Computational Screening of MXene Electrodes for Pseudocapacitive

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C: Energy Conversion and Storage; Energy and Charge Transport

Computational Screening of MXene Electrodes for Pseudocapacitive Energy Storage Cheng Zhan, Weiwei Sun, Paul R.C. Kent, Michael Naguib, Yury Gogotsi, and De-en Jiang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b11608 • Publication Date (Web): 05 Dec 2018 Downloaded from http://pubs.acs.org on December 6, 2018

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The Journal of Physical Chemistry

Computational Screening of MXene Electrodes for Pseudocapacitive Energy Storage Cheng Zhan,1 Weiwei Sun,2 Paul R. C. Kent,2,3 Michael Naguib,4 Yury Gogotsi,5 and De-en Jiang1,* 1Department 2Computational

of Chemistry, University of California, Riverside, California, 92521, United States

Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States

3Center

for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States

4Department

of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, United States

5Department

of Materials Science and Engineering and A. J. Drexel Nanomaterials Institute, Drexel University, Philadelphia, PA, 19104, United States

*Corresponding author. Email: [email protected]

Abstract: MXenes (two-dimensional transition metal carbides and nitrides) are promising materials for capacitive energy storage due to the large chemical space of existing and potential compositions, but only a few of them have been experimentally explored. In this work, we computationally screen a series of MXene electrodes (Mn+1XnTx: M=Sc, Ti, V, Zr, Nb, Mo; X=C, N; T=O, OH; n=1-3) to simulate their pseudocapacitive performance in the aqueous H2SO4 electrolyte. We find that nitride MXenes exhibit better pseudocapacitive performance than carbide MXenes. Especially, Ti2NTx is predicted to have a high gravimetric capacitance over a wide voltage window, while Zrn+1NnTx MXenes are predicted to possess the best areal capacitive performance. Evaluating the descriptors for the capacitance trends, we find that more positive hydrogen adsorption free energy (weak binding to H) and smaller change of the potential at the point of zero charge after H binding lead to higher capacitance. Our work provides helpful guidance to selectively develop high-performance MXene pseudocapacitors and to further screen MXene electrodes. Keywords: MXene, pseudocapacitance, density functional theory, screening, descriptor

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Introduction MXenes are a large family of two-dimensional (2D) materials including transition metal carbides, nitrides, and carbonitrides.1 The chemical formula of MXene can be expressed as Mn+1XnTx, where M is a transition metal (Sc, Ti, V, Zr, Nb, Mo, etc.), X is C or N, and T represents the surface terminal groups (such as –O, –OH, and –F). MXenes have shown promise in capacitive energy storage,2-4 lithium and sodium ion batteries,5-7 electrocatalysis,8-9 gas sensors,10-11 and many other applications. MXenes’ performance in capacitive energy storage is most promising. For example, Ti3C2Tx has shown high volumetric capacitance and gravimetric capacitance with excellent cyclability.1213

MXene exhibits pseudocapacitance in the aqueous H2SO4 electrolyte due to the reversible

surface redox reaction of hydrogen binding. In aqueous salt or ionic liquid electrolytes, MXene shows mainly the electric double-layer (EDL) capacitance.13-16 In organic electrolytes, MXene can have intercalation pseudocapacitance, especially in the presence of Li+ or Na+.17-19 To achieve high capacitance for MXene electrodes, H2SO4 solution is the most promising electrolyte due to the its contribution surface redox reaction. In Table S1, we listed the reported capacitances of MXene electrodes in comparison with other conventional pseudocapacitor materials, such as RuO2,20-22 poly-pyrrole,23 and benzoquinone.24 One can see that MXene as a pseudocapacitor not only has promising capacitance, but also exhibits much better cyclability. Previous studies have focused on Ti3C2Tx,13-14, 16, 25 in addition to a few other MXenes such as Mo2CTx26 and Mo2TiC2Tx,27 despite the diversity of the large MXene family.1 Because MXene synthesis has many technical challenges, experimentally exploring the capacitive performance of the complete MXene family would be very time-consuming. Thus, exploring the pseudocapacitive performance of MXene from a computational perspective is an effective way to help experimentalists design supercapacitors with improved energy storage ability. In this work, we computationally screen the energy storage of Mn+1XnTx MXenes (Mn+1XnTx: M=Sc, Ti, V, Zr, Nb, Mo; X=C, N; T=O, OH; n=1, 2, 3 ) in H2SO4, based on a recently developed model that incorporates the surface-redox pseudocapacitance in the total capacitive energy storage of MXene in H2SO4.28 Moreover, we will explore descriptors that can correlate the capacitances of MXenes with some easily computable and relevant quantities.


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Results and discussion The structure of M2XT2 with the solvation layers is shown in Figure 1 as an example.29 The structure of M3X2T2 and M4X3T2 can be derived from M2X by extending the M and X layers following the ABC stacking order. The termination group T can occupy either the fcc site (Figure 1a,b) or the hcp site (Figure 1c,d). We calculated the relative stability of fcc and hcp configurations for each MXene (Table S2). Since T can be either O or OH, the MXene structures for the redox pair Mn+1XnO2 and Mn+1Xn(OH)2 are selected by the following rules: (1) If both –O and –OH are more stable at the fcc (hcp) site, we use the fcc (hcp) model; (2) if one terminal group is more stable at the fcc site, while the other is more stable at the hcp site, we use the site for which the group has stronger relative stability. This consistent choice of either an fcc or hcp model ensures that we have a most likely surface for reversible hydrogen binding at different coverages, a key step for our prediction of the capacitance.

Figure 1. Model of the M2XT2 MXene with the terminal group T at two different sites: (a) and (b), side and top views of the T groups at the fcc sites (T not directly above M); (c) and (d), side and top views of the T groups at the hcp sites (T directly above M). Color scheme: Red, terminal group T; cyan, transition metal M; gray: carbon or nitrogen X.


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Our first screening criteria are the electronic structure and magnetic property. The results from density functional theory (DFT) calculation are listed in Table S2. To be a high-rate electrode material, metallic MXenes are preferred. Hence, Sc2C(OH)2, Ti2CO2, and Zr2CO2, which are semiconducting (consistent with a previous study30), can be eliminated. In addition, to avoid complication from the magnetic properties, which may be both termination and coverage dependent, we leave out V3C2O2, Sc2NO2, V2NO2, V3N2O2 and V4N3(OH)2 for a future study. Since the pseudocapacitive performance of MXene in the aqueous H2SO4 electrolyte competes with hydrogen evolution reaction (HER) at negative potentials,8 it is necessary to screen MXenes to eliminate those that are too active for HER. The differential hydrogen adsorption free energy is a good descriptor to assess the HER activity.31 We calculated the average hydrogen adsorption free energy (ΔGH, which shows the overall binding trend) and the differential hydrogen adsorption free energy at the optimal H coverage (ΔGHOPT, which reflects the HER activity). From Figure 2, one can see that Sc-based MXenes (Sc2C, Sc3C2, Sc4C3, Sc3N2 and Sc4N3) exhibit relatively stronger binding ability to H atom, with GH close to or less than zero. So we eliminated them for consideration.

Figure 2. Hydrogen adsorption free energy of 2D MXenes: ΔGH , average hydrogen adsorption free energy; ΔGHOPT, the hydrogen adsorption free energy at optimal hydrogen coverage.


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After our quick screening on electronic structure, magnetic property, and hydrogen binding ability, 24 candidates have been identified. Following our previous work,28 we predicted the capacitive energy storage in the aqueous H2SO4 electrolyte for the selected MXene candidates. Briefly, we computed the free energy of a solvated MXene electrode at different applied potentials and H coverages as well as determined the potentials at the point of zero charge before and after H binding. These values then allowed us to determine the stored charge (Q) as a function of the applied potential (V). From these curves, we then derived the differential and integral capacitances. The details are described in the Methods section. From the simulated gravimetric or specific differential capacitances for carbides (Figure 3a) and nitrides (Figure 3b), one can see that most MXenes exhibit a roughly flat differential capacitance curve across our simulated voltage range, except V2C, Ti2N, and Zr2N. If we use a common voltage window of -0.5 to 0.5 V, we can obtain the specific (Figure 4a,b) and areal (Figure 4c,d) integral capacitances. In the carbide MXenes (Figure 4a,c), V2C exhibit highest specific capacitance of 350 F/g, while Zr4C3 exhibit highest areal capacitance that over 60 μF/cm2. In the nitride MXenes (Figure 4b,d), Ti2N exhibit highest gravimetric capacitance over 450 F/g. In all MXene candidates, Ti2N has the highest gravimetric capacitance due to both Ti’s low atomic weight and the favorable redox chemistry (discussed later), while Zr2N, Zr3N2, and Zr3N2 exhibit the highest and similar areal capacitances. Since experimentally synthesized MXenes have a multilayer structure, a large volumetric capacitance is expected for MXenes that have large areal capacitances. Comparing carbides with nitrides of the same metal and stoichiometry, we found that nitride MXenes have better capacitive performance than carbide MXenes for most cases. Due to the difficulty in the nitride MXene synthesis, so far only Ti4N3 and Ti2N were successfully synthesized.32-33 Thus, there is no available experimental data to directly compare with our predictions. However, there have been recent experimental findings of other nitride pseudocapacitors. For instance, Morel et al. reported the pseudocapacitance of VN34 and Xiao et al. found the promising pseudocapacitive performance of 2D metallic MoN.35 Moreover, Wen and Yang et al. found that the nitrogen doping in Ti3C2Tx can increase the pseudocapacitance.36 These recent progress suggests that nitride MXenes may be available soon for testing our predictions. In terms of structural stability, a recent DFT study analyzed the formation energies of 72 different MXenes and concluded that all the -O and -OH functionalized carbide and nitride MXenes have very negative formation energies, indicating their thermodynamic stability.37


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Figure 3. Predicted differential capacitances of MXene electrodes: (a) specific capacitance of carbide MXenes; (b) specific capacitance of nitride MXenes; (c) areal capacitance of carbide MXenes; (d) areal capacitance of nitride MXenes.

Table 1. Predicted and experimental capacitances (F/g) of MXene in 1M H2SO4. MXene

Theory

Experiment

Ti3C2Tx

230a

235,b 245c

Mo2CTx

150d

190e

V2CTx

350d

380f

aRef.

28; bRef. 14; cRef. 16; dPresent work; eRef. 26; fRef. 38.

The reliability of our model and prediction for the capacitance of Ti3C2Tx in H2SO4 has been discussed previously28 and is summarized in Table 1. In addition, we listed recently measured experimental capacitances for Mo2CTx and V2CTx in H2SO4 for comparison. The reported experimental capacitance of Mo2CTx in H2SO4 at 190 F/g26 also agrees reasonably well with our predicted capacitance of 150 F/g at the same voltage window. A more recent experimental work


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reported the capacitance of V2C in 1M H2SO4 to be ~380 F/g at the scan rate of 5 mV/s,38 in good agreement with our predicted capacitance of 350 F/g. For other MXenes in Figure 4, no experimental data are available, so our calculations indicate promising MXenes to try.

Figure 4. Predicted integral capacitances of MXene electrodes: (a) specific capacitance of carbide MXenes; (b) specific capacitance of nitride MXenes; (c) areal capacitance of carbide MXenes; (d) areal capacitance of nitride MXenes. The voltage window is from -0.5 V to +0.5 V vs SHE.

To understand what determines the capacitive performance of MXenes, we studied the factors that can be correlated to the charge-storage trend, in order to find a descriptor of pseudocapacitance. As shown in Figure 5, we found that the change or shift of the potential at the point-of-zero-charge (VPZC) from Mn+1XnO2 to Mn+1Xn(OH)2 is closely related to the amount of charge stored: the charge storage (blue dot; right axis) is higher if the VPZC change (gray bar) is smaller. We use ΔVPZC, defined as one half of the VPZC change from Mn+1XnO2 to Mn+1Xn(OH)2, to represent the VPZC shift. The charge stored can be expressed as a function of ΔGH and ΔVPZC as descriptors (see the Methods section). Briefly, ΔGH is computed by hydrogen adsorption simulation via DFT and ΔVPZC is calculated from the Fermi levels of MXene in both reduced and oxidized forms with a continuum solvation model. As shown in Figure S1, the agreement between this descriptor approach and the DFT results (Figure 4) is very good. One can see from the 2D color map (Figure 6) that large ΔGH


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and low ΔVpzc lead to higher charge storage per unit of formula. Placing the MXene candidates onto this map, one can see that Zr-based nitride MXenes (Zr2N, Zr3N2 and Zr4N3) show the highest charge storage per unit of formula, consistent with the areal capacitance trends in Figure 4.

Figure 5. Shift in the potential at the point-of-zero-charge (VPZC) from Mn+1XnO2 to the reduced Mn+1Xn(OH)2 form (bars; left axis) and charge storage per formula unit (blue dot; right axis) of 24 MXene electrode candidates.

Figure 6. Charge storage per formula unit vs the shift in the potential at the point-of-zero-charge (ΔVPZC) and hydrogen adsorption free energy (ΔGH). Voltage window is from -1V to 1V vs SHE. Values (in (|e| per Mn+1XnTx) for the contour lines are given at right.


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The correlation of ΔVpzc with the redox charge storage of MXenes can be understood from the Fermi-level shift from Mn+1XnO2 to Mn+1Xn(OH)2, as ΔVpzc is proportional to the Fermi-level shift. For MXenes with higher capacitances, it takes smaller shifts in the Fermi level to have the complete two-electron transfer; in other words, the more metallic the MXenes are, the higher the capacitances. Further test of this insight in more MXenes such as bimetallic, doped, and defected ones is warranted. To understand why most nitride MXenes have higher capacitances than their carbide counterparts, we compare their Fermi-level shifts from Mn+1XnO2 to Mn+1Xn(OH)2 in Figure S2. We find that changing X from C to N for the same Mn+1XnO2 MXene lowers ΔVpzc, thereby making the system more metallic. This explains the nitrides’ higher capacitances. Summary and conclusions In summary, we have conducted a computational screening of the pseudocapacitive Mn+1XnTx MXene electrodes in the H2SO4 electrolyte. 24 MXene electrode candidates were selected by considering electronic structure, magnetism, and hydrogen adsorption energy calculated via DFT. Simulated pseudocapacitive charging curves showed that most of the candidates exhibited better capacitive performance than Ti3C2Tx, a prototypical MXene comprehensively reported before. Our screening indicated that the nitrides tends to have better capacitive performance than carbides: Zr2N, Zr3N2, and Zr4N3 were predicted to have highest charge storage per unit formula and Ti2N to have the highest specific capacitance. Moreover, the hydrogen adsorption energy (ΔGH) and the shift in the potential at PZC (ΔVPZC) were found to be the key quantities that dominate MXenes’ charge storage. A promising MXene pseudocapacitor should have large ΔGH and low ΔVPZC. This rule can be applied to pseudocapacitive MXene electrode design and high-throughput screening in the future. Methods Geometry optimization and electronic structure calculations with DFT were performed using the Quantum Espresso package.39 The Perdew–Burke-Ernzerhof functional (GGA-PBE) of generalized-gradient approximation was used for electron exchange and correlation.40 Ultrasoft pseudopotentials were used to describe the nuclei-electron interaction.41 A plane wave basis with the energy cutoff of 40 Ry and a k-mesh of 7 × 7 × 1 (for sampling the Brillouin zone) were used for structure optimizations, and a higher cutoff of 60 Ry and a k-mesh of 21 × 21 × 1 were used


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for single-point calculations of optimized geometries. Spin polarization was applied to test the magnetic property of MXenes. To assess the hydrogen binding ability of MXene, we calculated the average and differential hydrogen adsorption free energy. The average hydrogen adsorption free energy is defined by: 1

∆𝐺𝐻 = 2(𝐺(𝑀𝑛 + 1𝑋𝑛(𝑂𝐻)2) ―𝐺(𝑀𝑛 + 1𝑋𝑛𝑂2) ―𝐺(𝐻2))

(1)

The free energy difference between Mn+1Xn(OH)2 and Mn+1XnO2 was obtain the following: 𝐺(𝑀𝑛 + 1𝑋𝑛(𝑂𝐻)2) ―𝐺(𝑀𝑛 + 1𝑋𝑛𝑂2) = 𝐸(𝑀𝑛 + 1𝑋𝑛(𝑂𝐻)2) ―𝐸(𝑀𝑛 + 1𝑋𝑛𝑂2) +∆𝑍𝑃𝐸 (2) The free energy of a hydrogen molecule is defined as: 7

𝐺(𝐻2) = 𝐸(𝐻2) +𝑍𝑃𝐸(𝐻2) + 2𝑘𝐵𝑇 ― 𝑇𝑆𝐻2

(3)

All quantities in equation (3) can be obtained from DFT and standard thermodynamic database. To assess the HER activity of MXene, we also computed the differential hydrogen adsorption free energy at coverages of 0.25 ML, 0.5 ML, 0.75 ML and 1.00 ML. When the calculated differential hydrogen adsorption free energy is closest to 0 eV, the corresponding coverage is treated as the optimal coverage. For the energy and PZC calculation of a solvated electrode, we performed DFT calculation with an implicit solvation model implemented in the JDFTx code.42-43 Identical parameters and settings were used for the electronic DFT part as used in the single-point Quantum Espresso calculations. For the solvation part, we used the charge-asymmetric nonlocally determined localelectric (CANDLE) model, which has shown excellent reliability in predicting the solvation energy and PZC of metal electrodes.44 To simulate the ionic strength of 1M H2SO4, our implicit solvation model was based on a 3M monovalent aqueous solution. The pseudocapacitive charging simulation was carried out by following our previously proposed method;28 namely, the free energy function of any intermediate state (partially oxidized/reduced MXene layer) at a fixed electrode potential 𝜑 can be expressed as: 𝐺(𝑥,𝜑) = 𝐸(𝑥) +𝑥𝐸𝑍𝑃𝐸 +𝑄(𝑉(𝑥,𝜑))𝜑 + 𝐸𝐸𝐷𝐿(𝑉(𝑥,𝜑)) +(1 ― 𝑥)𝜇𝐻 +

,

(4)

where E(x) is the total electronic energy of a solvated electrode with the H coverage of x in zero surface charge, while EZPE is the zero-point energy (ZPE) difference between x=0 and x=1 states. We use the ZPE of M2XTx to represent the ZPE of M3X2Tx and M4X3Tx if they share the same “M” and “X”. The ZPE contributions calculated by DFT for different M2XTx systems were listed in Table S3. 𝑄𝜑 is the electrical work to move the charge Q (net charge on the electrode) from


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zero potential (in the bulk electrolyte) to the electrode with the potential 𝜑. EEDL is the energy electric double layer contributed by the electrode charge Q. The last term is the chemical potential of a solvated proton in the electrolyte. In the third and fourth terms, V(x, 𝜑) is the relative potential with respect to the potential at the PZC at coverage x and the electrode potential 𝜑, given by: 𝑉(𝑥,𝜑) = 𝜑 ― 𝜑𝑃𝑍𝐶(𝑥)

(5)

Since our previous study has proved that the E(x) and 𝜑𝑃𝑍𝐶(𝑥) can be approximately described by linear equations, in this work, we only performed DFT calculation on Mn+1XnO2 (x=0) and Mn+1Xn(OH)2 (x=1). 𝐺(𝑥,𝜑) and 𝜑𝑃𝑍𝐶(𝑥) values for x between 0 and 1 were derived from linear interpolation. More technical details of our method can be found in our previous work.28 One can also obtain 𝜑𝑃𝑍𝐶(𝑥) from: 𝜑𝑃𝑍𝐶(𝑥) = 𝐸0 +∆𝑉𝑃𝑍𝐶 ―𝑥 ∗ [(𝐸0 + ∆𝑉𝑝𝑧𝑐) ― (𝐸0 ― ∆𝑉𝑃𝑍𝐶)] ,

(6)

where E0 is the standard redox potential calculated from ∆𝐺𝐻 = ―𝐹𝐸0 and ∆𝑉𝑃𝑍𝐶 is one half of the 𝜑𝑃𝑍𝐶 change from Mn+1XnO2 to Mn+1Xn(OH)2. ΔGH and ΔVPZC are descriptors that can be directly obtained from DFT. With the estimated values of 𝜑𝑃𝑍𝐶(𝑥), we can then use Eqs. (4) and (5) to derive the charge stored in the MXene electrode at an applied voltage. Acknowledgements This research is sponsored by the Fluid Interface Reactions, Structures, and Transport (FIRST) Center, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC0205CH11231. Supporting Information Reported performance of conventional pseudocapacitors; lattice parameters and phase stability/property for MXenes examined; zero-point-energy (ZPE) differences between M2XO2 and M2X(OH)2 calculated by DFT; differential hydrogen adsorption free energy of MXene electrode candidates at optimal hydrogen coverage; comparison of charge storage predicted by the


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Computational Screening of MXene Electrodes for Pseudocapacitive

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