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        Analysis of the interaction energies between and within graphite particles during mechanical exfoliation

        2018-11-01 05:21:50YINLiDENGChuanDENGFeiGEXiaoling
        新型炭材料 2018年5期

        YIN Li, DENG Chuan, DENG Fei, GE Xiao-ling

        (1. School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai 200237, China;2. Department of Material Science and Engineering, Chongqing Jiaotong University, Chongqing 400047, China)

        Abstract: A method for calculating the interaction energies between and within graphite particles is established by analyzing their thickness and lateral size distribution from AFM and SEM images of 300 particles during mechanical exfoliation at different times. The energy for exfoliating graphite sheets by breaking van der Waals (vdW) bonds, the energy for fracturing graphite sheets by breaking covalent bonds, the potential energies for restacking graphite sheets and the lateral aggregation of graphite particles are analyzed. Results show that the vdW interaction between graphite sheets is the key factor that leads to their restacking. Restacking and lateral aggregation become more active than exfoliation as exfoliation progresses. The energy for exfoliating graphite sheets by breaking vdW bonds is 4 times less than that the potential energy for restacking graphite sheets, and 2 orders of magnitude less than that the energy for fracturing graphite sheets by breaking covalent bonds. The increased number of exfoliated and fractured graphite sheets leads to a considerable increase in the restacking and lateral aggregation by vdW interaction. The coulombic energy is weak and can be ignored. The model has implications for the fabrication of aggregation-free graphite sheets with high aspect ratios.

        Key words: Mechanical exfoliation; Interaction energy; van der Waals; Potential energy of aggregation

        1 Introduction

        Graphene has potential applications in many technological devices, such as supercapacitors[1], nano-electronics[2], transparent conductive films[3]and nano-electromechanical systems[4,5]. Graphene has outstanding physical, mechanical and chemical properties[5,6]. Hence, many researchers have studied its applications and preparation. To obtain the one atom thick carbon material discovered by Novoselov and Geim[7], both bottom-up and top-down methods were established and have continued to be developed[8-10]. Compared with the bottom-up methods such as epitaxial growth and chemical vapor deposition[11-14], the top-down methods such as mechanical exfoliation and liquid exfoliation, produce graphene at large scale[15-20]. Exfoliating graphite in stirred media milling is a popular and important method for producing graphene because of its high exfoliation efficiency[19-23]. However, the yields of graphene have been low in many studies. For examples, the yields achieved by Knieke et al were 5%-10%[19], and 4.3% by Damm et al[20]. Therefore, it is of great importance to investigate the mechanical performance of graphite particles in the exfoliation process to understand the basic structural transformations and energy transfers involved in mechanical exfoliation and fabrication of free-standing graphene sheets.

        In stirred media milling, the graphite particles are broken by stress input, which consists of shear, compression and torsion energy[21,24,25]. The lateral and frontal dimensions, the thickness and size of the graphite particles, decrease because of stress developed during milling. However, there has been a common problem for many materials besides graphite during stirred media milling. That is milling consumes more and more stress energy when the dimensions of the material become smaller and smaller by milling[21,25-27]. This is a general phenomenon for grinding[28], comminuting[29,30]and milling[22,27]of a material. Due to the unclear nature of the material, the efficiency of the process and the quality of the exfoliated graphite are limited.

        There are some methods used to analyze energy consumed in the fracture processes of particles. However, few can be used for graphite. Tavares and King studied the fracture process of a single particle using a method based on continuum damage mechanics to describe breakage by repeated low-energy stressing[26,31,32]. Their studies helped to describe a single particle’s fracture law. However, it is hard to use their works to directly explain the fracture process and energy consumption mechanism of the graphite particles that have a unique 3D structure and discrete size distribution in exfoliation. Furthermore, the modeling methods based on the functions of energy-size reduction such as population balance model[23,28]and energy-size reduction model[27,28], are popular for studying energy consumption in the fracture processes. However, their results can not be correlated to the fracture mechanism of the material itself, but to the empirical equations that are determined by fitting parameters.

        To elucidate the structural transformation mechanisms of graphite in mechanical exfoliation, there are two aspects that need to be studied, which are energy consumption during the structural transformations and the calculation of the energy terms. In this paper, the energy interactions of the graphite structure are investigated and a model based on the thickness distribution and lateral size distribution of graphite are developed to calculate the energy consumed in structure transformations.

        2 Analysis of structural transformations of graphite particles

        During the exfoliation process in the stirred media milling, there are two structural transformations of graphite particles[19,20,33]. The one is the exfoliation of graphite sheets and the other is the fracture of bulk. The milling process of graphite in the stirred media milling includes the exfoliation of graphite sheets, the fracture of graphite bulks and the aggregation which hindering the decrease of the size of graphite particles.

        The structural transformations of graphite particles are related to the breaking interaction force within particles. Between two parallel graphene sheets, there ia van der Waals (vdW) interaction[19,34]that hinders the exfoliation of the sheets. For one-layer graphene, the carbon atom within each layer covalently bonds with three neighbor atoms in the sp2hybrid orbital. In the rest of the p orbital, electrons are delocalized to form a π bond[35,36]. These bonds between carbon atoms hinder the fracturing of the graphite sheets[33,37]. In addition, the graphite in water behaves as charged particles. The potential energy of the particles acting as bonding energy leads to the restacking of exfoliated graphite sheets and the aggregation of fractured graphite bulks[38,39]. The structural transformations of graphite particles in the exfoliation are presented in the Fig. 1. And the energy interactions within the graphite structure are given in supporting information.

        Fig. 1 The structural transformations of graphite particles during exfoliation. Breaking the vdW interactions leads to the exfoliation of graphite sheets; breaking the covalent bonds leads to the fracturing of the graphite bulk; the exfoliated sheets and fractured bulks are restacked and aggregated by potential energy, respectively.

        3 Energy interactions within the graphite structure and their correlation to the lateral size and thickness distributions of graphite particles during stirred media milling

        To analyze the mechanism of structural transformations of graphite, the vdW energy of exfoliating graphite sheetsEV, the covalent energy of fracturing bulksEc, the potential energy of restacking graphite sheetsEL, and the potential energy of aggregating graphite bulkEBshould be studied in depth. In this section, a model is proposed based on the size and thickness distributions of graphite particles to calculateEV,ELandEB, and stress energy input (the energy stressed on graphite particles only)ENis measured to determineEc.

        The two structural transformations, the exfoliation of graphite sheets and the fracturing of graphite bulk, can be characterized by the thickness and lateral size distributions, respectively. The thickness distribution characterizes the competing result of exfoliating and restacking of sheets. Accordingly, the lateral size distribution characterizes the compromising result of fracturing and aggregating the bulk. The exfoliation and restacking have an opposite effect on the thickness of graphite sheets, and the fracture and aggregation of graphite bulks have an opposite effect on the lateral size of graphite sheet. These four processes lead to changes of structural change of graphite particles during the stirred media milling. The relationship between the structural change and the total energy consumed in the stirred media milling is obtained as follows, the derivation process is given in Supporting information:

        (1)

        Eq. (1) reveals the relationship between the structural change of graphite particles and the energy consumed in a structural transformation. The tenability of the hypothesis is discussed in Supporting Information.

        3.1 Van der Waals energy in exfoliating graphite sheets EV

        The van der Waals interaction energy in exfoliating graphite sheetsEVis obtained based on Eq. (1):

        (2)

        (3)

        wheredis the interlayer separation of graphite (0.335 nm),hiis the thickness of leveli,Dis the thickness of a graphene sheet (0.35 nm).

        3.2 The potential energy of restacking graphite sheets EL

        The process of restacking graphite sheets is opposite to exfoliating graphite sheets. According to Eq. (1), the potential energy of restacking graphite sheetsELis given by

        (4)

        where the surface area for a thickness ofxiisSLiwith a mass fraction ofVLi.SLiis equal toSVibecause exfoliation is opposite to restacking.eLiis the aggregation potential energy of changing thickness fromxi+1toxi. According to the hypothesis for restacking graphite sheets, the energy required for changing the thickness of graphite fromxitoxjis equal to the energy required for changing fromxitoxk, then toxj(where i>k>j).eLican be obtained as

        eLi=δLi·(4Aεrε0kξ2e-kD-Aπρ2C/2D4)

        (5)

        where δLiis the layer difference between the thicknessxi+1andxi.

        3.3 The potential energy of aggregating bulks EB

        The process of aggregating graphite bulk is similar to that of restacking graphite sheets. The potential energy for aggregating bulkEBis obtained as

        (6)

        whereδBiis the layer difference betweenxiandxi+1. The size of the two aggregated bulks is the disc-equivalent diameter, which is obtained by combining the two sizes of the two bulks.eBiis the energy of aggregating graphite bulks to increase sizeRi+1toRi. According to the hypothesis for aggregating bulks, the

        energy of aggregating graphite bulks to increase lateral size fromRktoRk+nis equal to the total energy for aggregating graphite bulks to increase lateral size fromRktoRk+m, then toRk+n, where m

        eBi=rBieBm

        (7)

        whererBiis ratio of the surface area difference (Ri+1-Ri).eBmis the mean value of energy consumed in aggregating graphite bulk having arbitrary lateral size (in size distribution), which is given as

        (8)

        In the following sections, the structural transformations of graphite during mechanical exfoliation is described by the thickness and size distributions, and the energy discussed above is calculated to gain insight into the energy interactions and the mechanisms of the structural transformations of graphite involved in mechanical exfoliation and fabrication of free-standing graphene.

        4 Experimental

        4.1 Materials

        Natural flake graphite (Qingdao Chenyang Graphite Co. Ltd., Qingdao, China) with a mean particle size of 4 μm and a purity >99.5% was used in the milling experiments.

        4.2 Mechanical exfoliation in milling

        The milling experiment was carried out in a lab-scale stirred media mill (model SFJ-400, Shanghai XianDai Environmental Engineering Technique Co. Ltd., Shanghai, China). In this mill, the volume of the ceramic chamber is 600 mL. The stirrer is three wear resistant helical blades whose length is 60 cm. The experimental set-up is operated in batch mode. Yttria-stabilized zirconia milling beads (Tosoh Corporation, Tokyo, Japan) with an average diameter of 100 μm are used as the milling media. These beads have a density of 6 050 kg/m3and a chemical composition of 95% ZrO2and 5% Y2O3, according to the manufacturer. For a typical exfoliation experiment using the stirred media mill, the chamber of the mill (volume 600 mL) is loaded with 180 mL of de-ionized water, 0.2 g of graphite and 500 g of ZrO2beads[19,20]. The graphite in device is continuously milled for 15 h, and the thickness and size distribution are tested every 3 h. Changes in the thickness and lateral size distribution in the five 3h-time points are recorded and used in Eq. (2), (4) and (6).

        4.3 Preparation and characterization

        The thickness and the lateral size of graphite particles are characterized by Atomic Force Microscopy (AFM), Laser Particle Analysis (LPA) and Scanning Electron Microscopy (SEM). The freshly milled samples are homogenously deposited onto a silicon wafer by spin-coating, with a 300 nm thick SiO2layer on top. To determine the exact thickness of the graphite sheets the AFM NanoScope III (Digital Instruments/Veeco, Santa Barbara, CA, USA) is used in tapping mode using silicon tips with a resonance frequency of 320 kHz. The SEM images are obtained using an SEM EVOMA15 (Carl Zeiss NTS GmbH, Oberkochen, Germany). The LPA Mastersizer 3000 (Malvern Instruments Ltd, Worcestershire, UK) is used to analyze the particle size distributions. Five groups of samples are taken from the chamber after being milled for 3, 6, 9, 12 and 15 h. Each group contains 5 samples that are taken from the well-distributed mixture at different depths and horizontal positions in the chamber. The final size distribution of each group represents the mean distribution of 5 samples. Zeta potential measurements are carried out on a Malvern Zetasizer Nano system with irradiation from a 633 nm He-Ne laser. The samples are injected into folded capillary cells, and the measurements are conducted at 20 ℃ and at the neutral pH of the solution. Theξ-potential result holds strictly if the uniform surface charges of plate are large enough for edge charge to be neglected and its radius is much larger than the double layer thickness[40]. Because the double layer thickness k-1is 0.0125 nm in our samples, these criteria is observed here.

        By measuring the no-load (no graphite) torque and the loaded (graphite) torque during the milling process, the stressing energy input (the energy stressed on graphite)ENis determined[41-44]as

        (9)

        whereNis the energy input per second (J/s),tis the milling time (here, 3 h is the time of one milling phase),Tis the torque measured during the milling (Nm),T0is the no-load torque (Nm), and n is the number of revolutions of the loaded stirrer (the number of revolutions of the no-load stirrer is 1 000 r/min). n is measured by using a flash frequency velocimeter “DT2239B” (ShenZhen WeiFeng Instrumen Co. Ltd., Shenzhen, China). The relationship betweenTand n is as follows:T=9549.297×P/n, wherePis the power (kW) of the device. It is necessary to state that our experiment result is a kind of special situation because the similar stressing energy will lead to different or not quite equivalent particle size and thickness distributions. However, the tendencies of changing particle size and thickness distributions will be the same. Hence the analysis of the mechanism of graphite structural transformation will not be affected.

        5 Results and discussion

        5.1 Structural transformations of graphite during exfoliation

        First, the structural transformations of graphite in exfoliation from the results of experiment are analyzed. The sheet images presented in Fig. 2a, b show that the exfoliated graphite sheets are resulted from breaking vdW interactions between the graphite layers. Fig. 2b and c are partial enlarged images from Fig. 2a. The superimposed structure in them shows the restacked graphite sheets. The vertical view image presented in Fig. 2(c) shows the cross-section of graphite layers. In Fig. 2e and f, the adjacent structure of the graphite shows the aggregated graphite particles. The AFM image (presented in Fig. 3) shows the exfoliation and restacking of graphite sheets, and the fracture and aggregation of graphite bulk at the nano-scale. The structural transformations of graphite during the mechanical exfoliation match well with the assumed processes presented in Fig. 1.

        The size distributions of samples milled for 0, 3, 6, 9, 12, and 15 h measured by LPA are presented in Fig. 4. Their development shows the dimension of the graphite structure do not monotonically become thinner or smaller. They remain constant or go in the opposite direction as milling progresses. It gets harder to decrease lateral size of graphite by inputting constant energy as the resistant energy gets stronger with the progress of milling. The energy consumed in decreasing the graphite size is balanced with the resistant energy. And the aggregation of graphite become intense with the growth of the resistant energy.

        Fig. 3 AFM images of the milled sample. The top image shows a typical 20 μm × 20 μm square showing large numbers of graphene flakes. In the middle are three zoomed-in images of individual flakes. Below each image is a line scan taken vertically through the center of the image.

        Fig. 4 The size distributions of milled graphite. Insert: partial enlarged image of the region enclosed by the black square. The graphite is milled in surfactant-free, de-ionized water. The stirrer tip speed is set to 1 000 r/min, and 100 μm ZrO2 beads are used as the media. The size distribution of sample is measured every three hours.

        By analyzing the AFM and the SEM results, the thickness distribution of the graphite is obtained. The large graphite is thicker than the small graphite. The height and lateral size of graphite flakes are analyzed by a “Nanoscope” software from AFM. The height and lateral size of graphite flakes are determined by the scale bar in the vision of single graphite flake by SEM. The flakes with lateral size below 20 μm are analyzed by AFM (because the probe of Si in AFM will be broken easily if the lateral size is bigger than 20 μm) and those above 20 μm are analyzed by SEM. By statistical analysis of the height and lateral size of 300 graphite flakes via AFM and SEM, an accurate relationship between the layers and the lateral size of graphite is determined as shown in Fig. 5. There is an approximate relationship between the thickness and the lateral size of graphite, the thickness of the graphite corresponds one-to-one with lateral size. The thickness distributions (Fig. 6) are obtained by combining Fig. 4 and Fig. 5. The relationship presented in Fig. 5 simplifies the experiment that involved in measuring the thickness distribution of the whole graphite, and the calculation ofEVin Eq. (2),ELin Eq. (4) andEBin Eq. (6), by giving the layer of graphite an arbitrary size.

        Fig. 5 The rough relationship between the layers and the lateral size of graphite obtained by measuring the height and lateral size of 300 graphite flakes by AFM and SEM.

        Fig. 6 The thickness distributions obtained by combining Fig. 4 and Fig. 5. Insert: partial enlarged image of the region enclosed by the black square.

        5.2 Calculation of the energy consumption of structural transformations

        The parametersSVi、SLi(i is the hours of milling) and ξ in Eq. (2), Eq. (4) and Eq. (6) are determined here. Based on the LAP measurements, the specific surface areasSiof graphite milled for 0, 3, 6, 9, 12 and 15 h in 150 g de-ionized water are 3.78, 3.54, 3.15, 2.83, 2.59 and 1.709 8 m2/g, respectively. Here,RViis determined by the thickness distribution and presented in Fig. 10.SViandSLican be determined bySVi=SLi=Si·RVi. In the section 3.2, the aggregation energy expressions only strictly hold for |ξ| < 25 mV. Based on the measurements of the Zeta potentials ξ of the graphite-water mixture milled for 0, 3, 6, 9, 12 and 15 h are -28.0, -25.8, -20.4, -18.8, -15.4 and -12.8 mV, respectively. In addition, the hypothesis proposed for Eq. (2) has different meanings whenEV,EL, andEBare calculated. Its tenability is discussed in Appendix B. TheEC,EV,ELandEBconsumed in the mechanical exfoliation during 0-3 , 3-6 , 6-9 , 9-12 and 12-15 h, are calculated by using Eq. (1), Eq. (2), Eq. (4) and Eq. (6), and the results compared withENare presented in Fig. 7.

        Fig. 7 With equal stressing energy input EN, the vdW interaction energy of exfoliating graphite sheets EV, the covalent bonding energy of fracturing graphite bulk Ec, the potential energy of restacking graphite sheets EL and the potential energy of aggregating graphite bulk EB are calculated in exfoliation during 0-3, 3-6, 6-9, 9-12 and 12-15 h.

        5.3 Analysis of energy interaction of graphite structures

        Fig. 7 shows that more energy is consumed in the exfoliating graphite sheets, restacking graphite sheets, and aggregating graphite bulk; less energy is consumed in the fracturing of the graphite bulk. The vdW interaction energy of the exfoliating graphite sheets is 2 orders of magnitude less than the energy consumed in fracturing graphite bulk. The aggregation and restacking behaviors of graphite gets more active than the fracture and exfoliation behaviors with the progress of milling. This result agrees well with the growth of lateral sizes (Fig. 4) and thickness (Fig. 6).

        The energy consumed in the restacking graphite sheets and the energy consumed in the exfoliation of the graphite sheets have opposite effects on the thickness of graphite in milling. In Fig. 8,ELis 4 times greater thanEV, which means that the energy consumed in the restacking graphite sheets is 4 times greater than in the exfoliating graphite sheets. The growth ofEVandELcan be explained by the increased relative cumulative mass fractionRi(0)-Ri(t) of thicknessxiin Eq. (4). The restacking energy of the graphite sheetsELconsists of the vdW interaction energy termELVand the coulomb energy termELC.ELVis the main part ofEL, whereasELCis negligible. The vdW interaction between the two graphite sheets is the key factor that leads to restacking of the graphite sheets.

        Fig. 8 Comparison of the vdW interaction energy of exfoliating graphite sheets EV, the potential energy of restacking graphite sheets EL, and the vdW energy term ELV of ELand the coulomb energy term ELC of EL.

        The energy consumed in the restacking graphite sheets and the energy consumed in the exfoliation of the graphite sheets have opposite effects on the lateral size of graphite in milling. The growth ofEBis resulted from the increased relative cumulative mass fractionRi(0)-Ri(t) of lateral sizeRi. The decreasedECis resulted from the increasing potential energy of aggregating graphite bulk derived from constantEN. The aggregation energy of the graphite bulksEBconsists of the vdW interaction energy termEBVand the coulomb energy termEBC, according to Supporting Information. Fig. 8 shows thatEBVis the main part ofEB, whereasEBCis negligible. The van der Waals interactions between the two graphite bulks are the key factor that leads to aggregation of the graphite bulks.

        Fig. 9 Comparison of the covalent bonding energy of fracturing graphite bulk EC, the potential energy of aggregating graphite bulk EB, and the vdW energy term EBVand the coulomb energy term EBC of EB.

        Fig. 10 The relative cumulative mass fraction of graphite size in the periods 0-3, 3-6, 6-9, 9-12 and 12-15 h. Inset: the relative surface area ratio and the relative bulk area ratio in each time period of milling.

        5.4 The mechanism of energy interaction of graphite in mechanical exfoliation

        The van der Waals interactions are the key factor that hinders the exfoliation of graphite sheets and causes the restacking graphite sheets and the aggregation of graphite bulk. In Fig. 11. The total coulomb energy is negligible compared with the vdW energy, which increases from 6% at 0-3 h to 78% at 12-15 h, and the covalent bonding energy derived fromENdecreases from 94% at 0-3 h to 22% at 12-15 h. Most parts ofENare converted to vdW energy as mechanical exfoliation proceeds. The mechanism of energy interaction of graphite is as follows. As graphite exfoliation proceeds, the increasing amount of exfoliated graphite leads to an increased surface area and an enhanced vdW interaction energy. The graphite bulk fractures more as the covalent bonds are broken, releasing the vdW interaction energy that casues the increased aggregation behaviors of the graphite bulks. This means that the process of exfoliating graphite sheets is the process of releasing more vdW energy between the graphite sheets, and the process of fracturing the graphite bulk is the process of converting covalent bonding energy to vdW energy between the graphite bulks.

        Fig. 11 The proportion of stressing energy input EN devoted to vdW energy (the sum of EL, ELV and EBV), coulomb energy (the sum of ELC and EBC) and covalent bonding energy (EC).

        5.5 Suggestions for fabricating graphene sheets by mechanical exfoliation

        As the potential energy of restacking and aggregation continuously grows in exfoliation, the restacking graphite sheets and aggregation of graphite bulk should be avoided in fabricating free-standing graphene. The stabilization by surfactant-coating of graphite to prevent restacking and aggregation will be achieved only if there is a dynamic equilibrium between the potential energy of the restacking and aggregation and the resisting energy which is generated from organic solvents. According to our findings, the potential energy of restacking graphite sheets is 4 times greater than the vdW energy of exfoliating graphite sheets, so the corresponding resisting energy controlled by surfactant or organic solvent should be 4 times greater than the vdW energy of the exfoliating graphite sheets in the whole mechanical exfoliation.

        Based on our findings, the covalent bonding energy of fracturing the graphite bulk is two orders of magnitude greater than the vdW energy of the exfoliating graphite sheets, a critical stressing energy input given by stress field is needed to obtain graphite sheets with high aspect ratios. The energy components that go toward the exfoliation of graphite sheets and the fracturing of the graphite bulk are closely related to the tangential energy and the compressive energy in the stress field, respectively. The challenge is to determine how much the stressing energy input is needed toward the fracturing of the graphite bulk and the exfoliation of graphite sheets.The tangential energy should be greater than the energy of exfoliating graphite sheets, and the compressive energy should be two orders of magnitude less than the tangential energy to prevent the fracturing of the graphite bulk. The stress field, which provides critical stressing energy input, is obtained by controlling the process parameters such as media size, velocity and structure of the stirrer, which will be studied in the future.

        6 Conclusions

        This paper describes the structural transformations and energy interactions of graphite during mechanical exfoliation. A model is proposed based on the energy of interactions between graphite structures to calculate the vdW energy of the exfoliating graphite sheets, the covalent bonding energy of the fracturing graphite bulk, the potential energy of the restacking graphite sheets, and the potential energy of the aggregating graphite bulk. The mechanism of energy interaction of graphite structures shows that, as the amount of exfoliated graphite sheets increases and the fractured graphite bulk increases, more lateral and frontal areas of the graphite are released, leading to a large increase in the potential energy of the restacking sheets and aggregating bulk of graphite. This also hinders the exfoliation of the graphite sheets and the fracturing of the graphite bulk. The vdW energy of the exfoliating graphite sheets is 4 times less than that the potential energy of the restacking graphite sheets, which is 2 orders of magnitude less than the covalent bonding energy of the fracturing graphite bulk. The results of the model agree well with the increasing thickness and lateral size of the graphite in their distributions. The total coulomb energy of interaction between graphite structures in the mechanical exfoliation is negligible, the vdW energy is the main energy component that hinders the exfoliation of the graphite sheets and leads to an increased potential energy of the restacking graphite sheets and aggregation of graphite bulk. To avoid the restacking graphite sheets and aggregation of graphite bulk, the corresponding growth resistant energy generated by an organic solvent is needed to achieve a dynamic equilibrium between them and to achieve stable, aggregation-free, surfactant-coated graphene. Furthermore, the covalent bonding energy of the fracturing graphite bulk is two orders of magnitude greater than the vdW energy of the exfoliating graphite sheets, so it is important to control the critical stressing energy input provided by the stress field. In the stress field, the tangential energy is greater than the energy of exfoliating graphite sheets, and the compressive energy is two orders of magnitude less than the tangential energy.

        Acknowledgments

        The authors are grateful for financial support from Shanghai Huali Superfines Co., Ltd. The authors thank Mrs. Wang Jin from the School of Chemical Engineering of East China University of Science and Technology (ECUST) for LAP measurements, Mr. Zhou Kai from the School of Chemistry and Molecular Engineering of ECUST for SEM support, as well as Mr. Wang Hui from the Center of Analysis and Testing of ECUST for AFM support.

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