Langmuir 1997, 13, 2533-2537
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Contact Electrification and the Interaction Force between a Micrometer-Size Polystyrene Sphere and a Graphite Surface B. Gady and R. Reifenberger* Department of Physics, Purdue University, West Lafayette, Indiana 47907
D. S. Rimai and L. P. DeMejo Office Imaging Research and Technology Development, Eastman Kodak Company, Rochester, New York 14653-6402 Received July 2, 1996. In Final Form: December 11, 1996X Two independent techniques are used to measure the interaction force between a single 3 µm radius polystyrene sphere and an atomically flat, highly oriented pyrolytic graphite substrate. The variation of the interaction force with the surface-to-surface separation between the sphere and plane is determined using both a static and a dynamic atomic force technique. The measured interaction force is dominated at long range by an electrostatic force arising from localized charges triboelectrically produced on the sphere when it makes contact with the substrate. For small sphere-substrate separations, evidence for a van der Waals force is observed. The data provide consistent estimates for both the Hamaker coefficient and the triboelectrically produced charge which can be measured to an accuracy of (10 electrons.
Introduction To better understand such phenomena as particle adhesion to flat substrates, it is useful to characterize the nature of the interaction forces acting on individual particles. As shown previously, this can be done by attaching micrometer-size particles to an atomic force cantilever and measuring the interaction force gradient using an oscillating cantilever technique.1 In that study, both a van der Waals and electrostatic contribution to the interaction force were identified. In the present study, we attempt to better characterize the electrostatic contribution to the interaction and obtain quantitative estimates on the charge transfer between the sphere and substrate. This is accomplished by using two independent techniques to measure the interaction force acting between an individual insulating spherical particle and a grounded, conducting substrate. Using two techniques allows us to better assess the reliability of our results and adds confidence to the model required to understand our data. In this study, the interaction between a 3 µm radius polystyrene sphere and a grounded highly oriented pyrolytic graphite (HOPG) substrate was investigated using two independent atomic force microscope (AFM) techniques. The advantages of using an AFM configuration for such studies is the ability to measure subnanonewton forces combined with the flexibility in attaching arbitrary objects to the AFM cantilever.1-4 This later modification to the standard AFM cantilever allows for the investigation of the interaction forces between any micrometer-size object and a flat substrate. Under ideal conditions, a van der Waals interaction force is expected. Recently, however, Burnham et al.5,6 demonstrated that X Abstract published in Advance ACS Abstracts, February 15, 1997.
(1) Gady, B.; Schleef, D.; Reifenberger, R.; DeMejo, L. P.; Rimai, D. S. Phys. Rev. B 1996, 53, 8065. (2) Martin, Y.; Williams, C. C.; Wickramasinghem, H. K. J. Appl. Phys. 1987, 61, 4723. (3) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Nature 1991, 353, 239. (4) Mackel, R.; Baumgartner, H.; Ren, J. Rev. Sci. Instrum. 1993, 64, 1897. (5) Burnham, N. A.; Colton, R. J.; Pollock, H. M. Phys. Rev. Lett. 1992, 69, 144.
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force measurements taken with a nonoscillating AFM tip attached to a cantilever could be modeled using an electrostatic ‘patch charge’ effect, whereby it was proposed that attractive long-range forces arise from localized variations in the Fermi energies of the materials. Alternatively, Hays proposed that, in general, interaction forces between micrometer-size particles and flat substrates could be explained in terms of a nonuniform triboelectrically produced charge on the particle.7 This latter proposal is in qualitative agreement with our initial data.1 In what follows, we present new results for the interaction force and interaction force gradient acting on a 3 µm radius polystyrene sphere as a function of the surfaceto-surface distance above a flat HOPG surface. This new data allow a quantitative estimate for the charge transfer that results when the polystyrene sphere comes into contact with the HOPG substrate. Experimental Considerations Two techniques were used to measure the interaction between a polystyrene sphere and a flat surface using AFM techniques. The two methods can be broadly classified as static and dynamic modes of AFM operation. The first technique is a direct measurement of the force between a sphere mounted on an AFM cantilever and a grounded HOPG substrate. This technique is generally suited for soft cantilevers and long-range forces. The second method employs a frequency modulation technique to measure a force gradient between the sphere and substrate. This technique is better suited for small interaction forces and stiffer cantilevers. As will be shown below, our data indicate that these two independent modes of operation yield good agreement for both the electrostatic and van der Waals contribution to the interaction force between a 3 µm radius polystyrene sphere and an HOPG substrate. A polystyrene sphere was mounted on the edge of an AFM cantilever8 using a microscopic drop of Norland Optical Cement No. 68 on the tip of the cantilever with the aid of an optical (6) Burnham, N. A.; Colton, R. J.; Pollock, H. M. Nanotechnology 1993, 4, 64. (7) Hays, D. A. Adhesion of charged particles. In Fundamentals of Adhesion and Interfaces; Rimai, D. S., DeMejo, L. P., Mittal, K. L., Eds.; VSP: Utrecht, 1995; pp 61--71. (8) Available from Park Scientific Instruments, Sunnyvale, CA 94089.
© 1997 American Chemical Society
2534 Langmuir, Vol. 13, No. 9, 1997
Gady et al.
microscope system with an overall magnification of 750×. Experiments have shown that this cement remains viscous for a sufficiently long time to accurately position the sphere in the cement with the aid of a micromanipulator. The particle was pressed into the cement to allow close contact of the particle with the cantilever. As discussed previously, the cement was cured by exposure to UV light for approximately 10-15 min.9 As discussed below, there is some evidence that the exposure of the sphere to UV light during the curing process sensitizes the sphere for contact electrification. After curing, the sphere and cantilever were mounted inside a home-built AFM system, which is enclosed in a small, stainless steel chamber.9 Detection of the cantilever displacement as a function of the sphere-substrate separation distance was done using a laser deflection method and phase sensitive detection.10-12 A 68030 CPU-based computer system, similar to that described previously,13 controlled the experiment. The spring constants of all cantilevers were independently calibrated by measuring the resonance frequency of the bare cantilevers, as discussed elsewhere.14 To avoid problems with adsorbed layers of water, all measurements were performed in a partial vacuum of ∼20 mTorr after purging the system repeatedly with dry nitrogen. To measure the interaction force directly, the cantilever remains fixed as the substrate is moved toward the lever. As the sphere-substrate separation decreases, the lever deflection measures the interaction force. Using the spring constant k and measuring the deflection, a force can be calculated from Hooke’s law
Finter ) k(z - z0)
(1)
By measuring the deflection of the lever when it jumps to contact with the surface, an absolute calibration of surface-to-surface separation, z0, can be obtained. Noncontact (dynamic mode) force gradients can be determined by measuring the resonant frequency of the mounted cantilever as a function of z0. As the separation distance decreases, the gradient of the interaction force causes a reduction in the resonance frequency. This effect can be understood by considering the equation of motion for a driven cantilever oscillating at a frequency ω and located at a position z0 from the surface:
mz¨ + γz˘ - k(z - z0) + Finter(z) ) Fd cos(ωt)
(2)
In eq 2, m is the mass of the sphere, γ is a constant describing the damping of the cantilever, k is the measured spring constant of the cantilever (∼2 N/m), Finter is the interaction force of interest, and Fd is the driving force applied to the cantilever. It has been shown that the shift in resonance frequency ω0(z0) when compared to the resonance frequency at infinite separation (ω∞) provides a first-order approximation to the interaction force gradient15
[ ( )]
∂Finter ω0(z0) )k 1∂z ω∞
2
(3)
Theoretical Considerations A priori, a model to explain the interaction between a micrometer-size sphere and a grounded plane should take into account at least two contributions. One contribution is due to the van der Waals interaction between macroscopic objects. The force of interaction has been derived elsewhere for various interacting geometries.16 For a sphere interacting with a flat plane, the force in the nonretarded limit is given by (9) Schaefer, D. M.; Carpenter, M.; Gady, B.; Reifenberger, R.; DeMejo, L. P.; Rimai, D. S. J. Adhesion Sci. Technol. 1995, 9, 1049. (10) Meyer, G.; Amer, N. M. Appl. Phys. Lett. 1988, 53, 1045. (11) Meyer, G.; Amer, N. M. Appl. Phys. Lett. 1988, 53, 2400. (12) Alexander, S.; Hellemans, L.; Marti, O.; Schneir, J.; Elings, V.; Hansma, P. K.; Longmire, M.; Gurley, J. J. Appl. Phys. 1989, 65, 164. (13) Piner, R.; Reifenberger, R. Rev. Sci. Instrum. 1989, 60, 3123. (14) Cleveland, J. P.; Manne, S.; Bocek, D.; Hansma, P. K. Rev. Sci. Instrum. 1993, 64, 403. (15) Ducker, W. A.; Cook, R. F.; Clarke, D. R. J. Appl. Phys. 1990, 67, 4045. (16) Hamaker, H. C. Physica 1937, 58, 1058.
Fvdw ) -
HR 6z02
(4)
where H is the Hamaker coefficient, R is the radius of the sphere, and z0 is the surface-to-surface separation.17 This equation describes the van der Waals interaction for a sphere-plane geometry as determined by the Derjaguin approximation. The well-defined power law dependence (z0 - 2) on the interaction force serves as a clear signature for the identification of a van der Waals interaction. The second contribution is due to any net electric charge that may reside on the sphere. In principle, contributions to the interaction force from both a uniformly charged sphere and a localized distribution of charge on the sphere need to be considered. In vacuo, a convenient form for the electrostatic force between a sphere of radius R at a potential V and a flat plane a distance R + z0 from the center of the sphere is given by18
Fel )
[
-2π0R2V2
]
8R(R + z0) 1 + (5) 2 2(z0 + R) [4(R + z0)2 - R2]2 + ...
The first term in eq 5 describes the force between a grounded conducting plane and a uniform charge distribution frozen in place on the sphere. The higher order terms describe polarization effects that result when the sphere is moved closer to the plane. If the charges are trapped, as is the case here, only the first term is required. The electrostatic potential V can be related to the charge Q on the sphere using the capacitance C of a sphere of radius R whose center is suspended a distance of R + z0 above a conducting plane19
C)
Q ) 4π0R[1 + r + ...] V
(6)
where r ) R/2 (R + z0). Expressions for the relevant force gradient can be obtained by differentiating eqs 4 and 5 with respect to the separation distance. Equation 5 can be used to discuss two limiting charge distributions on an insulating sphere. The first case is a uniform distribution spread over the entire sphere (Figure 1a). The second is a localized charge distribution within the volume of the sphere (Figure 1b). Such localized charge might arise by a triboelectric charging of the sphere on contact with a conducting plane. This second possibility will likely require the presence of a localized charge at the bottom of the sphere, extending over a spherical region characterized by some effective radius Reff
