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Enhanced electrochemical and thermal transport properties of graphene/ MoS heterostructures for energy storage: Insights from multi-scale modeling 2

Feng Gong, Zhiwei Ding, Yin Fang, Chuan-Jia Tong, Dawei Xia, Yingying Lv, Bin Wang, Dimitrios Vassilios Papavassiliou, Jiaxuan Liao, and Mengqiang Wu ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b19582 • Publication Date (Web): 11 Apr 2018 Downloaded from http://pubs.acs.org on April 11, 2018

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ACS Applied Materials & Interfaces

Enhanced electrochemical and thermal transport properties of graphene/MoS2 heterostructures for energy storage: Insights from multi-scale modeling Feng Gonga*, Zhiwei Dingb, Yin Fangc, Chuan-Jia Tongd, Dawei Xiaa, Yingying Lve, Bin Wangf*, Dimitrios V. Papavassiliouf*, Jiaxuan Liaoa, and Mengqiang Wua a

School of Materials and Energy, University of Electronic Science and Technology of China, Chengdu 611731, China b

Department of Material Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA c

James Franck Institute, University of Chicago, Chicago 60637, IL., USA

d

Beijing Computational Science Research Center, Beijing 100193, China e

Department of Materials Science and Engineering, University of Wisconsin-Milwaukee, Baltimore 21201, MD, USA

f

School of Chemical, Biological, and Materials Engineering, University of Oklahoma, Norman, Oklahoma, 73019, United States

*

Corresponding Authors. E-mail: [email protected] (D. V. P), [email protected] (F. G) and [email protected] (B. W) 1 ACS Paragon Plus Environment

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ABSTRACT Graphene has been combined with molybdenum disulfide (MoS2) to ameliorate the poor cycling stability and rate performance of MoS2 in lithium ion battery (LIB), yet the underlying mechanisms remain less explored. Here, we develop multi-scale modeling to investigate the enhanced electrochemical and thermal transport properties of graphene/MoS2 heterostructures (GM-Hs) with complex morphology. The calculated electronic structures demonstrate the greatly improved electrical conductivity of GM-Hs compared to MoS2. Increasing the graphene layers in GM-Hs not only improves the electrical conductivity, but also stabilizes the intercalated Li atoms in GM-Hs. It is also found that GM-Hs with 3 graphene layers could achieve and maintain a high thermal conductivity of 85.5 W/(m·K) at a large temperature range (100~500K), nearly six times that of pure MoS2 (~15 W/(m·K)), which may accelerate the heat conduction from electrodes to the ambient. Our quantitative findings may shed light on the enhanced battery performances of various graphene/metal transition chalcogenide composites in energy storage devices.

KEYWORDS: graphene/MoS2 heterostructure, electrochemical, electronic structures, thermal conductivity, multi-scale modeling

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1. Introduction The use of 2-dimensional (2D) molybdenum disulfide (MoS2) has drawn substantial attention because of its unique chemical and physical properties

1-4

. In

energy storage, because of the weak interlayer van der Waals interaction, MoS2 has been considered as a promising anode candidate for both lithium ion batteries (LIBs) and sodium ion batteries (SIBs)

5-7

. However, when applied as anode, pure MoS2

always suffers from low specific capacity and poor cycling stability caused by structural disorder during the charge/discharge cycles

8-9

. Hence, the combination of

MoS2 and carbonaceous materials (e.g. 2D graphene) has been developed to improve the capacity and cycling stability. For instance, various graphene/MoS2 hybrids, such as 3D graphene/MoS2 nanocomposites and graphene/MoS2 aerogels, have been fabricated as anode materials for both LIBs

10-11

and SIBs

12-13

. With the addition of

graphene, the graphene/MoS2 hybrids can achieve the elevated specific capacity and the enhanced cycling stability, as well as the superb rate performance. Different from the 3D graphene/MoS2 hybirds, more recently, we developed 2D graphene/MoS2 heterostructures with a well-defined interface for high-performance LIBs 8. When applied as anodes for LIBs, the 2D graphene/MoS2 heterostructures exhibited an ultrahigh specific capacity of ~1400 mAh g-1 after 300 cycles at 100 mA g-1, and a reversible capacity of ~420 mAh g-1 after 300 cycles, even at 10,000 mA g-1. Although the experimental studies have qualitatively shown the enhanced battery performances of the graphene/MoS2 heterostructures, the mechanisms for this behavior are still not clear. Several computational studies have been conducted to 3 ACS Paragon Plus Environment


address this issue

14-15

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: prior studies were focused on the electrical conductivity of

graphene/MoS2 composites, however, thermal transport properties that may affect the battery performance have not been investigated. In addition, the existing works only considered the graphene-monolayer/MoS2-monolayer heterostructures, which may not accurately replicate the realistic morphology of GM-Hs in experiments. For example, the previous study showed that there were 1 to 3 layers of graphene sheets on MoS2 8. Here we systematically and quantitatively investigate the electrochemical and thermal transport properties of different GM-Hs via a multi-scale modeling approach. The density functional theory with van der Waals force correction were applied to calculate the electronic band structures and density of states, as well as the binding energies of different GM-Hs. The thermal transport properties of pure MoS2, pure graphene and GM-Hs were thoroughly investigated by using non-equilibrium molecular dynamics simulations. The number of graphene layers and the intercalated Li atoms were varied to explore their effects on the electrochemical properties of the heterostructures. The effects of the temperature and the MoS2-graphene interlayer distance on the thermal transport properties of GM-Hs were also investigated quantitatively. 2. Computational details 2.1 Density Functional Theory (DFT) calculations All DFT calculations were performed using Vienna ab initio Simulation Package (VASP) 16. The projector augmented wave (PAW) potentials were used to describe the electron-ion interactions

17

. The generalized-gradient approximation (GGA) of 4 ACS Paragon Plus Environment

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Perdew-Burke-Ernzerhof

(PBE)

was

applied

to

calculate

the

electronic

exchange-correlation energy.18-19 The plane wave cutoff energy was set as 400 eV as in our previous studies.20-22 Higher cutoff energies were tested and they did not show significant difference for the total energies the systems. For structural relaxation, the convergence criteria were set to 10-4 eV for calculations of electronic energy and 0.02 eV·Å-1 for force, respectively. Since the lattice constants of MoS2 and graphene sheets are 3.19 Å and 2.47 Å, respectively, (5×5) graphene layers are positioned together with a (4×4) MoS2 layer to form heterostructure, as illustrated in Figure 1(b). In this heterostructure, the lattice mismatch between MoS2 and graphene monolayers was less than 3%. To precisely describe the interlayer van der Waals (vdWs) force between graphene and MoS2, the PBE density functional with vdWs correction was employed (optB88-vdW-DF)

23-24

. The optB88-vdW-DF could yield accurate equilibrium

distance and energy between 2D materials in several systems 25. The thickness of the vacuum layer was set to be 15 Å for all calculations to avoid the influence from neighboring systems. For the Brillouin zone integration, a 4×4×1 Γ-centered Monkhorst–Pack k point sampling was adopted for structural optimization 26, while a 6×6×1 Γ-centered Monkhorst–Pack k point sampling was utilized to obtain more accurate electronic density of states (DOS). 2.2 Non-Equilibrium Molecular Dynamics simulations Classical non-equilibrium molecular dynamics (NEMD) simulations were carried out to investigate the thermal transport properties of MoS2 and graphene 5 ACS Paragon Plus Environment


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nanosheets as well as GM-Hs. NEMDs have been widely used to study the thermal transport and mechanical properties of various nanomaterials

27-29

. All NEMD

simulations in this study were performed using the Large-scale Atomic/Molecular Massively

Parallel

Simulator

30

(LAMMPS)

.

Stillinger-Weber (SW) potential by Jiang et al.

31

A

recently

parameterized

was employed to describe the

interatomic interaction within MoS2 monolayer. More accessible than the previous SW potential, the newly parameterized SW potential does not require the modification of LAMMPS codes with the introduction of more atom types 31. Within each layer of graphene, the optimized Tersoff potential was utilized to depict the interatomic interactions

32

. In GM-Hs, the 12/6 Lennard-Jones (L-J) potential was adopted to

model the weak van der Waals interactions between graphene and MoS2 33. The L-J potential is expressed as:  σ 12 V (rij ) = 4ε    rij  

σ  r  ij

   

6

   

(1)

where rij is the distance between atom i and atom j. The used values of ε and σ for different atoms in the L-J potential are listed in Table 1, in which r0 is the distance where the potential reaches the minimum value. Table 1. Used values of parameters for different atoms in the L-J potential 33-34. Atom 1 C C S Mo S

Atom 2 S Mo Mo Mo S

ε (eV) 0.00735 0.00332 0.02489 0.00243 0.01187

σ (Å) 3.513 3.075 3.157 2.719 3.595

r0 (Å) 3.943 3.452 3.544 3.052 4.035

The thermal conductivity of GM-Hs were determined by applying constant heat 6 ACS Paragon Plus Environment

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flux within the heterostructures

35

, as shown in Figures 1c and 1d. The time

increment in all calculations was 0.5 fs. Before applying heat flux, the energy of the initial system was firstly minimized by using the conjugate gradient minimization scheme. Then the system was equilibrated at 300 K for 100,000 time steps under constant pressure (NPT). Following that, the system was allowed to further equilibrate for another 100,000 time steps under constant volume and constant temperature (NVT). Subsequently, the system was switched to constant volume and constant energy (NVE) ensemble. Constant heat flux was applied by continuously adding a small amount of energy (q) into the heating zone in each time step, and removing half of the energy (q/2) from the two cooling zones, as shown in Figure 1c. When the system reached thermal steady state, the thermal conductivity of GM-Hs was obtained as follows:

 q  ∂T K =   2 A∆t  ∂x where A, ∆t and

(2)

∂T are the cross section area perpendicular to the x axis, the time ∂x

increment and the temperature gradient along the x direction. The factor 2 appears because heat is transferred to both sides of the domain from the heating zone. The heterostructure was divided into slabs to calculate the temperature gradient along the x direction. The temperature of each slab, Tslab , was calculated by averaging the kinetic energy of the atoms in the slab as follows: 3 Nk BTslab = 2

N

1

∑ 2 mv

2

i i

(3)

i



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where k B is the Boltzmann constant, N, mi and vi are the number of atoms in the slab, the mass and the velocity of atom i, respectively. The thermal conductivities of MoS2 and graphene monolayers were calculated by using the method described above.

(a)

(b)

(c)

(d)

Figure 1. Top and side views of MoS2 monolayer (a) and 3GM-Hs (b). The interlayer distance between graphene and MoS2 is 3.37 Å, while the distance between two graphene layers is 3.4 Å. The yellow, cyan and black balls represent S, Mo and C atoms, respectively. (c)-(d) Schematic plot of model setup for NEMD simulations: constant energy q is added into the heating zone and q/2 is removed from the cooling zone at both sides, so that the energy of the system is conserved in the x direction. (c) Top view of the model setup; (d) Side view of the model setup.

3. Results and Discussion 3.1 Electronic structures of graphene/MoS2 heterostructures 8 ACS Paragon Plus Environment

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Since there were 1 to 3 graphene layers on MoS2 surface in our experimental study 8, the models of pure MoS2 monolayer and GM-Hs with 1 ~ 3 graphene layers were built. For simplification, we utilize graphene/MoS2 (GM-H), 2graphene/MoS2 (2GM-H) and

3graphene/MoS2 (3GM-H) to represent the graphene/MoS2

heterostructures with one, two and three graphene layers, respectively. Figures 1a and 1b illustrate the model of pure MoS2 and 3GM-H (The models of GM-H and 2GM-H are displayed in Figure S1). The distance between MoS2 and graphene is 3.37 Å 14, while the interlayer distance of graphene is 3.4 Å 33. To quantitatively investigate the enhancement of the electrical conductivity of pure MoS2 with graphene, the band structures and local electronic density of states (LDOS) of all four structures were calculated and presented in Figure 2. The pure MoS2 exhibited the typical semiconductor behavior with a direct band gap of ~1.8 eV (Figure 2a), which is consistent with the previous studies

15

. This

calculated band gap is lower than the experimentally measured band gap and calculations using many body Green’s function 20-21. This underestimation of the band gap is caused by the semi-local PBE functional used in the work. The current work adopted a large supercell, for which Green’s function calculations become very challenging. In addition, the band gap underestimation doesn’t affect our conclusion since this work is focused on modulation of the band structure and thermal transport properties (see below).



(a)

(b)

(c)

(d)

Figure 2. Band structures and local electronic density of states (LDOS) of (a) MoS2 monolayer, (b) GM-H, (c) 2GM-H and (d) 3GM-H. The Fermi level is set to zero. The semiconducting behavior of pure MoS2 may partially explain its poor rate performance in energy storage devices

36

. When combined with one graphene

monolayer, the GM-Hs displayed a semi-metallic feature, as shown in Figure 2b. In the band structures of graphene/MoS2, the Dirac cone was observed at K points in first Brillouin zone, which squares with the band structures of pure graphene. The weak van der Waals interaction between graphene and MoS2 does not significantly modulate the band structures of graphene, remaining the Dirac cones in GM-H. The LDOS of GM-H shows the weak peaks of electronic states around the Fermi level, which are contributions from the graphene monolayer (Figure 2b). Both the band structures and LDOS of graphene/MoS2 indicate the ameliorated electrical 10 ACS Paragon Plus Environment

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conductivity of graphene/MoS2 hybrids, owing to the introduction of graphene. Figures 2c and 2d present the band structures and LDOS of 2GM-Hs and 3GM-Hs, respectively. With the increase of graphene layers, the band structures of graphene/MoS2 hybrids were modified significantly. When there were two graphene layers, two Dirac cones were observed around the K point - a typical band structure for a bilayer graphene 15. The peaks of electronic states around the Fermi level were also heightened by adding more graphene (Figure 2c), manifesting the further improved conductivity of 2GM-Hs

37

. For 3GM-Hs, the band structures and LDOS

(Figure 2d) exhibited enhanced electron density around the Fermi level. This enhanced DOS provides more channels for carrier transport, resulting in improved electronic conductivity of 3GM-Hs. It is noted that the strong overlap between the LDOS of Mo and S atoms was maintained in all heterostructures, which means the bonds between Mo and S atoms stably remained in all heterostructures. 3.2 Binding energies between Li atoms and graphene/MoS2 heterostructures The model of Li intercalated GM-Hs is exemplified in Figure 3a and the binding energies between Li atoms and different heterostructures are presented in Figure 3b. For comparison, the binding energies of Li atoms ( Ebinding ) were averaged by the number of Li atoms (n), as calculated in 38

Ebinding = ( Egraphene/MoS2 + n × ELi − Egraphene/nLi/MoS2 ) / n

(4)

where Egraphene/MoS2 , E Li , and Egraphene/nLi/MoS2 are the DFT-calculated energies of GM-Hs, one single Li atom in the gas phase or in the bulk phase, and the graphene/nLi/MoS2 heterostructures, respectively. 11 ACS Paragon Plus Environment


3.0 2.8 2.6

1 Li 2 Li 3 Li

2.4 2.2 1.0

2.0

Binding Energy (eV)

(b)

(a)

Binding Energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1.8 1.6 1.4

0.5

MoS2

1 Li 2 Li 3 Li

Bulk Li

0.0 -0.5 -1.0

1.2

Li

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MoS2 Gr/MoS2 2Gr/MoS2 3Gr/MoS2

Gr/MoS2 2Gr/MoS2 3Gr/MoS2

Figure 3. (a) Schematic plot of Li atoms intercalated in between graphene and MoS2. (b) Average binding energies of intercalated Li atoms in pure MoS2 monolayer and different GM-Hs by using the Li atom in the gas phase. The insert in (b) is the plot of average binding energies of Li atoms in pure MoS2 monolayer and different GM-Hs by using the Li atom in the bulk phase.

As presented in Figure 3b, when using the energy of Li atoms in the gas phase, Li atoms have a binding energy of about 2.4 eV per Li atom in all heterostructures, which is close to the reported value in a previous study (2.3 eV per Li atom)

14

.

Compared to that in MoS2 monolayer (~1.9 eV), Li atoms have higher binding energy (2.2~2.5 eV) in all GM-Hs, indicating the more stable Li intercalation in heterostructures. In GM-Hs, the binding energy per Li atom slightly increases with the graphene concentration (2.2 eV for GM-Hs vs. 2.75 eV for 3GM-Hs), which may be ascribed to the increased van der Waals interaction between Li and more graphene 39. The binding energy of per Li atom seemed to decrease with the number of Li atoms from 1 to 3, which may be ascribed to the interactions among Li atoms. When using the energy of Li atoms in the bulk phase (Insert in Figure 3b), the same trend persists. The electronic structures of different GM-Hs were also greatly modulated with the intercalation of Li atoms, which is due to the electron transfer from Li atoms to 12 ACS Paragon Plus Environment

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GM-Hs (Figure S2). 3.3 Thermal conductivity of graphene/MoS2 heterostructures Overheating in LIBs or SIBs not only significantly attenuates the capacity of batteries, but also accelerates the decomposition of electrolyte, causing serious safety problems. Thus, electrodes should effectively conduct heat to the ambient. Adding polymer binders and carbon black into active materials cannot enhance the thermal conductivity of electrodes significantly, because both of them have a low thermal conductivity (

Enhanced Electrochemical and Thermal Transport Properties of

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