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Langmuir 2002, 18, 716-721
Correction of Microrheological Measurements of Soft Samples with Atomic Force Microscopy for the Hydrodynamic Drag on the Cantilever J. Alcaraz,† L. Buscemi,† M. Puig-de-Morales,† J. Colchero,‡ A. Baro´,‡ and D. Navajas*,† Unitat de Biofı´sica i Bioenginyeria, Facultat de Medicina, Universitat de BarcelonasIDIBAPS, Casanova 143, E-08036 Barcelona, Spain, and Laboratorio de Nuevas Microscopı´as, Departamento de Fı´sica de la Materia Condensada, C-III, Universidad Auto´ noma de Madrid, E-28049 Madrid, Spain Received July 16, 2001. In Final Form: October 21, 2001 Force measurements with atomic force microscopy (AFM) in liquid are subjected to the hydrodynamic drag force artifact (Fd) due to viscous friction of the cantilever with the liquid. This artifact may be especially relevant in microrheological studies of soft samples. Common approaches estimate Fd at a certain distance above the sample and subtract its value from the contact force measured on the sample. However, this procedure can underestimate Fd at contact. The aim of this work was to assess the effect of the hydrodynamic drag in microrheological AFM measurements of soft samples in liquid at low Reynolds numbers (Re < 1). Drag forces of water on rectangular and V-shaped cantilevers were measured in noncontact when subjecting the substrate to low-amplitude (35 nm) sinusoidal oscillations at different frequencies (1-200 Hz) and tip-substrate distances (h) (0.2-3 µm). Fd increased proportionally with the relative velocity (v). Moreover, the drag factor b(h) defined as Fd/v rose when the cantilever approached the substrate. Thus, the hydrodynamic drag exhibited locally a pure viscous behavior. Drag factor dependence on distance was well-fitted (r2 ≈ 0.95) by the scaled spherical model b(h) ) 6πηaeff2/(h + heff), where η is the viscosity of the liquid, aeff is the effective radius of the cantilever, and heff is the effective height of the tip. Drag factor at contact was estimated as b(0) ) 1.38 × 10-6 (rectangular) and 1.55 × 10-6 Ns/m (V-shaped) by extrapolating b(h) to h ) 0. Drag factor measured at 2 µm underestimated b(0) by 30-50%. Thus, correction of the hydrodynamic artifact with drag factor measured a few micrometers above the surface could result in substantial errors in AFM microrheological measurements of soft samples. Our results suggest that drag artifact in contact microrheological measurements under low Re can be accurately estimated by b(0). Precise correction of drag artifact could lead to an improvement in scan speed in contact AFM imaging and in pulling speed in force spectroscopy studies.
Introduction 1
The ability of the atomic force microscopy (AFM) to explore samples in liquid with high force resolution has been used recently to probe microrheological properties of soft samples in their natural aqueous environment. Examples include complex fluids,2 polymers,3-5 proteins6,7 and living cells.5,8-11 In these studies the tip of the AFM cantilever squeezes the surface of the sample, and the cantilever bending force (F) and the sample indentation * Corresponding author. Telephone: +34 93 402 4525. Fax: +34 93 402 4516. E-mail:
[email protected]. † Universitat de BarcelonasIDIBAPS. ‡ Universidad Auto ´ noma de Madrid. (1) Binnig, G.; Quate, C. F.; Gerber, C. Phys. Rev. Lett. 1986, 56, 930. (2) O’Shea, S. J.; Welland M. E. Langmuir 1998, 14, 4186. (3) Braithwaite, G. J. C.; Luckham, P. F. J. Colloid Interface Sci. 1999, 218, 97. (4) Nakajima, K.; Yamagucii H.; Lee J. C.; Kageshima J. Jpn. J. Appl. Phys. 1997, 36 (6B), 3850. (5) Mahaffy, R. E.; Shih, C. K.; MacKintosh, F. C.; Ka¨s, J. Phys. Rev. Lett. 2000, 85, 880. (6) Nemes, Cs.; Rozlosnik, N.; Ramsden, J. J. Phys. Rev. E 1999, 60, R1166. (7) Radmacher, M.; Fritz, M.; Cleveland, J. P.; Walters, D. A.; Hansma, P. K. Langmuir 1994, 10, 3809. (8) A-Hassan, E.; Heinz, W.; Antonik, M. D.; D’Costa, N. P.; Nageswaran, S.; Schoenenberger, C. A.; Hoh, J. H. Biophys. J. 1998, 74, 1564. (9) Shroff, S. G.; Saner, D. R.; Lal, R. Am. J. Physiol. 1995, 269, C286. (10) Wu, H. W.; Kuhn, T.; Moy, V. T. Scanning 1998, 20, 389. (11) Radmacher, M.; Fritz, M.; Kacher, C. M.; Cleveland, J. P.; Hansma, P. K. Biophys. J. 1996, 70, 556.
(δ) are measured. Rheological properties of the sample are obtained from the relationship between F and δ. The indentation is commonly produced by displacing either the sample or the cantilever with a piezoactuator or a magnetic device. Microrheology of the sample has been probed by applying steps10 or more commonly triangular6 and sinusoidal5 oscillations. The bandwidth of the measurements is usually limited to low frequencies (
