Exfoliation of Electrolyte-Intercalated Graphene: Molecular Dynamics

Subscriber access provided by NEW YORK UNIV

Article

Exfoliation of Electrolyte-Intercalated Graphene: Molecular Dynamics Simulation Study One-Sun Lee, and Marcelo Andrés Carignano J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b03217 • Publication Date (Web): 07 Jul 2015 Downloaded from http://pubs.acs.org on July 11, 2015

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 26

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

The Journal of Physical Chemistry

Exfoliation of Electrolyte-Intercalated Graphene: Molecular Dynamics Simulation Study

One-Sun Lee* and Marcelo A. Carignano

Qatar Environment and Energy Research Institute, Hamad Bin Khalifa University, Qatar Foundation, Doha, Qatar, P. O. Box 5825

*Corresponding Author Electronic mail: [email protected] Phone: +974 4454 7184 Fax: +974 4454 1528

1 ACS Paragon Plus Environment


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

Page 2 of 26

Abstract Ethylene carbonate (EC) is one of the most common electrolyte for lithium ion batteries, but it has a narrow working temperature range. Despite the structural similarity, propylene carbonate (PC) has wider working temperature range as an electrolyte but it induces exfoliation of graphite anode. To understand the different behavior of EC and PC electrolytes at the atomistic level, we performed molecular dynamics (MD) simulations of electrolyte intercalated graphene sheets. We observed no diffusion of electrolyte between graphene sheets when interlayer distance is less than 6 Å, but both of EC and PC form monolayer between graphene sheets with comparable density when interlayer distance is 7 ~ 8 Å. Because of the size difference, the intercalated PC molecules induce longer separation distance between graphene sheets compared to that of EC. The longer separation with PC intercalant induces more frequent sliding-exfoliation movement. We found that the exfoliation diffusion coefficient of the graphene sheet with PC intercalant is ~200 times larger than that with EC intercalant. One graphene diffuses and exfoliates from other graphene through sliding displacement rather than vertical separation because of steric interaction with electrolyte molecules in the bulk phase. For calculating the free energy changes of exfoliation, we constructed potential of means force using steered molecular dynamics simulations, and found that the energy barrier of exfoliation of EC intercalated graphene sheets is ~45 kcal/mol where it is ~4 kcal/mol for PC intercalated graphene sheets. We also analyzed the static and dynamic properties of electrolyte confined between two graphene sheets. The self-diffusion coefficient of confined PC is larger than that of EC, but smaller in the bulk phase. We also found that the decaying of the dipole rotation autocorrelation of confined electrolyte is slower than that in the bulk phase. The dynamic properties of the graphene in two different electrolytes reported in this paper can be used for designing new anode materials with better performance.

Keywords


Page 3 of 26

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


Exfoliation, Carbonate Electrolyte, Molecular Dynamics Simulation, Graphene, Diffusion, Lithium Ion Battery, Potential of Mean Force



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

Page 4 of 26

I. Introduction There have been significant scientific and technological attentions to lithium-ion batteries (LIB) for many years because of their long cycle life, high energy density, and wider operating temperature range.1-3 LIB is a recyclable battery in which lithium ions move from cathode to anode through electrolyte during charging and back to cathode when discharging. Ethylene carbonate (EC) shown in Figure 1 (A) is one of the most common electrolyte because of its high compatibility with graphite electrodes, but the major disadvantage of EC is its high melting point of 36.4C.4 Therefore, EC is used with other co-solvent such as dimethyl or diethyl carbonate to increase the melting point. In contrast, propylene carbonate (PC) shown in Figure 1 (B) is stable at lower temperature with melting point of – 48.8C despite the structural similarity to EC.4 Even though PC-based electrolyte would be more advantageous, however, the graphite of anode exfoliates in PC-based electrolyte which causes battery failure.5 To explain why PC behaves so differently from EC with regard to exfoliation, the cointercalation model proposed by Besenhard et al. has been frequently used.6 They suggest that lithium ions are solvated by polar electrolytes, and the complex of lithium ion and electrolytes intercalate into the graphite together and form a ternary graphite intercalation compound (GIC). The intercalated EC molecules chemically decompose and the products form a stable film,6 where PC and its decomposition products exert interlayer stress in the graphite and induce exfoliation.7 There have been many theoretical and experimental researches about the origin of the different behavior of EC and PC when they are intercalated in graphite.6-15 For example, Chung G. et al. studied the origin of graphite exfoliation using electrochemical methods varying cation size, electrolyte structure, and graphite structure. They suggested that electrolyte cointercalation is a critical process for both graphite exfoliation and interface formation.16 With density functional theory (DFT) calculation of GIC, Tasaki K. et al. suggest that three or four electrolyte solvent molecules intercalate accompanying a lithium ion, and the intercalants induce interlayer distance increase to a point at which graphite is not


Page 5 of 26

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


able to maintain their structural integrity at lower salt concentration. At high salt concentration, however, they suggest that lithium ions are solvated by more counter ions having a smaller electrolyte solvation number, and form stable GIC without destruction of graphite structur.17 However, the dynamic properties of graphite and electrolyte are still unknown even though they are necessary to understand how this system functions. For a deeper understanding of the system, we performed molecular dynamics (MD) simulations of EC or PC intercalated graphene sheets at the atomistic level (Figures 1 (C) and (D)). First, we calculated the diffusion of electrolyte between graphene sheets varying the interlayer distance. When interlayer distance is less than 6 Å, no diffusion of electrolyte between graphene sheets is observed, while both of EC and PC form monolayer between graphene sheets and have comparable density when interlayer distance is 7 ~ 8 Å. Then, we monitored the structural fluctuations of the EC or PC intercalated graphene sheets for 40 ns, and found that the exfoliation diffusion coefficient of a graphene sheet of PC intercalated system is about 200 times higher than that of EC intercalated system. We also calculated potential of means force (PMF) of exfoliation, and found that the energy barrier of exfoliation of EC intercalated system is about five times higher that that of PC intercalated system. In addition, we analyzed the static and dynamic properties of electrolyte confined between two graphene sheets. The self-diffusion coefficient of PC is larger than that of EC when confined, but smaller in the bulk phase. We also found that the decaying of the dipole rotation autocorrelation of electrolyte is slower when confined comparing to the bulk phase, which is opposite to the faster decaying of confined water molecules.18 This is the first report about the dynamic structural features of stacked graphene sheets in different electrolytes at the atomistic level to the best of our knowledge. The information of this report can be used for designing new anode materials with better performance.



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

Page 6 of 26

II. Computational Details Diffusion of Electrolyte between Graphene Sheets The system composed of two graphene sheets and carbonate electrolytes (EC or PC) is shown in Figure 1 (D). To test the diffusion of electrolyte molecules between graphene sheets, we varied the interlayer distance from 6 to 10 Å by 0.5 Å. The space between graphene sheets remained void for the initial configuration of system. The number of EC or PC in the simulation box is 615 ~ 630 and the initial dimension of the system is 50  50  50 Å3. The system is equilibrated for 1000 steps using the conjugate gradient method, and followed by 6 ns MD simulation at 300 K with NpT ensemble. During MD simulation, the position of each carbon atom of graphene sheets is fixed with harmonic constraint of 10 kcal/mol/Å2. MD simulation of Exfoliation With the simulations of the diffusion of electrolyte between graphene sheets, we found that both of EC and PC form monolayer between graphene sheets when the interlayer distance is 7 ~ 8 Å (More details are in Results and Discussion). Since we are interested in exfoliation of graphene sheet when a graphene sheet is separated from other stacked graphene by intercalated electrolyte molecules, we adapted the system of graphene sheets separated by 8 Å immersed in EC or PC electrolytes. The number of EC or PC in the simulation box is 729 and the initial dimension of the system is 50  50  50 Å3. Racemic mixture of (R)- and (S)-PC is used for the simulation of PC electrolyte. To equilibrate the system, we performed a 100 ps MD simulation with an NVT ensemble at 500 K. During the equilibrium simulation, the position of two graphene sheets is fixed. The electrolyte molecules diffuse into the space between graphene sheets during this simulation. After this first equilibrium simulation, we performed a 100 ps second equilibrium simulation with an NVT ensemble at 300 K. The lateral motion of graphene is restricted, while the orthogonal motion of graphene is allowed during the second equilibrium simulation. The conformation obtained from second equilibrium simulation is used for the production


Page 7 of 26

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


simulations. In the production simulation, a 40 ns MD simulation was performed using the NPT ensemble at 300 K with a damping coefficient of 5 ps–1 of Langevin dynamics.19 Langevin piston method with a 100 fs piston period was adapted to keep the pressure at 1 atm (damping time constant was 50 fs and piston temperature was 300 K).19-20 Instead of using stacked graphene sheets for more realistic anode model, the position of one graphene were constrained during the production period to monitor the exfoliation of the other graphene sheet that no position constrain was applied. Therefore, the fixed graphene sheet is considered as a terminal sheet of the stacked graphene sheets. For the position constraint of one graphene sheet, the atomic coordinates of one carbon in the center of one graphene were constrained during the production period to monitor the exfoliation of the other graphene sheet. With the particle-mesh Ewald method, full electrostatics was employed with a 1 Å grid width.21 Using a group based cutoff, nonbonded interactions were updated every 10 time steps. We used SHAKE algorithm22 to hold rigid covalent bonds involving hydrogen. A 2 fs time step was used for all simulations, and we saved atomic coordinates by every 2 ps for the trajectory analysis. The equilibrated volume with NpT ensemble is ~44  44  44 Å3 for EC and ~47  47  47 Å3 for PC. We also performed MD simulations of the system composed of only electrolyte (729 EC or PC molecules) without graphene sheets for the comparison with the system above. Potential of Mean Force We calculated PMF of graphene exfoliation in EC or PC intercalated system using steered molecular dynamics (SMD) simulation.23-24 During SMD simulation, the position of one graphene is fixed by applying harmonic constraint while the other graphene sheet is pulled with constant velocity of 2.5 Å/ns along the sliding direction that is parallel with the plane of the fixed graphene sheet. A harmonic constraint with a spring constant of 100 kcal/mol/Å2 is used for pulling the center of one graphene sheet, and the total length of the pulling reaction coordinate is 32.5 Å. We divided the reaction coordinate into 13 consecutive sections with each section length of 2.5 Å. At each section, the system is equilibrated for 500 ps while constraining the position of two graphene sheets, and SMD simulation data 7 ACS Paragon Plus Environment


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

Page 8 of 26

were collected during another 1 ns. Eight independent simulations were performed at each section for constructing PMF. We adapted Jarzynski equation to construct the PMF from SMD simulations.25-26

A    1 ln exp W 

(1)

where A is a free energy difference,  is the product of Boltzmann factor and temperature, and W is the non-equilibrium work obtained from SMD simulation. With equation (2), we obtained the nonequilibrium work done by the pulling force. W  kv  0 dtx t  x 0  vt t

(2)

where k is the force constant and v is the velocity of pulling. The reaction coordinate at t´ is x(t´) and the initial position of the center of mass of the pulled graphene sheet is x0. We adapted second order cumulant expansion equation for calculating equation (1).23-24

A  W 



W 2

2

 W

2



(3)

We divided the pulling reaction coordinate into 13 sections and performed the constant velocity SMD simulations independently through each section. We adapted matching relation to assemble each PMF profile.27-28 We used NAMD229 for all MD simulations and VMD30 for all the graphics shown in this report. Force Field Parameters

The energy function used in the simulations has the form



  K b  b    K       K 1 cosn     K     2

U b, , ,,rij 

b

2



0

bonds

angle



 nonbond

2



0

dihedral

 min 2  min 6  Rij q Rij  iq j          rij   rij     0 rij

 ij  

imp

0

impropers

(4)

where Kb (bond), K (angle), K (dihedral), and Kimp (improper) are force constants. The equilibrium values of bond (b), angle (), dihedral (), and improper () are represented by the subscript 0, and n


Page 9 of 26

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


determining the periodicity of the dihedral potential in the interval [0,2π]. Lennard-Jones (LJ) 6-12 and Coulombic terms determine the nonbonded interaction; 0 is the effective dielectric constant, qi is the partial atomic charge, rij is the distance between atoms i and j, Rijmin is the distance at the LJ minimum and ij is the LJ well depth. The geometric mean (  ij   ii jj ) and arithmetic mean ( Rijmin 

Rimin  R min j ) 2

is used for calculating ij and Rijmin , respectively. The parameters of each term of the energy function are adapted from previous literatures (See supporting information).31-34



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

Page 10 of 26

III. Results and Discussion

The number density of electrolyte between graphene sheets for the last 1 ns of the electrolyte diffusion simulation is shown in Figure 1 (E). When interlayer distance (d) is less than 6 Å, no diffusion of electrolyte between graphene sheets is observed. EC form a monolayer between graphene sheets when d = 6.5 ~ 8 Å and double layer when d = 10 Å; PC form a monolayer between graphene sheets when d = 7 ~ 8.5 Å. Monolayer of EC and PC have comparable density when d = 7 ~ 8 Å. Since we are interested in exfoliation of graphene sheet when a graphene sheet is separated from other stacked graphene by intercalated electrolyte molecules, we adapted the system of graphene sheets separated by 8 Å for the following production MD simulation where the position of one graphene is fixed and no coordinate constraint is applied to the other graphene. The top and side views of EC or PC electrolyte molecules between graphene sheets are shown in Figures 2 (A) and (B). During the 40 ns production simulations, there have been continuous exchanges of electrolyte molecules between the bulk phase and the space between graphene sheets where the average residence time of electrolyte between graphene sheets is 21 ps for EC and 24 ps for PC. Even though the interlayer distance is allowed to vary during the production simulations, no complete separation of two graphene sheets was observed and the electrolyte between graphene sheets maintain the monolayer structure. However, the distance and angle between graphene sheets show significant fluctuations during the production simulations. For the analyses of the fluctuation of relative structure of two graphene sheets, we measured the orthogonal distance (dz in Figure 3 (A)) and the sliding distance (dxy in Figure 3 (B)) between graphene sheets. The average dz is 7.2 ± 0.1 Å in EC and 7.8 ± 0.2 Å in PC. Because the radius of gyration is 1.68 ± 0.02 Å for EC and 1.99 ± 0.17 Å for PC, their diameter difference is ~0.6 Å and comparable with the dz difference. Therefore, we concluded that the difference of the interlayer distance came from the size difference of intercalated EC and PC. The interlayer distance obtained from our simulations is comparable with the calculation results reported by Tasaki K. et al.17 The interlayer distance they found using DFT method is 5.9 ~ 6.9 Å for Li+–EC intercalants and 7.0 ~ 8.5 Å for Li+–PC intercalants. The 10 ACS Paragon Plus Environment

Page 11 of 26

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


difference between average sliding distance, dxy, is more obvious (Figure 3 (B)). The average dxy is 1.5 ± 0.8 Å in EC and 5.3 ± 3.3 Å in PC. The distribution of dxy in EC has one narrow peak at 1.5 Å, but the distribution of dxy in PC is broader and has two peaks at 2 Å and 7.5 Å. Even though the maximum dxy in PC is about 15 Å, however, no complete separation between sheets was observed. We performed three independent simulations of the system, and the distribution of dxy of each simulation is comparable. Therefore, we speculated that a longer simulation is needed to observe the complete separation between graphene sheets. The representative conformations of graphene sheets in EC or PC are also shown in the inset of Figure 3 (B). Almost the entire area of two graphene sheets superimposes when dxy = 2 Å for EC, but only half of their area superimpose when dxy = 7.5 Å for PC. The selfdiffusion coefficient of graphene is 2.1  10–13 m2/sec in EC and 4.1  10–11 m2/sec in PC. Therefore, the exfoliation diffusion of graphene sheets in PC is ~200 times faster than that of EC (Table 1). Because of the steric interactions with electrolyte molecules in the bulk phase, the motion of graphene along the axis vertical to its surface is restricted, but the sliding motion of graphene is more relevant to the exfoliation. The interaction energy between graphene sheets (Egg) in EC or PC electrolytes is calculated during the production simulations, and its distribution is shown in Figure 3 (C). The Egg for EC and PC shows distinctively different distributions, and the Egg in PC is higher than that in EC by 0.57 ± 0.13 meV/atom. The interaction energy we obtained is comparable with the values reported in the previous literature. Chen X. et al. calculated the interlayer energy between two graphene sheets using various ab initio methods.35 According to their calculation, the interlayer interaction energy between two graphene sheets is minimum at ~3.2 Å and increases as the separation distance increases, and reaches ~1 meV/atom when the separation distance is 7 Å. In our simulations, the PC-intercalated interlayer distance, dz, is longer than EC-intercalated interlayer distance by 0.6 Å, and the difference of dz induced lower interaction energy for PC-intercalated graphene. Ayala et al. also reported the separation of interaction between stacked graphene by intercalation.36 With their calculation, it was found that the 11 ACS Paragon Plus Environment


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

Page 12 of 26

intercalation of sulfuric acid separated the sheets by 7.6 ~ 8.0 Å and decoupled the electronic interaction between the sheets. For a deeper understanding of exfoliation of graphene sheet, we calculated PMF of graphene exfoliation in EC or PC electrolytes using SMD simulation.23-24 During SMD simulation, the position of one graphene is fixed by applying harmonic constraint while the other graphene sheet is pulled with constant velocity along the sliding reaction coordinate that is parallel with the plane of the fixed graphene sheet. Snapshots of graphene sheets during SMD simulation are shown in Figure 4 (A), and the PMF is shown Figure 4 (B). The energy barrier for exfoliation of graphene sheet of EC intercalated system is ~45 kcal/mol, where it is ~4 kcal/mol for PC intercalated system. The energy barrier for exfoliation of PC intercalated system is low enough to observe exfoliation when the external perturbation is applied to the system. For example, Zhu et al. found that PC is an excellent solvent for achieving exfoliated graphene oxide (GO) dispersion.37 They observed exfoliation of GO when GO is dispersed in PC and treated by bath sonication. For the analyses of dynamic properties of electrolyte, we calculated the self-diffusion constant of electrolyte both in the bulk phase and the confined state between graphene sheets. The diffusion coefficient (DEC or PC) of EC and PC are listed in Table 2. The diffusion coefficients in the bulk phase obtained from our simulations are comparable with experiments. Even though there is no reported value of diffusion coefficient of confined electrolyte, our results are comparable with the diffusion coefficient of lithium ion confined between graphene sheets. By using electrochemical method, Persson et al. calculated the self-diffusion coefficient of lithium ion between graphene sheets to be 4.4  10–10 m2/s.38 In our simulations, compared to the bulk phase, DEC is reduced from 7.5 to 2.6  10–10 m2/sec, and DPC is reduced from 4.5 to 3.4  10–10 m2/sec. Therefore, DPC is higher than DEC between graphene sheets even though DEC is higher than DPC in the bulk phase. With the larger space between graphene sheets because of longer dz (Figure 3 (A)), PC intercalants diffuse faster than EC intercalants. Moreover, as


Page 13 of 26

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


shown in the coordination number39 of EC and PC (Figure 5 (A)), the density of PC is lower than EC between graphene sheets as well as in the bulk phase. However, the diffusion coefficient of both of EC and PC electrolytes is smaller than that of bulk phase. Abe S. et al. calculated the energy barrier of EC diffusion on the surface of graphene using DFT methods, and found that the energy barrier was less than 0.2 kcal/mol.40 With this energy barrier, they suggested that EC molecules could diffuse on the graphene surface at room temperature. Since the energy barrier induced by graphene surface is low, we concluded that the slow diffusion rate of confined electrolytes is due to the steric interactions with the neighboring electrolyte molecules. The behavior of confined carbonate electrolytes between graphene sheets is opposite from the motion of water molecules between graphene sheets. Cieoro G. et al. studied the dynamic properties of water molecules confined between graphene sheets using DFT-based MD simulations.18 With their calculation, it was found that the diffusion coefficient of confined water was almost three times larger than that of bulk water. We also calculated the rotational properties of electrolyte confined between graphene sheets and compared them with those in the bulk phase. Equation (5) is used for the calculation of the autocorrelation function of the rotation of the dipole moment of electrolyte. t n  t n

t  t    

  t  t    t 0  0 tn

 t  t 

(5)

t 0

, where t  is the dipole moment at time t and ab is the scalar product of a and b. The dipole rotational autocorrealtion function of electrolyte is shown in Figure 5 (B). The rotational autocorrelation function of confined electrolyte is decaying slower than that of the bulk phase, and this is opposite to the faster rotation of confined water molecules as reported by Cieoro G. et al.18 They found that faster rotational motion of confined water molecules comparing with the bulk phase because of increased rate of formation and breaking of the hydrogen bonding between confined water molecules. For the confined



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

Page 14 of 26

electrolyte in our simulations, however, the steric interactions with the graphene and neighboring electrolyte molecules dominate and restrict the rotational motion. The conformation analyses of electrolyte molecules between graphene sheets are shown in Figures 6 (A) and (B). We defined two structural parameters ( is the angle between the graphene plane and the vector of the O=C bond of the carbonate molecule;  is the angle between the graphene plane and the ring of the carbonate molecule. See the graphical definitions in the insets in Figures 6 (A) and (B)) and measured their distributions. With the distribution of , we found that the vector containing the O=C bond is parallel with the graphene plane for both EC and PC. With the distribution of , we found that both EC and PC molecules are rotated relative to the graphene plane around the axis containing the O=C bond. Because of the steric interaction between the graphene and –CH3 group of PC, PC is rotated more (±25) than EC (±13). Tasaki K. et al. also found that PC is rotated with the axis containing the O=C bond when confined between graphene sheets.17 The representative conformations of EC and PC between graphene sheets are shown in Figures 6 (C) and (D). With the conformation analysis, we found that both of EC and PC electrolyte molecules are rotated with the axis containing the O=C bond, and the vector of the O=C bond is parallel with the graphene planes. Conclusion

To understand the different exfoliation properties of graphene sheets intercalated by EC or PC electrolytes, we performed MD simulations of the system composed of two graphene sheets immersed in EC or PC electrolytes. With the model we simulated in this report, we found that the size difference between PC and EC could induce different exfoliation behavior of graphene even without chemical decomposition of intercalated electrolyte. With the larger radius of gyration, the PC intercalants separate graphene sheets more effectively than EC intercalants. The graphene sheet separated by PC intercalants self-diffuses ~200 times faster than that separated by EC intercalants. We calculated PMF of exfoliation using SMD simulations, and found that the energy barrier of exfoliation of EC intercalated system is


Page 15 of 26

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


about eleven times higher that that of PC intercalated system. We also found that the self-diffusion and rotational motion of confined electrolyte between graphene sheets are different from the bulk phase properties. The self-diffusion coefficient DPC is larger than DEC for confined electrolyte, but smaller in the bulk phase. The decaying rate of the rotational autocorrelation of confined electrolyte is slower than that of the bulk phase because of steric interactions with graphene and the neighboring electrolyte molecules. The findings in this study have implications for rational design of new carbon-based anode materials with higher efficiency and stability. Supporting Information:

Force field parameters for MD simulation and the equation for self-diffusion coefficient. This material is available free of charge via the Internet at http://pubs.acs.org/. Acknowledgement:

We thank Qatar Environment and Energy Research Institute for the support.



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

Page 16 of 26

Table 1. Exfoliation diffusion coefficient of graphene sheet in EC and PC electrolytes. EC DGraphene

2.1  10–13 m2/s

PC DGraphene

4.1  10–11 m2/s

Table 2. Self-diffusion coefficients of EC and PC in confined and the bulk phases. Experimental values

in the bulk phase obtained by the pulse-gradient spin-echo NMR method are also listed for comparison. Confined (Simulation)

Bulk (Simulation)

Bulk (Experiment)41

DEC

2.6

7.5

8.0

DPC

3.4

4.5

5.8

Units are in  10–10 m2/s.


Page 17 of 26

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


Figure 1. Chemical structures of (A) EC, (B) PC, and (C) graphene sheet. (D) Initial configuration of

the system for MD simulations. Diffusion of electrolyte between graphene sheets is tested varying the interlayer distance from 6 to 10 Å by 0.5 Å. (E) Number density of electrolyte between graphene sheets during the last 1 ns of electrolyte-diffusion simulations. The number of electrolyte molecules between graphene sheets is divided by the area of graphene sheet (2.5  2.0 nm2) to obtain the number density. Both of EC and PC form a monolayer between graphene sheets and have comparable density when d = 7 ~ 8 Å, and EC form double layer when d = 10 Å.



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

Page 18 of 26

Figure 2. Top and side views of (A) EC- and (B) PC-intercalated graphene sheets. Other electrolyte

molecules in the bulk phase are not shown for clarity. Snapshots were taken when two graphene sheets superimpose (sampled at 35 ns for EC and 38.4 ns for PC). Electrolyte molecules form a monolayer between graphene sheets. Dotted circles with diameter of 10, 20, and 30 Å are added for helping the readability of the dimensions of the system. One of the graphene is not shown in the top views for clarity.


Page 19 of 26

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


Figure 3. Structural and energy fluctuation distributions of EC- or PC-intercalated graphene shteets. (A)

The average orthogonal distance, dz, between graphene sheets is 7.2 ± 0.1 Å in EC, and 7.8 ± 0.2 Å in PC. The definition of dz and dxy is shown in the inset. (B) The average sliding distance, dxy, between graphene sheets is 1.5 ± 0.8 Å in EC, and 5.3 ± 3.3 Å in PC. Representative conformations of graphene are shown in the inset. The conformation of graphene is sampled at dxy = 1.5 Å for EC and at dxy = 7.5 Å for PC. (C) The average interaction energy between graphene sheets is –1.49 ± 0.06 meV/atom in EC and –0.92 ± 0.11 meV/atom in PC.



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

Page 20 of 26

Figure 4. (A) Snapshots of graphene sheets along the SMD reaction coordinate at dxy = 0, 10, 20, and 30

Å. During SMD simulation, the position of one graphene is fixed while the pulling force is applied to the center of other graphene sheet along the sliding reaction coordinate that is parallel with the plane of the fixed graphene sheet. The direction of force for SMD simulation is shown with red arrow. (B) Potential of mean force of graphene exfoliation in EC and PC intercalated system. The energy barrier of exfoliation is ~4 kcal/mol for PC intercalated system and ~45 kcal/mol for EC intercalated system. The definition of dxy is shown in the inset.


Page 21 of 26

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


Figure 5. (A) Coordination number of EC and PC between graphene sheets and in the bulk phase. The

number of the carbonyl oxygen atoms of EC or PC is used for the calculation. EC has a higher density than PC in both cases. (B) Dipole rotation autocorrelation function of EC and PC. The rotational autocorrelation function of confined electrolyte is decaying slower than that of the bulk phase.



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

Page 22 of 26

Figure 6. (A) Distribution of the angle () between the graphene plane and the vector of the O=C bond

of EC or PC. Average value of  is 90 for both EC and PC. (B) Distribution of the angle () between the carbonate ring and graphene sheet. The ring of EC is rotated by ±13 relative to the graphene plane with the rotation axis containing the O=C bond. The ring of PC is rotated more (±25) than that of PC because of steric interaction between the –CH3 group and graphene. Representative conformations of (C) EC and (D) PC confined between graphene sheets are shown. Only one carbonate molecule is shown for clarity.


Page 23 of 26

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


References:

(1) Huggins, R., Advanced Batteries: Materials Science Aspects; Springer: New York, 2008. (2) Winter, M.; Besenhard, J. O.; Spahr, M. E.; Novak, P. Insertion Electrode Materials for Rechargeable Lithium Batteries. Adv. Mater. 1998, 10, 725-763. (3) Mukhopadhyay, A.; Sheldon, B. W. Deformation and Stress in Electrode Materials for Li-Ion Batteries. Prog. Mater. Sci. 2014, 63, 58-116. (4) Lide, D. R., Handbook of Chemistry and Physics; Taylor & Francis Group: Boca Raton, 2005; Vol. 86. (5) Fong, R.; Vonsacken, U.; Dahn, J. R. Studies of Lithium Intercalation into Carbons Using Nonaqueous Electrochemical-Cells. J. Electrochem. Soc. 1990, 137, 2009-2013. (6) Besenhard, J. O.; Winter, M.; Yang, J.; Biberacher, W. Filming Mechanism of Lithium-Carbon Anodes in Organic and Inorganic Electrolytes. J. Power Sources 1995, 54, 228-231. (7) Besenhard, J. O.; Fritz, H. P. Cathodic Reduction of Graphite in Organic Solutions of Alkali and NR4+ Salts. J. Electroanal. Chem. 1974, 53, 329-333. (8) Leung, K.; Budzien, J. L. Ab Initio Molecular Dynamics Simulations of the Initial Stages of Solid-Electrolyte Interphase Formation on Lithium Ion Battery Graphitic Anodes. Phys. Chem. Chem. Phys. 2010, 12, 6583-6586. (9) Tasaki, K. Density Functional Theory Study on Structural and Energetic Characteristics of Graphite Intercalation Compounds. J. Phys. Chem. C 2014, 118, 1443-1450. (10) Wang, Y. X.; Nakamura, S.; Ue, M.; Balbuena, P. B. Theoretical Studies to Understand Surface Chemistry on Carbon Anodes for Lithium-Ion Batteries: Reduction Mechanisms of Ethylene Carbonate. J. Am. Chem. Soc. 2001, 123, 11708-11718. (11) Zhao, H.; Park, S.-J.; Shi, F.; Fu, Y.; Battaglia, V.; Ross, P. N., Jr.; Liu, G. Propylene Carbonate (PC)-Based Electrolytes with High Coulombic Efficiency for Lithium-Ion Batteries. J. Electrochem. Soc. 2014, 161, A194-A200. (12) Campana, F. P.; Buqa, H.; Novak, P.; Koetz, R.; Siegenthaler, H. In Situ Atomic Force Microscopy Study of Exfoliation Phenomena on Graphite Basal Planes. Electrochem. Commun. 2008, 10, 1590-1593. (13) Chung, G. C.; Jun, S. H.; Lee, K. Y.; Kim, M. H. Effect of Surface Structure on the Irreversible Capacity of Various Graphitic Carbon Electrodes. J. Electrochem. Soc. 1999, 146, 1664-1671. (14) Marquez, A.; Balbuena, P. B. Molecular Dynamics Study of Graphite/Electrolyte Interfaces. J. Electrochem. Soc. 2001, 148, A624-A635. (15) Zhang, X. R.; Kostecki, R.; Richardson, T. J.; Pugh, J. K.; Ross, P. N. Electrochemical and Infrared Studies of the Reduction of Organic Carbonates. J. Electrochem. Soc. 2001, 148, A1341A1345. (16) Chung, G. C.; Kim, H. J.; Yu, S. I.; Jun, S. H.; Choi, J. W.; Kim, M. H. Origin of Graphite Exfoliation - an Investigation of the Important Role of Solvent Cointercalation. J. Electrochem. Soc. 2000, 147, 4391-4398. (17) Tasaki, K.; Goldberg, A.; Winter, M. On the Difference in Cycling Behaviors of Lithium-Ion Battery Cell between the Ethylene Carbonate- and Propylene Carbonate-Based Electrolytes. Electrochim. Acta 2011, 56, 10424-10435. (18) Cicero, G.; Grossman, J. C.; Schwegler, E.; Gygi, F.; Galli, G. Water Confined in Nanotubes and between Graphene Sheets: A First Principle Study. J. Am. Chem. Soc. 2008, 130, 1871-1878. (19) Martyna, G. J.; Tobias, D. J.; Klein, M. L. Constant-Pressure Molecular-Dynamics Algorithms. J. Chem. Phys. 1994, 101, 4177-4189. (20) Feller, S. E.; Zhang, Y. H.; Pastor, R. W.; Brooks, B. R. Constant-Pressure Molecular-Dynamics Simulation - the Langevin Piston Method. J. Chem. Phys. 1995, 103, 4613-4621.



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

Page 24 of 26

(21) Darden, T.; York, D.; Pedersen, L. Particle Mesh Ewald - an NLog(N) Method for Ewald Sums in Large Systems. J. Chem. Phys. 1993, 98, 10089-10092. (22) Andersen, H. C. Rattle - A Velocity Version of the Shake Algorithm for Molecular-Dynamics Calculations. J. Comput. Phys. 1983, 52, 24-34. (23) Park, S.; Khalili-Araghi, F.; Tajkhorshid, E.; Schulten, K. Free Energy Calculation from Steered Molecular Dynamics Simulations Using Jarzynski's Equality. J. Chem. Phys. 2003, 119, 3559-3566. (24) Park, S.; Schulten, K. Calculating Potentials of Mean Force from Steered Molecular Dynamics Simulations. J. Chem. Phys. 2004, 120, 5946-5961. (25) Jarzynski, C. Nonequilibrium Equality for Free Energy Differences. Phys. Rev. Lett. 1997, 78, 2690-2693. (26) Jarzynski, C. Equilibrium Free-Energy Differences from Nonequilibrium Measurements: A Master-Equation Approach. Phys. Rev. E 1997, 56, 5018-5035. (27) Pangali, C.; Rao, M.; Berne, B. J. Monte-Carlo Simulation of the Hydrophobic Interaction. J. Chem. Phys. 1979, 71, 2975-2981. (28) Yu, T.; Lee, O.-S.; Schatz, G. C. Steered Molecular Dynamics Studies of the Potential of Mean Force for Peptide Amphiphile Self-Assembly into Cylindrical Nanofibers. J. Phys. Chem. A 2013, 117, 7453-7460. (29) Kale, L.; Skeel, R.; Bhandarkar, M.; Brunner, R.; Gursoy, A.; Krawetz, N.; Phillips, J.; Shinozaki, A.; Varadarajan, K.; Schulten, K. NAMD2: Greater Scalability for Parallel Molecular Dynamics J. Comput. Phys. 1999, 151, 283-312. (30) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual Molecular Dynamics J. Mol. Graph. 1996, 14, 33-38. (31) Hummer, G.; Rasaiah, J. C.; Noworyta, J. P. Water Conduction through the Hydrophobic Channel of a Carbon Nanotube. Nature 2001, 414, 188-190. (32) Silva, L. B.; Gomide Freitas, L. C. Structural and Thermodynamic Properties of Liquid Ethylene Carbonate and Propylene Carbonate by Monte Carlo Simulations. Theochem-J. Mol. Struct. 2007, 806, 23-34. (33) Takeuchi, M.; Kameda, Y.; Umebayashi, Y.; Ogawa, S.; Sonoda, T.; Ishiguro, S.-i.; Fujita, M.; Sano, M. Ion-Ion Interactions of LiPF6 and LiBF4 in Propylene Carbonate Solutions. J. Mol. Liq. 2009, 148, 99-108. (34) MacKerell, A. D., Jr.; Bashford, D.; Bellott, M.; Dunbrack, R. L., Jr.; Evanseck, J. D.; Field, M. J.; Fischer, S.; Gao, J.; Guo, H.; Ha, S., et al. All-Atom Empirical Potential for Molecular Modeling and Dynamics Studies of Proteins. J. Phys. Chem B 1998, 102, 3586-3616. (35) Chen, X.; Tian, F.; Persson, C.; Duan, W.; Chen, N.-x. Interlayer Interactions in Graphites. Sci. Rep. 2013, 3, 3046. (36) Ayala, I. G.; Cordero, N. A.; Alonso, J. A. Surfactant Effect of Sulfuric Acid on the Exfoliation of Bilayer Graphene. Phys. Rev. B 2011, 84, 165424. (37) Zhu, Y.; Stoller, M. D.; Cai, W.; Velamakanni, A.; Piner, R. D.; Chen, D.; Ruoff, R. S. Exfoliation of Graphite Oxide in Propylene Carbonate and Thermal Reduction of the Resulting Graphene Oxide Platelets. ACS Nano 2010, 4, 1227-1233. (38) Persson, K.; Sethuraman, V. A.; Hardwick, L. J.; Hinuma, Y.; Meng, Y. S.; van der Ven, A.; Srinivasan, V.; Kostecki, R.; Ceder, G. Lithium Diffusion in Graphitic Carbon. J. Phys. Chem. Lett. 2010, 1, 1176-1180. (39) Brostow, W. Radial-Distribution Function Peaks and Coordination Numbers in Liquids and in Amorphous Solids. Chem. Phys. Lett. 1977, 49, 285-288. (40) Abe, S.; Watari, F.; Tachikawa, H. Interaction of Ethylene Carbonate and Graphene Chip: Density Functional Theory Study. Jpn. J. Appl. Phys. 2012, 51, 01AH07.


Page 25 of 26

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


(41) Hayamizu, K.; Aihara, Y.; Arai, S.; Martinez, C. G. Pulse-Gradient Spin-Echo 1H, 7Li, and 19F NMR Diffusion and Ionic Conductivity Measurements of 14 Organic Electrolytes Containing LiN(SO2CF3)2. J. Phys. Chem. B 1999, 103, 519-524.



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

Schematic representation of exfoliation of graphene sheet 50x50mm (300 x 300 DPI)

ACS Paragon Plus Environment

Page 26 of 26

Exfoliation of Electrolyte-Intercalated Graphene: Molecular Dynamics

Recommend Documents