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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
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, Berlin Heidelberg, pp 105–115
Biria A, Maleki M, Fried E (2013) Continuum theory for the edge of an open lipid bilayer. Adv Appl Mech 21:1–78
Cammarata RC (2009) Generalized thermodynamics of surfaces with applications to small solid systems. Solid State Phys 61:1–75
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
Chatzigeorgiou G, Meraghni F, Javili A (2017) Generalized interfacial energy and size effects in composites. J Mech Phys Solids 106:257–282
Chhapadia P, Mohammadi P, Sharma P (2011) Curvature-dependent surface energy and implications for nanostructures. J Mech Phys Solids 59(10):2103–2115
Courant R, Hilbert D (1953) Methods of mathematical physics, vol I (First English ed.). Interscience Publishers, Inc., New York
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
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
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
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
de Gennes PG, Brochard-Wyart F, Quere D (2004) Capillarity and wetting phenomenon. Springer, New York
Gurtin ME, Murdoch AI (1975a) Addenda to our paper a continuum theory of elastic material surfaces. Arch Ration Mech Anal 59(4):389–390
Gurtin ME, Murdoch AI (1975b) A continuum theory of elastic material surfaces. Arch Ration Mech Anal 57(4):291–323
Gurtin ME, Murdoch AI (1978) Surface stress in solids. Int J Solids Struct 14(6):431–440
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
Gurtin ME, Fried E, Anand L (2010) The mechanics and thermodynamics of continua. Cambridge University Press, Cambridge
Haiss W (2001) Surface stress of clean and adsorbate-covered solids. Rep Prog Phys 64(5):591
Henann DL, Bertoldi K (2014) Modeling of elasto-capillary phenomena. Soft Matter 10(5): 709–717
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
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
Huang Z, Wang J (2013) Micromechanics of nanocomposites with interface energy effect. Handbook of micromechanics and nanomechanics. Pan Stanford Publishing, Singapore
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
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
Javili A, Ottosen NS, Ristinmaa M, Mosler J (2018) Aspects of interface elasticity theory. Math Mech Solids 23:1004–1024
Li S, Wang G (2008) Introduction to micromechanics and nanomechanics. World Scientific Publishing Company, Singapore
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
Miller RE, Shenoy VB (2000) Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11(3):139
Müller P, Saúl A (2004) Elastic effects on surface physics. Surf Sci Rep 54(5–8):157–258
Murdoch AI (2005) Some fundamental aspects of surface modelling. J Elas 80(1–3):33
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
Park HS (2008) Strain sensing through the resonant properties of deformed metal nanowires. J Appl Phys 104(1):013516
Park HS, Klein PA, Wagner GJ (2006) A surface Cauchy–Born model for nanoscale materials. Int J Numer Methods Eng 68(10):1072–1095
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
Steigmann D, Ogden R (1997) Plane deformations of elastic solids with intrinsic boundary elasticity. Proc R Soc London A 453:853–877
Steigmann D, Ogden R (1999) Elastic surface substrate interactions. Proc R Soc London A 455:437–474
Style RW, Hyland C, Boltyanskiy R, Wettlaufer JS, Dufresne ER (2013) Surface tension and contact with soft elastic solids. Nat Commun 4:2728
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
Suo Z, Lu W (2000) Forces that drive nanoscale self-assembly on solid surfaces. J Nanopart Res 2(4):333–344
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
Wang ZQ, Zhao YP, Huang ZP (2010) The effects of surface tension on the elastic properties of nanostructures. Int J Eng Sci 48(2):140–150
Acknowledgments
Support from the University of Houston and the M. D. Anderson Professorship is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this entry
Cite this entry
Mozaffari, K., Yang, S., Sharma, P. (2020). Surface Energy and Nanoscale Mechanics. In: Andreoni, W., Yip, S. (eds) Handbook of Materials Modeling. Springer, Cham. https://doi.org/10.1007/978-3-319-44680-6_48
Download citation
DOI: https://doi.org/10.1007/978-3-319-44680-6_48
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-44679-0
Online ISBN: 978-3-319-44680-6
eBook Packages: Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics