Effects of heteroatom doping on the performance of graphene in sodium-ion batteries: A density functional theory investigation

Accepted Manuscript Effects of heteroatom doping on the performance of graphene in sodium-ion batteries: A density functional theory investigation Kimal Chandula Wasalathilake, Godwin A. Ayoko, Cheng Yan PII:

S0008-6223(18)30806-6

DOI:

10.1016/j.carbon.2018.08.071

Reference:

CARBON 13426

To appear in:

Carbon

Received Date: 10 July 2018 Revised Date:

24 August 2018

Accepted Date: 31 August 2018

Please cite this article as: K.C. Wasalathilake, G.A. Ayoko, C. Yan, Effects of heteroatom doping on the performance of graphene in sodium-ion batteries: A density functional theory investigation, Carbon (2018), doi: 10.1016/j.carbon.2018.08.071. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Effects of Heteroatom Doping on the Performance of Graphene in Sodiumion Batteries: A Density Functional Theory Investigation Kimal Chandula Wasalathilake, Godwin A. Ayoko and Cheng Yan* School of Chemistry, Physics and Mechanical Engineering, Queensland University of

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*Corresponding author. Email: [email protected] (Cheng Yan)

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Technology (QUT), Brisbane QLD 4001, Australia

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Effects of Heteroatom Doping on the Performance of Graphene in Sodium-ion Batteries: A Density Functional Theory Investigation Kimal Chandula Wasalathilake, Godwin A. Ayoko and Cheng Yan*

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School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology (QUT), Brisbane QLD 4001, Australia Abstract

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Heteroatom doped-graphene is a potential candidate as an anode material in sodium-ion batteries (SIBs). However, one of the major issues holding back its development is that a complete understanding of the doping effects accounting for the Na-ion storage of heteroatom-doped

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graphene has remained elusive. In this work, first principles calculations have been conducted to systematically investigate the electronic and geometric effects in various heteroatom-doped graphene. Graphene doping with pyridinic-N, pyrrolic-N, F and B improves the electrochemical Na storage due to the electronic effect which originates from electron deficient sites (i.e. defects or electron deficient atoms). On the other hand, P doping improves the Na storage ability of

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graphene due to the geometric effect caused by bond length mismatch. In contrast, the introduction of graphitic-N and S into graphene is inefficient for Na storage because of their inability to accept electrons from Na. Interestingly, the diffusion energy barriers obtained for Na on doped graphene are lower than that for the pristine graphene. Furthermore, co-doping strategy

1. Introduction

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is predicted to achieve even better Na storage capacity due to the synergistic effect.

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Recently, sodium-ion batteries (SIBs) have emerged as a promising alternative to Li-ion batteries (LIBs) for long term and large-scale energy storage, due to high abundance of sodium, low cost, inherent safety and considerable energy density [1, 2]. The working principle of SIBs is similar to LIBs, and involves the migration of sodium ions from the cathode to the anode during charging, and back to the cathode during discharging. However, the practical application of SIBs is delayed due to the relatively low reversible capacity and poor rate capability which are attributed to the alteration in electrochemical kinetics caused by large radius of Na+ compared to Li+. The large sized Na+ leads to sluggish diffusion efficiency, high volumetric change and *Corresponding author. Email: [email protected] (Cheng Yan)

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severe pulverization of anode materials [2-4]. Furthermore, it may result in an unstable solidelectrolyte-interface which adversely affects the reversible capacity and cycle stability. Therefore, development of electrode materials with high specific capacities and cycling

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stabilities with good reversibility is essential for practical application of SIBs. Even though graphite has been utilized as a common anode material in LIBs, it has proved to be unsuitable for SIBs due to the insufficient inter-layer distance for sodium intercalation, poor thermodynamic stability and the formation of NaC70 instead of NaC6 [5, 6]. In recent years carbonaceous materials [7-9], transition metal oxides [10, 11] and alloys [12, 13]

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were investigated as anode materials in SIBs. Among carbon-based materials, graphene has attracted increasing attention as a top prospect to achieve higher battery performance due to its

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excellent electrical properties and unique two-dimensional (2D) structure with high surface area. Wang et al. used reduced graphene oxide (rGO) and achieved a reversible capacity of 174.3 mAhg-1 at a current density of 0.04 Ag-1[14]. Expanded graphite prepared by a two-step oxidation-reduction process exhibited a reversible capacity of 284 mAhg-1 at a current density of 0.02 Ag-1[15]. Meanwhile doping of graphene with boron, nitrogen, phosphorous, sulfur or other heteroatoms has proved to be an effective method to tailor the electronic and chemical properties

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of graphene [16]. Recently, heteroatom-doped graphene has been used as anode materials for SIBs. Li et al. proved that nitrogen-doped carbon nanosheets could exhibit a specific capacity of 250 mAhg-1 at a current density of 0.1 Ag-1[17]. It was reported that large-area carbon nanosheets doped with phosphorous has a high reversible capacity of 328 mAhg-1 even at a high

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current density of 20 Ag-1[18]. Despite a remarkable capacity improvement has been achieved by heteroatom doping of graphene, it is not clear how the Na adsorption is improved. Thus, more

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theoretical studies performed at molecular level considering atomic energies, kinetics, chemical and physical interactions are essential to explore the underlying mechanisms of Na adsorption of various doped structures. Several density functional theory (DFT) studies have been carried out to explore the sodium interaction with B-doped graphene [19], N-doped graphene [20] and confirmed that the underlying mechanisms are quite different. Therefore, the interaction between Na and different doped structures deserves further investigation. Furthermore, a parallel comparison between various doped graphene structures based on analogous doping concentration is still in the absence. A systematic consideration of doped graphene structures is in utmost need to guide the sensible design of SIB anode materials for improved performance. *Corresponding author. Email: [email protected] (Cheng Yan)

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In this study, N, B, S, P and F-doped graphene were modeled using DFT to evaluate their interaction with sodium, in terms of adsorption energy, charge transfer, electron density difference and density of states. Diffusion barrier, structural deformation and multiple Na storage capacity were also investigated to guide the future screening and design of heteroatom-doped

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graphene anodes with better performance. 2. Computational Methods

The adsorption energy, bond length, charge transfer and density of states near Fermi energy

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region are examined within density functional (DFT) theory by DMol3 package [21, 22]. The generalized gradient approximation (GGA) with Perdew–Burke–Ernzerhof (PBE) functional [23] was employed to describe the electron-electron exchange correlations. To consider the van der

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Waals interaction, a long-range dispersion correction via Tkatchenko and Scheffler’s (TS) scheme [24] was used. It has been shown that the TS scheme provides good accuracy in adsorption energies and diffusion barriers for Na–carbon systems [25]. Double numerical plus polarization (DNP) was specified as the basis set and DFT semi-core pseudopods were employed to describe core electrons. The k-points were generated using the general Monkhorst-Pack

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scheme [26] for the Brillouin zone sampling and k-points of 3 x 3 x 1 were used for structural configuration optimizations of periodic models. A dense 8 x 8 x 1 k-points grid was used to calculate density of states (DOS) for the electronic relaxation. The convergence tolerances of energy, maximum force and maximum displacement were set to 2.0 × 10−5 Ha, 4 × 10−3 Ha Å−1

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and 5 × 10−3 Å, respectively. Pristine graphene and X-doped graphene structures (X= N, B, S, P and F) were modeled as a 4 x 4 x 1 super cell. X-doped graphene used in this study was modeled corresponding to a doping concentration around 3.2 at% which is consistent with the doping

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concentration reported experimentally [27-29]. Periodic boundary conditions (PBC) were applied with a vacuum distance of 20 Å along the z-direction in order to avoid the interaction between the original structure and neighbouring layers. To model bilayer graphene (BLG), an undoped graphene layer was introduced to the top of the existing undoped/doped graphene layer and after optimization the layered structure showed AB stacking. The amount of charge transfer between Na and host materials were estimated using the Mulliken population analysis. The charge density difference of the optimized structures was calculated by CASTEP package [30] by using a plane wave energy cut-off of 517 eV. The charge density difference is calculated by the formula, ∆ρ = *Corresponding author. Email: [email protected] (Cheng Yan)

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ρTotal – (ρgraphene + ρNa), where ρTotal, ρgraphene and ρNa are the real-space electronic charge distributions of Na adsorbed graphene, graphene and isolated Na, respectively. Diffusion barrier calculations were performed using the nudged elastic band (NEB) method. Initially the Linear Synchronous Transit/ Quadratic Synchronous Transit (LST/QST) search algorithm was used to

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locate the transition state and then NEB method was used to confirm the transition state on the minimum energy path (MEP). 3. Results and Discussion

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3.1. Heteroatom-doping of graphene

Figure 1 shows the computational models of doped graphene structures. When a nitrogen atom is doped into graphene, mainly it can exist in three bonding configurations within the carbon lattice

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(graphitic N, pyridinic N, and pyrrolic N). Therefore, geometric structures of three possible configurations were built and optimized to represent graphitic-N (NG1), pyridinic -N (NG2) and pyrrolic -N (NG3).

Previous experimental studies have reported that pyridinic-N bonding

configuration is stable in the presence of mono-vacancy while pyrrolic-N energetically favours a di-vacancy defect [31, 32]. Thus, NG2 was obtained by replacing a carbon atom with one

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nitrogen atom and removing another carbon atom to create a mono-vacancy defect. Furthermore, NG3 was obtained by substituting one carbon atom with one nitrogen atom to form a five

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membered-ring while removing another carbon atom to create a di-vacancy defect. As the

*Corresponding author. Email: [email protected] (Cheng Yan)

Figure 1. Top and front views of optimized structures of a) graphene, b) NG1, c) NG2, d) NG3, e) BG, f) SG, g) PG and h) FG. Selected adsorption sites are shown in each structure. Grey, blue, orange, yellow, pink and cyan represent carbon, nitrogen, boron, sulfur, phosphorous and fluorine atoms, respectively. This notation is used throughout the paper.

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electronic configuration of nitrogen is 2s2 2p3, in graphitic-N (NG1) three of those valence electrons form three σ bonds with neighbouring carbon atoms. Another electron engages in the formation of a π bond and the other electron partially involves in the π*-state of the conduction band [33]. This is well supported by the DOS of NG1 (Figure S1), where it can be seen that the

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major band features have moved towards the valence band and the Fermi level has moved to the conduction band due to extra π electrons, changing the conductive behaviour to n-type. In NG2 and NG3, the Fermi level is slightly shifted to the valence band since the defects impose the ptype effect by withdrawing electrons from the graphene sheet[34]. Localized acceptor-like peaks

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near the Fermi level at the top of the conduction band, suggest that NG2 and NG3 have the ability to attract electrons on their defective sites. Boron, sulfur and phosphorous-doped graphene were modelled by substituting one C atom with a dopant atom, and they are referred as

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BG, SG, and PG, respectively. Since the electron configuration of boron is 2s2 2p1, when doped onto graphene, it binds with the three closest carbon atoms and lacks one electron compared to carbon. According to DOS of BG (Figure S1), the Fermi level has depressed in to the valence band indicating that it has become a p-type conductor with an electron-deficient system. Graphene basal place undergoes a structural distortion when it is doped with sulfur and

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phosphorous atoms because of the larger atomic radii compared to carbon. Both sulfur and phosphorous form a pyramidal like bonding configuration with the neighbouring three carbon atoms and they are pulled out of the plane by 0.38 Å and 0.56 Å respectively. Since the electron configuration of fluorine (2s2 2p5) limits the hybridization of fluorine atom to sp-type, it bonds

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with one carbon atom in the vicinity of a vacancy site[35]. A recent experimental study further confirms that F is most likely to undergo a substitution reaction with the oxygen functional

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groups of GO rather than substituting a carbon atom in the basal plane [36]. Furthermore, Qian et al. has experimentally demonstrated that C-F bond is always accompanied by the presence of structure defects containing vacancies [37]. Therefore, FG was obtained by bonding F atom with one C atom and removing another C atom to create a mono-vacancy defect. As the unbonded electrons of the fluorine atom have strong repulsion against the unpaired electrons of the unbonded neighbouring carbon atoms, the F-C bond sticks out of the basal plane and the carbon atom is pulled out of the plane by 0.91 Å.

*Corresponding author. Email: [email protected] (Cheng Yan)

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3.2. Na adsorption sites and adsorption energies In order to find the most favourable Na adsorption site for each structure, we considered three possible adsorption sites (Figure 1), i.e. on the top of the hexagon (H site), on the top of C or X

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atom (T site, where X=N, B, S, P or F), and on the top of the middle of a C-C or C-X bond (B site). To investigate the adsorption behaviour of sodium on doped graphene, we calculated the adsorption energy according to, =

−(

+

)/

(1)

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where ETotal, Egraphene and ENa are total energy of the Na adsorbed graphene, energy of graphene in the same cell and energy of an isolated Na atom respectively; nNa is the number of adsorbed

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Na atoms. According to the above definition, more negative adsorption energy value implies stronger (energetically favourable) interaction between graphene and Na atoms. Simulations were carried out for different adsorption sites for each structure and the calculated adsorption energies are summarized in Table 1 and Table S1.

Table 1. The most stable site for Na adsorption, adsorption energy (Ead) and charge transfer from Na to graphene structures

Adsorption energy (eV) -1.63 -1.32 -3.06 -3.25 -2.51 -1.55 -2.47 -2.45

Charge transfer (e) -0.70 -0.69 -0.81 -0.77 -0.81 -0.70 -0.79 -0.81

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Graphene NG1 NG2 NG3 BG SG PG FG

Most stable adsorption site H H2 H1 H1 H1 T1 T1 H1

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Structure

NG3 and NG2 exhibit significantly high adsorption energies of -3.25 eV and -3.06 eV

respectively, towards Na than undoped graphene of -1.63 eV. In both the instances, Na remains stable at the centre of the defect (Figure 2c-d) as the surface dangling bonds which arise from the formation of vacancies induce strong attraction to Na. Furthermore, graphene doping with B, P and F leads to the strengthening of Na-graphene interaction with adsorption energy values of 2.51 eV, -2.47 eV and -2.45 eV, respectively. According to our results, the most favourable adsorption site in BG is at the hollow site containing B atom (C5B). In the optimized structure *Corresponding author. Email: [email protected] (Cheng Yan)

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Figure 2. Optimized interaction geometry of Na and a) graphene, b) NG1, c) NG2, d) NG3, e) BG, f) SG, g) PG and h) FG. The distances between the nearest atom and Na are shown. (Na atoms are represented by purple)

(Figure 2e), Na atom slightly moves away from the centre of the hexagon and moves towards B

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because of the increased attraction. Interestingly in PG, the most energetically favourable adsorption is obtained when Na adsorbs from the opposite side of the plane protrusion triggered by P (Figure 2g). In the case of FG, Na remains stable above the mono-vacancy defect which is formed due to the formation of the F-C bond (Figure 2h).

NG1 exhibits the weakest adsorption energy of -1.32 eV out of the doped graphene

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structures considered here. Interestingly, Na remains to be stable at a hollow site (Figure 2b) which is entirely surrounded by C atoms (C6) rather than a hollow site containing a nitrogen atom (C5N).

Similar to graphitic-nitrogen, S is also unable to provide adequate attraction

towards Na. The adsorption energy of SG is close to undoped graphene, suggesting that

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introducing S to graphene would be an unsuccessful effort to improve the performance of the Na-ion battery. One might argue that S doping would improve the attraction towards Na, inspired

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by its successful application in a broad range of catalytic reactions [38]. However our results lie on the opposite side and well explains why a S-doped graphene anode delivered a reversible capacity of 262 mAhg-1 at a current density of 0.1 Ag-1 [39]whereas a pyridinic and pyrrolic Ndoped graphene anode delivered a significantly high reversible capacity of 815.2 mAhg-1 even at a current density of 0.2 Ag-1 [40]. The weak interaction between Na and NG1 can be attributed to the electron-rich nature of nitrogen atom, which limits the ability of Na to donate electrons to graphene near N atom [41]. Due to the high electro-negativity of N (3.04) which is significantly higher than C (2.55), we found that N has withdrawn a charge of 0.47e from the neighbouring carbon atoms, as electrons *Corresponding author. Email: [email protected] (Cheng Yan)

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tend to flow towards N. Upon adsorption, Na moves away from the electron-rich nitrogen atom and lies in a region where it can easily donate charge to carbon atoms. Therefore, Na prefers to remain at a hollow site consisting of carbonic hexagon (C6) rather than C5N. As reported by Debrota et al. [42], the corrugation of the carbon basal plane caused by chemically different However, as the

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dopants, alters the surface reactivity towards various adsorbates.

electronegativity of S (2.58) is almost identical to C, we observed only a small charge transfer (0.09 e) from sulfur to the graphene basal plane. Therefore the negligible electronegativity difference outweighs the potential surface reactivity caused by the structural distortion and

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consequently, SG transforms to an electron-balanced system like graphene. This further confirms why SG exhibits similar attraction like graphene towards Na.

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Although NG2 and NG3 consist of a high electronegative N atom, those N-doped structures are capable of inducing strong interaction with Na due to the presence of defects. According to Figure 3a & b, the charge of Na has transferred to the nitrogen-decorated defective region, as evidenced by the green region representing the charge accumulation. The vacancy at the defective region breaks the symmetry in the π-electron system of carbon, causing the localization of charge-electron density on the defect. We found that charge of 0.81e and 0.77e

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have gained by NG2 and NG3 from Na, respectively, proving the fact that these electron deficient sites generate tendency to accept electrons. This supports the view that the strong trapping of Na by NG2 and NG3 is caused mainly by Coulomb interaction following charge transfer. When boron is introduced to the graphene matrix, since B has one electron less than

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carbon, graphene becomes an electron deficient system. The electrons in the B-C bond moves towards the more electronegative C. Therefore, these electron deficient sites are attracted by

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electron rich Na. Using Mulliken charge analysis we found that Na atom donates a charge of 0.81e to BG surface, almost completely ionizing the Na atom. The saturation of the electrondeficient B-C bond results in a strong chemical bond between BG and Na ion (Figure 3c).The enhanced attraction of PG towards Na can be attributed to the localized structural distortion near the P atom. Furthermore, there is also a possibility of the delocalized π electrons of graphene to be partially broken in the vicinity of the P atom [38]. Figure 3d demonstrates the strong interaction of PG with Na, in which a significant charge accumulation can be seen around the neighbouring carbon atoms as a result of the structural effect caused by P. 2s2 2p5 electron configuration leads to sp-type hybridization of F atom to bond with only one carbon atom in FG *Corresponding author. Email: [email protected] (Cheng Yan)

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causing a mono-vacancy site. Due to the strong repulsion between the unbonded electron pairs

*Corresponding author. Email: [email protected] (Cheng Yan)

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of F and the unpaired electrons of two neighbouring C atoms, the F atom is pushed away from

*Corresponding author. Email: [email protected] (Cheng Yan)

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Figure 3. Charge density difference plots for Na adsorption on a) NG2, b) NG3, c) BG, d) PG, and e) FG

the graphene basal plane. Although FG should have weak interaction with Na due to the *Corresponding author. Email: [email protected] (Cheng Yan)

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electron-rich nature of the fluorine atom as graphitic-nitrogen, the mono-vacancy created by the F-C bond transforms it to an electron-deficient region which has the tendency to accept electrons from Na atoms. Upon Na adsorption, FG gains a significant electron charge of 0.81 e from Na. According to the charge difference plot (Figure 3e), large number of electrons accumulate

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around the mono-vacancy site and a significant amount of electrons is lost from Na, demonstrating the strong interaction of FG with Na.

To further understand the adsorption mechanism of Na and host materials, the partial density of states (PDOS) of different atomic states of Na adsorbed doped-graphene structures are

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presented in Figure 4. The peaks of Na 3s appear above the Fermi level in the PDOS contributing

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only to the conduction band, which gives the clear indication that Na is fully ionized. Na 3s

Figure 4. Partial density of states (PDOS) of a) graphene, b) NG1, c) NG2, d) NG3, e) BG, f) SG, g) PG and h) FG with Na.

*Corresponding author. Email: [email protected] (Cheng Yan)

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peaks lie above the Fermi level at almost the same position in graphene, NG1 and SG, further confirming the similar adsorption energy values of these systems, leading to poor adsorption of Na. Whereas, Na 3s peaks of all the other doped-graphene structures lie far above the Fermi level exhibiting the strong adsorption energy. The N 2p peaks of NG2, NG3, B 2p peak of BG and F

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2p peak of FG do not overlap with Na 3s peaks, further confirming that the strong Na adsorption is caused by the Coulomb interaction. However, the overlapping of Na 3s orbital with C 2p orbital of PG (figure g), shows the influence of the localized structure effect, resulting in

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overlapping with sp3-C with Na atom through the outer s orbital forming a strong covalent bond. 3.3. Intercalation energies

Formation of solid-electrolyte-interface (SEI) at low operating potentials of the anode can

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potentially hamper the transportation and adsorption of Na+ ions, affecting the capacity retention over long-term cycling. Therefore suppression of the SEI layer is essential for better cycling performance and safety of the cell. One strategy to mitigate the uncontrolled formation of SEI on the anode surface, is to use multi-layer graphene [19]. To investigate the influence of multi-layer doped graphene towards the trapping of Na atoms, we calculated the intercalation energy of Na

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in un-doped and doped bi-layer graphene (BLG) structures. The intercalation energies for Na inserted in BLG were calculated according to, =

– (

+

)

(2)

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where ETotal, EBLG and ENa are total energy of Na inserted BLG, energy of BLG and energy of an isolated Na atom respectively. Figure S2 shows the energetically favourable configurations of Na

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adsorbed BLG structures. In general, there is stronger bonding strength in BLG compared to single layer graphene as the intercalated Na atom interacts with both sides of graphene sheets [43]. BLG doped with pyrrolic-N, F and pyridinic-N exhibit stronger attraction towards Na with intercalation energies of -3.60 eV to -3.65 eV than undoped BLG of -2.60 eV by raising the intercalation energy by about 1.0 eV.

P-doped and B-doped BLG exhibit relatively high

intercalation energies, whereas S-doped BLG is unable to make any considerable impact on increasing the attraction towards Na, as similar to S-doped single layer structure. The situation is even worse for the graphitic-N doped BLG as the intercalation energy drops to -2.14 eV, further

*Corresponding author. Email: [email protected] (Cheng Yan)

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confirming the ineffectiveness of graphitic-N as a dopant for graphene to be used as a Na-ion battery anode. 3.4. Electrochemical performance and cycling stability

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One of the key parameters which decides whether a material can be effectively applied to SIBs, is the Na storage capacity of the anode material. To gain further insight into the sodiation process of heteroatom-doped graphene, structures of different sodiated phases were examined. Adsorption of one to six Na atoms on both sides (double-side adsorption) of the substrate was

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evaluated and figure 5 illustrates the optimized geometries of six Na atoms (n=6) adsorbed on doped-graphene structures.

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Upon adsorption of six Na atoms, all the doped-graphene structures along with pristine graphene have become asymmetric and the adsorption configurations have changed significantly.

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Although initially we found that single Na atom prefers to remain stable at hollow sites in

Figure 5. The optimized geometries of six Na atoms adsorbed on a) graphene, b) NG1, c) NG2, d) NG3, e) BG, f) SG, g) PG and h) FG. (Atoms which are adsorbed from the opposite side of the plane are represented by crimson)

*Corresponding author. Email: [email protected] (Cheng Yan)

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graphene, NG1 and BG, when multiple atoms are introduced to the substrate, they tend to move away from hollow sites while only one or two Na atoms remain at hollow sites. In NG2 and NG3, two Na atoms are distributed on both sides and around the nitrogen-decorated vacancy while other atoms have moved away from the defective site even though Na energetically

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favours the adsorption sites in the vicinity of the defect. In both SG and PG, the Na adsorption behaviour is quite similar, in which one Na atom remains at the hollow site slightly close to S/P atom, while other Na atoms have distributed away from the centre. In the case of FG, one Na atom remains adsorbed at the defective region and another atom is adsorbed from the opposite

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side of the F atom. All the other Na atoms are distributed across the substrate from both sides of

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the graphene sheet.

Figure 6. The relationship between the average adsorption energies and the number of Na on graphene structures

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Figure 6 shows the double-side adsorption energy profile of doped-graphene structures as a function of Na atoms from one to six and, it is evident that the magnitude of Eads decreases with the increasing number of Na atoms (Table S2). The reduction of the adsorption energy is

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attributed to two main factors. One is the weakened interaction between Na atoms and the substrate itself. The charge transfer from the Na atom to doped graphene structures reduces significantly as the number of Na atoms increases. The other factor is the enhanced repulsion between Na atoms in high Na loadings. Thus, we describe the sodiation process of dopedgraphene as a competition between the attraction of Na by the substrate and repulsion forces between Na atoms. We find that for any Na loading, double-side adsorption is always more favourable than single-side adsorption, due to the minimization of Na-Na repulsion. At low Na loadings, since the chemical bonding dominates the adsorption, Na atoms remain at their most *Corresponding author. Email: [email protected] (Cheng Yan)

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favourable adsorption sites. However at high loadings, Na atoms are forced to shift away from their favourable adsorption sites to minimize the repulsion between them. The maximum Na capacity limit of each doped-graphene (Table S3) was obtained by

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further introducing Na atoms to the surface until the adsorption energy (eV/Na) becomes positive. The theoretical specific capacity was calculated according to equation (3) [44], =−

(3)

where n, NA, e, ε and M stands for maximum number of Na atoms adsorbed per mole of doped

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graphene, Avogadro constant, elementary charge, ratio for conversion of mAh to Coulombs (=3.6) and molar mass of doped-graphene. The theoretical capacity of undoped graphene was

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calculated to be 308 mAhg-1 and agrees well with the reversible capacities of 300 mAhg-1 [45] and 284 mAhg-1 [15] obtained experimentally for hard carbon and expanded graphite anodes in SIB respectively. The highest theoretical specific capacity of 384 mAhg-1 was given by NG3 as the pyrrolic nitrogen-decorated defective region effectively overpowers the repulsion between adjacent Na ions. Even at a low doping concentration (3.2 %), NG3 has a high theoretical specific capacity compared to transition metal-based anodes like Ti3C2 MXene (352 mAhg-1),

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MoS2 (335 mAhg-1) and NbSe2 monolayer (312 mAhg-1) [46-48].

Table 2. X-C (X= N, B, S, P and F) and C-C bond lengths before and after Na adsorption

Before Adsorption (n = 0) d(X-C) d(C-C) 1.42 1.42 1.33 1.44 1.45 1.43 1.49 1.43 1.63 1.42 1.62 1.42 1.35 1.43

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Substrate

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NG1 NG2 NG3 BG SG PG FG

After Adsorption (n = 6) d(X-C) d(C-C) 1.42 1.43 1.36 1.43 1.44 1.43 1.48 1.42 1.76 1.42 1.80 1.43 1.40 1.43

Cycling stability is another key attribute of a high-performance Na-ion battery material. Excessive deformation of the anode material during sodiation/desodiation could result in a drastic reduction of capacity in a few cycles [49]. Therefore, the distances of X-C bond (X= N, B, S, P and F) and C-C bond lengths after adsorption of six Na atoms were measured to evaluate *Corresponding author. Email: [email protected] (Cheng Yan)

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the degree of deformation (Table 2). In all the structures, C-C bond length remains almost unchanged and it only varies by 0.01 Å. The distance between the dopant atom and the carbon atom only undergoes very small displacements in NG1, NG2, NG3 and BG (≤ 0.03 Å). However, the average bond lengths of S-C and F-C in SG and FG, increase by 7.8% and 3.33%

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respectively, compared to their original bond lengths during the sodiation. Furthermore, the highest structural deformation is experienced by PG, when P-C bond length increases by 11% after adsorption of six Na atoms. Since N and B-doped graphene structures retain the planar structure due to the almost identical atomic radius to C after doping, the bond length between the

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dopant atom and the neighbouring carbon atom does not deform significantly after adsorption of multiple Na atoms, maintaining the structural integrity of the graphene sheet. However, the

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introduction of atoms like S, P and F into graphene, deforms the basal plane considerably. At high Na loadings, most of the Na atoms are displaced away from the favourable adsorption sites, causing the neighbouring atoms to push the dopant atom away from the basal plane. Therefore, large structural deformations experienced by FG, SG and PG may potentially affect the cycling performance of the electrode adversely.

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3.5. Surface migration of Na ion on graphene structures

Ionic conductivity is a key factor which determines the rate performance of SIB electrode materials and directly depends on the migration of Na ions. For high charge-discharge rates and high power densities of the battery, fast Na diffusion is essential. The temperature-dependent

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∆() *

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metal-ion diffusion coefficient can be evaluated by the Arrhenius equation: +

(4)

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where D0, ∆Eb, k and T are pre-exponential factor, activation energy (diffusion barrier), Boltzmann’s constant and the absolute temperature. According to the equation, at constant temperature, Na diffusion mobility depends on the magnitude of the energy barrier (∆Eb). We quantified the Na diffusion energy barrier for each structure by employing the climbing-image nudged elastic band (NEB) method. For ease of comparison, we considered the lowest energy barrier for Na migration along a diffusion pathway towards the most favourable adsorption site in each doped-graphene structure. The ∆Eb values and the corresponding diffusion pathways are shown in the Figure 7. The diffusion energy barrier for pristine graphene was found to be 0.096 *Corresponding author. Email: [email protected] (Cheng Yan)

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eV and agrees with the value previously reported in literature [20]. Interestingly, the energy

*Corresponding author. Email: [email protected] (Cheng Yan)

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barriers of Na diffusion into and out of (Figure S3) the most favourable adsorption site on all the

*Corresponding author. Email: [email protected] (Cheng Yan)

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doped-graphene structures have reduced considerably compared to pristine graphene, ensuring

Figure 7. Calculated energy barriers (∆Eb) for sodium diffusion into the most favourable adsorption site on a) graphene, b) NG1, c) NG2, d) NG3, e) BG, f) SG, g) PG and h) FG

*Corresponding author. Email: [email protected] (Cheng Yan)

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good ionic conductivity with small energy barriers. The diffusion barrier has significantly dropped by 82-85% when Na diffuses towards the most favourable adsorption sites in NG1 and SG respectively. Such behaviour can be attributed to the electron-electron repulsion between Na atom and doped atom (graphitic N and S), which forces Na to migrate away from the dopant.

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Though NG2 and NG3 exhibit high adsorption energies, the diffusion along the surface is not restrained as N-doping eliminates carbon-centered radicals near the defect regions [50]. Furthermore, introduction of B, P and F atoms do not negatively affect the diffusion kinetics of Na as the energy barrier is not influenced by the strong affinity towards Na.

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Moreover, desodiation or sodium desorption is another critical aspect of an anode material which should be examined in order to get a better understanding of the discharge

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process of the SIB. A high desodiation energy is unfavourable for an anode as it affects the cycling performance of the battery. Therefore, desodiation energy was examined by computing the energy barrier along the minimum energy path (MEP) of Na moving from the most stable adsorption site to a reasonably far distance (9 Å) and the results are shown in Figure S4. Interestingly, the desodiation energy of NG2, NG3, BG, PG and FG were calculated to be 0.85 eV, 0.87 eV, 0.63 eV, 0.84 eV and 0.88 eV, respectively and they are well below the energy

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barriers reported for delithiation in LIBs [51]. This further ascertains that the enhanced adsorption of the doped-graphene materials does not adversely affect the desorption pathway of Na ions.

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Based on the insights gained from our theoretical study we found that doping graphene with pyridinic-N, pyrrolic-N, F and B improves the electrochemical Na storage of graphene due to the electronic effect originates from vacancy sites or electron deficient dopants. Whereas P doping

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improves the Na storage properties of graphene due to the geometric effect originate from the mismatch of bond length. To go a step further from the findings to seek another breakthrough,

*Corresponding author. Email: [email protected] (Cheng Yan) Figure 8. Comparison of the average adsorption energies of Na on NP-G, NG3 and PG

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we wanted to determine if there is a synergetic effect of doping with two different atoms, on improving the electrochemical performance of graphene. Based on this consideration, we built a model of pyrrolic-N, P codoped graphene (NP-G) and calculated its multiple Na atom storage capacity (Figure S5 and Table S4). Compared to NG2 and PG, NP-G exhibited superior Na

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storage capacity (Figure 8) due to abundant adsorption sites originating from both electronic and geometric effect with a theoretical specific capacity of 402 mAhg-1. Clustering of metal adatoms is a serious issue which drastically reduces the charge/discharge capacity in rechargeable batteries[41]. To be considered as an excellent electrode material for Na-ion batteries, it should

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have a low possibility for Na cluster formation. Clustering of Na may occur if the adsorption energy drops below the cohesive energy of bulk Na (-1.15 eV) [52]. Interestingly even at a high

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number of Na loading (n=6), the adsorption energy of Na in NP-G is higher than the cohesive energy of Na, which ascertains that no cluster formation of Na takes place during adsorption. Interestingly, the energy barrier of NP-G when Na+ diffuses from an adsorption site to the most energetically favourable site is 0.093 eV (Figure S6) and it is still smaller than that on graphene (0.096 eV). Thus, in a perspective of strong Na storage capacity and favourable diffusion

4. Conclusions

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kinetics, codoped graphene is a good candidate for anode materials in NIBs.

In this work, we find that different dopants significantly affect the Na adsorption behaviour of graphene, attributed to electronic (i.e. defects, electron deficient dopants) and

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geometric factors. For example, doping of pyridinic-N, pyrrolic-N and F, introduces carbon vacancy defects to the basal plane of graphene, creating electron acceptor states to gain electrons from Na atoms. Doping of B does not create any defects, but transforms graphene to an electron-

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deficient system and builds stronger attraction with Na. Graphene doping with P leads to a structural distortion near the P atom, facilitating the adsorption of Na atoms through the localized structural effect. Interestingly, the diffusion energy barrier for Na diffusion has been lowered by the introduction of the heteroatoms. However, the considerable structural deformation in F and P-doped graphene at high Na loadings, could potentially damage the cycling performance of the anode in the long run. Meanwhile, doping of graphitic-N turns out to be ineffective due to the electron-rich nature, which shows limited ability to accept electrons from Na. Introduction of S causes less impact on graphene, due to the negligible electronegativity difference with C, *Corresponding author. Email: [email protected] (Cheng Yan)

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resulting in an electron-balanced system as graphene with inadequate attraction towards Na adsorption. In addition to single heteroatom-doping, two different heteroatom-doping is predicted to have excellent Na storage capacity and favourable diffusion kinetics. Thus, we believe this work may provide a better understanding of heteroatom-doped graphene and

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significant implications towards the design of novel graphene-based anodes with improved sodium adsorption and diffusion in sodium-ion batteries. Acknowledgements

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The authors wish to acknowledge the High Performance Computing and Research Support (HPC) group in Queensland University of Technology for access to its computation resources. KW would like to acknowledge QUT for financial support via QUTPRA scholarship. The

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financial support from the ARC DP project (DP180102003) is appreciated.

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*Corresponding author. Email: [email protected] (Cheng Yan)