Correction: Duburg et al. Composite Polybenzimidazole Membrane with High Capacity Retention for Vanadium Redox Flow Batteries. Molecules 2021, 26, 1679

The authors wish to make the following changes to their paper [1].

2. Results

Original:

Table 1. V(IV) diffusion through NR212, FAP-450, and PP-PBI.

Name	Slope [V(IV)] vs. t (M∙L−1∙h−1)	V(IV) Diffusion (cm2∙min−1)
NR212	(650 ± 8) × 10−6	(744 ± 9) × 10−8
FAP-450	(259 ± 1) × 10−6	(351 ± 1) × 10−8
PP-PBI	(18 ± 2) × 10−6	(14 ± 1) × 10−8

Table 1. V(IV) diffusion through NR212, FAP-450, and PP-PBI.

Name	Slope [V(IV)] vs. t (M∙L−1∙h−1)	V(IV) Diffusion (cm2∙min−1)
NR212	(650 ± 8) × 10−6	(744 ± 9) × 10−8
FAP-450	(259 ± 1) × 10−6	(351 ± 1) × 10−8
PP-PBI	(18 ± 2) × 10−6	(14 ± 1) × 10−8

To be replaced with:

Table 1. V(IV) diffusion through NR212, FAP-450, and PP-PBI.

Table 1. V(IV) diffusion through NR212, FAP-450, and PP-PBI.

Name	Slope [V(IV)] vs. t (M∙L−1∙h−1)	V(IV) Diffusion (cm2∙min−1)
NR212	(650 ± 8) × 10−6	(744 ± 9) × 10−9
FAP-450	(259 ± 1) × 10−6	(351 ± 1) × 10−9
PP-PBI	(18 ± 2) × 10−6	(14 ± 1) × 10−9

Explanation for the correction:

We observed an error in the calculations of the vanadium (IV) diffusion values; as a result of this, the order of magnitude of these values has been corrected to 10⁻⁹ cm²∙min⁻¹ from 10⁻⁸ cm²∙min⁻¹.

3. Discussion

Original:

V(IV) diffusion through the composite PP-PBI membrane was found to be the lowest ((14 ± 1) × 10⁻⁸ cm²∙min⁻¹), while commercial Nafion^® NR212 suffered the highest V(IV) diffusion ((744 ± 9) × 10⁻⁸ cm²∙min⁻¹),

To be replaced with:

V(IV) diffusion through the composite PP-PBI membrane was found to be the lowest ((14 ± 1) × 10⁻⁹ cm²∙min⁻¹), while commercial Nafion^® NR212 suffered the highest V(IV) diffusion ((744 ± 9) × 10⁻⁹ cm²∙min⁻¹).

Explanation for the correction:

We observed an error in the calculations of the vanadium (IV) diffusion values; as a result of this, the order of magnitude of these values has been corrected to 10⁻⁹ cm²∙min⁻¹ from 10⁻⁸ cm²∙min⁻¹.

4. Materials and Methods

Original:

The dry weight of the membrane (w_dry) was obtained after drying it under vacuum at 55 °C for 22 h. The weight measurement was carried out in a closed vial to limit the uptake of moisture from the air. Then, the weight of the membrane in the wet state (w_wet) was determined after immersion for 2 days in deionized water or in 1.6 M vanadium in 2 M H₂SO₄ and 0.05 M H₃PO₄ electrolyte (SOC −50%, 3.5 oxidation state, Oxkem, Reading, United Kingdom), followed by the removal of droplets on the surface with a tissue. In this case, the wet weight was measured in a vial to reduce the evaporation of water from the membrane. Lastly, water and electrolyte uptake of pristine m-PBI and of commercial membranes NR212 and FAP-450 was calculated according to Equation (1).

$$\mathrm{Uptake}=\frac{w_{\mathit{wet}}-w_{\mathit{dry}}}{w_{\mathit{dry}}}·100\%$$

(1)

To be replaced with:

The dry weight of the membrane (m_dry) was obtained after drying it under vacuum at 55 °C for 22 h. The weight measurement was carried out in a closed vial to limit the uptake of moisture from the air. Then, the weight of the membrane in the wet state (m_wet) was determined after immersion for 2 days in deionized water or in 1.6 M vanadium in 2 M H₂SO₄ and 0.05 M H₃PO₄ electrolyte (SOC −50%, 3.5 oxidation state, Oxkem, Reading, United Kingdom), followed by the removal of droplets on the surface with a tissue. In this case, the wet weight was measured in a vial to reduce the evaporation of water from the membrane. Lastly, water and electrolyte uptake of pristine m-PBI and of commercial membranes NR212 and FAP-450 was calculated according to Equation (1).

$$\mathrm{Uptake}=\frac{m_{\mathit{wet}}-m_{\mathit{dry}}}{m_{\mathit{dry}}}·100\%$$

(1)

Explanation for the correction:

The change described above has been made to be in line with the commonly used scientific unit of mass (m).

Original:

The measurements were carried out by filling two quartz cuvettes (Hellma Analytics, Zumikon, Switzerland) with 2.5 mL of solution from the MgSO₄ flask. Each time, the measured solution was transferred back to the VOSO₄ flask to avoid significant volume changes.

To be replaced with:

The measurements were carried out by filling two quartz cuvettes (Hellma Analytics, Zumikon, Switzerland) with 2.5 mL of solution from the MgSO₄ flask. Each time, the measured solution was transferred back to the MgSO₄ flask to avoid significant volume changes.

Explanation for the correction:

The correction described above has been made as the measured solutions were transferred back into the MgSO₄ flask and not the VOSO₄ flask.

Original:

Lastly, the change in weight (∆w) was calculated according to Equation (4). In Equation (4), w_i and w_f are the initial and final weight, respectively.

$$\Delta w=\frac{wf-wi}{wi}·100\%$$

(4)

To be replaced with:

Lastly, the change in weight (∆m) was calculated according to Equation (4). In Equation (4), m_i and m_f are the initial and final weight, respectively.

$$\Delta m=\frac{mf-mi}{mi}·100\%$$

(4)

Explanation for the correction:

The change described above has been made to be in line with the commonly used scientific unit of mass (m).

Original:

Efficiencies and discharge capacity are calculated according to Equations (5)–(8). In Equations (5)–(7), Q_ch and Q_dis are the charges for the discharge and the charge process, while V_dis and V_ch are the discharge and charge volumes. In Equation (8), Q_theoretical is the theoretical charge, n is the number of moles, F is the Faraday constant (96,485 C∙mol⁻¹), and z is the charge.

$$\eta C=\frac{Q_{\mathit{dis}}}{Q_{\mathit{ch}}}·100\%$$

(5)

$$\eta V=\frac{V_{\mathit{dis}}}{V_{\mathit{ch}}}·100\%$$

(6)

$$\eta E=(\eta C·\eta V)·100\%$$

(7)

$$Q_{\mathit{theoretical}}=I·t=n·(F·z)$$

(8)

To be replaced with:

Efficiencies and discharge capacity are calculated according to Equations (5)–(8). In Equations (5)–(7), Q_ch and Q_dis are the charges for the discharge and the charge process, while $\overline{U}$_ch and $\overline{U}$_dis are the average voltages during charge and discharge, respectively. In Equation (8), Q_theoretical is the theoretical charge, n is the number of moles, F is the Faraday constant (96,485 C∙mol⁻¹), and z is the number of electrons associated with the electrochemical reaction.

$$\eta C=\frac{Q_{\mathit{dis}}}{Q_{\mathit{ch}}}·100\%$$

(5)

$$\eta V=\frac{{\overline{U}}_{\mathit{dis}}}{{\overline{U}}_{\mathit{ch}}}·100\%$$

(6)

$$\eta E=(\eta C·\eta V)·100\%$$

(7)

$$Q_{\mathit{theoretical}}=I·t=n·(F·z)$$

(8)

Explanation for the correction:

The changes described above were made to avoid confusion between the average voltages in the cell ($\overline{U}$) and the unit volt (V). Furthermore, the description of this symbol was corrected to the average voltage instead of volume, which was a typing mistake. The last change was made to provide a clearer description of the symbol z as “charge” did not provide the desired clarity.

5. Conclusions

Original:

This asymmetric composite membrane showed the lowest V(IV) diffusivity ((14 ± 1) × 10⁻⁸ cm²∙min⁻¹) as compared to the commercial Nafion^® NR212 and Fumasep^® FAP-450, (744 ± 9) × 10⁻⁸ and (351 ± 1) × 10⁻⁸ cm²∙min⁻¹, respectively.

To be replaced with:

This asymmetric composite membrane showed the lowest V(IV) diffusivity ((14 ± 1) × 10⁻⁹ cm²∙min⁻¹) as compared to the commercial Nafion^® NR212 and Fumasep^® FAP-450, (744 ± 9) × 10⁻⁹ and (351 ± 1) × 10⁻⁹ cm²∙min⁻¹, respectively.

Explanation for the correction:

We observed an error in the calculations of the vanadium (IV) diffusion values; as a result of this, the order of magnitude of these values has been corrected to 10⁻⁹ cm²∙min⁻¹ from 10⁻⁸ cm²∙min⁻¹.

The authors apologize for any inconvenience caused and state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.