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Article Experimental and Modeling Analysis of Holey Electrodes for High-Power-Density Li-Ion Batteries

Yu-Ren Huang 1 , Cheng-Lung Chen 2,*, Nen-Wen Pu 3,*, Chia-Hung Wu 4, Yih-Ming Liu 5, Ying-Hsueh Chen 3, Meng-Jey Youh 6 and Ming-Der Ger 5,* 1 Department of Applied Science, R.O.C. Naval Academy, Zuoying, Kaohsiung 813, Taiwan; [email protected] 2 Department of Chemistry, National Sun Yat-Sen University, Kaohsiung 804, Taiwan 3 Department of Electrical Engineering, Yuan Ze University, Zhongli, Taoyuan 320, Taiwan; [email protected] 4 School of Defense Science, Chung Cheng Institute of Technology, National Defense University, Dasi, Taoyuan 335, Taiwan; [email protected] 5 Department of Chemical & Materials Engineering, Chung Cheng Institute of Technology, National Defense University, Dasi, Taoyuan 335, Taiwan; [email protected] 6 Department of Mechanical Engineering, Ming Chi University of Technology, Taishan, New Taipei City 243, Taiwan; [email protected] * Correspondence: [email protected] (C.-L.C.); [email protected] (N.-W.P.); [email protected] (M.-D.G.); Fax: +886-7-525-3908 (C.-L.C.)

 Received: 28 October 2020; Accepted: 20 November 2020; Published: 22 November 2020 

Abstract: The performances of -ion batteries (LIBs) using holey graphene (HGNS) as the anode material are compared with those using non-holey graphene (GNS). The effects of graphene holes on ion transport are analyzed with a combined experiment/modeling approach involving (MD) simulations. The large aspect ratio of GNS leads to long transport paths for Li ions, and hence a poor rate capability. We demonstrate by both experiments and simulations that the holey structure can effectively improve the rate capability of LIBs by providing shortcuts for Li ion diffusion through the holes in fast charge/discharge processes. The HGNS anode exhibits a high specific capacity of 745 mAh/g at 0.1 A/g (after 80 cycles) and 141 mAh/g at a large of 10 A/g, which are higher than the capacity values of the GNS counterpart by 75% and 130%, respectively. MD simulations also reveal the difference in lithium ion transport between GNS and HGNS anodes. The calculations indicate that the HGNS system has a higher diffusion coefficient for lithium ions than the GNS system. In addition, it shows that the holey structure can improve the uniformity and quality of the solid electrolyte interphase (SEI) layer, which is important for Li ion conduction across this layer to access the electrode surface. Moreover, quantum chemistry (QC) computations show that carbonate (EC), a cyclic carbonate electrolyte with five-membered-ring , has the lowest binding energy of 1.32 eV and is the most favorable for lithium-ion transport through the SEI layer. A holey structure facilitates uniform dispersion of EC on graphene sheets and thus enhances the Li ion transport kinetics.

Keywords: holey graphene; lithium ion battery; molecular dynamics; diffusion; rate capability; solid electrolyte interphase; ethylene carbonate

1. Introduction The ever-growing markets of electric vehicles and portable electronic devices have created great demands for novel technologies. In addition, long-term storage units for surplus

Crystals 2020, 10, 1063; doi:10.3390/cryst10111063 www.mdpi.com/journal/crystals Crystals 2020, 10, 1063 2 of 16 energy have become an essential part of integrated renewable energy systems. Owing to their long operation and high capacity, lithium-ion batteries (LIBs) are often regarded as the first choice for most energy storage applications. However, there is an urgent need to upgrade the commercial LIBs in order to cope with the increasing requirements on the performance of energy storage devices and systems. For example, further progress on the performances of high-rate charging and discharging in LIBs is keenly demanded in many applications. One key method to improve LIB performances is to replace the anode (i.e., negative electrode) with advanced materials [1]. Graphene has been considered by many a possibility to address this issue [2,3]. Using graphene as the anode material not only doubles the theoretical specific capacity of LIBs by storing Li on both faces of each graphene sheet but also improves Li-ion diffusion and the high-rate charge/discharge capability. Although graphene offers higher chemical diffusivity for Li ions 7 6 2 (10− –10− cm /s) [4,5] than graphite, its two-dimensional (2-D) structure leads to the problem of easy restacking, which can significantly reduce the Li-ion diffusion rate [6–8]. Therefore, several ways of creating anti-restacking 3-dimensional (3-D) graphene structures [9–15] have been proposed. Even if restacking of graphene is avoided, its large 2-D geometry and excellent impermeability render it an undesirable diffusion barrier for Li ions and molecules. To overcome this obstacle, researchers have proposed and demonstrated ways to create holes on graphene sheets, and these holes have proven useful in improving the ionic transport of graphene electrodes [16–20]. In addition to the research works where graphene has been studied in half-cells, there have also been several studies which investigated the performance of full Li-ion cells where graphene anodes are used in combination with cathodes such as LiNi0.5Mn1.5O4 [21] and LiFePO4 [22–24]. Such studies can better reflect the reality of graphene in LIBs. The LIB electrolyte usually consists of a common organic solution with a mixture of linear and cyclic carbonates as . Another essential component that dictates the charge/discharge dynamics in a LIB is the thin layer formed spontaneously at the interface between the electrode and the electrolyte, as Li ions need to pass through it in order to reach or escape the electrode surface during the charge/discharge cycle [1,25,26]. This passivation layer, which is called the solid electrolyte interphase (SEI) [27–29], is formed during the first few cycles when the electrolyte solvents decompose reductively on the anode and the decomposed products cover the electrode surface. Once formed, the SEI should be ion-conducting to facilitate the transport of lithium ions during intercalation and deintercalation, but nonconducting for to avoid further decomposition of the electrolyte. It must also have good chemical stability and low solubility in the electrolyte. Additionally, it is very important that the SEI layer exhibits good uniformity in morphology and chemical composition in order to ensure the good performance of an LIB. Herein, we report a study of the benefits of holey graphene on the performances of LIBs using both theoretical and experimental methods. The theoretical calculation methods employed were molecular dynamics (MD) simulation and quantum chemistry (QC). The holey graphene not only increase the specific surface area and hence the battery capacity, but also improve the accessibility and diffusivity of lithium ions. Additionally, our molecular dynamics simulation shows that the unique holey morphology can greatly facilitate the formation of a more uniform SEI on the carbonaceous anode, which will result in favorable electrochemical performance of the LIB.

2. Experimental Details

2.1. Preparation of Pristine and Holey Graphene Samples The high-purity graphite powder (purity > 99.9995%; 200 mesh) used to prepare GO was purchased from Alfa Aesar. It was first oxidized to obtain graphene oxide (GO) using the Staudenmaier method. An amount of 5 g of natural graphite powder was added into a mixture of (87.5 mL, 95%) and (45 mL, 65%). chlorate (5.5 g) was next added slowly into the solution, which was cooled with an bath to avoid a temperature rise, and then stirred for over 96 h. After that, Crystals 2020, 10, 1063 3 of 16 the mixture was added with a 5% solution of HCl (Sigma-Aldrich, 37%) and then centrifuged until the sulfate ions were removed from the solution. The solution was then repetitively diluted with deionized and centrifuged until its pH values became 7.0. The neutral solution was filtered with 0.5-µm-pore-size filter paper and then dried by baking at 80 ◦C for 24 h. After baking, the filtered GO was ground into powder. To prepare exfoliated pristine graphene (GNS) samples, an appropriate amount of graphene oxide powder was inserted in an Ar-filled quartz tube furnace, which was then heated from room temperature to 1100 ◦C at a rate of 10 ◦C/min and held at that temperature for 1 h. As for the production of holey graphene (HGNS), a modified approach called ultra-rapid heating [16] was used. The Ar-filled quartz tube furnace was preheated to 1100 ◦C. To maximize the heating rate for GO, we quickly opened a hinged-type flange on one end of the quartz tube and then inserted a long-handled stainless-steel tool containing GO powder rapidly into the center of the quartz tube to dump the powder onto the heated inner wall of the tube. To maintain the inert atmosphere, the Ar flow rate was raised throughout this process, and then the furnace was immediately sealed again afterwards. Since the GO powder was in direct thermal contact with the hot quartz tube, the heat transfer was very fast, and the instantaneous heating rate for the dumped GO can be as high as 300 ◦C/s or 18,000 ◦C/min, resulting in severe hole-punching, instead of mere exfoliation, of graphene sheets due to violent CO2 gas generation. The HGNS was kept in the furnace at 1100 ◦C for 1 h to remove the functional groups.

2.2. Characterizations The microstructures and morphologies of the GNS and HGNS samples were characterized by X-ray diffractometry (XRD, Rigaku, Tokyo, Japan, D/Max 2200) and scanning electron microscopy (SEM, JEOL, Tokyo, Japan, JSM-6500), respectively. The specific surface area values for GNS and HGNS were determined from the N2 physisorption isotherms obtained with a Micromeritics (Norcross, GA, USA) ASAP 2020 Surface Area and Porosity Analyzer by the Brunauer–Emmett–Teller (BET) method. The Raman spectra of the samples were obtained with a Renishaw (Wotton-under-Edge, UK) inVia using a 514.5 nm excitation wavelength. The elemental compositions of the GO, GNS, and HGNS samples were determined by elemental analysis (EA, Thermo Scientific, Waltham, MA, USA, FlashEA 2000 CHNS-O Analyser).

2.3. Electrochemical Measurements The CR2032 type coin cell structure was adopted for electrochemical measurements. To fabricate the working electrode, 80 wt.% of GNS (or HGNS) and 20 wt.% of polyvinylidene difluoride (PVDF) were mixed well in NMP and spread onto a circular copper foil. The layer thickness was set at 3 µm, and the masses of the GNS and HGNS electrodes were 0.7 and 0.5 mg, respectively. The mass loading of the electrodes was 0.45 and 0.32 mg/cm2 for GNS and HGNS, respectively. The electrolyte was 1 M LiPF6 dissolved in the mixture of ethylene carbonate (EC), dimethyl carbonate (DMC), ethyl methyl carbonate (EMC), and Diethyl carbonate (DEC), and the separator used was a Celgard® 2400 polypropylene membrane. The counter electrode was a pure lithium foil. The galvanostatic charge–discharge measurements were recorded with a battery auto-test system (AcuTech, New Taipei, Taiwan, BAT-750B) in a voltage range from 0.01 to 3 V (vs. Li/Li+) at various current densities.

3. Simulations

3.1. Simulated Systems Molecular dynamics (MD) simulation was carried out to study the morphologies and physical properties of graphene/electrolyte composites. The lithium salt, LiPF6, and graphene molecules were mixed with a solution containing various organic components. Given in Table1 are the structures and physical properties of these organic molecules: EC, DMC, EMC, and DEC [27]. Crystals Crystals2020, 10Crystals ,2020 x FORCrystals, 10 2020 PEER, x FOR2020, 10 REVIEW, ,PEERx 10 FOR, x FORREVIEW PEER PEER REVIEW REVIEW 4 of 16 4 of 164 of 416 of 16

simulatedsimulated forsimulated comparison.simulated for comparison. for comparison.for The comparison. HGNS The HGNS The The HGNS molecule HGNS constructed molecule molecule constructed constructedaccording constructed according to according Schniepp according to Schniepp toet al.Schniepp to [30] Schniepp et al. is shown[30] et al. etis [30] al.shown [30] is shown is shown in Figurein Figure 1. inThe Figurein 1.red FigureThe and 1. red The 1.white andThe red whitecolorsred and and white colorsrepresent white colors represent colors O representand represent OH and , O H and Oatoms, respectively. and H atoms,H respectively. atoms, respectively. Each respectively. GNS Each or GNSEach HGNS Each orGNS HGNS GNS or HGNSor HGNS containscontains 14 epoxycontains 14contains epoxyand 14 14 14and hydroxyl epoxy 14 and hydroxyl and 14groups, hydroxyl 14 hydroxyl groups, randomly groups, randomly groups, distributed randomly randomly distributed ondistributed the distributed ongraphene the on graphene theon plane. thegraphene graphene plane.The ratio plane. The plane. of ratio The The ofratio ratio of of C atomsC atomsreplacedC atoms Creplaced atoms with replaced epoxy replacedwith epoxywithand with hydroxylepoxy and epoxy hydroxyl and groups and hydroxyl hydroxyl groups in GNS groups in groupsand GNS in HGNS and GNSin GNS HGNS wasand and HGNSset was HGNSto aboutset was to was setabout10%. setto Theaboutto10%. about The10%. 10%. The The dimensionsdimensions dimensionsof thedimensions ofGNS the andof GNS the of HGNS theandGNS GNS HGNS sheetsand and HGNS sheetsin HGNS the sheets insimulation sheetsthe in simulation the in are thesimulation 26.41simulation are Å26.41 ×are 27.68 are26.41Å × 26.41 Å27.68 Å[31,32]. × Å 27.68Å × [31,32]. 27.68The Å [31,32].holes Å The [31,32]. holes The The holes holes are distributed in a random way to fit the actual material state as shown in Figure 1. are distributedCrystalsare2020 inaredistributed, 10 a , distributed 1063random in way a in random toa randomfit the way actual way to fit tomaterial the fit theactual actualstate material as material shown state instate asFigure shown as shown 1. in Figure in Figure 1. 1. 4 of 16

Table 1.Table Chemical Table1. ChemicalTable structures 1. Chemical 1. structuresChemical and structures pr structuresopertiesand pr andoperties of and prtheoperties prcyclic ofoperties the an cyclicofd the linearof anthecyclicd carbonate cycliclinear and an carbonatelineard solvents.linear carbonate carbonatesolvents. solvents. solvents. Table 1. Chemical structures and properties of the cyclic and linear carbonate solvents. EC EC EC EC DMC DMCDMC DMC EMC EMC EMCEMC DEC DEC DECDEC EthyleneEthylene EC DimethylDimethylDMC EthylEMC Ethylmethyl methyl Ethylene EthyleneDimethyl DimethylEthyl methyl Ethyl methylDiethyl DEC Carbonate Ethylene Dimethyl Ethyl methyl Diethyl CarbonateDiethylDiethyl Carbonate Carbonate CarbonateCarbonate CarbonateCarbonate Carbonate Carbonate CarbonateCarbonate Carbonate Carbonate CarbonateCarbonate Diethyl Carbonate Carbonate Carbonate Carbonate MolecularMolecularMolecular Molecular 3 4 3 3 6 3 4 8 3 5 10 3 C3H4OC3 H OC3 HC4O3H3 4OC3 3H6OC3 H OC3 HC6O3H3 6O3 C4H8OC3 H OC4 HC8O4H3 8O3 C5H10OC3 H OC5H C105OH310 O3 formulaformula Molecularformula formula formula C3H4O3 C3H6O3 C4H8O3 C5H10O3

Structural Structural StructuralStructural formula formulaformula formula formula

MolecularMolecular MolecularMolecularMolecular weight 88.06 90.08 104.11 118.13 88.06 88.06 88.0688.06 90.08 90.08 90.0890.08 104.11 104.11 104.11 104.11 118.13 118.13 118.13 118.13 weightweight weight weightDensity 1.32 g/cm3 1.069 g/cm3 1.012 g/cm3 0.975 g/cm3 3 3 3 3 Density 1.323 g/cm 3 3 1.0693 g/cm 3 3 1.0123 g/cm 3 3 0.9753 g/cm 3 3 Density DensityViscosityDensity1.32 g/cm 1.321.32 g/cm 1.85 g/cm1.069 cP g/cm 1.069 0.5851.069 g/cm cP g/cm 1.012 g/cm 0.65 1.012 cP1.012 g/cm g/cm 0.975 0.748 g/cm cP 0.9750.975 g/cm g/cm ViscosityViscosity ViscosityViscosity 1.85 cP 1.85 cP 1.85 1.85 cP cP 0.585 cP 0.585 cP 0.585 0.585 cP cP 0.65 cP 0.65 cP 0.65 0.65 cP cP 0.748 cP 0.748 cP 0.748 0.748 cP cP Boiling point 243 ◦C 90.5 ◦C 107.5 ◦C 126 ◦C BoilingBoiling pointBoiling pointBoiling point 243 point °C 243 °C 243 243°C °C 90.5 °C 90.5 °C 90.5 90.5 °C °C 107.5 °C 107.5 °C 107.5 107.5 °C °C 126 °C 126 °C 126 126°C °C Melting point 38 ◦C 3 ◦C 14 ◦C 43 ◦C MeltingMelting Melting Melting − − 38 °C 38 °C 38 °C38 °C 3 °C 3 °C 3 °C 3 °C −14 °C− 14 °C− 14− °C14 °C −43 °C− 43 °C− 43− °C43 °C point point pointpoint The compositions of the simulated systems are given in Table2. Two systems containing graphene

sheets (GNS, C284H14O28) and holey graphene sheets (HGNS, C275H14O28), separately, were simulated for comparison. The HGNS molecule constructed according to Schniepp et al. [30] is shown in Figure1. Table 2.Table Simulation Table2. SimulationTable 2.conditions Simulation 2. Simulation conditions of conditionsthe conditionstwo of the systems. twoof the of systems. thetwo two systems. systems. The red and white colors represent O and H atoms, respectively. Each GNS or HGNS contains 14 epoxy and 14 hydroxyl groups,Component randomlyComponentComponent distributedComponent System on System 1 the Systemgraphene 1 System System 1 plane. System 1 2 System The 2 System ratio 2 of 2 C atoms replaced with epoxy and hydroxylGNS groups GNS in GNSGNSGNS and5 HGNS5 was5 set50 to about0 10%.0 The0 dimensions of the GNS and HGNS sheets in the simulationHGNS are 26.41 Å0 27.68 Å [31,32 5]. The holes are distributed in a HGNS HGNSHGNS 0 × 0 0 5 5 5 random way to fit the actual material6 state as shown in Figure1. LiPF6 LiPF LiPFLiPF6 206 20 20 2020 20 20 20 EC 360 360 ECTable 2. SimulationEC EC360 conditions of360 the360 360 two systems. 360360 DMC DMC DMCDMC 48 48 48 4848 48 48 48 Component System 1 System 2 EMC EMC EMCEMC 40 40 40 4040 40 40 40 GNS 5 0 DEC DEC DECDEC 132 132 132132 132 132 132132 HGNS 0 5 LiPF6 20 20 EC 360 360 DMC 48 48 EMC 40 40 DEC 132 132

3.2. Simulation Method All simulation runs were performed in (N,V,T) condition with Nóse–Hoover thermostat at 298 K using the BIOVIA (San Diego, CA, USA) Materials Studio 6 package. The UNIVERSAL force field was chosen for the simulations [33]. The trajectories were integrated via the Verlet leapfrog algorithm and the time step of integration was set to 1.0 femtosecond. A gradually-reducing-box (GRB) method was adopted in order to construct reasonable GNS/electrolyte and HGNS/electrolyte composite systems. To begin with, the GNS, or HGNS, the ions of electrolyte, and all of the solvent molecules were randomly arranged into a large box. The initial box size of each system was set to 0.1 g/cm3 so that molecules were well separated in distance and the inter-molecular interactions were very weak. MD simulation was executed until the system reached thermal equilibrium. Next, the box size was compressed slightly

(say, 1% in each dimension) so that the molecules were slightly closer to each other; MD simulation was then performed again to thermally equilibrate the compressed box. The procedure was repeated until the density of the simulated system reached its experimental density. Crystals 2020, 10, 1063 5 of 16 Crystals 2020, 10, x FOR PEER REVIEW 5 of 16

Figure 1. (a) Dimensions (in Å) of the constructed holey graphene (HGNS). (b) Tilted view of HGNS revealingFigure 1. the(a) Dimensions epoxy and hydroxyl (in Å) of groups. the cons Thetructed red and holey white graphene colors are (HGNS). for O and (b) HTilted atoms, view respectively. of HGNS revealing the epoxy and hydroxyl groups. The red and white colors are for O and H atoms, Therespectively. final box sizes of the two simulated systems were 45 Å 45 Å 45 Å. Figure2 displays a × × snapshot of the simulation box (system 2) in the initial stage of the repetitive compression procedure. Clearly,3.2. Simulation the HGNS Method sheets and the electrolyte molecules were randomly distributed. After the final box size was reached, an additional MD run of 1000 ps was carried out to further relax the system. Finally, All simulation runs were performed in (N,V,T) condition with Nóse–Hoover thermostat at 298 the trajectories were recorded every 20 steps for a total time period of 50 ns. Figure3 is a snapshot of K using the BIOVIA (San Diego, CA, USA) Materials Studio 6 package. The UNIVERSAL our HGNS/electrolyte system for the final-size box. was chosen for the simulations [33]. The trajectories were integrated via the Verlet leapfrog algorithm and the time step of integration was set to 1.0 femtosecond. A gradually-reducing-box (GRB) method was adopted in order to construct reasonable GNS/electrolyte and HGNS/electrolyte composite systems. To begin with, the GNS, or HGNS, the ions of electrolyte, and all of the solvent molecules were randomly arranged into a large box. The initial box size of each system was set to 0.1 g/cm3 so that molecules were well separated in distance and the inter-molecular interactions were very weak. MD simulation was executed until the system reached thermal equilibrium. Next, the box size was compressed slightly (say, 1% in each dimension) so that the molecules were slightly closer to each other; MD simulation was then performed again to thermally equilibrate the compressed box. The procedure was repeated until the density of the simulated system reached its experimental density.

Crystals 2020, 10, x FOR PEER REVIEW 6 of 16

The final box sizes of the two simulated systems were 45 Å × 45 Å × 45 Å. Figure 2 displays a Crystals 2020, 10, x FOR PEER REVIEW 6 of 16 snapshot of the simulation box (system 2) in the initial stage of the repetitive compression procedure. Clearly, the HGNS sheets and the electrolyte molecules were randomly distributed. After the final The final box sizes of the two simulated systems were 45 Å × 45 Å × 45 Å. Figure 2 displays a box size was reached, an additional MD run of 1000 ps was carried out to further relax the system. snapshot of the simulation box (system 2) in the initial stage of the repetitive compression procedure. Finally, the trajectories were recorded every 20 steps for a total time period of 50 ns. Figure 3 is a Clearly, the HGNS sheets and the electrolyte molecules were randomly distributed. After the final snapshot of our HGNS/electrolyte system for the final-size box. box size was reached, an additional MD run of 1000 ps was carried out to further relax the system. Crystals 2020, 10, 1063 6 of 16 Finally, the trajectories were recorded every 20 steps for a total time period of 50 ns. Figure 3 is a snapshot of our HGNS/electrolyte system for the final-size box.

Figure 2. Snapshot of the initial simulation box for the HGNS/electrolyte system.

FigureFigure 2.2. SnapshotSnapshot ofof thethe initialinitial simulationsimulation boxbox forfor thethe HGNSHGNS/electrolyte/electrolyte system.system.

Figure 3. Snapshot of the HGNS/electrolyte system for the final-size box in thermal equilibrium. Figure 3. Snapshot of the HGNS/electrolyte system for the final-size box in thermal equilibrium. 4. Results and Discussion

4.1. ExperimentalFigure 3. Snapshot Results of the HGNS/electrolyte system for the final-size box in thermal equilibrium. The microstructures of GO, GNS, and HGNS were characterized by XRD (see Figure4a). For GO, the (002) peak shifted from 26.3◦ (for graphite) to 12.5◦, because the interlayer spacing increased from 0.34 nm to 0.71 nm as a result of oxidation and intercalation. By contrast, the XRD patterns for GNS and HGNS show no diffraction peak, which indicates that the pristine and holey graphene samples both have a high degree of exfoliation. The difference in structural defects between GNS and HGNS can be revealed by Raman spectra. The peak at 1585/cm is the G-band, which corresponds to the stretching of the ordered sp2 atoms, whereas the peak at 1335/cm is the D-band, which is related Crystals 2020, 10, x FOR PEER REVIEW 7 of 16

4. Results and Discussion

4.1. Experimental Results The microstructures of GO, GNS, and HGNS were characterized by XRD (see Figure 4a). For GO, the (002) peak shifted from 26.3° (for graphite) to 12.5°, because the interlayer spacing increased from 0.34 nm to 0.71 nm as a result of oxidation and intercalation. By contrast, the XRD patterns for GNS and HGNS show no diffraction peak, which indicates that the pristine and holey graphene samples Crystalsboth have2020, a10 high, 1063 degree of exfoliation. The difference in structural defects between GNS and HGNS7 of 16 can be revealed by Raman spectra. The peak at 1585/cm is the G-band, which corresponds to the stretching of the ordered sp2 carbon atoms, whereas the peak at 1335/cm is the D-band, which is to disordered carbon and defects. The intensity ratio ID/IG is routinely used as an indicator for the related to disordered carbon and defects. The intensity ratio ID/IG is routinely used as an indicator for quality of carbon materials. In Figure4b, HGNS has a significantly higher D-band intensity than GNS. the quality of carbon materials. In Figure 4b, HGNS has a significantly higher D-band intensity than It confirmed that the structure of graphene is severely damaged by the gas punching the sheets during GNS. It confirmed that the structure of graphene is severely damaged by the gas punching the sheets the ultra-rapid heating process for HGNS preparation. Table3 shows the elemental composition, during the ultra-rapid heating process for HGNS preparation. Table 3 shows the elemental which was determined by EA, and the C/O ratio for GO, GNS and HGNS samples. The oxygen content composition, which was determined by EA, and the C/O ratio for GO, GNS and HGNS samples. The in GO is as high as 38% due to the severe oxidation process. The significantly increased C/O ratios for oxygen content in GO is as high as 38% due to the severe oxidation process. The significantly GNS and HGNS after thermal reduction confirm the obtaining of high-purity graphene samples as a increased C/O ratios for GNS and HGNS after thermal reduction confirm the obtaining of high-purity result of the removal of oxygen functional groups at 1100 C. graphene samples as a result of the removal of oxygen functional◦ groups at 1100 °C.

FigureFigure 4.4. (a) X-ray didiffractometryffractometry (XRD) results forfor graphenegraphene oxide (GO), non-holeynon-holey graphene (GNS) andand HGNS.HGNS. ((bb)) RamanRaman spectraspectra forfor GNSGNS andand HGNS.HGNS.

Table 3. EA anlysis of GO, GNS and HGNS samples. Table 3. EA anlysis of GO,GNS and HGNS samples. Sample C (at.%) O (at.%) C/O (at.%) Sample C (at.％) O (at.％) C/O (at.％) GOGO 62 3838 1.6 1.6 GNS 98.3 1.7 58 GNSHGNS 98.3 99.1 0.91.7 110 58 HGNS 99.1 0.9 110 Figure5a,b display the SEM images of GNS and HGNS, respectively, revealing the di fference in their morphology. In Figure5a, GNS, which was produced by thermal reduction /exfoliation of GO at a Figure 5a,b display the SEM images of GNS and HGNS, respectively, revealing the difference in heating rate of 10 ◦C/min, exhibits a relatively flat morphology except for a few wrinkles, a typical featuretheir morphology. of Staudenmaier In Figure GNS. 5a, As weGNS, reduced which GO was at produced an extremely by thermal high-temperature reduction/exfoliation ramp rate (HGNS), of GO aat high a heating density rate of of holes 10 °C/min, with sizes exhibits ranging a relatively from ~5 flat to 300 morphology nm appeared except (see for Figure a few5 b)wrinkles, and the a surface typical significantlyfeature of Staudenmaier roughened. TheGNS. mechanism As we reduced for the creationGO at an of holeyextremely morphology high-temperature is as follows. ramp On rate GO sheets,(HGNS), there a high exist density many of severely holes wi oxidizedth sizes regionsranging which from ~5 are to mechanically 300 nm appeared weaker (see than Figure other 5b) areas. and Whenthe surface GO was significantly heated up roughened. ultra-rapidly The (about mechanis 18,000m K for/min), the thecreation gas produced of holey from morphology the reduction is as reactionsfollows. On built GO up sheets, an enormous there exist pressure, many which severely punched oxidized the weakerregions spotswhich and are created mechanically a large numberweaker ofthan through-holes. other areas. When GO was heated up ultra-rapidly (about 18,000 K/min), the gas produced from Figure5c,d show the –desorption isotherm curves of GNS and HGNS, respectively. According to the IUPAC definition, both curves are type IV isotherms. In the low relative pressure range (less than 0.1), nitrogen adsorption capacity is very low, indicating a small number of micropores in both samples. At higher relative pressure (larger than 0.4), there is a clear hysteresis loop displaying the presence of abundant mesopores. These results are in agreement with those previously reported in the literature [34,35]. The values of specific surface area for holey and non-holey graphene samples calculated with the BET method were drastically different: 310 m2/g for GNS vs. 780 m2/g for HGNS. This indicates that the specific surface area of graphene is highly dependent on the heating Crystals 2020, 10, x FOR PEER REVIEW 8 of 16 the reduction reactions built up an enormous pressure, which punched the weaker spots and created a large number of through-holes. Figure 5c,d show the nitrogen adsorption–desorption isotherm curves of GNS and HGNS, respectively. According to the IUPAC definition, both curves are type IV isotherms. In the low relative pressure range (less than 0.1), nitrogen adsorption capacity is very low, indicating a small number of micropores in both samples. At higher relative pressure (larger than 0.4), there is a clear hysteresis loop displaying the presence of abundant mesopores. These results are in agreement with those previously reported in the literature [34,35]. The values of specific surface area for holey and Crystalsnon-holey2020, graphene10, 1063 samples calculated with the BET method were drastically different: 310 m2/g8 of for 16 GNS vs. 780 m2/g for HGNS. This indicates that the specific surface area of graphene is highly dependent on the heating rate, and the large number of holes created by ultra-rapid heating results rate, and the large number of holes created by ultra-rapid heating results in a significant increase in in a significant increase in surface area. The measured pore volumes for GNS and HGNS were 1.4 surface area. The measured pore volumes for GNS and HGNS were 1.4 and 3.4 cm3/g, respectively. and 3.4 cm3/g, respectively.

Figure 5. SEM images of (a) GNS and (b) HGNS; and nitrogen adsorption–desorption isotherm curves Figure 5. SEM images of (a) GNS and (b) HGNS; and nitrogen adsorption–desorption isotherm curves of (c) GNS and (d) HGNS. of (c) GNS and (d) HGNS. To compare the performance of the two different LIB anodes made separately of GNS and HGNS, To compare the performance of the two different LIB anodes made separately of GNS and we carried out 80 cycles of galvanostatic charge/discharge measurements at various current densities, HGNS, we carried out 80 cycles of galvanostatic charge/discharge measurements at various current and the measured capacity vs. cycle number curves for the two LIBs are displayed in Figure6. densities, and the measured capacity vs. cycle number curves for the two LIBs are displayed in Figure The Coulombic efficiency for both samples is also shown. Both samples were first charged/discharged 6. The Coulombic efficiency for both samples is also shown. Both samples were first at a low current density of 0.1 A/g, and then every 10 cycles the current density was elevated stepwise charged/discharged at a low current density of 0.1 A/g, and then every 10 cycles the current density to 0.3, 0.5, 1, 3, 5, and 10 A/g. For the last 10 cycles, the current density was brought back down to was elevated stepwise to 0.3, 0.5, 1, 3, 5, and 10 A/g. For the last 10 cycles, the current density was 0.1 A/g. Evidently, the results demonstrated the advantages of HGNS over GNS not only in specific brought back down to 0.1 A/g. Evidently, the results demonstrated the advantages of HGNS over capacity but also in rate capability. At any current density, the HGNS anode always shows higher GNS not only in specific capacity but also in rate capability. At any current density, the HGNS anode capacity than the GNS counterpart. Specifically, HGNS exhibits a high capacity of 745 mAh/g at always shows higher capacity than the GNS counterpart. Specifically, HGNS exhibits a high capacity 0.1 A/g (after 80 cycles) and 141 mAh/g at a high current density of 10 A/g, which are higher than the corresponding capacity values of GNS by 75% and 130%, respectively.

Crystals 2020, 10, x FOR PEER REVIEW 9 of 16 of 745 mAh/g at 0.1 A/g (after 80 cycles) and 141 mAh/g at a high current density of 10 A/g, which are higher than the corresponding capacity values of GNS by 75% and 130%, respectively. The fast decay of capacity in the first cycle can be ascribed to the irreversible process of SEI formation. HGNS suffered larger capacity loss and showed slightly lower Coulombic efficiency in the 1st cycle than GNS because of its larger specific surface area, which leads to higher irreversible capacity because more SEI would form at the interface between the electrolyte and the active material [17]. Even so, HGNS still surpassed GNS considerably in all test conditions, indicating that a holey structure definitely can improve the specific capacity and the rate capability of a graphene-based LIB anode. The comparison of our electrochemical results with those previously reported for other Crystals 2020, 10, 1063 9 of 16 graphene nanosheets (2-D and 3-D) is shown in Table 4. Clearly, our results here are comparable to, or in some cases even better than, these reported works.

FigureFigure 6. RateRate capability, capability, Coulombic Coulombic efficiency, efficiency, and cycle performance of GNS and HGNS at various currentcurrent densities densities from 0.1 to 10 A/g. A/g. The fast decay of capacity in the first cycle can be ascribed to the irreversible process of SEI Table 4. Comparison of graphene anodes in lithium ion batteries. formation. HGNS suffered larger capacity loss and showed slightly lower Coulombic efficiency in the 1st cycle thanMaterials GNS because of its larger specificSignificant surface area, Findings which leads Observed to higher irreversibleRefs. capacity because more SEI would form atThe the HGNS interface anode between exhibits the a electrolytehigh specific and capacity the active of 745 material [17]. Even so, HGNS still surpassed GNSmAh/g considerably at 0.1 A/g in(after all test 80 cycles) conditions, and indicating141 mAh/g that at a a large holey structure Holey graphene (HGNS); This definitely can improve the specificcurrent capacity of 10 and A/g the(after rate 70 capability cycles), which of agraphene-based are higher than LIB anode. pristine graphene (GNS) work The comparison of our electrochemicalthe capacity results values with of those the GNS previously counterpart reported by 75% for and other graphene nanosheets (2-D and 3-D) is shown in Table4. Clearly,130%, our respectively. results here are comparable to, or in some

cases even better than, these reportedThe works. TiO2/GNS composite anode exhibits a specific capacity of ~170 mAh/g at 0.1 A/g (after 100 cycles) and Table 4. Comparison of graphene anodes in lithium ion batteries. TiO2/GNS composite; ~70 mAh/g at a large current of 5 A/g (after 100 cycles). [36] GNSMaterials The GNS anode Significant exhibits a Findings specific Observed capacity of ~78 mAh/g Refs. at 0.1The A/g HGNS (after anode 100 exhibitscycles) aand high ~20 specific mAh/g capacity at a of large 745 mAhcurrent/g at 0.1 Aof/g 5 (after A/g 80(after cycles) 100 and cycles). 141 mAh /g at a Holey graphene (HGNS); pristine large current of 10 A/g (after 70 cycles), which are higher This work graphene (GNS) The GNS reduced from high-grade GO has a specific GNS reduced from high- than the capacity values of the GNS counterpart by 75% surface area of 493 m2/g, and exhibits a reversible grade GO at 1050°C; and 130%, respectively. specificThe TiO capacity2/GNS composite of 835 anodemA/g exhibits at 0.05 a specificA/g (1st capacity cycle), GNS reduced from [37] of ~170which mAh drops/g at 0.1 to A~700/g (after mAh/g 100 cycles) after and 15 ~70cycles. mAh /g medium-grade GO at a large current of 5 A/g (after 100 cycles). TiO2/GNS composite; GNS The GNS reduced from medium-grade GO has a specific [36] 1050°C The GNS anode exhibits a specific capacity of ~78 mAh/g surfaceat area 0.1 A of/g (after121m 1002/g, cycles) and exhibits and ~20 mAh a reversible/g at a large specific current of 5 A/g (after 100 cycles). The GNS reduced from high-grade GO has a specific surface area of 493 m2/g, and exhibits a reversible specific GNS reduced from high-grade GO at capacity of 835 mA/g at 0.05 A/g (1st cycle), which drops to 1050 C; ~700 mAh/g after 15 cycles. ◦ [37] GNS reduced from medium-grade GO The GNS reduced from medium-grade GO has a specific 2 1050 ◦C surface area of 121m /g, and exhibits a reversible specific capacity of 438 mAh/g at 0.05 A/g (1st cycle), which drops to ~320 mAh/g after 15 cycles. Crystals 2020, 10, 1063 10 of 16

Table 4. Cont.

Materials Significant Findings Observed Refs. The reduced GNS anode exhibits a reversible capacity of ~330 mAh/g at 0.05 A/g (1st cycle). Hydrazine reduced GNS; The e-beam reduce GNS anode exhibits reversible capacity [38] Electron-beam reduced GNS of ~1054 mAh/g at 0.05 A/g (1st cycle), which drops to 784 mAh/g after 15 cycles. The reversible capacity at a current density of 0.05 A/g is GNS; 540, 730, and 784 mAh/g for GNS, GNS+CNT, GNS+CNT; and GNS+C60, respectively. However, the reversible [3] GNS+C60 capacity after 20 cycles decays to 290,480, and 600 mAh/g for GNS, GNS+CNT, and GNS+ C60, respectively. The a-SnO2/graphene delivers a capacity of 700 mAh/g in 80th cycle at a current density of 0.1 A/g. At a-SnO /graphene aerogel [15] 2 a larger current density of 1.6 A/g, it drops to 269 mAh/g (50th cycle). At rates of 0.5 C and 1 C, the composite electrode delivered AGN/S composite (3D porous high specific capacities of 1143 mAh/g and 927 mAh/g, network of activated graphene [19] respectively. After 100 cycles, the capacity decays to 766 confining sulfur) and 686 mAh/g, respectively.

4.2. Simulation Results In the electrochemical measurements, clearly, the presence of holes on graphene sheets can increase the performance of rapid charge/discharge and enhance the power density, suggesting that the holes provide shortcuts for the transport of Li+ and solvent molecules. To better understand the effects of graphene’s holes on the dynamical behaviors of the ions and molecules in LIBs, MD simulation was carried out for the two aforementioned systems. The atomic diffusion constant, D, can be obtained theoretically from the slope of the linear region on the curve of mean square displacement (MSD) versus time t:

1 * * 2 D lim R(t) R (0) (1) ∼ t 6th| − | i →∞ * where R is the atomic position, and the angle brackets denote the ensemble average. Plotted in Figure7 are the calculated curves of MSD vs. t for lithium ions in the two systems: HGNS/electrolyte and GNS/electrolyte. The corresponding diffusion constants of Li+ obtained from the linear-region slopes of the curves are 9.98 10 7 and 8.62 10 7 cm2/s for HGNS and GNS systems, respectively. × − × − This simulation confirms that the diffusivity of lithium ions is affected by the holes in graphene. In the HGNS system, the holey structure allows faster transport of Li ions across the planar graphene by taking the shortcuts through holes; in the GNS system, without a holey structure, the 2-D graphene sheet leads to long and winding transport paths of Li ions as well as a lower diffusion coefficient. Note that, due to the limit of our calculation capability, the lateral dimensions of both the graphene sheets and the holes in our miniature simulation systems are 2 to 3 orders of magnitude smaller than reality. Even in such a small cell, the effect of holes on Li+ diffusion is clearly demonstrated. Thus a significantly larger difference is expected in real LIBs. Table5 displays the di ffusion coefficients for Li+ and each constituent molecule (EC, DMC, EMC, and DEC) in both the GNS and the HGNS systems. For all organic solvent molecules, the diffusion coefficients in the HGNS system are higher than those in the GNS system. In the same system, the magnitudes of diffusion constants for different solvent molecules are quite close. This indicates that the solvent molecules were mixed homogeneously in the solution. Additionally, the diffusion constants of Li ion (with much smaller size) are very similar to those of the solvents. This indicates that Li ions moved together with solvent molecules. Crystals 2020, 10, x FOR PEER REVIEW 11 of 16 constantsCrystals 2020 of ,Li10 ,ion 1063 (with much smaller size) are very similar to those of the solvents. This indicates11 of 16 that Li ions moved together with solvent molecules.

FigureFigure 7. Mean 7. Mean square square displacement displacement (MSD) (MSD) vs. vs.t fort forlithium lithium ions ions in the in the two two different different systems. systems. Table 5. Diffusion coefficients (in cm2/s) of Li+ and solvent molecules in the two systems. Table 5. coefficients (in cm2/s) of Li+ and solvent molecules in the two systems. Li+ EC DMC EMC DEC Li+ EC DMC EMC DEC 7 7 7 7 7 GNS 8.62 10 −7 8.61 10−7 8.62 −710 8.41−7 10 8.33−7 10 GNS 8.62× × 10− 8.61 × ×10 − 8.62 × 10× − 8.41 × 10 × 8.33− × 10 × − 7 7 7 7 7 HGNSHGNS 9.98 × 1010−−7 9.969.96 × 1010−7− 9.939.93 × 10−710 − 9.96 × 9.9610−7 10 9.96− × 109.96−7 10− × × × × × Furthermore, to analyze the intermolecular distance, various radial distribution functions (RDFs) Furthermore,were calculated. to analyze The RDFs the between intermolecular two kinds distance, of atoms, various i and radial j, are distribution calculated as functions follows: (RDFs) were calculated. The RDFs between two kinds of atoms, i and j, are calculated as follows: 𝑉(∆𝑁 (𝑟→𝑟+∆𝑟 )) 𝑔 (𝑟) = V ∆Nij(r r + ∆r) (2) g (r) = → (2) ij 4𝜋𝑟 2∆𝑟𝑁 𝑁 4πr ∆rNiN j wherewhere ∆𝑁∆N(𝑟→𝑟+∆𝑟(r r + ∆) r is) isthe the ensemble-averaged ensemble-averaged number number of ofj aroundj around i withini within a spherical a spherical shell shell with with ij → thethe radius radius between between r andr and r +r Δ+r,∆ Nr,i andNi and Nj areNj arethe thenumbers numbers of iof andi and j, respectively,j, respectively, and and V isV theis the system system volume.volume. The The lithium lithium ions ions and and electrolyte electrolyte molecules molecules in inthe the radial radial distribution distribution between between which which the the intermolecularintermolecular distance distance is small is small will will form form a compound a compound more more easily. easily. TheThe plots plots of RDFs of RDFs for forLi-graphene Li-graphene and and for Li/s forolvents Li/solvents in GNS in GNS and andHGNS HGNS systems systems are shown are shown in Figuresin Figures 8 and8 9,and respectively.9, respectively. There There is a striking is a striking contrast contrast between between the two the twodiagrams. diagrams. In Figure In Figure 8, all8 , RDFsall RDFsexhibit exhibit a single a single predominant predominant peak, peak, located located at r ~ at 4r Å.~ 4However, Å. However, in Figure in Figure 9, in9, inaddition addition to tothe the majormajor peak peak at around at around 3–4 3–4 Å, Å,there there are are many many non-negligible non-negligible secondary secondary peaks. peaks. The The major major peaks peaks of RDF of RDF in inthe the GNS GNS systems systems had had very very narrow narrow distributions distributions an andd their their intensities intensities are are about about three three times times as high as as those in the HGNS system.system. By contrast, the HGNS system has significantlysignificantly widerwider RDFs.RDFs. In Inthe the GNS GNS system, system, the thesingle single narrow narrow peak peak indicate indicatess that thatthese these ions/molecules ions/molecules tend tendto gather to gather at theat graphene the graphene edges, edges, rather rather than distribute than distribute unifor uniformlymly on graphene’s on graphene’s surface. surface. On the On other the hand, other the hand, multiplethe multiple peaks peaksand relatively and relatively broader broader distributions distributions of RDF of RDF in the in HGNS the HGNS system system suggest suggest that that the the Li Li ionsions and and the the carbonate carbonate electrolytes electrolytes are are quite quite un uniformlyiformly dispersed dispersed on on the the holey holey graphene graphene sheets. sheets. AfterAfter some some complicated complicated redox redox reactions reactions between between Li Liions ions and and carbonate carbonate electrolytes, electrolytes, the the SEI SEI film film formsforms on on the the surface surface of of the anodeanode [39[39].]. In In our our simulations, simulations, the the diff differenterent distribution distribution patterns patterns of lithium of lithiumions andions carbonate and carbonate electrolytes electrol onytes the on HGNS the HGNS and GNSand GNS suggest suggest that that a more a more uniform uniform SEI filmSEI film might mightform form on the on surfacethe surface of HGNS. of HGNS. A dense A dense and uniform and uniform SEI can SEI inhibit can inhibit the tunneling the tunneling of electrons of electrons and thus andavoid thus furtheravoid further reduction reduction of the electrolyte,of the electrolyte, which iswhich important is important for the stabilityfor the stability of LIBs of [40 LIBs]. [40]. SEI is a multiple-component passivation layer on the anode. For Li-ion batteries, SEI is formed at the anode because the electrolytes decompose there at the operating potential during charging and

Crystals 2020, 10, x FOR PEER REVIEW 12 of 16 Crystals 2020, 10, x FOR PEER REVIEW 12 of 16 formform aa solidsolid layerlayer onon thethe surfacesurface ofof thethe activeactive materimaterial.al. SEISEI conductsconducts LiLi ionsions butbut notnot electrons,electrons, andand isis almostalmost impenetrableimpenetrable toto electrolyteelectrolyte molecules.molecules. SoSo onceonce anan initialinitial SEISEI layerlayer hashas formed,formed, itsits furtherfurther growthgrowth isis suppressedsuppressed duedue toto thethe impenetrabilityimpenetrability ofof electrolyteelectrolyte moleculesmolecules [41,42].[41,42]. TheThe lithium-ionlithium-ion transportabilitytransportability inin LIBLIB waswas dependentdependent uponupon thethe spspontaneousontaneous chemicalchemical andand elelectrochemicalectrochemical reactionsreactions ofof thethe SEI.SEI. However,However, MDMD simulationssimulations showedshowed thatthat thethe unimpairedunimpaired structurestructure ofof GNSGNS leadsleads toto thethe non-non- idealideal formationformation ofof SEISEI films,films, becausebecause LiLi ionsions andand ororganicganic electrolyteselectrolytes tendtend toto gathergather atat thethe edgeedge ofof Crystalsgraphenegraphene2020 ,ratherrather10, 1063 thanthan dispersedisperse ununiformlyiformly onon thethe surface.surface. AA lessless ununiformiform SEISEI filmfilm isis unfavorableunfavorable12 of forfor 16 + LiLi+ conduction.conduction.

Figure 8. Radial distribution functions (RDFs) of Li ions and carbonate electrolytes in the GNS system. FigureFigure 8.8. Radial distribution functionsfunctions (RDFs)(RDFs) ofof LiLi ionsions andand carbonate electrolyteselectrolytes inin thethe GNSGNS system.system.

Figure 9. RDFs of Li ions and carbonate electrolytes in the HGNS system. Figure 9. RDFs of Li ions and carbonate electrolytes in the HGNS system. SEI is a multiple-component passivation layer on the anode. For Li-ion batteries, SEI is formed at the anode because the electrolytes decompose there at the operating potential during charging and form a solid layer on the surface of the active material. SEI conducts Li ions but not electrons, and is almost impenetrable to electrolyte molecules. So once an initial SEI layer has formed, its further growth is suppressed due to the impenetrability of electrolyte molecules [41,42]. The lithium-ion transportability in LIB was dependent upon the spontaneous chemical and electrochemical reactions of the SEI. However, MD simulations showed that the unimpaired structure of GNS leads to the Crystals 2020, 10, x FOR PEER REVIEW 13 of 16

The MD simulations suggested that Li+ moved along with solvent molecules. This indicates that complexes were formed between lithium and solvent molecules. Therefore, we employed quantum chemistry (QC) calculations to evaluate the stability of forming complexes of Li+ and different solvent Crystals 10 molecules.2020, In, 1063QC calculations, density functional theory (DFT) was employed [43]. We adopted13 of 16 Becke’s three-parameter hybrid functional combined with the Lee–Yang–Parr correlation functional methodnon-ideal (B3LYP) formation [44]. of SEI films, because Li ions and organic electrolytes tend to gather at the edge of grapheneFigure rather 10 displays than disperse the optimized uniformly geometries on the surface. and the A corresponding less uniform SEI electron film is binding unfavorable energy for obtainedLi+ conduction. from QC calculations for the Li+(electrolyte) complexes—Li+(EC), Li+(DMC), Li+(EMC), and Li+(DEC).The MDThe simulationsbinding energy suggested is in the that order Li+ movedEC < EMC along < DEC with < solvent DMC molecules.and the values This are indicates 1.32, 1.34, that 2.23,complexes and 3.26 were eV, formed respectively. between Electron lithium transfer and solvent to the molecules. Li+(EC) complex, Therefore, which we employed has the minimum quantum bindingchemistry energy, (QC) calculationsyields the most to evaluate stable complexes. the stability Ou ofr simulation forming complexes result agrees of Li with+ and the di ffexperimentalerent solvent findingsmolecules. reported In QC earlier calculations, [45–47]. density functional theory (DFT) was employed [43]. We adopted Becke’sThe three-parametermolecular structure hybrid of EC functional is a five-membe combinedred with ring, the but Lee–Yang–Parr those of DMC, correlation EMC and functional DEC are linear.method It (B3LYP)has been [ 44pointed]. out that linear carbonates have the advantages of low melting points and low viscosity,Figure 10 while displays EC theprovides optimized a much geometries higher and the constant. corresponding They can electron form bindinghomogeneous energy mixtures,obtained fromwhich QC can calculations possess the for benefits the Li +of(electrolyte) high dielectric complexes—Li constant, low+(EC), viscosity Li+(DMC), (i.e., higher Li+(EMC), ion conductivity),and Li+(DEC). and The bindingthe melting-temperature energy is in the order suppre ECssion< EMC of

Figure 10. Optimized geometries of the neutral and reduced Li+-solvent complexes from B3LYP QC Figure 10. Optimized geometries of the neutral and reduced Li+-solvent complexes from B3LYP QC calculations. The binding energy of Li+ with (a) ethylene carbonate (EC), (b) dimethyl carbonate calculations. The binding energy of Li+ with (a) ethylene carbonate (EC), (b) dimethyl carbonate (DMC), (c) ethyl methyl carbonate (EMC), and (d) Diethyl carbonate (DEC) are given vs. Li/Li+. (DMC), (c) ethyl methyl carbonate (EMC), and (d) Diethyl carbonate (DEC) are given vs. Li/Li+. The molecular structure of EC is a five-membered ring, but those of DMC, EMC and DEC are 5.linear. Conclusions It has been pointed out that linear carbonates have the advantages of low melting points and low viscosity,The holey while structure EC provides on 2-D a much graphene higher nanosheets dielectric constant. results in They shorter can Li-ion form homogeneous transport paths mixtures, in the charge/dischargewhich can possess processes, the benefits which of high significantly dielectric constant,improves low the viscosityrate capabilities (i.e., higher of LIBs. ion conductivity), These holes alsoand enhance the melting-temperature the specific capacity suppression of LIBs because of EC [ 48the]. hole In the edges aspect can of provide reduction additional potential, active the trendsites forrevealed Li-ion bystorage. our QC The calculation HGNS anode is consistent boasts a with high the capacity conclusions of 745 of mAh/g Wang etat al.0.1[ 27A/g], that(after is, 80 the cycles) cyclic andcarbonate, 141 mAh/g EC, hasat a ahigh higher current electron density affi ofnity 10 thanA/g, linearwhereas carbonates the GNS (DMC,counterpart DEC, offers EMC). only Owing 425 and to this 61 mAh/gfavorable by contrast. electron transfer property of EC, in the formulae for LIB electrolyte, generally, EC is the key constituent.To reveal the mechanism for the enhancement of specific capacity and high-rate performance in the HGNS-based anodes, MD simulations were carried out to examine the lithium-ion transport in HGNS/electrolyte5. Conclusions and GNS/electrolyte systems. The simulation confirmed that HGNS offers higher diffusionThe holeycoefficients structure for onLi ions 2-D grapheneand electrolyte nanosheets molecules results than in shorterGNS, which Li-ion is transport consistent paths with in the the charge/discharge processes, which significantly improves the rate capabilities of LIBs. These holes also enhance the specific capacity of LIBs because the hole edges can provide additional active sites for Li-ion storage. The HGNS anode boasts a high capacity of 745 mAh/g at 0.1 A/g (after 80 cycles) Crystals 2020, 10, 1063 14 of 16 and 141 mAh/g at a high current density of 10 A/g, whereas the GNS counterpart offers only 425 and 61 mAh/g by contrast. To reveal the mechanism for the enhancement of specific capacity and high-rate performance in the HGNS-based anodes, MD simulations were carried out to examine the lithium-ion transport in HGNS/electrolyte and GNS/electrolyte systems. The simulation confirmed that HGNS offers higher diffusion coefficients for Li ions and electrolyte molecules than GNS, which is consistent with the experimental results. Additionally, Li ions and the carbonate electrolytes are more uniformly dispersed on HGNS than on GNS. This might lead to a great difference in the formation and the uniformity of SEI films in the two systems. Additionally, QC calculations showed that Li+-EC has the lowest binding energy, which would promote the formation of a favorable SEI layer. We have demonstrated that appropriate MD simulations can be used in combination with experiments to investigate the advantages of HGNS anodes in LIBs and to provide further insight into the ion transport and electrochemical properties.

Author Contributions: Formal analysis: Y.-R.H.; Investigation: C.-L.C., C.-H.W., N.-W.P.; Methodology: Y.-M.L.; Data curation: Y.-H.C., M.-J.Y.; Project administration: M.-D.G., N.-W.P., Y.-R.H.; Resources: M.-D.G., C.-L.C., N.-W.P., M.-J.Y.; Validation: Y.-M.L., M.-J.Y.; Writing—original draft: Y.-R.H.; N.-W.P.; Supervision: C.-L.C., M.-D.G., N.-W.P. Writing—review & editing: N.-W.P., Y.-R.H.; Conceptualization: C.-L.C.; Funding acquisition: M.-D.G., Y.-R.H, N.-W.P. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Ministry of Science and Technology (MOST), Taiwan, grant numbers 107-2113-M-012-001-MY2 and 109-2221-E-155-014. Conflicts of Interest: The authors declare no coflict of interest.

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