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Theoretical Study on the Quantum Capacitance Origin of Graphene Cathodes in Lithium Ion Capacitors

Theoretical Study on the Quantum Capacitance Origin of Graphene Cathodes in Lithium Ion Capacitors

catalysts

Article Theoretical Study on the Quantum Origin of Cathodes in Ion

Fangyuan Su 1, Li Huo 2, Qingqiang Kong 1, Lijing Xie 1 and Chengmeng Chen 1,*

1 CAS Key Laboratory of Materials, Institute of Chemistry, Chinese Academy of Sciences, Taiyuan 030001, Shanxi, China; [email protected] (F.S.); [email protected] (Q.K.); [email protected] (L.X.) 2 College of and Engineering, Taiyuan University of Technology, Taiyuan 030001, Shanxi, China; [email protected] * Correspondence: [email protected]; Tel.: +86-351-404-9061

 Received: 4 September 2018; Accepted: 3 October 2018; Published: 11 October 2018 

Abstract: (QC) is a very important character of the graphene cathode in lithium ion capacitors (LIC), which is a novel kind of electrochemical energy conversion and storage device. However, the QC electronic origin of the graphene cathode, which will affect the electrochemical reaction at the electrode/electrolyte interface, is still unclear. In this article, the QC of various kinds of graphene cathode is investigated systematically by DFT calculation. It was found that the value and origin of QC strongly depend on the defects and alien of graphene. Graphene with pentagon defects possesses a higher QC than pristine graphene due to the contribution from the electronic states localized at the carbon pentagon. The introduction of graphitic B can contribute to QC, while graphitic N and P does not work in the range of the LIC cathode. Single vacant defect graphene and pyrrolic N-doped graphene demonstrate very high QC due to the presence of states associated with the σ orbital of unbonded carbon atoms. However, pyridinic graphene shows an even higher QC because of the states from the N . For the residual O in graphene, its QC mainly originated from the pz states of carbon atoms and the effect of O, especially the O in bridged functional group (–COC–), is very limited. These results provide new insight into further study of the catalytic behavior and the design of a high performance graphene cathode for LIC.

Keywords: DFT calculations; defect; ; quantum capacitance; graphene

1. Introduction Lithium ion (LIC) is a kind of hybrid electrochemical energy conversion and storage device typically consisting of a capacitive cathode and an intercalated anode. The capacitive cathode can bring excellent rate performance, while the intercalated anode enhances its capacity. Therefore, LICs possess high power and high energy density simultaneously and can fill the gap between the lithium ion battery and a . is used as the cathode [1], while the negative electrode is mainly composed of [2–5], hard carbon [6,7], lithium titanate [8], etc. A capacitive cathode uses ion to store energy. The larger specific surface area means higher specific capacity and higher energy density. At the same time, the electronic conductivity of the electrode should be high to suppress the ohmic resistance when the LIC is charged/discharged at a high current rate. Therefore, the capacitive cathode of the LIC should possesses both a high specific surface area and good electronic conductivity simultaneously. Recently, graphene has also been used as an effective novel cathode for its particularly large specific area and high electronic conductivity [9–13].

Catalysts 2018, 8, 444; doi:10.3390/catal8100444 www.mdpi.com/journal/catalysts Catalysts 2018, 8, 444 2 of 14

As for the electrical double layer formed at the interface of the graphene/electrolyte, the total capacitance, Ctot, can be theoretically divided into two parts, the capacitance from graphene (Cgraphene) and the capacitance from the electrolyte(CElectrolyte), with the following relationship:

1/Ctot = 1/Cgraphene + 1/CElectrolyte (1)

Here, Cgraphene represents the capacitance of single layered graphene. Celectrolyte combines the Helmholtz capacitance and the diffuse capacitance. However, since the electrolyte concentration in commercial LIC is usually high (~1 mol/L), the diffuse capacitance can be excluded. It is well known that the Cgraphene of pristine graphene is limited by the (DOS) of graphene near the , which is extremely low compared with that of metallic materials [14]. In fact, the DOS of single layered pristine graphene at the Fermi level is zero. Therefore, the capacitance is limited by DOS and is called quantum capacitance (QC), which is smaller than CElectrolyte. The QC of pristine graphene has been investigated widely by experimental and theoretical calculations [15–19]. It is generally accepted that QC shows a V-like shape near the zero point potential with a value less than 10 µF/cm2, depending on the applied voltage range [15,17]. Thus, according to Equation (1), the enhancement of Ctot is limited by Cgraphene. Consequently, pristine graphene is rarely introduced as a cathode in LICs. On the other hand, modified graphene materials, such as activated graphene [10], reduced graphene [9,12,20,21], and graphene networks [5,11,22], which are abundant in defects and alien atoms, are widely used. According to the number of missing carbon atoms in graphene, there are many types of defects [23], which are shown in Figure1. The Stone–Wales (SW) defect, in which four carbon become two pentagons and two heptagons (55-77), is the simplest case because no carbon atom is lost. When one carbon atom is lost, D1 defected graphene is formed. Due to the Jahn–Teller distortion, a new C–C bond will be formed and hence a pentagon and nonagon (5-9) will be present [24,25]. The topological structure is complex for D2 type defected graphene, in which two carbon atoms are lost. It is known that there are at least three kinds of D2 structures, 5-8-5 (D2_I), 555-777 (D2_II) and 5555-6-7777 (D2_III), whose formation energy follows the order of D2_I > D2_III > D2_II [25]. When more carbon atoms are lost, the defects can be viewed as combinations of the point defects discussed above. Other than defects, doping is also used to tailor the electronic structure of graphene. Alien atoms in these modified graphene cathodes are mostly N, because N has a similar size as the carbon atom and is easy to be introduced into the graphene lattice through various experiments. According to the C–N bonding type, there are three kinds of N in graphene: graphitic N (bonding with three C atoms in ), pyrrolic N (bonding with two C atoms in pentagon) and pyridinic N (bonding with two C atoms in hexagon). At the same time, B and P atoms are also introduced in the graphene lattice. Experimental methods employed to introduce N, P and B atoms consist of , thermal , hydrothermal and chemical vapor deposition (CVD), which have been reviewed in [26–28]. O atoms can also be found in reduced graphene oxide (rGO) due to its graphene oxide (GO) precursor. Up to now, the QC of graphene with various structural defects [9,29–32] and alien doping atom [33–37] has been investigated in the voltage range of . Based on the calculation results, the QC of modified graphene strongly depends on the applied voltage range. In contrast to the supercapacitor, the bias voltage range of the graphene cathode in LICs is about 0–1.0 V [38,39], because the whole work voltage window of LICs is about 3.0–4.0 V (vs Li+/Li) or even higher. In this voltage range, we still lack a deep understanding of the required structural information of graphene for its application. Also, the effect of P, B and residual O elements on the QC of the graphene cathode is rarely investigated. The origin of the QC of those kinds of graphene materials in the voltage of the LIC cathode is still not clear. Irreversible electrolyte oxidation will be caused by the catalytic effect of carbon materials [40,41], and hence the cycle will get worse. Higher QC may enhance the activity of the graphene cathode toward electrolyte decomposition because of the higher DOS near the Fermi level. Hence, it is very important to illustrate the origin of QC because it is closely related to the catalytic behavior of the graphene cathode in LIC. Catalysts 2018, 8, 444 3 of 14

Catalysts 2018, 8, x FOR PEER REVIEW 3 of 14 To explore the surface structure and the corresponding electronic structure to promote the QC behavior of graphene materials in this voltage range, graphene with various point defects and N, P, B, B, O atoms were investigated by DFT calculations in this work. Firstly, graphene with the SW, D2 O atoms were investigated by DFT calculations in this work. Firstly, graphene with the SW, D2 defect defect and graphitic N, P and B was studied because their bands with a high π character contribute and graphitic N, P and B was studied because their bands with a high π character contribute to QC to QC when graphene-based LIC is charged. Then the QC of the D1-defected graphene and graphene when graphene-based LIC is charged. Then the QC of the D1-defected graphene and graphene with with pyrrolic N and pyridinic N were investigated to assess the effect of the bands associated with pyrrolic N and pyridinic N were investigated to assess the effect of the bands associated with localized localized σ states. Finally, the effect of the residual O in the graphene was also evaluated. The results σ states. Finally, the effect of the residual O in the graphene was also evaluated. The results clearly clearly illustrate the origin of graphene QC for the cathode in LIC. It is expected that the theoretical illustrate the origin of graphene QC for the cathode in LIC. It is expected that the theoretical results may results may facilitate the design of high QC graphene materials by modifying the structure and facilitate the design of high QC graphene materials by modifying the structure and surface chemistry. surface chemistry.

FigureFigure 1. 1. GeometricGeometric structure structure of of pristine pristine and and defected defected graphene. graphene. (a) (Pristine,a) Pristine, (b) (SWb) SW(55-77), (55-77), (c) D1 (c) (5- D1 9),(5-9), (d) (D2_Id) D2_I (5-8-5), (5-8-5), (e) D2_II (e) D2_II (555-777) (555-777) and and (f) D2_III (f) D2_III (5555-6-7777). (5555-6-7777).

2.2. Results Results and and Discussion Discussion 2.1. Point Defects 2.1. Point Defects The QC and the excessive surface charge density (ESCD) of pristine and SW, D2 defected graphene The QC and the excessive surface charge density (ESCD) of pristine and SW, D2 defected are shown in Figure2a,b, respectively. As shown in Figure2a, the QC of pristine graphene, which graphene are shown in Figure 2a,b, respectively. As shown in Figure 2a, the QC of pristine graphene, increases with voltage, reaches about 18(9.9) µF/cm2 at the voltage of 1.0(0.6) V. It can be attributed which increases with voltage, reaches about 18(9.9) μF/cm2 at the voltage of 1.0(0.6) V. It can be to the shape of its DOS profile in the energy range between -1 eV and the Fermi level shown in attributed to the shape of its DOS profile in the energy range between -1 eV and the Fermi level shown Figure3a. Since the QC is calculated based on the fixed-band approximation, the shape of the QC plot in Figure 3a. Since the QC is calculated based on the fixed-band approximation, the shape of the QC follows that of the corresponding DOS profile. At the same time, its ESCD also increases with voltage plot follows that of the corresponding DOS profile. At the same time, its ESCD also increases with monotonously and the peak value of 9.0(3.3) µC/cm2 can be found when voltage reaches 1.0(0.6) V. voltage monotonously and the peak value of 9.0(3.3) μC/cm2 can be found when voltage reaches The result here is very close to previous reports [29,30,34]. The behavior of SW defected graphene is 1.0(0.6) V. The result here is very close to previous reports [29,30,34]. The behavior of SW defected very similar to pristine graphene when voltage is below 0.6 V. Hence there is no obvious difference graphene is very similar to pristine graphene when voltage is below 0.6 V. Hence there is no obvious that can be found in the ESCD. However, when the voltage further increases, the QC of SW defected difference that can be found in the ESCD. However, when the voltage further increases, the QC of graphene becomes higher, and hence the ESCD increases accordingly. D2-I defected graphene also SW defected graphene becomes higher, and hence the ESCD increases accordingly. D2-I defected follows the situation of the pristine graphene when the voltage is lower, although the QC becomes graphene also follows the situation of the pristine graphene when the voltage is lower, although the smaller than that of pristine graphene when the voltage is higher than 0.7 V. Therefore, only minor QC becomes smaller than that of pristine graphene when the voltage is higher than 0.7 V. Therefore, differences in QC can be found among pristine, SW and D2-I defected graphene, other than very only minor differences in QC can be found among pristine, SW and D2-I defected graphene, other minor variations when the voltage is near 1.0 V. However, when it comes to the other two kinds of D2 than very minor variations when the voltage is near 1.0 V. However, when it comes to the other two defected graphene (D2_II and D2_III), the situation is totally different. kinds of D2 defected graphene (D2_II and D2_III), the situation is totally different.

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60 25 pristine pristine 50 (a) (b) -2 2 SW 20 SW - 40 D2_I D2_I

C cm 15 F cm D2_II

D2_II 

 30 / D2_III / 10 D2_III 20  QC 10 5 0 0 0.2 0.4 0.6 0.8 1.0 0.20.40.60.81.0 Voltage/V Voltage / V

FigureFigure 2. 2.EnergyEnergy storage performance performance ofpristine of pristine and graphene and graphene with Stone–Wales with Stone–Wales (SW) and D2 (SW) defects. and D2 defects.(a) quantum (a) quantum capacitance capacitance (QC) and (QC) (b) excessive and (b) surfaceexcessive charge surface density charge (ESCD). density (ESCD). Unlike the cases of pristine, SW and D2_I defected graphene, where the QC increases in a linear fashion,Unlike the the QC cases of D2_II of pristine, and D2_III SW defected and D2_I graphene defect showsed graphene, multiple where peaks and the fluctuatesQC increases following in a linear fashion,the increase the QC of of voltage. D2_II and This D2_III phenomenon defected can graphe alsone be shows attributed multiple to their peaks fluctuating and fluctuates DOS profile, following thewhich increase will of be voltage. shown in This Figure phenomenon3d,e. The QC can of thealso D2_II be attributed and D2_III to peak their at fluctuating 48.09 µF/cm DOS2 and profile, which41.93 willµF/cm be shown2 when in voltage Figure is 3d,e. 0.84 andThe 1.0QC V, of respectively. the D2_II and Although D2_III their peak QC at is48.09 lower μF/cm than2 thatand 41.93 μF/cmof pristine2 when graphenevoltage is in 0.84 a certain and 1.0 voltage V, respectively. range, the ESCD Although of D2_II their and QC D2_III is lower defected than graphene that of ispristine graphenemuch higher, in a certain being 24.77voltage and range, 15.30 µtheC /cmESCD2 when of D2_II the voltage and D2_III reaches defected 1.0 V. Therefore,graphene inis ordermuch to higher, beingimprove 24.77 the and energy 15.30 storage μC /cm ability2 when of LIC,the thevoltage D2_II reaches and D2_III 1.0 typeV. Therefore, defect should in beorder favored to improve in the the energygraphene storage cathode. ability of LIC, the D2_II and D2_III type defect should be favored in the graphene The QC can be attributed to the DOS near the Fermi level of different kinds of graphene. In order cathode. to illustrate the difference in QC behavior, the band structure, DOS and band-decomposed charge The QC can be attributed to the DOS near the Fermi level of different kinds of graphene. In order density (BDCD, 1.0 eV below the Fermi level) are shown in Figure3. When graphene is used as to illustratethe cathode the of difference LIC, the electron in QC must behavior, be extracted the band from structure, the cathode DOS when and the band-decomposed LIC is charged. Thus, charge densitythe available (BDCD, electron 1.0 eV states below under the theFermi Fermi level) level are determine shown thein energyFigure storage3. When ability graphene of the electrode. is used as the cathodeSW and of D2_ILIC, defectedthe electron graphene must showe be extracted almost thefrom same the DOS cathode as pristine when graphene the LIC is in charged. energy range Thus, the availablebetween electron -1.0 eV andstates the under Fermi level.the Fermi Thus level the QC dete behaviorrmine ofthe the energy three kinds storage of graphene ability of are the nearly electrode. SWidentical. and D2_I However, defected due graphene to the increase showe of almost available the states same shown DOS in as the pristine DOS of gr D2_IIaphene (Figure in 3energyd) and range betweenD2_III -1.0 (Figure eV 3ande) defected the Fermi graphene, level. Thus their QCthe areQC muchbehavior higher of thanthe three that of kinds the first of graphene three kinds are of nearly identical.graphene. However, The band due gap tocan the beincrease found inof D2_IIavailable and D2_IIIstates shown defected in graphene, the DOS andof D2_II hence (Figure their QC 3d) and D2_IIIfluctuates (Figure with 3e) voltage. defected At thegraphene, same time, their the QC electronic are much states higher of D2_II than and that D2_III of defectedthe first graphenethree kinds of are much higher than that of the previous kinds of graphene, so their QC are much higher. graphene. The can be found in D2_II and D2_III defected graphene, and hence their QC The origin of the QC is another interesting issue, especially for the D2_II and D2_III defected fluctuates with voltage. At the same time, the electronic states of D2_II and D2_III defected graphene graphene. From the BDCD, it can be seen that the bands associated with the pz orbital contribute to arethe much QC, higher regardless than of that the typesof the of previous graphene. kinds Due toof thegraphene, delocalization so their effect, QC theare electronmuch higher. density of theThe pristine origin graphene of the QC was is very another small. interesting When the electrodeissue, especially is charged, for the D2_II are and extracted D2_III from defected graphene.each carbon From atom the uniformly. BDCD, itHowever, can be seen the presencethat the ofbands a point associated defect affects with the the electron pz orbital distribution. contribute to theAs QC, reflected regardless in Figure of the3b,c, types it is theof graphene. states that mainlyDue to localize the delocalization at the carbon effect, atoms aroundthe electron the defect density of theregion pristine that graphene contribute was to the very QC. small. These statesWhen are the derived electrode from is the charged, pz orbital electrons of carbon are atoms. extracted As for from eachthe carbon SW defect, atom the uniformly. electron density However, of the the carbon presence atoms of in a pentagons point defect and affects in their the equivalent electron positions distribution. As inreflected the sub-lattice in Figure is higher 3b,c, it than is the other states atoms, that and mainly hence localize the states at the localized carbon at atoms those carbon around atoms the defect contribute mostly to the QC. The same situation can also be found in graphene with D2 defects. D2_II region that contribute to the QC. These states are derived from the pz orbital of carbon atoms. As for and D2_III showed different electron densities, as shown in Figure3d,e. This is because the number of the SW defect, the electron density of the carbon atoms in pentagons and in their equivalent positions bands of D2_III defected graphene between -1.0 eV and the Fermi level is smaller than that of D2_II, in the sub-lattice is higher than other atoms, and hence the states localized at those carbon atoms due to the difference in topological structure. The BDCD of each band of D2_II and D2_III in this contributeenergy range mostly is shownto the inQC. Figure The same S1 and situation S2, respectively. can also Each be found band shows in graphene a different with BDCD. D2 defects. Bands D2_II andmostly D2_III localized showed on different pentagons electron and on densities, certain carbon as shown atoms ininpentagons Figure 3d,e. can This both is be because found in the D2_II. number of bands of D2_III defected graphene between -1.0 eV and the Fermi level is smaller than that of D2_II, due to the difference in topological structure. The BDCD of each band of D2_II and D2_III in this energy range is shown in Figure S1 and S2, respectively. Each band shows a different BDCD. Bands mostly localized on pentagons and on certain carbon atoms in pentagons can both be found in D2_II. Thus, the electron density of carbon pentagons of D2_II defected graphene was much higher in this energy range. However, only one band mostly localized on a certain carbon atom and a very small

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Thus,Catalysts the electron2018, 8, x FOR density PEER REVIEW of carbon pentagons of D2_II defected graphene was much higher5 of 14in this energy range. However, only one band mostly localized on a certain carbon atom and a very small partpart of the of bandthe band mostly mostly localized localized on on pentagon pentagon can can be be found found inin D2_III.D2_III. Therefore, D2_III D2_III possesses possesses less electronless electron density density than D2_II than D2_II andthe and electron the electron density density is moreis more localized localized on on certain certain carbon atoms. atoms.

Figure 3. Band structure, density of states (DOS) and band-decomposed charge density (BDCD) Figure 3. Band structure, density of states (DOS) and band-decomposed charge density (BDCD) iso- 3 iso-sourcessources (0.006 (0.006 e/Bohr e/Bohr3) of) ( ofa) (pristine;a) pristine; (b) SW; (b) SW;(c) D2_I; (c) D2_I; (d) D2_II (d) D2_IIand (e) and D2_III (e) defected D2_III defected graphene. graphene.

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Catalysts 2018, 8, 444 6 of 14 2.2. Doped Graphene Here, N, P and B are introduced to replace the carbon atom in pristine graphene and the QC 2.2. Doped Graphene behavior is investigated. As shown in Figure 4, there is an obvious difference in the QC of doped graphene.Here, When N, P the and voltage B are introduced is low (for to replaceexample, the be carbonlow 0.3 atom V), in the pristine QC of graphene all three and kinds the of QC doped behavior is investigated. As shown in Figure4, there is an obvious difference in the QC of doped graphene is higher than that of the pristine graphene. However, when the voltage increases, the N graphene. When the voltage is low (for example, below 0.3 V), the QC of all three kinds of doped and P-doped graphene show lower QC compared to the B-doped and pristine graphene. The QC of graphene is higher than that of the pristine graphene. However, when the voltage increases, the N B-dopedand P-doped graphene graphene is the show highest. lower Since QC comparedN and P toare the n-type B-doped donators, and pristine the Fermi graphene. level The of QCthe ofsystem positivelyB-doped shift, graphene while is the the whole highest. DOS Since profile N and is Psimila are n-typer to that donators, of pristine the Fermi graphene. level ofTherefore, the system the QC profilepositively of N- shift,and P-doped while the graphene whole DOS is profile the nearly is similar same to as that that of pristineof pristine graphene. graphene Therefore, in shape, the QCbut with a positivelyprofile of N-shifted and P-doped minimum. graphene The ESCD is the nearlyalso follow same asa similar that ofpristine pattern. graphene When the in shape,voltage but iswith below 0.7 V, alla positively three doped shifted minimum. show The a ESCD higher also ESCD. follow Ho awever, similar when pattern. the When voltage the voltageis above is 0.7 below V, the N- and0.7 P-doped V, all three graphene doped show graphenes worse show performance a higher ESCD. (less than However, 6 μC/cm when2) compared the voltage to is pristine above 0.7 graphene V, 2 (9.0the μC/cm N- and2), P-dopedwhile B-doped graphene graphene show worse can performance have an (lessESCD than over 6 µ C/cm23 μC/cm) compared2. Therefore, to pristine B-doped 2 2 graphenegraphene is a (9.0 veryµC/cm good), candidate while B-doped for a grapheneLIC cathode, can havewhile an the ESCD N- and over P-doped 23 µC/cm graphene. Therefore, can only be usedB-doped under graphene low voltage is a very conditions good candidate (below for 0.3 a LICV). cathode, while the N- and P-doped graphene can only be used under low voltage conditions (below 0.3 V).

2 40 25 - pristine pristine (a) 20 (b) -2 F cm 30 N N  P / P 15

B C cm B

20 

/ 10  10 5 Capacitance 0 0 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 Voltage / V Voltage / V

FigureFigure 4. 4.EnergyEnergy storage storage performance performance ofof dopeddoped graphene. graphene. (a )(a quantum) quantum capacitance capacitance (QC) (QC) and ( band) (b) excessiveexcessive surface surface charge charge density density (ESCD).

TheThe band band structure, structure, DOS DOS and and BDCD BDCD of doped graphenegraphene are are shown shown in in Figure Figure5. For5. For N- andN- and P- P-doped graphene, the Fermi level shift up into the conduction band due to the electron donation by doped graphene, the Fermi level shift up into the conduction band due to the electron donation by the N and P atom, as shown in Figure5a,b. Hence the QC of these two graphenes are much higher the N and P atom, as shown in Figure 5a,b. Hence the QC of these two graphenes are much higher in in the low voltage range (below 0.3 V) because their DOS are higher when energy is below 0.3 eV. theHowever, low voltage their range DOS decrease (belowwhen 0.3 V) the because energy decrease. their DOS Therefore, are higher the QC when become energy smaller is thanbelow that 0.3 eV. However,of the pristine their DOS graphene decrease (above when 0.3 V). the Although energy theirdecrease. DOS increaseTherefore, after the the QC minimum, become the smaller QC of than the that of theN- andpristine P-doped graphene graphene (above is still 0.3 lower V). than Although that of the their pristine DOS graphene increase in after the voltage the minimum, range between the QC of the0 N- and and 1.0 P-doped V. The results graphene are different is still for lower B-doped than graphene. that of the As pristine B is an electron graphe acceptor,ne in the the voltage Fermi range betweenlevel of 0 B-dopedand 1.0 V. graphene The results shift are downward different into for the B-doped valence graphene. band of graphene. As B is an Thus, electron a higher acceptor, DOS the Fermican level be found of B-doped in the energy graphene range shift between downward the Fermi in levelto the and valence−1.0 eV. band Hence of graphene. the QC and Thus, ESCD a of higher DOSB-doped can be graphenefound in arethe much energy higher range than between that of pristinethe Fermi graphene. level and Therefore, −1.0 eV. for Hence an LIC the cathode QC and in ESCD of B-dopedwhich the graphene electron is are extracted much when higher it isthan charged, that anof pristine electron-accepting graphene. Therefore, is highly for favored. an LIC cathode From the BDCD shown in Figure5, it can be seen that the band with a high p character contributes in which the electron is extracted when it is charged, an electron-acceptingz dopant is highly favored. to the QC of these three kinds of doped graphene, which follow the case of defected graphene. For the From the BDCD shown in Figure 5, it can be seen that the band with a high pz character N- and B-doped graphene, this is the state caused by the alien atom and the carbon atoms connecting contributesto the alien to atomthe QC and of their these equivalent three kinds in the of same doped sublattice. graphene, However, which the follow P atom the seldom case hasof defected an graphene.effect on For the the voltage N- and range B-doped of LIC. Thegraphene, split DOS this of is the the N, state P and caused B atom by in dopedthe alien graphene atom and shown the in carbon atomsFigure connecting S3 also supports to the alien this result. atom and their equivalent in the same sublattice. However, the P atom seldom has an effect on the voltage range of LIC. The split DOS of the N, P and B atom in doped graphene shown in Figure S3 also supports this result.

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Figure 5. Band structure, density of states (DOS) and band-decomposed charge density (BDCD) 3 3 Figureiso-surface 5. Band of structure, (a) N-doped density graphene of states (0.003 (DOS) e/Bohr and band-decomposed); (b) P-doped graphene charge density (0.003 (BDCD) e/Bohr )iso- and 3 surface(c) B-doped of (a) grapheneN-doped (0.006graphene e/Bohr (0.003). e/Bohr3); (b) P-doped graphene (0.003 e/Bohr3) and (c) B- 3 2.3.doped Unbonded graphene Atoms (0.006 e/Bohr ).

2.3. UnbondedAs mentioned Atoms above, an unbonded atom is present in D1 defected graphene and graphene with pyrrolic and pyridinic N. Therefore, the σ band associated with the unbonded atoms should also As mentioned above, an unbonded atom is present in D1 defected graphene and graphene with affect QC. pyrrolic and pyridinic N. Therefore, the σ band associated with the unbonded atoms should also The QC and ESCD of the three kinds of graphene are shown in Figure6. Compared to the pristine affect QC. graphene, they all deliver much higher QC. Graphene with pyrrolic and pyridinic N even peakes The QC and ESCD of the three kinds of graphene are shown in Figure 6. Compared to the at 108.6 µF/cm2 (0.45 V) and 84.8 µF/cm2 (1.0 V), respectively. As shown in Figure6b, when the pristine graphene, they all deliver much higher QC. Graphene with pyrrolic and pyridinic N even voltage reaches 1.0 V, the ESCD of the D1 defected graphene and graphene with pyridinic and pyrrolic peakes at 108.6 μF/cm2 (0.45 V) and 84.8 μF/cm2 (1.0 V), respectively. As shown in Figure 6b, when N are 44.6, 53.8, 75.5 µC/cm2, respectively, higher than that of the pristine graphene (9.0 µC/cm2). the voltage reaches 1.0 V, the ESCD of the D1 defected graphene and graphene with pyridinic and Therefore, the presence of unbonded atoms can contribute markedly to the ability. pyrrolic N are 44.6, 53.8, 75.5 μC/cm2, respectively, higher than that of the pristine graphene (9.0 Considering that C is typically around 20 µF/cm2 [15], C no longer limits C , and it is μC/cm2). Therefore, electrolytethe presence of unbonded atoms can contributegraphene markedly to the energytot storage the Celectrolyte that dominates Ctot. ability. Considering that Celectrolyte is typically around 20 μF/cm2 [15], Cgraphene no longer limits Ctot, and The electronic structure and BDCD of graphene with unbonded atoms are shown in Figure7. It is it is the Celectrolyte that dominates Ctot. found that the DOS of D1 defected graphene is very high near the Fermi level. These states mostly stem The electronic structure and BDCD of graphene with unbonded atoms are shown in Figure 7. It from the unbonded carbon atom, as shown in Figure S4. In the pyrrolic N configuration, the electronic is found that the DOS of D1 defected graphene is very high near the Fermi level. These states mostly states of the pyrrolic N atom are mainly below −2.5 eV, as shown in Figure S4. Therefore, it cannot stem from the unbonded carbon atom, as shown in Figure S4. In the pyrrolic N configuration, the

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Catalysts 2018, 8, x FOR PEER REVIEW 8 of 14 electronic states of the pyrrolic N atom are mainly below −2.5 eV, as shown in Figure S4. Therefore, beelectronicit effectively cannot statesbe usedeffectively of the inthe pyrrolic used voltage inN theatom range voltage are of mainly a LICrange cathode below of a LIC−2.5 (0–1.0 cathodeeV, V)as shown while (0–1.0 thein V) Figure states while S4. derived the Therefore, states from derived the σ itfromorbital cannot the ofbe σunbonded effectively orbital of carbonusedunbonded in atomthe voltagecarbon are available rangeatom ofare fora LICavaila energy cathodeble storage. for (0–1.0 energySince V) whilestorage. there the are Sincestates two therederived unbonded are two carbonfromunbonded the atoms σ orbitalcarbon in graphene of atoms unbonded in with graphene carbon pyrrolic atomwith N, thearepyrrolic availableavaila N,ble the for states availableenergy are morestorage. states abundant areSince more there near abundant are the two Fermi near level.unbondedthe Fermi Finally, carbonlevel. the QCFinally, atoms of graphene in the graphene QC of with graphene with pyrrolic pyrrolic with N isN, pyrrolic much the available higher N is much thanstates higher that are of more than D1 defectedabundant that of D1 graphene. near defected Inthegraphene. pyridinic Fermi level. In N-doped pyridinic Finally, graphene, the N-doped QC of the graphenegraphene, distinct with the DOS distinctpyrrolic peak DOS betweenN is much peak− betweenhigher1.0 eV than and −1.0 that the eV Fermiof and D1 the defected level Fermi is due level primarilygraphene.is due primarily to In the pyridinicσ bandto the N-doped localized σ band graphene, localized on the N theon atom, distincttheas N shownatom, DOS peakas by shown the between corresponding by the−1.0 corresponding eV and split the DOS Fermi insplit level Figure DOS 7 in andisFigure due Figure primarily 7 and S4. However,Figure to the σS4. band the However, band localized associated the on band thewith N associated atom, the σasorbital shown with from bythe the σ the orbitalcorresponding two unbonded from the split carbontwo DOS unbonded atomsin isFigurecarbon hard to7 atomsand be detected Figure is hard S4. in to thisHowever, be energy detected the range. inband this A associated C–Cenergy bond range. with tends Athe to C–C σ form orbital bond due fromtends to the the to fact twoform that unbonded due the to distance the fact ofcarbonthat the twothe atoms unbondeddistance is hard of carbonto the be detectedtwo atoms unbonded isin thethis smallestenergy carbon range. compared atoms A C–Cis tothe bond D1 smallest defected tends tocomparedgraphene form due andto theD1 graphene factdefected withthatgraphene pyrrolicthe distance and N. graphene of the two with unbonded pyrrolic N. carbon atoms is the smallest compared to D1 defected graphene and graphene with pyrrolic N. 120 80 120 pristine 80 pristine pristine (a) D1 (b) pristine 2 D1 -2 - 90(a) D1 60 (b) 2 D1 -2 - 90 pyrrolic 60 pyrrolic pyrrolic pyrrolic C cm F cm pyridinic pyridinic C cm F cm pyridinic   60 40 pyridinic  

60/ 40 / / /

/ / 

QC  QC 3030 20 20

0 0 0 0 0.20.40.60.81.00.20.40.60.81.0 0.20.40.60.81.00.20.40.60.81.0 Voltage / V Voltage / V Voltage / V Voltage / V FigureFigureFigure 6.6. 6. EnergyEnergy Energy storage storage performance performance of of pristine, pristine,of pristine, D1 D1 deD1 defectedfected defected graphene graphene graphene and and grapheneand graphene graphene with with pyrrolicwith pyrrolic pyrrolic N andNN and pyridinicand pyridinic pyridinic N. N. (a N. )(a quantum )( aquantum) quantum capacitance capacitance capacitance (QC) (QC) (QC) and and ( and(bb)) excessiveexcessive (b) excessive surface surface charge charge charge density density density (ESCD). (ESCD). (ESCD).

FigureFigure 7.7. BandBand structure, structure, density density of states of states (DOS) (DOS) and band-decomposed and band-decomposed charge chargedensity density(BDCD) (BDCD)iso- surces (0.006 e/Bohr3) of3 (a) D1 defected graphene; (b) pyrrolic and (c) pyridine N doping graphene. iso-surcesFigure 7. (0.006 Band e/Bohr structure,) of density (a) D1 defected of states graphene; (DOS) and (b )band-decomposed pyrrolic and (c) pyridine charge N density doping (BDCD) graphene. iso- surces (0.006 e/Bohr3) of (a) D1 defected graphene; (b) pyrrolic and (c) pyridine N doping graphene.

Catalysts 2018, 8, 444 9 of 14 Catalysts 2018, 8, x FOR PEER REVIEW 9 of 14

2.4.2.4. ResidualResidual OxygenOxygen OxygenOxygen isis usuallyusually foundfound inin GOGO fabricatedfabricated byby thethe modifiedmodified Hummer’sHummer’s method.method. AfterAfter heatheat treatmenttreatment or chemical reduction, reduction, most most of of the the O O will will be be removed, removed, but but there there are are still still many many residual residual O- O-containingcontaining functional functional groups, groups, su suchch as as bridged bridged oxygen oxygen (–COC–) (–COC–) and and hydroxyl hydroxyl (–OH) and carbonylcarbonyl (C=O)(C=O) [[42].42]. We focusfocus onon thethe groupsgroups locatedlocated onon thethe basalbasal planeplane ofof rGOrGO inin thisthis work.work. Therefore,Therefore, C=O,C=O, whichwhich is mostly found found at at the the edge edge of of rGO, rGO, was was not not considered considered and and only only bridged bridged oxygen oxygen (–COC–) (–COC–) and andhydroxyl hydroxyl (–OH) (–OH) are areinvestigated. investigated. The TheQC QCand and ESCD ESCD of rGO of rGO with with –COC– –COC– and and –OH –OH are are shown shown in inFigure Figure 8.8 The. The QC QC of of the the two two types types of of rGO rGO are are higher higher than than that of pristinepristine graphenegraphene inin thisthis figure.figure. Therefore,Therefore, thethe presence presence of of both both types types of O of have O have a positive a positive effect oneffect the energyon the storageenergy ability,storage although ability, thealthough O in –COC– the O hasin a–COC– very limited has a effect.very limited The QC effect. of rGO The with QC –OH of fluctuates rGO with with –OH increasing fluctuates voltage with andincreasing peaks atvoltage 29.5 µ F/cmand peaks2, while at the29.5 capacitance μF/cm2, while peak the of capacitance rGO with –COC– peak of is rGO 21.6 µwithF/cm –COC–2. The ESCDis 21.6 ofμF/cm two2 kinds. The ESCD of rGO of are two 11.3 kindsµC/cm of rGO2 and are16.6 11.3µ μC/cmC/cm2 and, respectively. 16.6 μC/cm Therefore,2, respectively. the energy Therefore, storage the abilityenergy of storage rGO with ability residual of rGO O with atoms residual is similar O atoms to that is similar of graphene to that with of graphene D2_III, which with D2_III, is still which lower thanis still D2_II lower defected than D2_II graphene defected and graphene graphene and with graphene B and unbonded with B and atoms. unbonded atoms.

30 20 pristine pristine 2 25 - (a) -COC- (b)

-2 15 -COC- 20 -OH

F cm -OH  C cm

/ 15 10  / / QC 10  5 5 0 0 0.20.40.60.81.0 0.2 0.4 0.6 0.8 1.0 Voltage / V Voltage / V FigureFigure 8.8. Energy storagestorage performanceperformance ofof graphenegraphene withwith differentdifferent residueresidue oxygen.oxygen. ((aa)) quantumquantum capacitancecapacitance (QC)(QC) andand ((bb)) excessiveexcessive surfacesurface chargecharge densitydensity (ESCD).(ESCD).

AsAs shownshown inin FigureFigure8 ,8, a a band band gap gap can can be be seen seen in in the the electronic electronic structure structure of rGOof rGO with with –OH, –OH, thus thus its QCits QC fluctuates fluctuates with with increasing increasing voltage. voltage. The OThe atoms O at inoms both in kindsboth kinds of rGO of contributerGO contribute to electronic to electronic states belowstates thebelow Fermi the level.Fermi The level. BDCD The resultsBDCD showresults that show the that states the of states the O of atom, the O as atom, well asas the wellπ electronas the π fromelectron carbon from atoms, carbon are atoms, the origin are th ofe origin QC. However, of QC. However, most of themost states of the stemming states stemming from the from O atom the inO theatom –COC– in the group–COC– are group located are belowlocated− below1.0 eV. −1.0 As eV. shown As shown in Figure in Figure9a and 9a Figure and Figure S5, the S5, partial the partial DOS (pDOS)DOS (pDOS) of O inof the O in –COC- the –COC- functional functional group group peaks peaks at −2.45 at eV.−2.45 The eV. BDCD The BDCD of O in of the O energyin the energy range betweenrange between−3.0 eV −3.0 and eV the and Fermi the Fermi level islevel much is highermuch higher than that than between that between the −1.0 the eV −1.0 and eV Fermi and Fermi level. Therefore,level. Therefore, the O atomthe O in atom the –COC–in the –COC– group group have no have obvious no obvious positive positive effecton effect the on QC the and QC ESCD and inESCD the potentialin the potential range ofrange the LICof the cathode. LIC cathode. Only when Only the when applied the applied voltage voltage is up to is 2.45V, up to the 2.45V, O in the the O –COC– in the really–COC– contributes. really contributes. The O in The the O –OH in the group –OH also group show also similar show behavior. similar Inbehavior. Figure9 Inb andFigure Figure 9b and S6, theFigure pDOS S6, and the BDCDpDOS ofand O inBDCD –OH of is higherO in –OH than is that higher of the than O inthat –COC–. of the However, O in –COC–. its contribution However, its is stillcontribution not fully utilizedis still not until fully the utilized applied until voltage the applied is above voltage 2.15 V. is above 2.15 V. OtherOther thanthan itsits ownown contribution,contribution, thethe presencepresence ofof thethe OO atomatom alsoalso affectaffect thethe electronelectron distributiondistribution ofof graphene.graphene. Unlike Unlike the the pristine pristine graphene, in in wh whichich the states contributingcontributing toto QCQC distributedistribute homogeneouslyhomogeneously onon eacheach carboncarbon atom,atom, onlyonly thethe statesstates quasi-localizedquasi-localized onon carboncarbon atomsatoms thatthat areare notnot inin thethe sublatticesublattice ofof thethe carboncarbon atomatom connectingconnecting thethe OO contributecontribute toto QC.QC. ThisThis isis duedue toto thethe factfact thatthat sincesince thethe OO atomatom formform aa covalentcovalent bondbond withwith thethe carboncarbon atomsatoms inin thethe graphenegraphene lattice,lattice, thethe ppzz orbitalorbital ofof thethe carboncarbon atomsatoms connectedconnected toto OO atomsatoms participateparticipate inin thisthis bond.bond. However,However, consideringconsidering thatthat thethe limitedlimited effecteffect onon QCQC andand thethe presencepresence ofof oxygenoxygen atomsatoms willwill decreasedecrease thethe electronicelectronic conductivityconductivity andand eveneven causecause irreversibleirreversible sideside reactions,reactions, OO shouldshould bebe furtherfurther removed before the graphene being used in LIC. PseudocapacitancePseudocapacitance can can be be found found in a supercapacitorin a supercapacitor with aqueous with aqueous electrolyte electrolyte when oxygen-containing when oxygen- carboncontaining materials carbon are materials used as are the used electrode as the due electr to theirode due electrochemical to their electrochemical reaction with reaction H+. However, with H+. However, an aprotic , such as carbonate (EC), propylene carbonate (PC), dimethyl

Catalysts 2018, 8, 444 10 of 14 Catalysts 2018, 8, x FOR PEER REVIEW 10 of 14 carbonatean aprotic (DMC), solvent, is used such in as LIC ethylene electrolyte carbonate due to (EC), its high propylene working carbonate voltage. Thus, (PC), pseudocapacitance dimethyl carbonate will(DMC), very seldom is used inbe LICfound electrolyte for O atoms due toin itsLIC. high working voltage. Thus, pseudocapacitance will very seldom be found for O atoms in LIC.

Figure 9. Band structure, density of states (DOS) and band-decomposed charge density (BDCD) Figureiso-surfaces 9. Band (0.006e/Bohr structure, density3) of (a of) graphene states (DOS) with and –COC–; band-decomposed (b) graphenewith charge –OH. density (BDCD) iso- surfaces (0.006e/Bohr3) of (a) graphene with –COC–; (b) graphene with –OH. 3. Theoretical Calculation Methods 3. TheoreticalMany studies Calculation have used Methods the DFT method to compute the QC of graphene. Most of these are based onMany fixed-band studies approximation, have used the in DFT which method the band to compute structure the and QC the of DOSgraphene. of graphene Most of are these assumed are basedto be on not fixed-band affected by approximation, the electron extracting in which process the band [19,30 structure–35,43]. Althoughand the DOS the resultof graphene will be moreare assumedaccurate to if be the not band affected structure by the variation electron is extracti taken intong process account [19,30–35,43]. [44,45], the fixed-band Although approximation the result will is bestill more adopted accurate here if because the band it provides structure a quick variation response is taken for comparison. into account [44,45], the fixed-band approximationQ is the is surface still adopted charge here on because the graphene, it provides and a quickφ is theresponse applied for voltagecomparison. in the graphene cathode.Q is the Hence, surface charge on the graphene, and ϕ is the applied voltage in the graphene cathode. +∞ Hence, Z Q = e DOS(E) × f(E)dE (2)  Q− e∞ DOS(E) f(E)dE (2)  1 f(E) = (3) 1 + exp1 (E/kT) f(E) (3) 1 exp E / kT f(E) is the Fermi–Dirac distribution function of the electrons, and E is the relative energy with respect f(E)to is the the Fermi Fermi–Dirac level. e is distribution the elementary function charge. of Accordingthe electrons, to theand definition E is the relative of capacitance, energy with the derivative respect todQ/d the Fermiϕ equals level. the QCe is (CtheQ), elementary charge. According to the definition of capacitance, the derivative dQ/dφ equals the QC (CQ), +∞ Z 2 ( − ϕ) dQ 2  sech2 ( E e /2kT) CQ = =dQe 2 DOS(E)sech×  (E e ) / 2kT dE (4) CeDOS(E)ϕQ   dE d d4kT 4kT (4)  −∞

 is the excessive surface charge density when ϕ changes. The graphene electrochemical potential is shifted by eϕ when the applied bias voltage is ϕ.

 Q Q e DOS(E) f(E) f(E e ) dE 0       (5) 

Catalysts 2018, 8, 444 11 of 14

σ is the excessive surface charge density when φ changes. The graphene electrochemical potential is shifted by eφ when the applied bias voltage is φ.

+∞ Z σ = Q0 − Qϕ = e DOS(E) × [f(E) − f(E − eϕ)]dE (5) −∞

The variation range of φ is 0–1.0 V in this calculation. DFT calculation was performed within the Perdew–Burke–Ernzerhof generalized gradient approximation (GGA-PBE), using the Vienna Ab Initio Simulation Package (VASP 5.4) [46]. The projector augmented wave (PAW) method was employed to describe the interaction between core and valence electrons [47]. The cutoff plane wave basis was set to be a 550 eV. 6 × 6 lateral supercell with a of 14.796 Å, used for different kinds of graphene. A vacuum slab with a thickness of 20 Å was set above the graphene sheet. The conjugate gradient relaxation algorithm with a fixed lattice constant was used for ionic position optimization, and this relaxation process will stop when all forces are smaller than 0.01. A 5 × 5 × 1, 9 × 9 × 1, and 12 ×12 × 1 k-point mesh was used to sample the for optimization, energy and DOS calculation.

4. Conclusions We find that point defects and alien atoms promote the QC behavior and hence the energy storage ability of graphene cathodes in LIC. However, the results strongly depend on the detailed structures and the electron origin was different. D2_II, D2_III and B-doped graphene possess much higher QC than pristine graphene, while SW, D2_I, graphitic N and P have no obvious effect on the voltage range of 0–1.0 V. D1 defected graphene and graphene with pyrrolic, pyridine N show very high QC and their energy storage ability is greatly improved due to the presence of unbonded atoms. Therefore, these types of graphene are good candidates for LIC cathodes. The presence of O can also promote the energy storage ability of graphene cathodes in LIC. However, the enhancement is very limited. When it comes to the real word, it is very difficult to fabricate graphene with the exact structure investigated in this paper. Many kinds of defects and are present in graphene simultaneously and only certain structures dominate. For graphitic N, P and B, post-high temperature heat treatment can be used to improve their content in the graphene lattice. Graphene with pyridinic N or pyrrolic N can be obtained by carefully choosing the precursor of C and N in the CVD [48] or thermal annealing process [49]. For the point defects, the hardest work is almost tailoring their type and position in the graphene lattice. Considering that the formation energy is different, post-heat treatment may also be employed to control the point defects. The QC origin of the graphene cathode can provide insight for further studies of its catalytic effect on electrolyte oxidation when the LIC is charged. Graphene with defects and graphitic N, and P and B dopant will be stable with electrolyte due to the relatively stable π states contributing to the QC. However, when unbonded atoms are present in the graphene, the electrolyte may be easily decomposed due to the high reactive σ states. Therefore, the D1 defected graphene and graphene with pyrrolic, pyridine N should be utilized with great care although they show excellent energy storage ability. Further profound work on this catalytic electrochemical reaction mechanism is ongoing.

Supplementary Materials: The following are available online at http://www.mdpi.com/2073-4344/8/10/444/s1, Figure S1: Band structure, DOS and band-decomposed charge density iso-surces (0.003 e/Bohr3) of D2_II defected graphene; Figure S2: Band structure, DOS and band-decomposed charge density iso-surces (0.003 e/Bohr3) of D2_III defected graphene; Figure S3: Split DOS of alien atoms in B, N and P doped graphene; Figure S4: Split DOS and spin density of D1 defected graphene and graphene with pyrrolic and pyridinic N; Figure S5: Split DOS of O in –COC– group and the band-decomposed charge density iso-surces (0.01 e/Bohr3) at different energy range; Figure S6: Split DOS of O in –OH group and the band-decomposed charge density iso-surces (0.01 e/Bohr3) at different energy range. Author Contributions: Investigation and writing original draft, F.S.; formal analysis and review and editing, L.H.; validation, Q.K.; data curation, L.X., project administration, C.C. Catalysts 2018, 8, 444 12 of 14

Funding: This research was funded by the National Natural Science Foundation of China (grant number 51402325), the Scientific and Technological Key Project of Shanxi Province (grant number MC2016-04 and 20141101003). Acknowledgments: The authors acknowledge the Supercomputer Center in Lvliang, China, for providing computational resources. Conflicts of Interest: The authors declare no competing financial interest.

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