Study of adhesion between microspheres and rubber surfaces accompanied by meniscus formation and sedimentation
© The Author(s) 2017
Received: 1 November 2016
Accepted: 26 January 2017
Published: 6 February 2017
This paper reports on the adhesion characteristics between microspheres and rubber surfaces. Silica, polystyrene, and poly(methyl methacrylate) microspheres were deposited on cis-1,4-polybutadiene (BR) films. A BR meniscus formed on the sphere surfaces when the film thickness was less than the diameters of the spheres. Additionally, the attractive forces acting on the spheres in the direction of the BR films were examined via atomic force microscopy. Sedimentation of the spheres occurred for films with thicknesses much greater than the diameters of the microspheres in all systems. Interestingly, this wetting process occurred even in the silica/BR system, despite the incompatibility of these materials. The driving force for meniscus formation is the difference between the surface free energy of BR (γ BR) and that of the spheres (γ sphere). For all systems, γ BR is lower than γ sphere, i.e., the BR surface is more stable than those of the spheres, and thus a meniscus forms to stabilize the system. Once a meniscus formed, a downward force acted on the spheres to embed them into the BR film. Sedimentation eventually ceased when the angle between the tangential line of the sphere and the rubber surface became equal to the equilibrium contact angle determined by Young’s equation. Interestingly, the sedimentation behavior was nearly identical for spheres with various surface free energy values except in terms of their final positions. The same sedimentation phenomena were studied with crosslinked BR films. In contrast to the experiments performed using various types of spheres, the sedimentation behavior varied with different rubber characteristics. The results of these studies indicate that the sedimentation behavior mainly depends on the physical properties of the rubbers used, although the physical properties of the spheres are in determining their final depth.
KeywordsAdhesion Interface Surface free energy Meniscus Sedimentation
Pressure-sensitive adhesive (PSA) is a common means of adhesion used in various fields. Examples of daily use include adhesive tape or sticky paper. PSAs are also used in industrial fields such as building materials and cars. However, the phenomenon of adhesion is complex because of the many factors involved, such as surface free energy, viscoelasticity, and cohesion. Many studies have been conducted to investigate the nature of adhesion, most of which have focused on the various adhesion properties between spheres and substrates.
One of the most important aspects involved is the adhesive force. In particular, many theories have been proposed to address deformation induced by the adhesion of spheres on substrates. For example, Johnson et al.  investigated the deformation of macroscopic gelatin spheres and presented a theory known as the Johnson–Kendall–Roberts (JKR) theory, which takes a thermodynamic approach to adhesion. An adhesion energy between a rubber ball and a flat smooth glass surface was investigated by Roberts et al. . They observed the time-dependence of contact radius and surface energy with the equation based on JKR theory. These values eventually reached the certain values. The detail of time-dependence of fracture and adhesion energy was investigated by Presson et al. . Furthermore, Derjaguin et al.  proposed the Derjaguin–Muller–Toporov (DMT) theory, which includes long-range forces. The JKR theory and the DMT theory each have a certain range of validity . In addition to these theories, the Maugis–Pollock (MP) theory was presented by Maugis et al. . In comparison with the JKR and DMT theories, which assume purely elastic deformation, the MP theory is unique in addressing plastic deformation. High degrees of deformation in substrates have also been studied, for example in a paper by Rimai et al. using a plasticized polystyrene substrate and soda-lime glass spheres [7–9]. Under these conditions, Rimai et al. observed sedimentation of the spheres into the substrate and extended the JKR, DMT, and MP theories to include an understanding of the substrate deformation.
Aside from deformation studies, systems of spheres and substrates have also been investigated to determine the fundamental physical properties of polymers. For instance, Sharp et al.  directly assessed the near-surface properties of polystyrene films by monitoring how gold nanoparticles became embedded. The adhesive force between spheres and substrates coated with low viscosity liquids, such as water or silicon oil, have been investigated using a capillary bridge with atomic force microscopy (AFM) [11–14]. The measured force has been fitted to a hydrodynamic force, van der Waals attraction, electrostatic repulsion, hydrodynamic drag, and the restoring force of a cantilever [11, 13]. In addition to these forces, Ally et al.  has taken capillary forces into account, which has been a topic of interest among researchers for many years. Cross  and Pietsch  and their coworkers showed that the capillary force component results from the direct action of the surface free energy, with further details recently reported by Butt et al. .
In contrast to studies of deformation and adhesive force performed on low viscosity materials, few reports on the initiation of the adhesion process and wetting progress in viscoelastic materials are available. Therefore, the relationship between the initial stage of stickiness and the physical properties of polymers is not well understood.
In this study, we have investigated the adhesion characteristics between micro-scale spheres and rubber films with large thicknesses relative to the sphere diameters. Viscoelastic materials such as rubber generally require a long time to become wetted. To address this problem, we used spheres with sizes on the order of microns. For such small spheres, wetting at the surface proceeds in a sufficiently short time that we were able to observe the process. Additionally, we were able to observe deformation of the viscoelastic material caused by wetting. We focused on four main factors in order to investigate the process of adhesion, including two physical properties of the spheres, the surface free energy and the sphere size, in addition to the surface free energy, and viscoelasticity of rubber.
cis-1,4-Polybutadiene (BR) (BR01) was supplied by JSR Corp. The glass transition temperature T g of this material is −108 °C, while the number average of the molecular weight M n is 121,193 and M w/M n is 4.36. Dicumyl peroxide (DCP), which is a crosslinking agent for BR, was purchased from Sigma-Aldrich, Inc. Three types of silica spheres (Hyprecia) were obtained from Ube-Exsymo Co., Ltd with diameters of 5, 10, and 50 μm. Polystyrene (PS) spheres (SBX-12) and poly(methyl methacrylate) (PMMA) spheres (MB-8) were supplied by Sekisui Plastics Co., Ltd with diameters of 12 and 8 μm, respectively.
Rubber film preparation
Rubber films were prepared with two thicknesses. To prepare thin BR films with thicknesses around 500 nm, a BR solution in toluene (3.0 wt%) was spin-coated at 2000 rpm for 30 s onto a single-crystal silicon wafer with a native oxide layer (Mitsubishi Materials Trading Corp.). The film was dried for at least 24 h at room temperature and the film thickness was evaluated with an ellipsometer (SA-101; Photonic Lattice, Inc.).
Rubber films with large thicknesses compared to the diameter of the spheres were prepared by a solvent cast method. A BR solution in toluene (10 wt%) was cast onto a silicon wafer and the resulting film was dried for 24 h at room temperature in ambient conditions and for 24 h under vacuum. The film thickness was determined to be around 160 μm by scanning electron microscopy (SEM) (SM-200; Topcon Corp.). For thicker films, a crosslinked BR film was also made using a BR solution in toluene (10 wt%; DCP 1.5 phr for rubber). After drying in ambient conditions followed by vacuum drying, the film was annealed at 130 °C for 0, 15, 20, 25, and 30 min to induce crosslinking. Hereafter, the crosslinked samples are denote by the crosslinking time appended to BR (e.g., BR15 describes a BR film crosslinked for 15 min).
The surface free energies of the rubber films were evaluated with the Owens–Wendt equation . Because two types of contact angles are required for this evaluation, we used ultrapure water and diiodomethane, and determined the contact angles with a Dropmaster 300 from Kyowa Interface Science Co., Ltd.
The storage modulus G′ and the loss modulus G″ of the rubber were measured with a rheometer (parallel plate, \(\phi\) = 25 mm, 20 °C, Rheometrics dynamic mechanical spectrometer RDS-7700; Rheometrics, Inc.).
Test for adhesion of spheres to rubber surfaces
The spheres were deposited onto the rubber films, then nitrogen gas was blown across the rubber surfaces to remove any unattached spheres. The interfacial area between the spheres and the rubber was imaged using SEM after resting the samples for a designated length of time.
Force-distance curves from particle probe measurements
The adhesion between the silica spheres and thin rubber films was investigated by AFM. These measurements used a silicon cantilever with a silica sphere at the tip (23.9 N/m spring constant, 10 μm silica sphere diameter, 400 nm/s scanning rate, Novascan Technologies, Inc.).
The attractive force was also measured by AFM by first moving the sample stage to approach the cantilever and pausing the approach after contact occurred between the substrate and the cantilever following a jump in the force curve. Then, the measured force returned to 0 N, the sample stage was fixed, and the changes in detected force with time were recorded.
Equilibrium contact angle measurements
A 500-nm-thick BR film was produced using the above method. The film was scratched with tweezers, and submicron fragments of BR that remained attached to the tip of the tweezers were placed on a flat silica glass surface. Changes in the contact angle with time were observed by SEM.
Results and discussion
Figure 5 also shows that sedimentation eventually ceased at a certain depth, depending on the type of sphere. The final depths were 85% for silica spheres, 95% for PS spheres, and 96% for PMMA spheres. The angle between the rubber surface and the tangential line to the sphere at its final position, θ end, was calculated using the final depth, δ/D. These values were 45°, 26°, and 23°, respectively. According to Eqs. (4) and (5), the sedimentation should cease when the meniscus has vanished. Disappearance of the meniscus requires that Δp = 0 and θ = π − \(\phi\), then F Lap = 0 and F cap = 0.
Dependence on sphere size
Dependence on rubber type
First, the surface free energy of BR0 is nearly the same as that of BR15 according to Fig. 10a; however, the shear modulus increase with crosslinking time. Therefore, the flow of BR15 from the bottom to the side of a sphere and the sedimentation of BR15 were slower than that of BR0. This result suggests that the sedimentation velocity relies on the viscoelasticity of the rubber film. Secondly, BR30 clearly exhibited a different terminal sedimentation position than the other two samples. Because the surface free energy of BR30 is larger than those of BR0 and BR15, the positions predicted by Young’s equation and thus the final depths were different. These results indicate that the sedimentation mechanism is strongly influenced by the physical properties of the rubber film, such as surface free energy and viscoelasticity. These results are also in agreement with Eqs. (4) and (5), which indicate that the attractive force depends only on the physical properties of the rubber.
A meniscus formed immediately on the sphere surfaces after they were deposited. This result indicates that an attractive force develops in a short time span (<10 s).
The system was stabilized as a result of meniscus formation and microspheres becoming embedded in the rubber film.
Young’s equation is valid to describe the final sphere depth. In other words, the angle between the rubber surface and the tangential line of the sphere in its final position, θ end, is equal to the equilibrium contact angle, θ eq, in Young’s equation.
Sedimentation behavior mainly depends on the physical properties of the rubber.
Sedimentation behavior is nearly independent of the physical properties of the spheres.
The physical properties of the spheres are particularly important in determining their final depth.
atomic force microscopy
scanning electron microscopy
- T g :
glass transition temperature
- M n :
number average of the molecular weight
- M w :
weight average of the molecular weight
- M w/M n :
molecular weight distribution
- G′ :
- G″ :
- E :
- G :
- ν :
- F meniscus :
- F Lap :
- F cap :
- Δp :
- S :
- R 1, R 2 :
curvature radii of an interface
- (1/R 1 + 1/R 2):
surface curvature of an interface
- γ S :
surface free energy of the solid
- γ L :
surface free energy of the liquid
- γ SL :
interfacial free energy between the liquid and the solid
- l :
length of the contact line
- \(\phi\) :
- θ :
- D :
diameter of the sphere
- δ :
- δ/D :
- θ end :
angle between the rubber surface and the tangential line to the sphere at its final position
- θ eq :
equilibrium contact angle in Young’s equation
- w :
work of adhesion
- at :
SM prepared the manuscript, observed sedimentation of PS sphere and PMMA sphere. HI conceived of the study, did observations with system of silica sphere and BR film, and carried out AFM measurement. TO conceived of the study, participated in its design and coordination, and revised the draft manuscript. All authors read and approved the final manuscript.
The authors declare that they have no competing interests.
Availability of data and materials
All materials we used were supplied by the companies which we wrote in the material section of main manuscript.
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