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Surface Energy and Nanoscale Mechanics

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Handbook of Materials Modeling

Abstract

The mechanical response of nanostructures, or materials with characteristic features at the nanoscale, differs from their coarser counterparts. An important physical reason for this size-dependent phenomenology is that surface or interface properties are different than those of the bulk material and acquire significant prominence due to an increased surface-to-volume ratio at the nanoscale. In this chapter, we provide an introductory tutorial on the continuum approach to incorporate the effect of surface energy, stress, and elasticity and address the size-dependent elastic response at the nanoscale. We present some simple illustrative examples that underscore both the physics underpinning the capillary phenomenon in solids as well as a guide to the use of the continuum theory of surface energy.

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References

  • Altenbach H, Eremeyev VA, Morozov NF (2013) Mechanical properties of materials considering surface effects. In: IUTAM symposium on surface effects in the mechanics of nanomaterials and heterostructures. Springer, pp 105–115

    Google Scholar 

  • Biria A, Maleki M, Fried E (2013) Continuum theory for the edge of an open lipid bilayer. Adv Appl Mech 21:1–78

    Google Scholar 

  • Cammarata RC (2009) Generalized thermodynamics of surfaces with applications to small solid systems. Solid State Phys 61:1–75

    Article  Google Scholar 

  • Cammarata R, Sieradzki K, Spaepen F (2000) Simple model for interface stresses with application to misfit dislocation generation in epitaxial thin films. J Appl Phys 87(3):1227–1234

    Article  ADS  Google Scholar 

  • Chatzigeorgiou G, Meraghni F, Javili A (2017) Generalized interfacial energy and size effects in composites. J Mech Phys Solids 106:257–282

    Article  ADS  MathSciNet  Google Scholar 

  • Chhapadia P, Mohammadi P, Sharma P (2011) Curvature-dependent surface energy and implications for nanostructures. J Mech Phys Solids 59(10):2103–2115

    Article  ADS  MathSciNet  Google Scholar 

  • Courant R, Hilbert D (1953) Methods of mathematical physics, vol I (First English ed.). Interscience Publishers, Inc., New York

    MATH  Google Scholar 

  • Duan H, Wang Jx, Huang Z, Karihaloo BL (2005) Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress. J Mech Phys Solids 53(7): 1574–1596

    Article  ADS  MathSciNet  Google Scholar 

  • Duan H, Wang J, Karihaloo BL (2009) Theory of elasticity at the nanoscale. In: Advances in applied mechanics, vol 42. Elsevier, Amsterdam, pp 1–68

    Google Scholar 

  • Fischer F, Waitz T, Vollath D, Simha N (2008) On the role of surface energy and surface stress in phase-transforming nanoparticles. Prog Mater Sci 53(3):481–527

    Article  Google Scholar 

  • Fried E, Todres RE (2005) Mind the gap: the shape of the free surface of a rubber-like material in proximity to a rigid contactor. J Elast 80(1–3):97–151

    Article  MathSciNet  Google Scholar 

  • de Gennes PG, Brochard-Wyart F, Quere D (2004) Capillarity and wetting phenomenon. Springer, New York

    Book  Google Scholar 

  • Gurtin ME, Murdoch AI (1975a) Addenda to our paper a continuum theory of elastic material surfaces. Arch Ration Mech Anal 59(4):389–390

    Article  Google Scholar 

  • Gurtin ME, Murdoch AI (1975b) A continuum theory of elastic material surfaces. Arch Ration Mech Anal 57(4):291–323

    Article  MathSciNet  Google Scholar 

  • Gurtin ME, Murdoch AI (1978) Surface stress in solids. Int J Solids Struct 14(6):431–440

    Article  Google Scholar 

  • Gurtin M, Weissmüller J, Larche F (1998) A general theory of curved deformable interfaces in solids at equilibrium. Philos Mag A 78(5):1093–1109

    Article  ADS  Google Scholar 

  • Gurtin ME, Fried E, Anand L (2010) The mechanics and thermodynamics of continua. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Haiss W (2001) Surface stress of clean and adsorbate-covered solids. Rep Prog Phys 64(5):591

    Article  ADS  Google Scholar 

  • Henann DL, Bertoldi K (2014) Modeling of elasto-capillary phenomena. Soft Matter 10(5): 709–717

    Article  ADS  Google Scholar 

  • Huang Z, Sun L (2007) Size-dependent effective properties of a heterogeneous material with interface energy effect: from finite deformation theory to infinitesimal strain analysis. Acta Mech 190(1–4):151–163

    Article  Google Scholar 

  • Huang Z, Wang Jx (2006) A theory of hyperelasticity of multi-phase media with surface/interface energy effect. Acta Mech 182(3–4):195–210

    Article  Google Scholar 

  • Huang Z, Wang J (2013) Micromechanics of nanocomposites with interface energy effect. Handbook of micromechanics and nanomechanics. Pan Stanford Publishing, Singapore

    Google Scholar 

  • Ibach H (1997) The role of surface stress in reconstruction, epitaxial growth and stabilization of mesoscopic structures. Surf Sci Rep 29(5–6):195–263

    Article  ADS  Google Scholar 

  • Javili A, McBride A, Steinmann P (2013) Thermomechanics of solids with lower-dimensional energetics: on the importance of surface, interface, and curve structures at the nanoscale. A unifying review. Appl Mech Rev 65(1):010802

    Article  ADS  Google Scholar 

  • Javili A, Ottosen NS, Ristinmaa M, Mosler J (2017) Aspects of interface elasticity theory. Math Mech Solids 23:1081286517699041

    MathSciNet  MATH  Google Scholar 

  • Li S, Wang G (2008) Introduction to micromechanics and nanomechanics. World Scientific Publishing Company, Singapore

    Book  Google Scholar 

  • Liu L, Yu M, Lin H, Foty R (2017) Deformation and relaxation of an incompressible viscoelastic body with surface viscoelasticity. J Mech Phys Solids 98:309–329

    Article  ADS  MathSciNet  Google Scholar 

  • Miller RE, Shenoy VB (2000) Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11(3):139

    Article  ADS  Google Scholar 

  • Müller P, Saúl A (2004) Elastic effects on surface physics. Surf Sci Rep 54(5–8):157–258

    Article  ADS  Google Scholar 

  • Murdoch AI (2005) Some fundamental aspects of surface modelling. J Elas 80(1–3):33

    Article  MathSciNet  Google Scholar 

  • Pala RGS, Liu F (2004) Determining the adsorptive and catalytic properties of strained metal surfaces using adsorption-induced stress. J Chem Phys 120(16):7720–7724

    Article  ADS  Google Scholar 

  • Park HS (2008) Strain sensing through the resonant properties of deformed metal nanowires. J Appl Phys 104(1):013516

    Article  ADS  Google Scholar 

  • Park HS, Klein PA, Wagner GJ (2006) A surface cauchy–born model for nanoscale materials. Int J Numer Methods Eng 68(10):1072–1095

    Article  MathSciNet  Google Scholar 

  • Sharma P, Ganti S, Bhate N (2003) Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities. Appl Phys Lett 82(4):535–537

    Article  ADS  Google Scholar 

  • Steigmann D, Ogden R (1997) Plane deformations of elastic solids with intrinsic boundary elasticity. In: Proceedings of the royal society of London A: mathematical, physical and engineering sciences, the royal society, vol 453, pp 853–877

    Article  MathSciNet  Google Scholar 

  • Steigmann D, Ogden R (1999) Elastic surface substrate interactions. In: Proceedings of the royal society of London A: mathematical, physical and engineering sciences, the royal society, vol 455, pp 437–474

    Article  ADS  MathSciNet  Google Scholar 

  • Style RW, Hyland C, Boltyanskiy R, Wettlaufer JS, Dufresne ER (2013) Surface tension and contact with soft elastic solids. Nat Commun 4:2728

    Article  ADS  Google Scholar 

  • Style RW, Jagota A, Hui CY, Dufresne ER (2017) Elastocapillarity: surface tension and the mechanics of soft solids. Ann Rev Conden Matter Phys 8:99–118

    Article  ADS  Google Scholar 

  • Suo Z, Lu W (2000) Forces that drive nanoscale self-assembly on solid surfaces. J Nanopart Res 2(4):333–344

    Article  Google Scholar 

  • Wang J, Huang Z, Duan H, Yu S, Feng X, Wang G, Zhang W, Wang T (2011) Surface stress effect in mechanics of nanostructured materials. Acta Mechanica Solida Sinica 24(1):52–82

    Article  Google Scholar 

  • Wang ZQ, Zhao YP, Huang ZP (2010) The effects of surface tension on the elastic properties of nano structures. Int J Eng Sci 48(2):140–150

    Article  Google Scholar 

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Acknowledgements

Support from the University of Houston and the M. D. Anderson Professorship is gratefully acknowledged.

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Correspondence to Pradeep Sharma .

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Mozaffari, K., Yang, S., Sharma, P. (2019). Surface Energy and Nanoscale Mechanics. In: Andreoni, W., Yip, S. (eds) Handbook of Materials Modeling. Springer, Cham. https://doi.org/10.1007/978-3-319-50257-1_48-1

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  • DOI: https://doi.org/10.1007/978-3-319-50257-1_48-1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-50257-1

  • Online ISBN: 978-3-319-50257-1

  • eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics

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