-300 at 50% SOC. Each battery cell was rested at open-circuit voltage (OCV) for 5 minutes prior to the EIS measurement. The tests were conducted using a potentiostatic signal with an amplitude of 10 mV over a frequency range of 60 kHz to 100 mHz (10 points per decade). The morphology, oxygen contents, and graphitization degree of electrodes were measured using a scanning electron microscope (SEM) (JSM-7100, JEOL, Japan), X-ray photoelectron spectroscopy (Kratos Analytical Limited, Japan), X-ray diffraction (XRD) (D8 ADVANCE, BRUKER, USA), and Raman spectroscopy (inVia Qontor, Renishaw Ltd., United Kingdom). All the tests were conducted at 23 ± 0.5 ℃.

Battery tests
All VRFBs were constructed with two 40 × 40 mm2 electrodes separated by a Nafion membrane (70×70 mm2) and housed between graphite flow-field plates in a zero-gap structure. Due to the significantly different mechanical properties of Nafion series membranes, the corresponding electrodes are adjusted accordingly. Specifically, batteries with Nafion 212, 115, and 117 membranes employed 2.50 mm-thick graphite felt electrodes and graphite bipolar plates with serpentine flow fields (SFFs). The battery with a Nafion 211 membrane incorporated 1.75-mm-thick graphite felt electrodes and bipolar plates with serpentine flow fields SFFs. The battery with an NC700 was assembled with 0.70 mm-thick carbon clothes electrodes and bipolar plates with interdigitated flow fields. Positive and negative electrolytes (40.00 mL, or equivalent vanadium content) were stored in reservoirs and circulated via a Longer BT100 peristaltic pump (Longer Precision Pump Co., Ltd., UK).

A VRFB equipped with Nafion 212 was adapted for IVFBs testing by replacing vanadium electrolytes with iron-vanadium electrolytes. First, a VRFB assembled with Nafion 212 was fully charged using 40 mL of V3.5+/3.00 M H SO as both positive and negative electrolytes, yielding 40 mL of V2+/3.00 M H SO on the negative side. Then, the positive electrolytes (VO+) were pumped into the tank, and the positive-side chamber was washed with deionized water and purged with N for 1 min. Finally, the positive electrolyte was replaced with 1.70 M Fe3+/3.00 M H SO electrolytes.

All battery tests were operated under N protection using Arbin 179539 (Arbin Instruments, USA) for data recording. The cut-off voltage range was 0.90-1.60 V for all VRFB experiments and 0.60-1.60 V for IVFB experiments. All VRFB and IVFB tests were conducted over 400 or 1000 cycles at 51 rpm (2.5 mL min-1 cm-2) without any interventions during cycling. All battery cycling tests were performed at 28 ± 3 ℃.

BSE determination
Determining the balanced state of a VRFB under specified operating conditions is essential for designing BSEs. Specifically, we define the balanced state under specific conditions as one where the capacity decay rate is less than 0.03% per cycle or 0.08% per hour. In addition, the test must last longer than 8 h and include more than 20 cycles, with the discharge capacity showing a monotonic decay versus time or cycle number over the investigated range. The electrolyte concentrations at the balanced state are used for designing BSEs. To ensure the accuracy of these measurements, we converted the electrolytes at the balanced state to V3+|VO2+ through full discharge followed by aerial oxidation. To compensate for the elevated average vanadium valence of electrolytes that occurs during cycling due to side reactions, the VO+ content in the initial electrolyte was experimentally increased. The detailed procedure as shown below:

First, operate a VRFB under specified conditions and record the discharge capacity versus time curve. Second, calculate the capacity decay rates over 20 cycles in the quasi-steady region of the discharge capacity curve. Third, identify the region where the discharge capacity decay rate is below 0.03% per cycle. Fourth, stop cycling and fully discharge the battery at a constant voltage of 0.8 V until the current falls below 0.1 A. Fifth, stir the negative electrolyte using a magnetic stirrer and oxidize it in air for 4 hours to convert the surplus V2+ to V3+. Sixth, dilute the negative and positive electrolytes 15-fold with deionized water and measure the V3+ and VO2+ concentrations using a UV-Visible Spectrophotometer.

The definition and identification method for the balanced state in IVFBs are the same as those for VRFBs. Here, the state of the IVFB after 160 cycles was selected as its balanced state, and the ion concentrations were measured using an inductively coupled plasma-optical emission spectrometer (ICP-OES; Avio-200, PerkinElmer) at 23 ± 0.5 °C following 7500-fold dilution with deionized water. The results show that vanadium ion concentrations are 0.914 M and 1.072 M in the positive and negative electrolytes, respectively, and iron ion concentrations are 1.324 M and 0.876 M, respectively.

Simulation methods
Molecular dynamics (MD) simulations were conducted using the GROMACS 2021 software package. To minimize the initial energy of each system, the steepest descent method was employed, with a force tolerance set at 1 kJ (mol−1 nm−1) and a maximum step size of 0.001 ps prior to the MD calculations. Periodic boundary conditions were applied in all three spatial dimensions. The leapfrog algorithm was utilized to integrate the Newtonian equations of motion. The simulations were performed in an NPT ensemble, with a total simulation time of 20 ns. During the NPT simulations, pressure was maintained at 1 bar using the Parrinello-Rahman barostat in an isotropic manner, while the temperature was controlled at 298.15 K by the V-rescale thermostat. Electrostatic interactions were assessed using the Particle-Mesh Ewald (PME) method with fourth-order interpolation, and a cutoff of 1.0 nm was applied for short-range van der Waals interactions. The specific topology and parameters for the MD simulations are provided in Supplementary Data 1.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript describes an electrolyte engineering strategy — “balanced-state electrolytes” (BSEs) — for mitigating\nvanadium crossover caused capacity fade in VRFBs. The benefits of applying BSEs are well validated, showing significant\nimprovement over traditional symmetric electrolyte systems. However, several key areas still need clarification,\nstrengthening, or additional experimental support, prohibiting the manuscript from meeting the standard for publishing on\nNature Communication. Some comparison experiments are not rigorously conducted, and the scientific presentation could\nalso be improved. Wherever the manuscript is going to be submitted, the following concerns should be resolved.\nMajor concerns:\n1. Conceptual novelty and presentation\na, The idea of tuning both concentration and valence to manage crossover-induced capacity decay is interesting and well-\nmotivated. However, regarding the scientific presentation, the authors are making simple things complicated.\nIf starting with V3.5+ and assuming no side reaction, the only thing that crossover will lead to is the concentration imbalance\nof the positive side and the negative side. Keeping moving the electrolyte of the concentrated side into the diluted side to\nkeep the amount of substance (total vanadium) identical for both sides will keep the cell balanced, until crossover of\nvanadium from both sides balancing each other. The eventual crossover-balanced electrolytes shall have the same\nconcentration and volume as the BSE. By knowing the crossover constants of all vanadium ions under operation pressures\nwould directly give the composition of BSE. BSE allows the amount of substance in the positive and negative side\nunchanged because the crossover cancels each other. Authors should explain the determination of the BSE composition in\na more explicit and clear way.\nFurthermore, from this perspective, the authors may consider building an automatic adjusting system, monitoring the volume\nand the concentration of each sides of the electrolyte and adding an automatic side-pumping system (with pumping rate\nbalancing the osmosis pressure and sub-cell balancing the side reaction: DOI https://doi.org/10.1039/D4EE02450H) to\nrealize the auto-optimized BSE. If such an automatic monitored system with near zero fading would be demonstrated, this\nmanuscript can be accepted by Nature Communication.\nb, The term \"balanced-state electrolyte\" lacks precise definition early in the manuscript, increasing the reading barrier to\naudiences.\nc, Many experimental results are repetitive. Authors should consider moving some of the repetitive figures and supporting\ndata into SI (e.g., Fig 4a(crossover is more time-dependent than cycling dependent), 4f-j, 5a-c).\nd. Fig. 1e, 2s, S4, S6 are not helpful and confuse the readers. The authors should just write down the formula, the chemical\nreactions and balance them. The reviewer tried to count these colored balls and found them not even balanced regarding\nnumbers. There is no point in using them if these figures are not accurate, can be simplified by words, only cause pain and\nare not aesthetically beautiful. The authors should simply use an example case and write the chemical composition to\nexplain the problem of crossover and the authors’ solution.\ne. The title is not accurate. The authors are dealing with the imbalance of crossover in vanadium redox flow battery, not\novercoming membrane limitations in flow batteries: membrane selectivity are not improved in this manuscript and this\nmethod is not useful for other flow batteries that uses different active species in the positive and genitive electrolyte.\n2. Experimental design\na, The exact procedure for determining the BSE composition is not clearly outlined in the main text. Authors should move\nessential elements of the BSE determination procedure into the main Methods section.\nb, The manuscript is about balancing the crossover of VRFB with various membranes, yet the permeation constants of all\nfour Vanadium ions through each membranes are not quantified or measured in this manuscript. The manuscript also\napplied different flow rates on each side of the cell to control the osmosis pressure balance when using asymmetric BSEs. The\npressure drop may also influence the permeation (crossover) of ions. The measurement of these conditioned constants\ncan be scientifically and practically useful, since these constants should provide stronger rationale regarding the\ndetermination of BSE compositions.\nc. The testing parameters are not controlled, using comparison with two or more parameters changed (Figure 4a, 4c). The\neffect of cell configuration (electrode thickness, flow field, etc.) was not controlled across different membranes, especially for\nNC700 and N211 (see SI Section 3). Authors should consider justifying and quantifying how these differences in hardware\ndesign influence the results or standardize them across comparisons.\n3. Modeling and theoretical analysis\na, Authors should describe the performance of their cells using a mechanistic framework (e.g., based on Nernst–Planck,\nPoisson–Nernst, or coupled Fickian transport) equation, with permeation and migration constants measured as suggested,\nto demonstrate a straight-forward model that can guide designs of electrolytes. In this case, MD simulations are not as\ninformatic for readers – the diffusion rates of ions are changed just because the concentration gradients/differences are\nchanged.\nb, What is the chemical difference between TE and BSE rather than concentration? In that case, what is the physical\nexplanation of TE and BSE having different “vanadium ions’ energies” in Nafion? This raises concern regarding the MD\nsimulation results.\nc, If the authors insists on the MD simulations, the current MD simulations are oversimplified. The simulation is limited to ion\ndiffusivity. The simulation should be coupled with membrane hydration and Donan potential shifts under real operating\npotential gradients with a longer simulation time.\nd, Fig. 3h is not informatic. What should readers learn from Fig 3h?\ne. Fig. 3i is not explained, and the abbreviation MSD showed without spelled out in the manuscript. What does MSD (nm2)\nmean?\nf. Fig. 3k may be too obvious: why would someone expect the hydration of V2+ changed if just changing a 1.7 M V2+\nsolution into a 2.0 M V2+ solution?\n4. Electrochemical performance claims\na, The authors mentioned side reactions at line 184, demonstrating adding V5+ to balance the cell SOC. Authors should\nspecify the side reactions and their effects, noting that side reaction of carbon electrode aging is evitable by using inert\ne\nelectrodes. Side reactions of HER or ORR should be balanced by adding V4+ or introducing reactants\n(https://doi.org/10.1039/D4EE02450H, https://doi.org/10.1016/j.jpowsour.2023.233770)\nb, Fig 2h shows no apparent difference, contracting against the statement.\nc. Line 317: Fig. S16 does not show apparent difference between these two membranes, contracting against the statement.\nd. Line 373: no clear experimental evidence of modulating the interactions between vanadium ions and sulfonic acid groups,\ncontracting against the statement. The authors only changed the concentration of the electrolytes.\nMinor concerns:\n5. Broader impact and scalability\nThe cost analysis (Fig. 5h) indicates the practical significance of the BSE approach. However, the assumptions behind the\n>40% cost reduction are not fully transparent. Author should include their detail TEA with a table listing assumptions (e.g.,\nmembrane price, electrolyte cost per kg, system lifetime) and perform a sensitivity analysis with fare comparison with\nprevious/commercial rebalancing techniques.\n6. Language and clarity\nWhile the manuscript is generally readable, grammatical inconsistencies and stylistic issues detract from the clarity (e.g., line\n209-210 sentence has no verb). Authors should also revise for clarity, especially in experimental procedures and\ndescriptions of diffusion processes.", "reviewer_2": "In this work, the authors propose an electrolyte design based on balanced-state electrolytes, rather than membrane design,\nto mitigate the capacity decay of redox flow batteries. This approach addresses the trade-off between ion conductivity and\nthe permeability of active materials in VRFBs. While the study presents an interesting strategy to enhance the cycling\nstability of flow batteries, certain sections require modification and further discussion. I would recommend publication in\nthis journal after major revision.\n1. In the Abstract, the authors state that “battery employing a 15 μm-thick Nafion membrane with\nbalanced-state electrolytes\nachieves a 77.6% reduction in capacity decay rate (over 1,000 cycles) compared to a system using a 183 μm thick Nafion\nmembrane with conventional electrolytes.” It would be helpful to also provide the capacity fading rate per cycle or the\ncapacity retention after 1,000 cycles. Additionally, please specify the total testing duration (in hours) for 1,000 cycles.\nFurthermore, for a more accurate evaluation of the electrolyte design effect on capacity decay, the comparison should be\nconducted using Nafion membranes of the same thickness.\n2. In the Abstract, the authors state that “Crucially, the balanced state electrolyte approach removes membrane limitations in\nredox flow battery development and opens new avenues for advanced electrolyte design.”. To claim that this approach can\nremove membrane limitations, it would be necessary to evaluate its performance with a wider variety of membrane types,\nrather than testing solely with a Nafion membrane.\n3. In page 2, the authors state that “The cation exchange membrane (CEM) is a critical component in RFBs, ideally\nconducting proton while preventing the crossover of active species.\". However, the choice of ion exchange membrane for an\nRFB depends on the type of active material used. Some active materials require an anion exchange membrane, while\nothers can operate with a porous membrane without ion selectivity. For acidic electrolytes, proton conductivity is important,\nwhereas in alkaline electrolytes, conductivity of other ions may be more relevant. Please clarify which specific type of RFB\nthis study focuses on. Additionally, note that in many RFBs employing organic active materials such as quinones, capacity\ndecay is generally not dominated by active material crossover.\n4. In page 2, the authors state that “Despite these advances, challenges persist in the applicability of these membranes in\ninorganic/organic RFB systems, including low proton conductivity, scalability issues, escalated costs, and long-term stability\nconcerns.”. However, in most organic RFB systems, active material crossover is generally not a significant issue. This\nsentence should be revised accordingly.\n5. In Figs. 1-3, please revise the discharge capacity units from Ah to volumetric discharge capacity (Ah/L), as volumetric\ncapacity is a more relevant metric for evaluation.\n6. In page 4, the authors state that “Fig. 1a shows that the discharge capacity of the VRFB with Nafion 212 first increases for\na short period and then rapidly decays between about 10-200 cycles.\". Please provide an explanation for the initial short-\nterm increase in discharge capacity.\n7. In page 6, the authors state that “The complex ion transport model in VRFBs, combined with the dynamic evolution of\nelectrolytes over extended cycling, complicates this task.\". Please explain more clearly on the meaning of “dynamic\nevolution” in this context, providing specific details.\n8. In Fig. 3, could you also provide data on power density, voltage efficiency, or energy efficiency? In the Introduction, it is\nstated that this electrolyte design method can address the trade-off between ion conductivity and selectivity without\ncompromising power density, which is a key advantage over membrane design. Therefore, this aspect should also be\naddressed and supported with relevant data in the study.\n9. In Fig. 3, please also indicate the total testing time for 400 cycles.\n10. In Fig. 4, the thickness of the Nafion membrane should be kept the same in order to isolate and accurately assess the\neffect of the electrolyte design on the stability of VRFBs with balanced-state electrolytes.\n11. Overall, the experimental data presented focuses solely on VRFBs using a Nafion membrane. Although this system is\ndescribed as a model, additional validation with other types of RFBs employing different active materials and membranes is\nnecessary to substantiate the claim that this electrolyte design strategy is universally adaptable for RFBs without membrane\nlimitations. Therefore, I recommend conducting further tests with at least two or three different combinations of active\nmaterials and membranes.", "reviewer_3": "This manuscript proposes balanced‑state electrolytes (BSEs) that deliberately break symmetry in concentration and average\nvalence between positive and negative tanks to counteract net crossover in vanadium redox flow batteries (VRFBs). By\ntuning concentration and valence, the authors claim to hold the net transmembrane flux near zero over a cycle, enabling thin\nNafion membranes without sacrificing capacity retention. Representative results include: with BSEs, N212 (51 μm)\noutperforms N117 (183 μm) using traditional electrolytes, cutting the capacity‑decay rate from 0.061% to 0.025% per cycle\nover 1,000 cycles and reaching CE = 97.79% at 50 mA cm⁻² (main Fig. 4a,d; p. 25–26).\nThe approach extends to N211 (25 μm) and NC700 (15 μm) with decay rates down to 0.015% per cycle, alongside a >41.7%\nCAPEX reduction projected for a 1 MW/4 MWh system (main abstract; Fig. 5e–h; pp. 15–16; SI Tab. S2).\nMechanistically, the authors quantify flux reversal/neutralization (net flux 4.59% vs 38.94% for BSEs vs TEs) using volume‑\nand concentration‑shift analysis (SI Eq. S13–S14; Fig. S15, p. 10–11).\nThe idea is practically appealing—use electrolyte design to escape the conductivity–selectivity trade‑off of Nafion rather\nthan inventing bespoke membranes.\nMajor comments\nGeneralizable, reproducible procedure for identifying the “balanced state.”\nThe present recipe infers BSEs from the first “horizontal region” (~107 h) in the discharge‑capacity–time trace (main Fig. 2e‑\nf), which is sensitive to current, SOC window, temperature, and cell hardware. Please formalize a predict–set–verify\nworkflow: given membrane type, current density, SOC range, and temperature, output the target P/N concentrations and\npositive‑tank average valence (with uncertainty). Publishing a minimal open script that couples Fig. 2b (net‑flux map) with SI\nSections 1 & 2 would make this widely reusable.\nDisentangle temperature and water‑migration effects.\nThe capacity ripples track day–night temperature changes (main Fig. 3b; SI Fig. S7), and hydraulic/viscous effects were\nprobed via unequal flow (main Fig. 2h; SI Fig. S5), but the quantitative roles of water transport and acid strength remain\nunclear. Please (i) repeat a key N212/N211/NC700 comparison in a constant‑temperature environment (e.g., 25 ± 0.1 °C),\nand (ii) co‑track acid molarity/viscosity/volume on both sides with water content (e.g., titration or Karl Fischer). This will\nbound how much of the benefit arises from species flux versus water/osmotic effects.\nBridge the MD to measurable transport; release inputs.\nThe MD results suggest reduced V³⁺ diffusion and altered ion–sulfonate interactions under BSEs (main Fig. 3h–j; SI\nFig. S11–S13). For reproducibility, please share topology/parameters and bench‑mark simulated diffusivities against values\ninferred from self‑discharge/EIS or literature for each ion/species. A brief sensitivity check (water content, ionic strength)\nwould increase confidence in the mechanism.\nCost model sensitivity and operating envelope.\nThe >41.7% CAPEX reduction (main Fig. 5h) is compelling but scenario‑dependent. Please add a tornado or scenario\nanalysis varying membrane cost (±50%), energy efficiency (80–86%), lifetime (500–3,000 cycles), and pump power\n(viscosity‑dependent) to test the robustness of the conclusion.\nAdaptive maintenance of the balanced state.\nSince electrode aging shifts SOC windows and kinetics (main Fig. 4e–h; SI Fig. S19/S24), demonstrate a closed‑loop\ncorrection (periodic tiny additions of VO²⁺ or acid, or controlled dilution) that keeps the net flux near zero over long cycling,\nand report how often corrections are needed. This would strengthen the practicality claim.\nMinor comments\na) Error bars and replicates. Many plots (e.g., Fig. 3c–f; Fig. 5a,b,e,f) lack uncertainty. Please report n and add error bars or\nshaded confidence bands.\nb) UV–Vis quantification. Provide the calibration curves and fitting ranges for the A/B peaks used to back‑calculate\nconcentrations/valence (SI Fig. S17, S22).\nc) Terminology and units. Standardize viscosity (mPa·s) and wording (replace “pulling acid” with “diluting with 3 M H₂SO₄”\nper SI Sec. 1.1).\nd) Operating conditions. State EIS SOC and temperature for each spectrum; specify flow‑field geometries per membrane in\nthe main text (now mostly in SI §3).\ne) Data and code. Provide raw cycling/OCV/self‑discharge data and the script used to construct the net‑flux map (main\nFig. 2b) and cost model (Fig. 5h) as supplementary files.\nRecommendation\nMajor revision. The concept is strong and well supported across membranes; addressing the above points—especially a\nportable method to determine/maintain the balanced state and clearer control of temperature/water transport—would make\nthe paper suitable for Nature Communications"}, "author_response": "Dear Editors and Reviewers,\nThank you for your and reviewers’ comments and affirmation to our manuscript entitled\n“Balanced-State Electrolytes Overcome Membrane Limitations in Redox Flow Batteries”\n(NCOMMS-25-45545-T), which are very valuable and helpful for improving this paper. We\nconsidered these comments seriously and revised the manuscript and supplementary information\nbased on them. The point-to-point responses to the comments are listed as follows:\nComments from reviewers: in black\nAuthor response: in blue\nRevisions in manuscript, and SI: in red\nThe literature and figures mentioned in the responses are sorted in order of appearance in this letter\nstarting with references labelled R, while literature and figures used in the revised manuscript are\nsorted in the order of the manuscript.\nReviewer #1\nThis manuscript describes an electrolyte engineering strategy — “balanced-state electrolytes”\n(BSEs) — for mitigating vanadium crossover caused capacity fade in VRFBs. The benefits of\napplying BSEs are well validated, showing significant improvement over traditional symmetric\nelectrolyte systems. However, several key areas still need clarification, strengthening, or additional\nexperimental support, prohibiting the manuscript from meeting the standard for publishing on\nNature Communication. Some comparison experiments are not rigorously conducted, and the\nscientific presentation could also be improved. Wherever the manuscript is going to be submitted,\nthe following concerns should be resolved.\nResponse:\nWe sincerely thank the reviewer for the valuable comments and for recognizing the merit\nof our work. We have elaborated the concept and scope of application of BSEs and have\nsuccessfully validated their application in the vanadium-iron redox flow battery system. In addition,\nwe have moved the detailed procedures for BSEs to the main Method section, provided additional\nexperimental evidence, incorporated additional modelling and theoretical analyses, specified\nworking conditions for electrochemical tests, and polished the manuscript with the help of a native\nEnglish speaker.\nPoint-by-point responses are provided below.\nMajor concerns:\n1. Conceptual novelty and presentation\na, The idea of tuning both concentration and valence to manage crossover-induced capacity\ndecay is interesting and well-motivated. However, regarding the scientific presentation, the\nauthors are making simple things complicated.\na1) If starting with V3.5+ and assuming no side reaction, the only thing that crossover will lead\nto is the concentration imbalance of the positive side and the negative side.\nResponse:\nWe appreciate the reviewer for the valuable comments. Side reactions among vanadium ions\ninduced by crossover are unavoidable during cycling, because V2+ and V3+ are reducing species\nwhereas VO2+ and VO+ are oxidizing species, as shown below. [R1]\nV 2 + + 2 V O +2 + 2 H + → 3 V O 2 + + H\nV3++VO+ →2VO2+ (Eq. R2)\nVO++2V2+ +4H+ →3V3+ +2H O (Eq. R3)\n2 2\nVO2+ +V2++2H+ →2V3++H O (Eq. R4)\n2\nthe positive side. Consequently, V2+crossover causes not only concentration imbalance but also\nvalence imbalance (the amount of VO+ less than that of V2+ on the negative side) between the\n2\npositive and the negative electrolytes. Moreover, vanadium species diffuse through Nafion\nmembranes at markedly different rates, in the order V2+ > VO2+ > VO + > V3+. [R2]\ndrives a net flux of electrolyte from the negative to the positive side, rendering VO+ depleted\n2\nrelative to V2+. As a result, crossover leads to both the concentration and valence imbalance between the positive and negative electrolytes. More\ndetails about the theoretical analysis of crossover and its experimental validation are provided in\nour previous study. [R3]\n[R1] Li Y, Skyllas-Kazacos M, Bao J. A dynamic plug flow reactor model for a vanadium redox\nflow battery cell. J. Power Sources. 311: 57-67. (2016)\n[R2] Sun C, Chen J, Zhang H, Han X, Luo Q. Investigations on transfer of water and vanadium\nions across Nafion membrane in an operating vanadium redox flow battery. J. Power Sources.\n195(3): 890-897 (2010)\n[R3] Wang Z, et al. An electrolyte with elevated average valence for suppressing the capacity decay\nof vanadium redox flow batteries. ACS Cent. Sci. 9(1): 56-63 (2022)\na2) Keeping moving the electrolyte of the concentrated side into the diluted side to keep the\namount of substance (total vanadium) identical for both sides will keep the cell balanced, until\ncrossover of vanadium from both sides balancing each other. The eventual crossover-balanced\nelectrolytes shall have the same concentration and volume as the BSE.\nResponse:\nWe thank the reviewer for this comment. In this work, the vanadium redox flow battery (VRFB)\nwas assembled with a Nafion 212 membrane and initially filled with TEs (1.70 M V3.5+, 40 mL)\non both the positive and negative sides. The BSEs for the VRFB equipped with Nafion 212\noperating at 200 mA cm-2 are 1.91 M V3.55+ and 1.17 M V3.50+ for the positive and negative\nelectrolytes, respectively. To preserve the total vanadium mass balance, the electrolyte volumes\nwere adjusted to 35.60 mL for the positive side and 58.12 mL for the negative side under the BSE\ncondition.\n4 0  1 .7 0\n1 .9 1\n= 3 5 .6 0 (Eq. R5)\n4 0  1 .7 0\n1 .1 7\n= 5 8 .1 2 (Eq. R6)\nThe combined volume of the positive (35.60 mL) and negative (58.12 mL) electrolytes in the\nVRFB employing BSEs totals 93.72 mL—higher than the 80 mL (40 + 40 mL) in the traditional-\nelectrolyte VRFB (1.70 M V3.50+). Therefore, even if the vanadium-ion amounts are maintained\nidentically across the positive and negative sides of a VRFB through precise redistribution of\nelectrolytes during cycling, the same concentration and volume cannot be achieved.\nFurthermore, the BSE for a VRFB is defined by a crossover flux of vanadium ions from the\nnegative to the positive side that is counterbalanced by an equivalent flux in the opposite direction.\nAccording to Fick’s law (Eq. R7), the flux of vanadium ions across a membrane depends on their\ndiffusion rate across the membrane and the concentration gradient between the two sides. Thus,\nboth the electrolyte concentration and the state of charge (SOC) of a VRFB significantly influence\nthe vanadium ion flux across the membrane, as depicted in Fig. 2b. This indicates that the balanced\nstate represents a dynamic equilibrium during charge–discharge processes. The balanced state of\na VRFB is therefore not a fixed state but varies with specific operating conditions. As demonstrated\nin this work, the BSEs (P 1.91 M V3.55+; N 1.170 M V3.50+) for a VRFB assembled with Nafion 212\nmembrane and operated at 200 mA cm-2 differs from that of a VRFB with an NC700 membrane\n(P 1.83 M V3.54+; N 1.15 M V3.50+).\n(Eq. R7)\nwhere, 𝐽 is the flux (mol m⁻² s⁻¹); D is the diffusion coefficient (m² s⁻¹) and is ∇𝐶 is the\nconcentration gradient.\nJ = − D  C\n1 0\n8\n6\n4\n2\n0\n0\n0\n0\n0\n0\n0 .3 0 .6 0 .9 1 .2 1 .5 1 .8\nhe\nNet fl u\nx t\nO\no\ns i\nt\nti ve\nsi\nde\np\negrahc\nfo\netatS\nP /N C o n c e n tr a tio n r a tio\nN F R\n1\n1\n0\n0\n.7\n.2\n.6\n.1\n6\nfl u\nx t\ng\no\na ti\nve\nsi\nde\nhe\nne\nt\n> 2 .0\nFig. 2b Effect of electrolyte concentrations in the positive and negative sides on the net flux ratio at different\nSOCs.\na3) By knowing the crossover constants of all vanadium ions under operation pressures would\ndirectly give the composition of BSE. BSE allows the amount of substance in the positive and\nnegative side unchanged because the crossover cancels each other. Authors should explain the\ndetermination of the BSE composition in a more explicit and clear way.\nResponse:\nWe thank the reviewer for raising this point. We have clarified the description of the BSEs for a\nVRFB in the revised manuscript and added a section detailing how to determine the BSE\ncomposition in the revised supplementary information, as detailed below.\nIn practice, the direct measurement of the crossover quantities of all vanadium ions during charge–\ndischarge cycling is extremely challenging, owing to side reactions and dynamic variations in\nelectrolyte concentration, volume, and valence. Here, we treat VRFBs during cycling as dynamic\ndiffusion systems and leverage their self-balancing capability to determine electrolyte\nconcentration. Characterizing the electrolyte composition at the balanced state of a VRFB under\nspecific operating conditions enables the design of corresponding BSEs. Consequently, our\napproach in this work does not require prior knowledge of the precise crossover constants of\ndifferent Nafion membranes to determine the BSE compositions. This highlights the unique\nadvantage of our proposed strategy: it provides a universal, experimentally driven framework for\nderiving balancing solutions for different membrane materials and operating scenarios, without\nthe prerequisite of engaging in the characterization of intrinsic membrane parameters. Differences\nin cell configuration and operating conditions are inherently captured in the resulting balanced\nstate, leading to distinct BSEs—as demonstrated by the differing BSE compositions for VRFBs\nusing N212 (P 1.91 M V3.55+; N 1.170 M V3.50+) versus N211 membranes (P 1.83 M V3.54+; N 1.15\nM V3.50+).\nIn the revised Manuscript [Section BSE determination]\nDetermining the balanced state of a VRFB under specified operating conditions is essential for\ndesigning BSEs. Specifically, we define the balanced state under specific conditions as one\nwhere the capacity decay rate is less than 0.03% per cycle or 0.08% per hour. In addition, the test\nmust last longer than 8 h and include more than 20 cycles, with the discharge capacity showing a\nmonotonic decay versus time or cycle number over the investigated range. The electrolyte\nconcentrations at the balanced state are used for designing BSEs. To ensure the accuracy of these\nmeasurements, we converted the electrolytes at the balanced state to V3+|VO2+ through full\ndischarge followed by aerial oxidation. To compensate for the elevated average vanadium valence\nthat occurs during cycling due to side reactions, the VO+ content in the initial electrolyte was\n2\nexperimentally increased. The detailed procedure is described in the supplementary information.\nIn the revised Supplementary Information [Section BSE determination]\nFirst, operate a VRFB under specified conditions and record the discharge capacity versus time\ncurve. Second, calculate the capacity decay rates over 20 cycles in the quasi-steady region of the\ndischarge capacity curve. Third, identify the region where the discharge capacity decay rate is\nbelow 0.03% per cycle. Fourth, stop cycling and fully discharge the battery at a constant voltage\nof 0.8 V until the current falls below 0.1 A. Fifth, stir the negative electrolyte using a magnetic\nstirrer and oxidize it in air for 4 hours to convert the surplus V2+ to V3+. Sixth, dilute the negative\nand positive electrolytes 15-fold with deionized water and measure the V3+ and VO2+\nconcentrations using a UV-Visible Spectrophotometer.\na4) Furthermore, from this perspective, the authors may consider building an automatic adjusting\nsystem, monitoring the volume and the concentration of each sides of the electrolyte and adding\nan automatic side-pumping system (with pumping rate balancing the osmosis pressure and sub-\ncell balancing the side reaction: DOI https://doi.org/10.1039/D4EE02450H) to realize the auto-\noptimized BSE. If such an automatic monitored system with near zero fading would be\ndemonstrated, this manuscript can be accepted by Nature Communication.\nResponse:\nWe thank the reviewer for raising this point. We have tried to validate the automatic balance system\nwith a reflow setup, as shown in Fig. R1a-b. Initially, the positive and negative sides were filled\nwith 1.7 M electrolyte volumes of 35.6 mL and 44.4 mL, respectively. The smaller positive volume\nwas designed to compensate for the anticipated concentration increase due to vanadium crossover,\nthereby maintaining equal total vanadium content on both sides after equilibrium. As expected,\ngravity-driven flow through a connecting pipe occurred when the positive electrolyte volume\nincreased due to crossover. The initial discharge capacity was low, which is attributed to a\ntemporary shortage of positive electrolyte, but it increased with cycling (Fig. R1c). Early-cycle\nfluctuations are caused by non-equilibrium transport of ions and water across the Nafion\nmembrane [R4]. The subsequent capacity increase is attributed to the rising positive electrolyte\nconcentration caused by crossover, which enhances the vanadium content at the same volume.\nHowever, after reaching the values comparable to those of the VRFB employing BSE, the capacity\ndecayed linearly. This linear decay might suggest that the final electrolyte characteristics in the\nreflow system differ from those in the BSEs, as further analysed in the response in a1 and a2.\nTo further demonstrate the effectiveness and applicability of our proposed BSEs method, we have\nextended it to iron-vanadium flow batteries (IVFBs), which suffer from severe crossover issues.\nAs shown in Fig. R2, the accumulated discharge capacity improved 56.36% from 388.37 to 607.25\nAh over 400 cycles when conventional electrolytes were replaced with the BSEs, demonstrating\ngood effectiveness and applicability. Details on the BSEs for IVFBs have been added to the revised\nmanuscript and supplementary information, as detailed below.\na b\nReflow\nPositive pipe\nelectrolyte\n35.6 ml\ntank\n44.4\nml\nPositive tank\nNegative\nelectrolyte\nNegative tank\ntank\nc\nd\n1\n1\n0\n0\n0\n0\n0\n.2\n.0\n.8\n.6\n.4\n.2\n.0\n0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0\n)h\nA\n(\ny tic\na\np\na\nc\ne\ng\nr\na\nh\nc\nsiD\nT\nP\nE\n3\ns\n5 .6 N\nB S\n4 4 .4\nE\nm\nsL\nR e flo w\nC y c le n u m b e r\n@ 2 0 0 m A\n2 5 ℃\n-2 c m\n84\n)%\n(\ny\nc\ne\nn c81\niffe\ne\ng\na\ntlo78\nV\nTEs BSEs\nP 35.6 N 44.4 mL Reflow\n75\n0 100 200 300 400 500\nCycle number\nFig. R1 Reflow setup for automatically balancing electrolytes between the positive and negative sides of\nVRFBs during cycling. a, Schematic of the reflow setup. b, Optical image of the reflow system for VRFBs.\nc-d, Discharge capacity and voltage efficiency of VRFBs with TEs, BSEs, and reflow system.\n)hA(\nyticapac\negrahcsiD\n1\n1\n1\n1\n0\n0\n.6\n.4\n.2\n.0\n.8\n.6 @\n0\n2 0 0 m A c m\n5 0\n-2\n1 0 0 1 5 0\nC y c\n2 0\nle n\n0\nu m b e r\n2\n5\n5\n6\n0\n.3 6 % ­\n3 0 0\n.7S 2+ M V ||1\nE s\n3 5 0\n.7 M F e\n4\n3+\n0 0\nFig. R2 Comparison of iron-vanadium flow batteries using conventional electrolytes (P 1.7 M V2+; N 1.7\nM Fe3+) versus balanced state electrolytes (BSEs, P 1.072 M V2+ + 0.876 M Fe2+; N 1.324 M Fe3+ + 0.914\nM VO2+).\nIn the revised Manuscript [Fig. 5]\n)hA(\nyticapac\negrahcsiD\n1.5\n1.2\n0.9\n0.6\n0.3\nN\n17.4%\n60.6%\n60 120\nT est tim\n180\ne (h )\n240 300\na b\nc\ne\n1.5\n1.2\n0.9\n0.6\n0.3\nN C 700 15 \n0\nm\n80 160 240 320 400\n)hA(\nyticapac\negrahcsiD\n1.5\n1.2\n0.9\n0.6\n0.3\nN\nC 700 B S E s\n13.6%\n60.6%\n60 120\nT est tim\n180\ne (h )\n240 300\n)h\nA (\ny\ntica\np a\nc eg\nra\nh\ncsiD\n)hA(\nyticapac\negrahcsiD\n1.6\n1.2\n0.8\n0.4\nN 211 25 \n0\n@ 200 m A\nm\ncm -2\n80 160\nC\nC\ny\ny\ncle n\ncle n\nu\nu\nm\nm\nb\nb\ner\ner\n240\n85.1%\n8 4 .8 %\n­\n­\nN\nN C\nN C\n2 1 1 B\n2 1 1 T\nS E s\nE s\nE s\nd\n100 1 MW/4 MWh f 0.0 a m： Membrane thickness T 1 h 5 is  w m ork g 1.6\n)% ( eg a tn ecrep tso C 7 5 2 5 0 5 6 2 2 9 . . 7 6 9 9 2.19 10.8 5 1 8 0 . 0 3 )‰ ( eta r y a ced y tica p a C 0 1 1 2 2 . . . . . 5 0 5 0 5 E A ne d rg v 2 y . 4 S F to  u r m a 4 n g 6 c e t  M . m a A M te d r a v .2 t . 0 e F 2 r 4 u N . n 2 4 a c 0 0 t t 4 N 2 . .  6 2 M S a m  t u a . m s t C e ta r o i 2 m n 0 . 2 2 m 3 0 u 2 n 2 A . A 2 4 n 0 n 0 g 2 g e  0 ew w m . 5 C . 4 C h  7 e h m m 0 e , m  20 , m 2 2 5 024 )h A ( y tica p a c eg ra h csiD 1 1 1 0 . . . . 4 2 0 8 1 B . S 7 E M s V2+||1.7M Fe3+ 56 @ .3 6 2 % 00 ­ mA cm-2\n0 3.0 0.6\nElectrolyte Membrane Capital 76 78 80 82 84 86 0 50 100 150 200 250 300 350 400\ncost cost cost Energy efficinecy (%) Cycle number\nFig. 5 Suppression of crossover with BSEs in RFBs. Effects of BSEs on improving a, discharge capacity\nof the VRFB with N211. b, Discharge capacity comparison between the VRFBs with N211 and N117. c,\nEffects of BSEs on improving the capacity retention rate of the VRFB with NC700. d, Capacity retention\nrates comparison between the VRFB with NC700/BSEs and that of N117/TEs. e, Capital cost analysis in a\nVRFBs with advanced designed membranes reported in the last five years. g, Effects of BSEs (P 1.072 M\nV2+ + 0.876 M Fe2+; N 1.324 M Fe3+ + 0.914 M VO2+) on improving the capacity retention rate of the\nIVFB with N212.\nIn the revised Manuscript [Line 373, Page 15]\nTo further demonstrate the effectiveness and applicability of our proposed BSEs method, we have\nextended it to iron-vanadium flow batteries (IVFBs), which suffer from severe crossover issues.\nThe accumulated discharge capacity improved 56.36% from 388.37 to 607.25 Ah over 400 cycles\nwhen conventional electrolytes (P 1.70 M V2+; N 1.70 M Fe3+) were replaced with the BSEs (P\n1.072 M V2+ + 0.876 M Fe2+; N 1.324 M Fe3+ + 0.914 M VO2+), indicating successful suppression\nof the crossover, as shown in Fig. 5g.\nIn the revised Manuscript [Section Materials]\nIron (II) sulfate heptahydrate (FeSO ‧7H O CAS Number: 7782-63-0) and Iron (III) chloride\n4 2\nhexahydrate FeCl ‧6H O (CAS Number: 7447-40-7) were purchased from Sigma-Aldrich.\n3 2\nIn the revised Manuscript [ Section Battery tests]\nA VRFB cell equipped with Nafion 212 was adapted for IVFBs testing by replacing vanadium\nelectrolytes with iron-vanadium electrolytes.\nIn the revised Manuscript [Section Electrolytes preparation]\n1.70 M Fe3+/3.00 M H SO electrolyte was prepared by dissolving FeCl ‧6H O in 3.00 M H SO\n2 4 3 2 2 4\nsolution.\nIn the revised Manuscript [Section Characterization techniques]\nIon concentrations in the positive and negative electrolytes of IVRFs were measured using an\nInductively Coupled Plasma –Optical Emission Spectrometer (Avio-200, PerkinElmer) following\n7500-fold dilution with deionized water.\nIn the revised Manuscript [Section Battery tests]\nAll the battery tests were conducted under N protection using Arbin 179539 (Arbin instruments,\n0.60-1.60 V for IVFB experiments.\nIn the revised Supplementary Information [Section 1.2 Electrolyte preparation for IVFBs]\nThe BSEs for IVFBs were prepared as follows. For the positive side, 11.62 g VOSO ·5H O was\n4 2\nadded to 40 mL of 1.70 M Fe3+/3.00 M H SO solution and then diluted with 11.36 mL of 3.00 M\n2 4\nH SO , serving as the positive electrolyte. For the negative side, 11.45 g FeSO ‧7H O was added\n2 4 4 2\nto 40 mL of 1.70 M V2+/3.00 M H SO solution and then diluted with 23.43 mL of 3.00 M H SO ,\n2 4 2 4\nserving as the negative electrolyte.\nIn the revised Supplementary Information [Section 1.4.2 BSEs for IVFBs]\nThe definition and identification method for the balanced state in IVFBs are the same as those for\nVRFBs. Here, we selected the state of an IVFB after 160 cycles as its balanced state and measured\nion concentration using an Inductively Coupled Plasma –Optical Emission Spectrometer (Avio-\n200, Perkin Elmer) following 7500-fold dilution with deionized water. The results show that\nvanadium ion concentrations are 0.914 M and 1.072 M in the positive and negative electrolytes,\nrespectively, and iron ion concentrations are 1.324 M and 0.876 M, respectively.\nIn the revised Supplementary Information [Section 4 IVFB test]\nFirst, a VRFB assembled with Nafion 212 was fully charged using 40 mL of V3.5+/3.00 M H SO\n2 4\nas both the positive and negative electrolytes, yielding 40 mL of V2+/3.00 M H SO on the negative\n2 4\nside. Then, the positive electrolytes (VO+) were pumped into tank and the positive-side\n2\nchamber was washed with deionized water and purged with N for 1 min. Finally, the positive\n2\nelectrolyte was replaced with 1.70 M Fe3+/3.00 M H SO electrolytes. In IVFB testing with the\n2 4\nBSEs, the same flow battery cell was employed.\nIn the revised Supplementary Information [Fig. S38]\n)hA(\nyticapac\negrahcsiD\n1\n1\n1\n1\n0\n0\n.6\n.4\n.2\n.0\n.8\n.6 @\n0\n2 0 0 m A c m -2\n5 0 1 0 0\nT e st tim e (h )\n1 5 0\nB a la n c e d sta te p o sitio\n2 0 0\nn\nIV\n5 0\nFig. S38 Discharge capacity versus time for an IVFB using TEs (P 1.70 M Fe3.0+; N 1.70 M V2.0+).\n[R4] Mu D, Zhao Y, Yu L, et al. Asymmetric vanadium flow batteries: long lifespan via an\nanolyte overhang strategy. Phys. Chem. Chem. Phys. 19(43): 29195-29203 (2017).\nb, The term \"balanced-state electrolyte\" lacks precise definition early in the manuscript, increasing\nthe reading barrier to audiences.\nResponse:\nWe appreciate the reviewer for the valuable comments. We have clarified the definition of the\nbalanced state of electrolytes (BSE) for VRFBs in the revised manuscript upon its first\nintroduction, with details provided below.\nIn the revised Manuscript [Line 79, Page 3]\nIdeally, the balanced-state electrolyte in a VRFB is defined by a crossover flux of vanadium ions\nfrom the negative to the positive side that is counterbalanced by an equivalent flux in the opposite\ndirection.\nc, Many experimental results are repetitive. Authors should consider moving some of the\nrepetitive figures and supporting data into SI (e.g., Fig 4a (crossover is more time-dependent\nthan cycling dependent), 4f-j, 5a-c).\nResponse:\nThanks for your important suggestion. The repeated experimental data have been moved to the SI\nin the revised manuscript, as shown below.\nIn the revised Manuscript [Figs. 4 and 5]\nBefore cycling After Cycling 0.012\nm h O\n/)Z 0.008\n(m\nI-\n0.004\n0.000\n0.028 0.032 0.036 0.040\nRe(Z)/Ohm\nmhO/)Z(mI-\n0.06\n0.04\n0.02\n0.00\nN\nN\n0.04\nSE Es s\nR e(Z\n0.06\n)/O h m\n0.08\n120\n)%\n(\ny cn eiciffe\ncib\nm o lu\no C\n9\n9\n9\n9\n9\n8\n6\n4\n2\n0\n1\n1\n9\n8\n1\n0\n0\n0\n0\n0\n)%\n( y cn\neiciffe\neg\na tlo\nV\nN212 BSEs 70\nN117 TEs\n88\n50 100 150 200\nCurrent densiy (mA cm-2)\n1.2\n1.0\n0.8\n0.6\n0.4\n0.2\n0 100 200\n60.6%\n300 400 500 600 700\n)h\nA\n(\ny tica\np\na\nc\neg\nra\nh csiD\n10.7%\nT est tim e (h )\nN\nN\nSE Es s\na b\nc d e\n( y cn 84 3.4%\neiciffe\neg\n80\na tlo 76\nV\n0 505 0995500 1000 1050\nCycle number\nFig. 4 Stability of VRFBs with balanced-state electrolytes. Comparison of VRFBs with BSEs (P 1.91\nM V3.55+; N 1.17 M V3.50+) combining with N212 (51 μm) and TEs (P 1.70 M V3.50+; N 1.70 M V3.50+)\ncombining with N117 (183 μm) in a, discharge capacity vs. test time, b, EIS spectrum, c, coulombic/voltage\nefficiency. d, Voltage efficiency and e, EIS spectrum of the VRFB with BSEs before and after cycling.\na\n)hA(\nyticapac\negrahcsiD\nc\n)hA(\nyticapac\negrahcsiD\ne\n)%( egatnecrep\ntsoC\n1.6\n1.2\n0.8\n0.4\n1.5\n1.2\n0.9\n0.6\n0.3\n100\n75\n50 25\n0\n-2 @ 200 m A cm\nN C 700 15  m\n0\n62.79\n29.69 2.19\nE lectrolyte\ncost\n80\n80\n10.8\nM em b ran\ncost\ne\n160\n160\n100\n58.3\nC ap ital\ncost\nC\nC\ny\ny\ncle n\ncle n\nu\nu\nf\n240\nm b er\n240\nm b er\n0.0\n0.5 1.0\n1.5 2.0 2.5\n3.0\n76\n85.1%\n8 4 .8 %\n­\n­\n80\n320\n320\nN 2 1 1 T E s\nN C 700 T E s\n400\n84 86\nb\n)hA(\nyticapac\negrahcsiD\nd\n)hA(\nyticapac\negrahcsiD\ng\n1.5\n1.2\n0.9\n0.6\n0.3\n1.5\n1.2\n0.9\n0.6\n0.3\n0\nN\nN\nN\n17.4%\n60.6%\n60 120\nT est tim\n180\ne (h )\n240 300\nC 700 B S E s\n13.6%\n60.6%\n60 120\nT est tim\n180\ne (h )\n240 300\n40 m\n24 m 46 m 46 m\n15 m\n40 m\n54 m\nA ngew .C hem , 2024 E A ne d\nrg\nv\ny\n.\nS\nF\nto\nu\nra\nn\ng\nc\ne\nt\nM\n.\na A\nM\nte d r\na\nv .2\nt\n. 0\ne\nF 2\nr\n4 u\nN .\nn\n2 a\nc\n0 t\nt\nN 2\n.\n. 2\nM\nS at u\na\n. s\nt\nC\ne\nta\nr\no i\n2\nm n\n0\n.\n2\n2 m\n3\n0 u 2 n 2 .\nA\n20\nn\n2\ng\n0\new.Chem, 2025\n)‰( etar yaced\nyticapaC\na m ： M em brane thickness\nE n erg y efficin ecy (% )\nT his w\n70  m\nork\n)hA( yticapac\negrahcsiD\n1.6\n1.4 1.2\n1.0 0.8\n0.6\n0\n1.7 M V B S E s\n50 100\n2+ 3+ ||1.7M F e\n150 200\nC y cle n u m\n5 6 .3 6 % ­\n@ 200 m A cm\n250 300 350\nb er\n-2\nof the VRFB with N211. b, Discharge capacity comparison between the VRFBs with N211 and N117. c,\nEffects of BSEs on improving the capacity retention rate of the VRFB with NC700. d, Capacity retention\nrates comparison between the VRFB with NC700/BSEs and that of N117/TEs. e, Capital cost analysis in a\nVRFBs with advanced designed membranes reported in the last five years. g, Effects of BSEs (1.072 M\nV2+ + 0.876 M Fe2+; 1.324 M Fe3+ + 0.914 M VO2+) on improving the capacity retention rate of the\nIVFB with N212.\nIn the revised Supplementary Information, we have added Fig. S19, S20, S22, S29, S30, and S34,\nwith details provided below.\nN212 (51 m) BSEs\n1.2\nN117 (183 m) TEs\n)h\nA1.0\n(\ny\ntic\na0.8\np 159.5%­\na\nc\ne0.6\ng\nr\na\nh\nc0.4\nsiD\n0.2 @ 200 mA cm-2\n0 200 400 600 800 1000\nCycle number\nFig. S19 Cycling performance of VRFBs comparing BSEs (P 1.91 M V3.55+; N 1.17 M V3.50+) combining\nwith N212 (51 μm) to TEs (P 1.70 M V3.50+; N 1.70 M V3.50+) with N117 (183 μm).\nc d\n0 cycle\nAfter cycling P\nAfter cycling N\n).u\n.a\n(\ny tisn\ne tn\nI\nPDF#41-1487:002 0 0 2 100 101\n10 20 30 40 50\n2 theta (degree)\n)u.a(\nytisnetnI\n1 0\n9\n7\n6\n4\n3\n5\n0\n5\n0\n5\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n05\n7\no sitiv e\nC\nC -O\nO O H\n5 3 4\nB in d\nH\nin g e n e\nC = O\nA fte r\nc y c lin g\nB e fo r\nc y c lin\n5 3 1\nr g y (e v )\ne\ng\n5 2 8\na b\n10000\n7500\n5000\n2500\n1200 1400 1600 1800 2000\nD G\nBefore cycling\nAfter cycling P\nAfter cycling N\n)u D\n.a G\n(\ny tisn\ne\nI\nI\nD\nD\n/\n/\nI\nI\nG\nG\n=\n=\n0\n1\n.\n.\n9\n1\n5\n2\n3\n7 tn ID/IG=1.061\nI\nRaman shift (cm-1)\n)u.a(\nytisnetnI\n1\n1\n1\n4\n2\n0\n8\n6\n4\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n5 3 7\ne\nC O\nB in\nC -O\nO H\n5 3 4\nd in g e\nH\nn e r g y\nC =\n5 3 1\n(e v )\nO\nA fte r\nc y c lin g\nB e fo r e\nc y c lin g\n5 2 8\nFig. S20 Electrode degradation in VRFBs with BSEs after cycling. a-b, XPS spectra of the electrode\non the positive and negative sides before and after cycling. c, XRD and d, Raman spectra of electrodes\nbefore and after cycling.\n1 2\n8\n4\n0\n0\n0\nT E s\ne\n%\n4.59%\n38.94\n)%\n(\noitar\nxulf\nteN\nA\nB\nfte r\nS\n7\ns\n5 .7 2 h A fte r 1 7 5 .6 7 h\nFig. S22 Electrolyte net flux between the positive and negative sides in VRFBs with BSEs (P 1.91 M\nV3.55+; N 1.17 M V3.50+) and TEs (P 1.70 M V3.50+; N 1.70 M V3.50+) combining with N212 before and\nafter cycling.\n)%\n(\nycneiciffe\ncibmoluoC\n1 0\n9\n9\n8\n0\n6\n2\n8\n5 0\nN\nN\n2 1 1 B S E\n2 1 1 T E s\n1 0 0 1\nC u r r e\ns\n5 0\nn t d e\n2n 0 0\nsiy (m\n2 5A 0\nc m\n3 0\n-2)\n0 3 5 0\nFig. S26 Effects of BSEs on improving the coulombic efficiency of the VRFB with N211.\n1\n1\n0\n0\n0\n.6\n.2\n.8\n.4\n.0\n0 7 1 4 2 1 2 8 3 5\n)V\n( e\ng a\ntlo\nv\ntiu\nc\nri\nc\nn\ne p\nO\nV O + d\n2\nisa p\nT\np e\nim\na r\ne (h )\nN\nV\n1 .1\n2+ d\nP\nP\nP\nP\nisa p\n/N 1 .7 0\n1 .8 3 M\n1 .9 3 M\n2 .0 3 M\n3.50+ V\np e a r\nM\nV\nV\nV\n3.50+ V3.54+\n3.56+\n3.58+\nFig. S27 Self-discharge curves of VRFBs with the N211 membrane and different electrolytes.\n)%\n(\nycneiciffe\ncibmoluoC\n9\n9\n9\n9\n9\n9\n8\n7\n6\nN\nN\n5 0\nCC1 7 0 0 B\n7 0 0 T\n1 7 T\nC u r r\nS E s\nE s\nE s\n1 0 0\ne n t d e n siy (m\n1 5\nA\n0\nc m -2)\n2 0 0\nFig. S33 Effects of BSEs on improving the coulombic efficiency of the VRFB with an NC700.\nd. Fig. 1e, 2s, S4, S6 are not helpful and confuse the readers. The authors should just write down\nthe formula, the chemical reactions and balance them. The reviewer tried to count these colored\nballs and found them not even balanced regarding numbers. There is no point in using them if\nthese figures are not accurate, can be simplified by words, only cause pain and are not aesthetically\nbeautiful. The authors should simply use an example case and write the chemical composition to\nexplain the problem of crossover and the authors’ solution.\nResponse:\nWe sincerely apologize for the unsatisfactory experience. The relevant content has been removed,\nand the corresponding descriptions have been simplified in both the revised manuscript and the\nsupplementary information, as detailed below.\nIn the revised Manuscript [Fig. 1]\na\n)hA(\nyticapac\negrahcsiD\nb)1-L\nlom(\nnoitartnecnoc\nsnoI\ne)hA(\nyticapac\negrahcsiD\n1 .2\n1 .0\n0 .8\n0 .6\n0 .4\n2 .1\n1 .8\n1 .5\n1 .2\n0 .9\n1 .2\n1 .0\n0 .8\n0 .6\n0 .4\nN\n0\n0\n@\n0\n2\n2\n1\n0\n2 5\nC\nA\n0 m\n1  m\n5 0\na th o ly\nn o ly te\n5 0\nA c m\n5 0\nte\n-2\n1 0 0\n1 0 0\n1 0 0\n1 5 0 2 0 0 2 5 0\nC y c le n u m b e r\n1 5 0 2 0 0 2 5 0\nC y c le n u m b e r\n1 5 0 2 0 0 2 5 0\nC y c le n u m b e r\n3 0 0\n3 0 0\n3 0 0\n@ 8 -2 2 0 0 m A c m\n8\n7\n7\n7\n3 5 0 4 0 0\n6\n3\n2\n3 5 0 4 0 0\nN 2 1 2 5 1  m\nN 1 1 5 1 2 7  m\nN 1 1 7 1 8 3  m\n3 5 0 4 0 0\n4 )%\n(\n1 ycneici\n8 ffe\nega\n5 tloV\n2\n)s·aPm(\nytisocsiv\ncitameniK\nmhO/)Z(mI-\nc\n)hA(\nyticapac\negrahcsiD\nd\n)%\n(\nycneiciffe\negatloV\nf\n0\n0\n0\n0\n0\n0\n1 .5\n1 .2\n0 .9\n0 .6\n0 .3\n8 8\n8 4\n8 0\n7 6\n7 2\n.0 5\n.0 4\n.0 3\n.0 2\n.0 1\n.0 0\n0\n0\n5 0 4 0 0 4 5 0\nC y c le n u m b e r\nR e fr e sh e le c tr o ly te\n5 0 4 0 0 4 5 0\nC y c le n u m b e r\nN 2 1 2 5 1  m\nN 1 1 5 1 2 7  m\nN 1 1 7 1 8 3  m\n.0 4 0 .0 5 0 .0 6 0 .0 7\nR e (Z )/O h m\n0\n5 0 0\n5 0 0\n.0 8\nFig. 1 Battery performances and electrolyte properties vary with cycling. a, Discharge capacity/voltage\nefficiency and b, electrolytes’ concentration/viscosity change with cycling of the VRFB equipped with\nNafion 212 and traditional electrolytes at 200 mA cm-2. c, Discharge capacity and d, voltage efficiency of\nVRFB after refreshing electrolytes. e, Comparison of discharge capacity decay and f, electrochemical\nimpedance spectroscopy (EIS) in VRFBs with Nafion 212/115/117 (Named as N212/N115/N117).\nIn the revised Manuscript [Line 115, Page 4]\nSpecifically, it results in a deficiency of VO+ on the positive side (supplementary information，\n2\nsection 3)…\nIn the revised Manuscript [Fig. 2]\n)hA(\nyticapac\negrahcsiD\n1\n1\n0\n0\n0\n.5\n.2\n.9\n.6\n.3\nP P\n1 1\n1 2\n.7.8.9.0\n4\n0000\nM M\nC y c le\n8 0\nn u m b e\n1r 2\nN\n0\n1 .7 0 M\n1 6 0\na b c\negrahc\nfo etatS\n8\n6\n4 2\n0\n0\n0 0\n0\n7 9 .6\n5 .0 1\n1 5 0\nC u r\n6 9 .8\n6 .9 9\n2 0 0\nr e n t d e n\n5 9 .2\n9 .1 2\n2 5 0\nsity m(\nR ech argeab le N on -d isch arge\n4 7 .8 3 5 .6\n1 4 1 1 .4\n3 0 0 3 5 0\n-2 A c m )\n1 0\n0\n0\nd e\n)h1.2\nA\n( y tic 1.0\na p\na c0.8\ne\ng\nr\na h0.6\nc siD\n0.4 P 1.70 M VO2+ N 1.70 M V3+\nHorizontal region\n0 30 60 90 120 150 180\nDischarge time (h)\nf h\n1.5 P 51 rpm N 51 rpm\n1.2\n)h A )h A P 96 rpm N 51 rpm )h A 1.2\n( y tic\na p a c\ne g r a h c siD\n1\n0\n0 0\n.\n.\n.\n.\n0\n8\n6 4 P 1.70 M V3.5+ N 1.70 M V3.5+\n( y tic\na p a c\ne g r a h c siD\n1\n0 0\n.\n.\n.\n2\n9\n6\n( y tic\na p a c\ne g r a h c siD\n1\n0 0\n.\n.\n.\n0\n8 6 0 1 m m l l V V O O 2 2 + +\nP 1.91 M VO2+ N 1.17 M V3+ 0.3 P 1.70 M V3.5+ N 1.70 M V3.5+ 0.4 2 ml VO 2 + 3 ml VO 2 +\n0 30 60 90 120 150 0 40 80 120 160 200 0 30 60 90 120 150\nCycle number Cycle number Cycle number\n)1-L\nlom(\nnoitartnecnoC\n2\n1\n1\n1\n0\n.1\n.8\n.5\n.2\n.9\nV\n.7\n0\n3+ c o n c n e tr a tio n\n2+ O c o n c n e tr a tio n\n1 .7\n1 .1 7\nh 1\nT e st tim e\n0 7\n1\nh\n.9 1\ng\n1 0\n8\n6\n4 2\n0\n0\n0\n0 0\n0\n0 .3 0 .6 0 .9 1 .2 1 .5 1 .8\nNet\nfl u\nx t\np\nt\no\no\ns i\nt\nt\nh iv e e side\negrahc\nfo etatS\nP /N C o n c e n tr a tio n r a tio\nN F R\n1\n1 0\n0\n.7\n.2 .6\n.1\n6\nt h\nfl\ne\nu n x e t g o a tive side > 2 .0\nFig. 2 Suppressing capacity decay of VRFBs via the adjustment of vanadium ion transport across the\nmembrane. a, Electrolyte concentrations on the positive and negative sides affect the net flux ratio under\ndifferent SOCs (the diffusion rates were based on Sun’s23 study (Table S1), NFR is the net flux ratio between\nthe positive and negative sides). b, Effects of increasing the concentration of VO2+ electrolyte on capacity\ndecay. c, Range of SOC in the discharge process under different current densities. d, Discharge capacity\nvaries with test time. e, Concentration of electrolytes on the positive and negative sides after 107.56 h (200\ncycles). f, Performance of VRFB with the electrolyte concentrations at balanced state (P 1.91 and N 1.17\nM). g, Hydro pressure effects on suppressing capacity decay of VRFBs. h, Additional VO+ effects on\n2\nsuppressing capacity decay of VRFBs (Letters P and N represent positive and negative electrolyte\nrespectively).\nIn the revised Manuscript [Line 145, Page 6]\nSpecifically, reducing the negative electrolyte concentration while increasing that of the positive\nconcentration mitigates vanadium ion crossover from negative to positive and promotes its reverse\ntransport. Consequently, these opposing fluxes counter each other, resulting in minimal net\ncrossover and stable cell balance.\nIn the revised Supplementary Information [ Section 3.1]\nIn VRFBs, the vanadium ions transported from one side to the other side induce side reactions,\nthat cause an imbalance in electrolyte valence on the positive and negative sides, as illustrated\nbelow. [S1]\nReactions associated with vanadium ion transport from the negative side to the positive side:\nV 2 + + 2 V O +2 + 2 H + → 3 V O 2 + + H\nV2++VO2++2H+ →2V3++H O (Eq. S6)\nReactions associated with vanadium ion transport from the positive side to the negative side:\nV O +2 + 2 V 2 + + 2 H + → 3 V O 2 + + H\nV O +2 + V 3 + → 2 V O 2 + (Eq. S9)\nVO2+ +V2++2H+ →2V3++H O (Eq. S10)\nVO+and V2+, respectively. While the crossover of V2+ and VO+ ultimately consumes twice as much\n2 2\nas VO+ and V2+, respectively. Combine with the diffusion rates of vanadium ions across the Nafion\n2\nseries membranes (V2+ > VO2+ >VO+ > V3+).[S2]; this results in a net flux of V2+ transport from\n2\nthe negative to the positive side during cycling, accompanied by twice the expected consumption\nof VO+. Consequently, crossover leads to the accumulation of surplus V2+ on the negative side,\n2\nwhereas a deficiency of VO+ arises on the positive side.\nV\n1\n2+\nV\nit\n2 +\ni a l s t a t\n1 0 V\n+ VO 2\ne\nO +2\n( P\n( P\nS y m\ne le c t\n: a M\nA s y m\ne l e c t\n: a M\nm e t r ic\nr o l y t e s\n; N : a M\nm e t r ic\nr o l y t e s\n; N : b M\n)\n)\nC r o s s o v e r\n2+ + 2+ 2 V + 4 V O 6 V O 2\nP o s it iv e s id e r e a c t io n\n2+ + 2+ V + 2 V O 3 V O 2\nP o s it iv e s id e r e a c t io n\n+ 2+ 3+ V O + 2 V 3 V 2\nN e g a t iv e s id e r e a c t io n\nA f t e r c r o\n2 + 8 V\n2+ V\n6 0 %\nC a p a c it y r e\n2 + 7 V 3 + 3 V\n3+ V\n2+ V\n1 0 0 %\nC a p a c i t y r e\ns s o v e r\n+ 6 V O 22+ 6 V O\n2+ VO\n+ VO 2\nt e n t io n\n+ 7 V O 22+ 3 V O\n2+ VO\n+ VO 2\nt e n t io n\nFig. S1 Schematic illustration of the enhanced discharge capacity in a VRFB employing an\nasymmetric electrolyte (Note: P and N denote the positive and negative electrolytes, respectively).\nAs depicted in Fig. S1, the initial state assumes 10 V2+ and 10 VO+ on the negative and positive\n2\nsides, respectively. In a VRFB operated with symmetric electrolytes, crossover leads to the\ntransport of two V2+ ions from the negative to the positive side, accompanied by the consumption\nof 4VO+ ions. This imbalance in vanadium-ion content and valence across the two sides\n2\nconsequently reduces the capacity to 60%. By contrast, in the VRFB working with asymmetric\nelectrolytes the amount of V2+ transport from the negative to the positive side is counterbalanced\nby an equivalent flux of VO+ in the opposite direction. Therefore, the contents and valence of\n2\nvanadium ions on the positive and negative sides remain balanced, preserving 100% capacity\ndespite crossover.\n1\n2+ V\n2+ V\n0\n82V\nF u l l C\nV\n2 + V\nV\n2 + V\n3 + V3+\nh a r\n3 .5 +\n1 0\n+ V O 2\n> 3 .5 +\n1 0\n+ VO 2\ng\nV\nV\ne\nO\nO\n+2\n+2\nC\nC\nh\nh\na\na\nr\nr\ng\ng\ne\ne\n/\n/\nd\nd\nis\nis\nc\nc\nh\nh\na\na\nr\nr\ng\ng\ne\ne\nc\nc\ny\ny\nc\nc\nlin\nlin\ng\ng\nC r o\n2+ 2 V + 4 V O\nP o s it iv e s\n2+ 2 V + 4 V\nP o s it iv e s\ns s o v e r\n+ 6 V O 2\nid e r e a c t io\n+ O 6 V 2\nid e r e a c t io\n2+ \nn\n2+ O\nn\nA f t e r\n2 + 8 V\n2+ V 6\nC a p a c it\n2 + 6 V\n3 + 2 V\n3+ V\n2+ V\nC a p a c i\nc r o s s o v e r\n+ 6 V O 22+\n2+ VO\n+ VO 2 0 %\ny r e t e n t io n\n+ 6 V O 22+\n2+ VO\n+ VO 2\n8 0 %\nt y r e t e n t io n\nFig. S7 Schematic of surplus 𝐕𝐎+ for suppressing capacity decay.\nbalance between the positive and negative electrolytes under equivalent crossover conditions,\nthereby substantially reducing the capacity decay rate.\n[S1] Li Y, Skyllas-Kazacos M, Bao J. A dynamic plug flow reactor model for a vanadium redox\nflow battery cell. J. Power Sources. 311: 57-67. (2016)\n[S2] Sun C, Chen J, Zhang H, Han X, Luo Q. Investigations on transfer of water and vanadium\nions across Nafion membrane in an operating vanadium redox flow battery. J. Power\nSources. 195(3): 890-897 (2010)\ne. The title is not accurate. The authors are dealing with the imbalance of crossover in vanadium\nredox flow battery, not overcoming membrane limitations in flow batteries: membrane selectivity\nare not improved in this manuscript and this method is not useful for other flow batteries that uses\ndifferent active species in the positive and genitive electrolyte.\nResponse:\nWe thank the reviewer for this insightful comment. We have revised the title from “Balanced-State\nElectrolytes Overcome Membrane Limitations in Redox Flow Batteries” to “Balanced-State\nElectrolytes Overcome Crossover in Redox Flow Batteries” Furthermore, we have successfully\napplied the BSE strategy to iron-vanadium flow batteries with promising results, as detailed in our\nresponses to points a4) and c.\n2. Experimental design\na, The exact procedure for determining the BSE composition is not clearly outlined in the main\ntext. Authors should move essential elements of the BSE determination procedure into the main\nMethods section.\nResponse:\nWe thank the reviewer for this valuable suggestion. We have moved the determination procedure\nof BSE into the main Method section in the revised manuscript, as shown below.\nIn the revised Manuscript [Section BSE determination]\nDetermining the balanced state of a VRFB under specified operating conditions is essential for\ndesigning BSEs. Specifically, we define the balanced state under specific conditions as one\nwhere the capacity decay rate is less than 0.03% per cycle or 0.08% per hour. In addition, the test\nmust last longer than 8 h and include more than 20 cycles, with the discharge capacity showing a\nmonotonic decay versus time or cycle number over the investigated range. The electrolyte\nconcentrations at the balanced state are used for designing BSEs. To ensure the accuracy of these\nmeasurements, we converted the electrolytes at the balanced state to V3+|VO2+ through full\ndischarge followed by aerial oxidation. To compensate for the elevated average vanadium valence\nof electrolytes that occurs during cycling due to side reactions, the VO+ content in the initial\n2\nelectrolyte was experimentally increased. The detailed procedure is described in the supplementary\ninformation.\nb, The manuscript is about balancing the crossover of VRFB with various membranes, yet the\npermeation constants of all four Vanadium ions through each membrane are not quantified or\nmeasured in this manuscript. The manuscript also applied different flow rates on each side of the\ncell to control the osmosis pressure balance when using asymmetric BSEs. The pressure drop may\nalso influence the permeation (crossover) of ions. The measurement of these conditioned constants\ncan be scientifically and practically useful, since these constants should provide stronger rationale\nregarding the determination of BSE compositions.\nResponse:\nWe thank the reviewer for these insightful and constructive comments. We fully appreciate the\nconcern regarding the quantification of individual vanadium ion permeation coefficients, which is\nindeed an important aspect of membrane studies. The core objective of our work, however, was to\npropose and validate a balancing strategy that does not rely on the prior acquisition of these\nintrinsic membrane parameters.\nTo directly address the reviewer's concern regarding pressure effects, we have quantified the\neffects of pressure drop on vanadium ion transport across the Nafion membrane in the revised\nsupplementary information. The quantified results clearly demonstrate that the pressure drop\nwithin the operational range has an insignificant effect on vanadium ion permeation rates, further\nsupporting the previous report [R5] that diffusion is the dominant transport mechanism. Detailed\ninformation is provided below. In VRFBs, vanadium ion transport across the membrane is\npredominantly governed by diffusion, with net migratory and convective fluxes being negligible\n[R5]. Therefore, the diffusion rates of vanadium ions across the Nafion membrane, as reported in\n[R2] and summarized in Tab. S1, were used to evaluate the influence of electrolyte concentration\non the net flux ratio between the positive and negative sides (Fig. 2a).\nFurthermore, the methodological cornerstone of this study is the exploitation of the self-balancing\ncapability of VRFBs. We operated a VRFB equipped with a Nafion membrane under specific\noperating conditions until it reached a balanced state. By characterizing the electrolytes in VRFBs\noperating at this balanced state, we determined the concentrations required for the BSEs. Thus,\nthis approach yields distinct BSE compositions for VRFBs under varying operating conditions,\nindependent of direct knowledge of vanadium-ion permeation across different Nafion membranes.\nAs demonstrated here, the BSEs for a VRFB assembled with N212 are (P 1.91 M V3.55+; N 1.170\nM V3.50+), whereas those for a VRFB using N211 are (P 1.83 M V3.54+; N 1.15 M V3.50+).\nConsequently, our approach in this work does not require prior knowledge of the precise\npermeation constants of different Nafion membranes to determine the BSE compositions. This\nhighlights the unique advantage of our proposed strategy: it provides a universal, experimentally\ndriven framework for deriving balancing solutions for different membrane materials and operating\nscenarios, without the prerequisite of engaging in the characterization of intrinsic membrane\nparameters.\nWe believe this conceptual innovation offers a fresh perspective for membrane research and\nelectrolyte engineering in VRFBs. We thank the reviewer again for prompting us to articulate this\nmore clearly.\nTab. S1 The diffusion rate of vanadium ions across Nafion membranes. [S1]\nVanadium ions V2+ V3+ VO2+ VO +\nIn the revised Supplementary Information [Fig. S6].\n)1-L\nlom(\nnoitartnecnoc\n+2OV\n0\n0\n0\n0\n0\n0\n.5\n.4\n.3\n.2\n.1\n.0\n2 0\n3\n6\n9\n0 r\n0 r\n0 r\n3 0\nppp mmm\n4T 0e 5\nst tim\n0e\n(h\n6) 0 7 0 8 0\na b\n)Lm(\nnoitulos\nfo\nemuloV\n3\n2\n1\n1\n0\n4\n8\n2\n6\nV\ng\nO\nS O\n2+ \nVO2+ varies with time at different symmetric flow rates. b, Volume of MgSO and VO2+ solutionafter 80\n4\nhours (Note: The reported volume of MgSO solution excludes the volume removed for sampling).\nelectrodes with a size of 20.00 × 20.00 mm2 were used as the electrodes. 20.00 mL of 1.70 M\nMgSO and 1.70 M VOSO solution were pumped into the two sides of the cell using a peristaltic\n4 4\npump, Longer BT100. Hydraulic pressure differences were generated and studied by changing the\npump speed from 30 to 90 rpm.\nAs shown in Fig. S6, neither the VO2+ concentration in the MgSO solutions nor the solution\n\nvolumes changed significantly over the tested flow rates, indicating that the effect of pressure drop\ndifferences on vanadium ion crossover is negligible.\n[R5] Pilonetto L F, Staciaki F, Nobrega E, et al. Mitigating the capacity loss by crossover\ntransport in vanadium redox flow battery: A chemometric efficient strategy proposed using\nfinite element method simulation. Chem. Eng. J. 474: 145336 (2023).\n[R2] Sun C, Chen J, Zhang H, Han X, Luo Q. Investigations on transfer of water and vanadium\nions across Nafion membrane in an operating vanadium redox flow battery. J. Power\nSources. 195(3): 890-897 (2010)\nc. The testing parameters are not controlled, using comparison with two or more parameters\nchanged (Figure 4a, 4c). The effect of cell configuration (electrode thickness, flow field, etc.)\nwas not controlled across different membranes, especially for NC700 and N211 (see SI Section\n3). Authors should consider justifying and quantifying how these differences in hardware\ndesign influence the results or standardize them across comparisons.\nResponse:\nThanks for your valuable comment. We have moved Fig. 4a into the supplementary information\nin the revised manuscript, as detailed in our response to question (c) on conceptual novelty and\npresentation.\nTo compare the electrolyte utilization during long-term cycling, discharge capacity versus cycle\nnumber is appropriate. This is because VRFBs with different membranes and electrolytes deliver\nidentical cumulative discharge capacities when operated for the same duration at the same current\ndensity. In contrast, discharge capacity versus time is more suitable for analysing capacity decay\nrates according to Fick’s law. Therefore, to comprehensively demonstrate the improvement in\nelectrolyte utilization and the reduction in capacity decay afforded by BSEs in VRFBs, both\nrepresentations—against cycle number and against time—are necessary.\nGiven the significantly different mechanical properties of Nafion membranes, corresponding\nelectrode adjustments were made. To isolate hardware-related effects, we compared their cycling\nperformances (Fig. R3). All configurations exhibited stable long-term performance. VRFBs\nassembled with GF-2.5 and GF-1.75 showed nearly identical performance in discharge capacity,\ncoulombic efficiency, and voltage efficiency. The VRFB with carbon cloth (CC) exhibited a similar\ndischarge capacity trend to those with GF-2.5 and GF-1.75 for the first 100 cycles, and a higher\ncapacity thereafter (Fig. R3a). This is attributed to CC’s superior mass transfer ability, resulting\nfrom its smaller electrode thickness (0.7 mm vs. 2.5 mm and 1.75 mm), which enhances\nperformance as concentration polarization from crossover becomes more significant. This\nadvantage is also reflected in its higher voltage efficiency after 100 cycles (Fig. R3b).\nFurthermore, as noted in our response to comment b in the Experimental section, BSE\nconcentrations were determined by characterizing electrolytes from VRFBs operating at a\nbalanced state. Differences in cell configuration and operating conditions are inherently captured\nin the resulting balanced state, leading to distinct BSEs—as demonstrated by the differing BSE\ncompositions for VRFBs using N212 (P 1.91 M V3.55+; N 1.170 M V3.50+) versus N211 membranes (P\n1.83 M V3.54+; N 1.15 M V3.50+). Thus, the effectiveness and applicability of the BSE method\nremain unaffected by hardware variations, demonstrating its universality. This highlights the\nunique advantage of our proposed strategy: it provides a universal, experimentally driven\nframework for deriving balancing solutions for different hardware materials and operating\nscenarios.\n)hA(\nyticapac\negrahcsiD\n)%\n(\nycneiciffe\ncibmoluoC\n)%\n(\nycneiciffe\negatloV\na\n1 .2\n1 .0\n0 .8\n0 .6\n0 .4\n0 .2\nb1\n0 0\n9 6\n9 2\n8 8\n8 4\n8 0\nc8\n8\n8 4\n8 0\n7 6\n7 2\n0\n0\n0\n1\n1\n1\n0\n0\n0\n0\n0\nC\nC\ny\ny\ny\nc\nc\nc\nle\nle\nle\n0\nu\n0\nu\n0\nu\n0\nm\n0\nm\n0\nm\nb\nb\nb\ne\ne\ne\nr\nr\nr\n3\n3\n3\n0\n0\n0\n0\n0\nG F -1 .7 5\nC C\n4 0\nG F -2 .5\nG F -1 .7 5\nC C\n4 0\nG F -2 .5\nG F -1 .7 5\nC C\n4 0\n0\n0\n(a), coulombic efficiency (b), and voltage efficiency (c) of VRFBs using different electrodes and graphite\nplates. (Note: GF-2.5 and GF-1.75 denote graphite felt electrodes of 2.5 and 1.75mm thickness, respectively;\nCC denotes a carbon cloth electrode of 0.7 mm thickness.)\nVRFBs assembled with GF-2.5 and GF-1.75 electrodes used graphite plates with serpentine flow\nfields, whereas the VRFB assembled with the CC electrode used graphite plates with interdigitated\nflow fields. All VRFB tests employed Nafion 212 as the separator and 40 mL of 1.70 M V3.5+ as\nelectrolytes on the positive and negative sides.\n3. Modeling and theoretical analysis\na, Authors should describe the performance of their cells using a mechanistic framework (e.g.,\nbased on Nernst–Planck, Poisson–Nernst, or coupled Fickian transport) equation, with\npermeation and migration constants measured as suggested, to demonstrate a straight-forward\nmodel that can guide designs of electrolytes. In this case, MD simulations are not as informatic\nfor readers – the diffusion rates of ions are changed just because the concentration\ngradients/differences are changed.\nResponse:\nThank you for your valuable suggestion. In this work, MD simulations were employed to partially\nelucidate the effects of BSEs on vanadium ion transport across the membrane at the molecular\nscale. We agree with your idea about using Nernst–Planck based mechanistic framework to\ndescribe battery performances and have incorporated a 2D simulation model (Fig. R4a) generated\nusing Comsol-Multiphysics® software, as shown below.\nFig. R4b illustrates that the theoretical capacity of a VRFB with TEs decreases significantly over\ntime owing to crossover. This stems from the substantially disparate diffusion rates of vanadium\nions across Nafion membranes (V2+ > VO2+ >VO+ > V3+), which results in the net flux of\n2\nelectrolyte transport from the negative to the positive sides, producing a steadily increasing\nconcentration disparities between the two sides (Fig. R4c). During cycling, V2+ and VO+ are\n2\nconsumed on the negative and positive sides, respectively, due to side reactions (Eqs. R1-R4).\nConsequently, the contents of V2+ and VO+ diminish substantially over time, while those of V3+\n2\nand VO2+ increase, leading to a widening disparity between them over time (Fig. R4d). Hence,\nenhancing vanadium ion transport from the positive to the negative side while reducing the reverse\nflux can mitigate crossover-induced capacity loss. As demonstrated in a VRFB using BSEs,\ncrossover is effectively counteracted by elevating the positive-side electrolyte concentration and\nlowering that on the negative side, reflected in its stable theoretical capacity over time (Fig. R4e).\nThe electrolyte concentrations on both sides likewise remain at stable values over time within the\nBSE-equipped VRFB (Fig. R4f). In contrast to the progressively widening disparities in V2+/VO+\n2\nand VO2+/V3+ contents over time in the VRFB with TEs (Fig. R4d), the contents in the VRFB with\nBSEs were stably maintained at a high matching value (Fig. R4g).\nThe initially lower theoretical capacity of the BSE-based VRFB compared with the TE-based\nsystem arises from the elevated average vanadium valence (V3.55+), which results in a reduction of\ncapacity. Nevertheless, long-term testing reveals that raising the average vanadium valence from\n3.50 to 3.55 enhances VRFB stability, as evidenced in Fig. R5. These results align closely with the\nexperimental data. We have added the simulation results in the revised supplementary information.\nevitageN\nO u\nInM\ntle t\nle t em\na\nb\nO\nr\nu tle t\nIn le t a n e\nevitisoP\nb)hA(\nyticapac\nlaciteroehT\ne)hA(\nyticapac\nlaciteroehT\n2.0\n1.8\n1.6\n1.4\n1.2\n2.0\n1.8\n1.6\n1.4\n1.2\n0\n0\n100\nT\n200\nest tim\n200\nest tim\n300\n（ ） e m in\n300\n（ ） e m in\n400\n500\n)M(\nnoitartnecnoc\netylortcelE\n)M(\nnoitartnecnoc\netylortcelE\nc2.1\n1.8\n1.5\n1.2\n0.9\nf2.1\n1.8\n1.5\n1.2\n0.9\n0\nP\nN\nP\n2+ 3+ egative electrolyte— V + V\n2+ ositive electrolyte— V O + V O\n100 200 300 400\n（ ） T est tim e m in\n2+ 3+ egative electrolyte— V + V\n2+ ositive electrolyte— V O + V O\n100 200 300 400\n（ ） T est tim e m in\n+2\n+2\nT E\n500\ns\ns\nd\n)lomm(\nsnetnoc\nsnoI\ng\n)lomm(\nsnetnoc\nsnoI\n40\n32\n24\n16\n8\n0\n40\n32\n24\n16\n8\n0\n0\n0\n2+ + T E s D ifference betw een V and V O 2 2+ 3+ D ifference betw een V O and V\n100 200 300 400 500\n（ ） T est tim e m in\nB SE s 2+ + D ifference betw een V and V O 2\n2+ 3+ D ifference betw een V O and V\n100 200 300 400 500\n（ ） T est tim e m in\nFig. R4 Simulated cell performance using the TEs (P 1.70 M V3.50+; N 1.70 M V3.50+) and BSEs (P 1.91\nM V3.55+; N 1.170 M V3.50+). a, 2D model built with Comsol software. b-d, Theoretical capacity, electrolyte\nconcentration on the positive and negative sides, and difference between V2+ and VO+, as well as V3+ and\npositive and negative sides, and difference (absolute value) between V2+ and VO+ as well as V3+ and VO2+\n2\nin the VRFB with BSEs at different times. [R3]\n2.0\n)h\nA 1.8\n(\ny\ntic\na\np 1.6\na\nc\nla\nc\nite 1.4\nr\no\ne\nh T P 1.70 M V3.50+; N 1.70 M V3.50+\n1.2\nP 1.91 M V3.55+; N 1.17 M V3.50+\nP 1.91 M V3.50+; N 1.17 M V3.50+\n0 100 200 300 400 500\nTest time （min）\nFig. R5 Effect of elevating the average vanadium valence on capacity decay.\nAll simulations in Figs. R4 and R5 were performed at 50 states of charge (SOC). A comparative\nanalysis of VRFB performance using TEs and BSEs across different SOCs is presented in Fig. R6.\nExperimental results indicate that the SOC for a VRFB equipped with an N212 and operated at\n200 mA cm-2 ranges from about 10 to 80 (Fig. 2c). Accordingly, we compared the theoretical\ncapacity of VRFBs using BSEs after 250 and 500 min to that employing TEs over this SOC range,\nas depicted in Fig. R6a-b. The data reveal that BSEs deliver superior performance to TEs over\nmost of the SOC range, particularly at high SOCs. At SOCs of 10 and 20, the crossover from the\npositive to the negative side dominates vanadium ion flux across the membrane, consequently\nresulting in lower performance than that observed with TEs. Throughout the entire charge–\ndischarge process, the net crossover in VRFBs with BSEs was minimized between the positive\nand negative sides, which enabled a stable discharge capacity over time.\na\n)hA(\nyticapac\nlaciteroehT\n1\n1\n1\n0\n.8\n.5\n.2\n.9\n2 5 0\n1 0\nm in\n2 0 3 0 4 0\nS O C\n5\n(%\n0\n)\n6 0 7 0\nT\nB\nE s\nS E\n8 0\ns\nb\n)hA(\nyticapac\nlaciteroehT\n1\n1\n1\n0\n.8\n.5\n.2\n.9\n5 0 0\n1 0\nm in\n2 0 3 0 4 0\nS O C\n5\n(%\n0\n)\n6 0 7 0\nT\nB\nE s\nS E\n8 0\ns\nFig. R6 Performance comparison of VRFBs using TEs and BSEs at different SOCs. Battery\nperformance after a, 250 and b, 500 min.\nIn VRFBs, vanadium ion transport across membrane is predominantly governed by diffusion, with\nnet migratory fluxes being negligible [R1]. Accordingly, electric field and electrochemical\nreactions were excluded from the simulation, which focused on evaluating theoretical capacity\nretention governed by vanadium ions crossover and side reactions—an approach widely adopted\nin VRFB modeling studies [R6-8]. The transport of vanadium ions through the electrodes and\nmembrane is described using the Nernst–Planck equation (Eq. R8). The side reactions induced by\nvanadium ions crossover are summarized in Eqs. R1–R4. The simulation was studied using the\nTransport of Diluted Species in Porous Media and Chemistry modules in Comsol-Multiphysics®\nsoftware.\nN\ni\nD\ni\nC\ni\nz\ni\nF\nR T\nD Ci\ni i\nC\ni\n \n   = −\n −  + (Eq. R8)\nwhere 𝑁⃗⃗⃗ , D, C, ,and φ are the flux, diffusion coefficient, bulk concentration, and ionic potential\n𝑖 i i i\nof vanadium ions (i= 2, 3, 4, 5, represents V2+, V3+, VO2+, and VO+) , respectively, within the\n2\nelectrode and membrane; F, R, T, and v are the Faraday’s constant, the universal gas constant,\ntemperature, and electrolyte velocity. Here, the velocity of ions transport in electrode and\nmembrane was set to 0.00439 m/s and 0, respectively.\nSide reactions for the vanadium ions transport from the negative to the positive sides:\nV 2 + + 2 V O +2 + 2 H + → 3 V O 2 + + H\nV 3 + + V O +2 → 2 V O 2 + (Eq. R2)\nSide reactions for the vanadium ions transport from the positive to the negative sides:\nV O +2 + 2 V 2 + + 4 H + → 3 V 3 + + 2 H\nV O 2 + + V 2 + + 2 H + → 2 V 3 + + H\nAs shown in Eqs. (R1) - (R4), the crossover of V3+ and VO2+ consumes equivalent amounts\nVO+ and V2+, respectively. While the crossover of V2+ and VO+ ultimately consumes twice as much\n2 2\nas VO+ and V2+, respectively. Consequently, because vanadium species exhibit markedly different\n2\ndiffusion coefficients through Nafion membranes (V2+ > VO2+ >VO+ > V3+), crossover results in\n2\nnet transport of V²⁺ from the negative to the positive sides. This leads to the accumulation of\nsurplus V2+ on the negative side, whereas a deficiency of VO+ arises on the positive side. As a\n2\nresult, crossover leads to both concentration and valence imbalances between the positive and\nnegative electrolytes.\nThe Electrolyte concentration (M) at different SOCs is listed below.\nTab. R1 Electrolyte concentration (M) at different SOCs.\nP/N 40 mL 1.7 M V3.50+ P 35.6 mL 1.91 M V3.55+, N P 35.6 mL 1.91 M V3.50+, N 58.1\nSOC\nCommercial electrolyte 58.1 mL1.17 M V3.50+ BSEs mL1.17 M V3.50+ BSEs\nV2+/V3+ VO2+/VO + V2+/V3+ VO2+/VO + V2+/V3+ VO2+/VO +\n2 2 2\n10 0.170/1.530 1.530/0.170 0.117/1.053 1.624/0.286 0.117/1.053 1.719/0.191\n20 0.340/1.360 1.360/0.340 0.234/0.936 1.432/0.478 0.234/0.936 1.528/0.382\n30 0.510/1.190 1.190/0.510 0.351/0.819 1.241/0.669 0.351/1.349 1.337/0.573\n40 0.680/1.020 1.020/0.680 0.468/0.702 1.050/0.860 0.468/0.702 1.146/0.764\n50 0.850/0.850 0.850/0.850 0.585/0.585 0.859/1.051 0.585/0.585 0.955/0.955\n60 1.020/0.680 0.680/1.020 0.702/0.468 0.668/1.242 0.702/0.468 0.764/1.146\n70 1.190/0.510 0.510/1.190 0.819/0.351 0.477/1.433 0.819/0.351 0.573/1.337\n80 1.360/0.340 0.340/1.360 0.936/0.234 0.286/1.624 0.936/0.234 0.382/1.528\nHere, the SOC in the VRFB using BSEs is defined as being equivalent to that in a VRFB using\nTEs at the same charge capacity. The diffusion rate of vanadium ions in electrolytes and across the\nNafion membrane is adopted from reported works [R2, R8].\n[R2] Sun C, Chen J, Zhang H, et al. Investigations on transfer of water and vanadium\nions across Nafion membrane in an operating vanadium redox flow battery. J. Power Sources, 196(3): 1578-1585 (2011).\n[R3] Wang Z, et al. An electrolyte with elevated average valence for suppressing the capacity decay\nof vanadium redox flow batteries. ACS Cent. Sci. 9(1): 56-63 (2022)\n[R5] Pilonetto L F, Staciaki F, Nobrega E, et al. Mitigating the capacity loss by crossover transport\nin vanadium redox flow battery: A chemometric efficient strategy proposed using finite\nelement method simulation. Chem. Eng. J. 474: 145336 (2023).\n[R6] Chou Y S, Yen S C, Arpornwichanop A, et al. Mathematical model to study vanadium ion\ncrossover in an all-vanadium redox flow battery. ACS Sustainable Chem. Eng. 9(15): 5377-\n5387 (2021).\n[R7] Oreiro S N, Bentien A, Sloth J, et al. Crossover analysis in a commercial 6 kW/43kAh\nvanadium redox flow battery utilizing anion exchange membrane. Chem. Eng. J. 490: 151947\n(2024).\n[R8] You D, Zhang H, Sun C, et al. Simulation of the self-discharge process in vanadium redox\nflow battery. J. Power Sources, 196(3): 1578-1585 (2011).\nb, What is the chemical difference between TE and BSE rather than concentration? In that case,\nwhat is the physical explanation of TE and BSE having different “vanadium ions’ energies” in\nNafion? This raises concern regarding the MD simulation results.\nResponse:\nWe appreciate the reviewer for the valuable comments. Besides the concentration difference, the\naverage vanadium valence differs between TE (V3.5+) and BSE (V3.55+). Changing the vanadium\nion concentration influences the affinity of vanadium ions for water, as reported by Li et al. [R9].\nAdditionally, V-O-V and V-O-S interactions (between SO 2-, HSO -, and VO+) are strengthened\n4 4 2\nas the electrolyte concentration increasing [R10]. To probe the changes in solvation and\ncoordination, we performed 51V NMR and V K-space (k3-weighted) extended X-ray absorption\nfine structure (EXAFS) of VO+ at different concentrations. (Fig. R7). Both the upfield shift of the\n2\n51V resonance and the slight shift of the V-O peak to larger R values with\ndecreasing VO+ concentration indicate a modified coordination environment. These data support\n2\nthe view that increasing the positive electrolyte concentration and the average vanadium valence\nin BSEs alters the interaction strength of vanadium ions with the sulfonate groups of Nafion. In\nthe MD simulations, these experimentally motivated compositional differences between TEs and\nBSEs are explicitly implemented in the simulation boxes. The different \"vanadium ions’ energies\"\nobtained in Nafion therefore arise naturally from the altered local environment, that is, from\nchanges in ion-water and ion-sulfonate interactions induced by the BSE formulation.\na\n).u.a(\nytisnetnI\n-6 6 0\n1\n1\n0\n.7.3.9 M\nM\nM\n-6\nC\n0 0\nh e m ic a\n-5 4 0\nl sh ift (p p m )\n-4 8 0\n51V\nb\n|)k(λ\n3kTF|\n)\n0\n1\n1\n0\n.5\n.7.3.9 M\nM\nM\n1 .0\nR + α\nV – O\n(Å )\n1 .5\nV R -S p a\n2 .0\nc e\nFig. R7 Variations of VO+ in hydrated solvent structures at different concentrations. a-b Nuclear\n𝟐\nmagnetic resonance of 51V and k3‐weighted X-ray absorption fine structure for VO+ electrolyte at\n2\nconcentrations of 1.7/1.3/0.9 M.\n[R9] Mu, C., Li, T., Zhan, C., Fu, Q., Zhang, Y., Zhang, L., & Li, X. \"Harnessing Solvation\nChemistry of Pentavalent Vanadium for Wide‐temperature Range Vanadium Flow Batteries.\nAngew. Chem. Int. Edit.: e202508456 (2025).\n[R10] Kausar, N., Howe, R., & Skyllas-Kazacos, M. Raman spectroscopy studies of concentrated\nvanadium redox battery positive electrolytes. J. Appl. Electrochem., 31(12), 1327-1332\n(2001).\nc, If the authors insists on the MD simulations, the current MD simulations are oversimplified. The\nsimulation is limited to ion diffusivity. The simulation should be coupled with membrane hydration\nand Donan potential shifts under real operating potential gradients with a longer simulation time.\nResponse:\nThank you for this insightful suggestion regarding the coupling of membrane hydration and\nDonnan potential shifts. We agree that incorporating these phenomena would provide a more\ncomprehensive view. However, simulating ion transport under real operating potential gradients\nover macroscopic timescales (hours to days, as relevant for diffusion in VRFBs) presents a\nfundamental challenge for molecular dynamics (MD). The computational cost of simulating\nbeyond microsecond timescales with explicit chemistry and external fields is currently\nprohibitive. In this work, MD simulations were not employed as a quantitative predictive tool but\nrather served to provide qualitative support for the proposed mechanism. Therefore, our MD\nsimulations were focused on revealing a key intrinsic property—the inherent diffusion energy\nbarrier of vanadium ions across various Nafion membranes. MD simulations are uniquely suited\nto resolve the transient interactions between ions and the polymer matrix, thereby revealing the\neffects of BSEs on vanadium ion transport across the membrane at the molecular scale. We agree\nthat a continuum-based model (e.g., based on the Nernst-Planck framework) is the more\nappropriate and feasible tool. We have added a 2D simulation model (Fig. R4a) using Comsol-\nMultiphysics® software, as detailed in the response to question 3a.\nFig. R4b illustrates that the theoretical capacity of a VRFB with TEs decreases significantly over\ntime owing to crossover. This stems from the substantially disparate diffusion rates of vanadium\nions across Nafion membranes (V2+ > VO2+ >VO+ > V3+), which results in the net flux of\n2\nelectrolyte transport from the negative to the positive sides, producing a steadily increasing\nconcentration disparities between the two sides (Fig. R4c). Specifically, the contents of V2+ and\nVO + diminish substantially over time, while those of V3+ and VO2+ increase, leading to a widening\n2\ndisparity between them over time due to crossover and side reactions (Fig. R4d). Hence,\nenhancing vanadium ion transport from the positive to the negative side while reducing the reverse\nflux can mitigate crossover-induced capacity loss. In a VRFB using BSEs, crossover is effectively\ncounteracted by elevating the positive-side electrolyte concentration and lowering that on the\nnegative side, reflected in its stable theoretical capacity over time (Fig. R4e). The electrolyte\nconcentrations on both sides likewise remain at stable values over time within the BSE-equipped\nVRFB (Fig. R4f). In contrast to the progressively widening disparities in V2+/VO+ and VO2+/V3+\n2\ncontents over time in the VRFB with TEs (Fig. R4d), the contents in the VRFB with BSEs were\nstably maintained at a high matching value (Fig. R4g).\nevitageN\nO u\nInM\ntle t\nle t em\na\nb\nO\nr\nu tle t\nIn le t a n e\nevitisoP\nb)hA(\nyticapac\nlaciteroehT\ne)hA(\nyticapac\nlaciteroehT\n2.0\n1.8\n1.6\n1.4\n1.2\n2.0\n1.8\n1.6\n1.4\n1.2\n0\n0\n100\nT\n200\nest tim\n200\nest tim\n300\n（ ） e m in\n300\n（ ） e m in\n400\n500\n)M(\nnoitartnecnoc\netylortcelE\n)M(\nnoitartnecnoc\netylortcelE\nc2.1\n1.8\n1.5\n1.2\n0.9\nf2.1\n1.8\n1.5\n1.2\n0.9\n0\nP\nN\nP\n2+ 3+ egative electrolyte— V + V\n2+ ositive electrolyte— V O + V O\n100 200 300 400\n（ ） T est tim e m in\n2+ 3+ egative electrolyte— V + V\n2+ ositive electrolyte— V O + V O\n100 200 300 400\n（ ） T est tim e m in\n+2\n+2\nT E\n500\ns\ns\nd\n)lomm(\nsnetnoc\nsnoI\ng\n)lomm(\nsnetnoc\nsnoI\n40\n32\n24\n16\n8\n0\n40\n32\n24\n16\n8\n0\n0\n0\n2+ + T E s D ifference betw een V and V O 2 2+ 3+ D ifference betw een V O and V\n100 200 300 400 500\n（ ） T est tim e m in\nB SE s 2+ + D ifference betw een V and V O 2\n2+ 3+ D ifference betw een V O and V\n100 200 300 400 500\n（ ） T est tim e m in\nFig. R4 Simulated cell performance using the TEs (P 1.70 M V3.50+; N 1.70 M V3.50+) and BSEs (P 1.91\nM V3.55+; N 1.170 M V3.50+). a, 2D model built with Comsol software. b-d, Theoretical capacity, electrolyte\nconcentration on the positive and negative sides, and difference between V2+ and VO +, as well as V3+ and\npositive and negative sides, and difference (absolute value) between V2+ and VO + as well as V3+ and VO2+\n2\nin the VRFB with BSEs at different times.\nThe initially lower theoretical capacity of the BSE-based VRFB compared with the TE-based\nsystem arises from the elevated average vanadium valence (V3.55+), which results in a reduction of\ncapacity. Nevertheless, long-term testing reveals that raising the average vanadium valence from\n3.50 to 3.55 enhances VRFB stability, as evidenced in Fig. R5. These results align closely with the\nexperimental data. We have added the simulation results in the revised supplementary information.\n2.0\n)h\nA 1.8\n(\ny\ntic\na\np 1.6\na\nc\nla\nc\nite 1.4\nr\no\ne\nh T P 1.70 M V3.50+; N 1.70 M V3.50+\n1.2\nP 1.91 M V3.55+; N 1.17 M V3.50+\nP 1.91 M V3.50+; N 1.17 M V3.50+\n0 100 200 300 400 500\nTest time （min）\nFig. R5 Effect of elevating the average vanadium valence on capacity decay.\nd, Fig. 3h is not informatic. What should readers learn from Fig 3h?\nResponse:\nWe thank the reviewer for raising this point. We have deleted Fig. 3h in the revised manuscript.\ne. Fig. 3i is not explained, and the abbreviation MSD showed without spelled out in the manuscript.\nWhat does MSD (nm2) mean?\nResponse:\nWe apologize for this oversight. MSD refers to the Mean Squared Displacement. The full definition\nhas been added to the revised manuscript, as indicated below.\nIn the revised Manuscript [Page 10, Fig. 3i]\ni, Mean Squared Displacement (MSD) of …\nf. Fig. 3k may be too obvious: why would someone expect the hydration of V2+ changed if just\nchanging a 1.7 M V2+ solution into a 2.0 M V2+ solution?\nResponse:\nWe thank the reviewer for this comment. According to the study by Kausar et al. [R10], various\ncopolymeric vanadium species form when the electrolyte concentration exceeds 2.0 M, which\nstrengthens the V–O–V and V–O–S interactions (involving SO₄²⁻, HSO₄⁻, and VO+).\nwe reduced the V2+ concentration from 1.70 M to 1.17 M and adjusted the concentrations of other\nvanadium ions during the preparation of the BSEs. These modifications may attenuate variations\nin the hydrated structure of V2+.\n[R10] Kausar, N., Howe, R., & Skyllas-Kazacos, M. Raman spectroscopy studies of concentrated\nvanadium redox battery positive electrolytes. J. Appl. Electrochem., 31(12), 1327-1332\n(2001).\n4. Electrochemical performance claims\na, The authors mentioned side reactions at line 184, demonstrating adding V5+ to balance the\ncell SOC. Authors should specify the side reactions and their effects, noting that side reaction of\ncarbon electrode aging is evitable by using inert electrodes. Side reactions of HER or ORR\nshould be balanced by adding V4+ or introducing reactants\n(https://doi.org/10.1039/D4EE02450H, https://doi.org/10.1016/j.jpowsour.2023.233770)\nResponse:\nWe thank the reviewer for raising this point. Side reactions in VRFBs comprise the aerial oxidation\nof V2+ (Eq. S11) and the hydrogen evolution reaction (HER) (Eq. S12). The oxidation of V2+\ninduced by air increases the contents of V3+, thereby improving the concentration of VO+on the\n2\npositive side during charging. The HER generates more VO+ on the positive side than the amount\n2\nof V2+ on the negative side during the charge process. These two side reactions elevate the average\nvanadium valence in the electrolytes during cycling. We have specified these side reactions in the\nrevised manuscript and supplementary information.\n2\n+ 4 H + → 4 V 3 + + 2 H\n2H++2e− →H (Eq. S12)\ngood performance, a trade-off between side reactions and electrode activity has been implemented.\nIn this work, although the cells were operated under N protection during battery tests, air ingress\n2\nremains unavoidable during electrolyte and cell preparation, as well as in flow pipes. Additionally,\nwe set the cut-off voltage to 1.6-0.9 V [R11] during VRFB tests, which is lower than 1.7 V adopted\nin the second mentioned reference to limit side reactions of HER and ORR. Nevertheless, HER\nmay still exist during long-term cycling coupled with air-induced V2+ oxidation, thereby elevating\nthe average vanadium valence of electrolytes. In the first mentioned reference, the authors\ndemonstrated that VO+ electrolyte can be reduced to lower valence electrolyte working as\n2\ncatholyte count to formic acid anolytes in their LFARFCs. In this work, we aimed to identify the\nbalanced state of electrolytes to prepare BSEs. Therefore, we added VO+ to the positive\n2\nelectrolytes to match the balanced state, which features an elevated average vanadium valence of\nelectrolytes induced by HER and aerial oxidation.\n[R11] Wei X, Nie Z, Luo Q, et al. Nanoporous polytetrafluoroethylene/silica composite separator\nas a high‐performance all‐vanadium redox flow battery membrane[J]. Advanced Energy\nMaterials, 2013, 3(9): 1215-1220.\nIn the revised Manuscript [Line 190, Page 7]\nBesides concentration variations, the average vanadium valence of the electrolyte is also elevated\nduring cycling due to side reactions (hydrogen evolution reaction and air-induced V2+ oxidation,\nEq. S15, Eq. S16) on the negative side…\nIn the revised Supplementary Information [ Section 3.2]\n2\n+ 4 H + → 4 V 3 + + 2 H\nV2+ is highly sensitive to oxygen and is readily oxidized to V3+ by air. The oxidation of V2+\ninduced by air increases V3+ content, thereby improving the concentration of VO+on the positive side during\n2\ncharging.\n2\n(Eq. S12)\nThe HER generates more VO+ on the positive side than the amount of V2+ on the negative side\n2\nduring the charge process. The air-induced V2+ oxidation and HER elevate the average vanadium\nvalence of electrolytes during cycling.\nb, Fig 2h shows no apparent difference, contracting against the statement.\nResponse:\nWe thank the reviewer for raising this point. Yes, there is no apparent difference between the two\nflow rates in Fig. 2h. In the manuscript, we described that the pressure drop difference between\nthe positive and negative sides is increased due to the viscosity variation after adjusting the\nelectrolyte concentrations for the balanced state. However, this asymmetric pressure drop has a\nminimal effect in suppressing capacity decay, as evidenced by the experimental results (Fig. 2h).\nTo make the description clearer, we changed the phraseology in the revised manuscript, as shown\nbelow.\nIn the revised Manuscript [Line 179, Page 7]\nAlthough adjusting electrolyte concentrations to achieve the balanced state increases the pressure\ndrop difference between the positive and negative sides owing to viscosity changes (Fig. S5a),\nthis exerts only a negligible effect on mitigating capacity decay, as evidenced by the lack of discernible\ndifferences in Fig. 2g.\nc. Line 317: Fig. S16 does not show apparent difference between these two membranes,\ncontracting against the statement.\nResponse:\nWe thank the reviewer for raising this point. The discharge capacity curves versus cycle number\nfor VRFBs using N212 and N211 do not have an apparent difference after 50 cycles, by which\npoint the electrolytes are close to the balanced state. The discharge capacity of the VRFB with\nN211 is higher than that with N212 at the initial stage, but decreases rapidly to similar values to\nthose with N212 after around 50 cycles, as shown in Fig. S16. To enhance clarity, we have added\nclarifying phrases in the revised manuscript, as shown below.\n)%\n(\nycneiciffe\negatloV\n)hA(\nyticapac\negrahcsiD\nb\n93\n90\n87\n84\n81\nc\n1.6\n1.2\n0.8\n0.4\n0.0\n0\na\n212 51 \n50\n50\nmhO/)Z(mI-\nm\n0.020\nN 211 25  m\nN 212 51  m\n0.015\n0.010\n0.005\n0.0000.020\n0.025 0.030\nR e(Z )/O h\nN 211 25  m\n100 150 200\nC y cle n u m\n100 150 200\nC y cle n u m\nm\nb\nb\ner\ner\n250\n250\n0.035\n250\n250\n0.040\n300\n300\n@ 200 m\n350\nN 211\n400\n98\n91\n84\n77\n70\n)%\n(\nycneiciffe\ncibmoluoC\nFig. S16 Performance comparison of VRFBs employing N212 and N211 membranes with traditional\nelectrolytes. a, The EIS spectrum b, voltage/coulombic efficiency, and c, discharge capacity of VRFBs\nusing N212 and N211 membranes over cycling.\nIn the revised Manuscript [Line 310, Page 13]\nDecreasing the Nafion membrane thickness from 51 μm (N212) to 25 μm (N211) greatly reduces\nmembrane resistance and improves voltage efficiency. However, it leads to more severe capacity\ndecay than N212 in the first 50 cycles (Fig. S23).\nd. Line 373: no clear experimental evidence of modulating the interactions between vanadium ions\nand sulfonic acid groups, contracting against the statement. The authors only changed the\nconcentration of the electrolytes.\nResponse:\nWe thank the reviewer for this insightful comment. We have added Raman and XPS spectra in the\nrevised supplementary information to validate the interactions between vanadium ions and sulfonic\nacid groups (Fig. S17). Results show that the Raman peak position of sulfonic acid groups shifts\nupon immersion of the Nafion membrane in vanadium electrolytes, demonstrating the interactions\nbetween vanadium ions and sulfonic acid groups [R12]. It is more evident in the XPS results (Fig.\nS17b), where both the position and intensity of the O 1s peak attributable to the sulfonic acid\ngroups (534.89 eV) markedly shift to lower values after introducing vanadium ions into Nafion\nmembranes [R13, R14]. These results are consistent with prior reports of such interactions between\nvanadium ions and the sulfonic acid groups in Nafion membranes by Cho [R15] and Vijayakumar\n[R16]. Furthermore, increasing the vanadium ion concentration strengthens the interaction\nbetween vanadium ions and the sulfonic acid sites of Nafion, thereby reducing vanadium ion\npermeability. [R16]\nIn the revised Supplementary Information [Fig. S17]\n).u.a(\nytisnetnI\n1 0 4 0\nN\nN\nN\nN\nN\na\naaaa\nfio n -H\nfio n -V\nfio n -V\nfio n -V\nfio n -V\n1 0 5 0\nS O 22+\n3+\n2+ O\n+ O\n4\nm\n1 0 6\na n\n-S\n0\nsh\nO -3\nift (c\n1m 0 7 0\n-1)\n1 0 8 0\na b\n)s(\nstnuoC\n)s(\nstnuoC\n5 2 8\nF it\n2+ V O D a ta\nO 1 S\nH S O 2 4\n2+ V\n3+ V\n5 3 1\nB e n d in g e n\nV\ne r\n-O\n5 3 4\ng y (e v\nO\n)\n1\n-C\nS\nF 2 -O -C F 2\n-S O -3\n+ V O\n2\n5 3 7\n-\nFig. S17 Interactions between vanadium ion and sulfonic acid groups. a, Raman and b, XPS spectra of\nNafion 212 immersed in different solutions.\nIn these tests, Nafion 212 was immersed separately for 5 days in 3.0 M H SO , 1.7 M V2+, V3+,\n2 4\nVO2+, and VO+. As depicted in Fig. S17a, the Raman peak position of sulfonic acid groups shifts\n2\nupon immersion of the Nafion membrane in vanadium electrolytes, demonstrating the interactions\nbetween vanadium ions and sulfonic acid groups [S5]. It is more evident in the XPS results (Fig.\nS17b), where both the position and intensity of the O 1s peak attributable to the sulfonic acid\ngroups (534.89 eV) markedly shift to lower values after introducing vanadium ions into Nafion\nmembranes [S6, S7].\n[R12] Choi, J. S., Tsui, J. H., Xu, F., Lee, S. H., Sung, S. K., Lee, H. J., & Kim, D. H. Fabrication\nof micro‐and nanopatterned Nafion thin films with tenable mechanical and electrical\nproperties using thermal evaporation‐induced capillary force lithography. Adv. Mater.\nInterfaces, 8(7), 2002005, (2021).\n[R13] Nguyen, H. T. T., Jung, D., Park, C. Y., & Kang, D. J. (2015). Synthesis of single-crystalline\nsodium vanadate nanowires based on chemical solution deposition method. Mater. Chem.\nPhys. 165, 19-24.\n[R14] Ma Andersen S. The importance of ion selectivity of perfluorinated sulfonic acid membrane\nfor the performance of proton exchange membrane fuel cells. J. Fuel Cell Sci. Tech. 12(6):\n061010, (2015).\n[R15] Cho H S, Ohashi M, Van Zee J W. Absorption behaviour of vanadium in Nafion®. J. Power\nSources. 267: 547-552 (2014).\n[R16] Vijayakumar M, Govind N, Li B, et al. Aqua-vanadyl ion interaction with Nafion®\nmembranes. Front. Energy Res. 3: 10, (2015).\nMinor concerns:\n5. Broader impact and scalability\nThe cost analysis (Fig. 5h) indicates the practical significance of the BSE approach. However,\nthe assumptions behind the >40% cost reduction are not fully transparent. Author should include\ntheir detail TEA with a table listing assumptions (e.g., membrane price, electrolyte cost per kg,\nsystem lifetime) and perform a sensitivity analysis with fare comparison with\nprevious/commercial rebalancing techniques.\nResponse:\nWe thank the reviewer for this suggestion. A detailed calculation process and a cost table have\nbeen included in the supplementary information, as provided below.\nOur cost analysis focused solely on the membrane and electrolyte components. As shown in Fig.\n3, VRFBs employing BSEs demonstrate superior energy efficiency compared to those using\ntraditional electrolytes (TEs). This higher efficiency translates into an advantage in power-density-\nrelated costs. Furthermore, the average viscosity of the BSEs is 3.958 mPa·s, lower than the 4.456\nmPa·s of the TEs, suggesting a reduction in pump power loss. However, no direct correlation exists\nbetween capital costs and power density or pump power. We therefore consider only the membrane\nand electrolyte costs as a proportion of the overall system costs (based on a 1 MW/4 MWh system)\nwhen calculating the capital cost reduction upon adoption of BSEs. The details of this calculation\nare provided below.\nIn the revised Supplementary Information [ Section 7]\nTab. S2 Electrolyte utilization in VRFBs with different systems.\nAccumulated discharge capacity Discharge capacity over\nVRFB system\nover 400 cycles (Ah) 400 cycles (Ah cycle-1 mol-1)\nCurrent advanced\n225.10281 4.137919301\nsystem\nSystem with BSEs 486.2741 8.938862132\nThe discharge capacity of electrolytes per cycle per mol (D CP / Ah mol⁻¹) is calculated as follows:\nD\nC P\n=\nD\nC\nA\nN\nC\nO\n\n1 0 0\nV E \nE\n(Eq. S24)\nwhere D , C , V , and E represent the accumulated discharge capacity (Ah), the cycle number,\nAC NO E C\nthe electrolyte volume (mL), and the electrolyte concentration (M), respectively.\nThe capital cost reduction for a VRFB system using BSEs and NC700 can be calculated as\nbelow:\nC\nC r\n= ( C\nR -M\n+ C\nR -E\n) − ( C\nR -M\n M\nC R\n+ C\nR -E\n E\nC R\n) (Eq. S25)\nwhere, C is the capital cost reduction ratio; C and C are the cost ratio of membrane (10.08%)\nCr R-M R-E\nand electrolyte (62.79%), respectively, over the capital cost of a current advanced 1 MW/4 MWh\nVRFB system;[32] M and E are the corresponding cost ratios of the membrane and electrolyte\nCR CR\nin the BSEs and NC700 based system [33] relative to a currently advanced VRFB system.\n472.281\nM = (Eq. S26)\nCR 2329.825\nE\nC R\n=\n4\n8\n.1\n.9\n3\n3\n7\n8\n9\n8\n1\n6\n9\n2\n(Eq. S27)\nHence, the capital cost reduction for a VRFB system with BSEs compared to the current advanced\nVRFB system can be obtained:\nC\nC r\n= ( 1 0 .0 8 + 6 2 .7 9 ) −\n\n1 0 .0 8 \n2\n4\n3\n7\n2\n2\n9\n.2\n.8\n8\n2\n1\n5\n+ 6 2 .7 9 \n4\n8\n.1\n.9\n3\n3\n7\n8\n9\n8\n1\n6\n9\n2\n\n= 4 1 .7 6 (Eq. S28)\nThe specific costs of electrolyte and membrane in different VRFB systems are listed in Tab. S3.\nTab. S3 Membrane and electrolyte costs as a proportion of the capital cost in a 1 MW/4 MWh VRFB\nsystem. [S8, S9]\nDischarge\ncapacity over Electrolyte to\nMembrane Membrane cost/ Membrane to\n400 cycles capital cost\ntype m2 ($) capital cost ratio\n(Ah cycle-1 ratio\nmol-1)\nCurrent\nadvanced N212 2329.825 10.80% 4.14 62.79%\nsystem\nSystem with\nNC700 472.281 2.19% 8.94 29.08%\nBSEs\n[S8] Chen H, Zhang X, Wu S, et al. A comparative study of iron-vanadium and all-vanadium\nflow battery for large scale energy storage. Chem. Eng. J. 429: 132403 (2022).\n[S9] https://www.fuelcellstore.com/pfsa-d50u-proton-exchange-membrane-87010020?search\n= Nafion 212\n6. Language and clarity\nWhile the manuscript is generally readable, grammatical inconsistencies and stylistic issues\ndetract from the clarity (e.g., line 209-210 sentence has no verb). Authors should also revise for\nclarity, especially in experimental procedures and\ndescriptions of diffusion processes.\nResponse:\nWe are grateful for these corrections. We have revised the manuscript to address the grammatical\ninconsistencies and stylistic issues, and to improve clarity throughout. The manuscript has been\nrefined by a native English speaker.\nReviewer #2 (Remarks to the Author):\nIn this work, the authors propose an electrolyte design based on balanced-state electrolytes, rather\nthan membrane design, to mitigate the capacity decay of redox flow batteries. This approach\naddresses the trade-off between ion conductivity and the permeability of active materials in VRFBs.\nWhile the study presents an interesting strategy to enhance the cycling stability of flow batteries,\ncertain sections require modification and further discussion. I would recommend publication in\nthis journal after major revision.\nResponse:\nWe are grateful to the reviewer for their encouraging assessment. We have provided a point-by-\npoint response to each of their detailed comments below.\n1. In the Abstract, the authors state that “battery employing a 15 μm-thick Nafion membrane with\nbalanced-state electrolytes\nachieves a 75.4% reduction in capacity decay rate (over 1,000 cycles) compared to a system using a 183 μm thick Nafion\nmembrane with conventional electrolytes.” It\nwould be helpful to also provide the capacity fading rate per cycle or the capacity retention after\n1,000 cycles. Additionally, please specify the total testing duration (in hours) for 1,000 cycles.\nFurthermore, for a more accurate evaluation of the electrolyte design effect on capacity decay, the\ncomparison should be conducted using Nafion membranes of the same thickness.\nResponse:\nThanks for your valuable suggestions. We have added the fading rate per cycle in the revised\nmanuscript as shown below. The test duration of the VRFB employing a 15 μm-thick Nafion\nmembrane with balanced-state electrolytes is 695.65 h over 1,000 cycles, whereas that of the\nVRFB using a 183 μm-thick Nafion membrane with traditional electrolytes is 283.54 h. We have\ncompared the BSEs effects on the capacity decay of VRFB with Nafion 212 in Fig. 3a. It shows\nthat the capacity decay rate of a VRFB with the BSEs reduced by 86.3% from 0.182% to 0.025%\nper cycle, over 400 cycles. To enhance clarity, we have emphasized that the tests were conducted\nin VRFBs using Nafion 212, as detailed below. The comparison between a battery employing a 15\nμm-thick Nafion membrane with balanced-state electrolytes and a system using a 183 μm-thick\nNafion membrane with conventional electrolytes aims to highlight the advantages of BSEs.\nIn the revised Manuscript [Line 25, Page 1, Section abstract]\na battery employing a 15 μm-thick Nafion membrane with balanced-state electrolytes achieves a\n75.4% reduction in capacity decay rate— from 0.061% to 0.015% per cycle over 1,000 cycles—\ncompared to a system using a 183 μm-thick Nafion membrane with traditional electrolytes.\nIn the revised Manuscript [Fig. 3a]\nA VRFB employing an N212 membrane with the BSEs (P 1.91 M V3.55+; N 1.170 M V3.50+) exhibit\nan 86.3% reduction in capacity decay rate—from 0.182% to 0.025% per cycle—and a 71.0%\nincrease in accumulated discharge capacity (from 256.97 to 439.35 Ah) over 400 cycles, compared\nto that using traditional electrolytes (P 1.70 M V3.50+; N 1.70 M V3.50+) (Fig. 3a).\nBSEs\n1.2\nTEs\n)h\nA\n(\ny\n1.0\ntic\na\np\na0.8\nc e 71.0%­\ng\nr\na h0.6\nc\nsiD\n0.4\n@ 200 mA cm-2\n0 50 100 150 200 250 300 350 400\nCycle number\nFig. 3a, Effects of BSEs (P 1.91 M V3.55+; N 1.17 M V3.50+) on suppressing capacity decay of VRFBs using\nN212.\n2. In the Abstract, the authors state that “Crucially, the balanced state electrolyte approach\nremoves membrane limitations in redox flow battery development and opens new avenues for\nadvanced electrolyte design.”. To claim that this approach can remove membrane limitations,\nit would be necessary to evaluate its performance with a wider variety of membrane types,\nrather than testing solely with a Nafion membrane.\nResponse:\nThanks for your suggestions. The BSEs are defined by a crossover flux of vanadium ions from th\ne negative to the positive side that is counterbalanced by an equivalent flux in the opposite directi\non. The methodological cornerstone of this study is the exploitation of the self-balancing capabilit\ny of VRFBs. We operated a VRFB equipped with a Nafion membrane under specific oper\nating conditions until it reached a balanced state. By characterizing the electrolytes in VRFBs ope\nrating at this balanced state, we determined the concentrations required for the BSEs. We evaluat\ned tw o other widely studied membranes—polybenzimidazole (PBI) and sulfonated poly (ethe\nr ether ketone) (SPEEK)—both of which exhibited a linea r decay in discharge capacity with cycl\ning and failed to reach a balanc ed state [R17, R18] (Figs. R8 and R9), suggesting that they are no t\nviable.To be more rigorous, we have corrected “the balanced-state electrolyte approach re\nmoves membrane limitations” to “significantly reduces membrane limitations” in the revised man\nuscript, as shown below.\n[Figure Redacted]\n[Figure Redacted]\nIn the revised Manuscript [Line 28, Page 1 and Section conclusion]\nCrucially, the balanced-state electrolyte approach significantly reduces membrane limitations in\nredox flow battery…\nFurthermore, this work significantly reduces membrane limitations in redox flow battery\ndevelopment…\n3. In page 2, the authors state that “The cation exchange membrane (CEM) is a critical component\nin RFBs, ideally conducting proton while preventing the crossover of active species.\". However,\nthe choice of ion exchange membrane for an RFB depends on the type of active material used.\nSome active materials require an anion exchange membrane, while others can operate with a\nporous membrane without ion selectivity. For acidic electrolytes, proton conductivity is important,\nwhereas in alkaline electrolytes, conductivity of other ions may be more relevant. Please clarify\nwhich specific type of RFB this study focuses on. Additionally, note that in many RFBs employing\norganic active materials such as quinones, capacity decay is generally not dominated by active\nmaterial crossover.\nResponse:\nThanks for your valuable suggestions. In this work, our focus is specifically on aqueous flow\nbatteries employing acidic electrolytes. We have clarified this scope in the revised manuscript, as\nindicated below.\nIn the revised Manuscript [Line 37, Page 2]\nThe cation exchange membrane (CEM) is a critical component in aqueous RFBs operating in\nacidic electrolytes.\n4. In page 2, the authors state that “Despite these advances, challenges persist in the applicability\nof these membranes in inorganic/organic RFB systems, including low proton conductivity,\nscalability issues, escalated costs, and long-term stability concerns.”. However, in most organic\nRFB systems, active material crossover is generally not a significant issue. This sentence should\nbe revised accordingly.\nResponse:\nThanks for your corrections. We have we have revised the manuscript and clarified the types of\nRFBs to aqueous RFBs employing acidic electrolytes, as detailed below.\nIn the revised Manuscript [Line 44and 46, Page 2]\nDespite these advances, challenges persist in the applicability of these membranes in aqueous\nRFBs with acidic electrolytes …\nConsequently, almost all the commercially available membranes for such RFBs are Nafion-based\nmembranes…\n5. In Figs. 1-3, please revise the discharge capacity units from Ah to volumetric discharge capacity\n(Ah/L), as volumetric capacity is a more relevant metric for evaluation.\nResponse:\nThanks for your suggestion. In VRFBs, electrolyte volumes change during cycling, making the\nunit Ah/L problematic for assessing long-term performance. Furthermore, in this work, we\nmitigated capacity decay by formulating BSEs. This approach required different electrolyte\nvolumes for BSEs and TEs to maintain identical total vanadium contents. Consequently,\nconverting discharge capacity from Ah to Ah/L would yield different initial values, obscuring a\ndirect comparison of cycling performance between the two systems.\n6. In page 4, the authors state that “Fig. 1a shows that the discharge capacity of the VRFB with\nNafion 212 first increases for a short period and then rapidly decays between about 10-200 cycles.\".\nPlease provide an explanation for the initial short-term increase in discharge capacity.\nResponse:\nWe thank the reviewer for this insightful comment. The initial increase in discharge capacity arises\nfrom non-equilibrium transport of ions and water across the Nafion membrane. [R4] As shown in\nFig. R10a, voltage efficiency remains unchanged during this increase, indicating that it does not\nstem from variations in activity. At this stage, the limiting factor for capacity is the active material\nin the positive electrolyte. [R4] Crossover drives vanadium-ion transport from the negative to the\npositive side (Figs. 1b and S21) and increases VO2+ contents on the positive side through side\nreactions (Eq. S5 &S7). This interpretation is supported by the experiment in Fig. R10b: adding\n10 mL of VO2+ electrolyte to the positive side markedly improved the discharge capacity and\neliminated the initial rising trend.\n)1-L\nlom(\nnoitartnecnoc\nsnoI\n2\n1\n1\n1\n0\n.1\n.8\n.5\n.2\n.9\nA\nan th o\no ly\n5 0\nlyte te\n1 0 0 1 5 0\nC y c le\n2 0\nn\n0\nu m b e r\n2 5 0 3 0 0\nC\nA\n3 5\nan\n0\nth o\no ly\nlyte te\n4 0 0\n6\n5\n4\n3\n2\n)s·aPm(\nytisocsiv\ncitameniK\nFig. 1b Electrolyte concentration/viscosity change with cycling of the VRFB equipped with Nafion 212\nand traditional electrolytes at 200 mA cm-2.\na b\n)1-L.lom(\nnoitartnecnoC\n2.0\n1.6\n1.2\n0.8\n0.4\n0.0\n2.1\n1.4\n0.7\n0.0\nB\nC ath olyte\nefore cyclin g\nA n olyte\nA fter cyclin g\nA fter cyclin g\nB\nT\nS\nE\nE\ns\ns\n1- ) L\n.lo\nm\nn ( o\nita\rtn\necn\no\nC\n)lm(\nemuloV\n63\n56\n49\n42\n35\n50\n45\n40\n35\nB efore cyclin g\nA n olyte\nA fter cyclin g\nB S E\nT E\ns\ns\nB\nC ath olyte\\efore cyclin g\nA n olyte\nl) m\nem (\nu\nlo\nV\nc\nC ath olyte\nB efore cyclin g\nA n olyte\nA fter cyclin g\nd\nFig. S21 Changes in electrolytes before and after cycling. (a-b) Volume and concentration changes in\nVRFBs with BSEs (P 1.91 M V3.55+; N 1.17 M V3.50+) (c-d) Volume and concentration changes in VRFBs\nwith TEs (P 1.70 M V3.50+; N 1.70 M V3.50+).\n)hA(\nyticapac\negrahcsiD\n1\n1\n1\n1\n0\n0\n.3\n.2\n.1\n.0\n.9\n.8\nN\n0\n2 1 2 5 1 \n1\nm\n2 0\nn u m\n@\nb\n2\ne\n0\nr\n0 m\n3 0\nA c m -2\n4 0\n9\n8\n7\n7\n6\n6\n0\n4\n8\n2\n6\n0\n)%\n(\nycneiciffe\negatloV\n)hA(\nyticapac\negrahcsiD\n1\n1\n1\n0\n.4\n.2\n.0\n.8\n@\n0\n2 0 0\nP\nP\nm\n/N\n/N\nA c m\n4 0 m L\n4 0 m L\n1 0\nC y\n-2\n3.5+ V\n3.5+ V + P\n2 0\nc le n u m\nN\n1 0 m\nb e r\n1 2 5 1\n2+ V O\n3 0\n m\n4 0\na b\nFig. R10 Initial rise in the discharge capacity of VRFBs. a, Cycling performance showing discharge\ncapacity and voltage efficiency. b, Influence of VO2+ concentration in the positive electrolyte on the\ndischarge capacity (All tests were conducted at 25 °C).\nV 2 + + 2 V O +2 + 2 H + → 3 V O 2 + + H\nV 3 + + V O +2 → 2 V O 2 + (Eq. S9)\n[R4] Mu D, Zhao Y, Yu L, et al. Asymmetric vanadium flow batteries: long lifespan via an\nanolyte overhang strategy. Phys. Chem. Chem. Phys. 19(43): 29195-29203 (2017).\n7. In page 6, the authors state that “The complex ion transport model in VRFBs, combined with\nthe dynamic evolution of electrolytes over extended cycling, complicates this task.\". Please\nexplain more clearly on the meaning of “dynamic evolution” in this context, providing specific\ndetails.\nResponse:\nWe thank the reviewer for this comment. The concentration and volume of positive and negative\nelectrolytes vary with cycling caused by crossover, as illustrated in Figs. 1a-b and Fig. S21.\nFurthermore, side reactions (detailed below) triggered by crossover result in an imbalance both in\nthe concentration and vanadium valence of electrolytes between the positive and negative sides,\nwhich influences the SOC of electrolytes during the charge and discharge process. This SOC\nvariation, which significantly affects the vanadium ion flux across the membrane (Fig. 2b), along\nwith concentration-driven water transfer, governs the dynamic behaviour. Moreover, changes in\nelectrolyte concentration affect water transport between the positive and negative sides.\nVanadium\nions drag different amounts of water during crossover (V2+·6H O, V3+·6H O, VO2+·5H O,\n2 2 2\nVO +·4H O) [R4], compelling H+·2H O transport in the opposite direction to maintain the\n2 2 2\nelectroneutrality. [R2] The complex interplay during ion transport results in the characteristic\nmulti-stage dynamics of discharge capacity observed during cycling (Fig. 1a), consistent with prior\nreports [R19].\nSide reactions for the vanadium ions transport from the negative to the positive sides:\nV 2 + + 2 V O +2 + 2 H + → 3 V O 2 + + H\nV 3 + + V O +2 → 2 V O 2 + (Eq. R2)\nSide reactions for the vanadium ions transport from the positive to the negative sides:\nV O +2 + 2 V 2 + + 4 H + → 3 V 3 + + 2 H\nV O 2 + + V 2 + + 2 H + → 2 V 3 + + H\na\n)hA(\nyticapac\negrahcsiD\nb\n1 .2\n1 .0\n0 .8\n0 .6\n0 .4\n2 .1\n1 .8\n1 .5\n1 .2 0 .9\nN\n0\n0\n2 1 2 5 1  m\n5 0\n5 0\n1 0 0\n1 0 0\n1 5 0\n1 5 0\nC y c\n2 0 0\nle n u\n2 0 0\nm b e r\n2 5 0\n2 5 0\n3 0 0\n3 0 0\n@ 2 0 0 m A\n3 5 0\nC a th o A n o ly\n3 5 0\n-2 c m\n4 0 0\nly te te\n4 0 0\n8\n8\n7\n7\n7\n4\n1\n8\n5\n2\n)%\n(\nycneiciffe\negatloV\n1-L )\nlo\nm\nn\n(\no\nita r tn\ne\nc\nn o c s n o I C A an th o o ly lyte te\nC y c le n u m b e r\n6\n5\n4\n3 2\n)s·a\nP m\ny\n(\ntis\no c s iv\nc\nita m e n iK\nFig. 1 Battery performances and electrolyte properties vary with cycling. a, Discharge capacity/voltage\nefficiency and b, electrolytes’ concentration/viscosity change with cycling of the VRFB equipped with\nNafion 212 and traditional electrolytes at 200 mA cm-2.\na\n)Lm(\nemuloV\nc\n)Lm(\nemuloV\n6 3\n5 6\n4 9\n4 2\n3 5\n5 0\n4 5\n4 0\n3 5\n3 0\nC\nB\nC\nB\na th o ly te\ne fo r e c y c lin\na th o ly te\ne fo r e c y c lin\ng\ng\nA\nA\nn o ly te\nA fte r c y c lin g\nn o ly te\nA fte r c y c lin g\nB S E\nT E\ns\ns\nb\n)1-L\nlom(\nnoitartnecnoC\nd\n)1-L\nlom(\nnoitartnecnoC\n2 .0\n1 .6\n1 .2\n0 .8\n0 .4\n0 .0\n2 .1\n1 .4\n0 .7\n0 .0\nC a th o ly te\nB e fo r e c y c lin g\nC a th o ly te\nB e fo r e c y c lin g\nA n\nA n o ly te\nA fte r c y\no ly te\nA fte r c y\nc lin\nc lin\nB\ng\nT\ng\nS E s\nE s\nFig. S21 Changes in electrolytes before and after cycling. (a-b) Volume and concentration changes in\nVRFBs with BSEs (P 1.91 M V3.55+; N 1.17 M V3.50+) (c-d) Volume and concentration changes in VRFBs\nwith TEs (P 1.70 M V3.50+; N 1.70 M V3.50+).\n1 0\n8\n6\n4\n2\n0\n0\n0\n0\n0\n0\n0 .3 0 .6 0 .9 1 .2 1 .5 1 .8\nhe\nNet fl u\nx t\nO\no\ns i\nt\nti ve\nsi\nde\np\negrahc\nfo\netatS\nP /N C o n c e n tr a tio n r a tio\nN F R\n1\n1\n0\n0\n.7\n.2\n.6\n.1\n6\nfl u\nx t\ng\no\na ti\nve\nsi\nde\nhe\nne\nt\n> 2 .0\nFig. 2b Electrolyte concentrations on the positive and negative sides affect the net flux ratio under\ndifferent SOCs.\n[R2] Sun C, Chen J, Zhang H, et al. Investigations on transfer of water and vanadium ions across\nNafion membrane in an operating vanadium redox flow battery. J. Power Sources. 195(3):\n890-897, (2010).\n[R4] Mu D, Zhao Y, Yu L, et al. Asymmetric vanadium flow batteries: long lifespan via an\nanolyte overhang strategy. Phys. Chem. Chem. Phys. 19(43): 29195-29203 (2017).\n[R19] Lei Y, Zhang B W, Bai B F, et al. A transient electrochemical model incorporating the\nDonnan effect for all-vanadium redox flow batteries. J. Power Sources. 299: 202-211, (2015).\n8. In Fig. 3, could you also provide data on power density, voltage efficiency, or energy efficiency?\nIn the Introduction, it is stated that this electrolyte design method can address the trade-off between\nion conductivity and selectivity without compromising power density, which is a key advantage\nover membrane design. Therefore, this aspect should also be addressed and supported with relevant\ndata in the study.\nResponse:\nThanks for your valuable suggestion. We have included a comparison of the power density in\nVRFBs using BSEs and TEs in the revised manuscript. Fig. 3h shows that the power density of\nVRFB is improved by adopting BSEs compared to that employing TEs due to the enhanced VE\n(Fig. S9). To clarify the influence of BSEs on VRFB power density, we have added relevant\ndiscussion in the revised text, as detailed below.\n)2-mc\nW(\nytisned\nrewoP\n0\n0\n0\n0\n.3\n.2\n.2\n.2\n0\n7\n4\n1\n@ 2\n1\n0 0 m A\n5\nc\n0\nm -2\nC\n1\ny\n0 0\nc le n u\n2\nm\n0 0\nb e r\n3 0 0\nB\nT\n0\ns\nFig. 3h Power density of VRFBs with BSEs and TEs at different cycles (calculated with\nmedium voltage).\na\n)%\n(\nycneiciffe\negatloV\n90\n87\n84\n81\n78\n@ 200 m A cm\nT E s\nB S E s\n0\n-2\n50 100 150\nC y\n200\ncle n u m b er\n250 300 350 400\n98\n91\n84\n77\n70\n)%\n(\nycneiciffe\ncibmoluoC\nmhO/)Z(mI-\nb\n0.009\n0.006\n0.003\n0.000\nT E s\nB S E s\n0.030\nR\n0.033\ne(Z )/O h m\n0.036\nFig. S9 Performance comparison of VRFBs with balanced-state electrolytes (BSEs) and traditional\nelectrolytes (TEs). Comparison of a, the voltage/coulombic efficiency and b, electrochemical impedance\nspectroscopy (EIS) spectrum.\nIn the revised Manuscript [Fig. 3h]\nmhO/)Z(mI-\na\n1.2\n)hA(\n1.0\nyticap\n0.8 ac\negra\n0.6 hcsiD\n0.4\nc\n99\n)%\n(\ny 98 cneiciff\n97 e\ncibmol\n96 uoC\n95\nf\n0.006\n0.004\n0.002\n0.000\ni 9\n6\n3\n0\n0\n@\n0\n-2 200 m A cm\n50 100\nB S E s\nT E s\n50 100 150 200\n-2 C u rren t d en siy (m A cm )\n3.50+ 3.50+ P 1.70 M V N 1.70 M V\n3.50+ 3.50+ P 1.70 M V N 1.17 M V\n0.028 0.030 0.032\nR e(Z )/O h m\n4000 8000 12000\n150 200\nC y cle n ud\n)%\n(\nycneiciffe\ncibmoluoC\n250\ng\n)V(\negatlov\ntiu\nc\nric\nn\nep\nO\n0.034\nj\n16000\nm b\n99\n98\n97\n96\n1.2\n0.9\n0.6\n0.3\ner\nN\nT\n7 1 .0 % ­\n250 300 350\n100 200 @ m A\n3+ 1.17 M V\n1.2 1.4 1.6 1.8\n2+ V O co n cen tra tio n (M )\nP 1.81 M V\nP 1.91 M V P 2.01 M V\nP /N 1.70 M\nN 1.17 M V\n40 80 120\nT im e (h )\nS E s\nE s\n400\n-2 cm\n2.0\n3.53+\n3.55+ 3.58+ O\n3.50+ V\n3.50+\n160\nb\n)hA(\nyticapac\negrahcsiD\ne\nh\nk\n1.2\n1.0\n0.8\n0.6\n0.4\n79\nT E\n60\n97\n13.7 h\ns\n70T\nest tim\n112\n143\n80e\n(h )\n130\n13.5 h\n176\n90 100\n.ON\nelcyC\n5.61x10-7\n-7 5.04x10\n3.31x10-7\n)2mn(\nDSM\nV V V\nV\n2+ T E s + O T E s 2 2+ B S E s\n+ O B S E 2 s\nT im e (p s)\n8.09x10-7\n@ cm 2 -1 s\n)1-lom\nJk(\nygrenE\n400\n200\n00\n-2000\n-4000\n-6000\nV\nT\n2+\nE s B S\n3+ V\nE s\nV O\nvan\n2+\nd\nC\ner W aals\nou lom b ic\n+ V O 2\n)2-mc\nW(\nytisned\nrewoP\n)r(g\n) 96 %(\nyc 93 neiciff\n90 e\ncibm\n87 oluoC\n84\n0.30\n0.27\n0.24\n0.21\n60 45\n30\n15\n0\n3.50+ P 1.70 M V N 1.70 M\n3.50+ P 1.70 M V N 1.17 M\n50 100 150\nC u rren t d en sity (m A\n-2 @ 200 m A cm\n1 50 100 200\nC y cle n u m b er\n2+ V T E s 2+ V B S E s\n0.2 0.3 0.4 r (n m )\n3.50+ V\n3.50+ V\n200\n-2 cm )\n300\nT E s\n400\n0.5\n100\n95 )%\n(\nycn\n90 eiciffe\n85 egatloV\n80\n10 8\n4\n2\nM V3.55+; N 1.17 M V3.50+) on suppressing capacity decay of VRFBs using N212. b, Fluctuation of discharge\ncapacity over time due to temperature variation. c, Effects of BSEs on coulombic efficiency. d, Coulombic\nefficiency vs. VO2+ concentration. e, Coulombic/voltage efficiency and f, VRFB resistance, after decreasing\nthe concentration of negative electrolyte from 1.7 to 1.17 M. g, Self-discharge curves of a VRFB with\ndifferent electrolyte concentrations. h, Comparison of VRFB power density using BSEs and TEs. i, Mean\nSquared Displacement (MSD) of V2+ and VO+ ions. j, van der Waals, and coulombic energy between\n2\nvanadium ions and sulfonic acid groups. k, Radial distribution function/coordination numbers of V2+ in\nNafion membrane with the BSEs and TEs (P 1.70 M V3.50+; N 1.70 M V3.50+).\nIn the revised Manuscript [ Line234, Page 9]\nFurthermore, the power density of the VRFB does not decrease using BSEs; rather, it improves\nmarkedly compared with that of the system using TE (Fig. 3h) due to the enhanced VE (Fig. S9).\n9. In Fig. 3, please also indicate the total testing time for 400 cycles.\nResponse:\nWe thank the reviewer for this comment. The VRFB employing BSEs exhibited a total testing\nduration of 289.49 hours over 400 cycles, which is significantly longer than the 175.67 hours\nrecorded for the system with TEs. This comparative data has been added to the revised\nsupplementary information.\nIn the revised Supplementary Information [ Line 243, Page 12]\nThe VRFB employing BSEs operated for 289.49 hours over 400 cycles, which is significantly\nlonger than the 175.67 hours achieved by the VRFB with TEs.\n10. In Fig. 4, the thickness of the Nafion membrane should be kept the same in order to isolate\nand accurately assess the effect of the electrolyte design on the stability of VRFBs with\nbalanced-state electrolytes.\nResponse:\nWe thank the reviewer for this suggestion. We have directly compared the effect of BSEs on\ncapacity decay in VRFBs equipped with the same thickness of Nafion membrane (Nafion 212) in\nFig. 3a. The data show that the use of BSEs reduces the capacity decay rate by 86.3%, from 0.182%\nper cycle to 0.025% per cycle over 400 cycles. To further highlight the practical benefit of this\napproach, we also compare a system employing BSEs with a thin (15 μm) Nafion membrane\nagainst one using traditional electrolytes with a thick (183 μm) membrane in Fig. 4a-d. This\ncomparison underscores the significant advantage of BSEs in enabling high performance with\nthinner, lower-resistance membranes. To enhance clarity, we have emphasized that the tests were\nconducted in VRFBs using Nafion 212, as detailed below.\nIn the revised Manuscript [Fig. 3a]\nA VRFB employing an N212 membrane with the BSEs (P 1.91 M V3.55+; N 1.170 M V3.50+) exhibit\nan 86.3% reduction in capacity decay rate—from 0.182% to 0.025% per cycle—and a 71.0%\nincrease in accumulated discharge capacity (from 256.97 to 439.35 Ah) over 400 cycles, compared\nto that using traditional electrolytes (P 1.70 M V3.50+; N 1.70 M V3.50+) (Fig. 3a).\n)hA(\nyticapac\negrahcsiD\n1\n1\n0\n0\n0\n.2\n.0\n.8\n.6\n.4\n@\n0\n2 0 0 m A c m\n5\n-2\n0 1 0 0 1 5 0\nC y c\n2 0\nle n\n0u\nm b e r\n2 5\n7\n0\n1 .0 % ­\n3 0 0 3 5 0\nB\nT\nSE E s\ns\n4 0 0\nFig. 3a Effects of BSEs (P 1.91 M V3.55+; N 1.17 M V3.50+) on suppressing capacity decay of VRFBs\nusing N212.\n11. Overall, the experimental data presented focuses solely on VRFBs using a Nafion membrane.\nAlthough this system is described as a model, additional validation with other types of RFBs\nemploying different active materials and membranes is necessary to substantiate the claim that this\nelectrolyte design strategy is universally adaptable for RFBs without membrane limitations.\nTherefore, I recommend conducting further tests with at least two or three different combinations\nof active materials and membranes.\nResponse:\nThanks for your valuable suggestions. We have applied this method to iron–vanadium flow\nbatteries (IVFBs), which suffer from severe crossover issues. The accumulated discharge capacity\nimproved 56.36% from 388.37 to 607.25 Ah over 400 cycles when conventional electrolytes were\nreplaced with the BSEs, demonstrating good effectiveness and applicability, as shown in Fig. R2.\nDetails regarding the IVFBs and the corresponding BSEs have been added to the revised\nmanuscript and supplementary information, with details provided below.\nHere, we treat VRFBs during cycling as dynamic diffusion systems and leverage their self-\nbalancing capability to determine electrolyte concentration. The methodological cornerstone of\nthis study is the exploitation of the self-balancing capability of VRFBs. We operated a VRFB\nequipped with a Nafion membrane under specific operating conditions until it reached a balanced\nstate. By characterizing the electrolytes in VRFBs operating at this balanced state, we determined\nthe concentrations required for the BSEs. As described in response to question 2, we have\nevaluated the effects of BSEs on two other widely studied membranes—polybenzimidazole (PBI)\nand sulfonated poly (ether ether ketone) (SPEEK). However, both PBI and SPEEK exhibit a linear\ndecay in discharge capacity with cycling [R17, R18] (Figs. R7, R8), which does not conform to\nthe definition of the balanced state.\nTo be more rigorous, we have corrected “the balanced-state electrolyte approach removes\nmembrane limitations” to “significantly reduces membrane limitations” in the revised manuscript,\nas shown below.\n)hA(\nyticapac\negrahcsiD\n1\n1\n1\n1\n0\n0\n.6\n.4\n.2\n.0\n.8\n.6 @\n0\n2 0 0 m A c m\n5 0\n-2\n1 0 0 1 5 0\nC y c\n2 0\nle n\n0\nu m b e r\n2\n5\n5\n6\n0\n.3 6 % ­\n3 0 0\n.7S 2+ M V ||1\nE s\n3 5 0\n.7 M F e\n4\n3+\n0 0\nFig. R2 Comparison of iron-vanadium flow batteries using conventional electrolytes (P 1.7 M V2+; N\n1.7 M Fe3+) versus balanced state electrolytes (BSEs, P 1.072 M V2+ + 0.876 M Fe2+; N 1.324 M Fe3+ +\n0.914 M VO2+).\n[R17] Wang Z, Ren J, Sun J, et al. The anion conductivity of acid-doped polybenzimidazole\nmembrane and utilization in mitigating the capacity decay of vanadium redox flow battery\nstacks. Chem. Eng. J., 474: 145621, (2023).\n[R18] Ding M, Ling X, Yuan D, et al. SPEEK membrane of ultrahigh stability enhanced by\nfunctionalized carbon nanotubes for vanadium redox flow battery. Front. Chem. 6: 286,\n(2018).\nIn the revised Manuscript [Fig. 5]\na\n)hA(\nyticapac\negrahcsiD\nc\n)hA(\nyticapac\negrahcsiD\ne\n)%( egatnecrep\ntsoC\n1.6\n1.2\n0.8\n0.4\n1.5\n1.2\n0.9\n0.6\n0.3\n100\n75\n50 25\n0\n-2 @ 200 m A cm\nN C 700 15  m\n0\n62.79\n29.69 2.19\nE lectrolyte\ncost\n80\n80\n10.8\nM em b ran\ncost\ne\n160\n160\n100\n58.3\nC ap ital\ncost\nC\nC\ny\ny\ncle n\ncle n\nu\nu\nf\n240\nm b er\n240\nm b er\n0.0\n0.5 1.0\n1.5 2.0 2.5\n3.0\n76\n85.1%\n8 4 .8 %\n­\n­\n80\n320\n320\nN 2 1 1 T E s\nN C 700 T E s\n400\n84 86\nb\n)hA(\nyticapac\negrahcsiD\nd\n)hA(\nyticapac\negrahcsiD\ng\n1.5\n1.2\n0.9\n0.6\n0.3\n1.5\n1.2\n0.9\n0.6\n0.3\n0\nN\nN\nN\n17.4%\n60.6%\n60 120\nT est tim\n180\ne (h )\n240 300\nC 700 B S E s\n13.6%\n60.6%\n60 120\nT est tim\n180\ne (h )\n240 300\n40 m\n24 m 46 m 46 m\n15 m\n40 m\n54 m\nA ngew .C hem , 2024 E A ne d\nrg\nv\ny\n.\nS\nF\nto\nu\nra\nn\ng\nc\ne\nt\nM\n.\na A\nM\nte d r\na\nv .2\nt\n. 0\ne\nF 2\nr\n4 u\nN .\nn\n2 a\nc\n0 t\nt\nN 2\n.\n. 2\nM\nS at u\na\n. s\nt\nC\ne\nta\nr\no i\n2\nm n\n0\n.\n2\n2 m\n3\n0 u 2 n 2 .\nA\n20\nn\n2\ng\n0\new.Chem, 2025\n)‰( etar yaced\nyticapaC\na m ： M em brane thickness\nE n erg y efficin ecy (% )\nT his w\n70  m\nork\n)hA( yticapac\negrahcsiD\n1.6\n1.4 1.2\n1.0 0.8\n0.6\n0\n1.7 M V B S E s\n50 100\n2+ 3+ ||1.7M F e\n150 200\nC y cle n u m\n5 6 .3 6 % ­\n@ 200 m A cm\n250 300 350\nb er\n-2\nof the VRFB with N211. b, Discharge capacity comparison between the VRFBs with N211 and N117. c,\nEffects of BSEs on improving the capacity retention rate of the VRFB with NC700. d, Capacity retention\nrates comparison between the VRFB with NC700/BSEs and that of N117/TEs. e, Capital cost analysis in a\nVRFBs with advanced designed membranes reported in the last five years. g, Effects of BSEs (P 1.072 M\nV2+ + 0.876 M Fe2+; N 1.324 M Fe3+ + 0.914 M VO2+) on improving the capacity retention rate of the IVFB\nwith N212.\nIn the revised Manuscript [Fig. 5g]\nTo further demonstrate the effectiveness and applicability of our proposed BSEs method, we have\nextended it to iron-vanadium flow batteries (IVFBs), which suffer from severe crossover issues.\nThe accumulated discharge capacity improved 56.36% from 388.37 to 607.25 Ah over 400 cycles\nwhen conventional electrolytes (P 1.70 M V2+; N 1.70 M Fe3+) were replaced with the BSEs (P\n1.072 M V2+ +0.876 M Fe2+; N 1.324 M Fe3+ +0.914 M VO2+), indicating successful suppression\nof the crossover, as shown in Fig. 5g.\nIn the revised Manuscript [Section Materials]\nIron (II) sulfate heptahydrate (FeSO ‧7H O CAS Number: 7782-63-0) and Iron (III) chloride\n4 2\nhexahydrate FeCl ‧6H O (CAS Number: 7447-40-7) were purchased from Sigma-Aldrich.\n3 2\nIn the revised Manuscript [ Section Battery tests]\nA VRFB cell equipped with Nafion 212 was adapted for IVFBs testing by replacing vanadium\nelectrolytes with iron-vanadium electrolytes.\nIn the revised Manuscript [Section Electrolytes preparation]\nThe 1.70 M V2+/3.00 M H SO , 1.70 M V3+/3.00 M H SO and 1.70 M VO2+/3.00 M H SO were\n2 4 2 4 2 4\nobtained by charging the commercial (1.70 M V3.50+ /3.00 M H SO ) electrolytes. 1.70 M Fe3+/3.00\n2 4\nM H SO electrolyte was prepared by dissolving FeCl ‧6H O in 3.00 M H SO solution.\n2 4 3 2 2 4\nIn the revised Manuscript [Section Characterization techniques]\nIon concentrations in the positive and negative electrolytes of IVRFs were measured using an\nInductively Coupled Plasma –Optical Emission Spectrometer (Avio-200, PerkinElmer) following\na 7500-fold dilution with deionized water.\nIn the revised Manuscript [Section Battery tests]\nAll the battery tests were conducted under N protection using Arbin 179539 (Arbin Instruments,\n0.60-1.60 V for IVFB experiments.\nIn the revised Supplementary Information [Section 1.2 Electrolyte preparation for IVFBs]\nThe BSEs for IVFBs were prepared as follows. For the positive side, 11.62 g VOSO ·5H O was\n4 2\nadded to 40 mL of 1.70 M Fe3+/3.00 M H SO solution and then diluted with 11.36 mL of 3.00 M\n2 4\nH SO , serving as the positive electrolyte. For the negative side, 11.45 g FeSO ‧7H O was added\n2 4 4 2\nto 40 mL of 1.70 M V2+/3.00 M H SO solution and then diluted with 23.43 mL of 3.00 M H SO ,\n2 4 2 4\nserving as the negative electrolyte.\nIn the revised Supplementary Information [Section 4 IVFB test]\nFirst, a VRFB assembled with Nafion 212 was fully charged using 40 mL of V3.5+/3.00 M H SO\n2 4\nas both the positive and negative electrolytes, yielding 40 mL of V2+/3.00 M H SO on the negative\n2 4\nside. Then, the positive electrolytes (VO+ ) were pumped into the tank and the positive-side\n2\nchamber was washed with deionized water and purged with N for 1 min. Finally, the positive\n2\nelectrolyte was replaced with 1.70 M Fe3+/3.00 M H SO electrolytes. In IVFB testing with the\n2 4\nBSEs, the same flow battery cell was employed.\nIn the revised Supplementary Information [Section 1.4.2 BSEs for IVFBs]\nThe definition and identification method for the balanced state in IVFBs are the same as those for\nVRFBs. Here, we selected the state of an IVFB after 160 cycles as its balanced state and measured\nion concentration using an Inductively Coupled Plasma –Optical Emission Spectrometer (Avio-\n200, Perkin Elmer) following 7500-fold dilution with deionized water. The results show that\nvanadium ion concentrations are 0.914 M and 1.072 M in the positive and negative electrolytes,\nrespectively, and iron ion concentrations are 1.324 M and 0.876 M, respectively.\nIn the revised Supplementary Information [Fig. S38]\n1.6\nIVFB\n)h 1.4\nA\n(\ny\ntic 1.2\na\np\na\nc\ne\n1.0 Balanced state position\ng\nr\na\nh c0.8\nsiD\n0.6 @ 200 mA cm-2\n0 50 100 150 200 250\nTest time (h)\nFig. S38 Discharge capacity versus time for an IVFB using TEs (P 1.70 M Fe3.0+; N 1.70 M V2.0+).\nReviewer #3 (Remarks to the Author):\nThis manuscript proposes balanced-state electrolytes (BSEs) that deliberately break symmetry in\nconcentration and average valence between positive and negative tanks to counteract net\ncrossover in vanadium redox flow batteries (VRFBs). By tuning concentration and valence, the\nauthors claim to hold the net transmembrane flux near zero over a cycle, enabling thin\nNafion membranes without sacrificing capacity retention. Representative results include:\nwith BSEs,\nN212 (51 μm) outperforms N117 (183 μm) using traditional electrolytes, cutting the\ncapacity-decay rate from 0.061% to 0.025% per cycle over 1,000 cycles and reaching\nCE = 97.79% at 50 mA cm⁻² (main Fig. 4a, d; p. 25–26). The approach extends to N211 (25 μm)\nand NC700 (15 μm) with decay rates down to 0.015% per cycle, alongside a >41.7%\nCAPEX reduction projected for a 1 MW/4 MWh system (main abstract; Fig. 5e–h; pp. 15–16; SI Tab. S2).\nThe approach extends to N211 (25 μm) and NC700 (15 μm) with decay rates down to 0.015% per cycle, alongside a >41.7% CAPEX reduction projected for a 1 MW/4 MWh system (main abstract; Fig. 5e–h; pp. 15–16; SI Tab. S2).\nMechanistically, the authors quantify flux reversal/neutralization (net flux 4.59% vs 38.94% for\nBSEs vs TEs) using volume- and concentration-shift analysis (SI Eq. S13–S14; Fig. S15, p. 10–\n11).\nThe idea is practically appealing—use electrolyte design to escape the conductivity–selectivity\ntrade-off of Nafion rather than inventing bespoke membranes.\nResponse: We appreciate the reviewer for taking the time to provide valuable comments and\nsuggestions that have helped improve the quality and clarity of our manuscript. We have\nthoroughly addressed all comments, and the revisions have significantly strengthened the paper.\nMajor comments\n1.Generalizable, reproducible procedure for identifying the “balanced state.”\nThe present recipe infers BSEs from the first “horizontal region” (~107 h) in the\ndischarge-capacity–time trace (main Fig. 2e–f), which is sensitive to current, SOC window,\ntemperature, and cell hardware. Please formalize a predict–set–verify workflow: given membrane\ntype, current density, SOC range, and temperature, output the target P/N concentrations and\npositive-tank average valence (with uncertainty). Publishing a minimal open script that couples\nFig. 2b (net-flux map) with SI Sections 1 & 2 would make this widely reusable.\nResponse:\nThanks for your suggestions. In Fig. 2e, a VRFB was assembled in a zero-gap structure using\ngraphite plates with serpentine flow fields. Two pieces of graphite felts (2.5 mm thickness,\nLiaoning Jingu Carbon Material Co., Ltd.) with the size of 40.00 × 40.00 mm2 were used as the\nelectrodes separated with a piece of Nafion 212. 40.00 mL of 1.70 M V3.50+ /3.00 M H SO\n2 4\nelectrolytes (supplied by Sichuan Xingming Energy Material Co., Ltd) were stored in the positive\nand negative reservoirs and circulated via a Longer BT100 peristaltic pump (Longer Precision\nPump Co., Ltd., UK). The VRFB was tested in a laboratory where the temperature fluctuated\nbetween 25 and 30 °C over diurnal cycles. The charge and discharge cycling was conducted using\nArbin 179539 (Arbin instruments, USA) at 200 mA cm-2 with N protection, with cut-off voltages\n2\nof 0.90-1.60 V. The SOC of this VRFB ranges from 6.99% to 76.79 % at the initial stage, as shown\nin Fig. 2c.\nFurthermore, in this work, we leveraged the self-balancing capability of VRFBs equipped with a\nNafion membrane to identify the balanced state under specific operating conditions. By\ncharacterizing the electrolytes in VRFBs operating at this balanced state, we determined the\nconcentrations required for the BSEs. Differences in membrane type, current density, SOC range,\nand temperature are inherently captured in the resulting balanced state, leading to distinct BSEs—\nas demonstrated by the differing BSE compositions for VRFBs using N212 (P 1.91 M V3.55+; N\n1.170 M V3.50+) versus N211 membranes (P 1.83 M V3.54+; N 1.15 M V3.50+). Thus, the effectiveness\nand applicability of the BSE method remain unaffected by hardware variations, demonstrating its\nuniversality. This highlights the unique advantage of our proposed strategy: it provides a universal, experimentally driven framework for deriving balancing solutions for different hardware materials\nand operating scenarios. We believe this conceptual innovation offers a fresh perspective for\nmembrane research and electrolyte engineering in VRFBs. We thank the reviewer again for\nprompting us to articulate this more clearly.\nWe clarified the description of the BSEs for a VRFB in the revised manuscript and added a section\ndetailing how to determine the BSE composition in the revised supplementary information, as\ndetailed below.\nThe workflow for balanced state characterization and the script of Fig. 2b have been added in the\nrevised manuscript and supplementary information, as shown below.\negrahc\nfo\netatS\n8\n6\n4\n2\n0\n0\n0\n0\n0\n7 9 .6\n5 .0 1\n1 5 0\nC u r\n6 9 .8\n6 .9 9\n2 0 0\nr e n t d e n\n5\n9\n2s\n9 .2\n.1 2\n5 0\nity m(\nR e c h a r g e a b le\nN o n -d isc h a r g e\n4 7 .8\n3 5 .6\n1 4 1 1 .4\n3 0 0 3 5 0\n-2 A c m )\n1 0\n0\nIn the revised Manuscript [Section BSE determination]\nDetermining the balanced state of a VRFB under specified operating conditions is essential for\ndesigning BSEs. Specifically, we define the balanced state under specific conditions as one\nwhere the capacity decay rate is less than 0.03% per cycle or 0.08% per hour. In addition, the test\nmust last longer than 8 h and include more than 20 cycles, with the discharge capacity showing a\nmonotonic decay versus time or cycle number over the investigated range. The electrolyte\nconcentrations at the balanced state are used for designing BSEs. To ensure the accuracy of these\nmeasurements, we converted the electrolytes at the balanced state to V3+|VO2+ through full\ndischarge followed by aerial oxidation. To compensate for the elevated average vanadium valence\nthat occurs during cycling due to side reactions, the VO+ content in the initial electrolyte was\n2\nexperimentally increased. The detailed procedure is described in the supplementary information.\nIn the revised Supplementary Information [Section BSE determination]\nFirst, operate a VRFB under specified conditions and record the discharge capacity versus time\ncurve. Second, calculate the capacity decay rates over 20 cycles in the quasi-steady region of the\ndischarge capacity curve. Third, identify the region where the discharge capacity decay rate is\nbelow 0.03% per cycle. Fourth, stop cycling and fully discharge the battery at a constant voltage\nof 0.8 V until the current falls below 0.1 A. Fifth, stir the negative electrolyte using a magnetic\nstirrer and oxidize it in air for 4 hours to convert the surplus V2+ to V3+. Sixth, dilute the negative\nand positive electrolytes 15-fold with deionized water and measure the V3+ and VO2+\nconcentrations using a UV-Visible Spectrophotometer.\nIn the revised Supplementary Information [At the end of this document]\nThe script of Fig. 2b can be found in the following link.\nhttps://figshare.com/s/fdae8069727545502da4\n2.Disentangle temperature and water-migration effects.\nThe capacity ripples track day–night temperature changes (main Fig. 3b; SI Fig. S7), and\nhydraulic/viscous effects were probed via unequal flow (main Fig. 2h; SI Fig. S5), but the\nquantitative roles of water transport and acid strength remain unclear. Please (i) repeat a key\nN212/N211/NC700 comparison in a constant-temperature environment (e.g., 25 ± 0.1 °C),\nand (ii) co‑track acid molarity/viscosity/volume on both sides with water content (e.g., titration or\nKarl Fischer). This will bound how much of the benefit arises from species flux versus\nwater/osmotic effects.\nResponse:\nThanks for your suggestion. We retested the effect of BSEs in a VRFB assembled with N212 at a\ncontrolled temperature of 25 ℃, as shown in Fig. R11. The results demonstrate that replacing TEs\nwith BSEs enhances the accumulated discharge capacity by 106.0%.\nWe also comparatively studied the acidity, viscosity, and volume of electrolyte in VRFBs using\nTEs and BSEs before and after cycling, as depicted in Fig. R12. Results show that the pH values\nexhibit no substantial change after cycling for VRFBs both employing TEs and BSEs (Fig. R12a).\nHowever, in TEs-based VRFBs, the viscosity of the positive electrolyte increases markedly,\nwhereas that of the negative electrolyte decreases substantially after cycling (Fig. R12b), owing to\nconcentration variations (Fig. 1b). In contrast, the viscosity decreases in the positive electrolyte\nbut increases in the negative electrolyte, highlighting the ability of BSEs to counteract crossover.\nFurthermore, the electrolyte volume in TE-based VRFBs expands slightly on the positive side and\ncontracts on the negative side after cycling, whereas these volume changes are more pronounced\nwhen BSEs are employed (Fig. R12c), underscoring the enhanced role of water transfer in the\nlatter configuration.\n)hA(\nyticapac\negrahcsiD\n1\n1\n0\n0\n0\n0\n.2\n.0\n.8\n.6\n.4\n.2\n@\n0\n2 0 0 m A c m\n5 0\n-2\n1 0 0 1 5 0\nC y c\n2 0\nle n\n0\nu m b e r\n2 5\n1\n0\n0 6 .0 % ­\n3 0 0\n2 5 ℃\n3 5 0\nT\nB\nES sE\ns\n4 0 0\nFig. R11 Effects of BSEs (P 1.91 M V3.55+; N 1.17 M V3.50+) on suppressing capacity decay of VRFBs at\n25 ℃.\neulav\nHp\na\n6\n4\n3\n1\n0\n.0\n.5\n.0\n.5\n.0\nP ositive electrolytes N egative electrolytes\nT E s F resh\n400 cycles electrolytes\nB S E s\n400 cycles\nb\n)s·aPm(\nytisocsiv\ncitameniK\n8\n6\n4\n2\n0 1.70 M\nF resh\nP ositive electrolyte\nN egative electrolyte\nB S E s B S E s 1.70 M\n)Lm(\nemulov\netylortcelE\nc\n60\n45\n30\n15\n0 1.70 M\nF resh\nP ositive electrolyte\nN egative electrolyte\nB S E s B S E s 1.70 M\nFig. R12 Variation of electrolyte composition after cycling. a, pH value b, kinematic viscosity, and c,\nvolume of electrolytes in VRFBs using TEs and BSEs before and after cycling operating at 25 ℃.\nIn the electrolyte pH tests, samples (1 mL) were diluted 60-fold with deionized water, and the pH\nwas measured using a pH pen (AZ8693; ERMANDA, China).\n)1-L\nlom(\nnoitartnecnoc\nsnoI\n2\n1\n1\n1\n0\n.1\n.8\n.5\n.2\n.9\nA\nan th o\no ly\n5 0\nlyte te\n1 0 0 1 5 0\nC y c le\n2 0\nn\n0\nu m b e r\n2 5 0 3 0 0\nC\nA\n3 5\nan\n0\nth o\no ly\nlyte te\n4 0 0\n6\n5\n4\n3\n2\n)s·aPm(\nytisocsiv\ncitameniK\nFig. 1b, Electrolyte concentration/viscosity change with cycling of the VRFB equipped with Nafion\n212 and traditional electrolytes at 200 mA cm-2.\n3. Bridge the MD to measurable transport; release inputs.\nThe MD results suggest reduced V3+ diffusion and altered ion–sulfonate interactions under BSEs\n(main Fig. 3h–j; SI Fig. S11–S13). For reproducibility, please share topology/parameters and\nbench-mark simulated diffusivities against values inferred from self-discharge/EIS or literature\nfor each ion/species. A brief sensitivity check (water content, ionic strength) would increase\nconfidence in the mechanism.\nResponse:\nWe thank the reviewer for this comment. The topology/parameters of H O+, V2+, V3+, VO2+, and\n2\nfollowing link, owing to the large number of parameters:\nhttps://figshare.com/s/fdae8069727545502da4\nWe have now benchmarked our MD simulations against experimental data and performed the\nrequested sensitivity analyses as follows:\nThe simulated diffusivities (Fig. R13) are compared with the experimental results (Tab. S1)\nreported by Professor Zhang [R2]. The simulated trends and orders of magnitude align well with\nthese independent experimental measurements, validating our model's predictive capability for\nrelative ion transport rates.\nTo assess the sensitivity of the simulations, models incorporating varying water contents were\nconstructed. The compositions of the different species in the simulation boxes are detailed in\nTables R7–R9. The results (Fig. R14) reveal that the diffusivity of V2+ increases substantially with\nrising water content in both TEs and BSEs systems, consistent with previous reports [R20]— the\nwater content of Nafion membranes exerts a profound influence on ion transport across the\nmembrane. The diffusivities of V2+ in BSEs-based system with different water contents are all\nlower than those in the TEs-based system.\nTab. R2 Topology/parameters of H O+ in MD simulation.\nPosition x (nm) -0.268 -0.307 -0.158 -0.311\nPosition y (nm) 0.141 0.207 0.136 0.040\nPosition z (nm) -0.002 0.079 0.004 0.009\nMass 15.999405 1.007941 1.007941 1.007941\nCharge -0.4001 0.4667 0.4667 0.4667\nBond length O-H (nm) — 0.0960 0.0960 0.0960\nBond Stretching O-H\n— 2.31154 2.31154 2.31154\n(kJ/mol/nm²) /×105\nO-H Angle (degree) — 104.500 104.500 104.500\nO-H Angle Bending\n— 4.182 4.182 4.182\n(kJ/mol/rad²) /×102\nsigma (nm) /×10-1 3.118146 2.571134 2.571134 2.571134\nepsilon (kJ/mol) /×10-1 2.510400 1.840960 1.840960 1.840960\nTab. R3 Topology/parameters of V2+ in MD simulation.\nAtoms V2+\nPosition x (nm) 0.100\nPosition y (nm) -0.007\nPosition z (nm) 0.007\nCharge 2.0000\nMass 50.941465\nsigma (nm) /×10-1 2.800986\nepsilon (kJ/mol) /×10-1 6.694400\nTab. R4 Topology/parameters of V3+ in MD simulation.\nAtoms V3+\nPosition x (nm) 0.093\nPosition y (nm) -0.004\nPosition z (nm) 0.005\nCharge 3.000\nMass 50.941465\nsigma (nm) /×10-1 2.800986\nepsilon (kJ/mol) /×10-1 6.694400\nTab. R5 Topology/parameters of VO2+ in MD simulation.\nAtoms V O\nPosition x (nm) -0.328 -0.227\nPosition y (nm) 0.078 0.098\nPosition z (nm) 0.000 0.165\nMass 50.941465 15.999405\nCharge 2.400800 -0.400800\nBond length O-V (nm)\n0.1770\nBond Stretching O-V\n3.095449\n(kJ/mol/nm²) /×105\nsigma (nm) /×10-1 2.800986 3.118146\nepsilon (kJ/mol) ×10-2 6.694400 25.10400\nTab. R6 Topology/parameters of VO + in MD simulation.\nPosition x (nm) -0.283 -0.374 -0.193\nPosition y (nm) 0.018 0.185 -0.150\nPosition z (nm) 0.062 0.019 0.104\nMass 50.941465 15.999405 15.999405\nCharge 1.4008 -0.200400 -0.2004\nBond length O-V (nm) — 0.1960 0.1960\nBond Stretching O-V\n— 2.286179 2.286179\n(kJ/mol/nm²) /×105\nAngle (degree) O-V — 180.00 180.00\nAngle Bending O-V\n— 2.4776 2.4776\n(kJ/mol/rad²) /×102\nsigma (nm) /×10-1 2.800986 3.118146 3.118146\nepsilon (kJ/mol) ×10-2 6.694400 25.10400 25.10400\na b\nV2+ TEs V3+ TEs @ cm2 s-1\n9 9\nVO+ TEs V3+ BSEs\n2) m\nn\nn\nD\n( (\nD\nS\nM\n3.31x10-7 S\nM 4.30x10-7 4.51x10-7\n3 3\n5.04x10-7 2.59x10-7\n@ cm2 s-1 1.20x10-7\n0 0\n0 4000 8000 12000 16000 0 4000 8000 12000 16000\nTime (ps) Time (ps)\nFig. R13 Simulated diffusivities of vanadium ions across Nafion membrane. a-b, Mean Squared\nDisplacement (MSD) of V2+ /VO + and V3+/ VO2+ across membrane.\nVanadium ions V2+ V3+ VO2+ VO +\n8.767 × 10−7 3.222 × 10−7 6.825 × 10−7 5.897 × 10−7\ncoefficient/ cm2 s−1\nTab. R7 Number of molecules added in different simulation systems.\nNafion (2×(-SO -)) V2+ V3+ VO2+ VO + H O+ H O\n3 2 3 2\nTEs 100 20 7 14 12 99 980\nBSEs 100 14 5 17 15 108 936\nTab. R8 Number of molecules added in different simulation systems.\nNafion (2×(-SO -)) V2+ V3+ VO2+ VO + H O+ H O\n3 2 3 2\nTEs 100 20 7 14 12 99 2940\nBSEs 100 14 5 17 15 108 2808\nTab. R9 Number of molecules added in different simulation systems.\nNafion (2×(-SO -)) V2+ V3+ VO2+ VO + H O+ H O\n3 2 3 2\nTEs 100 20 7 14 12 99 2940\nBSEs 100 14 5 17 15 108 2808\n)2mn(\nDSM\na\n2\n1\n1\n0\n0\n.0\n.5\n.0\n.5\n.0\n0\n9\n1\n2\n8\n9\n9\n0\n6\n5 0 0\nT\n1\nim\n0\n0 0 0\ne (p\n4\n.2 7\ns)\n8 .0 9 x 1\n-7 .9 x 1 0\n-7 x 1 0\n1 5 0 0\n0 -7\nT E s\n2 0 0 0\n)2mn(\nDSM\nb\n2\n1\n1\n0\n0\n.0\n.5\n.0\n.5\n.0\n0\n9\n1\n2\n3\n8\n8\n7 2 H O2\n0 8 H O2\n5 0 0\nT\n1\nim\n3\n0 .1 3\n0 0 0\ne (p s)\n5 .6 1 x 1\n-7 .7 x 1 0\n-7 x 1 0\n1 5 0 0\n0 -7\nB S E s\n2 0 0 0\nFig. R14 Water content effects on V2+ diffusion rate across Nafion membrane. a-b, Mean Squared\nDisplacement (MSD) of V2+ at traditional electrolytes (TEs) and balanced state electrolytes (BSEs).\n[R2] Sun C, Chen J, Zhang H, Han X, Luo Q. Investigations on transfer of water and vanadium\nions across Nafion membrane in an operating vanadium redox flow battery. J. Power\nSources. 195(3): 890-897 (2010)\n[R20] Mauritz, K. A., & Moore, R. B. State of understanding of Nafion. Chem. Rev. 104(10),\n4535-4586, (2004).\n4. Cost model sensitivity and operating envelope.\nThe >41.7% CAPEX reduction (main Fig. 5h) is compelling but scenario-dependent. Please add\na tornado or scenario analysis varying membrane cost (±50%), energy efficiency (80–86%),\nlifetime (500–3,000 cycles), and pump power (viscosity-dependent) to test the robustness of the\nconclusion.\nResponse:\nWe thank the reviewer for this suggestion. A detailed calculation process and a cost table have\nbeen included in the supplementary information, as provided below.\nOur cost analysis focused solely on the membrane and electrolyte components. As shown in Fig.\n3, VRFBs employing BSEs demonstrate superior energy efficiency compared to those using\ntraditional electrolytes (TEs). This higher efficiency translates into an advantage in power-density-\nrelated costs. Furthermore, the average viscosity of the BSEs is 3.958 mPa·s, lower than the 4.456\nmPa·s of the TEs, suggesting a reduction in pump power loss. However, no direct correlation exists\nbetween capital costs and power density or pump power. We therefore consider only the membrane\nand electrolyte costs as a proportion of the overall system costs (based on a 1 MW/4 MWh system)\nwhen calculating the capital cost reduction upon adoption of BSEs. The details of this calculation\nare provided below.\nIn the revised Supplementary Information [ Section 7]\nTab. S2 Electrolyte utilization in VRFBs with different systems.\nAccumulated discharge Discharge capacity over\nVRFB system capacity over 400 cycles 400 cycles (Ah cycle-1\n(Ah) mol-1)\nCurrent\nadvanced\n225.10281 4.137919301\nsystem\nSystem with\n486.2741 8.938862132\nBSEs\nThe discharge capacity of electrolytes per cycle per mol (D CP / Ah mol⁻¹) is calculated as follows:\nD 1000\nD = AC (Eq. S24)\nCP C V E\nNO E C\nwhere D , C , V , and E represent the accumulated discharge capacity (Ah), the cycle number,\nAC NO E C\nthe electrolyte volume (mL), and the electrolyte concentration (M), respectively.\nThe capital cost reduction for a VRFB system using BSEs and NC700 can be calculated as\nbelow:\nC\nC r\n= ( C\nR -M\n+ C\nR -E\n) − ( C\nR -M\n M\nC R\n+ C\nR -E\n E\nC R\n) (Eq. S25)\nwhere, C is the capital cost reduction ratio; C and C are the cost ratios of membrane\nCr R-M R-E\n(10.08%) and electrolyte (62.79%), respectively, over the capital cost of a current advanced 1\nMW/4 MWh VRFB system;[32] M and E are the corresponding cost ratios of the membrane\nCR CR\nin the BSEs and NC700 based system [33] relative to a currently advanced VRFB system.\n2\n4\n3\n7\n2\n2\n9\n.2\n.8\n8\n2\n1\nCR\n4.137919\nE = (Eq. S27)\nCR 8.938862\nHence, the capital cost reduction for a VRFB system with BSEs compared to the current advanced\nVRFB system can be obtained:\n 472.281 4.137919\nC =(10.08+62.79)−10.08 +62.79 =41.76 (Eq. S28)\nCr  2329.825 8.938862\nThe specific costs of electrolyte and membrane in different VRFB systems are listed in Tab.\nS3.Tab. S3 Membrane and electrolyte costs as a proportion of the capital cost in 1 MW/4 MWh\nVRFBs systems. [S8, S9]\nDischarge\nMembrane to Electrolyte to\nMembrane Membrane capacity over\ncapital cost capital cost\ntype cost/ m2 ($) 400 cycles (Ah\nratio ratio\ncycle-1 mol-1)\nCurrent\nadvanced N212 2329.825 10.80% 4.14 62.79%\nsystem\nSystem with\nNC700 472.281 2.19% 8.94 29.08%\nBSEs\n[S8] Chen H, Zhang X, Wu S, et al. A comparative study of iron-vanadium and all-vanadium\nflow battery for large scale energy storage. Chem. Eng. J. 429: 132403 (2022).\n[S9] https://www.fuelcellstore.com/pfsa-d50u-proton-exchange-membrane-87010020?search\n= Nafion 212\n5. Adaptive maintenance of the balanced state.\nSince electrode aging shifts SOC windows and kinetics (main Fig. 4e–h; SI Fig. S19/S24),\ndemonstrate a closed-loop correction (periodic tiny additions of VO2+ or acid, or controlled\ndilution) that keeps the net flux near zero over long cycling, and report how often corrections are\nneeded. This would strengthen the practicality claim.\nResponse:\nThanks for your valuable suggestion. All VRFB tests reported here were conducted over 400 or\n1000 cycles without any corrective interventions during cycling. The observed capacity decay thus\nencompasses the natural, gradual aging process of the electrodes, which is an intrinsic component\nof the long-term performance in these systems. We have clarified this point in the revised\nmanuscript.\nIn the revised Manuscript [Section, Battery tests]\nAll VRFB and IVFB tests were conducted over 400 or 1000 cycles without any interventions\nduring cycling.\nMinor comments\na) Error bars and replicates. Many plots (e.g., Fig. 3c–f; Fig. 5a, b, e, f) lack uncertainty. Please\nreport n and add error bars or shaded confidence bands.\nResponse:\nWe thank the reviewer for raising this point. The efficiency data for VRFBs under different\nworking conditions, presented in Figs. 3c-e and 5b, f are based on triplicate measurements (Fig.\nR15 and R16). Note: The recording interval for all tests in this experiment was set to 1 s to mitigate\nsubstantial fluctuations in the calculated efficiency arising from the data.\nThese repeated experiments show that the voltage efficiency exhibits considerably less fluctuation\nthan the coulombic efficiency (Fig. R15c).\nIn Fig. 3f, the EIS spectrum of VRFBs with different electrolytes was measured once, but the\nquality of contact between the battery tabs and electrochemical fixtures was repeatedly verified\nduring tests. In Fig. 3f, the reduction in battery resistance stems from the dilution of the negative\nelectrolyte with 3.0 M H₂SO₄.\nIn the long-term cycling (Fig. 5a and e), the effects of BSEs in suppressing capacity decay were\nrepeatedly verified across different membranes (N212, N211, and NC700), underscoring their\nexcellent repeatability and applicability.\na\n)%\n(\nycneiciffe\ncibmoluoC\n99\n98\n97\n96\nT\ns\n150\nen siy (m A\nR ep\n200\n-2 cm )\neat tests\n250\n)%\n(\nycneiciffe\ncibmoluoC\nb98.7\n98.4\n98.1\n97.8\n97.5\n97.2\n1.2\n100 200\nR ep eat tests\n1.4 1.6\n2+ V O co n cen tra\n-2 @ m A cm\n3+ N 1.17 M V\n1.8 2.0\ntio n (M )\n)%\n(\nycneiciffe\ncibmoluoC\nc\n96\n93\n90\n87\n84\n81\nP\nR ep eat tests\n3.50+ 1.70 M V N 1.70 M\n3.50+ 1.70 M V N 1.17 M\n100 150\nC u rren t d en sity (m A\n3.50+ V\n3.50+ V\n200\n-2 cm )\n250\n100\n95\n90\n85\n80\n75\n)%\n(\nycneiciffe\negatloV\nFig. R15 Replicate measurements of coulombic and voltage efficiency in VRFBs with\ndifferent electrolytes. a, Comparison of coulombic efficiency in VRFBs with TEs and BSEs. b,\nPositive electrolyte concentration effects on the coulombic efficiency of VRFBs. c, Negative\nelectrolyte concentration effects on the coulombic/voltage efficiency of VRFBs.\n1 0\n9\n9\n9\n9\n0\n8\n6\n4\n2\n5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0\n)%\n(\ny\nc\nn\ne\nic\niffe\nc\nib\nm\no\nlu\no\nC\nC u r r e n t d e n siy (m A c m\nN 2 1 1 B S E s\nN 2 1 1 T E s\nR e p e a t te sts\n-2)\n9\n9\n9\n9\n9\n9\n8\n7\n6\n5\n5 0 1 0 0 1 5 0\nR e p e a\n2\nt te\n0 0\nsts\n)%\n(\ny\nc\nn\ne\nic\niffe\nc\nib\nm\no\nlu\no\nC\na b\nN\nN\nN\nCC1 7 0 0 B\n7 0 0 T\n1 7 T\nC u r r\nS E s\nE s\nE s\ne n t d e n siy (m A c m -2)\nFig. R16 Repeat tests of coulombic/voltage efficiency in VRFBs. a-b, Effects of BSEs on coulombic\nefficiency of the VRFB with N211 and NC700.\nb) UV–Vis quantification. Provide the calibration curves and fitting ranges for the A/B peaks\nused to back-calculate concentrations/valence (SI Fig. S17, S22).\nResponse:\nThanks for your suggestion. The UV-Vis calibration curves have been added to the supplementary\ninformation. The corresponding concentration ranges for V3+ and VO2+ are 0.296–1.954 mol L⁻¹\nand 0.452–2.322 mol L⁻¹, respectively, which encompass all concentrations investigated in this\nstudy.\nIn the revised Supplementary Information [Fig. S25].\na 1.5 b\nV3+ VO2+\n1.2 2.0\n)u )u Abs= 19.19746 C\na (\ne c n 0.9\nAbs= 8.09847 C a (\ne c n\n1.5\na b a b\nr o sb 0.6 r o sb 1.0\nA a\n0.5\n0.3\n0.0\n0.03 0.06 0.09 0.12 0.15 0.18 0.00 0.03 0.06 0.09 0.12\nConcentration (mol L-1) Concentration (mol L-1)\nFig. S25 UV–Vis calibration curves. a-b Calibration curves for V3+ and VO2+ after 15-fold dilution with\ndeionized water.\nc) Terminology and units. Standardize viscosity (mPa·s) and wording (replace “pulling acid”\nwith “diluting with 3 M H₂SO₄” per SI Sec. 1.1).\nResponse:\nThanks for your corrections. We have corrected the unit of viscosity to mPa·s in both the main\ntext and the supplementary information. The term \"pulling acid\" has been replaced throughout\nthe manuscript and supplementary information documents. The specific revisions are detailed\nbelow.\nIn the revised Manuscript [Fig. 1b and Fig. S5a]\nThe viscosity unit has been revised from cP to mPa·s.\nIn the revised Supplementary Information [Page 1, Section 1.1].\nBy solving Eq. S1, we prepared the 1.17 M V3+ and V3.5+ electrolytes through separate dilution of\n40 mL of 1.70 M electrolytes with 18.12 mL of 3 M H₂SO₄ each. Similarly, the 1.15 M V3.5+\nelectrolyte was obtained by diluting 40 mL of 1.70 M V3.5+ with 19.13 mL of 3 M H SO .\n2 4\nd) Operating conditions. State EIS SOC and temperature for each spectrum; specify flow-field\ngeometries per membrane in the main text (now mostly in SI §3).\nResponse:\nThanks for your suggestions. We have added the operating conditions and the specific flow-field\ngeometry of the graphite plates used with each membrane in the revised manuscript. The detailed\nrevisions are provided below.\nIn the revised Manuscript [Section, Characterization]\nAll the tests were conducted at room temperature.\nIn the revised Manuscript [Section, Battery tests]\nSpecifically, batteries with Nafion 212, 115, and 117 membranes employed 2.50 mm-thick graphite\nfelt electrodes and graphite bipolar plates with serpentine flow fields (SFFs). The battery with a\nNafion 211 membrane incorporated 1.75-mm-thick graphite felt electrodes and bipolar plates with\nserpentine flow fields SFFs. The battery with an NC700 was assembled with 0.70 mm-thick carbon\nclothes electrodes and bipolar plates with interdigitated flow fields.\ne) Data and code. Provide raw cycling/OCV/self-discharge data and the script used to construct\nthe net-flux map (main Fig. 2b) and cost model (Fig. 5h) as supplementary files.\nResponse:\nThanks for your suggestions. We have included data used in the main text, the script of Fig. 2b,\nand cost model of Fig. 5h in the revised supplementary information, as shown below.\nIn the revised Supplementary Information [Section 8].\nAll data for the figures in the main text and the script for Fig. 2b are available via the following\nlink.\nhttps://figshare.com/s/fdae8069727545502da4\nDear Editors and Reviewers,\nWe sincerely thank you for the valuable comments and positive feedback on our revised\nmanuscript entitled “Balanced-State Electrolytes Overcome Crossover in Vanadium Redox Flow Batteries”\n(NCOMMS-25-45545A). These comments and feedback are highly valuable and have greatly\nhelped us improve the paper. We considered these comments seriously and revised the manuscript\nand supplementary information based on them. The point-to-point responses to the comments are\nlisted as follows:\nComments from reviewers: in black\nAuthor response: in blue\nRevisions in manuscript, and SI: in red\nReviewer #1\nThe authors have put considerable effort into the revision, and the manuscript has been improved\nsubstantially. The authors showed convincing evidence of the practicability of BSEs and extra\nbenefit from concentrated positive side. The characterization of the V species in the membrane\nsupported these benefits. Now the manuscript can be published on Nature Communication, with\ntwo things that the authors can consider.\n1. Direct measurement of crossover\nThe authors successfully showed that SOC influences crossover, concentrations of V species\naffect diffusion coefficient. The authors also argued that measuring the crossover of V species is\nout of scope. The reviewer believes, however, measuring the crossover of these four species with\na few different concentrations can not only strengthen the scientific clearance, but can also\ndirectly support many statements with a decoupled clean data. Since the authors claimed that\ndiffusion is dominating the crossover (not electromigration), the measurement of such crossover\nbecomes very easy: one H-cell containing one kind of V source in one side, with supporting\nelectrolyte only (V-free) in the other, can give authors a convincing crossover flux, as a function\nof source concentration. Thus, the estimated diffusion coefficient can be calculated.\nResponse:\nWe sincerely thank the reviewer for these valuable comments. To address this concern, we have\nperformed vanadium ion diffusion tests using a flow battery cell assembled with a Nafion 212\nmembrane and two electrodes under conditions that closely approximate actual vanadium redox\nflow battery (VRFB) operating conditions. The diffusion test for V2+ was conducted under N\n2\nprotection to avoid the influence of air-induced V2+ oxidation (Eq. R1). As shown in Fig. R1a, the\nflux of V2+ exhibits the highest value followed by those of VO2+, VO+, and V3+, which is consistent\n2\nwith a previous report. [R1] Moreover, Fig. R1b-e demonstrates that decreasing the electrolyte\nconcentration profoundly reduces vanadium ion flux across the Nafion membrane, whereas\nincreasing the concentration markedly enhances the flux. These results confirm that the transport\nof vanadium ions across the Nafion membrane can be approximated by Fick’s law. [R2]\n4V2++O +4H+ →4V3+ +2H O (Eq. R1)\n2 2\n)mpp(\nnoitartnecnoC\n100\n80\n60\n40\n20\n0\nV\nV\nV\n2+\n+ O\n22+\nO3+\n40\nest T im\n50\ne (h )\n1.70 M\n60 70\n)mpp(\nnoitartnecnoC\n100\n80\n60\n40\n20\n0\n20\n1.70 M V\n1.17 M V\n30\n2+\n2+\nT\n40\nest T im\n50\ne (h )\n60 70\n)mpp(\nnoitartnecnoC\n60\n40\n20\n0\n20\n1.70 M V\n1.17 M V\n30\n3+\n3+\n50\ne (h )\n60 70\na b c\nd 60 e 60 fx10-6\n)m\np\n1 1 . . 7 9 0 1 M M V V O O 2 2 + + )m\np\n1 1 . . 7 9 0 1 M M V V O O 2 2 + + 1-\n2\n) n im\nm\n6 1 1 . . 1 9 7 1 M M 1.70 M\np ( n\no ita\rtn\necn o C\n4\n2\n0\n0\np ( n\no ita\rtn\necn o C\n4\n2\n0\n0\ntn c\ne\n(\niciffeo\nc n o isu\n4\n2\nffiD\n0 0 0\n20 30 40 50 60 70 20 30 40 50 60 70 V2+ V3+ VO2+ VO 2 +\nTest Time (h) Test Time (h)\nFig. R1 Vanadium ion diffusion tests across an N212 membrane. a, Diffusion fluxes of various\nvanadium ions in 1.70 M electrolyte. b-c, Effect of reducing electrolyte concentration from 1.70\nto 1.17 M on the diffusion fluxes of V2+ and V3+. d-e, Effect of increasing electrolyte concentration\nfrom 1.70 to 1.91 M on the diffusion fluxes of VO2+ and VO+. f Variation of vanadium ion diffusion\n2\ncoefficients with electrolyte concentration.\nThe diffusion coefficients of vanadium ions across a Nafion 212 membrane were calculated using\nthe following equation: [R1]\nl n\n\nC\nA\nC\n−\nA\nC\nB\n\n= D\nV\nA\nB\nL\nt (Eq. R2)\nwhere D is the diffusion coefficient (m2 s−1), A is the effective membrane area (m2), L is the\nmembrane thickness (m), C is the vanadium ion concentration on the enrichment side\nA\n(mol L−1), C is the vanadium ion concentration on the deficiency side (mol L−1), and t is the test\nB\ntime (s). In this calculation, the volume of deficiency side (V ) and C were assumed constant.\nB A\nThe resulting values (Fig. R1f) exhibit good agreement with independent measurements reported\npreviously. [R1] These results further demonstrate that modulating the concentration of vanadium\nions alters their diffusion rate across the Nafion membrane. We have added these experiments to\nthe revised manuscript and the supplementary information.\nIn these experiments, a flow battery cell equipped with a Nafion 212 membrane and two electrodes\nwith a size of 40.00 × 40.00 mm2 was employed. For each test, 20 mL of vanadium electrolyte was\ncirculated on one side of the cell, while an equimolar MgSO solution in 3 M H SO served as the\n4 2 4\ncounter electrolyte on the opposite side. Both solutions were pumped at a flow rate corresponding\nto 51 rpm using a Longer BT100-2J peristaltic pump.\nThe paired electrolyte compositions were as follows:\n1) Standard concentration (1.70 M): 1.70M V2+, V3+, VO2+, or VO+ in 3 M H SO versus 1.70\n2 2 4\nM MgSO in 3 M H SO .\n4 2 4\n2) Reduced concentration (1.17 M): 1.17 M V2+or V3+ in 3 M H SO versus 1.17 M MgSO in\n2 4 4\n2 4\n3) Increased concentration (1.91 M): 1.91 M VO2+or VO+ in 3 M H SO versus 1.91 M MgSO\n2 2 4 4\nin 3 M H SO .\n2 4\nVanadium ion concentrations were determined using an Inductively Coupled Plasma–Optical\nEmission Spectrometer (Avio-200, PerkinElmer). Samples (0.2 ml) were withdrawn and diluted\n7500-fold (for vanadium electrolytes) or 750-fold (for counter solutions) with deionized water\nprior to analysis.\n[R1] Sun C, Chen J, Zhang H, Han X, Luo Q. Investigations on transfer of water and vanadium\nions across Nafion membrane in an operating vanadium redox flow battery. J. Power\nSources. 195(3): 890-897 (2010)\n[R2] Sukkar T, Skyllas-Kazacos M. Membrane stability studies for vanadium redox cell\napplications. J. Appl. Electrochem. 34: 137-145 (2004)\nIn the revised manuscript [Line 250, Page 11]\nThe effects of varying electrolyte concentration on the crossover flux and diffusion coefficients of\nvanadium ions across the Nafion membrane were confirmed by diffusion experiments (Fig. S16).\nIn the revised supplementary information [Line 293, Page 15]\n)mpp(\nnoitartnecnoC\n100\n80\n60\n40\n20\n0\nV\nV\nV\n2+\n+ O\n22+\nO3+\n40\nest T im\n50\ne (h )\n1.70 M\n60 70\n)mpp(\nnoitartnecnoC\n100\n80\n60\n40\n20\n0\n20\n1.70 M V\n1.17 M V\n30\n2+\n2+\nT\n40\nest T im\n50\ne (h )\n60 70\n)mpp(\nnoitartnecnoC\n60\n40\n20\n0\n20\n1.70 M V\n1.17 M V\n30\n3+\n3+\n50\ne (h )\n60 70\na b c\nd 60 e 60 fx10-6\n)m\np\n1 1 . . 7 9 0 1 M M V V O O 2 2 + + )m\np\n1 1 . . 7 9 0 1 M M V V O O 2 2 + + 1-\n2\n) n im\nm\n6 1 1 . . 1 9 7 1 M M 1.70 M\np ( n\no ita\rtn\necn o C\n4\n2\n0\n0\np ( n\no ita\rtn\necn o C\n4\n2\n0\n0\ntn c\ne\n(\niciffeo\nc n o isu\n4\n2\nffiD\n0 0 0\n20 30 40 50 60 70 20 30 40 50 60 70 V2+ V3+ VO2+ VO 2 +\nTest Time (h) Test Time (h)\nFig. S16 Vanadium ion diffusion tests across an N212 membrane. a, Diffusion fluxes of various\nvanadium ions in 1.70 M electrolyte. b-c, Effect of reducing electrolyte concentration from 1.70\nto 1.17 M on the diffusion fluxes of V2+ and V3+. d-e, Effect of increasing electrolyte concentration\nfrom 1.70 to 1.91 M on the diffusion fluxes of VO2+ and VO+. f Variation of vanadium ion diffusion\n2\ncoefficients with electrolyte concentration.\nAs shown in Fig. S16a, the flux of V2+ exhibits the highest value followed by those of VO2+, VO+,\n2\nand V3+, which is consistent with a previous report.S2 Moreover, Fig. S16b-e demonstrates that\ndecreasing the electrolyte concentration profoundly reduces vanadium ion flux across the Nafion\nmembrane, whereas increasing the concentration markedly enhances the flux. These results\nconfirm that the transport of vanadium ions across the Nafion membrane can be approximated by\nFick’s law.S7\nThe diffusion coefficients of vanadium ions across a Nafion 212 membrane were calculated using\nthe following equation:S2\nl n\n\nC\nA\nC\n−\nA\nC\nB\n\n= D\nV\nA\nB\nL\nt (Eq. S22)\nwhere D is the diffusion coefficient (m2 s−1), A is the effective membrane area (m2), L is the\nmembrane thickness (m), C is the vanadium ion concentration on the enrichment side\nA\n(mol L−1), C is the vanadium ion concentration on the deficiency side (mol L−1), and t is the test\nB\ntime (s). In this calculation, the volume of deficiency side (V ) and C were assumed constant.\nB A\nThe resulting values (Fig. S16f) exhibit good agreement with independent measurements reported\npreviously.S2 These results further demonstrate that modulating the concentration of vanadium ions\nalters their diffusion rate across the Nafion membrane.\nIn these experiments, a flow battery cell equipped with a Nafion 212 membrane and two electrodes\nwith a size of 40.00 × 40.00 mm2 was employed. The diffusion test for V2+ was conducted under\nN protection to avoid the influence of air-induced V2+ oxidation. For each test, 20 mL of vanadium\n2\nelectrolyte was circulated on one side of the cell, while an equimolar MgSO solution in 3 M H SO\n4 2 4\nserved as the counter electrolyte on the opposite side. Both solutions were pumped at a flow rate\ncorresponding to 51 rpm using a Longer BT100-2J peristaltic pump.\nThe paired electrolyte compositions were as follows:\n1) Standard concentration (1.70 M): 1.70M V2+, V3+, VO2+, or VO+ in 3 M H SO versus 1.70\n2 2 4\nM MgSO in 3 M H SO .\n4 2 4\n2) Reduced concentration (1.17 M): 1.17 M V2+or V3+ in 3 M H SO versus 1.17 M MgSO in\n2 4 4\n2 4\n3) Increased concentration (1.91 M): 1.91 M VO2+or VO+ in 3 M H SO versus 1.91 M MgSO\n2 2 4 4\nin 3 M H SO .\n2 4\nVanadium ion concentrations were determined using an Inductively Coupled Plasma–Optical\nEmission Spectrometer (Avio-200, PerkinElmer). Samples (0.2 ml) were withdrawn and diluted\n7500-fold (for vanadium electrolytes) or 750-fold (for counter solutions) with deionized water\nprior to analysis.\n2. The accuracy of the title\nAlthough the authors showed that the penalty from the crossover in Fe-V RFBs can be overcame\nusing the same strategy, this strategy does not really solve the major problem caused by\ncrossover in asymmetric RFBs such as Fe-Cr, Fe-V batteries. Ideally, these batteries should have\nFe and Cr separated, since the existence of crossovered Fe into the other side introduces severe\nHER side reactions. Authors mixed Fe-V making an after-crossover electrolyte is a decent\ndemonstration of BSEs, but such batteries may not be commercially favored (~50% of the V-Fe\ncapacity wasted, co-existence Fe in V side). BSEs can still be useful for batteries using the same\nredox core in both sides, which is VRFB the authors focused on. The authors may consider\nadjusting the tile into \"Balanced-State Electrolytes Overcome Crossover in Vanadium Redox\nFlow Batteries\", which is more accurate and straightforward.\nResponse:\nWe sincerely thank the reviewer for the valuable comments. We have changed the title to\n“Balanced-State Electrolytes Overcome Crossover in Vanadium Redox Flow Batteries” in the\nrevised manuscript and supplementary information.\nIn the revised manuscript [Title]\nBalanced-State Electrolytes Overcome Crossover in Vanadium Redox Flow Batteries\nIn the revised supplementary information [Title]\nBalanced-State Electrolytes Overcome Crossover in Vanadium Redox Flow Batteries\nReviewer #2\nThe authors have addressed my comments appropriately, and the manuscript has improved as a\nresult. The remaining issues are minor and can be handled during the editorial process.\nResponse:\nWe are grateful to the reviewer for their recognizing the merit of our work.\nReviewer #3\nThank you for the thorough revision and detailed point-by-point response. The manuscript is\nsignificantly clearer and more convincing after revision.\nThe most important improvement is the explicit “balanced state/BSE determination” workflow\nnow presented in the Methods and expanded in the SI. This makes the approach far more\nreproducible and portable across membranes and operating conditions. I also appreciate the\naddition of a physics-based transport model (COMSOL/Nernst–Planck) to place the performance\ntrends and crossover mitigation into a mechanistic framework; this directly addresses my\nprevious concern that the narrative relied too heavily on simplified interpretations of MD.\nFinally, several presentation issues have been handled appropriately (e.g., removal of a non-\ninformative panel, clearer discussion of side reactions and their impact on average valence, and\nnew experimental evidence supporting ion–sulfonate interactions). I have no further major\nconcerns.\nResponse:\nWe really appreciate the reviewer’s positive comments on our work."}]

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