Mechanical behaviors of micro-nano systems associated with van der Waals interaction

QIN Wen; KOU Zepu; LIU Xiaofei; ZHANG Zhuhua

doi:10.6052/1000-0992-24-019

Article Contents

Article Navigation > Advances in Mechanics > 2024 > Accepted Manuscript

Qin W, Kou Z P, Liu X F, Zhang Z H. Mechanical behaviors of micro-nano systems associated with van der Waals interaction. Advances in Mechanics, in press doi: 10.6052/1000-0992-24-019

Citation:

Qin W, Kou Z P, Liu X F, Zhang Z H. Mechanical behaviors of micro-nano systems associated with van der Waals interaction. Advances in Mechanics, in press doi: 10.6052/1000-0992-24-019

Qin W, Kou Z P, Liu X F, Zhang Z H. Mechanical behaviors of micro-nano systems associated with van der Waals interaction. Advances in Mechanics, in press doi: 10.6052/1000-0992-24-019

Citation:

Qin W, Kou Z P, Liu X F, Zhang Z H. Mechanical behaviors of micro-nano systems associated with van der Waals interaction. Advances in Mechanics, in press doi: 10.6052/1000-0992-24-019

PDF( 6848 KB)

Mechanical behaviors of micro-nano systems associated with van der Waals interaction

doi: 10.6052/1000-0992-24-019 cstr: 32046.14.1000-0992-24-019

Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

More Information

Corresponding author: liuxiaofei@nuaa.edu.cn; chuwazhang@nuaa.edu.cn
Received Date: 2024-05-27
Accepted Date: 2024-09-04

Available Online: 2024-09-14

Abstract

Abstract

van der Waals (vdW) interactions originating from quantum and thermal fluctuations are ubiquitous in natural and artificial systems. Accurate descriptions and characterizations of vdW interactions are crucial to understanding the mechanical behavior and realizing the mechanical design of micro-/nano-systems. This review summarized recent research progresses on vdW-dependent mechanical behaviors of micro-/nano-systems. First, we introduced vdW theories for atomic and molecular systems, including pairwise approximation, nonlocal density functional theory, adiabatic-connection fluctuating-dissipation theorem and many-body dispersion theory, as well as theories for continuum systems, including analytic, semi-analytic and numerical Lifshitz theory. Then, we reviewed the effects of vdW interactions on typical mechanical behaviors of two-dimensional materials and nano- and micro-electromechanical systems. We also discussed fascinating effects emerged from vdW interaction, including repulsive vdW force, non-monotonic vdW trap, Casimir rotational torque, Casimir flipping torque and vdW screening. Finally, we analyzed limitations of current vdW theories and presented the outlook for future development.
- van der Waals interaction,
- quantum effect,
- micro-electromechanical system,
- two-dimensional material,
- mechanical behavior

FullText(HTML)

References(126)

References

[1]	朗道, 栗弗希兹. 2012. 流体动力学. 李植, 译. 第5版. 北京: 高等教育出版社, 1-608 (Landau, Lifshitz. 2012. Fluid mechanics. Li Z, translate. 5th edition. Beijing: Higher Education Press, 1-608 (in Chinese). Landau, Lifshitz. 2012. Fluid mechanics. Li Z, translate. 5th edition. Beijing: Higher Education Press, 1-608 (in Chinese.
[2]	商克栋, 郑韶先, 鞠鹏飞, 等. 2018. 南海海洋大气环境二硫化钼纳米多层薄膜摩擦学行为研究. 摩擦学学报, 38 (4): 417-429 (Shang K D, Zheng S X, Ju P F, et al. 2018. Tribological performance of MoS₂/Pb-Ti nano-multilayer coating applied in marine atmospheric environment of South China Sea. Tribology, 38 (4): 417-429 (in Chinese). Shang K D, Zheng S X, Ju P F, et al. 2018. Tribological performance of MoS₂/Pb-Ti nano-multilayer coating applied in marine atmospheric environment of South China Sea. Tribology, 38(4): 417-429 (in Chinese.
[3]	温诗铸. 2018. 摩擦学原理. 第5版. 北京: 清华大学出版社, 1-484 (Wen S Z. 2018. Principles of tribology. 5th edition. Beijing: Tsinghua University Press, 1-484 (in Chinese)). Wen S Z. 2018. Principles of tribology. 5th edition. Beijing: Tsinghua University Press, 1-484 (in Chinese).
[4]	Ambrosetti A, Ferri N, DiStasio J R A, et al. 2016. Wavelike charge density fluctuations and van der Waals interactions at the nanoscale. Science, 351(6278): 1171-1176. doi: 10.1126/science.aae0509
[5]	Ambrosetti A, Silvestrelli P L. 2019. Faraday-like screening by two-dimensional nanomaterials: A scale-dependent tunable effect. J. Phys. Chem. Lett., 10(9): 2044-2050. doi: 10.1021/acs.jpclett.9b00860
[6]	Antezza M, Chan H B, Guizal B, et al. 2020. Giant Casimir torque between rotated gratings and the $\theta $ = 0 anomaly. Phys. Rev. Lett., 124(1): 013903. doi: 10.1103/PhysRevLett.124.013903
[7]	Aykol M, Hou B, Dhall R, et al. 2014. Clamping instability and van der Waals forces in carbon nanotube mechanical resonators. Nano Lett., 14(5): 2426-2430. doi: 10.1021/nl500096p
[8]	Barash Y S. 1978. Moment of van der Waals forces between anisotropic bodies. Radiophys. Quantum Electron., 21(11): 1138-1143. doi: 10.1007/BF02121382
[9]	Bixon M, Zwanzig R. 1971. Brownian motion of a nonlinear oscillator. J. Stat. Phys., 3(3): 245-260. doi: 10.1007/BF01011383
[10]	Björkman T, Gulans A, Krasheninnikov A, et al. 2012a. Are we van der Waals ready. J. Phys.: Condens. Matter, 24(42): 424218. doi: 10.1088/0953-8984/24/42/424218
[11]	Björkman T, Gulans A, Krasheninnikov A, et al. 2012b. van der waals bonding in layered compounds from advanced density-functional first-principles calculations. Phys. Rev. Lett., 108(23): 235502. doi: 10.1103/PhysRevLett.108.235502
[12]	Boyer T H. 1974. Penetration of the electric and magnetic velocity fields of a nonrelativistic point charge into a conducting plane. Phys. Rev. A, 9(1): 68. doi: 10.1103/PhysRevA.9.68
[13]	Broer W, Lu B S, Podgornik R. 2021. Qualitative chirality effects on the Casimir-Lifshitz torque with liquid crystals. Phys. Rev. Res., 3: 033238.
[14]	Buks E, Roukes M L. 2001. Stiction, adhesion energy, and the Casimir effect in micromechanical systems. Phys. Rev. B, 63(3): 033402.
[15]	Canaguier-Durand A, Maia N P A, Cavero-Pelaez I, et al. 2009. Casimir interaction between plane and spherical metallic surfaces. Phys. Rev. Lett., 102(23): 230404. doi: 10.1103/PhysRevLett.102.230404
[16]	Casimir, Hendrick B G. 1948. On the attraction between two perfectly conducting plates. Proc. K. Ned. Akad. Wet., 51: 793-796.
[17]	Chan H, Aksyuk V, Kleiman R, et al. 2001a. Nonlinear micromechanical Casimir oscillator. Phys. Rev. Lett., 87(21): 211801. doi: 10.1103/PhysRevLett.87.211801
[18]	Chan H, Aksyuk V, Kleiman R, et al. 2001b. Quantum mechanical actuation of microelectromechanical systems by the Casimir force. Science, 291(5510): 1941-1944. doi: 10.1126/science.1057984
[19]	Chen F, Kou Z, Jiang Z, et al. 2024. Physical limit of nonlinear brownian oscillators in quantum trap. J. Phys. Chem. Lett., 15: 1719-1725. doi: 10.1021/acs.jpclett.3c03334
[20]	Chen L, Chang K. 2020. Chiral-anomaly-driven Casimir-Lifshitz torque between Weyl semimetals. Phys. Rev. Lett., 125: 047402.
[21]	Chu X, Dalgarno A. 2004. Linear response time-dependent density functional theory for van der Waals coefficients. J. Chem. Phys., 121(9): 4083-4088. doi: 10.1063/1.1779576
[22]	Deng Z, Smolyanitsky A, Li Q, et al. 2012. Adhesion-dependent negative friction coefficient on chemically modified graphite at the nanoscale. Nat. Mater., 11(12): 1032-1037. doi: 10.1038/nmat3452
[23]	Dienwiebel M, Verhoeven G S, Pradeep N, et al. 2004. Superlubricity of graphite. Phys. Rev. Lett., 92(12): 126101. doi: 10.1103/PhysRevLett.92.126101
[24]	Dion M, Rydberg H, Schröder E, et al. 2004. van der Waals density functional for general geometries. Phys. Rev. Lett., 92(24): 246401. doi: 10.1103/PhysRevLett.92.246401
[25]	Dobson J F, Wang J, Dinte B P, et al. 2005. Soft cohesive forces. Int. J. Quantum Chem., 101(5): 579-598. doi: 10.1002/qua.20314
[26]	Dzyaloshinskii I E, Lifshitz E M, Pitaevskii L P. 1961. The general theory of van der Waals forces. Adv. Phys., 10(38): 165-209. doi: 10.1080/00018736100101281
[27]	Fan L S, Tai Y C, Muller R S. 1988. Integrated movable micromechanical structures for sensors and actuators. IEEE Trans. Electron Devices, 35(6): 724-730. doi: 10.1109/16.2523
[28]	Franosch T, Grimm M, Belushkin M, et al. 2011. Resonances arising from hydrodynamic memory in brownian motion. Nature, 478(7367): 85-88. doi: 10.1038/nature10498
[29]	French R H, Parsegian V A, Podgornik R, et al. 2010. Long range interactions in nanoscale science. Rev. Mod. Phys., 82(2): 1887. doi: 10.1103/RevModPhys.82.1887
[30]	Gao H, Yao H. 2004. Shape insensitive optimal adhesion of nanoscale fibrillar structures. Proc. Natl. Acad. Sci., 101(21): 7851-7856. doi: 10.1073/pnas.0400757101
[31]	Gao W, Tkatchenko A. 2013. Electronic structure and van der Waals interactions in the stability and mobility of point defects in semiconductors. Phys. Rev. Lett., 111(4): 045501. doi: 10.1103/PhysRevLett.111.045501
[32]	Garcia-Sanchez D, Fong K Y, Bhaskaran H, et al. 2012. Casimir force and in situ surface potential measurements on nanomembranes. Phys. Rev. Lett., 109(2): 027202. doi: 10.1103/PhysRevLett.109.027202
[33]	Gies H, Klingmüller K. 2006. Casimir effect for curved geometries: Proximity-force-approximation validity limits. Phys. Rev. Lett., 96(22): 220401. doi: 10.1103/PhysRevLett.96.220401
[34]	Grimme S. 2004. Accurate description of van der Waals complexes by density functional theory including empirical corrections. J. Comput. Chem., 25(12): 1463-1473. doi: 10.1002/jcc.20078
[35]	Grimme S. 2006. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem., 27(15): 1787-1799. doi: 10.1002/jcc.20495
[36]	Grimme S, Antony J, Ehrlich S, et al. 2010. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys, 132(15): 154104. doi: 10.1063/1.3382344
[37]	Guo J, Zhao Y. 2004. Influence of van der Waals and Casimir forces on electrostatic torsional actuators. J. Microelectromech. Syst., 13(6): 1027-1035. doi: 10.1109/JMEMS.2004.838390
[38]	Harl J, Kresse G. 2008. Cohesive energy curves for noble gas solids calculated by adiabatic connection fluctuation-dissipation theory. Phys. Rev. B, 77(4): 045136. doi: 10.1103/PhysRevB.77.045136
[39]	Hartmann M, Ingold G L, Neto P A M. 2018. Advancing numerics for the Casimir effect to experimentally relevant aspect ratios. Phys Scr., 93(11): 114003. doi: 10.1088/1402-4896/aae34e
[40]	Hiller U. 1971. Form und funktion der hautsinnesorgane bei gekkoniden. Forma Functio, 4: 240-253.
[41]	Hu C, Chen J, Zhou X, et al. 2024. Collapse of carbon nanotubes due to local high-pressure from van der Waals encapsulation. Nat. Commun., 15(1): 3486. doi: 10.1038/s41467-024-47903-3
[42]	Huang J, Rauscher S, Nawrocki G, et al. 2017. Charmm36m: An improved force field for folded and intrinsically disordered proteins. Nat. Methods, 14(1): 71-73. doi: 10.1038/nmeth.4067
[43]	Jiang Z, Chen F, Kou Z, et al. 2023. Large Casimir flipping torque in quantum trap. J. Phys. Chem. B, 128(1): 350-357.
[44]	Kardar M, Golestanian R. 1999. The “friction” of vacuum, and other fluctuation-induced forces. Rev. Mod. Phys., 71(4): 1233. doi: 10.1103/RevModPhys.71.1233
[45]	Kavokine N, Bocquet M L, Bocquet L. 2002. Fluctuation-induced quantum friction in nanoscale water flows. Nature, 602(7895): 84-90.
[46]	Khestanova E, Guinea F, Fumagalli L, et al. 2016. Universal shape and pressure inside bubbles appearing in van der Waals heterostructures. Nat. Commun., 7(1): 12587. doi: 10.1038/ncomms12587
[47]	Klimchitskaya G, Mohideen U, Mostepanenko V. 2009. The Casimir force between real materials: Experiment and theory. Rev. Mod. Phys., 81(4): 1827. doi: 10.1103/RevModPhys.81.1827
[48]	Kolmogorov A N, Crespi V H. 2005. Registry-dependent interlayer potential for graphitic systems. Phys. Rev. B, 71(23): 235415. doi: 10.1103/PhysRevB.71.235415
[49]	Lebègue S, Harl J, Gould T, et al. 2010. Cohesive properties and asymptotics of the dispersion interaction in graphite by the random phase approximation. Phys. Rev. Lett., 105(19): 196401. doi: 10.1103/PhysRevLett.105.196401
[50]	Lee K, Murray É D, Kong L, et al. 2010. Higher-accuracy van der Waals density functional. Phys. Rev. B, 82(8): 081101. doi: 10.1103/PhysRevB.82.081101
[51]	Lennard-Jones J E. 1931. Cohesion. Proc. Phys. Soc., 43(5): 461. doi: 10.1088/0959-5309/43/5/301
[52]	Leven I, Azuri I, Kronik L, et al. 2014. Inter-layer potential for hexagonal boron nitride. J. Chem. Phys., 140(10): 104106. doi: 10.1063/1.4867272
[53]	Levitov L S. 1989. van der Waals’ friction. Europhys. Lett., 8(6): 499-504. doi: 10.1209/0295-5075/8/6/002
[54]	Lifshitz E M. 1956. The theory of molecular attractive force between solid bodies. J. Exp. Theor. Phys., 29: 83-94.
[55]	Lorentz H A. 1907. Abhandlungen über theoretische physik. Teubner, 2: 1907.
[56]	Li B, Yin J, Liu X, et al. 2019. Probing van der Waals interactions at two-dimensional heterointerfaces. Nat. Nanotechnol., 14(6): 567-572. doi: 10.1038/s41565-019-0405-2
[57]	Li B, Liu X, Guo W. 2021. Probing interactions at two-dimensional heterointerfaces by boron nitride-wrapped tip. Nano Res., 14: 692-698. doi: 10.1007/s12274-020-3098-9
[58]	Li M, Reimers J R, Dobson J F, et al. 2018. Faraday cage screening reveals intrinsic aspects of the van der Waals attraction. Proc. Natl. Acad. Sci., 115(44): 10295-10302.
[59]	Liu X, Hermann J, Tkatchenko A. 2016. Communication: Many-body stabilization of non-covalent interactions: Structure, stability, and mechanics of Ag₃Co(Cn)₆ framework. J. Chem. Phys., 145(24): 241101. doi: 10.1063/1.4972810
[60]	Liu X, Zhang Z, Guo W. 2018. van der Waals screening by graphenelike monolayers. Phys. Rev. B, 97(24): 241411. doi: 10.1103/PhysRevB.97.241411
[61]	Liu X, Yang J, Guo W. 2020. Semiempirical van der Waals method for two-dimensional materials with incorporated dielectric functions. Phys. Rev. B, 101(4): 045428. doi: 10.1103/PhysRevB.101.045428
[62]	Liu Z, Yang J, Grey F, et al. 2012. Observation of microscale superlubricity in graphite. Phys. Rev. Lett., 108(20): 205503. doi: 10.1103/PhysRevLett.108.205503
[63]	Lim C H Y X, Nesladek M, Loh K P. 2014. Observing high-pressure chemistry in graphene bubbles. Angew. Chem., Int. Ed., 53(1): 215-219. doi: 10.1002/anie.201308682
[64]	Lim C H Y X, Sorkin A, Bao Q, et al. 2013. A hydrothermal anvil made of graphene nanobubbles on diamond. Nat. Commun., 4(1): 1556.
[65]	London F. 1930. Zur theorie und systematik der molekularkräfte. Z. Angew. Phys., 63(3): 245-279.
[66]	Mak K F, Lee C, Hone J, et al. 2010. Atomically thin MoS₂: A new direct-gap semiconductor. Phys. Rev. Lett., 105(13): 136805. doi: 10.1103/PhysRevLett.105.136805
[67]	Marom N, Bernstein J, Garel J, et al. 2010. Stacking and registry effects in layered materials: The case of hexagonal boron nitride. Phys. Rev. Lett., 105(4): 046801. doi: 10.1103/PhysRevLett.105.046801
[68]	Mohideen U, Roy A. 1998. Precision measurement of the Casimir force from 0.1 to 0.9 μm. Phys. Rev. Lett., 81(21): 4549. doi: 10.1103/PhysRevLett.81.4549
[69]	Munday J N, Capasso F, Parsegian V A. 2009. Measured long-range repulsive Casimir–Lifshitz forces. Nature, 457(7226): 170-173. doi: 10.1038/nature07610
[70]	Munday J N, Iannuzzi D, Barash Y, et al. 2005. Torque on birefringent plates induced by quantum fluctuations. Phys. Rev. A, 71: 042102
[71]	Neto P M, Lambrecht A, Reynaud S. 2005. Roughness correction to the Casimir force: Beyond the proximity force approximation. Europhys. Lett., 69(6): 924. doi: 10.1209/epl/i2004-10433-9
[72]	Neto A C, Guinea F, Peres N M, et al. 2009. The electronic properties of graphene. Rev. Mod. Phys., 81(1): 109. doi: 10.1103/RevModPhys.81.109
[73]	Ouyang W, Mandelli D, Urbakh M, et al. 2018. Nanoserpents: Graphene nanoribbon motion on two-dimensional hexagonal materials. Nano Lett., 18(9): 6009-6016. doi: 10.1021/acs.nanolett.8b02848
[74]	Parsegian V, Weiss G H. 1972. Dielectric anisotropy and the van der Waals interaction between bulk media. J. Adhes., 3(4): 259-267. doi: 10.1080/00218467208072197
[75]	Parsegian V. 2005. Van der Waals forces: A handbook for biologists, chemists, engineers, and physicists. New York: Cambridge University Press, 277-318.
[76]	Pendry J B. 1997. Shearing the vacuum-quantum friction. J. Phys. Condens. Matter, 9(47): 10301. doi: 10.1088/0953-8984/9/47/001
[77]	Persson B, Zhang Z. 1998. Theory of friction: Coulomb drag between two closely spaced solids. Phys. Rev. B, 57(12): 7327. doi: 10.1103/PhysRevB.57.7327
[78]	Ponder J W, Case D A. 2003. Force fields for protein simulations. Adv. Protein. Chem., 66: 27-85.
[79]	Rahi S J, Emig T, Graham N, et al. 2009. Scattering theory approach to electrodynamic Casimir forces. Phys. Rev. D, 80(8): 085021. doi: 10.1103/PhysRevD.80.085021
[80]	Rammer J. 2011. Quantum field theory of non-equilibrium states. Cambridge: Cambridge University Press, 79-119.
[81]	Reid M H, Rodriguez A W, White J, et al. 2009. Efficient computation of Casimir interactions between arbitrary 3D objects. Phys. Rev. Lett., 103(4): 040401. doi: 10.1103/PhysRevLett.103.040401
[82]	Reid M H, White J, Johnson S G. 2013. Fluctuating surface currents: An algorithm for efficient prediction of Casimir interactions among arbitrary materials in arbitrary geometries. Phys. Rev. A, 88(2): 022514. doi: 10.1103/PhysRevA.88.022514
[83]	Rokni H, Lu W. 2020. Direct measurements of interfacial adhesion in 2d materials and van der Waals heterostructures in ambient air. Nat. Commun., 11(1): 5607. doi: 10.1038/s41467-020-19411-7
[84]	Rytov S. 1959. Theory of electrical fluctuations and thermal radiation. Bedford: Air Force Cambridge Research Center, 1-265.
[85]	Satterthwaite P F, Zhu W, Jastrzebska-Perfect P, et al. 2024. van der Waals device integration beyond the limits of van der Waals forces using adhesive matrix transfer. Nat. Electron., 7(1): 17-28.
[86]	Schaich W L, Harris J. 1981. Dynamic corrections to van der Waals potentials. J. Phys. F: Met. Phys., 11(1): 65-78. doi: 10.1088/0305-4608/11/1/011
[87]	Somers D A, Garrett J L, Palm K J, et al. 2018. Measurement of the Casimir torque. Nature, 564(7736): 386-389. doi: 10.1038/s41586-018-0777-8
[88]	Somers D A T, Munday J N. 2015. Rotation of a liquid crystal by the Casimir torque. Phys. Rev. A, 91: 032520.
[89]	Somers D A, Munday J N. 2017. Casimir-Lifshitz torque enhancement by retardation and intervening dielectrics. Phys. Rev. Lett., 119: 183001.
[90]	Song Y, Mandelli D, Hod O, et al. 2018. Robust microscale superlubricity in graphite/hexagonal boron nitride layered heterojunctions. Nat. Mater., 17(10): 894-899. doi: 10.1038/s41563-018-0144-z
[91]	Sparnaay M J. 1958. Measurements of attractive forces between flat plates. Physica, 24(6-10): 751-764. doi: 10.1016/S0031-8914(58)80090-7
[92]	Stöhr M, Sadhukhan M, Al-Hamdani Y S, et al. 2021. Coulomb interactions between dipolar quantum fluctuations in van der Waals bound molecules and materials. Nat. Commun., 12(1): 137. doi: 10.1038/s41467-020-20473-w
[93]	Sun H. 1998. Compass: An ab initio force-field optimized for condensed-phase applications overview with details on alkane and benzene compounds. J. Phys. Chem. B, 102(38): 7338-7364. doi: 10.1021/jp980939v
[94]	Tang K, Qi W, Wei Y, et al. 2022. High-throughput calculation of interlayer van der Waals forces validated with experimental measurements. Research, 2022: 9765121.
[95]	Teodorovich E. 1978. On the contribution of macroscopic van der Waals interactions to frictional force. Proc. R. Soc. London A, 362(1708): 71-77. doi: 10.1098/rspa.1978.0121
[96]	Thiyam P, Parashar P, Shajesh K V, et al. 2018. Distance-dependent sign reversal in the Casimir-Lifshitz torque. Phys. Rev. Lett., 120: 131601.
[97]	Tkatchenko A, Scheffler M. 2009. Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data. Phys. Rev. Lett., 102(7): 69-72.
[98]	Tkatchenko A, Rossi M, Blum V, et al. 2011. Unraveling the stability of polypeptide helices: Critical role of van der Waals interactions. Phys. Rev. Lett., 106(11): 118102. doi: 10.1103/PhysRevLett.106.118102
[99]	Tkatchenko A, DiStasio J R A, Car R, et al. 2012. Accurate and efficient method for many-body van der Waals interactions. Phys. Rev. Lett., 108(23): 236402. doi: 10.1103/PhysRevLett.108.236402
[100]	Tsoi S, Dev P, Friedman A L, et al. 2014. van der Waals screening by single-layer graphene and molybdenum disulfide. Acs Nano, 8(12): 12410-12417. doi: 10.1021/nn5050905
[101]	van der Waals J D. 1873. On the continuity of the gas and liquid state. [Ph. D. thesis]. Netherlands: University of Leiden, 301.
[102]	Vasu K, Prestat E, Abraham J, et al. 2016. van der Waals pressure and its effect on trapped interlayer molecules. Nat. Commun., 7(1): 12168. doi: 10.1038/ncomms12168
[103]	Volokitin A I, Persson B N J. 1999. Theory of friction: The contribution from a fluctuating electromagnetic field. J. Phys. Condens. Matter, 11(2): 345. doi: 10.1088/0953-8984/11/2/003
[104]	Volokitin A I, Persson B N J. 2002. Dissipative van der Waals interaction between a small particle and a metal surface. Phys. Rev. B, 65(11): 115419. doi: 10.1103/PhysRevB.65.115419
[105]	Volokitin A I, Persson B N J. 2006. Quantum field theory of van der Waals friction. Phys. Rev. B, 74(20): 205413. doi: 10.1103/PhysRevB.74.205413
[106]	Volokitin A I, Persson B N J. 2007. Near-field radiative heat transfer and noncontact friction. Rev. Mod. Phys., 79(4): 1291. doi: 10.1103/RevModPhys.79.1291
[107]	Vydrov O A, Van V T. 2010. Nonlocal van der Waals density functional: The simpler the better. J. Chem. Phys., 133: 244103. doi: 10.1063/1.3521275
[108]	Wang G, Dai Z, Wang Y, et al. 2017. Measuring interlayer shear stress in bilayer graphene. Phys. Rev. Lett., 119(3): 036101. doi: 10.1103/PhysRevLett.119.036101
[109]	Wang G, Dai Z, Xiao J, et al. 2019. Bending of multilayer van der Waals materials. Phys. Rev. Lett., 123(11): 116101. doi: 10.1103/PhysRevLett.123.116101
[110]	Wang H, Zhang L, Han J, et al. 2018. Deepmd-kit: A deep learning package for many-body potential energy representation and molecular dynamics. Comput. Phys. Commun., 228: 178-184. doi: 10.1016/j.cpc.2018.03.016
[111]	Wen J, Li W, Chen S, et al. 2016. Simulations of molecular self-assembled monolayers on surfaces: Packing structures, formation processes and functions tuned by intermolecular and interfacial interactions. Phys. Chem. Chem. Phys., 18(33): 22757-22771. doi: 10.1039/C6CP01049K
[112]	Werder T, Walther J H, Jaffe R, et al. 2003. On the water-carbon interaction for use in molecular dynamics simulations of graphite and carbon nanotubes. J. Phys. Chem. B, 107(6): 1345-1352. doi: 10.1021/jp0268112
[113]	Woods L, Dalvit D A R, Tkatchenko A, et al. 2016. Materials perspective on Casimir and van der Waals interactions. Rev. Mod. Phys., 88(4): 045003. doi: 10.1103/RevModPhys.88.045003
[114]	Wu Q, Yang W. 2002. Empirical correction to density functional theory for van der Waals interactions. J. Chem. Phys., 116(2): 515-524. doi: 10.1063/1.1424928
[115]	Xie R, Montanini P, Akarvardar K, et al. 2016. A 7 nm finfet technology featuring euv patterning and dual strained high mobility channels. IEEE, 2016 IEEE international electron devices meeting, San Francisco. San Francisco: IEEE, 2016 : 2-7.
[116]	Yang J, Liu X, Guo W. 2021. Nonmonotonous distance dependence of van der Waals screening by a dielectric layer. J. Phys. Chem. Lett., 12(20): 4993-4999. doi: 10.1021/acs.jpclett.1c00870
[117]	Yang K, Chen Y, Pan F, et al. 2016. Buckling behavior of substrate supported graphene sheets. Materials, 9(1): 32. doi: 10.3390/ma9010032
[118]	Yu H Y, Eckmann D M, Ayyaswamy P S, et al. 2016. Effect of wall-mediated hydrodynamic fluctuations on the kinetics of a brownian nanoparticle. Proc. R. Soc. A, 472(2196): 20160397. doi: 10.1098/rspa.2016.0397
[119]	Yu J, Chary S, Das S, et al. 2011. Gecko-inspired dry adhesive for robotic applications. Adv. Funct. Mater., 21(16): 3010-3018. doi: 10.1002/adfm.201100493
[120]	Yuet P K, Blankschtein D. 2010. Molecular dynamics simulation study of water surfaces: Comparison of flexible water models. J. Phys. Chem. B, 114(43): 13786-13795. doi: 10.1021/jp1067022
[121]	Zhang G X, Tkatchenko A, Paier J, et al. 2011. van der Waals interactions in ionic and semiconductor solids. Phys. Rev. Lett., 107(24): 245501. doi: 10.1103/PhysRevLett.107.245501
[122]	Zhang Y, Wang L. 2020. Effects of the van der Waals force on the vibration of typical multi-layered two-dimensional nanostructures. Sci. Rep., 10(1): 644. doi: 10.1038/s41598-020-57522-9
[123]	Zhang Y, Zhang H, Wang X, et al. 2024. Magnetic-field tuning of the Casimir force. Nat. Phys., 20: 1282-1287. doi: 10.1038/s41567-024-02521-0
[124]	Zhao W, Qiu H, Guo W. 2022. A deep neural network potential for water confined in graphene nanocapillaries. J. Phys. Chem. C, 126(25): 10546-10553. doi: 10.1021/acs.jpcc.2c02423
[125]	Zhao R, Li L, Yang S, et al. 2019. Stable Casimir equilibria and quantum trapping. Science, 364(6444): 984-987. doi: 10.1126/science.aax0916
[126]	Zhong W, Tomanek D. 1990. First-principles theory of atomic-scale friction. Phys. Rev. Lett., 64(25): 3054. doi: 10.1103/PhysRevLett.64.3054