R. C. Bowen

Mechanics of particle adhesion

The adhesion of particles to surfaces is accompanied by deformations of the materials arising from adhesion force-induced stresses. These deformations, which can be the result of an elastic, a nonlinear elastic, a viscoelastic, or a plastic response of the materials to the stresses, can significantly affect the forces needed to remove the particles from the substrate. The mechanics of adhesion-induced deformations between micrometer-size particles and various substrates are discussed in this paper. Examples of elastic and plastic deformations resulting from the adhesion forces are presented. The experimental results are analyzed in terms of various adhesion theories, which, under certain circumstances, permit the calculation of the thermodynamic work of adhesion for contacting solids. The ranges of validity of these theories and their predictions are discussed. Finally, adhesion-induced deformations which are not currently explicable in terms of these theories are presented.

Surface-force-induced deformations of monodisperse polystyrene spheres on planar silicon substrates

The contact radii between polystyrene spheres, having diameters between approximately 1.5 and 12 μm, and polished silicon wafers, arising from adhesion forces, were determined using scanning electron microscopy. It was found that the contact radius varied approximately as the square root of the particle radius. This dependence is consistent with nonelastic response models of adhesion, such as those proposed by Krupp [H. Krupp, Adv. Colloid Interface Sci. 1, 111 (1967)] and by Maugis and Pollock [D. Maugis and H. M. Pollock, Acta Metall. 32, 1323 (1984)], but is inconsistent with various elastic response models which assume Hertzian deformations. The experimentally determined contact radii are also compared to those obtained for polystyrene spheres on a polyurethane substrate [D. S. Rimai, L. P. DeMejo, and R. C. Bowen, J. Appl. Phys. 66, 3574 (1989)].

Adhesion‐induced deformations of polymeric substrates: Particle size dependence of the contact area

Adhesion‐induced deformations of a polyurethane substrate in contact with cross‐linked polystyrene spheres, having diameters ranging from less than 2 μm to approximately 12.5 μm were observed using scanning electron microscopy. The diameters of the contact areas were measured from the micrographs. It was found that the contact radius varied as the particle radius raised to the 0.75±0.05 power. Experimental results are compared to the predictions of various adhesion models. The results are also discussed in terms of the Dupre work of adhesion.

Adhesion-induced deformations of polyurethane substrates in contact with spherical glass particles : the effect of particle size on the radius of contact

Spherical glass particles having radii between approximately 0.5 and 100 *m were deposited onto a polyurethane substrate and the radii of contact, resulting from the adhesion forces between the particles and the substrate, were determined using SEM. For particles having radii less than approximately 5 μm, it was found that the contact radius varied as the particle radius to the 0.75 power. In addition, large menisci, presumably resulting from tensile interations, were observed. For particles having radii between 5 and 60 μm, the contact radius varied as the particle raidus to the 2/3 power. Stretching of the substrate was also observed for particles having radii of approximately 100 μm. This is probably a harbinger of the impending separation of the particle from the substrate, due to gravitational forces. The thermodynamic work of adhesion was calculated from the data and the results were compared with the predictions of several theories of particle adhesion.

Direct observations of deformations resulting from particle-substrate adhesion

Deformations of planar substrates and contacting particles due to surface forces, such as the van der Waals interactions, were postulated long ago. Direct observations of such deformations between submicrometer Kynar 301 F™ particles and substrates consisting of polyester-siloxane block copolymers or polished silicon, obtained using scanning electron microscopy (SEM), are presented. The deformations observed in the polyester-siloxane substrate are too large to be explained using Hertzian theory of elastic behavior but are consistent with the plastic deformation model of Krupp and the tensile model of Johnson et al. Potential experimental artifacts, such as space charge effects and the effect of using conducting coatings, are discussed.

Observations of adhesion-induced deformations between spheroidal gold particles and conducting substrates

Spheroidal gold particles, approximately 3 μm in diameter, were deposited on both hard and soft planar, electrically conducting substrates, and the interfaces were observed using scanning electron microscopy. It was observed that the particles appeared to embed into the softer substrate, but not into the harder one. The softer substrate also appeared to flow up the sides of the particles. The diameters of the craters formed are compared with the predictions based on Hertz’ [Zimon, Adhesion of Dusts and Powders (Consultants Bureau, New York, 1982)] model of elastic deformation, Krupp’s [Adv. Colloid Interface Sci. 1, 111 (1967)] model of plastic response [assuming van der Waals (Zimon, ibid. and Krupp, ibid.) interactions], and Johnson, Kendall, and Roberts’ [Proc. R. Soc. London Ser. A 324, 301 (1971)] model of tensile response due to surface tension. These calculations suggest that the observed deformation on the softer substrate is predominantly plastic rather than elastic and that surface tension is si...

Adhesion Induced Flow of a Soft Polyester-Polydimethylsiloxane Copolymer Substrate Over Micrometer and Submicrometer Size Spherical Particles: Observations of Anomalously Large Menisci, Interparticle Bridging and Particle Encapsulation

Abstract Observations made with a scanning electron microscope (SEM) provided direct evidence for a soft polyester-polydimethylsiloxane block copolymer substrate undergoing extensive surface-force-induced plastic deformation upon contact with micrometer or submicrometer size spherical particles. Anomalously large menisci were detected at the particle /substrate interfaces. Moreover, the substrate material appeared to bridge or encapsulate the particles. The heights of the contact menisci between the 2.2 micrometer radius polystyrene beads and the substrate were found to be approximately 0.4 micrometers; those between 3.6 micrometer radius glass spheres and the substrate were approximately 0.5 micrometers. The heights of the observed menisci were found to be large compared with the values calculated using Tabors analysis (D. Tabor, J. Colloid Interface Sci. 58, 2 (1977)) based on the elastic model proposed by Johnson, Kendall and Roberts (K. L. Johnson, K. Kendall, and A. D. Roberts, Proc. R. Soc. London ...

The Adhesion of Particles to Polymer Coated Substrates

A rigid polyester substrate was overcoated with 10 μm, 25 μm, and 50 μm thick coatings of polystyrene containing varying concentrations of plasticizer between 0% and 20%. Micrometer-size glass spheres were deposited onto these substrates and the deformations of the substrates resulting from the forces of adhesion were then examined using scanning electron microscopy (SEM). For substrates which were in the glassy phase, the power law dependence of the contact radius on particle radius was 0.48. In contrast, for the case of rubbery substrates, the contact radius was found to vary as the particle radius to the 0.65 power. These results are consistent with the predictions of the adhesion models of Maugis and Pollock [D. Maugis and H. M. Pollock, Acta Metall. 32, 1323 (1984) and Johnson et al., [K. L. Johnson, K. Kendall, and A. D. Roberts, Proc. Roy. Soc. London Ser. A 324, 301 (1971)], respectively. This implies that, depending on the glass transition temperature of the substrate, either plastic or elastic deformations can occur. Also presented and discussed is the observation of critical engulfment, whereby the surface forces draw the particle substantially or totally into the substrate.

Effects of bulk and surface properties of materials on adhesion-induced deformations between submicrometer diameter particles and substrates

—Spherical particles of polyvinylidene fluoride (PVF2), of 0.3 μm diameter, were deposited onto various substrates including polyester, a polyester-polydimethylsiloxane block copolymer (hereafter referred to as PSBC), and polished silicon. The adhesion force-induced deformations between the particles and substrates were then observed using scanning electron microscopy (SEM). It was found that the particles embedded most deeply into the soft PSBC. No embedding of the particles into the Si wafers was observed, although the particles, themselves, appeared to flatten. The particles were also observed to embed into the polyester, although to a lesser extent than they did into the PSBC. Moreover, when the particles contacted samples of polyester which had been plasma-treated in argon, the embedding decreased. Measured contact area diameters are compared to predictions of various models of adhesion. The effect of the thickness of a conducting (Au/Pd) coating on the appearance of the contact zone is also discussed.

Effects of thin, semi‐rigid coatings on the adhesion‐induced deformations between rigid particles and soft substrates

Glass particles, having nominal radii of approximately 20 μm, were deposited onto polyurethane substrates, which had been overcoated with a 5‐μm‐thick thermoplastic layer, and the surface‐force‐induced contact radii were measured using scanning electron microscopy. It was found that the size of the deformations depends only on the modulus of the coating and not on the modulus of the underlying substrate. The measured contact radii were found to scale with the Young’s modulus of the substrate for the uncoated polyurethane substrates according to the predictions of the JKR model [K. L. Johnson, K. Kendall, and A. D. Roberts, Proc. R. Soc. London Ser. A 324, 301 (1971)]. However, the contact radii on the overcoated substrates appear to be more accurately predicted by the DMT theory [B. V. Derjaguin, V. M. Muller, and Yu P. Toporov, J. Colloid Interface Sci. 53, 314 (1975)].