270 9. APPLICATION OF ATOMIC FORCE MICROSCOPy ε Shear strain � Shear viscosity Pa s � Exponential damping length m � Mass per unit length of cantilever kg m �1 � c Cantilever density kg m �3 � fluid Fluid density kg m �3 � Shear stress N m �2 φ Phase difference between substrate <strong>and</strong> cantilever ° � Frequency � R � vacuum Resonant frequency Resonant frequency in vacuum � Correction factor References [1] G. Binnig, C.F. Quate, Ch. Berger, Atomic force microscope, Phys. Rev. Lett. 56 (9) (1986) 930–933. [2] W.W. Scott, B. Bhushan, Use of phase imaging in atomic force microscopy for measurement of viscoelastic contrast in polymer nanocomposites <strong>and</strong> molecularly thick lubricant films, Ultramicroscopy 97 (2003) 151–169. [3] P.K. Hansma, J.P. Clevel<strong>and</strong>, M. Radmacher, D.A. Walters, P.E. Hillner, M. Bezanilla, M. Fritz, D. Vie, H.G. Hansma, C.B. Prater, J. Massie, L. Fukunaga, J. Gurley, V. Elings, Tapping mode atomic force microscopy in liquids, Appl. Phys. Lett. 64 (13) (1994) 1738–1740. [4] D. Dowson, C.M. Taylor, Cavitation in bearings, Ann. Rev. Fluid Mech. 11 (1979) 35–66. [5] Y.H. Zang, J.S. Aspler, M.Y. Boluk, J.H. De Grace, Direct measurement of tensile stress (“tack”) in thin ink films, J. Rheol. 35 (1991) 345–361. [6] A. Unsworth, D. Dowson, V. Wright, Cracking joints. A bioengineering study of cavitation in the metacarpophalangeal joint, Ann. Rheum. Dis. 30 (1971) 348–358. [7] H. Spikes, The borderline of elastohydrodynamic <strong>and</strong> boundary lubrication, Proc. Instn. Mech. Eng. 214 (2000) 23–37. [8] M.T. Tyree, The cohesion-tension theory of sap ascent, J. Exp. Bot. 48 (1997) 1753–1765. [9] H. Lakrout, P. Sergot, C. Creton, Direct observations of cavitation <strong>and</strong> fibrillation in a probe tack experiment on model acrylic pressure sensitive adhesive, J. Adhes. 69 (1999) 307–359. [10] G.J.C. Braithwaite, G.H. McKinley, Microrheometry for studying the rheology <strong>and</strong> dynamics of polymers near interfaces, J. Appl. Rheol. 9 (1999) 27–33. [11] A. Zosel, The effect of fibrillation on the tack of pressure sensitive adhesives, Int. J. Adhes. Adhes. 18 (1998) 265–271. [12] H. Strasburger, Tacky adhesion, J. Colloid Sci. 13 (1958) 218–231. [13] W.H. Banks, C.C. Mill, Tacky adhesion – a preliminary study, J. Colloid Sci. 8 (1953) 137–147. [14] F.C. MacKintosh, C.F. Schmidt, Microrheology, Curr. Opin. Coll. Int. Sci. 4 (1999) 300–307.
REFERENCES 271 [15] C. Clasen, G.H. McKinley, Gap-dependent microrheometry of complex liquids, J. Non-Newtonian Fluid Mech. 124 (2004) 1–10. [16] A. Mukhopadhyay, S. Granick, Micro- <strong>and</strong> nanorheology, Curr. Opin. Coll. Int. Sci. 6 (2001) 423–429. [17] P. Attard, Measurement <strong>and</strong> interpretation of elastic <strong>and</strong> viscoelastic properties with the atomic force microscope, J. Phys. Condens. Matter 19 (2007) 1–33. [18] A. Maali, B. Bhushan, Nanorheology <strong>and</strong> boundary slip in confined liquids using atomic force microscopy, J. Phys. Condens. Matter 20 (2008) 1–11. [19] J.N. Israelachvili, G.E. Adams, Measurement of the forces between two mica surfaces in aqueous solutions in the range 0–100 nm, J. Chem. Soc. Faraday Trans. 74 (1978) 975–980. [20] E. Pelletier, J.P. Montfort, F. Lapique, Surface force apparatus <strong>and</strong> its application to nanorheological studies, J. Rheol. 38 (4) (1994) 1151–1168. [21] C.D.F. Honig, W.A. Ducker, Squeeze film lubrication in silicone oil: experimental test of the no-slip boundary condition at solid–liquid interfaces, J. Phys. Chem. C 112 (2008) 17324–17330. [22] M. Hennemeyer, S. Burghhardt, R.W. Stark, Cantilever micro-rheometer for the characterization of sugar solutions, Sensors 8 (2008) 10–22. [23] N. Ahmed, D.F. Nino, V.T. Moy, Measurement of solution viscosity by atomic force microscopy, Rev. Sci. Instrum. 72 (2001) 2731–2734. [24] N. Belmiloud, I. Dufour, A. Colin, L. Nicu, Rheological behavior probed by vibrating microcantilevers, App. Phys. Lett. 92 (2008) 41907. [25] G.Y. Chen, T. Thundat, E.A. Wachter, R.J. Warmack, Adsorption-induced surface stress <strong>and</strong> its effects on resonance frequency of microcantilevers, J. Appl. Phys. 77 (8) (1995) 3618–3622. [26] N.A. Burnham, R.J. Colton, Measuring the nanomechanical properties <strong>and</strong> surface forces of materials using an atomic force microscope, J. Vac. Sci. Technol. 7 (4) (1989) 2906–2913. [27] B. Du, O.K.C. Tsui, Q. Zhang, T. He, Study of elastic modulus <strong>and</strong> yield strength of polymer thin films using atomic force microscopy, Langmuir 17 (2001) 3286–3291. [28] J. Domke, M. Radmacher, Measuring the elastic properties of thin polymer films with the atomic force microscope, Langmuir 14 (1998) 3320–3325. [29] W.A. Ducker, T.J. Senden, R.M. Pashley, Direct measurement of colloidal forces using an atomic force microscope, Nature 353 (1991) 239–241. [30] O.I. Vinogradova, G.E. Yakubov, Dynamic effects on force measurements. 2. Lubrication <strong>and</strong> the atomic force microscope, Langmuir 19 (2003) 1227–1234. [31] P.G. Hartley, F. Grieser, P. Mulvaney, G.W. Stevens, Surface forces <strong>and</strong> deformation at the oil–water interface probed using AFM force measurement, Langmuir 15 (1999) 7282–7289. [32] R.E. Mahaffy, C.F. Shih, F.C. MacKintosh, J. Käs, Scanning probe-based frequencydependent microrheology of polymer gels <strong>and</strong> biological cells, Phys. Rev. Lett. 85 (4) (2000) 880–883. [33] J.L. Alonso, W.H. Goldmann, Feeling the forces: atomic force microscopy in cell biology, Life Sci. 72 (2003) 2553–2560. [34] K.E. Bremmell, A. Evans, C.A. Prestidge, Deformation <strong>and</strong> nano-rheology of red blood cells: an AFM investigation, Coll. Surf. B Biointerfaces 50 (2006) 43–48. [35] Y-Z. Hu, S. Granick, Microscopic study of thin film lubrication <strong>and</strong> its contributions to macroscopic tribology, Tribology Lett. 5 (1998) 81–88. [36] G. Gillies, C.A. Prestidge, P. Attard, An AFM study of the deformation <strong>and</strong> nanorheology of cross-linked PDMS droplets, Langmuir 18 (2002) 1674–1679. [37] G. Gillies, C.A. Prestidge, Interaction forces, deformation <strong>and</strong> nano-rheology of emulsion droplets as determined by colloid probe AFM, Adv. Colloid Interface Sci. 108–109 (2004) 197–205.
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