Brush Deformation Effects on Poly Vinyl Acetal Brush Scrubbing

In an earlier study, we found that PVA brushes have viscoelastic properties. We demonstrated the high normal forces that are generated at high compression speeds.³⁹ Here, we focused on the compression direction (i.e., the compression or release process). Figure 2 shows a schematic of the experimental set up. In this experiment, we compressed the PVA brush to 4 mm and measured normal forces every 0.5 mm. After reaching 4 mm, we released the compression. We measured the force immediately after compression and after 1 min. We filled the container with ultra-pure water up to half of the height of the container, to prevent the brush from drying during measurements.

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Figure 3 shows a schematic of the experimental setup for shear force measurements. The shear forces (Fs) generated by sliding the PVA brushes on a plate were measured with a load cell (MRD-10 N, A&D Company). The brush was slid after 60 s compressing the brush in order to reduce the viscoelastic effects on normal force. The natural frequency of the load cell was 17 kHz, so that the load cell would be sufficiently responsive. Type-A, type-B, and type-C brushes were used to investigate the effects a skin layer for shear force. The plate materials were glass, polymethylmethacrylate (PMMA), and polytetrafluoroethylene (PTFE). The corresponding contact angles (θ) to water for each surface were 28°, 61°, and 97°, respectively. The sliding speed V was varied from 1 to 50 mm/s, and the brush compression distance d was varied from 1 to 3 mm. To investigate the effects of brush rotation, we measured the shear forces of sliding brushes rotating on a PMMA plate. In this case, the brushes were rotated about an axis vertical to the plate. Type-D brushes were also used in this experiment. The brush rotation speed n was varied from 0 to 150 rpm, the sliding speed V was varied from 10 to 100 mm/s, and the compression distance d was fixed at 1 mm. Brush deformation during brush sliding was also observed at both the side and bottom using a high-speed video camera. A mirror was used to observe from the bottom.

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Figure 4 shows a schematic of the experimental set up for torque measurements. In this experiment, we measured the torque T generated by a brush rotating on test pieces. Using this setup, we can almost neglect brush deformation effects and evaluate the friction from the direct contact between the brushes and surfaces. The torque T was measured with a torque meter (UTM II-0.05, Unipluse Corporation) attached to the rotating shaft. We used several plates and semiconductor wafers with films as test samples. The films were SiO₂, SiOC, SiN, Cu, and W. The test pieces were fixed to the containers. In the experiments, the containers were filled with chemical solutions composed of ultra-pure water (UPW), a citric acid aqueous solution (CA, 23%, pH = 2), and ammonium hydroxide (NH₄OH, 0.5%, pH = 11.4). Torque measurements were started when the torque value stabilized. There is a relaxation process of normal forces because of viscoelasticity effects. We only used a type-D brush in this experiment, because the type-D brush had a large contact area and showed large differences in T, depending on the plate material.

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Figure 5 shows the normal force (F_n) as a function of brush compression distance d. F_n increased with increasing d. However, the compression and release processes produce different F_n values, despite having the same compression distance (i.e. hysteresis loop). Because of the viscoelasticity of the PVA brushes, F_n decreased after 60 s in the compression process. This approximately 6% reduction occurred because of relaxation. In contrast, F_n increased after 60 s in the release process, and the relaxed values did not change after several minutes. This result indicates that it is difficult to keep the compression conditions constant by monitoring normal force or compression distance, because normal force is dependent on compression history. Therefore, the control of brush compression distance was the only compression process conducted in this study.

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First, the PVA brush was accelerated during sliding to ascertain reproducibility how the sliding speed V depends on shear forces F_s. This is because the shear forces are greatly depending on the individual differences of brushes and how to attach the brush to a holder. Figures 6 and 7 show a time series of F_s on a PMMA plate. As shown in Figs. 6a, 6b, and 6c, F_s increased with increasing V for all brush types when V was increase from 1 to 10 mm/s. For further increases in V from 10 to 50 mm/s, F_s either increased or was unchanged, as shown in Figs. 7b and 7d. However, F_s decreased with increasing V in the case of a type-A brush, which has a skin layer on the contact surface, as shown in the Fig. 7a. These results indicate that the dependence of sliding speed on shear force was affected by the existence of a skin layer on the contact surface.

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Next, we compare time-averaged shear forces on a different plate. Figure 8 shows as a function of brush sliding speed V. As shown in Fig. 8a, there were no significant differences in the value of the type-A brush for all materials. In contrast, the value of the type-B and C brushes for PTFE were smaller than those for PMMA and glass, as shown in Figs. 8b and 8c. Additionally, there was no correlation between shear force and surface wettability.

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With the exception of the large sliding speed case for type A, increased with increasing V. These tendencies in wettability and sliding speed dependence were perfectly different from the results of our earlier study using PVA roller brushes, which had skin layers. Hara et al. showed that the shear forces decreased with increasing rotation speeds and that they were highly dependent on surface wettability. However, their other results show the shear force generated by single nodule sliding were not influenced by surface wettability.³⁷ We consider that these results are due to the reduction of apparent contact area because of the large brush deformation. Moreover, this speed dependence is somewhat unusual, even when we consider basic friction principles. The frictional force should decrease when the object begins to move because the static friction coefficient is smaller than the dynamic friction coefficient in the general friction system. However, we showed shear force at the beginning of motion was constant. And the shear forces increased with the increasing the sliding speed. These results suggest that the dynamic friction is larger than the static friction.

In addition, the value for type-A was larger than that for type-B and type-C. Additionally, was approximately the same for type-B and type-C. These results indicate that the shear force values depended on the skin layer on the contact area, but not the side.

Figure 9 show the observation results for sliding the brush from the side with a high-speed video camera. Figure 9a, 9b, and 9c show the different brush types (d = 1 mm). Figures 9i shows the compressed brushes before sliding, and (ii), and (iii) show the brush shapes for 10 mm/s and 50 mm/s, respectively. As shown in Fig. 9i, the shape of the brush prior to sliding was slightly trapezoidal, because the bottom area of the brush was increased by brush compression. With increases in sliding speed, the brushes were greatly deformed. We measured brush deformation angles (θ) from observation images to estimate the amount of brush deformation. The value of θ for V = 50 mm/s (about 40°) was larger than that at 10 mm/s (about 30°) for all brush types.

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Furthermore, we observed the brushes from the bottom. From the observation results and Fig. 9, the PVA brush was sliding after the brush holder moved. In other words, initially, the PVA brush adhered to the surface. See supplementary material for videos corresponding to Figs. 9a-9c and for videos showing the brush from bottom view at the start to the sliding.

The brush sliding experiments showed that when a skin layer was present on the contact surface, shear forces depended on sliding speeds. The brushes having a skin layer showed large shear forces. Additionally, brush deformation increased with increasing brush sliding speed. The shear forces were also large when the sliding speeds increased. Next, we focus on brush deformation and the existence of a skin layer.

First, we discuss brush deformation. Initially the brush adhered to the surface, then slid. If we assume that the brush shape was a trapezoidal, then the front part of the brush was more compressed, and the local compression distance increased, as shown in Fig. 10. In contrast, the rear part of the brush was released from loading because it was stretched. Finally, the load at the rear part of the brush became 0, and the brush separated from the surface, as shown in Fig. 9.

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Second, we discuss how shear forces depend on sliding speeds. In terms of overall tendencies, the brush deformation angle increased with increasing brush sliding speed. Generally, shear forces increased with increasing normal forces. Therefore, when a larger local compression concentration region occurs in the front part created, larger shear forces and deformations were observed. These types of deformation-induced friction are observed for soft materials such as rubber, and are called hysteresis friction.

As shown in Fig. 8, the value of type A was larger than that of types B and C. This means that the real contact area for type-A was larger than that for type-B because type-A has a skin layer with a lower porosity layer. Therefore, as shown in Fig. 6a, shear force decreased with increasing sliding speed for type-A, because the decrease in the adhesion term was larger than the increase in the hysteresis term. In contrast, the real contact areas of type-B and type-C were smaller than that of type A, because the contact surfaces were covered in a higher-porosity layer. In brief, the magnitude correlation between the two terms determined the contribution of each term to the overall shear force.

We considered the shear force of the sliding deformable brush to be generated in a high normal load region at the front part of the brush, as mentioned above. Hence, we predicted that shear force was reduced with the brush rotation because brush deformation was suppressed. Figure 11 shows the time-averaged shear force value as a function of brush rotation speed n. decreased with increasing n for all brush types. The tendencies of these decreases depended on the sliding speeds V. For brush types A, and B, showed a steep decline at low n values when V = 10 mm/s. In contrast, remained almost constant at n values below 100 rpm when V = 50 mm/s. For a type-D brush, gradually decreased with increasing n when V = 100 mm/s. These results indicated that brush size affected the relationship between rotation speed and sliding speed.

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Figure 12 shows the observation results for sliding brush shape with rotation. For V = 10 mm/s, brush deformation was suppressed at n = 40 rpm. By increasing sliding speed V = 50 mm/s, brush deformation was not suppressed at the same rotation. When the rotation speed was increased further to 100 rpm, deformation was again suppressed. From these results, both shear force and brush deformation were suppressed with brush rotation. Additionally, brush rotation effects declined with increases in brush sliding speeds. Moreover, these results indicated that brush deformation was an index of shear force. Hence, we predicted that the shear force can be estimated from the relationship between the amount of brush deformation and the brush rotation speed. See supplementary material for movies corresponding to Figs. 12a–12c showing the sliding brush.

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We demonstrated that a simple model could predict how brush rotation reduces shear force. First, we estimated the starting time for brush sliding, using results observed from the bottom of the brush. The time until the brush slides t_s is given as

Where m is the travel distance for the traverse actuator before the brush slides. Here, in the case of type-A, type-B and type-C, m was approximately 1.5 mm. Next, we assume that this deformed brush was rotated. Then shear force in the x direction F_sx is decreased. As a result, the deformation direction is also shifted. For example, if the brush was rotated 90°, F_sx should be zero as shown in Fig. 13. Note that we measured the shear forces for sliding direction. The time until the brush rotated 90° t_r is given as

Then, the ratio of the two times t_r and t_s is defined as η.

η is an index of brush deformation magnitude. In the case of large η, the shear force is large because the brush deformation grows enough to start sliding before the brush deformation suppressed by brush rotation. On the other hands, in the case of small η, the deformation of the brush is suppressed by the brush rotation before the deformation increases. So, the shear force is small.

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There is a limit to the amount of brush deformations, so there is also an upper limit on the η value. The upper limit on η is defined η_c. We define η_c as the point at which shear forces do not change, even for brush rotation. Hence, when η_c > η, brush deformation is not reduced by rotation. Here, we selected η_c from our shear force measurement results. We explain the definition of η_c using the results for type-A. As shown in Fig. 11a, the shear forces up to n < 40 rpm were approximately the same for a no-brush-rotation condition at V = 50 mm/s. Above n = 50 rpm, shear forces were decreasing by rotation. Therefore, the η value for V = 50 mm/s and n = 40 rpm was defined as η_c.

From the above definitions, shear forces were estimated from η values. F_s was proportional to η and defined as

Here, F_s0 is shear force without brush rotation. If η was larger than η_c, F_s would have the same value for a no-brush-rotation condition.

In Fig. 11, we also plotted the model predictions. The shear force model well reproduced the experimental results for all brush types. Therefore, for the present study, we conclude that the deformation state of a brush can be calculated from shear force. We not evaluate the contact conditions (i.e., the combination of materials). Next, to evaluate the contact conditions between PVA brushes and several plates for low deformation conditions, we measured the torque T generated by brush rotation on test pieces.

In our final set of experiments, we investigated the torque generated by PVA brush rotations on a plate. In this setup, brush deformations were small and only a twisted mode was used. Additionally, we could ignore the local deformation-induced concentrations observed in sliding experiments. Therefore, we can evaluate friction according to the real contact area.

Figure 14 shows an example of torque T when a type-D brush was used on different plates or films in chemical solutions. For cases using citric acid aqueous solution (CA) and ultrapure water (UPW), T decreased with increasing brush rotation speeds n, for all cases except W film and PTFE plates. We believe that this was due to the real contact area, as discussed in sliding experiments. These results match those in our earlier study.³⁷

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Next, we focus on T for NH₄OH. The torques on SiO₂ and SiOC were lower in NH₄OH than in UPW. These results are also in good agreement with those of earlier studies regarding roller-type brushes with skin layers by Philipossian et al.⁴⁰ and Nishio et al.⁴¹ This is because Si based films are dissolved in high pH chemicals. The dissolved surface plays a role in lubrication. Hence, NH₄OH showed low torques. T values were large on a Cu film. These results are the same as those by Nishio et al.⁴¹ These results may have occurred because of a nascent exposed Cu surface, which was highly active.

In all liquids, T values for W film were independent of n. We believe that this occurred because of the high surface energy of W. However, this was not clear at the present stage. As shown in the torque measurements, clear differences appeared for different combinations of liquids and surface films. From these results, we conclude that torque measurements are a suitable experiment for evaluating contact conditions.