Skip to main content
SpringerLink
Log in

Physical Principles of Force–Distance Curves by Atomic Force Microscopy

  • Chapter
  • First Online:
Mechanical Properties of Polymers Measured through AFM Force-Distance Curves

Part of the book series: Springer Laboratory ((SPLABORATORY))

Abstract

The atomic force microscope (AFM) is increasingly employed not only to acquire topography images of samples but also to measure force–distance curves. Such curves, beyond playing a major role in the theoretical study of surface interactions, are meanwhile a fundamental tool in surface science, nanotechnology, biology and many other fields of research.

Force–distance curves find their application in the study of numerous material properties, such as mechanical properties, surface charge densities, adhesion and Hamaker constants.

One of the most important applications of AFM force–distance curves is the study of mechanical properties of polymers. Compared to other instruments, the AFM has in this case two major advantages. First of all, elastic moduli of samples can be measured with high resolution from some GPa down to some MPa, which is the range of the elastic moduli of common polymers. Second, force–distance curves can be acquired in an array over the sample. This is a fundamental tool for the characterization of the lateral variation of sample properties and hence for the study of confined polymers and polymer blends.

The first part of this book is divided in two chapters dealing with the theoretical and practical aspects of force–distance curves. Theoretical aspects, handled in this chapter, are focused on mechanical properties of polymers.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Binnig G, Quate CF, Gerber C (1986) Atomic force microscope. Phys Rev Lett 56:930–933

    Article  Google Scholar 

  2. Binnig G, Rohrer H, Gerber C, Weibel E (1982) Surface studies by scanning tunneling microscopy. Phys Rev Lett 49:57–61

    Article  Google Scholar 

  3. Lewis A, Isaacson M, Harootunian A, Muray A (1984) Development of a 500 Å spatial resolution light microscope. Ultramicroscopy 13:227–232

    Article  Google Scholar 

  4. Pohl DW, Denk W, Lanz M (1984) Optical stethoscopy – Image recording with resolution lambda/20. Appl Phys Lett 44:651–653

    Article  Google Scholar 

  5. Tortonese M (1997) Cantilevers and tips for atomic force microscopy. IEEE Eng Med Bio 16:28–33

    Article  CAS  Google Scholar 

  6. Fleming AJ (2013) A review of nanometer resolution position sensors: operation and performance. Sensors Actuators A: Phys 190:106–126

    Article  CAS  Google Scholar 

  7. Meyer G, Amer NM (1988) Novel optical approach to atomic force microscopy. Appl Phys Lett 53:1045–1047

    Article  Google Scholar 

  8. Bhushan B (ed) (2004) Springer handbook of nanotechnology. Springer, Berlin

    Google Scholar 

  9. Schönherr H, Vancso GJ (2010) Scanning force microscopy of polymers. Springer, Heidelberg

    Book  Google Scholar 

  10. Hamada E, Kaneko R (1992) Micro-tribological evaluations of a polymer surface by atomic force microscopes. Ultramicroscopy 42:184–190

    Article  Google Scholar 

  11. Cappella B, Dietler G (1999) Force-distance curves by atomic force microscopy. Surf Sci Rep 34:1–104

    Article  CAS  Google Scholar 

  12. Butt H-J, Cappella B, Kappl M (2005) Force measurements with the atomic force microscope: technique, interpretation and applications. Surf Sci Rep 59:1–152

    Article  CAS  Google Scholar 

  13. Ferry JD (1961) Viscoelastic properties of polymers. Wiley, New York

    Google Scholar 

  14. Aimé JP, Elkaakour Z, Odin C, Bouhacina T, Michel D, Curély J, Dautant A (1994) Comments on the use of the force mode in atomic force microscopy for polymer films. J Appl Phys 76:754–762

    Article  Google Scholar 

  15. Hertz H (1881) Über die Berührung fester elastischer Körper. J Reine Angew Math 92:156–171

    Google Scholar 

  16. Johnson KL, Kendall K, Roberts AD (1971) Surface energy and the contact of elastic solids. Proc R Soc Lond A 324:301–313

    Article  CAS  Google Scholar 

  17. Derjaguin BV, Müller VM, Toporov YP (1975) Effect of contact deformations on the adhesion of particles. J Colloid Interf Sci 53:314–326

    Article  CAS  Google Scholar 

  18. Müller VM, Yushchenko VS, Derjaguin BV (1980) On the influence of molecular forces on the deformation of an elastic sphere and its sticking to a rigid plane. J Colloid Interf Sci 77:91–101

    Article  Google Scholar 

  19. Müller VM, Derjaguin BV, Toporov YP (1983) On two methods of calculation of the force of sticking of an elastic sphere to a rigid plane. Colloids Surf 7:251–259

    Article  Google Scholar 

  20. Sneddon IN (1965) The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int J Engng Sci 3:47–57

    Article  Google Scholar 

  21. Attard P, Parker JL (1992) Deformation and adhesion of elastic bodies in contact. Phys Rev A 46:7959–7971

    Article  Google Scholar 

  22. Pashley MD, Pethica JB, Tabor D (1984) Adhesion and micromechanical properties of metal surfaces. Wear 100:7–31

    Article  CAS  Google Scholar 

  23. Maugis D (1992) Adhesion of spheres: the JKR-DMT transition using a Dugdale model. J Colloid Interf Sci 150:243–269

    Article  CAS  Google Scholar 

  24. Maugis D (1999) Contact, adhesion and rupture of elastic solids. Springer, Berlin

    Google Scholar 

  25. Johnson KL (2000) Contact mechanics and adhesion of viscoelastic spheres. ACS Symp Ser 741:24–41

    Article  CAS  Google Scholar 

  26. Oliver WC, Pharr GM (1992) An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res 7:1564–1583

    Article  CAS  Google Scholar 

  27. Briscoe BJ, Fiori L, Pelillo E (1998) Nano-indentation of polymeric surfaces. J Phys D Appl Phys 31:2395–2405

    Article  CAS  Google Scholar 

  28. King RB (1987) Elastic analysis of some punch problems for a layered medium. Int J Solids Struct 23:1657–1664

    Article  Google Scholar 

  29. Pharr GM, Oliver WC, Brotzen FR (1992) On the generality of the relationship among contact stiffness, contact area, and elastic-modulus during indentation. J Mater Res 7:613–617

    Article  CAS  Google Scholar 

  30. Van Landingham MR, Chang NK, Drzal PL, White CC, Chang SH (2005) Viscoelastic characterization of polymers using instrumented indentation. I. Quasi-static testing. J Polym Sci B: Polym Phys 43:1794–1811

    Article  Google Scholar 

  31. Balasundaram K, Cao Y, Raabe D (2008) Identifying the limitation of Oliver and Pharr method in characterizing the viscoelastic-plastic materials with respect to indenter geometry. Mater Res Soc Symp Proc 1137:49–54

    Article  Google Scholar 

  32. Tranchida D, Piccarolo S, Loos J, Alexeev A (2007) Mechanical characterization of polymers on a nanometer scale through nanoindentation. A study of pile-up and viscoelasticity. Macromolecules 40:1259–1267

    Article  CAS  Google Scholar 

  33. Israelachvili J (1992) Intermolecular and surface force. Academic Press, London

    Google Scholar 

  34. Gao C (1997) Theory of menisci and its applications. Appl Phys Lett 71:1801–1803

    Article  CAS  Google Scholar 

  35. Eastman T, Zhu D-M (1996) Adhesion forces between surface-modified AFM tips and a mica surface. Langmuir 12:2859–2862

    Article  CAS  Google Scholar 

  36. Weisenhorn AL, Hansma PK, Albrecht TR, Quate CF (1989) Forces in atomic force microscopy in air and water. Appl Phys Lett 54:2651–2653

    Article  Google Scholar 

  37. Butt H-J (1991) Electrostatic interaction in atomic force microscopy. Biophys J 60:777–785

    Article  CAS  Google Scholar 

  38. Gillies G, Prestidge GA (2005) Colloid Probe AFM investigation of the influence of cross-linking on the interaction behavior and nano-rheology of colloidal droplets. Langmuir 21:12342–12347

    Article  CAS  Google Scholar 

  39. Dimitriadis EK, Horkay F, Maresca J, Kachar B, Chadwick RS (2002) Determination of elastic moduli of thin layers of soft material using the atomic force microscope. Biophys J 82:2798–2810

    Article  CAS  Google Scholar 

  40. Derjaguin BV, Landau LD (1941) Theory of the stability of strongly charged lyophobic sols and of the adhesion of strongly charged particles in solution of electrolytes. Acta Phys URSS 14:633–662

    Google Scholar 

  41. Verwey EJW, Overbeek JTG (1948) Theory of stability of lyophobic colloids. Elsevier, Amsterdam

    Google Scholar 

  42. O’Shea SJ, Welland ME, Pethica JB (1994) Atomic-force microscopy of local compliance at solid–liquid interfaces. Chem Phys Lett 223:336–340

    Article  Google Scholar 

  43. Butt H-J (1991) Measuring electrostatic, van der Waals, and hydration forces in electrolyte solutions with an atomic force microscope. Biophys J 60:1438–1444

    Article  CAS  Google Scholar 

  44. Rabinovich YI, Yoon RH (1994) Use of atomic-force microscope for the measurements of hydrophobic forces between silanated silica plate and glass sphere. Langmuir 10:1903–1909

    Article  CAS  Google Scholar 

  45. Milner ST, Witten TA, Cates ME (1988) A parabolic density profile for grafted polymers. Europhys Lett 5:413–418

    Article  CAS  Google Scholar 

  46. Milner ST, Witten TA, Cates ME (1988) Theory of the grafted polymer brush. Macromolecules 21:2610–2619

    Article  CAS  Google Scholar 

  47. Dolan AK, Edwards SF (1974) Theory of stabilization of colloids by adsorbed polymer. Proc R Soc Lond A 337:509–516

    Article  CAS  Google Scholar 

  48. Fleer GJ, Scheutjens JHMH, Vincent B (1984) The stability of dispersions of hard spherical particles in the presence of nonadsorbing polymer. ACS Symp Ser 240:245–263

    Article  CAS  Google Scholar 

  49. Biggs S (1995) Steric and bridging forces between surfaces bearing adsorbed polymer – an atomic-force microscopy study. Langmuir 11:156–162

    Article  CAS  Google Scholar 

  50. Plazek DJ, Ngai KL (1996) The glass temperature. In: Mark JE (ed) Physical properties of polymers handbook. AIP Press, New York

    Google Scholar 

  51. Doi M (1993) Viscoelastic and rheological properties. In: Cahn RW, Haasen P, Kramer EJ (eds) Structure and properties of polymers. Wiley, Weinheim

    Google Scholar 

  52. Fried JR (1996) Sub-Tg transitions. In: Mark JE (ed) Physical properties of polymers handbook. AIP Press, New York

    Google Scholar 

  53. Peyser P (1989) Glass transition temperature of polymers. In: Brandrup J, Immergut EH (eds) Polymer handbook. AIP Press, New York

    Google Scholar 

  54. Fox T, Flory P (1954) The glass temperature and related properties of polystyrene – influence of molecular weight. J Polym Sci 14:315–319

    Article  CAS  Google Scholar 

  55. Rubinstein M, Colby RH (2003) Polymer physics. Oxford University Press, Oxford

    Google Scholar 

  56. Williams ML, Landel RF, Ferry JD (1955) Mechanical properties of substances of high molecular weight. The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids. J Am Chem Soc 77:3701–3707

    Article  CAS  Google Scholar 

  57. Chyasnavichyus M, Young SL, Tsukruk VV (2014) Probing of polymer surfaces in the viscoelastic regime. Langmuir 30:10566–10582

    Article  CAS  Google Scholar 

  58. Cappella B, Kaliappan SK, Sturm H (2005) Using AFM force distance curves to study the glass-to-rubber transition of amorphous polymers and their elastic–plastic properties as a function of temperature. Macromolecules 38:1874–1881

    Article  CAS  Google Scholar 

  59. Cohen SR, Kalfon-Cohen E (2013) Dynamic indentation by instrumented nanoindentation and force microscopy: a comparative review. Beilstein J Nanotechnol 4:815–833

    Article  CAS  Google Scholar 

  60. Lu H, Wang B, Ma J, Huang G, Viswanathan H (2003) Measurement of creep compliance of solid polymers by nanoindentation. Mech Time-Depend Mater 7:189–207

    Article  Google Scholar 

  61. Jäger A, Lackner R (2009) Finer-scale extraction of viscoelastic properties from nanoindentation characterised by viscoelastic-plastic response. Strain 45:45–54

    Article  Google Scholar 

  62. Braunsmann C, Proksch R, Revenko I, Schäffer TE (2014) Creep compliance mapping by atomic force microscopy. Polymer 55:219–225

    Article  CAS  Google Scholar 

  63. Asif SAS, Wahl KJ, Colton RJ (1999) Nanoindentation and contact stiffness measurement using force modulation with a capacitive load–displacement transducer. Rev Sci Instrum 70:2408–2413

    Article  CAS  Google Scholar 

  64. Asif SAS, Wahl KJ, Colton RJ, Warren OL (2001) Quantitative imaging of nanoscale mechanical properties using hybrid nanoindentation and force modulation. J Appl Phys 90:1192–1200

    Article  Google Scholar 

  65. Burnham NA, Gremaud G, Kulik AJ, Gallo PJ, Oulevey F (1996) Materials’ properties measurements: choosing the optimal scanning probe microscope configuration. J Vac Sci Technol B 14:1308–1312

    Article  CAS  Google Scholar 

  66. Nalam PC, Gosvami NN, Caporizzo MA, Russell J, Composto RJ, Carpick RW (2015) Nano-rheology of hydrogels using direct drive force modulation atomic force microscopy. Soft Mater 11:8165–8178

    Article  CAS  Google Scholar 

  67. Odegard GM, Gates TS, Herring HM (2005) Characterization of viscoelastic properties of polymeric materials through nanoindentation. Exp Mech 45:130–136

    Article  Google Scholar 

  68. White CC, VanLandingham MR, Drzal PL, Chang NK, Chang SH (2005) Viscoelastic characterization of polymers using instrumented indentation. II Dynamic testing. J Pol Sci B: Pol Phys 43:1812–1824

    Article  CAS  Google Scholar 

  69. Chakravartula A, Komvopoulos K (2006) Viscoelastic properties of polymer surfaces investigated by nanoscale dynamic mechanical analysis. Appl Phys Lett 88:131901

    Article  Google Scholar 

  70. Bouaita N, Bull SJ, Fernandez Palacio J, White JR (2006) Dynamic nanoindentation of some polyolefins. Pol Eng Sci 46:1160–1172

    Article  CAS  Google Scholar 

  71. Zhou J, Komvopoulos K (2007) Interfacial viscoelasticity of thin polymer films studied by nanoscale dynamic mechanical analysis. Appl Phys Lett 90:021910

    Article  Google Scholar 

  72. Zhang Y-F, Bai S-L, Yang D-Y, Zhang Z, Kao-Walter S (2008) Study on viscoelastic properties of the epoxy surface by means of nanodynamic mechanical analysis. J Pol Sci B: Pol Phys 46:281–288

    Article  CAS  Google Scholar 

  73. Lu YC, Shinozaki DM (2010) Temperature dependent viscoelastic properties of polymers investigated by small-scale dynamic mechanical analysis. Exp Mech 50:71–77

    Article  CAS  Google Scholar 

  74. Takahashi R, Okajima T (2015) Mapping power-law rheology of living cells using multi-frequency force modulation atomic force microscopy. Appl Phys Lett 107:173702

    Article  Google Scholar 

  75. Hecht FM, Rheinlaender J, Schierbaum N, Goldmann WH, Fabry B, Schäffer TE (2015) Imaging viscoelastic properties of live cells by AFM: power-law rheology on the nanoscale. Soft Mater 11:4584–4591

    Article  CAS  Google Scholar 

  76. Nakajima K, Ito M, Wang D, Liu H, Nguyen HK, Liang X, Kumagai A, Fujinami S (2014) Nano-palpation AFM and its quantitative mechanical property mapping. Microscopy 63:193–207

    Article  CAS  Google Scholar 

  77. Igarashi T, Fujinami S, Nishi T, Asao N, Nakajima K (2013) Nanorheological mapping of rubbers by atomic force microscopy. Macromolecules 46:1916–1922

    Article  CAS  Google Scholar 

  78. Tranchida D, Kiflie Z, Piccarolo S (2007) Viscoelastic recovery behavior following atomic force microscope nanoindentation of semicrystalline poly(ethylene). Macromolecules 40:7366–7371

    Article  CAS  Google Scholar 

  79. Cappella B, Sturm H (2002) Comparison between dynamic plowing lithography and nanoindentation methods. J Appl Phys 91:506–512

    Article  CAS  Google Scholar 

  80. Du B, Tsui OKC, Zhang Q, He T (2001) Study of elastic modulus and yield strength of polymer thin films using atomic force microscopy. Langmuir 17:3286–3291

    Article  CAS  Google Scholar 

  81. Johnson KL (1970) The correlation of indentation experiments. J Mech Phys Solids 18:115–126

    Article  Google Scholar 

  82. Mencik J, Munz D, Quandt E, Weppelmann ER (1997) Determination of elastic modulus of thin layers using nanoindentation. J Mater Res 12:2475–2484

    Article  CAS  Google Scholar 

  83. Perriot A, Barthel E (2004) Elastic contact to a coated half-space: effective elastic modulus and real penetration. J Mater Res 19:600–608

    Article  CAS  Google Scholar 

  84. Jung Y-G, Lawn BR, Martyniuk M, Huang H, Hu XZ (2004) Evaluation of elastic modulus and hardness of thin films by nanoindentation. J Mater Res 19:3076–3080

    Article  CAS  Google Scholar 

  85. Clifford CA, Seah MP (2006) Modelling of nanomechanical nanoindentation measurements using an AFM or nanoindenter for compliant layers on stiffer substrates. Nanotechnology 17:5283–5292

    Article  CAS  Google Scholar 

  86. Tsukruk VV, Sidorenko A, Gorbunov VV, Chizhik SA (2001) Surface nanomechanical properties of polymer nanocomposite layers. Langmuir 17:6715–6719

    Article  CAS  Google Scholar 

  87. Kovalev A, Shula H, Lemieux M, Myshkin N, Tsukruk VV (2004) Nanomechanical probing of layered nanoscale polymer films with atomic force microscopy. J Mater Res 19:716–728

    Article  CAS  Google Scholar 

  88. Doerner MF, Nix WD (1986) A method for interpreting the data from depth-sensing indentation instruments. J Mater Res 1:601–609

    Article  Google Scholar 

  89. Gao H, Chiu CH, Lee J (1992) Elastic contact versus indentation modeling of multilayered materials. Int J Solids Struct 29:2471–2492

    Article  Google Scholar 

  90. Cappella B, Silbernagl D (2008) Nanomechanical properties of polymer thin films measured by force–distance curves. Thin Solid Films 516:1952–1960

    Article  CAS  Google Scholar 

  91. Cappella B, Silbernagl D (2007) Nanomechanical properties of mechanical double-layers: a novel semiempirical analysis. Langmuir 23:10779–10787

    Article  CAS  Google Scholar 

  92. Silbernagl D, Cappella B (2010) Mechanical properties of thin polymer films on stiff substrates. Scanning 32:282–293

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. BAM, Federal Institute of Materials Research and Testing, Berlin, Germany

    Brunero Cappella

Authors
  1. Brunero Cappella
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Cappella, B. (2016). Physical Principles of Force–Distance Curves by Atomic Force Microscopy. In: Mechanical Properties of Polymers Measured through AFM Force-Distance Curves. Springer Laboratory. Springer, Cham. https://doi.org/10.1007/978-3-319-29459-9_1

Download citation

Publish with us

Policies and ethics

Search

Navigation