4.1. Capacity Decay during Long-Term Cycling
a includes the discharge capacity as a function of cycle number for the first 30 cycles for different pure cast film and GORE-SELECT®
membranes. In Figure 2
a, the capacity decay data for the pure cast membrane with EW800 has only been reported for the first 15 cycles since the cell capacity became unstable due to membrane degradation. Figure 2
b shows the theoretical capacity utilization for different membranes over the same duration. It is important to note that the theoretical capacity is determined using Cell 1 (from Figure 1
) while charging the initial electrolyte; half of the total charge transferred to the electrolyte during the initial charge is evaluated as the theoretical capacity. Since both electrolytes were similar (1.5 mol/L V(IV) as VOSO4
O (Alfa Aesar) dissolved in 3.3 mol/L H2
), half of the total initial charge corresponds to the full capacity window for an operating VRFB.
As shown in Figure 2
a,b, the capacity and theoretical capacity utilization both decrease during cycling. The theoretical capacity utilization is an important metric for assessing overall vanadium ion utilization within a VRFB cell. Due to imposing voltage limits while maintaining cycling current (in this work, 0.2 V and 1.9 V), the theoretical capacity utilization is always lower than 100% since the total content of all dissolved vanadium ions cannot be utilized. The properties of the ion-exchange membrane directly affect the theoretical capacity utilization through the crossover rate. A higher rate of crossover decreases the open-circuit voltage (OCV) of the cell and consequently results in reaching the voltage limits sooner during a cycle, all other contributing parameters being equal. The theoretical discussion of such an effect is the focus of a previous publication [27
]. According to Figure 2
b, at the end of 30 cycles, the reinforced/EW1100 exhibits the highest magnitude of theoretical capacity utilization of ~64%, and the non-reinforced/EW800 shows the lowest theoretical capacity utilization (~59%, at the end of just 15 cycles). Furthermore, as seen in Figure 2
b, increased equivalent weight results in increased theoretical capacity utilization for both reinforced and non-reinforced membranes. Comparing similar equivalent weights of non-reinforced and reinforced membranes, reinforcement increases the theoretical capacity utilization. For example, the EW1100 membrane showed 2% greater capacity utilization resulting from reinforcement; for the EW950 membrane, reinforcement increases the theoretical capacity utilization by 3% at the end of 30 cycles compared to non-reinforced.
includes the discharge capacity decay for different membranes as a function of cycle number and as a function of time. Here, the capacity decay is defined as the ratio of the decrease in discharge capacity to the initial discharge capacity of the battery.
According to Figure 3
a, the reinforced EW1100 membrane exhibits the lowest rate of capacity decay (~22% at the end of 30 cycles), and non-reinforced EW800 shows the highest rate of capacity decay (~24% at the end of just 15 cycles). It is important to note that, although the number of cycles for all of the experimental membranes was 30 (except non-reinforced EW800), the total cycling time for the different configurations varied due to different ohmic overpotentials imposed as a function of membrane conductivity. However, in general, cycling experiments were conducted over the course of approximately 100 h. Similar to Figure 3
a, the reinforced membrane with EW1100 exhibits the lowest rate of capacity decay (~22% at the end of ~100 h), and non-reinforced EW800 results in the highest rate of capacity decay (~24% at the end of ~59 h) as a function of time.
According to Figure 3
, increased equivalent weight mitigates capacity decay for both non-reinforced and reinforced membranes. As shown in Figure 3
, increasing the equivalent weight from 950 to 1100 g·mol−1
decreases the capacity decay by ~3% at the end of 30 cycles. The effect on capacity decay is more pronounced when increasing equivalent weight from 800 to 950 g·mol−1
for reinforced membranes in which the capacity decay decreased by 7% at the end of 30 cycles. Furthermore, it can be observed from Figure 3
that reinforcement decreases the capacity decay for identical EW membranes. Comparing the non-reinforced and reinforced membranes, for the case of EW1100 and EW950, reinforcement decreased the capacity decay by ~1.5% at the end of 30 cycles.
The observed differences in capacity decay are primarily due to vanadium crossover since the other components (electrodes, flow fields and electrolyte) were kept consistent. Figure 4
a includes coulombic efficiency for the membranes in this work. The coulombic efficiency was calculated here as the ratio of discharge capacity over charge capacity at 100 mA/cm2
. The coulombic efficiency for all membranes tested in this work exceeded 95%. Figure 4
b shows the voltage efficiency for the membranes over a range of current density. Voltage efficiency is defined here as the ratio of average discharging voltage over the average charging voltage up to 150 mA/cm2
. As shown in Figure 4
b, increasing the current density decreases the voltage efficiency for all experiments; voltage efficiencies exceeded 75% at 150 mA/cm2
. Figure 4
c shows polarization curve results at 50% SoC for cells based on each membrane. Figure 4
d includes power density data for membranes as a function of current density for discharging conditions. As shown, a power density of 181–190 mW/cm2
was achieved at a discharge current density of 150 mA/cm2
. Furthermore, it is important to note for clarity that the polarization curves and power density curves are shown just for discharge conditions since the charge and discharge cases were nearly symmetric.
It is important to note that, according to Figure 4
a, coulombic efficiency for different membranes does not exhibit a direct correlation to increased equivalent weight or the addition of membrane reinforcement. The primary reason for such a trend lies in the definition of coulombic efficiency for VRFB systems. Coulombic efficiency is defined as the ratio of the discharge capacity over charge capacity [36
]; therefore, for a membrane, both of these quantities can be small compared to the theoretical capacity while the cell still achieves high coulombic efficiency. Therefore, comparing Figure 4
a with Figure 3
, capacity fade as a function of cycle number or/and capacity decay as a function of time is a better metric to assess the viability of a particular membrane. Such a metric better represents superior ionic selectivity and the reduction of the vanadium crossover rate.
According to Figure 4
, voltage efficiency and polarization curves do not show a linear correlation to either increased equivalent weight and/or membrane reinforcement. An ideal ion-exchange membrane would decrease vanadium ion crossover and ohmic overpotential simultaneously. However, if the reduction of vanadium ion crossover via use of a particular membrane is obtained at the cost of increased ohmic overpotential, the polarization curves and voltage efficiency (consequently the power density) show a negative impact, as evidenced by Figure 4
b–d. This observation has been further clarified through measuring area-specific resistance (ASR) associated with each membrane.
includes pre- and post-cycling ASR values for each pair of membranes at 100 mA·cm2
(see Supplemental Figure S2
). For all experimental membranes, the ASR value increased during cycling (~9%–18%). For non-reinforced and reinforced membranes, increasing the equivalent weight yielded increased ASR: increasing equivalent weight from 800 to 950 g·mol−1
increased the ASR by ~36%, and increasing the equivalent weight from 950 to 1100 g·mol−1
increased the ASR by another ~16%. Considering the reinforced membranes, increasing the equivalent weight from 800 to 950 g·mol−1
increased the ASR by ~43%, while increasing the equivalent weight from 950 to 1100 g·mol−1
increased the ASR by a similar ~16%.
Furthermore, across all equivalent weights, reinforcement increased the ASR. Comparing the non-reinforced with reinforced membranes, for the EW1100 and EW950 sets, the ASR increases by ~18% due to membrane reinforcement, and for the EW800 pair, the increase in ASR is ~13%. In summary, the non-reinforced EW800 exhibits the lowest (0.15 Ω·cm2) and the reinforced EW1100 results in the highest value (0.28 Ω·cm2) of ASR.
A comparison of results in Table 1
and Figure 3
reveals that both of these membrane modification techniques (reinforcement and increased equivalent weight) resulted in decreased capacity decay; therefore, this simultaneous mixed effect is the primary reason for the trend observed for polarization curves, coulombic and voltage efficiencies and the power density graphs shown in Figure 4
. This mixed effect has been further clarified in the next section. The increase in ASR during cycling results in an increase in ohmic overpotential as tabulated in Table 1
for the case of constant discharge at 100 mA·cm−2
4.2. Crossover of Vanadium Ions
The major source for discharge capacity decay during cycling (as shown in Figure 3
) is the undesired transport of vanadium ions through the ion-exchange membrane. In general, concentration gradient and electric field are the main driving forces for vanadium ion crossover. In this work, we have investigated the crossover of vanadium ions as a function of concentration gradient only. Among vanadium ions, concentration gradient-driven crossover has been assessed via focusing on the transport of V(IV) since the electrolyte preparation does not require any additional charge/discharge processes, ensuring uniform electrolyte composition.
shows the concentration of vanadium V(IV) ion on the vanadium-deficient side over a twenty-four-hour time period; the crossover behavior observed here corresponds to conditions at SoC = 0% on the positive side. The UV-Vis spectra were recorded at 6-h intervals (five sampling spectra) for each membrane, and the recorded spectra were utilized to calculate the concentrations shown in Figure 5
As shown in Figure 5
, the concentrations of diffused V(IV) to the vanadium-deficient side differ as a function of membrane composition. The maximum concentration of diffused V(IV) at the end of a 24-h crossover test was measured for the non-reinforced membrane with EW800 (~0.114 mol·L−1
), and the minimum concentration was achieved by reinforced membrane with EW1100 (~0.023 mol·L−1
). The concentration of diffused vanadium V(IV) ions shown in Figure 5
can be used to obtain the permeability values for different membrane morphologies using the slope of a semi-natural log plot, formulated in Equation (7).
As indicated by Equation (7), the slope of semi-natural log plots (see Supplemental Figure S3
) can be used to calculate permeability values; here, it is necessary to incorporate the expanded thickness of the membranes in the modeling framework. To this end, a solution of aqueous sulfuric acid and vanadium (3.3 mol/L acid, 1.5 mol/L vanadium (V(III)/V(IV) mix) was prepared, and the membranes were soaked in this solution for more than a week at room temperature. This composition was chosen to reflect the only stable vanadium species that can coexist in the membrane; V(II) and V(V) are expected to react with V(III) and V(IV). While the external solution is known to influence membrane properties, it is the internal environment that defines membrane properties. Figure 6
shows the thickness of the membranes measured after soaking in electrolyte. To measure the thickness, three sets of measurements were conducted using a digital micrometer (Mitutoyo, Kawasaki, Japan), and each reported thickness value was the average of all measurements; error bars were calculated based on the deviation of maximum and minimum thickness measurements from the average value.
As shown in Figure 6
, the nominal thickness for all membranes tested was 30 μm. However, expansion (degree of swelling) differed significantly as a function of membrane properties. As a general trend, for both non-reinforced and reinforced membranes, the expansion was greater for higher equivalent weights. For example, among the non-reinforced membranes, EW1100 exhibits ~62% expansion in the through-plane direction, and EW800 shows ~35%. However, the reinforced EW1100 membrane expanded by ~29%, and reinforced EW800 expanded by ~16.5%. As expected, the addition of reinforcement significantly decreases through-plane expansion. The quantitative details of the cation exchange membranes tested in this work are shown in Table 2
includes the resultant permeability values, based on the linear fits formulated in Equation (7). It is important to note that, for calculating the permeability values of V(IV) ions for each membrane, the thickness of the membranes equilibrated with the aqueous vanadium and sulfuric acid (as tabulated in Table 2
) was utilized.
According to Figure 7
, it is clear that, for both non-reinforced and reinforced membranes, increasing the equivalent weight decreases the V(IV) ion permeability. For non-reinforced membranes, decreasing the equivalent weight from 1100 down to 950 g·mol−1
increases the V(IV) permeability by 42%, and further decreasing the equivalent weight to 800 g·mol−1
results in 155% greater V(IV) permeability. In comparison, for reinforced membranes, decreasing the equivalent weight from 1100 down to 950 g·mol−1
increases the V(IV) permeability by 39%, and further decreasing the equivalent weight to 800 g·mol−1
further increases the V(IV) permeability by 109%.
includes the numerical values of V(IV) permeability for each ion-exchange membrane, as well as the diffusive transport parameter, which has been formulated based on Equation (8). The diffusive transport parameter is utilized to calculate the concentration-gradient-induced crossover flux according to the mathematical formulation provided in our previous publication [15
It is also important to quantify the effect of reinforcement on the reduction of V(IV) permeability. Figure 8
is a plot of V(IV) ion permeability and ASR as a function of equivalent weight. When comparing similar equivalent weights, reinforcement decreases the V(IV) permeability for all three compositions considered in this work. However, the effect is not linear. As shown in Figure 8
, the observed trend for the ASR is the opposite of V(IV) permeability and exhibits an increase as a function of increased equivalent weight and reinforcement.
For the EW800 membranes, reinforcement decreased the V(IV) permeability by ~47%; for EW950, reinforcement decreased the V(IV) permeability by ~35%; and for EW1100, the reduction of V(IV) permeability as a function of membrane reinforcement was ~33%.
As discussed earlier, the primary reason for capacity fade as a function of cycling was assumed to be the crossover of vanadium ions. Therefore, to validate this assumption, it is critical to investigate any correlation between the discharge capacity decay and the V(IV) ion permeability values. As shown in Figure 3
, the discharge capacity of cells with different configurations decreased as a result of cycling regardless of the type of membrane, but with different rates. No contribution is expected from side reactions since the voltage limits avoided their onset and also due to the lack of observed gas generation. In addition, component degradation should be negligible or consistent since all tests were conducted under identical conditions. Thus, the crossover of vanadium ions should be the primary driver of capacity fade.
includes the discharge capacity decay at the end of 30 cycles (or approximately 90 h) for non-reinforced and reinforced membranes as a function of vanadium V(IV) permeability. In Figure 9
, the discharge capacity decay data associated with non-reinforced EW800 have been extrapolated since the cycling test for this membrane was only conducted for the first 15 cycles.
As is evident in Figure 9
, there exists a strong correlation between the discharge capacity decay at the end of cycling with V(IV) permeability values. According to Figure 9
, for non-reinforced membranes, increasing the equivalent weight from 800 to 950 g·mol−1
, decreases the discharge capacity decay (after 90 h) from 53%–25% while decreasing the V(IV) permeability by 61%, and further increasing the equivalent weight to 1100 g·mol−1
decreases the discharge capacity decay to 22%, while the V(IV) permeability decreases by 30%.
A similar trend was observed for reinforced membranes: increasing the equivalent weight from 800 to 950 g·mol−1 decreases the discharge capacity decay from 31% down to 24%, while decreasing the V(IV) permeability by 52%; further increasing the equivalent weight from 950 to 1100 g·mol−1 decreases the discharge capacity decay to 21%, while decreasing the V(IV) permeability by 28%.
Finally, it is important to quantify vanadium crossover as a function of membrane thickness. As shown in Figure 6
, the ion-exchange membranes selected for this work all had a nominal thickness of 30 μm; however, when soaked in a solution of aqueous sulfuric acid and vanadium, they swelled as a function of membrane reinforcement and equivalent weight. Given the permeability and swelling responses to EW, the following figure compares vanadium ion permeability (V(IV)) as a function of through-plane membrane swelling.
As shown in Figure 10
, V(IV) permeability decreases for both the pure cast film and GORE-SELECT®
membranes as a function of increased through-plane membrane swelling. As tabulated in Table 2
, increased equivalent weight increases through-plane swelling, and this results in reduced permeability for V(IV) ion. Therefore, an inverse correlation exists between swelling and permeability for pure cast film and GORE-SELECT®
membranes. The likely cause of this relationship is greater membrane thickness impeding V(IV) crossover.
A physicochemical description of the two distinct trends observed in Figure 8
is also of interest. First, as shown in Figure 8
, increased equivalent weight results in decreased V(IV) permeability for both pure cast film and reinforced membranes. A macroscopic mathematical model based on conservation of mass, charge, momentum, and energy along with a meso-scale model based on dissipative particle dynamics (DPD) has previously been used to assess vanadium ion crossover behavior due to a concentration gradient [15
]. Based on the macroscopic model of vanadium ion transport through polymeric membranes, vanadium crossover under the concentration gradient can be best described by the diffusive transport parameter [15
]. As included in Table 3
, the diffusive transport parameter decreases with increased equivalent weight. With a concentration-gradient-induced driving force for vanadium ion crossover, increased equivalent weight results in greater membrane swelling (as shown in Figure 6
), resulting in higher diffusion resistance via increased path-length for the transport of vanadium ions; accordingly, the diffusive transport parameter is decreased. A meso-scale model description of vanadium ion transport has also been formulated by others based on DPD simulations, and it shows that increasing equivalent weight results in a stronger vanadium-sulfonate bond and accordingly more structured configuration. The stronger anion-cation interaction (V(IV) and sulfonate) as a function of increased equivalent weight, thus results in decreased diffusivity of vanadium ions [37
As shown in Figure 8
, membrane reinforcement results in decreased vanadium ion permeability for all equivalent weights. This observation is likely due to water transport behavior through the membranes; advection of vanadium ions through the membrane is influenced by water transport. It is well-established that water permeability through the membranes is both in equilibrium (solubility) and non-equilibrium (diffusivity) and is a strong function of the porous structure of the membrane [38
]. Water transport has two distinct steps including surface adsorption (permeation through the surface) and internal absorption and transport across the membrane (diffusion); accordingly, the water transport rate is governed by water uptake and release rates [40
]. The implementation of reinforcement decreases vanadium ion permeability by acting as a molecular sieve in the porous structure of the membrane [39
]. The porous structure of the reinforced layer allows for the transport of water molecules while decreasing the transport of vanadium ions (V(IV)) by size exclusion. Accordingly, the contribution of vanadium ion transport via advection increases with decreased equivalent weight. Therefore, as shown in Figure 8
, the inclusion of reinforcement results in a sharper decrease in vanadium permeability for lower equivalent weight membranes.