First-Principles Calculation of Quantum Capacitance of Codoped

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A First Principle Calculation of Quantum Capacitance of Co-Doped Graphenes as Supercapacitor Electrodes S. Morteza Mousavi-Khoshdel, Ehsan targholi, and Mohammad Jafar Momeni J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b07943 • Publication Date (Web): 09 Nov 2015 Downloaded from http://pubs.acs.org on November 16, 2015

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The Journal of Physical Chemistry

A First Principle Calculation of Quantum Capacitance of Co-doped Graphenes as Supercapacitor Electrodes Morteza Mousavi-Khoshdel*, †, Ehsan Targholi†, Mohammad J. Momeni† †

Industrial Electrochemical Research Laboratory, Department of Chemistry, Iran University of Science and Technology, Tehran, Iran

*

To whom correspondence should be addressed: P.O. Box: 16846-13114. Fax: (+98) 77491204. Phone: (+98) 77240540. E-mail: [email protected]

ACS Paragon Plus Environment

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ABSTRACT Graphene and graphene-based materials, due to many advantages, are used in the supercapacitor electrodes. The main limitation of these electrodes is their low quantum capacitance, which is a direct result of the shortage states near the Fermi level. Using first principle density functional theory calculations, this report explored the quantum capacitance of Si, S, P doped garphene and their co-doped with nitrogen atom. The findings imply that using the phosphorus and nitrogen doped graphenes, as electrode materials for supercapacitors could be a worthwhile strategy. Quantum capacitance calculations confirmed the greater advantage of some co-doped graphenes compared with those of doped ones and pristine graphene.


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1. Introduction Supercapacitors are one of the most interesting electrical energy storage device due to their great advantages such as high power density, operation in wide range of temperature, no memory effect, long life cycle and good stability.1-3 Many efforts are being made to design the new electrode materials for supercapacitors with high power and high energy density.4-6 Graphene and its derivatives have become one of the most promising electrode materials for supercapacitors because of their many advantages such as a high surface area and high electrical conductivity.7-10 However, the limitation of graphene-based supercapacitors is their low energy density.11-14 Doping/co-doping of graphene with p-elements heteroatoms (B, N, P, S, Si) has proven to be a good approach for improving capacitive performance of graphene as supercapacitor electrode. Doped and co-doped graphenes applied successfully in supercapacitor electrodes and indicated better electrochemical behavior with respect to pristine graphene.15-18 Based on results of recent reports,15,

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co-doping graphene with N, P or N, S atoms increase

energy density and specific capacitance of supercapacitor relative to single atom doping of graphene. The total capacity of graphene-based supercapacitors can be considered as series combined of double layer capacitance (CD) and quantum capacitance (CQ).14, 20-21 This statement is valid as long as we do not have the pseudo-capacitance. A deficiency in each of the mentioned capacitances (CD and CQ) can affect the total capacity. Until the last few years, trying to increase the area-specific capacitance was limited to provide strategies to increase the available surface area of the electrode to the electrolyte ions, which this would increases the double layer capacitance. Biener et al. have been able to synthesize graphene-derived electrode with both electrode surfaces in contact with the electrolyte solution.22-23 However, results were contrary to what was expected; The area-specific capacitance has been proven to reduce along with raising the active surface area at the single layer graphene.23-24 It has been found that reduction in areaspecific capacitance of monolayer graphene related to their low concentration of surface electronic state near the Fermi level.13-14, 21 Beside, Jeong and coworkers reported that they were able to achieve a fourfold increase in capacitance in comparison to pristine graphene using of N-


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doped graphene.25 It was confirmed that changes in the electronic structure of graphene by doping of nitrogen have led to increased capacity.14,

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So, it was concluded that the limiting

factor in total capacity of graphene-based supercapacitors is their finite quantum capacitance, which related to their electronic properties.13-14, 21 Recently, much attention has been paid to find solutions for increasing the quantum capacitance of graphene-based materials.20, 26-28 The results indicated that the use of boron-doped and nitrogen-doped graphene could be used as electrode materials in asymmetric supercapacitors. In another research, Hwang et al. reported that metal-doping graphene can efficiently mitigate the quantum capacitance limitation.27 It was also reported that existence of structural defects at appropriate concentrations may also enhances the quantum capacitance.20-21 In our previous work it was found that functionalization of graphene make an increase in the quantum capacitance.28 In this study using DFT calculations the effects of co-doping of graphene (with PN, SN and SiN) on its geometrical structure, electronic properties and quantum capacitance have been investigated.

2. Computational method Calculations were carried out within the framework of density functional theory (DFT) using a local density approximation scheme, as implemented as a part of SIESTA package.29 The generalized-gradient approximation (GGA) for the exchange-correlation functional with the parameterization of Perdew-Burke-Ernzerhof (PBE)30 were used. The core electrons were represented by norm-conserving nonlocal Troullier–Martins31 type pseudopotential and valence electron wavefunctions are expanded as a linear combination of numerical pseudoatomic orbitals. Double-zeta plus polarization (DZP) basis set with a 50 meV energy cut-off, which defines the radial confinement of orbitals, was used. DZP basis set proved to be sufficient for quantum mechanical study of materials with a good accuracy at reasonable computational cost. Real-space integration were performed on a grid with a cut-off kinetic energy of 400 Ry. Periodic DFT calculations were implemented on a 5 × 5 hexagonal supercell (50 atoms) to study the effects of doping/co-doping on graphene electronic structure. To avoid graphene sheet interaction with its periodic images, a vacuum gap of 15 Å in z direction were used. Full geometrical relaxations were fulfilled with Broyden32 method until maximum forces on each atom become less than 0.04 eV/Å. Brillouin zone was sampled with a 4 × 4 × 1 MonkhorstACS Paragon Plus Environment

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Pack33 grid and spin polarization calculations were considered for systems with an odd number of electrons. For obtaining density of state (DOS) a 30 × 30 × 1 Monkhorst-Pack of k-point mesh was used.

3. Results and discussion 3.1. Geometrical and electronic properties of co-doped graphenes According to previous studies, N-doped graphene exists in three configurations, i.e., graphitic, pyridinic and pyrrolic.34 It was also showed that nitrogen atoms incorporate to SN-graphene mainly in graphitic or pyrrolic configurations. But in PN-graphene, nitrogen atoms embed especially in pyridinic N groups.19, 35 In this report, silicon, phosphorus and sulfur atoms are codoped with three mentioned N-doped graphene structures. Optimized structures of P-doped and PN co-doped graphenes are depicted in Figure 1.

Figure 1. Optimized structures of P-doped and PN co-doped graphenes

Calculation results show a C-C bond length of 1.420 Å for pristine graphene, which is in good agreement with previous results36. In relaxed structure of P-doped graphene (P-Gr), phosphorus atom is projected from the graphene plane by 1.473 Å with a P-C bond length of 1.788 Å and CP-C bond angle of 97.582°. Along with phosphorus atom protrusion, three nearest neighbor


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carbon atoms slightly come out from graphene plane and adjacent C-C bond lengths altered from 1.420 to 1.408 and 1.441 Å. These data along with pyramidal-like structure are suggestive of a sp3 hybridization for phosphorus atom. Structural parameters including C-X bond length (X= P, Si, S), C-X-C bond angle and X-projection from graphene plane (hz) are given in Table 1.

Table 1: structural parameters for studied systems (X is indicative of P, Si or S atom) System

C-X (Å)

C-X-C

hz (Å)

P-Gr

1.788

97.582

1.473

PN-graphitic

1.801

96.475

1.519

PN-pyridinc

1.772

103.690

1.350

PN-pyrrolic

1.779

100.152

1.459

Si-Gr

1.777

102.882

1.486

SiN-graphitic

1.798

100.512

1.543

SiN-pyridinic

1.775

107.325

1.389

SiN-pyrrolic

1.778

103.890

1.471

S-Gr

1.769

98.933

1.350

SN-graphitic

1.770

99.375

1.369

SN-pyridinic

1.775

102.466

1.283

SN-pyrrolic

1.766

100.568

1.353

Band structures and density of states (DOS) were calculated for all fully optimized pristine and doped/co-doped garphene structures. In the band structure of pristine graphene with a zero gap (Figure S1 in supporting information), maximum of valence band (MVB) and minimum of conduction band (MCB) touch each other in Dirac point, which is indicative a semimetallic behavior.37 Band structure, DOS and PDOS of P-doped and PN co-doped graphenes are shown in figure 2. The electronic bands of studied structures are plotted along the usual Brilouin path of Γ − K − M − Γ.


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Figure 2. Band structure, DOS and PDOS for a) P-doped, b) PN-graphitic, c) PN-pyridinic and d) PN-pyrrolic graphenes.


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In the band structure of P-doped graphene, a closely flat band has appeared in the Fermi level, which resulted in a sharp peak in the DOS plot. Partial DOS (PDOS) data indicates a strong hybridization between P-3p and C-2p (three neighbors C atoms). Observed flat band in P-Gr band structure is a delocalized band, which the pz orbitals (peak I in DOS plot) of three carbon atoms bonded to P, have greater contribution relative to other carbons. Doping graphene with P atom open the band gap by a value of 0.52 eV. According to Hirshfeld population analysis, P atom donates 0.19 e to graphene plane; and the magnetic moment of P-doped graphene found to be 0.99 due to breaking of the symmetry of spin down and spin up populations. By embedding N atom (in graphitic configuration) in P-doped graphene, Fermi level shifted down 0.28 eV and the flat band in the vicinity of Fermi level which exists in P-Gr vanished; therefore some states near the Fermi level disappeared and a band gap of 0.75 eV is induced. Peak (I) in DOS plot of figure 2-b result from overlapping of C-2p and P-3p orbitals. In contrary, due to the presence of defect in pyridinic and pyrrolic PN co-doped graphenes, bands near the Fermi level moderately flattened relative to pristine graphene and as a result, new electronic states created in the proximity of Fermi level.20 These new electronic states could be clearly observed in DOS plots. PDOS analysis of PN-pyridinic graphene show that the states at -1.2 eV (peak I) mainly originates from nitrogen 2p orbitals and three peaks (II, III and IV) around Fermi energy primarily evolved from p orbitals of carbon atoms presented in the defect region and carbons connected to phosphorus atom. Band structure of PN-pyridnic graphene shows a 0.55 eV band gap. While in pyrrolic PN-graphene, a band gap of 0.46 eV has been found. Projection on atomic orbitals indicates that the emergence of new states (peaks II and IV) in pyrrolic PN co-doped graphene, attributed to carbon atoms with dangling bonds and states which denoted by peaks I and III arise from overlapping of pz orbitals of all carbon atoms (which not shown in figure 2-d). These states are delocalized over whole graphene plane while states represented by peaks II and IV are localized around dangling bonds. Band structures, DOS and PDOS plots of S-, Si-doped graphenes are shown in figrue 3.


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Figure 3. Band structure, DOS and PDOS of a) Si and b) S-doped graphene. In both Si-Gr and S-Gr, the minimum of conduction band shifted up while the maximum of valence band shifted down compared to pristine graphene, which form semiconductors with band gaps of 0.47 (S-Gr) and 0.24 eV (Si-Gr). Spin polarized calculations denotes a symmetric spinup and spin-down DOS which lead to a nonmagnetic state for S-Gr and Si-Gr. In DOS plot of Si(S)-Gr a prominent peak is observed near the Fermi level relative to pristine graphene which Si(S)-3p and C-2p (three carbon atoms bonded to Si(S)) orbitals have a significant contribution in its creation. These new states are a consequence of Si(S) projection from graphene plane, which disrupt the system of graphene and give some sp3-like character to atoms present in the doping region. The band structure and DOS and of SiN and SN co-doped graphenes are given in supporting information (figures S2 and S3).


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3.2. Quantum capacitance As mentioned in introduction section, the following equation can be used to describe the total capacity of graphene-based materials without pseudo-capacitance.

1

C

=

1 1 + C C

(1)

Where C , C and C are total capacitance, quantum capacitance and double layer capacitance, respectively. C can be defined as

where

and Φ" refer to differential

charge density and graphene potential. The excess charge density is obtained by equation (2). +,

= #$

-,

%&')[)&') − )&' − #Φ" )*'

(2)

Where D(E) is the density of state, f(E) is the Fermi-Dirac distribution function, E is the relative energy with reference to Fermi level and e is the elementary electric charge. Substitution of equation (2) in quantum capacitance equation yields the differential quantum capacitance. 01

./

+,

= #2 $

-,

%&')34 &' − )'

(3)

Where 34 &') is the thermal broadening function and stated as follow 20,13,14: 34 &') =

1 ' 7#8ℎ2 & ) 456 256 ;

(4)

Where 56 is Boltzmann’s constant and T is the temperature that considered to be 300 K in this work. The integrated quantum capacitance, which reported in this article, has been estimated numerically by equation (5): ./0) =

1 B $ . ?> ΄ A> ΄ ># C /

(5)

By the same token, the relation between stored charge and integrated quantum capacitance is given as follow equation 21: D

./0

First-Principles Calculation of Quantum Capacitance of Codoped

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