Local Mechanical Properties by Atomic Force Microscopy Nanoindentations

  • Davide Tranchida
  • Stefano Piccarolo
Part of the NanoScience and Technology book series (NANO)


The analysis of mechanical properties on a nanometer scale is a useful tool for combining information concerning texture organization obtained by microscopy with the properties of individual components. Moreover, this technique promotes the understanding of the hierarchical arrangement in complex natural materials as well in the case of simpler morphologies arising from industrial processes. Atomic Force Microscopy (AFM) can bridge morphological information, obtained with outstanding resolution, to local mechanical properties. When performing an AFM nanoindentation, the rough force curve, i.e., the plot of the voltage output from the photodiode vs. the voltage applied to the piezo-scanner, can be translated into a curve of the applied load vs. the penetration depth after a series of preliminary determinations and calibrations. However, the analysis of the unloading portion of the force curves collected for polymers does not lead to a correct evaluation of Young’s modulus. The high slope of the unloading curves is not linked to an elastic behavior, as would be expected, but rather to a viscoelastic effect. This can be argued on the basis that the unloading curves are superimposed on the loading curves in the case of an ideal elastic behavior, as for rubbers, or generally in the case of materials with very short relaxation times. In contrast, when the relaxation time of the sample is close to or even much larger than the indentation time scale, very high slopes are recorded.

Where AFM nanoindentations are concerned, one observes a dependence of the penetration, i.e., the relative motion between the sample and the tip (indenter), on the elastic properties of a material when using equivalent loads. This relationship becomes visible on samples that are homogeneous down to the scale of nanoindentation. The elastic modulus can be obtained by applying Sneddon’s elastic contact mechanics approach, since the contact between the tip and the sample is dominated by an elastic behavior with negligible plastic deformation. Under such circumstances, the dependence of the penetration on the load follows an exponent of 1.5, consistent with elastic contact mechanics and justified on the basis of the large elastic range exhibited by polymers, on the constraints due to the geometry of the deformation during indentation and to the critical yielding volume needed in order to induce plasticity. As a result, elastic moduli taken from AFM force curves show a very good agreement with bulk values obtained by macroscopic tensile testing. This is true for a broad range of polymers, from materials with rubbery to semi-crystalline, or even glassy behaviors. This result confirms that AFM nanoindentations in polymers take place mostly in the elastic range and opens the possibility of characterizing the mechanical behavior of polymers on an unparalleled small scale as compared to commercial depth-sensing instruments (DSIs), which use much blunter indenters.

A further application is discussed where, upon decreasing the load, and consequently the penetration depth, the scale becomes comparable to that of the underlying texture which is probed as opposed to the bulk material. Although this apparently presents a limitation on the resolution of the scale that can be mapped, this feature is discussed and shown to open the possibility of identifying properties of individual phases with their surroundings as well as the role of the connectivity among the phases.


Atomic force microscopy Nanoindentation Soft materials Polymers Elastic young’s modulus Nanoscale mapping Mechanical properties 


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  1. 1.
    Fratzl P, Weinkamer R (2007) Prog Mat Sci 52:1263Google Scholar
  2. 2.
    Meyers MA, Chen P-Y, Lin AYM, Seki Y (2008) Prog Mat Sci 53:1Google Scholar
  3. 3.
    Stolz RRM, Daniels AU, Van Landingham MR, Baschong W, Aebi U (2004) Biophys J 86:3269Google Scholar
  4. 4.
    Jiang H, Liu X-Y, Lim CT, Hsu CY (2005) Appl Phys Lett 86:163901Google Scholar
  5. 5.
    Bhushan B, Chen N (2006) Ultramicroscopy 106:755Google Scholar
  6. 6.
    Garcia R, Magerle R, Perez R (2007) Nature Materials 6:405Google Scholar
  7. 7.
    Bhushan B (2001)Wear 250:1105Google Scholar
  8. 8.
    Kim TW, Bhushan B (2007) Ultramicroscopy 107:902Google Scholar
  9. 9.
    Mailhot B, Bussière P-O, Rivaton A, Morlat-Thérias S, Gardette J-L (2004) Macrom Rapid Comm 25:436Google Scholar
  10. 10.
    Sergei VVG, Chizhik A, Luzinov I, Fuchigami N, Tsukruk VV (2001) Macrom Symposia 167:167Google Scholar
  11. 11.
    Briscoe BJ, Fiori L, Pelillo E (1998) J Phys D Appl Phys 31:2395Google Scholar
  12. 12.
    Tsukruk VV, Huang Z, Chizhik SA, Gorbunov VV (1998) J Mater Sci 33:4905Google Scholar
  13. 13.
    Chizhik SA, Huang Z, Gorbunov VV, Myshkin NK, Tsukruk VV (1998) Langmuir 14:2606Google Scholar
  14. 14.
    Low IM, Che ZY, Latella BA (2006) J Mater Res 21:1969Google Scholar
  15. 15.
    Bhushan B, Koinkar VN (1994) Appl Phys Lett 64:1653Google Scholar
  16. 16.
    VanLandingham SHMMR, Palmese GR, Huang X, Bogetti TA, Eduljee RF, Gillespie JW (1997) J Adhesion 64:31Google Scholar
  17. 17.
    VanLandingham JSVMR, Guthrie WF, Meyers GF (2001) Macrom Symposia 167:15Google Scholar
  18. 18.
    Tsukruk VV, Huang Z, Chizhik SA, Gorbunov VV (1998) J Mater Sci 33:4905Google Scholar
  19. 19.
    Herrmann K, Jennett NM, Wegener W, Meneve J, Hasche K, Seemann R (2000) Thin Solid Films 377:400Google Scholar
  20. 20.
    Bischel MS, VanLandingham MR, Eduljee RF, Gillespie JW, Schultz JM (2000) J Mater Sci 35:221Google Scholar
  21. 21.
    Du B, Liu J, Zhang Q, He T (2001) Polymer 42:5901Google Scholar
  22. 22.
    Tsukruk VV, Sidorenko A, Yang H, (2002) Polymer 43:1695Google Scholar
  23. 23.
    Beake BD, Leggett GJ (2002) Polymer 43:319Google Scholar
  24. 24.
    Hao HW, Barö AM, Saenz M (1991) J Vac Sci Technol B 9:1323Google Scholar
  25. 25.
    Cappella B, Dietler G (1999) Surf Sci Rep 34:1Google Scholar
  26. 26.
    Butt HJ, Cappella B, Kappl M (2005) Surface Sci Reports 59:1Google Scholar
  27. 27.
    Tsukruk VV, Gorbunov VV, Huang Z, Chizhik SA (2000) Polym Int 49:441Google Scholar
  28. 28.
    Burnham NA, Chen X, Hodges CS, Matei GA, Thoreson EJ, Roberts CJ, Davies MC, Tendler SJB (2003) Nanotechnology 14: 1Google Scholar
  29. 29.
    Holbery JD, Eden VLJ. (2000) Micromech Microeng 10:85Google Scholar
  30. 30.
    Matei GA, Thoreson EJ, Pratt JR, Newell DB, Burnham NA (2006) Rev Sci Instrum 77:83703Google Scholar
  31. 31.
    Richard SG, Mark GR (2007) Rev Sci Instrum 78:86101Google Scholar
  32. 32.
    Saltuk BA, Joseph AT (2007) Rev Sci Instrum 78:43704Google Scholar
  33. 33.
    Langlois ED, Shaw GA, Kramar JA, Pratt JR, Hurley DC (2007) Rev Sci Instrum 78:93705Google Scholar
  34. 34.
    Benjamin O (2007) Rev Sci Instrum 78:63701Google Scholar
  35. 35.
    Khurshudov A, Kato K (1995) Ultramicroscopy 60:11Google Scholar
  36. 36.
    Villarrubia JS (1997) J Res NIST 102:425Google Scholar
  37. 37.
    Tranchida D, Piccarolo S, Deblieck RAC (2006) Meas Sci Technol 17:2630Google Scholar
  38. 38.
    Hiroshi I, Toshiyuki F, Shingo I (2006) Rev Sci Instrum 77:103704Google Scholar
  39. 39.
    Loubet JL, Belin M, Durand R, Pascal H (1994) Thin Solid Films 253:194Google Scholar
  40. 40.
    Albrektsen O, Madsen LL, Mygind J, March KA (1989) J Phys E 22:39Google Scholar
  41. 41.
    Riis E, Simonsen H, Worm T, Nielsen U, Besenbacher (1989) F Appl Phys Lett 54:2530Google Scholar
  42. 42.
    Vieira S (1986) IBM J Res Develop 30:553Google Scholar
  43. 43.
    Graffel B, Mueller F, Mueller A-D, Hietschold M (2007) Rev Sci Instr 78:053706Google Scholar
  44. 44.
    Chiara S, Arthur B, Stephen RB, Frederick S (2007) Rev Sci Instrum 78:36111Google Scholar
  45. 45.
    Younkoo J, Jayanth GR, Chia-Hsiang M (2007) Rev Sci Instrum 78:93706Google Scholar
  46. 46.
    Landau LD, Lifshitz EM (1986) Theory of Elasticity. Pergamon Press, OxfordGoogle Scholar
  47. 47.
    Sneddon IN (1965) Int J Eng Sci 3:47Google Scholar
  48. 48.
    Ting TCT (1966) J Appl Mech 33:845Google Scholar
  49. 49.
    Kramer D, Huang H, Kriese M, Robach J, Nelson J, Wright A, Bahr D, Gerberich WW (1998) Acta Materialia 47:333Google Scholar
  50. 50.
    Oliver WC, Pharr GM (1992) J Mater Res 7:1564Google Scholar
  51. 51.
    Johnson KL, Kendall K, Roberts AD (1971) Proc Roy Soc London A324:301Google Scholar
  52. 52.
    Derjaguin BV, Muller VM, Toporov YP (1975) J Coll Interf Sci 53:314Google Scholar
  53. 53.
    Arivuoli D, Lawson NS, Krier A, Attolini G, Pelosi C (2000) Mat Chem Phys 66:207Google Scholar
  54. 54.
    Tranchida D, Piccarolo S, Soliman M (2006) Macromolecules 39:4547Google Scholar
  55. 55.
    Tranchida D, Piccarolo S (2005) Macr Rap Comm 26:1800Google Scholar
  56. 56.
    Tranchida D, Piccarolo S (2005) Polymer 46:4032Google Scholar
  57. 57.
    Tranchida D, Kiflie Z, Piccarolo S (2007) Atomic Force Microscope Nanoindentations to Reliably Measure the Young’s Modulus of Soft Matter. In: Méndez-Vilas A, Díaz J (eds) Modern Research and Educational Topics in Microscopy. Formatex, Badajoz, p 737Google Scholar
  58. 58.
    Tranchida D, Kiflie Z, Piccarolo S (2006) Macromolecular Rapid Commun 27:1584Google Scholar
  59. 59.
    Tranchida D, Kiflie Z, Piccarolo S (2007) Macromolecules 40:7366Google Scholar
  60. 60.
    Fischer-Cripps AC (2004) Nanoindentation, 2nd edn, Springer, BerlinGoogle Scholar
  61. 61.
    Wolf B (2000) Cryst Res Technol 35:377Google Scholar
  62. 62.
    Baltà-Calleja FJ (1985) Adv Pol Sci 66:117Google Scholar
  63. 63.
    Baltà-Calleja FJ (1994) Trends in Pol Sci 2:419Google Scholar
  64. 64.
    Goss CA, Blumfield CJ, Irene EA, Murray RW (1993) Langmuir 9:2986Google Scholar
  65. 65.
    Oliver WC, Pharr GM (2004) J Mater Res 19:3Google Scholar
  66. 66.
    Tranchida D, Piccarolo S, Loos J, Alexeev A (2007) Macromolecules 40:1259Google Scholar
  67. 67.
    Loubet JL, Georges JM, Meille J (1986) Nanoindentation Techniques in Materials Science and Engineering. ASTM, PhiladelphiaGoogle Scholar
  68. 68.
    Hochstetter G, Jimenez A, Loubet JL (1999) J Macromol Sc B-Phy 38:681Google Scholar
  69. 69.
    Kick F (1885) Das Gesetz der proportionalen Widerstunde und seine Anwendungen. Felix-Verlag, LeipzigGoogle Scholar
  70. 70.
    Cheng Y-T, Cheng CM (1998) J Appl Phys 84:1284Google Scholar
  71. 71.
    Lundberg B (1974) Int J Rock Mech Min Sci Geomech Abstr 11:209Google Scholar
  72. 72.
    Mata M, Alcalà JJ (2004) Mech Phys Solids 52:145Google Scholar
  73. 73.
    Malzbender J, de With GJ (2000) Mater Res 15:1209Google Scholar
  74. 74.
    Larsson P-L, Giannakopoulos AE, Söderlund E, Rowcliffe DJ, Vestergaard R (1996) Int J Solids Struct 33:221Google Scholar
  75. 75.
    Vaidyanathan R, Dao M, Ravichandran G, Suresh S (2001) Acta Mater 49:3781Google Scholar
  76. 76.
    Attaf MT (2004) Mater Lett 58:3491Google Scholar
  77. 77.
    Shan Z, Sitaraman SK (2003) Thin Solid Films 437:176Google Scholar
  78. 78.
    Fröhlich F, Grau P, Grellmann W (1977) Phys Status Solidi, A Appl Res 42:79Google Scholar
  79. 79.
    Suresh S, Nieh T-G, Choi BW (1999) Scr Mater 41:951Google Scholar
  80. 80.
    Hainsworth SV, Chandlera HW, Page TF (1996) J Mater Res 11:1987Google Scholar
  81. 81.
    Kim H, Kim TJ, (2002) Eur Ceram Soc 22:1437Google Scholar
  82. 82.
    Zeng K, Chiu C-H (2001) Acta Mater 49:3539Google Scholar
  83. 83.
    Andrews EW, Giannakopoulos AE, Plisson E, Suresh S (2002) Int J Solids Struct 39:281Google Scholar
  84. 84.
    Bernhardt EO (1941) Z Metöd 33:135Google Scholar
  85. 85.
    Li H, Bradt RC (1993) J Mater Sci 28:917Google Scholar
  86. 86.
    Bückle H (1959) Metall Rev 4:49Google Scholar
  87. 87.
    Bückle H (1965) Mikrohärterprüfung. Berliner Union Verlag, StuttgartGoogle Scholar
  88. 88.
    Quinn JB, Quinn GD (1997) J Mater Sci 32:4331Google Scholar
  89. 89.
    Hays C, Kendall EG (1973) Metallurgica 6:275Google Scholar
  90. 90.
    Ghosh S, Das S, Bandyopadhyay TK, Bandhopadhyay PP, Chattopadhyay AB (2003) J Mater Sci 38:1565Google Scholar
  91. 91.
    Meyer E (1908) V.D.I. Zeitshrift 52:645Google Scholar
  92. 92.
    Dao M, Challacoop N, Van Vliet KJ, Venkatesh TA, Suresh S (2001) Acta Mater 49:3899Google Scholar
  93. 93.
    Rother B, Steiner A, Dietrich DA, Jehn HA, Haupt J, Giessler W (1998) J Mater Res 13:2071Google Scholar
  94. 94.
    Herrmann K, Hasche K, Pohlenz F, Seemann R (2001) Meas Sci Techn 29:201Google Scholar
  95. 95.
    Cheng Y-T, Cheng CM (1998) Appl Phys Lett 73:614Google Scholar
  96. 96.
    DeRose JA, Revel JP (1997) Micr Microan 3:203Google Scholar
  97. 97.
    Atamny F, Baiker A (1995) Surf Sci 323:L314Google Scholar
  98. 98.
    Ramirez-Aguilar KA, Rowlen KL (1998) Langmuir 14:2562Google Scholar
  99. 99.
    Cappella B, Kaliappan SK, Sturm H (2005) Macromolecules 38:1874Google Scholar
  100. 100.
    Segedin CM (1957) Mathematika 4:156Google Scholar
  101. 101.
    Lee EH, Radok JRM (1960) J Appl Mech 82:438Google Scholar
  102. 102.
    Hilton HH, Yi S (1998) Int J Solids and Struct 35:3081Google Scholar
  103. 103.
    Hilton HH (1996) Mech of Comp Mater Struct 3:97Google Scholar
  104. 104.
    Sun YJ, Akhremitchev B, Walker GC (2004) Langmuir 20:5837Google Scholar
  105. 105.
    Swedlow JL (1975) Int J Fract Mech 1:210Google Scholar
  106. 106.
    Bobji MS, Biswas SK (1998) J Mater Res 13:3227Google Scholar
  107. 107.
    Myshkin NK, Petrokovets MI, Chizhik SA (1999) Tribol Int 32:379Google Scholar
  108. 108.
    Bowden FP, Tabor D (1950) Friction and Lubrication of Solids. Clarendon Press, OxfordGoogle Scholar
  109. 109.
    Archard JF (1957) Proc R Soc Lond A 243:190Google Scholar
  110. 110.
    Greenwood JA, Williamson JBP (1966) Proc R Soc Lond A 295:300Google Scholar
  111. 111.
    McCool JI (1986) Wear 107:37Google Scholar
  112. 112.
    Carbone G, Mangialardi L (2004) J Mech Phys Sol 52:1267Google Scholar
  113. 113.
    Buzio R, Boragno C, Valbusa U (2003) Wear 254:917Google Scholar
  114. 114.
    Myshkin NK, Petrokovets MI, Chizhik SA (1998) Tribol Int 31:79Google Scholar
  115. 115.
    Brucato V, Piccarolo S, La Carrubba V (2002) Chem Eng Sci 57:4129Google Scholar
  116. 116.
    Piccarolo S (1992) J Macromol Sci – Phys B 31:501Google Scholar
  117. 117.
    Welsh GE, Blundell DJ, Windle AH (2000) J Mater Sci 35:5225Google Scholar
  118. 118.
    Baltà-Calleja FJ, Garcia Gutierrez MC, Rueda DR, Piccarolo S (2000) Polymer 41:4143Google Scholar
  119. 119.
    Flores A, Baltà-Calleja FJ, Asano T (2001) J Appl Phys 90:6006Google Scholar
  120. 120.
    Welsh GE, Windle AH (2001) Polymer 42:5727Google Scholar
  121. 121.
    Shen YL, Guo YL (2001) Modell Simul Mater Sci Eng 9:391Google Scholar
  122. 122.
    Piccarolo S. (2006) Polymer 47:5610Google Scholar

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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Davide Tranchida
  • Stefano Piccarolo

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