Molecular dynamics study on dynamic interlayer friction of graphene and its strain effect

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A friction pair model with an annular graphene as slider is built to eliminate the influence of commensurability and edge effect. The effects of temperature, normal load, sliding velocity, support stiffness and axial strain on the friction between graphene layers are investigated. The coupling effect of temperature and other influencing factors are clarified. The results show that normal load increases the friction force by decreasing layer spacing. The friction is firstly enhanced as the sliding velocity increase and then is reduced by severe interlayer residual deformation and lattice resonance frequency at high sliding velocity. The support stiffness regulates the interlayer friction by affecting the atomic vibration amplitude of the graphene lattice. By mechanism analysis, it is found that by changing the number of atoms in friction region between layers and the frequency of lattice vibration, the strain can effectively regulate the dynamic friction between graphene layers. Our findings reveal the influence mechanism of affecting factor on dynamic friction of graphene and provide a fundamental understanding for the strains engineering of nanoscale friction. dynamic interlayer friction strain effects lattice vibration commensurability graphene Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 1. Introduction Graphene has become a research hot spot in the field of nanomechanics due to its excellent mechanical, thermal and electrical properties 1 – 4 . It has become an important nanocomponent due to its excellent physical properties with ultra-low interlayer friction 5 , 6 . With the rapid development of big data and cloud storage, Zheng et al. proposed the graphene can replace the diamond-like carbon (DLC) film as an important component for ultra-lubricated mechanical hard disk, which is expected to increase the disk storage capacity by 10 to 15 times 7 . However, the effect of high sliding speed on dynamic friction of graphene has not been clarified. Current studies indicate that the interlayer friction decrease significantly by rotating the upper layer of graphene at a certain angle to form the incommensurate registry with the substrate layer 8 , and this phenomenon is called superlubrication. However, the superlubrication phenomenon will be suppressed in some specific cases, such as ultra-high load 9 or contact with the low support stiffness of the substrate surface 10 . The interfacial friction of graphene layers is influenced by multi-factor coupling, such as the interlayer spacing and commensurability 11 , 12 , normal load, temperature, support stiffness, and relative sliding velocity 13 – 15 . Therefore, it is great academic and engineering value to clarify the effect rule and reveal the influence mechanism of the above factors in interlayer friction. The influence rule of normal load on nanoscale friction is complicated 16 , that it varies according to the contact commensurability of graphene layers 17 – 19 . The interlayer friction is enhanced with the increase of normal load when the contact of graphene slider and the graphene substrate is commensurate. In the case of incommensurate contact, low normal load has little effect on the interlayer friction. As the normal force increased to certain value, the rate at which friction increases with the increase of load is significantly accelerated due to the obvious ploughing phenomenon between the slider boundary atoms and substrate surface under high load. It can be seen that the influence of normal load on interlayer friction is related to the edge effect and contact commensurability 20 . In the traditional slider-substrate friction model, the relative sliding velocity affects the slip state of the graphene flake and then significant effect on the interlayer friction is caused as a result 21 . In the case of incommensurate contact, the degree to which the atoms are hindered by the potential barrier varies depending on the relative velocity. Thus the interlayer friction shows a complex variation law with relative velocity 22 – 25 . Moreover, previous studies model on graphene interlayer friction also have edge effects 26 . It can be seen that the edge effect and contact commensurability have introduced complex influences to the study of interlayer friction. The influence of multiple factors is often coupled together and the influence mechanism of the interlayer friction of graphene is still not clear. The effects of these factors on interlayer friction still need to be decoupled and in-depth studied, and the complex nature and mechanism behind the phenomena need to be further explored and revealed. In addition, studies have shown that the frictional properties and phenomena of nanomaterials are significantly affected by strain 27 – 29 . And strains applying to the graphene are supposed to reach critical state to satisfy the needs of engineering applications 30 . It has been found that the in-plane strain can change the static frictional force between graphene and silica substrate 31 – 33 . Applying uniaxial tensile strain to graphene can decrease friction by reducing the number of atoms between the indenter and graphene 34 , while the compressive strain can increase the friction coefficient 35 of the graphene interlayer friction. However, studies 36 have shown that the friction force increases significantly under slight compressive strain, although the number of atoms in contact area increased by a small amount. The mechanism of interfacial frictional strain effect is very complex, and the dominant factor is not the change of the number of atoms in contact area 21 , 37 , 38 . The strain causes incommensurate contact at the graphene interface resulting in the reduction of interlayer friction 39 , that could be the more acceptable explanation for the strain effect. The existing studies analyzed the effects of uniaxial tensile/compressive strain on the surface friction of graphene using lattice mismatch theory. From the perspective of energy dissipation, the strain effect has an inevitable effect on the lattice vibration, and thus affects the interfacial dynamic friction at nanoscale 40 . In the researches on strain effect using slider-substrate friction model 41 , the influence of commensurability and lattice vibration on friction caused by strain are coupled with each other, and even the edge effect is involved 42 . So far, there are few studies on the influence of strain effect on dynamic friction of graphene interface from the perspective of kinetic dissipation. The changes of the density of phonon states and the number of contact atoms induced by strain effect are not compared. The mechanism of strain effect on dynamic friction of nanointerface is not clear. Therefore, the research work at nanoscale dynamic friction should emphasize the comprehensive study of mechanism of the strain effect, as it has great potential for tuning the interfacial friction at nanoscale and extensive prospect of application. In this paper, an annular graphene rotational slider-substrate friction pair model is proposed to eliminate the effects of contact commensurability and edge effects. The effects of temperature, normal load, sliding velocity, support stiffness and axial strain on the interfacial friction between graphene layers are investigated using molecular dynamics (MD) simulation. The effect mechanism of various factors affecting friction are analyzed by numerical and theoretical analyses. By statistical analysis of phonon states density and examination of effective contact area between strained graphene layers, the regulation of interlayer friction by axial strain is revealed. 2. Simulation Model And Methods The Fig. 1 shows the physical model of rotational slider-substrate friction pair system with an annular shaped graphene flake slider laying on the rectangular graphene substrate with an equilibrium spacing of 0.34 nm. The spring with stiffness of 2.7 N/m is used to simulate the supporting effect to graphene substrate 43 , which has been widely used in recent nanoscale friction studies 12 , 44 , 45 . The rectangular graphene substrate has dimensions of 10nm in both length and width containing 3936 carbon atoms. The all sides of graphene substrate are bordered by fixed boundaries with a width of 2Å region for 384 carbon atoms in total. The upper layers of graphene has an inner ring radius of 2 nm and an outer ring radius of 3.7 nm with 1427 atoms, and the outer and inner ring boundaries have fixed boundaries of 2 Å respectively. The steady isothermal method is used to calculate the interlayer friction by recording the thermal energy in the simulations process. During rotation process, the crystal lattice mismatch of contact interface is constantly updated and the atoms in the contact area are stressed equally, which effectively avoids the influence of commensurability effects and edge effects. Uniaxial strain is applied to the substrate graphene boundary divided into armchai and zigzag for study the effect of strain on friction. The schematic of uniaxial strain loading on armchair graphene is shown in Fig. 2 . The uniaxial strain is applied to the green area after the system has reached stability and calculated as follows: \(\varepsilon =(L - {L_0})/{L_0}\) , Where the distance after the stretch is L , and the distance before the stretch is L 0 . The dynamic friction process between graphene layers is simulated using large-scale atomic/molecular massively parallel simulator package (LAMMPS). The carbon atoms on the edges of substrate graphene are fixed. The rest of atoms on substrate graphene are attached to a spring along z -oriented to simulate the supporting effect to the substrate. The normal load of 0.10 nN/atom ( z -oriented) are imposed on the each carbon atom of the upper graphene. The AIREBO 46 potential is used to describe the interlayer C-C bond interaction of the graphene. The time step is set to 1 fs in the all simulations process. Energy minimization is performed at the beginning of the simulations to achieve equilibrium. After a long-time relaxation, the upper annular graphene rotates at high speed around its central axis in the z -direction to simulate the dynamic interlayer sliding behavior. The heat generated by interlayer friction is recorded by using a Nose-Hoover thermostat after the system is sufficiently relaxed to reach stability of high speed rotation. The interlayer friction force of each atom is calculated by using steady isothermal method 47 . The energy dissipation rate by friction is computed using the energy data extracted by the Noes-Hoover thermostat: \(\Delta E=\int_{0}^{{\text{t}}} {Q'dt}\) where \(Q^{\prime}\) is the energy dissipation rate and \(\Delta E\) is the thermal energy produced by dynamic friction. Thus the friction between the layers is calculated as follows: \({F_f}=\frac{{Q'}}{{2\pi fR}}\) where f is the rotational frequency of the upper layer, and R is the rotational radius of the upper circle. 3. Results And Discussion 3.1 Normal load effects The rotational frequency of the upper annular graphene is 150 GHz (the relative velocity of the equivalent radius is 29.6 Å/Ps). The stiffness of supporting spring stiffness of the substrate graphene layer is 2.7 N/m. To study the temperature dependence of normal load effects, the environmental temperature is set ranging from 100K to 500K. As shown in Fig. 2 , the normal load is applied to each atoms of the upper annular graphene varies from 0.05 nN/atom to 0.4 nN/atom. The calculation results of the interlayer friction under different normal load are shown in Fig. 4 . It is observed that the normal load has great impact on friction. At the same temperature, the friction increases linearly with the normal load because the distance between the upper and substrate graphene decreases. And the friction force is increased with the temperature as well. Because the atomic lattice vibration frequency and vibration amplitude is relatively low under the lower temperature, that makes it easier for the atoms of the rapidly rotating annular graphene to pass through the energy barrier on the substrate graphene surface. Thus, the energy dissipation of relative sliding is reduced. With the increase of temperature, the friction is raised with the higher lattice vibration frequency and vibration amplitude, which strengthens the interlayer atomic interaction. These results show that, after blocking commensurability and edge effects using the annular rotating friction model, the interlayer friction is increased with the normal load and temperature. It implies that interlayer friction is positively correlated with normal load and temperature. The relative coefficient parameter α is defined to investigate coupling influence of temperature and normal load on the interlayer friction as follows: \(\alpha =\frac{{{F_{0.4nN}} - {F_{0.05nN}}}}{{{F_{0.05nN}}}}\) Where \({F_{0.4nN}}\) and \({F_{0.05nN}}\) represent the friction force when the normal load is 0.4nN/atom and 0.05nN/atom, respectively. The values of α under different temperatures are shown in Table 1 . At all temperatures, the interlayer friction is almost doubled as the normal load increases from 0.05nN/atom to 0.4nN/atom. At room temperature of 300K, the interlayer friction is increased by 91.69%, which is relatively low in contrast. When the temperature are 200K and 400K in the vicinity of the room temperature of 300K, the rate of interlayer friction increases with the normal load relatively larger than that at 300K, which is 118.29% at 200K and 121.67% at 400K respectively. Otherwise, the value of parameters α is 115.17% at 100K and 108.96 at 500K. This implies that temperature affects the amplifying efficiency of normal load effects on friction. Table 1 Parameters α under different temperatures Temperature/K 100 200 300 400 500 α 115.17% 118.29% 91.69% 121.67% 108.96% 3.2 Rotational frequency effects The normal load applied to the annular graphene is 0.1nN/atom and the supporting stiffness of the substrate graphene is 2.7N/m. At the same temperature, the rotational frequency of annular graphene is 50 ~ 400 GHz (the relative velocity of the equivalent radius is 9.87 ~ 78.94Å/Ps). The calculation results are shown in Fig. 5 . At the temperature of 300 K, the interlayer friction increases with the rotational frequency when the rotational frequency of annular graphene is below 300 GHz, after which the friction decreass with the increasing of the rotational frequency. The friction reaches its maximum value of 182.68fN/atom at the rotational frequency of 300 GHz. As the temperature increases, the rotational frequency that causes the maximum value of interlayer friction also increases. The reason of this phenomenon can be revealed from two aspects: velocity coupled thermal-induced resonance of the graphene lattice and the in-plane deformation of graphene resulted from interlayer friction. The relative velocity between the graphene layers increases with rotational frequency. As the relative sliding velocity is increased close to the lattice resonance frequency of the graphene interface, that causes the graphene interlayer lattice resonance 48 . The intense lattice resonance vibration leads to the aggravation of energy dissipation, resulting in the maximum of interlayer friction. As the temperature increases, the interlayer lattice resonance frequency of graphene increases, therefore the rotational frequency required to induce lattice resonance also increases correspondingly. On the other hand, in the interlayer viscous sliding process, the elastic deformation graphene undergoes the experiences of accumulation and release 49 . When the rotational frequency is higher than a certain key value, the deformation energy accumulated by the interlayer friction is difficult to be completely released in time and produce a certain amount of deformation, which results in the change of graphene lattice constant. The interlayer lattice mismatch is formed due to the difference in in-plane lattice constant between the graphene friction pair, and the interlayer friction is reduced as well. At low temperature, the thermal-induced lattice resonance effect is not obvious, so the friction-induced deformation mechanism of graphene has a significant effect on the interlayer friction. With the increase of temperature, the energy dissipation mechanism of thermal-induced resonance dominates, leading to the increase of rotational frequency required for interlayer lattice resonance.. The interlayer friction generally increases with temperature at the same rotational frequency. However, the interlayer friction force at 400 K is greater than that at 500 K when the rotational frequency is 300 GHz. The reason is that under the coupled influence of graphene rotational frequency of 300 GHz and temperature of 400 K, interlayer lattice resonance phenomenon is produced and makes the friction force greatly amplified. As shown in Fig. 5 , at the temperature of 300 K the interlayer friction at 350 GHz is about 5 times larger than that at 50 GHz. It can be seen that the friction dissipation can be reduced by avoiding the lattice resonance, which will be one of the effective ways of nanoscale friction regulation technology. 3.3 Supporting stiffness effects In practical applications, graphene is usually placed on the substrate or exists in the form of multiple layers of graphene. And different substrate materials have different support effects on the graphene substrate, so the interaction between graphene and substrate materials becomes one of the important factors affecting the interlayer friction of graphene 12 , 41 , 44 . To study the effect of supporting stiffness on graphene interlayer friction, the supporting stiffness is set to vary from 1 to 15nN/nm at the same temperature. The calculation results are shown in Fig. 6 . It is found that with the increase of support stiffness at all temperatures, the maximum value of interlayer friction occurs and their corresponding value of supporting stiffness falls in the range of 3–5 nN/nm.. When the maximum value of is reached, the interlayer friction decreases with the increase of supporting stiffness. This is due to fact that the substrate graphene is weakly constrained in out-of-plane direction when the supporting stiffness is low, which is easy for substrate graphene to form out-of-plane deformation when it squeezed by the annular graphene. This results in a relatively wide equilibrium distance between the graphene layers and low interlayer friction. With the increase of supporting stiffness, the ability of substrate graphene to resist out-of-plane deformation is improved and the equilibrium distance between graphene layers is reduced. Thus, the interaction between the upper annular and substrate graphene is promoted, resulting in the gradual increase of interlayer friction.. Meanwhile, from the perspective of lattice dynamics, the lattice vibration frequency of graphene substrate increases with supporting stiffness 12 , 44 , that increases the peak of interlayer potential barrier. This promotes energy dissipation during friction process and increases the interlayer friction. As the supporting stiffness continued to increase, the vibration amplitude of substrate graphene lattice are limited. The upper annular graphene is more easily to pass through the potential barrier of the substrate graphene surface. The interlayer interaction between the graphene layers is reduced, leading to lower energy dissipation during the sliding process, showing that the friction begins to decrease gradually with the increase of the supporting stiffness. As can be seen in Fig. 6 (a), there is no peak value of friction as the supporting stiffness increases at the temperature of 100 K. It is attributed to the lower frequency and amplitude of graphene lattice vibration at low temperature, and the thermal excitation effect of lattice vibration is weaken. Therefore, the inhibition effect on lattice vibration increases as the supporting stiffness increases, resulting in a decreasing trend of interlayer friction. 3.4 Uniaxial strain effects The calculation results of the friction under different uniaxial strain are shown in Fig. 7 . The results show the friction of graphene decreases with the tensile strain. When the tensile strain is 10%, the interlayer friction of armchair graphene decreases by 15.96%, while that of zigzag graphene decreases by 16.27%. Different from the tensile strain effect, when the uniaxial compressive strain is less than − 3%, the interlayer friction increases with the increase of compressive strain. On the contrary, when the compressive strain is greater than − 3%, the friction between graphene layers decreases as the compressive strain is enhanced. For the strain effects on nanoscale interfacial friction, the number of atoms in effective contact area is considered to be one of the important ways in which strain affects friction. In the process of strain loading, the number of atoms in the effective contact region of graphene friction pair is affected by the uniaxial strain. The number of atoms in the effective contact area under the strain is calculated as shown in Fig. 8 . It can be found that the number of atoms in the contact region increases from 1435 to 1538 as the tensile strain increases. This is because during uniaxial tensile deformation, the atoms located in non-contact region of the substrate graphene where is below the inner circle space of the annular graphene enter the sliding contact region. At the same time, a few of atoms enter the contact region from the lateral direction due to Poisson effect under uniaxial tensile strain. Since the number of atoms originally near the boundary of the contact region are moved outside of the contact region during tensile deformation of substrate graphene is less than the number of atoms entering the contact region, so the number of effective contact atoms increases. As the compression strain increases, the atoms near the contact boundary enter the contact region, and the number of atoms in the contact region of graphene increases from 1435 to 1672.It suggests that tensile strain decreases friction by reducing the number of atoms in effective contact 50 is inappropriate for the explanation of strain effects on interlayer friction. Although the number of effective contact atoms is a factor affecting the interlayer friction, it is not the dominant factor of the strain effect on nanoscale interfacial friction. Under the tensile strain, the amplitude of potential barrier on the surface of the substrate graphene is reduced, the atoms in annular graphene are easier to overcome the potential barrier and slide through the substrate graphene’ surface. As a result, the energy dissipation of interlayer friction behavior is reduced. The phonon spectra of graphene under uniaxial strain effect is calculated, as shown in Fig. 9 . As can be seen from Fig. 9 (a), with the increase of tensile strain, the phonon density shifts to the low frequency. It indicates that the uniaxial tensile strain weakens the interlayer lattice atomic interaction, making the phonon energy in relatively low energy state and increasing the number of low frequency phonons. A large number of low frequency phonons reduce the energy exchange in the friction process, so that the ordered kinetic energy hardly be dissipated efficiently, resulting in the reduction of friction force. As shown in Fig. 8 , the number of effective contact atoms increases under slight compressive strain. The interatomic interaction within the substrate graphene is enhanced, leading to an increase in the potential barrier form on the substrate graphene surface. In the process of interlayer sliding, more energy is needed to overcome the potential barrier which increases the interlayer friction. The phonon spectra of the graphene under compressive strain is shown in Fig. 9 (b). By phonon analysis, it shows that the phonon spectral peak drifts towards high frequency with the increase of compressive strain. The high frequency phonons promote the efficiency of energy exchange, and the ordered kinetic energy is dissipated more effectively, thus increasing the interlayer friction. However, the friction decreases with the increase of uniaxial compressive strain when the uniaxial compression strain is more than − 3%. The reason for the decrease of friction is that the uniaxial compression strain causes the substrate graphene to form obvious wrinkles, as shown in Fig. 10 . Local ripples have appeared in the substrate graphene after the compression strain reaches − 4%. And then the global wrinkles become prominent when the compression strain is -6%. The generation of wrinkles directly reduces the interfacial effective contact area between the substrate and the annular graphene, and also affects the vibration amplitude and frequency of the substrate graphene lattice. The interlayer interaction decreases and thus the friction is reduced. 4. Conclusion In this paper, the dynamic interlayer friction between graphene layers and its strain effect are investigated by molecular dynamics. It is found that the increase of the normal load and the temperature improves the friction by enhancing the interaction between graphene layers. The friction between graphene layers varies nonlinearly with relative velocity. And the graphene lattice resonates under the coupled influence of thermal effect and relative sliding velocity, resulting in the maximum friction at a specific rotational frequency. With the increase of temperature, the frequency of thermal-induced lattice resonance increases, so the rotational frequency that cause the maximum friction increases correspondingly.. Supporting stiffness increases interlayer friction by increasing the ability of the substrate to resist out-of-plane deformation. At the same time, the supporting stiffness limits the lattice vibration amplitude of the substrate, making it easier for the annular graphene to overcome the potential barrier of the substrate graphene surface thus reducing the energy dissipation during interlayer sliding. The friction is effectively decreased by tensile strain and the number of effective contact atoms is not the main reason for this reduction. The slight compressive strain increases the friction. However, when the strain is increased to more than − 3%, the wrinkles appears on the substrate graphene, which weakens the interlayer atomic interaction between the graphene layers, resulting in the decrease of interlayer friction with the increase of compressive strain. Phonon spectrum analysis shows that uniaxial strain changes the phonon energy distribution of graphene, and thus regulates the interlayer friction by adjusting the efficiency of energy exchange. In this paper, the innovative model for eliminating commensurability and edge effects are proposed. The effect of environmental variables and the strain effects on the friction are studied to reveal the influence mechanism. This work is expected to provide theoretical guidance for realizing the regulation of nanoscale friction as well as its strain engineering. Declarations Conflict of interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgment The authors wish to acknowledge the support from the National Nature Science Foundation of China (Grant No. 12102097, 12002094 and 52178193), Natural Science Foundation of Guangdong Province (Grant NO. 2020A1515010915, 2022A1515012037, 2018A030310310, and 2022A1515012086), Guangzhou Municipal Science and Technology Project （Grant No. 202102021026 and 202102020606）. References Guo, W., Bai, Q., Dou, Y., Chen, S. & Wang, H. Molecular dynamics simulation of frictional strengthening behavior of graphene on stainless steel substrate. Carbon 197 , 183-191, doi:10.1016/j.carbon.2022.06.030 (2022). Li, C., Tang, W., Tang, X.-Z., Yang, L. & Bai, L. A molecular dynamics study on the synergistic lubrication mechanisms of graphene/water-based lubricant systems. 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Lin, X., Zhang, H., Guo, Z. & Chang, T. Strain engineering of friction between graphene layers. Tribology International 131 , 686-693, doi:10.1016/j.triboint.2018.11.028 (2019). Yang, X. & Wang, W. Friction characteristics in graphene/MoS2 heterojunction. Surface Science 728 , doi:10.1016/j.susc.2022.122207 (2023). Chen, S. et al. Controlled friction on graphene via substrate deformation induced atomic pinning effect. Computational Materials Science 190 , doi:10.1016/j.commatsci.2021.110315 (2021). Li, J. et al. Load-oriented thickness-dependent friction behavior of graphene supported by substrate with different stiffnesses. Computational Materials Science 203 , doi:10.1016/j.commatsci.2021.111164 (2022). Liao, Y., Li, Z., Nie, W. & Xia, W. Effect of reconstructed vacancy defects on the crumpling behavior of graphene sheets. Forces in Mechanics 6 , doi:10.1016/j.finmec.2021.100057 (2022). Orekhov, N., Ostroumova, G. & Stegailov, V. High temperature pure carbon nanoparticle formation: Validation of AIREBO and ReaxFF reactive molecular dynamics. Carbon 170 , 606-620, doi:10.1016/j.carbon.2020.08.009 (2020). Cook, E. H., Buehler, M. J. & Spakovszky, Z. S. Mechanism of friction in rotating carbon nanotube bearings. Journal of the Mechanics and Physics of Solids 61 , 652-673, doi:10.1016/j.jmps.2012.08.004 (2013). Li, Q., Dong, Y., Perez, D., Martini, A. & Carpick, R. W. Speed dependence of atomic stick-slip friction in optimally matched experiments and molecular dynamics simulations. Phys Rev Lett 106 , 126101, doi:10.1103/PhysRevLett.106.126101 (2011). Zhao, L. & Cao, P. Temperature dependence of contact quality inducing suppression of stick–slip friction. Extreme Mechanics Letters 45 , doi:10.1016/j.eml.2021.101273 (2021). Fu, H., Chen, C. Y., Li, J. Q., Lan, Y. P. & Yuan, J. J. Influence of Na2S on the corrosion behavior of Q345 steel in sodium aluminate solution. Materials Research Express 6 (2019). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2810227","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Method Article","associatedPublications":[],"authors":[{"id":191486984,"identity":"74694081-b076-4091-abd2-fbfece6bbdbf","order_by":0,"name":"Shuang Gan","email":"","orcid":"","institution":"Guangzhou University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Shuang","middleName":"","lastName":"Gan","suffix":""},{"id":191486987,"identity":"6d569fe6-525b-40ac-9ba1-5d2fb7ce73b4","order_by":1,"name":"Jianzhang Huang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0klEQVRIiWNgGAWjYBACxhlgyoaBQQJEsxGvJY0ELRCVDIdJ0MI8u8fwc8Gv83bzZ/cYMHwoO8zAP7uBgMPmnDGWntl3O7lxzhkDxhnnDjNI3DlAQMuMHANp3p7bycwSOQbMvG2HGQwkEghqMf7N23MumQ2k5S+RWsykeX4csOMBaWEkTktamTVvQ3KChERawcGec+k8EjcIaDGckbz5Ns8fO3v5GckbH/wos5bjn0FISwPIqjaGRBB9AIh58KsHAnkw+YfBnqDKUTAKRsEoGLkAAJKWQJrZf4ggAAAAAElFTkSuQmCC","orcid":"","institution":"Guangzhou University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Jianzhang","middleName":"","lastName":"Huang","suffix":""},{"id":191486988,"identity":"159025b9-d6f9-4369-a219-519796893eeb","order_by":2,"name":"Yi Cai","email":"","orcid":"","institution":"Guangzhou University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Yi","middleName":"","lastName":"Cai","suffix":""},{"id":191486991,"identity":"ba7000a1-00b2-4383-b540-2a1a318a1386","order_by":3,"name":"Yingjing Liang","email":"","orcid":"","institution":"Guangzhou University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Yingjing","middleName":"","lastName":"Liang","suffix":""},{"id":191486992,"identity":"cf327a79-e91c-4421-864d-244c6ddae74a","order_by":4,"name":"Yijie Liu","email":"","orcid":"","institution":"Guangzhou University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Yijie","middleName":"","lastName":"Liu","suffix":""}],"badges":[],"createdAt":"2023-04-13 01:44:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2810227/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2810227/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":35895182,"identity":"516e95af-ba54-4584-b6d3-cde5f6e30a12","added_by":"auto","created_at":"2023-04-17 20:59:06","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":2062689,"visible":true,"origin":"","legend":"\u003cp\u003ePhysical model of rotational slider-substrate friction pair system. The substrate has dimensions of 10nm in both length and width and the upper layers of graphene has an inner ring radius of 2 nm and an outer ring radius of 3.7 nm.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-2810227/v1/4f986fef1b31521c2aaf0833.png"},{"id":35893926,"identity":"11f1fe26-12a0-4136-91ad-c5aaee9fa906","added_by":"auto","created_at":"2023-04-17 20:43:06","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":1478051,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic of graphene subjected to uniaxial strains. The uniaxial strain is applied to the green area and calculated as follows: \u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;, Where the distance after the stretch is L, and the distance before the stretch is L0.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-2810227/v1/31e260b879a9a10c7f4c6c25.png"},{"id":35893928,"identity":"bc711083-794c-412e-9b34-8d71a52ca79d","added_by":"auto","created_at":"2023-04-17 20:43:06","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":717404,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic of graphene subjected to normal load: each atom of the annular graphene in the orange region is subjected to normal load\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-2810227/v1/b386f381def699a8c3430148.png"},{"id":35893924,"identity":"569c1364-71d3-4bef-9a43-92d46b067803","added_by":"auto","created_at":"2023-04-17 20:43:06","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":31243,"visible":true,"origin":"","legend":"\u003cp\u003eThe effects of normal load on the interfacial friction of graphene under difference temperature\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-2810227/v1/7cb33b3e1268cd0797acf984.png"},{"id":35893923,"identity":"b17e7221-09c8-4b86-9dbb-436d505cf6cc","added_by":"auto","created_at":"2023-04-17 20:43:06","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":44620,"visible":true,"origin":"","legend":"\u003cp\u003eEffects of rotational frequency on the interfacial friction of graphene under difference temperature\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-2810227/v1/f5254abdfe1f4ced2a662c17.png"},{"id":35894756,"identity":"0de100a1-e96c-488b-a830-f69ea2daced3","added_by":"auto","created_at":"2023-04-17 20:51:06","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":44461,"visible":true,"origin":"","legend":"\u003cp\u003eThe effect of support stiffness on the interfacial friction of graphene under difference temperature\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-2810227/v1/d1575ff6071da86ff3679fee.png"},{"id":35894757,"identity":"bf7de54c-b9a5-48f0-964c-81e848bf2ac0","added_by":"auto","created_at":"2023-04-17 20:51:06","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":34792,"visible":true,"origin":"","legend":"\u003cp\u003eEffect of uniaxial strain on the interfacial friction of graphene (armchai graphene in upper window, zigzag graphene in lower window)\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-2810227/v1/524afcd9cb271d4eb38491ce.png"},{"id":35895431,"identity":"784824de-02df-4053-b9e2-9fd5aed44cfb","added_by":"auto","created_at":"2023-04-17 21:07:06","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":17523,"visible":true,"origin":"","legend":"\u003cp\u003eNumber of effective contact atoms of graphene\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-2810227/v1/4b99510012d2acb4a204a6dd.png"},{"id":35894758,"identity":"8be1967f-22cf-4554-9fa2-12abd983b66f","added_by":"auto","created_at":"2023-04-17 20:51:06","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":50892,"visible":true,"origin":"","legend":"\u003cp\u003ePhonon state density of graphene under uniaxial strain\u003c/p\u003e\n\u003cp\u003e(a is tensile strain, b is compressive strain)\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-2810227/v1/dfcac878709dbe4e3df3750c.png"},{"id":35893932,"identity":"df26c609-1df6-4e50-896e-f9153928af19","added_by":"auto","created_at":"2023-04-17 20:43:06","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":430471,"visible":true,"origin":"","legend":"\u003cp\u003eFormation process of the wrinkles in the substrate graphene under compressive strain loading\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-2810227/v1/4b5a7117bbd7a0589286b2a1.png"},{"id":37156992,"identity":"0274227a-02b3-48d7-9c80-ecf1937b72d8","added_by":"auto","created_at":"2023-05-17 20:29:25","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3855281,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2810227/v1/48cd220a-f79b-4d97-a29c-4fb75a11a1fa.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Molecular dynamics study on dynamic interlayer friction of graphene and its strain effect","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eGraphene has become a research hot spot in the field of nanomechanics due to its excellent mechanical, thermal and electrical properties\u003csup\u003e\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. It has become an important nanocomponent due to its excellent physical properties with ultra-low interlayer friction \u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e,\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. With the rapid development of big data and cloud storage, Zheng \u003cem\u003eet al.\u003c/em\u003e proposed the graphene can replace the diamond-like carbon (DLC) film as an important component for ultra-lubricated mechanical hard disk, which is expected to increase the disk storage capacity by 10 to 15 times\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e. However, the effect of high sliding speed on dynamic friction of graphene has not been clarified. Current studies indicate that the interlayer friction decrease significantly by rotating the upper layer of graphene at a certain angle to form the incommensurate registry with the substrate layer\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e, and this phenomenon is called superlubrication. However, the superlubrication phenomenon will be suppressed in some specific cases, such as ultra-high load\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e or contact with the low support stiffness of the substrate surface\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e. The interfacial friction of graphene layers is influenced by multi-factor coupling, such as the interlayer spacing and commensurability\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e,\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e, normal load, temperature, support stiffness, and relative sliding velocity\u003csup\u003e\u003cspan additionalcitationids=\"CR14\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. Therefore, it is great academic and engineering value to clarify the effect rule and reveal the influence mechanism of the above factors in interlayer friction.\u003c/p\u003e \u003cp\u003eThe influence rule of normal load on nanoscale friction is complicated\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e, that it varies according to the contact commensurability of graphene layers\u003csup\u003e\u003cspan additionalcitationids=\"CR18\" citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e. The interlayer friction is enhanced with the increase of normal load when the contact of graphene slider and the graphene substrate is commensurate. In the case of incommensurate contact, low normal load has little effect on the interlayer friction. As the normal force increased to certain value, the rate at which friction increases with the increase of load is significantly accelerated due to the obvious ploughing phenomenon between the slider boundary atoms and substrate surface under high load. It can be seen that the influence of normal load on interlayer friction is related to the edge effect and contact commensurability\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e. In the traditional slider-substrate friction model, the relative sliding velocity affects the slip state of the graphene flake and then significant effect on the interlayer friction is caused as a result\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. In the case of incommensurate contact, the degree to which the atoms are hindered by the potential barrier varies depending on the relative velocity. Thus the interlayer friction shows a complex variation law with relative velocity\u003csup\u003e\u003cspan additionalcitationids=\"CR23 CR24\" citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e. Moreover, previous studies model on graphene interlayer friction also have edge effects\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. It can be seen that the edge effect and contact commensurability have introduced complex influences to the study of interlayer friction. The influence of multiple factors is often coupled together and the influence mechanism of the interlayer friction of graphene is still not clear. The effects of these factors on interlayer friction still need to be decoupled and in-depth studied, and the complex nature and mechanism behind the phenomena need to be further explored and revealed.\u003c/p\u003e \u003cp\u003eIn addition, studies have shown that the frictional properties and phenomena of nanomaterials are significantly affected by strain\u003csup\u003e\u003cspan additionalcitationids=\"CR28\" citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e. And strains applying to the graphene are supposed to reach critical state to satisfy the needs of engineering applications\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e. It has been found that the in-plane strain can change the static frictional force between graphene and silica substrate\u003csup\u003e\u003cspan additionalcitationids=\"CR32\" citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e. Applying uniaxial tensile strain to graphene can decrease friction by reducing the number of atoms between the indenter and graphene\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e, while the compressive strain can increase the friction coefficient\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e of the graphene interlayer friction. However, studies\u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e have shown that the friction force increases significantly under slight compressive strain, although the number of atoms in contact area increased by a small amount. The mechanism of interfacial frictional strain effect is very complex, and the dominant factor is not the change of the number of atoms in contact area\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e,\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e,\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. The strain causes incommensurate contact at the graphene interface resulting in the reduction of interlayer friction\u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e, that could be the more acceptable explanation for the strain effect. The existing studies analyzed the effects of uniaxial tensile/compressive strain on the surface friction of graphene using lattice mismatch theory. From the perspective of energy dissipation, the strain effect has an inevitable effect on the lattice vibration, and thus affects the interfacial dynamic friction at nanoscale\u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e. In the researches on strain effect using slider-substrate friction model\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e, the influence of commensurability and lattice vibration on friction caused by strain are coupled with each other, and even the edge effect is involved\u003csup\u003e\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e. So far, there are few studies on the influence of strain effect on dynamic friction of graphene interface from the perspective of kinetic dissipation. The changes of the density of phonon states and the number of contact atoms induced by strain effect are not compared. The mechanism of strain effect on dynamic friction of nanointerface is not clear. Therefore, the research work at nanoscale dynamic friction should emphasize the comprehensive study of mechanism of the strain effect, as it has great potential for tuning the interfacial friction at nanoscale and extensive prospect of application.\u003c/p\u003e \u003cp\u003eIn this paper, an annular graphene rotational slider-substrate friction pair model is proposed to eliminate the effects of contact commensurability and edge effects. The effects of temperature, normal load, sliding velocity, support stiffness and axial strain on the interfacial friction between graphene layers are investigated using molecular dynamics (MD) simulation. The effect mechanism of various factors affecting friction are analyzed by numerical and theoretical analyses. By statistical analysis of phonon states density and examination of effective contact area between strained graphene layers, the regulation of interlayer friction by axial strain is revealed.\u003c/p\u003e"},{"header":"2. Simulation Model And Methods","content":"\u003cp\u003eThe Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the physical model of rotational slider-substrate friction pair system with an annular shaped graphene flake slider laying on the rectangular graphene substrate with an equilibrium spacing of 0.34 nm. The spring with stiffness of 2.7 N/m is used to simulate the supporting effect to graphene substrate\u003csup\u003e\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e, which has been widely used in recent nanoscale friction studies\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e,\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e,\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e. The rectangular graphene substrate has dimensions of 10nm in both length and width containing 3936 carbon atoms. The all sides of graphene substrate are bordered by fixed boundaries with a width of 2\u0026Aring; region for 384 carbon atoms in total. The upper layers of graphene has an inner ring radius of 2 nm and an outer ring radius of 3.7 nm with 1427 atoms, and the outer and inner ring boundaries have fixed boundaries of 2 \u0026Aring; respectively. The steady isothermal method is used to calculate the interlayer friction by recording the thermal energy in the simulations process. During rotation process, the crystal lattice mismatch of contact interface is constantly updated and the atoms in the contact area are stressed equally, which effectively avoids the influence of commensurability effects and edge effects.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eUniaxial strain is applied to the substrate graphene boundary divided into armchai and zigzag for study the effect of strain on friction. The schematic of uniaxial strain loading on armchair graphene is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The uniaxial strain is applied to the green area after the system has reached stability and calculated as follows:\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varepsilon =(L - {L_0})/{L_0}\\)\u003c/span\u003e\u003c/span\u003e, Where the distance after the stretch is \u003cem\u003eL\u003c/em\u003e, and the distance before the stretch is \u003cem\u003eL\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe dynamic friction process between graphene layers is simulated using large-scale atomic/molecular massively parallel simulator package (LAMMPS). The carbon atoms on the edges of substrate graphene are fixed. The rest of atoms on substrate graphene are attached to a spring along \u003cem\u003ez\u003c/em\u003e-oriented to simulate the supporting effect to the substrate. The normal load of 0.10 nN/atom (\u003cem\u003ez\u003c/em\u003e-oriented) are imposed on the each carbon atom of the upper graphene. The AIREBO\u003csup\u003e\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e potential is used to describe the interlayer C-C bond interaction of the graphene. The time step is set to 1 fs in the all simulations process. Energy minimization is performed at the beginning of the simulations to achieve equilibrium. After a long-time relaxation, the upper annular graphene rotates at high speed around its central axis in the \u003cem\u003ez\u003c/em\u003e-direction to simulate the dynamic interlayer sliding behavior. The heat generated by interlayer friction is recorded by using a Nose-Hoover thermostat after the system is sufficiently relaxed to reach stability of high speed rotation. The interlayer friction force of each atom is calculated by using steady isothermal method\u003csup\u003e\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e. The energy dissipation rate by friction is computed using the energy data extracted by the Noes-Hoover thermostat:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\Delta E=\\int_{0}^{{\\text{t}}} {Q\u0026#039;dt}\\)\u003c/span\u003e \u003c/span\u003e \u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(Q^{\\prime}\\)\u003c/span\u003e\u003c/span\u003e is the energy dissipation rate and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\Delta E\\)\u003c/span\u003e\u003c/span\u003eis the thermal energy produced by dynamic friction. Thus the friction between the layers is calculated as follows:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({F_f}=\\frac{{Q\u0026#039;}}{{2\\pi fR}}\\)\u003c/span\u003e \u003c/span\u003e \u003c/p\u003e \u003cp\u003ewhere \u003cem\u003ef\u003c/em\u003e is the rotational frequency of the upper layer, and \u003cem\u003eR\u003c/em\u003e is the rotational radius of the upper circle.\u003c/p\u003e"},{"header":"3. Results And Discussion","content":"\u003cdiv class=\"Section2\" id=\"Sec4\"\u003e\n \u003ch2\u003e3.1 Normal load effects\u003c/h2\u003e\n \u003cp\u003eThe rotational frequency of the upper annular graphene is 150 GHz (the relative velocity of the equivalent radius is 29.6 \u0026Aring;/Ps). The stiffness of supporting spring stiffness of the substrate graphene layer is 2.7 N/m. To study the temperature dependence of normal load effects, the environmental temperature is set ranging from 100K to 500K. As shown in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, the normal load is applied to each atoms of the upper annular graphene varies from 0.05 nN/atom to 0.4 nN/atom.\u003c/p\u003e\n \u003cp\u003eThe calculation results of the interlayer friction under different normal load are shown in Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e. It is observed that the normal load has great impact on friction. At the same temperature, the friction increases linearly with the normal load because the distance between the upper and substrate graphene decreases. And the friction force is increased with the temperature as well. Because the atomic lattice vibration frequency and vibration amplitude is relatively low under the lower temperature, that makes it easier for the atoms of the rapidly rotating annular graphene to pass through the energy barrier on the substrate graphene surface. Thus, the energy dissipation of relative sliding is reduced. With the increase of temperature, the friction is raised with the higher lattice vibration frequency and vibration amplitude, which strengthens the interlayer atomic interaction. These results show that, after blocking commensurability and edge effects using the annular rotating friction model, the interlayer friction is increased with the normal load and temperature. It implies that interlayer friction is positively correlated with normal load and temperature.\u003c/p\u003e\n \u003cp\u003eThe relative coefficient parameter \u003cem\u003e\u0026alpha;\u003c/em\u003eis defined to investigate coupling influence of temperature and normal load on the interlayer friction as follows:\u003c/p\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u0026nbsp;\u003cspan class=\"mathinline\"\u003e\\(\\alpha =\\frac{{{F_{0.4nN}} - {F_{0.05nN}}}}{{{F_{0.05nN}}}}\\)\u003c/span\u003e\u0026nbsp;\u003c/span\u003e\u003c/p\u003e\n \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F_{0.4nN}}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F_{0.05nN}}\\)\u003c/span\u003e\u003c/span\u003e represent the friction force when the normal load is 0.4nN/atom and 0.05nN/atom, respectively. The values of \u003cem\u003e\u0026alpha;\u003c/em\u003e under different temperatures are shown in Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. At all temperatures, the interlayer friction is almost doubled as the normal load increases from 0.05nN/atom to 0.4nN/atom. At room temperature of 300K, the interlayer friction is increased by 91.69%, which is relatively low in contrast. When the temperature are 200K and 400K in the vicinity of the room temperature of 300K, the rate of interlayer friction increases with the normal load relatively larger than that at 300K, which is 118.29% at 200K and 121.67% at 400K respectively. Otherwise, the value of parameters \u003cem\u003e\u0026alpha;\u003c/em\u003e is 115.17% at 100K and 108.96 at 500K. This implies that temperature affects the amplifying efficiency of normal load effects on friction.\u0026nbsp;\u003c/p\u003e\u0026nbsp;\u003ctable border=\"1\" id=\"Tab1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eParameters \u0026alpha; under different temperatures\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eTemperature/K\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e200\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e300\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e400\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e500\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026alpha;\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e115.17%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e118.29%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e91.69%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e121.67%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e108.96%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv class=\"Section2\" id=\"Sec5\"\u003e\n \u003ch2\u003e3.2 Rotational frequency effects\u003c/h2\u003e\n \u003cp\u003eThe normal load applied to the annular graphene is 0.1nN/atom and the supporting stiffness of the substrate graphene is 2.7N/m. At the same temperature, the rotational frequency of annular graphene is 50\u0026thinsp;~\u0026thinsp;400 GHz (the relative velocity of the equivalent radius is 9.87\u0026thinsp;~\u0026thinsp;78.94\u0026Aring;/Ps). The calculation results are shown in Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e. At the temperature of 300 K, the interlayer friction increases with the rotational frequency when the rotational frequency of annular graphene is below 300 GHz, after which the friction decreass with the increasing of the rotational frequency. The friction reaches its maximum value of 182.68fN/atom at the rotational frequency of 300 GHz. As the temperature increases, the rotational frequency that causes the maximum value of interlayer friction also increases. The reason of this phenomenon can be revealed from two aspects: velocity coupled thermal-induced resonance of the graphene lattice and the in-plane deformation of graphene resulted from interlayer friction. The relative velocity between the graphene layers increases with rotational frequency. As the relative sliding velocity is increased close to the lattice resonance frequency of the graphene interface, that causes the graphene interlayer lattice resonance\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e48\u003c/span\u003e\u003c/sup\u003e. The intense lattice resonance vibration leads to the aggravation of energy dissipation, resulting in the maximum of interlayer friction. As the temperature increases, the interlayer lattice resonance frequency of graphene increases, therefore the rotational frequency required to induce lattice resonance also increases correspondingly. On the other hand, in the interlayer viscous sliding process, the elastic deformation graphene undergoes the experiences of accumulation and release\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e. When the rotational frequency is higher than a certain key value, the deformation energy accumulated by the interlayer friction is difficult to be completely released in time and produce a certain amount of deformation, which results in the change of graphene lattice constant. The interlayer lattice mismatch is formed due to the difference in in-plane lattice constant between the graphene friction pair, and the interlayer friction is reduced as well. At low temperature, the thermal-induced lattice resonance effect is not obvious, so the friction-induced deformation mechanism of graphene has a significant effect on the interlayer friction. With the increase of temperature, the energy dissipation mechanism of thermal-induced resonance dominates, leading to the increase of rotational frequency required for interlayer lattice resonance..\u003c/p\u003e\n \u003cp\u003eThe interlayer friction generally increases with temperature at the same rotational frequency. However, the interlayer friction force at 400 K is greater than that at 500 K when the rotational frequency is 300 GHz. The reason is that under the coupled influence of graphene rotational frequency of 300 GHz and temperature of 400 K, interlayer lattice resonance phenomenon is produced and makes the friction force greatly amplified. As shown in Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e, at the temperature of 300 K the interlayer friction at 350 GHz is about 5 times larger than that at 50 GHz. It can be seen that the friction dissipation can be reduced by avoiding the lattice resonance, which will be one of the effective ways of nanoscale friction regulation technology.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv class=\"Section2\" id=\"Sec6\"\u003e\n \u003ch2\u003e3.3 Supporting stiffness effects\u003c/h2\u003e\n \u003cp\u003eIn practical applications, graphene is usually placed on the substrate or exists in the form of multiple layers of graphene. And different substrate materials have different support effects on the graphene substrate, so the interaction between graphene and substrate materials becomes one of the important factors affecting the interlayer friction of graphene\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e41\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e. To study the effect of supporting stiffness on graphene interlayer friction, the supporting stiffness is set to vary from 1 to 15nN/nm at the same temperature. The calculation results are shown in Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e. It is found that with the increase of support stiffness at all temperatures, the maximum value of interlayer friction occurs and their corresponding value of supporting stiffness falls in the range of 3\u0026ndash;5 nN/nm.. When the maximum value of is reached, the interlayer friction decreases with the increase of supporting stiffness. This is due to fact that the substrate graphene is weakly constrained in out-of-plane direction when the supporting stiffness is low, which is easy for substrate graphene to form out-of-plane deformation when it squeezed by the annular graphene. This results in a relatively wide equilibrium distance between the graphene layers and low interlayer friction. With the increase of supporting stiffness, the ability of substrate graphene to resist out-of-plane deformation is improved and the equilibrium distance between graphene layers is reduced. Thus, the interaction between the upper annular and substrate graphene is promoted, resulting in the gradual increase of interlayer friction..\u003c/p\u003e\n \u003cp\u003eMeanwhile, from the perspective of lattice dynamics, the lattice vibration frequency of graphene substrate increases with supporting stiffness\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e, that increases the peak of interlayer potential barrier. This promotes energy dissipation during friction process and increases the interlayer friction. As the supporting stiffness continued to increase, the vibration amplitude of substrate graphene lattice are limited. The upper annular graphene is more easily to pass through the potential barrier of the substrate graphene surface. The interlayer interaction between the graphene layers is reduced, leading to lower energy dissipation during the sliding process, showing that the friction begins to decrease gradually with the increase of the supporting stiffness. As can be seen in Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e (a), there is no peak value of friction as the supporting stiffness increases at the temperature of 100 K. It is attributed to the lower frequency and amplitude of graphene lattice vibration at low temperature, and the thermal excitation effect of lattice vibration is weaken. Therefore, the inhibition effect on lattice vibration increases as the supporting stiffness increases, resulting in a decreasing trend of interlayer friction.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv class=\"Section2\" id=\"Sec7\"\u003e\n \u003ch2\u003e3.4 Uniaxial strain effects\u003c/h2\u003e\n \u003cp\u003eThe calculation results of the friction under different uniaxial strain are shown in Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e. The results show the friction of graphene decreases with the tensile strain. When the tensile strain is 10%, the interlayer friction of armchair graphene decreases by 15.96%, while that of zigzag graphene decreases by 16.27%. Different from the tensile strain effect, when the uniaxial compressive strain is less than \u0026minus;\u0026thinsp;3%, the interlayer friction increases with the increase of compressive strain. On the contrary, when the compressive strain is greater than \u0026minus;\u0026thinsp;3%, the friction between graphene layers decreases as the compressive strain is enhanced.\u003c/p\u003e\n \u003cp\u003eFor the strain effects on nanoscale interfacial friction, the number of atoms in effective contact area is considered to be one of the important ways in which strain affects friction. In the process of strain loading, the number of atoms in the effective contact region of graphene friction pair is affected by the uniaxial strain. The number of atoms in the effective contact area under the strain is calculated as shown in Fig. \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e. It can be found that the number of atoms in the contact region increases from 1435 to 1538 as the tensile strain increases. This is because during uniaxial tensile deformation, the atoms located in non-contact region of the substrate graphene where is below the inner circle space of the annular graphene enter the sliding contact region. At the same time, a few of atoms enter the contact region from the lateral direction due to Poisson effect under uniaxial tensile strain. Since the number of atoms originally near the boundary of the contact region are moved outside of the contact region during tensile deformation of substrate graphene is less than the number of atoms entering the contact region, so the number of effective contact atoms increases. As the compression strain increases, the atoms near the contact boundary enter the contact region, and the number of atoms in the contact region of graphene increases from 1435 to 1672.It suggests that tensile strain decreases friction by reducing the number of atoms in effective contact\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e is inappropriate for the explanation of strain effects on interlayer friction. Although the number of effective contact atoms is a factor affecting the interlayer friction, it is not the dominant factor of the strain effect on nanoscale interfacial friction. Under the tensile strain, the amplitude of potential barrier on the surface of the substrate graphene is reduced, the atoms in annular graphene are easier to overcome the potential barrier and slide through the substrate graphene\u0026rsquo; surface. As a result, the energy dissipation of interlayer friction behavior is reduced. The phonon spectra of graphene under uniaxial strain effect is calculated, as shown in Fig. \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e. As can be seen from Fig. \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e(a), with the increase of tensile strain, the phonon density shifts to the low frequency. It indicates that the uniaxial tensile strain weakens the interlayer lattice atomic interaction, making the phonon energy in relatively low energy state and increasing the number of low frequency phonons. A large number of low frequency phonons reduce the energy exchange in the friction process, so that the ordered kinetic energy hardly be dissipated efficiently, resulting in the reduction of friction force.\u003c/p\u003e\n \u003cp\u003eAs shown in Fig. \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e, the number of effective contact atoms increases under slight compressive strain. The interatomic interaction within the substrate graphene is enhanced, leading to an increase in the potential barrier form on the substrate graphene surface. In the process of interlayer sliding, more energy is needed to overcome the potential barrier which increases the interlayer friction. The phonon spectra of the graphene under compressive strain is shown in Fig. \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e (b). By phonon analysis, it shows that the phonon spectral peak drifts towards high frequency with the increase of compressive strain. The high frequency phonons promote the efficiency of energy exchange, and the ordered kinetic energy is dissipated more effectively, thus increasing the interlayer friction. However, the friction decreases with the increase of uniaxial compressive strain when the uniaxial compression strain is more than \u0026minus;\u0026thinsp;3%. The reason for the decrease of friction is that the uniaxial compression strain causes the substrate graphene to form obvious wrinkles, as shown in Fig. \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e. Local ripples have appeared in the substrate graphene after the compression strain reaches \u0026minus;\u0026thinsp;4%. And then the global wrinkles become prominent when the compression strain is -6%. The generation of wrinkles directly reduces the interfacial effective contact area between the substrate and the annular graphene, and also affects the vibration amplitude and frequency of the substrate graphene lattice. The interlayer interaction decreases and thus the friction is reduced.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eIn this paper, the dynamic interlayer friction between graphene layers and its strain effect are investigated by molecular dynamics. It is found that the increase of the normal load and the temperature improves the friction by enhancing the interaction between graphene layers. The friction between graphene layers varies nonlinearly with relative velocity. And the graphene lattice resonates under the coupled influence of thermal effect and relative sliding velocity, resulting in the maximum friction at a specific rotational frequency. With the increase of temperature, the frequency of thermal-induced lattice resonance increases, so the rotational frequency that cause the maximum friction increases correspondingly.. Supporting stiffness increases interlayer friction by increasing the ability of the substrate to resist out-of-plane deformation. At the same time, the supporting stiffness limits the lattice vibration amplitude of the substrate, making it easier for the annular graphene to overcome the potential barrier of the substrate graphene surface thus reducing the energy dissipation during interlayer sliding. The friction is effectively decreased by tensile strain and the number of effective contact atoms is not the main reason for this reduction. The slight compressive strain increases the friction. However, when the strain is increased to more than \u0026minus;\u0026thinsp;3%, the wrinkles appears on the substrate graphene, which weakens the interlayer atomic interaction between the graphene layers, resulting in the decrease of interlayer friction with the increase of compressive strain. Phonon spectrum analysis shows that uniaxial strain changes the phonon energy distribution of graphene, and thus regulates the interlayer friction by adjusting the efficiency of energy exchange. In this paper, the innovative model for eliminating commensurability and edge effects are proposed. The effect of environmental variables and the strain effects on the friction are studied to reveal the influence mechanism. This work is expected to provide theoretical guidance for realizing the regulation of nanoscale friction as well as its strain engineering.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eConflict of interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgment\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors wish to acknowledge the support from the National Nature Science Foundation of China (Grant No. 12102097, 12002094 and 52178193), Natural Science Foundation of Guangdong Province (Grant NO. 2020A1515010915, 2022A1515012037, 2018A030310310, and 2022A1515012086), Guangzhou Municipal Science and Technology Project （Grant No. 202102021026 and 202102020606）.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eGuo, W., Bai, Q., Dou, Y., Chen, S. \u0026amp; Wang, H. 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Influence of Na2S on the corrosion behavior of Q345 steel in sodium aluminate solution. \u003cem\u003eMaterials Research Express\u003c/em\u003e \u003cstrong\u003e6\u003c/strong\u003e (2019).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"dynamic interlayer friction, strain effects, lattice vibration, commensurability, graphene","lastPublishedDoi":"10.21203/rs.3.rs-2810227/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2810227/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe mechanism of dynamic sliding friction between graphene layers and its strain effect is theoretically analyzed in this paper. A friction pair model with an annular graphene as slider is built to eliminate the influence of commensurability and edge effect. The effects of temperature, normal load, sliding velocity, support stiffness and axial strain on the friction between graphene layers are investigated. The coupling effect of temperature and other influencing factors are clarified. The results show that normal load increases the friction force by decreasing layer spacing. The friction is firstly enhanced as the sliding velocity increase and then is reduced by severe interlayer residual deformation and lattice resonance frequency at high sliding velocity. The support stiffness regulates the interlayer friction by affecting the atomic vibration amplitude of the graphene lattice. By mechanism analysis, it is found that by changing the number of atoms in friction region between layers and the frequency of lattice vibration, the strain can effectively regulate the dynamic friction between graphene layers. Our findings reveal the influence mechanism of affecting factor on dynamic friction of graphene and provide a fundamental understanding for the strains engineering of nanoscale friction.\u003c/p\u003e","manuscriptTitle":"Molecular dynamics study on dynamic interlayer friction of graphene and its strain effect","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-04-17 20:43:01","doi":"10.21203/rs.3.rs-2810227/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"956744c1-880b-429b-89d2-92b51b1ddfec","owner":[],"postedDate":"April 17th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2023-05-17T20:29:17+00:00","versionOfRecord":[],"versionCreatedAt":"2023-04-17 20:43:01","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-2810227","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2810227","identity":"rs-2810227","version":["v1"]},"buildId":"rHA-KDH7Qsr4HCuvH75dn","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}