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Langmuir 2004, 20, 5298-5303
Particle Adhesion Force Distributions on Rough Surfaces M. Go¨tzinger and W. Peukert* Institute of Particle Technology, Friedrich-Alexander-Universita¨ t Erlangen-Nu¨ rnberg, Cauerstraβe 4, 91058 Erlangen, Germany Received January 11, 2004. In Final Form: April 10, 2004 The effect of roughness on adhesion force distribution was studied in the gas phase. Spherical gold particles with diameters between 5 and 20 µm were generated in a flame process and glued onto atomic force microscope (AFM) cantilevers directly after. Nanostructured substrates with defined roughness were produced by a dip-coating process. The geometry of the adhering partners was determined by AFM imaging, and the adhesion force was measured with the AFM. Depending on the roughness of the particles and the substrates, three types of distribution functions can be identified; two of them can be explained with a simple model. The obtained adhesion force distributions not only agree with those experimentally recorded in previous studies of commercially important powders (e.g., alumina, toner, and gold on different substrates) but also agree with distributions reported in the literature.
Introduction Particle adhesion plays a major role in many industrial fields, for example, in the microelectronic industry (producing clean wafer surfaces), in coating applications (adhesion of powder paint), or in printing technology (transfer of toner particles in the electrophotographic process). Washbowls, rooftiles, or storefronts with tuned rough surfaces (“self-cleaning surfaces”) can commercially be acquired. Particle-particle interactions control the macroscopic behavior of powder systems, for example, in mixers, granulators, or fluidized beds. The key to controlling all of these techniques is the particle-particle and particle-substrate interactions. These complex interactions are influenced by material properties (e.g., the Hamaker constant and Young’s modulus), particle size and shape, surface properties (e.g., surface energy and roughness of the adhesion partners), external load, temperature, humidity, and electrostatic charges. They are, however, not yet fully understood. The most popular models for a smooth particle with diameter D interacting with a smooth substrate were derived by Johnson et al.1 (Johnson-Kendall-Roberts (JKR) model), Derjaguin et al.2 (Derjaguin-MullerToporov (DMT) model), Maugis,3 Maugis and Pollok,4 and Hamaker.5 The JKR, DMT, and Maugis models use the surface energy (γ1,2) to predict adhesion forces:
FDMT(R) ) 2πDγ1,2 FJKR(R) ) 1.5πDγ1,2
(1)
These models also consider deformations. Unfortunately, they describe the separation force of a particle which is in contact with the surface without providing any information on the interaction force as a function of the separation distance. Therefore, the Hamaker approach * Corresponding lfg.uni-erlangen.de.
author.
E-mail:
W.Peukert@
(1) Johnson, K. L.; Kendall, K.; Roberts, A. D. Proc. R. Soc. London, Ser. A 1971, 324, 301. (2) Derjaguin, B. V.; Muller, V. M.; Toporov, Y. P. J. Colloid Interface Sci. 1975, 53, 314. (3) Maugis, D. J. Colloid Interface Sci. 1992, 150, 243-269. (4) Maugis, D.; Pollock, H. Acta Metall. 1984, 32, 1323. (5) Hamaker, H. C. Physica 1937, 4, 1058-1072.
is widely used to model interaction of rough particles.6,7 According to Hamaker, the interaction force can be described using the following equation:
F)
AD 12a2
(2)
which is valid for a , D/2. Herein, a denotes the distance between the particle and the surface. In contact, the distance is usually set to a0 ) 0.3-0.4 nm. A denotes the Hamaker constant and D the particle diameter. Improved models8-10 take surface properties such as adsorbed layers into consideration. Cooper et al.11 developed sophisticated numerical concepts to calculate the adhesion force of a single particle with many asperity contacts. An early model considering the effect of roughness on particle adhesion was derived by Rumpf6:
FRumpf(a) )
[
]
A R D + 6 a2 2(a + R)2
(3)
R denotes the radius of a single asperity under consideration. Rabinovich et al.7 found that the asperity radius is not sufficient to describe the adhesion force on technically rough surfaces. Instead of the asperity radius (R), they used the root mean square (rms) value of the surface. They introduced an additional parameter, λ, which denotes the surface distance between the asperities.
FvdW )
[
AD 12a2
1+
1 + 16Dk1rms
(
λ2
1 k1rms 1+ a
) (
)
]
2
(4)
k1 is a proportional factor with a value of 1.817. The model is only valid for a small asperity height (r) and a large distance (λ). The rms roughness can be measured with an (6) Rumpf, H. Chem.-Ing.-Tech. 1974, 46 (1), 1. (7) Rabinovich, Y. I.; Adler, J. J.; Ata, A.; Singh, R. K.; Moudgil, B. M. J. Colloid Interface Sci. 2000, 232, 10. (8) Langbein, D. In Proceedings of Physics of Adhesion; Bayer AG: Karlsruhe, Germany, 1969. (9) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1992. (10) Go¨tzinger, M.; Peukert, W. J. Adhes. 2004, 80 (3), 223-242. (11) Cooper, K.; Gupta, A.; Beaudoin, S. J. Colloid Interface Sci. 2001, 234, 284.
10.1021/la049914f CCC: $27.50 © 2004 American Chemical Society Published on Web 05/25/2004
Adhesion Force Distributions on Rough Surfaces
atomic force microscope (AFM), for instance. All these models provide a mean adhesion force. Since the AFM has been invented,12 AFM studies of single particles have permitted scientists to gain new and valuable insight into adhesion processes.13-16 However, adhesion force measurements referring to one particle and only one position of a heterogeneous substrate may be of little value. Adhesion forces are, as experimentally observed, usually distributed. Adhesion force distributions were recorded for the first time when applying ultracentrifugation to a particle ensemble.17,18 However, force distributions are also typical for AFM measurements of single particles. Their width strongly depends on the type of heterogeneities of both adhesion partners. Evans19 developed a sophisticated theory concerning the rupture of biomolecules. According to his theory, the rupture turns out to be a statistical process. Grandy et al.20 performed AFM studies in the pulsed force mode and recorded a Gaussian adhesion force distribution when analyzing homogeneous polystyrene and polymethyl methacrylate. Force distributions have been occasionally reported in chemical force spectroscopy.21,22 Only a few researchers have drawn their attention to adhesion force distributions of hard, inorganic particles.11 The purpose of this paper is to reveal the influence of roughness on particle-substrate interactions. On the basis of a single particle interaction approach, it is shown for the first time how roughness affects adhesion force distribution. Available models describe the mean adhesion force as a function of roughness.6,7 In experimental studies of technical systems as well as of model systems especially prepared for studies in adhesion science, adhesion force distributions are always found. Adhesion force distributions can be interpreted in a physically reasonable way by applying the basic Hamaker concept. In this paper, we introduce three generic types of adhesion force distributions. These types of adhesion force distributions have been also identified experimentally by using model substrates with defined roughness. Experimental Section Defined, rough silica substrates and a polished, smooth silica substrate (rms < 0.3 nm) were studied. To produce substrates with defined roughness, silicon wafers were coated by a dipcoating process. The substrates were immersed in three different coating sols containing nearly monodisperse silica particles of 30, 110, and 240 nm in size. The particle size distribution was determined by a dynamic light scattering technique in an Ultra Particle Analyzer (UPA, Microtrak). The distribution is narrow with a standard deviation as low as 12%. The substrates were withdrawn from the coating sol extremely slowly, at a rate of 1 cm/day. At such a low velocity, the deposition and the drying processes are overlapping. Regular, homogeneous mono- or bilayers of the nanoparticles were produced consisting of 110 or 240 nm particles. However, if the sol which contains the 30 nm particles was used, a coating of an ∼200 nm thickness was obtained. (12) Binning, G.; Quate, C.; Gerber, G. Phys. Rev. Lett. 1986, 56, 930. (13) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Langmuir 1992, 8, 1831. (14) Heim, L. O.; Blum, J.; Preuss, M.; Butt, H. J. Phys. Rev. Lett. 1999, 83 (16), 3328. (15) Biggs, S.; Spinks, G. J. Adhes. Sci. Technol. 1998, 12, 461. (16) Cappella, B.; Dietler, G. Surf. Sci. Rep. 1999, 34, 1. (17) Krupp, H. Adv. Colloid Interface Sci. 1967, 1, 111-239. (18) Schubert, H.; Sommer, H.; Rumpf, H. Chem.-Ing.-Technol. 1976, 48, 716. (19) Evans, E. Faraday Discuss. 1998, 111, 1. (20) Grandy, D. B.; Hourston, D. J.; Price, D. M.; Reading, M.; Silva, G. G.; Song, M.; Sykes, P. A. Macromolecules 2000, 33, 9348. (21) Williams, J. M.; Han, T.; Beebe, T. P. Langmuir 1996, 12, 1291. (22) van der Vegte, E. W.; Hadziioannou, G. Langmuir 1997, 13, 4357.
Langmuir, Vol. 20, No. 13, 2004 5299 More details on the theory of structure formation in dip-coating processes can be found in the work of Gu¨nther and Peukert.23 After the drying stage, the coatings were sintered at 815 °C for 15 min. This procedure ensures that the nanoparticles remain in a fixed position throughout the adhesion measurements and that the surface chemistry is well defined. Furthermore, the surface chemistry of the substrate obtained was characterized using thermogravimetric-mass spectrometric analysis (TG-MS) (Netsch STA 409C+ Balzer, QME 125) and Fourier transform infrared (FTIR) spectroscopy (evacuable Bruker IFS 66v). After drying the sol in air, a distinct band located at 1645 cm-1 and a strong stretching band with a maximum at 3473 cm-1 were found. The distinct band is attributed to the bending of physisorbed water. The peak of the stretched band is shifted from 3473 to 3544 cm-1 if the temperature increases to 400 °C (band of strongly interacting vicinal OH groups). Furthermore, a band corresponding to bulk OH groups (internal silanols) was observed at 3680 cm-1 up to temperatures of 500 °C. Geminal OH groups (3737-42 cm-1) begin to form at higher temperatures and could not be completely removed at temperatures around 800 °C. A small amount of hydrocarbons which had desorbed at temperatures of 400 °C was also identified (2947 cm-1). In TG-MS, a strong weight loss of 6% is observed at 150 °C accompanied by a drastic increase of the water mass spectrometer signal. From this weight loss, it is concluded that the silica surface is covered by five to six monolayers of water. Performing contact angle measurements (diiodomethane, dimethyl sulfoxide, ethylene glycol, and water) and making use of the analyzing method of Wu24 permits one to determine the surface energy of the smooth silica substrates as 32.8 mN/m prior to heat treatment. After heating of the silica substrate to 800 °C, the surface energy increased to 70.1 mN/m, accompanied by a decrease of the contact angle of water and diiodomethane from 75 to
