Impurity Effects on Charging Mechanism and Energy Storage of

Article

Impurity Effects on Charging Mechanism and Energy Storage of Nanoporous Supercapacitors Cheng Lian, Kun Liu, Honglai Liu, and Jianzhong Wu J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 08 Jun 2017 Downloaded from http://pubs.acs.org on June 10, 2017

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The Journal of Physical Chemistry

Impurity Effects on Charging Mechanism and Energy Storage of Nanoporous Supercapacitors Cheng Lian1, Kun Liu2, Honglai Liu1*, and Jianzhong Wu2* 1

State Key Laboratory of Chemical Engineering, and School of Chemistry and Molecular

Engineering, East China University of Science and Technology, Shanghai, 200237, P. R. China 2

Departments of Chemical and Environmental Engineering, University of California, Riverside, CA 92521, USA

Abstract Room temperature ionic liquids (RTILs) have been widely used as electrolytes to enhance the capacitive performance of electrochemical capacitors also known as supercapacitors. Whereas impurities are ubiquitous in RTILs (e.g., water, alkali salts, and organic solvents), little is known about their influences on the electrochemical behavior of electrochemical devices. In this work, we investigate different impurities in RTILs in the micropores of carbon electrodes via the classical density functional theory (CDFT). We find that, at certain conditions, impurities can significantly change the charging behavior of electric double layers and the shape of differential capacitance curves even at very low concentrations. More interestingly, an impurity with a strong affinity to the nanopore can increase the energy density beyond a critical charging potential. Our theoretical predictions provide further understanding of how impurity in RTILs affects the performance of supercapacitors.

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■ Introduction Electric double layer capacitors (EDLCs), also known as supercapacitors, show great potential for energy storage due to their ultra-large capacitances per unit area in comparison to conventional capacitors. In comparison to other electrochemical devices for energy storage such as batteries, EDLCs have the advantages of greater power density and more sustainable life cycles1. The EDLC performance is strongly correlated with electrosorption of ionic species at the inner surfaces of microporous electrode2. Whereas aqueous electrolytes are often used as the charge carrier of conventional EDLCs, ionic liquids and organic electrolytes have the advantages of larger electrochemical windows and better thermal stability, making them attractive for application to the next generation of supercapacitors with higher energy and power densities2-5. Unlike electric double layer (EDL) near a planar metallic electrode, ion distribution in a supercapacitor typically involves porous electrodes with a broad range of morphologies and pore-size distributions6-10. A wide variety of carbon-based materials with tunable pore size, morphology, architecture and functionality, have been proposed to improve the capacitive performance7. The effects of the pore size on the EDL structure, capacitance, and ion transport have been studied in great details both experimentally and theoretically11-19. The EDLC capacitance shows an anomalous increase as the pore size becomes comparable to the dimensionality of the ionic species, suggesting that electrodes with sub-nano pores are a better choice than those with larger pores. However, the anomalous increase in pores below 1 nm was not observed in few other experiments20-21, and some theoretical work showed the anomalous increase may be diminished by a pore-width dependent permittivity22. The supercapacitor performance depends not only on the electrical potential and the geometric compatibilities of the electrode pores and ionic species but also on the surface

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properties of the electrode materials and impurities in the electrolytes23-30. Existing theoretical reports are mostly devoted to analyzing electrostatic interactions and confinement effects. Despite the omnipresence of impurities in RTILs, relatively little is known on how a small amount of chemicals in the ionic liquid may influence the EDLC performance31-33. Recent nuclear magnetic resonance experiments and molecular dynamics simulations have shown that the presence of impurities may lead to EDL charging drastically different from that for neat RTILs 34-35. It has been shown that EDL charging in RTILs almost always involves ion exchange (swapping of co-ions for counter-ions), and rarely occurs by counter-ion adsorption alone34-36. Ionophobic nanopores are able to enhance the energy storage capacity because the surface properties can drastically change the charging mechanism37. A new solvent-facilitated charging mechanism has been identified to enhance the electrical energy stored in nanopores38. It was found that the use of ‘porophilic’ solvents will create effectively ‘ionophobic’ pores, which have clear advantage for charge storage and potentially charging dynamics as well. One of the key difficulties in studying the impurity effect is that impurity species are present at extremely dilute bulk concentrations. Experimental tools such as Atomic Force Microscopy (AFM) and X-ray reflectometry were applied to study the structural properties of EDLs in a hybrid RTIL containing impurity species at the electrode surface33,

39-40

.

Computational methods, such as molecular dynamics (MD) simulations, were also been used to investigate the distribution of impurities near electrified interfaces25, 31, 41. It was found that a small amount of polar additives can boost the performance of ionic-liquid-based supercapacitors42. Due to the importance of impurity on the EDLC performance, more effort should be devoted to understanding the charging mechanism and capacitive behavior in RTILs containing impurities.

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In this work, we discuss the impurity effect on the charging and capacitive behaviors based on the classical density functional theory (CDFT). CDFT had been successfully used in studying the EDL structure and the capacitance of ionic liquids and organic electrolytes systems43-46. It has been shown that the CDFT predictions are able to capture the essential results from earlier experimental and simulation studies and provides microscopic insights into the electrochemical behavior of ionic liquids as the working electrolytes for supercapacitors47-49. Specifically, we are interested in the dependence of the capacitance and the mechanism of EDL charging on the impurity types in RTILs. This paper is structured as follows. First, we describe our coarse-grained models of RTILs and porous materials and provide a brief introduction to the classical DFT method. Next, we discuss the impurity effect on the EDL charging mechanism and the capacitive performance of EDLCs. Finally, we summarize the main results and possible impacts on future experimental work.

■ Models and Methods We consider a generic model for electric double layer (EDL) capacitors consisting of porous carbons and room-temperature ionic liquids (RTILs). Figure 1 presents a schematic setup for RTILs in the micropores of electrodes. Following the standard model for the characterization of the pore-size distributions of porous materials by gas adsorption50, we use slit pores to represent the geometry of porous carbons. The confined RTILs are at equilibrium with a bulk ionic liquid with impurities. We consider three types of impurities: 1) the impurity molecules accumulate inside the pore due to strong surface affinity (Figure 1a); 2) both ions and impurity molecules can enter the pore at low electrical potential (Figure 1b); 3) no impurity molecule can enter the pore due to surface repulsion (Figure 1c). In the coarse-grained model of the ionic

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liquid, both cations and anions are represented as charged hard spheres, and the blue sphere represents impurity molecules48, 51. We assume further that all particles have the same size and impurities molecules bear no net charge. Whereas the coarse-grained model ignores chemical details, it accounts for electrostatic correlations and ionic excluded volume effects importance for EDLC performance but neglected in conventional EDL theories. Approximately, the ionic model parameters are selected to match those corresponding to 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EMI-TFSI), a commercial ionic liquid widely used in electrochemical devices43. The number density of cations and anions is 2.32 nm-3, and that of impurity molecule is 1% of total number density.

Figure 1. Schematic representations of three scenarios considered in this work on the effects of impurities in the room temperature ionic liquids on supercapacitor performance.

With the above assumptions, the pair potential between ionic species is given by

∞, r < (σ i + σ j ) / 2 uij (r) =  2  Z i Z j e 4πε 0ε r r , r ≥ (σ i + σ j ) / 2

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(1)


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where r is the center-to-center distance between two spherical particles, e is the elementary charge, ε r is the dielectric constant, ε 0 is the permittivity of the free space, σ i and Z i are the diameter and the valence of particle i, respectively. In our DFT calculations, the valences of anions, cations and impurity are Z=-1, +1 and 0, and the diameter of all particles is fixed at

σ i = 0.5 nm . While the dielectric constant is unity if all components of the ionic liquid is explicitly considered, we assume a residual dielectric constant ε r = 2 to account for dispersion interactions and ionic polarizability not included in the coarse-grained model52. impurity may have different affinity with cation and anion41,

53

Even the

, we consider an idealized

impurity molecule with same repulsive interaction with cation and anion but different affinity with the electrodes. The electrode is modeled as a slit consisting of two symmetric hard walls of equal surface charge density. The non-electrostatic component of the external potential, or surface energy, acting on the impurity particles is represented by

 σ σ ∞, z < i or z > H − i Vi (z) =  2 2 ω , otherwise 

(2)

where ω represents the transfer energy, H is the surface-to-surface separation (or pore width), and z is the perpendicular distance from the surface. The competition of pore adsorption between ions and impurity molecules is controlled by transfer energy ω , which is equivalent to the resolvation energy introduced by Kondrat and Kornyshev to account for the energy cost to transfer an impurity molecule from the bulk to the slit pore37-38. A positive transfer energy means that the nanopore disfavors the adsorption of the impurity molecules compared to cations or anions, while a negative ω means that the pore favors impurity molecules. Because the

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residual dielectric is not much different from the dielectric constant for the carbon electrode, we assume that the image-charge effects are relatively unimportant for determining ionic distributions. Even when the surface potential is fixed, a discontinuity in the dielectric constant at the electrode-electrolyte interface leads to image forces because charge fluctuation near the electrode is correlated with atomic polarization inside the electrode. Classical density functional theory (CDFT) is used to calculate the ion distributions and subsequently the capacitance of EDLCs. At given temperature T and a set of ion concentrations in the bulk, ρi0 , CDFT predicts the ion distributions inside the pore

ρ i ( z ) = ρ i0 exp  − β Vi ( z ) − β Z i eψ ( z ) − β ∆µ iex ( z ) 

(3)

where β = 1/ (k BT ) , kB is the Boltzmann constant, Vi ( z ) is the non-electrostatic component of the external potential, and ∆µiex ( z ) accounts for electrostatic correlations and ionic excluded volume effects. The mean electrical potential, ψ ( z ) , is related to the local charge density by the Poisson equation

∇2ψ ( z ) = −

e

ε 0ε r

∑ Z ρ ( z) i

i

(4)

i

Eqs.(3) and (4) are solved self-consistently with the following boundary conditions for the electrical potential

ψ (0) = ψ ( H ) = ψ 0

(5)

The electrode potential, ψ 0 , is assumed constant at the surfaces of carbon electrode. The theoretical details in the classical DFT calculations are reflected in the last term on the right side of Eq.(3), ∆µiex ( z ) . Within the coarse-grained model, the local chemical potential accounts for thermodynamic non-ideality due to electrostatic correlations and ionic excluded

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volume effects. The former is represented by a quadratic expansion of the excess Helmholtz energy with respect to that of a bulk system54, and the latter is described by the modified fundamental measure theory55. The details for the local chemical potential could be found in our previous works54. Because the EDL capacitance is mainly affiliated with inhomogeneous ionic distributions due to the electrostatic charge, we expect that inclusion of the ion polarizability will not change the major conclusions of this work. If ∆µiex ( z ) = 0 , Eqs.(3) and (4) reduce to the conventional Poisson-Boltzmann (PB) equations56. To solve Eqs.(3) and (4) numerically, we start with an initial guess of the ionic density profiles, ρ i ( z ) . The local excess chemical potential for each ionic species and the local electrical potential, ∆µiex ( z ) and ψ ( z ) , are then calculated from the initial density profiles and the electric potentials at the boundaries. Subsequently, a new set of ionic density profiles are obtained from Eq.(3) and the procedure repeats until convergence. From the ion distributions and the electrical potential profiles, we can readily calculate the surface charge density (Q) following the Gauss law

Q = −ε 0ε r

∂ϕ ∂z

(6) z =0

In writing Eq.(6), we assume that the electric field inside the carbon material is negligible. The assumption is amount to that charge neutrality is always satisfied for ionic liquids in the slit pore. By integrating the Poisson equation, we can get 2 H /2 ∂ ψ ( z ) H /2 ∂ψ ( z ) −ε 0ε r = ε 0ε r ∫ dz = − ∫0 ρe ( z) dz 0 ∂z z =0 ∂z 2

(7)

Eq.(7) indicates that the charge neutrality is satisfied:

Q+∫

H /2

0

ρe ( z ) dz = 0

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(8)

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■ Results and Discussions For all systems considered in this work, the thermodynamic conditions of the bulk ionic liquid are located in the one-phase region of the phase diagram for the restricted primitive model of electrolytes57. Here the concentration of the room temperature ionic liquid is fixed at 3.8 M, the mole fraction of impurity at the bulk is 0.01, and the pore width is H=0.6 nm. We fix the impurity concentration at 1% mole fraction because it is not a controllable parameter in most experiments. We expect that the main conclusions will be the same if the impurity concentration is slightly changed (as long as it remains small). Figure 2 shows the DFT predictions for the surface charge density versus the surface energy ω for impurities molecules. The interaction between the impurity and the nanopore is reflected in the surface energy ω, which amounts to the impurity transfer energy from the bulk reservoir into the nanopore. A positive surface energy ω means that the nanopore disfavors the adsorption of the impurity molecules; while a negative ω means that the pore favors impurity adsorption. Because both cations and anions considered in this work have the same size and absolute valence, these plots are symmetric if they are extended to the negative side of the surface electrical potential. Figure 2 indicates that, regardless of the sign of the surface binding energy ω, the charge density of the electrode increases monotonically with the electrode potential. At large electrical potential, the surface charge density becomes independent of the surface energy because ion adsorption inside the pore is dominated by electrostatic interactions. The magnitude of the surface charge density, on the order of ~ 0.1 C/m2, is comparable to those observed in molecular dynamics simulation for carbon-based non-aqueous supercapacitors58-59. While the binding energy does not alter the range of the surface charge density, the charging curves are noticeably different for nanopores with different surface energies. If the impurity

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molecules are strongly favored inside the pores (e.g. ω = −20k BT ), their presence largely reduces the surface charge density at low potential and thus significantly changes the shape of the Q −ψ curve. For a pore that repels impurity molecules, surface charge density Q increases monotonically with the surface potential ψ , resembling the shape of a Langmuir adsorption isotherm.

Figure 2. Theoretical predictions for the surface charge density versus the electrical potential at different transfer energies of the impurity molecules. We may attain an understanding of the charging curves by considering the average number density of individual species inside the nanopores during the charging process. Figure

3a presents variations of the particle densities versus the surface electrical potential for the case with an impurity binding energy ω = −10k BT . The number densities of ionic species and impurity molecules in the pore are determined not only by their bulk densities but also by the surface

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attraction energies, and the latter is responsible for the large surface densities shown in Fig. 3(a). Here the surface charge density can even exceed the maximum packing fraction of uniform hard spheres because the pore width (0.6 nm) is slightly larger than the hard-sphere diameter (0.5 nm). As the surface potential increases, the pore gains electrical charge mainly by exchanging impurity for counterions (anions) from the bulk. When the charging potential larger than 1 V, virtually all impurity molecules have been depleted from the pore and the charging process is dominated by counterion insertion. For a slit pore with weak attraction ( ω = −5k BT ) to the impurity molecules (Figure 3b), the EDL charging reflects a combination of impurity-counterion exchange and coion-counterion exchange at low surface potential, and a counterion insertion at high surface potential. For a pore that disfavors impurity adsorption ( ω ≥ 0 ) in Figure 3c, the charging process consists of both coion-counterion exchange and counterion insertion. For all cases, the surface charge density remains the same at high surface potential because, at such conditions, only counterions are adsorbed inside the nanopores. Because cations and anions have the same size but opposite charge, the surface charge becomes negative but remains the same absolute values if the electrode potential is switched to negative.

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Figure 3. The number densities of ions and impurity molecules inside a nanopore of width H=0.6 nm with different transfer energies for the impurity molecules: (a) ω = −10k BT ; (b)

ω = −5k BT ; (c) ω = 0.0k BT .

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Three types of mechanisms have been identified for neat ionic liquids37, 60-62: (i) coioncounterion exchange, (ii) counterion insertion, and (iii) desorption of co-ions. When the ionic liquid is diluted with a solvent, two additional charging mechanisms had been proposed38: (iv) solvent swapping with co-ions, which themselves are forced out of the pore at higher voltages and replaced with counterions, and (v) direct swapping of solvent with counterions without the inclusion of co-ions in the pore at any voltage. Similar to the solvent effect on the charging mechanisms, we may identify two distinctive charging behaviors in the presence of impurity molecules: (vi) impurity-counterion exchange similar to the solvent effect as shown in (v), and (vii) impurity-counterion exchange concomitant with coion-counterion exchange, a combination of charging mechanisms (v) and (i). Like the solvent effect on the charging behavior, the transfer energy (surface energy ω ) determines which charging mechanism takes place. The performance of EDLCs can be measured in terms of differential capacitance Cd , which is defined as a derivative of the surface charge density with respect to the electrode potential:

Cd =

∂Q ∂ψ

(9)

The performance of EDLCs can be examined in terms of differential capacitance Cd . Figure 4 shows the dependence of the differential capacitance on the electrode potential ( Cd − ψ 0 curves) at conditions the same as those in Figure 2. As discussed above, the impurities have little effect on EDL charging when ω ≥ 0 . Similar to results for pure ionic liquids studied in our previous work2, 51, the Cd − ψ 0 curves exhibit an symmetric “bell shape”. At low electrode potential (here below 0.5 V), the near symmetric variations of cation and anion densities suggest that the dominant charging mechanism is the exchange of co-ions (cations) in the pore with the counterions (anions) from the bulk (Figure 3c). In this case, the differential capacitance

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decreases sharply because ion adsorption becomes quickly saturated at small electrical potential. At high electrode potential (here above 0.5 V), co-ions are totally depleted from the pore as indicated by the number density shown in Figure 3(c). In the latter case, the charging process is dominated by counterion insertion, which leads to a slower decline of the differential capacitance.

Figure 4. Differential capacitance as a function of applied potential shows a transition from a Bactrian camel shape to bell shape as the surface energy of the impurity molecules from attraction to repulsion. For impurity-disfavored nanopores ( ω ≥ 0 ), the two Cd − ψ 0 curves are almost identical because the impurity molecules do not enter the pore. When the transfer energy is elevated to ω = −20k BT and −10k BT , both counterions and coions are excluded from the nanopore at a low charging potential. In this case, the impurities are exchanged by counterions from the bulk only if the electrode potential is sufficiently large to overcome the surface energy ω . The differential capacitance increases to a maximum with the

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surface potential. A further increase of the electrode potential leads to the saturation of counterions inside the nanopore and thus a decline of the differential capacitance. In other words, the Cd −ψ curves exhibit a ‘Bactrian camel shape’. At large surface potential, the differential capacitance (~7 µF/cm2) is comparable to those from previous theoretical and experimental investigations for a wide range of non-aqueous supercapacitors with carbon electrodes63. For pores with minimal impurity effects, the bell-shaped charging curves are also in good agreement with previous publications51, 64. Although our model was not intended to capture the chemical details or the quantitative performance of any specific systems, the maximum differential capacitance (~ 30 µF/cm2) at the zero voltage is similar to that for 1-propyl-3-methylimidazolium tetrafluoroborate (PMIBF4) ionic liquid at Hg electrode (~ 28 µF/cm2)65.

The maximum

differential capacitance shown in Figure 4 is slightly larger than those reported in a previous work (~ 20 µF/cm2)66 because of different theoretical models and experimental systems were considered. Figure 4 indicates that the peak capacitance shifts to a higher potential as the surface becomes more attractive (viz., surface energy ω k BT falls from -5 to -20). A bell shape to the two-hump camel shape transition with different impurities in the differential capacitancecharging potential curves and this indicates that impurities may lead to different charging mechanisms.

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Figure 5. The energy per surface area as a function of the applied surface potential with different impurities. While an impurity with strong surface affinity may block a neutral pore thus reduces the energy density at low voltage, they can significantly increase the energy density at high voltage. The energy density in a nanopore could be obtained by ψ0

E = ∫ CdV dV 0

(10)

where Cd is the differential capacitance and ψ 0 corresponds to one half of the operation potential window (OPW). Figure 5 shows the energy density in the nanopore with different types of impurity. At low charging potentials, an impurity repelled from the nanopore yields the energy density higher than that corresponding to an impurity with a strong surface affinity. However, the trend is reversed at high charging potentials. In the former case ( ω ≥ 0 ), the impurity molecules hardly enter the nanopore thus have negligible effects on the energy density. 16


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If the impurity has a strong affinity with the pore surface ( ω < 0 ), the peak position of the differential capacitance shifts to higher potential as indicated in Figure 4. In that case, we can obtain a higher differential capacitance at larger charging potentials. According to Eq. (8), charging at large capacitance and potential yield a higher energy density.

■ Conclusions The impurity effect on capacitance was examined in our previous work using a similar theoretical model42. While the previous work was focused the capacitance as a function of the pore size a fixed charge potential (-1.5 V), this work investigates the influence of impurity on the charging mechanism and the energy density of electrical double layer (EDL) capacitors in terms of its affinity with the electrode walls. We demonstrate that, under conditions favoring impurity accumulation in the nanopores of the electrode, impurity can change the EDL charging mechanism even at low bulk densities. As the transfer energy of impurity molecules increases, the capacitance-potential curves can change from the bell shape to the two-hump camel shape, with the peak shifting toward a higher charging potential. The impurity effect on the charging behavior is similar to the solvent effect as studied by Rochester and coworkers38. The main difference is that the amount of impurity and solvent in the bulk is very different. As an ionophobic pore could be beneficiary for improving charge storage and charging dynamics, introduction of impurity molecules inside the pore makes it essentially more ionophobic thus enhances the energy storage. Our theoretical results suggest that special attention should be given to the nature of impurity and operation voltages when the surface properties nanoporous electrodes are modified to enhance the performance of EDLCs. It is worth noting that association between ions and impurity molecules, which might happen for impurity molecules with large polarity, may give rise to different pictures of the charging behavior. For impurity molecules

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without affinity to ionic species, their accumulation inside the pore will increase the charge storage and capacitance as shown in Figure 3, regardless of the polarity. The effects of ion binding with impurity molecules on the charging mechanism and energy density will be investigated in the future work. From a practical prospective, the impurity can be considered as either a contaminant or an additive to ionic liquids. Based on this study and our previous work42, 53

, we suggest new experimental strategies to introduce additives into ionic liquids with specific

surface binding affinity to the porous electrodes (e.g., by surface modifications). While significant efforts have been devoted to formulation of ionic liquid mixtures and selection of solvents49, much less is known on how supercapacitor performance may be influenced by potent additives at a low concentration. We hope that this work would inspire future experimental and computational efforts toward these directions.

■ AUTHOR INFORMATION Corresponding Author *Email: [email protected] *Email: [email protected]

Notes The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS This research was sponsored by the Fluid Interface Reactions, Structures and Transport (FIRST) Center, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences. Cheng Lian and Honglai Liu thank the financial support by the National Natural Science Foundation of China (No. 91334203) and the 111

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Project of China (No. B08021). The numerical calculations were performed at the National Energy Research Scientific Computing Center (NERSC).

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Impurity Effects on Charging Mechanism and Energy Storage of

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