Skip to main content

On the Application of Transition State Theory to Atomic-Scale Wear

Abstract

The atomic force microscope (AFM) tip is often used as a model of a single sliding asperity in order to study nanotribological phenomena including friction, adhesion, and wear. In particular, recent work has demonstrated a wear regime in which surface modification appears to occur in an atom-by-atom fashion. Several authors have modeled this atomic-scale wear behavior as a thermally activated bond breaking process. The present article reviews this body of work in light of concepts from formal transition state theory (also called reaction rate theory). It is found that this framework is viable as one possible description of atomic-scale wear, with impressive agreements to experimental trends found. However, further experimental work is required to fully validate this approach. It is also found that, while the Arrhenius-type equations have been widely used, there is insufficient discussion of or agreement on the specific atomic-scale reaction that is thermally activated, or its dependence on stresses and sliding velocity. Further, lacking a clear picture of the underlying mechanism, a consensus on how to measure or interpret the activation volume and activation energy is yet to emerge. This article makes suggestions for measuring and interpreting such parameters, and provides a picture of one possible thermally activated transition (in its initial, activated, and final states). Finally, directions for further experimental and simulation work are proposed for validating and extending this model and rationally interrogating the behavior of this type of wear.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

References

  1. de Boer, M.P., Mayer, T.M.: Tribology of MEMS. MRS Bull. 26, 302–304 (2001)

    Google Scholar 

  2. Romig Jr., A.D., Dugger, M.T., McWhorter, P.J.: Materials issues in microelectromechanical devices: science, engineering, manufacturability and reliability. Acta Mater. 51, 5837–5866 (2003)

    CAS  Article  Google Scholar 

  3. Maboudian, R., Ashurst, W.R., Carraro, C.: Tribological challenges in micromechanical systems. Tribol. Lett. 12, 95–100 (2002)

    Article  Google Scholar 

  4. Xu, S., Amro, N.A., Liu, G.Y.: Characterization of AFM tips using nanografting. Appl. Surf. Sci. 175, 649–655 (2001)

    Article  ADS  Google Scholar 

  5. Cruchon-Dupeyrat, S., Porthun, S., Liu, G.Y.: Nanofabrication using computer-assisted design and automated vector-scanning probe lithography. Appl. Surf. Sci. 175, 636–642 (2001)

    Article  ADS  Google Scholar 

  6. Lieber, C.M., Kim, Y.: Nanomachining and manipulation with the atomic force microscope. Adv. Mater. 5, 392–394 (1993)

    CAS  Article  Google Scholar 

  7. Vettiger, P., Cross, G., et al.: The ‘Millipede’—nanotechnology entering data storage. IEEE Trans. Nanotechnol. 1, 39–55 (2002)

    Article  ADS  Google Scholar 

  8. Szlufarska, I., Chandross, M., Carpick, R.W.: Recent advances in single-asperity nanotribology. J. Phys. D 41, 123001 (2008)

    Article  ADS  Google Scholar 

  9. Meyer, E., Hug, H.J., Bennewitz, R.: Scanning Probe Microscopy: The Lab on a Tip. Springer, New York (2003)

    Google Scholar 

  10. Khurshudov, A.G., Kato, K., Koide, H.: Nano-wear of the diamond AFM probing tip under scratching of silicon, studied by AFM. Tribol. Lett. 2, 345–354 (1996)

    CAS  Article  Google Scholar 

  11. Bloo, M.L., Haitjema, H., Pril, W.O.: Deformation and wear of pyramidal, silicon-nitride AFM tips scanning micrometre-size features in contact mode. Measurement 25, 203–211 (1999)

    Article  Google Scholar 

  12. Zhao, Q.L., Dong, S., Sun, T.: Investigation of an atomic force microscope diamond tip wear in micro/nano-machining. Key Eng. Mat. 202–203, 315–320 (2001)

    Article  Google Scholar 

  13. Maw, W., Stevens, F., et al.: Single asperity tribochemical wear of silicon nitride studied by atomic force microscopy. J. Appl. Phys. 92, 5103–5109 (2002)

    CAS  Article  ADS  Google Scholar 

  14. D’Acunto, M.: Theoretical approach for the quantification of wear mechanisms on the nanoscale. Nanotechnology 15, 795–801 (2004)

    Article  ADS  Google Scholar 

  15. Chung, K.-H., Lee, Y.-H., Kim, D.-E.: Characteristics of fracture during the approach process and wear mechanism of a silicon AFM tip. Ultramicroscopy 102, 161–171 (2005)

    CAS  Article  PubMed  Google Scholar 

  16. Liu, H., Klonowski, M., et al.: Advanced atomic force microscopy probes: wear resistant designs. J. Vac. Sci. Technol. B 23, 3090–3093 (2005)

    CAS  Article  Google Scholar 

  17. Tao, Z., Bhushan, B.: Surface modification of AFM silicon probes for adhesion and wear reduction. Tribol. Lett. 21, 1–16 (2006)

    CAS  Article  Google Scholar 

  18. Bhaskaran, H., Sebastian, A., Despont, M.: Nanoscale PtSi tips for conducting probe technologies. IEEE Trans. Nanotechnol. 8, 128–131 (2009)

    Article  ADS  Google Scholar 

  19. Kopycinska-Mueller, M., Geiss, R.H., Hurley, D.C.: Size-related plasticity effects in AFM silicon cantilever tips. Mater. Res. Soc. Symp. Proc. 924, 19–24 (2006)

    Google Scholar 

  20. Chung, K.H., Kim, D.E.: Fundamental investigation of micro wear rate using an atomic force microscope. Tribol. Lett. 15, 135–144 (2003)

    CAS  Article  Google Scholar 

  21. Tao, Z.H., Bhushan, B.: Surface modification of AFM Si3N4 probes for adhesion/friction reduction and imaging improvement. Trans. ASME 128, 865–875 (2006)

    CAS  Article  Google Scholar 

  22. Gotsmann, B., Lantz, M.A.: Atomistic wear in a single asperity sliding contact. Phys. Rev. Lett. 101, 125501 (2008)

    Article  ADS  PubMed  Google Scholar 

  23. Bhushan, B., Kwak, K.J.: Velocity dependence of nanoscale wear in atomic force microscopy. Appl. Phys. Lett. 91, 3 (2007)

    Article  Google Scholar 

  24. Kopta, S., Salmeron, M.: The atomic scale origin of wear on mica and its contribution to friction. J. Chem. Phys. 113, 8249–8252 (2000)

    CAS  Article  ADS  Google Scholar 

  25. Agrawal, R., Moldovan, N., Espinosa, H.D.: An energy-based model to predict wear in nanocrystalline diamond atomic force microscopy tips. J. Appl. Phys. 106, 064311 (2009)

    Article  ADS  Google Scholar 

  26. Gnecco, E., Bennewitz, R., Meyer, E.: Abrasive wear on the atomic scale. Phys. Rev. Lett. 88, 215501 (2002)

    CAS  Article  ADS  PubMed  Google Scholar 

  27. Bhaskaran, H., Gotsmann, B., et al.: Ultralow nanoscale wear through atom-by-atom attrition in silicon-containing diamond-like carbon. Nat. Nanotechnol. 5, 181–185 (2010)

    CAS  Article  ADS  PubMed  Google Scholar 

  28. Liu, J., Grierson, D.S., et al.: Preventing nanoscale wear of atomic force microscopy tips through the use of monolithic ultrananocrystalline diamond probes. Small 6, 1140–1149 (2010)

    CAS  Article  PubMed  Google Scholar 

  29. Christian, J.W.: The Theory of Transformations in Metals and Alloys. Pergamon, Oxford (2002)

    Google Scholar 

  30. Vineyard, G.H.: Frequency factors and isotope effects in solid state rate processes. J. Phys. Chem. Solids 3, 121–127 (1957)

    CAS  Article  ADS  Google Scholar 

  31. Hanggi, P., Talkner, P., Borkovec, M.: Reaction-rate theory—50 years after Kramers. Rev. Mod. Phys. 62, 251–341 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  32. Kauzmann, W.: Flow of solid metals from the standpoint of chemical-rate theory. Trans. AIME 143, 57–83 (1941)

    Google Scholar 

  33. Rohde, R.W., Pitt, C.H.: Dislocation velocities in nickel single crystals. J. Appl. Phys. 38, 876–879 (1967)

    CAS  Article  ADS  Google Scholar 

  34. Gibbs, G.B.: Thermodynamics of thermally-activated dislocation glide. Phys. Status Solidi 10, 507–512 (1965)

    Article  Google Scholar 

  35. Hirth, J.P., Nix, W.D.: An analysis of thermodynamics of dislocation glide. Phys. Status Solidi 35, 177–188 (1969)

    CAS  Article  Google Scholar 

  36. Kocks, U.F., Argon, A.S., Ashby, M.F.: Thermodynamics and kinetics of slip. Prog. Mater. Sci. 19, 1–281 (1975)

    Article  Google Scholar 

  37. Taylor, G.: Thermally-activated deformation of BCC metals and alloys. Prog. Mater. Sci. 36, 29–61 (1992)

    CAS  Article  Google Scholar 

  38. Gibbs, G.B.: On interpretation of experimental activation parameters for dislocation glide. Phil. Mag. 20, 867–872 (1969)

    CAS  Article  ADS  Google Scholar 

  39. Hull, D., Bacon, D.J.: Introduction to Dislocations, 4th edn. Butterworth-Heinemann, Oxford (1984)

    MATH  Google Scholar 

  40. Park, N.S., Kim, M.W., et al.: Atomic layer wear of single-crystal calcite in aqueous solution scanning force microscopy. J. Appl. Phys. 80, 2680–2686 (1996)

    CAS  Article  ADS  Google Scholar 

  41. Sheehan, P.E.: The wear kinetics of NaCl under dry nitrogen and at low humidities. Chem. Phys. Lett. 410, 151–155 (2005)

    CAS  Article  ADS  Google Scholar 

  42. Briscoe, B.J., Evans, D.C.B.: The shear properties of Langmuir-Blodgett Layers. Proc. R. Soc. Lond. A 380, 389–407 (1982)

    CAS  Article  ADS  Google Scholar 

  43. Helt, J.M., Batteas, J.D.: Wear of mica under aqueous environments: direct observation of defect nucleation by AFM. Langmuir 21, 633–639 (2005)

    CAS  Article  PubMed  Google Scholar 

  44. Hong, U.S., Jung, S.L., et al.: Wear mechanism of multiphase friction materials with different phenolic resin matrices. Wear 266, 739–744 (2009)

    CAS  Article  Google Scholar 

  45. Luan, B., Robbins, M.O.: The breakdown of continuum models for mechanical contacts. Nature 435, 929–932 (2005)

    CAS  Article  ADS  PubMed  Google Scholar 

  46. Mo, Y.F., Turner, K.T., Szlufarska, I.: Friction laws at the nanoscale. Nature 457, 1116–1119 (2009)

    CAS  Article  ADS  PubMed  Google Scholar 

  47. Krausz, A.S., Eyring, H.: Deformation Kinetics. Wiley, New York (1975)

    Google Scholar 

  48. Li, J.: The mechanics and physics of defect nucleation. MRS Bull. 32, 151–159 (2007)

    CAS  Google Scholar 

  49. Zhao, X.Y., Hamilton, M., et al.: Thermally activated friction. Tribol. Lett. 27, 113–117 (2007)

    CAS  Article  Google Scholar 

  50. Zhao, X., Phillpot, S.R. et al.: Transition from thermal to athermal friction under cryogenic conditions. Phys. Rev. Lett. 102, 1861021–1861024 (2009)

    Google Scholar 

  51. Jansen, L., Schirmeisen, A., et al.: Nanoscale frictional dissipation into shear-stressed polymer relaxations. Phys. Rev. Lett. 102, 4 (2009)

    Article  Google Scholar 

  52. Schirmeisen, A., Jansen, L., et al.: Temperature dependence of point contact friction on silicon. Appl. Phys. Lett. 88, 123108 (2006)

    Article  ADS  Google Scholar 

  53. Barel, I., Urbakh, M., et al.: Multibond dynamics of nanoscale friction: the role of temperature. Phys. Rev. Lett. 104, 066104 (2010)

    Article  ADS  PubMed  Google Scholar 

  54. Johnson, K.L.: Contact Mechanics. University Press, Cambridge (1987)

    Google Scholar 

  55. Carpick, R.W., Salmeron, M.: Scratching the surface: fundamental investigations of tribology with atomic force microscopy. Chem. Rev. 97, 1163–1194 (1997)

    CAS  Article  PubMed  Google Scholar 

  56. Zworner, O., Holscher, H., et al.: The velocity dependence of frictional forces in point-contact friction. Appl. Phys. A 66, S263–S267 (1998)

    Article  ADS  Google Scholar 

  57. Riedo, E., Gnecco, E., et al.: Interaction potential and hopping dynamics governing sliding friction. Phys. Rev. Lett. 91, 84502 (2003)

    CAS  Article  ADS  Google Scholar 

  58. Bouhacina, T., Aimé, J.P., et al.: Tribological behaviour of a polymer grafted in silanized silica probed with a nanotip. Phys. Rev. B 56, 7694–7703 (1997)

    CAS  Article  ADS  Google Scholar 

  59. Gnecco, E., Bennewitz, R., et al.: Velocity dependence of atomic friction. Phys. Rev. Lett. 84, 1172–1175 (2000)

    CAS  Article  ADS  PubMed  Google Scholar 

  60. Chen, J., Ratera, I., et al.: Velocity dependence of friction and hydrogen bonding effects. Phys. Rev. Lett. 96, 4 (2006)

    Google Scholar 

  61. Yi, S., Dube, M., Grant, M.: Thermal effects on atomic friction. Phys. Rev. Lett. 87, 174301 (2001)

    Article  ADS  Google Scholar 

  62. Gao, G.T., Mikulski, P.T., Harrison, J.A.: Molecular-scale tribology of amorphous carbon coatings: effects of film thickness, adhesion, and long-range interactions. J. Am. Chem. Soc. 124, 7202–7209 (2002)

    CAS  Article  PubMed  Google Scholar 

  63. Jarvis, M.R., Perez, R., Payne, M.C.: Can atomic force microscopy achieve atomic resolution in contact mode? Phys. Rev. Lett. 86, 1287–1290 (2001)

    CAS  Article  ADS  PubMed  Google Scholar 

  64. Harrison, J.A., Brenner, D.W.: Simulated tribochemistry—an atomic-scale view of the wear of diamond. J. Am. Chem. Soc. 116, 10399–10402 (1994)

    CAS  Article  Google Scholar 

  65. Kim, H.J., Karthikeyan, S., Rigney, D.: A simulation study of the mixing, atomic flow and velocity profiles of crystalline materials during sliding. Wear 267, 1130–1136 (2009)

    CAS  Article  Google Scholar 

  66. Rigney, D.A., Fu, X.Y., et al.: Examples of structural evolution during sliding and shear of ductile materials. Scr. Mater. 49, 977–983 (2003)

    CAS  Article  Google Scholar 

  67. Zhu, T., Li, J., et al.: Stress-dependent molecular pathways of silica-water reaction. J. Mech. Phys. Sol. 53, 1597–1623 (2005)

    MATH  CAS  Article  MathSciNet  ADS  Google Scholar 

  68. Zhu, T., Li, J., et al.: Temperature and strain-rate dependence of surface dislocation nucleation. Phys. Rev. Lett. 100, 4 (2008)

    Google Scholar 

  69. Crawford, J.H., Slifkin, L.M.: Point Defects in Solids. Plenum Publishing, New York (1972)

    Google Scholar 

  70. Liu, J., Notbohm, J.K. et al.: Method for characterizing nanoscale wear of atomic force microscope tips. ACS Nano (2010). doi:10.1021/nn100246g

Download references

Acknowledgments

RWC gratefully acknowledges financial support from the National Science Foundation under grant CMMI-0826076. Acknowledgment is made to the Donors of the American Chemical Society Petroleum Research Fund for partial support of this research. Illuminating discussions with Professors Vaclav Vitek and Mahadevan Khantha are gratefully acknowledged.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Robert W. Carpick.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Jacobs, T.D.B., Gotsmann, B., Lantz, M.A. et al. On the Application of Transition State Theory to Atomic-Scale Wear. Tribol Lett 39, 257–271 (2010). https://doi.org/10.1007/s11249-010-9635-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11249-010-9635-z

Keywords

  • Nanotribology
  • Contact mechanics
  • AFM
  • Unlubricated wear
  • Wear mechanisms