Buckled Graphene for Efficient Energy Harvest, Storage, and Conversion
aa r X i v : . [ c ond - m a t . m t r l - s c i ] A ug Buckled Graphene for Efficient Energy Harvest, Storage, andConversion
Jin-Wu Jiang ∗ Shanghai Institute of Applied Mathematics and Mechanics,Shanghai Key Laboratory of Mechanics in Energy Engineering,Shanghai University, Shanghai 200072, People’s Republic of China (Dated: September 6, 2018)
Abstract
Buckling is one of the most common phenomena in atomic-thick layered structures like graphene.While the buckling phenomenon usually causes disaster for most nano-devices, we illustrate onepositive application of the buckled graphene for energy harvest, storage, and conversion. Morespecifically, we perform molecular dynamical simulations to show that the buckled graphene canbe used to collect the wasted mechanical energy and store the energy in the form of internal knottingpotential. Through strain engineering, the knotting potential can be converted into useful kinetic(thermal) energy that is highly concentrated at the free edges of the buckled graphene. The presentstudy demonstrates potential applications of the buckled graphene for converting the dispersedwasted mechanical energy into the concentrated useful kinetic (thermal) energy.
PACS numbers: 72.20.mq, 62.25.-g, 61.48.GhKeywords: Buckled Graphene, Energy Harvest, Energy Storage, Energy Conversion but very small bending modulus. As a result of the quasi 2D nature, bucklingbecomes the most common phenomenon in graphene. For the buckling instability, Eulerbuckling theory states that the critical compression strain, above which graphene will bebuckled, is inversely proportional to the in-plane stiffness C and is proportional to thebending modulus D ; i.e., ǫ c ∝ D/C . According to the Euler buckling theory, the criti-cal strain for graphene is very small; i.e., the buckling phenomenon can easily take placein graphene. Consequently, the buckling process can be induced by very weak externaldisturbance like the thermal expansion effect. The buckling of graphene has attracted intensive research interests in past few years.
In most of these existing works, buckling brings negative effects on the mechanical, thermal,or electronic properties of graphene. However, in the present work, we will show that buckledgraphene can collect the wasted mechanical energy and convert the wasted energy into usefulconcentrated kinetic energy.It has been found that, the conversion of energy on the nanoscale level plays an importantrole in supporting the engineering of nano-devices. Chang performed molecular dynamicssimulations to examine the Domino-like energy transformation between the van der Waalspotential and the kinetic (thermal) energy in single-walled carbon nanotubes. Many workshave proposed to use graphene-based materials as flexible supercapacitors for energy storageand conversion.
In this paper, we demonstrate a mechanical route for the application of graphene forenergy collection, storage, and conversion. More specifically, the buckled graphene can beused to collect wasted mechanical energy, which is stored in the form of knotting potential.The energy stored in the buckled graphene can be converted into kinetic energy concentratedat the free edges of graphene. We also investigate possible methods to increase the efficiencyfor the energy conversion from the dispersed mechanical energy into the concentrated kineticenergy.The left structure in Fig. 1 (a) shows the thermalized configuration for graphene of dimen-sion 30 ×
200 ˚A. Both ends in the x-direction are fixed, while free boundary conditions areapplied in y and z-directions. The whole system is divided into the top, middle (mid), andbottom (bot) regions. Free edges are at the top and bottom regions. The interactions be-tween carbon atoms in graphene are described by the second generation Brenner potential. IG. 1: (Color online) Energy harvest, storage, and conversion using buckled graphene of dimension30 ×
200 ˚A at 1 K. (a) Graphene is buckled under external mechanical compression along the x-direction. (b) The buckled graphene is indented at the middle position, creating two knots (depictedby black stars), which move to the ± y ends at t=858 ps. These knots are stable at the free edgesof the buckled graphene. This step is to mimic the collection of the wasted mechanical energy(mimic by moving indenter), which is transformed into the potential energy of the knots. (c) Theknots are loosened by further compression along the x-direction, which leads to the conversion ofthe knoting potential energy into the kinetic energy concentrated at the ± y edges. (e) Side viewsfor the five configurations. Color is with respective to the z-coordinate of each atom. The standard Newton equations of motion are integrated in time using the velocity Verletalgorithm with a time step of 1 fs. The Nos´e-Hoover thermostat is used for maintainingthe constant temperature at 1 K and the constant pressure of 0 Pa. Molecular dynamicssimulations are performed using the publicly available simulation code LAMMPS. TheOVITO package is used for visualization. P o t en t i a l pe r a t o m ( m e V ) Time (ps)
I II III IV Vopt com ind opt comknot unknot topbotmid
FIG. 2: (Color online) Potential per atom for the top (black solid line), bottom (blue dashedline), and middle (red dotted line) regions during the energy collection, storage, and conversion ingraphene of dimension 30 ×
200 ˚A. There are five typical steps for the simulation. (I) Grapheneis thermalized within the NPT ensemble for 200 ps. (II) Graphene is buckled by compressionalong the x-direction. (III) The buckled graphene is indented and two knots are created. (IV) Theknotting graphene is thermalized within the NPT ensemble for another 200 ps. (V) The knots areloosened by further compression along the x-direction.
Fig. 1 displays the whole energy collection, storage, and conversion process in five simula-tion steps. First, the system is thermalized to the targeted pressure and temperature withinthe NPT (i.e. the particles number N, the pressure P and the temperature T of the systemare constant) ensemble for 200 ps. Second, graphene is buckled by compression along thex-direction for 200 ps at a strain rate of 10 − ps − , which results in a final compressive strainof 2% in the system. The structure is allowed to be fully relaxed in lateral directions duringmechanical loading. The buckled structure is shown by the right configuration in Fig. 1 (a).In the third step, the buckled graphene is indented by a spherical indenter tip. Theindenter is moving toward the buckled graphene at a constant speed of 0.01 ˚Aps − . Fig. 1 (b)shows that, during the indentation process, two knots (indicated by stars) are created inthe middle region and these knots will move to the top and bottom regions in the buckledgraphene. This step is to mimic the collection of the wasted mechanical energy. Morespecifically, the buckled graphene is hit by the indenter (with wasted mechanical energy) atthe central position, which leads to the formation of two knots, i.e., the wasted mechanicalenergy can be collected and stored as the potential for these two knots (indicated by stars).4 P o t en t i a l pe r a t o m ( m e V ) Time (ps)(a) topbotmid
100 150 200 250 840 845 850 855 860 K no t po s i t i on ( Å ) Time (ps)(b) topbot D y=4.3 D t D y=−4.3 D t FIG. 3: (Color online) The motion of the knots created in step III in Fig. 2. (a) A close-up of thepotential per atom during the motion of the knots. Both knots are in the middle region beforet=856 ps, after which one knot moves to the top region and the other knot moves to the bottomregion. (b) The time dependence for the position of the knots. These knots travel at a speed of430 ms − . Two horizontal dashed lines depict the boundary for the two edge regions in graphenealong the y-direction. We note that the third structure shown in Fig. 1 (b) is very stable, which indicates thatbuckled graphene can store energy in the form of potential energies for knots near the edge.In the fourth step, the buckled graphene with two knots are thermalized within theNPT ensemble for another 200 ps. In the fifth step, the system is compressed again in thex-direction, and the knots will be loosened eventually. As a result, the knotting potentialenergy is released as kinetic energy, most of which concentrates at the free edges of graphene.The fifth step is to mimic the usage of the knoting potential through mechanical engineering.We now illustrate the whole process by examining the potential energy and kinetic en-5 E k pe r D O F pe r k B ( K ) Time (ps)
I II III IV Vopt com ind opt comknot unknot topbotmid
FIG. 4: (Color online) The evolution of the total kinetic energies for the top, bottom, and middleregions in the graphene of dimension 30 ×
200 ˚A. The y-axis shows the total kinetic energy dividedby the total degrees of freedom for each region. P o t en t i a l pe r a t o m ( m e V ) Time (ps) D V D V e =0.016 e =0.02 h = D V / D V e FIG. 5: (Color online) The potential energy per atom for the top region in graphene, which isbuckled by compression with strain magnitude ǫ = 0 .
016 and 0.02. The dimension of the grapheneis 30 ×
200 ˚A. The potential variation during the knot formation is ∆ V , while the potential variationduring the loosening is ∆ V . The efficiency ( η = ∆ V / ∆ V ) of the energy collection is displayed inthe inset. ergy during these five simulation steps. Fig. 2 shows the potential per atom for grapheneduring the whole simulation process, which indicates that the wasted mechanical energy istransformed into the knotting potential in the middle region at t=600 ps. These knots moveto the top and bottom regions at t ≈
856 ps as shown in Fig. 3 (a), at which the potential6
IG. 6: (Color online) The energy conversion process for buckled graphene which is indented atposition y ind = , , and (with respective to the width in the y-direction). The dimension of thegraphene is 30 ×
200 ˚A. Color indicates the atomic z-coordinate. P o t en t i a l pe r a t o m ( m e V ) Time (ps)
I II III IV Vopt com ind opt comknot unknot
FIG. 7: (Color online) The potential energy per atom for the top region in buckled graphene, whichis indented at y ind = , , , , , and (with respective to the width in the y-direction). Thedimension of the graphene is 30 ×
200 ˚A. of the top and bottom regions increases suddenly while the potential of the middle regiondecreases. The potential energies of these two knots are recorded in Fig. 3 (b), giving aspeed of 430 ms − for the motion of the knot. Both knots are loosened at t ≈ P o t en t i a l pe r a t o m ( m e V ) Time (ps)
I II III IV Vopt com ind opt comknot unknot
FIG. 8: (Color online) The potential per atom for the top region in graphene of width 150, 200,250, and 300 ˚A in the y-direction. The length is 30 ˚A in the x-direction. P o t en t i a l pe r a t o m ( m e V ) Time (ps)
I II III IV Vopt com ind opt comknot unknot topbotmid
FIG. 9: (Color online) Potential per atom for the top (black solid line), bottom (blue dashed line),and middle (red dotted line) regions during the energy collection, storage, and conversion in zigzaggraphene of dimension 30 ×
200 ˚A. atoms in the edge (top and bottom) region. From this simulation step, we learn that thewasted mechanical energy is eventually converted into the concentrated kinetic (thermal)energy, which is useful for engineering nano-devices.We further examine possible effects from using different simulation parameters. In theabove second simulation step, graphene is buckled by compressive strain ǫ along the x-direction. We find that the magnitude of the strain has considerable effect on the efficiencyof the energy conversion. Fig. 5 shows that the potential variation during the knot formation8 P o t en t i a l pe r a t o m ( m e V ) Time (ps)
I II III IV Vopt com ind opt comknot unknot
P=0P=1atm
FIG. 10: (Color online) The potential per atom for the top region in graphene of dimension30 ×
200 ˚A at pressure 1 atm and 0 atm. is ∆ V , which can be regarded as the external mechanical energy that can be collected bythe buckled graphene. The potential variation during the loosening is ∆ V , which is thework to be done to utilize the stored energy. The efficiency of the energy conversion can bedefined as η = ∆ V / ∆ V . With the increase of ǫ , the potential variation during knotting(∆ V ) increases, while ∆ V decreases. Hence, the efficiency increases with increasing ǫ asshown in the inset of Fig. 5. The efficiency for the energy conversion can be as high as 47%for ǫ = 0 . Fig. 6 shows that the position of the indenter during the indentation process is not impor-tant. The buckled graphene is indented at different positions, but the same knoting structureis formed at the end. Fig. 7 shows that the evolution of the potential per atom is almost thesame for the buckled graphene that are indented at different positions. The position insensi-tivity is a nice property for energy collection in sense that the buckled graphene can collectthe wasted mechanical energy that is dispersed in the space. Fig. 8 shows that the widthof graphene has no effect on the whole energy collection and conversion processes either.However, the energy harvest/storage/conversion processes are dependent on the creation ofknots, that can be stable at the edges of the graphene ribbons. The knots are created atthe middle of the graphene ribbon, and the knots will travel to and stay at the free edges.Thus a proper width to length ratio is required for the knots to be stable at the edges of thegraphene ribbon. 9he above graphene ribbons are of armchair orientation along the x-direction. We showin Fig. 9 that the orientation of the graphene ribbon is not important for the performanceof the energy device. We found similar energy collection, storage, and conversion processesin the graphene of zigzag orientation in the x-direction.Considering the large Young’s modulus (about 1.0 TPa) for graphene, the internal stress(pressure) is usually several orders larger than the ambient pressure of 101.3 kPa. Morespecifically, for a typical strain ǫ = 0 .
01 used in the present work, the internal stress is σ = Eǫ = 1 . T P a × .
01 = 10
GP a , which is five orders larger than the ambient pressure.Hence, the ambient pressure is neglectable. This speculation is verified in Fig. 10, whichshows that the potential curve for pressure P = 1 atm is almost the same as the potentialcurve for P = 0.We note that the working temperature for the energy collection and conversion based onthe buckled graphene is related to the intrinsic energy scale in this energy device. Morespecifically, we have introduced the parameter η = ∆ V / ∆ V as the efficiency for the energydevice, with ∆ V as the potential variation during the knot formation and ∆ V as thepotential variation during unknotting. That is ∆ V is the energy that can be collected bythe buckled graphene, while ∆ V is the external work to be done to explore the energystored in the device. In other words, ∆ V serves as a potential barrier for the knot. Hence,the working temperature should be lower than T C = ∆ V /k B . Otherwise, the knot canbe loosened by the thermal vibration, i.e., the knot becomes thermally unstable, if thethermal vibration energy is larger than the potential barrier ∆ V . From Fig. 10, we have∆ V ≈
10 meV, so the critical temperature is about T C ≈
116 K. We have checked that theknot indeed becomes thermally unstable at room temperature, so the working temperaturefor the energy device should be lower than 116 K. From Fig. 5, the potential variation ∆ V will increase with increasing strain ǫ , so the critical temperature T C can be increased byincreasing strain ǫ . However, as shown in the above, the efficiency for the energy devicewill be decreased with the increase of ∆ V , so there is a trade-off between higher criticaltemperature and higher efficiency in the real-world application of the buckled graphene forenergy harvest/storage/conversion.Finally, the energy harvest and storage will be valuable for some physical processes,especially on the nanoscale level. As an example, we propose one possible application ofthe buckled graphene for energy harvest/storage/conversion in nanomechanical resonators,10hich can work at temperatures from room temperature down to 10 K. The resonantoscillation energy will be decayed into wasted mechanical energy after a long time, which canbe harvested by the buckled graphene discussed in the present work. The harvested energywill be stored in the buckled graphene as knotting potential. We have found in our workthat the stored energy can be converted into the thermal vibration that is highly localized atthe free edges, which will be useful for the actuation of some localized resonant oscillationsof the nanomechanical resonators. Overall, we have demonstrated in the above that the buckled graphene can be used tocollect wasted mechanical energy. The dispersed mechanical energy can be collected throughhitting the buckled graphene at various positions, which leads to the same final knottingconfiguration. The buckled graphene is long in the y-direction, and this large surface areais helpful for energy harvest. Furthermore, the collected energy can be converted into thekinetic energy concentrated at the two free edges, which may be useful for mechanicalengineering of nano-devices.In conclusion, we have investigated the application of buckled graphene to collect dis-persed mechanical energy. The mechanical energy is stored within the buckled graphene inthe form of knotting potential, which can be utilized as the kinetic energy localized at thefree edges of graphene. One advanced feature for the energy conversion process using buck-led graphene is that such system is able to collect mechanical energy that is highly dispersedin the space, and convert the energy into highly localized kinetic (thermal) energy.
Acknowledgements
The author thanks Tien-Chong Chang and Xing-Ming Guo at SHUfor helpful discussions. The work is supported by the Recruitment Program of Global YouthExperts of China, the National Natural Science Foundation of China (NSFC) under GrantNo. 11504225 and the start-up funding from Shanghai University. ∗ [email protected] C. Lee, X. Wei, J. W. Kysar, and J. Hone, Science , 385 (2008). Z.-C. Ou-Yang., Z. bin Su, and C.-L. Wang, Physical Review Letters , 4055 (1997). Z.-C. Tu and Z.-C. Ou-Yang, Physical Review B , 233407 (2002). M. Arroyo and T. Belytschko, Physical Review B , 115415 (2004). Q. Lu, M. Arroyo, and R. Huang, Journal of Physics D: Applied Physics , 102002 (2009). S. Timoshenko and S. Woinowsky-Krieger,
Theory of Plates and Shells, 2nd ed (McGraw-Hill,New York, 1987). W. Bao, F. Miao, Z. Chen, H. Zhang, W. Jang, C. Dames, and C. N. Lau, Nature Nanotech-nology , 562 (2009). Q. Lu and R. Huang, International Journal of Applied Mechanics , 443 (2009). W. J. Patrick, Journal of Computational and Theoretical Nanoscience , 2338 (2010). A. Sakhaee-Pour, Computational Materials Science , 266 (2009). S. C. Pradhan and T. Murmu, Computational Materials Science , 268 (2009). S. C. Pradhan, Physics Letters, Section A: General, Atomic and Solid State Physics , 4182(2009). O. Frank, G. Tsoukleri, J. Parthenios, K. Papagelis, I. Riaz, R. Jalil, K. S. Novoselov, andC. Galiotis, ACS Nano , 3131 (2010). A. Farajpour, M. Mohammadi, A. R. Shahidi, and M. Mahzoon, Physica E: Low-dimensionalSystems and Nanostructures , 1820 (2011). V. Tozzini and V. Pellegrini, Journal of Physical Chemistry C , 25523 (2011). S. Rouhi and R. Ansari, Physica E: Low-dimensional Systems and Nanostructures , 764(2012). G. I. Giannopoulos, Computational Materials Science , 388 (2012). M. Neek-Amal and F. M. Peeters, Applied Physics Letters , 101905 (2012). H. . Shen, Y. . Xu, and C. . Zhang, Applied Physics Letters , 131905 (2013). T. Chang, Physical Review Letters , 175501 (2008). M. D. Stoller, S. Park, Y. Zhu, J. An, and R. S. Ruoff, Nano Letters , 3498 (2008). Y. Wang, Z. Shi, Y. Huang, Y. Ma, C. Wang, M. Chen, and Y. Chen, Journal of PhysicalChemistry C , 131030 (2009). C. Liu, Z. Yu, D. Neff, A. Zhamu, and B. Z. Jang, Nano Letters , 4863 (2010). Z. Weng, Y. Su, D.-W. Wang, F. Li, J. Du, and H.-M. Cheng, Advanced Materials , 917(2011). D. A. Brownson, D. K. Kampouris, and C. E. Banks, Journal of Power Source , 4873(2011). D. W. Brenner, O. A. Shenderova, J. A. Harrison, S. J. Stuart, B. Ni, and S. B. Sinnott, ournal of Physics: Condensed Matter , 783 (2002). S. Nose, Journal of Chemical Physics , 511 (1984). W. G. Hoover, Physical Review A , 1695 (1985). S. J. Plimpton, Journal of Computational Physics , 1 (1995). A. Stukowski, Modelling and Simulation in Materials Science and Engineering , 015012(2010). M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, Prog. Photovolt: Res.Appl. , 701 (2014). C. Chen, S. Rosenblatt, K. I. Bolotin, W. Kalb, P. Kim, I. Kymissis, H. L. Stormer, T. F. Heinz,and J. Hone, Nature Nanotechnology , 861 (2009). A. M. van der Zande, R. A. Barton, J. S. Alden, C. S. Ruiz-Vargas, W. S. Whitney, P. H. Q.Pham, J. Park, J. M. Parpia, H. G. Craighead, and P. L. McEuen, Nano Letters , 4869(2010). D. Garcia-Sanchez, A. M. van der Zande, A. S. Paulo, B. Lassagne, P. L. McEuen, andA. Bachtold, Nano Letters , 1399 (2008)., 1399 (2008).