Langmuir 2008, 24, 2271-2273
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Effect of Tip Size on Force Measurement in Atomic Force Microscopy Leonard T. W. Lim,† Andrew T. S. Wee,† and Sean J. O’Shea*,‡ Department of Physics, National UniVersity of Singapore, Lower Kent Ridge Road, Singapore 119620, and Institute of Materials Research and Engineering, 3 Research Link, Singapore 117602 ReceiVed October 17, 2007. In Final Form: January 29, 2008 An atomic force microscope (AFM) has been used to study solvation forces at the solid-liquid interface between highly oriented pyrolytic graphite (HOPG) and the liquids octamethylcyclotetrasiloxane (OMCTS), n-hexadecane (n-C16H34), and n-dodecanol (n-C11H23CH2OH). Oscillatory solvation forces (F) are observed for various measured tip radii (Rtip ) 15-100 nm). It is found that the normalized force data, F/Rtip, differ between AFM tips with a clear trend of decreasing F/Rtip with increasing Rtip.
Induced molecular ordering in liquids by confining solid surfaces is an interesting aspect of the solid-liquid interface. Observable changes arise in the short-range solvation (or structural) forces1 acting between two solids in a liquid medium as a result of changes in liquid density and potential near the solid. This is of considerable importance from the fundamental viewpoint of confined materials and in practical applications of lubrication, adhesion, and coatings. Extensive studies on solvation forces in various systems have been done in the last two decades using the surface force apparatus (SFA)1-4 and, more recently, computer simulations5-8 and atomic force microscopy (AFM).9-12 Because of the difference in the interaction geometries between AFM and SFA experiments, the Derjaguin approximation13 is widely used as a method of scaling the measured forces obtained by AFM and SFA to enable comparisons to be made. By converting the force between the two surfaces to an energy per unit area, various forms of interactions (sphere-sphere, sphereflat, etc.) can be compared easily. For example, the Derjaguin approximation for a sphere on a flat surface (i.e., the AFM geometry) is given by1
F(D) ) 2πRtipW(D)
(1)
where W(D) is the interaction free energy between two planar surfaces and Rtip is the tip radius. For the case of two cylinders of radii R1 and R2 that are at an angle θ to each other (i.e., the geometry for SFA), the Derjaguin approximation gives * To whom correspondence should be addressed. E-mail:
[email protected]. † National University of Singapore. ‡ Institute of Materials Research and Engineering. (1) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: New York, 1992. (2) Christenson, H. K. J. Chem. Phys. 1983, 78, 6906. (3) Horn, R. G.; Israelachvili, J. N. J. Chem. Phys. 1981, 75, 1400. (4) Klein, J.; Kumacheva, E. Science 1995, 269, 816. (5) Gao, J. P.; Luedtke, W. D.; Landman, U. J. Phys. Chem. B 1997, 101, 4013-4023. (6) Gao, J. P.; Luedtke, W. D.; Landman, U. J. Chem. Phys. 1997, 106, 43094318. (7) Gelb, L. D.; Lynden-Bell, R. M. Phys. ReV. B 1994, 49, 2058-2066. (8) Porcheron, F.; Rousseau, B.; Schoen, M.; Fuchs, A. H. Phys. Chem. Chem. Phys. 2001, 3, 1155-1159. (9) Franz, V.; Butt, H. J. J. Phys. Chem. B 2002, 106, 1703-1708. (10) Lim, R.; Li, S. F. Y.; O’Shea, S. J. Langmuir 2002, 18, 6116-6124. (11) O’Shea, S. J.; Welland, M. E. Langmuir 1998, 14, 4186-4197. (12) Jarvis, S. P.; Uchihashi, T.; Ishida, T.; Tokumoto, H.; Nakayama, Y. J. Phys. Chem. B 2000, 104, 6091-6094. (13) Derjaguin, B. V. Kolloid Z. 1934, 69, 155.
F(D) )
2π xR1R2W(D) sin θ
(2)
Typically, R1 ≈ R2 and θ ) 90°, and eqs 1 and 2 are identical. The Derjaguin approximation will hold when the range of the force interaction and the separation between the surfaces are much less than the radius of curvature of the surfaces. However, recent work has begun to probe the limits of validity of the approximation. Todd and Eppell14 used a sharp silicon nitride AFM probe (Rtip ) 7 nm) and varied the range of the force interaction by changing the electrolyte concentration of aqueous solutions. They showed that the approximation matched the measured forces when the Debye length was small but overestimated the forces for large Debye lengths. Thus, a breakdown of the approximation was demonstrated, and under such conditions, they recommend using the surface element integration method.15 It has also been demonstrated theoretically16 that the superposition principle (analogous to the Derjaguin approximation) can be used to model solvation forces on rough surfaces provided the wavelength of the roughness is small. Rentsch and co-workers,17 using colloidal particles, found the approximation to be robust but suggested that a failure of the approximation is expected in sharp probe experiments where the tip radius is comparable to the interaction range. For short-range forces, as in this study, the Derjaguin approximation is expected to be valid, but one must also consider the tip topography of the measurement. In earlier AFM work, we showed that very blunt tips (Rtip ) 350 nm) can measure the same magnitude of solvation forces as ultrasharp tips (Rtip ≈ 14 nm).11 The underlying reason is that microasperities on the tip dominate the short-range interaction and force interactions with the macroscopic tip (Rtip) are secondary.18 Similar observations were made for tips consisting of well-characterized, clean colloid spheres (Rtip ) 10 µm).10 Recent studies show that nanoscale roughness also influences the adhesion force measured between a surface and colloid tips (Rtip ) 200 nm to 60 µm).19,20 A decrease in the adhesion force with increasing surface roughness (on the
