A graph describing the correlation between the contact area and the Young's modulus of the mushroom-shaped pillar when the substrate is paper. i). 21 Figure 18 A graph describing the correlation between the contact area and the Young's modulus of the mushroom-shaped pillar when the substrate is the line pattern surface. A graph describing the relationship between the theoretical adhesion strength versus the Young's modulus of the e-PUA/PCL blend for the paper and line pattern substrates.
E Young's modulus of the adhesive in the adaptation state p Approximation constants for the paper substrate l Approximation constants for the linear pattern.
Introduction
Previous researches
- Limitations of previous bio-inspired adhesives
- Shape-reconfigurable polymers as solutions
The mushroom-shaped column has a strong tensile strength because it has a rounded tip shape to avoid stress concentration [13-15]. To investigate the adhesion mechanism of the adhesive microstructures, a flat punch and mushroom-shaped model were previously reported [16]. Based on the research, the mushroom-shaped microstructure with the optimal tip thickness has high adhesion strength, while that with too thin or thick tip and the flat punch cannot adhere strongly due to the stress singularity.
The tip of mushroom-shaped pillars is severely distorted when the elastic modulus is lower (~1.5 MPa) than normal PDMS with 10% of the crosslinker concentration (~2.0 MPa) [34]. Based on the previous studies, it is confirmed that mushroom-shaped microstructures with low elastic modulus are advantageous in conformal contact with rough surfaces, whereas those with high elastic modulus have advantages in preventing crack propagation. In addition, a shape memory effect of the shape-reconfigurable polymer enables the reversible use of a mushroom-shaped column, as its shape can be recovered after the deformation.
The shape-reconfigurable polymers that allow their Young's modulus to be tuned with stimuli (Figure 8) are designated as a strong candidate material for a mushroom-shaped pillar and the solution to the limitations of conventional elastomers. The phenomenon that the mushroom-shaped column conformally comes into contact with surfaces by lowering Young's modulus and becomes fixed by regaining its modulus is called adaptation and fixation, respectively. With the reversible adjustment of the elastic modulus, the adhesion of the mushroom-shaped column can be significantly improved.
Research purpose and outline
Experimental result: Adhesion enhancement using e-PUA/PCL blend
After validating the material properties of the e-PUA/PCL blend, the elastic moduli were measured with different blend ratios as shown in Figure 12. The blend ratios written in the legend indicate the weight of e-PUA to the weight of PCL. As the proportion of e-PUA in the blend decreases, the Young's modulus increases without a thermal stimulus, while the modulus decreases with heating to 70 °C.
This is because PCL alternating between solid and liquid has more influence on Young's modulus than e-PUA with solid Young's modulus. From the experimental results, it is confirmed that the e-PUA/PCL mixture with a mixture ratio of 1:1 is the most suitable mixture to maximize the adhesion improvement effect because the gap between the elastic moduli with and without heating stimulus is the largest among three different mixing ratios. Consequently, the adhesion strength of the mushroom-shaped pillar with the designated mixing ratio was measured with respect to the paper and line pattern substrates at the preload of 10kPa (figure 13).
Withdrawal strength in adapted conditions was significantly higher than in non-adapted conditions. In this chapter, SEM and OM images and experimentally measured tensile strength of spongy columns made from a mixture of e-PUA and PCL were presented, which confirmed the phenomenon of increased adhesion. The fabricated thermally responsive mushroom-shaped pillars showed characteristics of conformal deformation along the surfaces by heating (adaptation), post-deformation hardening by cooling (fixation), and shape recovery by reheating.
Theoretical analysis: Adhesion enhancement mechanism
Theoretical backgrounds
The formula (1) must be modulated because the contact area of this study is not a perfect circle. This is the formula of the theoretical adhesion force, depending on the Young's modulus, the surface energy, the Poisson's ratio and the contact area. Finally, dividing Equation 5 by the area of a unit cell of the mushroom-shaped pillar array is required to obtain the final formula with a unit of Pa, the unit for experimental measurement of adhesion strengths.
This is the drag force formula where r is the radius of the main pole. As shown in equation 6, the increase in contact area (A) and elastic modulus (Ef) is critical for increasing adhesion. This verifies that the adaptation (maximization of the contact area by decreasing the elastic modulus) and fixation (recovery of the elastic modulus after adaptation) procedure is the main mechanism to enhance the adhesion of mushroom-shaped microstructures made of shape-reconfigurable polymer.
Finite element analysis
- Contact area analysis on the paper substrate
- Contact area analysis on the line pattern substrate
Based on the derived equation, the numerically predicted contact areas of the mushroom-shaped pillar made of the predetermined e-PUA/PCL blend (1:1 in the blend ratio) can be given by 89,604 μm2 and 1,013 μm2 for the stimulated state thermally (heating, 70 °C / Young's modulus: 0.6 MPa) and the original state (room temperature, 20 °C / Young's modulus: 210 MPa), respectively. A graph depicting the correlation between contact area versus Young's modulus of the mushroom-shaped post when the substrate is paper. The general trend of the result is very similar to that on the paper substrate.
The contact area between the mushroom-shaped pillar and the line pattern substrate decreases as the Young's modulus increases. I). Again, the relationship between the contact area of the mushroom-shaped pillar on the line pattern substrate and the Young's modulus was defined with mathematical approximation fitting, as shown in Figure 18. As shown in Figures 16 and 18, the relationships between the contact areas of the mushroom-shaped pillar on the paper and the line pattern substrate have a little difference, although the overall trend coincides.
In the case of the paper substrate, there is no significant change in the contact area for the Young's modulus from 500 MPa to 10 MPa, while the contact area increases sharply for the elastic modulus in the range of 10 to 0.01 MPa. In the case of the line pattern substrate, on the other hand, the contact area changes over the entire range of Young's modulus. As a result, the contact area in the same Young's modulus is generally higher than that of the paper substrate, because the universal shape of the line pattern substrate is flatter than the shape of the paper substrate.
Theoretical adhesion strengths
A plot depicting the relationship between theoretical adhesion strength versus contact area for paper substrates and the line model, based on Equation 6. Based on these results, it is theoretically verified that the main components of the adhesion enhancement mechanism using the reconfigurable polymer with shape are 1) increased contact area due to reduced elastic modulus in the fitting process and 2) recovered elastic modulus in the fixation procedure.
Comparison of theoretical results with experimental measurements
In summary, the contact areas of the mushroom-shaped column with respect to the variation of the elastic modulus on the predetermined substrates were calculated by FEA. With the results, the relationships between the contact area and Young's modulus were brought closer to interaction formulas and graphs. Consequently, the relationship between the theoretical adhesion force and the elastic modulus was obtained by combining the JKR adhesion formula and the FEA results.
As stated in equation 6, adhesion growth is mainly influenced by Young's modulus and contact area. Since these physical quantities can be actively modulated using the e-PUA/PCL blend, the improvement of adhesion through conformal adaptation with heat stimulation and subsequent fixation with cooling was theoretically confirmed. The high agreement between experimental measurement and numerical prediction of adhesion strengths also implies strong reliability of this study.
Condition setup for numerical analysis
- Material properties
- Substrate and mushroom-shaped pillar 3D modeling
- Boundary conditions
- Mesh refinement
Before calculating the contact area of the mushroom-shaped column, detailed modeling of substrates was performed for the following finite element analyzes in Abaqus. The boundary conditions for this FEA included the settling of the substrate and the displacement of the mushroom-shaped column. The displacement of the mushroom-shaped column was conditioned by setting the displacement to zero in the X and Z directions and to a preset value in the Y direction.
The mesh size of the mushroom-shaped pillar has been refined to be identical at each location, except for the fillet portion, for better convergence, as shown in Figure 27. The mesh size of the mushroom-shaped pillar, excluding the fillet portion, was set to 0 .5 μm. , which did not have too large or small a value that led to inaccurate calculation results or too many computer resources. The total number of nodes and elements of the mushroom-shaped pillar were 174580 and 165800, respectively.
The total number of nodes and elements of the line pattern substrate were 3861 and 3870, respectively. The random Lagrangian-Eulerian (ALE) adaptive mesh controls were also applied in this FEA because the deformation of the mushroom-shaped pillar was quite large. Since the mesh design of the substrates was quite simple, the warning marks highlighted by the yellow color only existed in the mushroom-shaped pillar.
Conclusion
Tian et al., "Adhesion and friction in gecko toe attachment and detachment," P Natl Acad Sci USA, vol. Varenberg, "Sponge-shaped geometry of contact elements in biological adhesive systems," J Adhes Sci Technol, vol. Yi et al., " Bio-inspired adhesive systems for next-generation green manufacturing,” Int J Pr Eng Man-Gt , vol.
Gorb, "Origins of superior adhesion performance of mushroom-shaped microstructured surfaces", Soft Matter, vol. Menon, "Investigation of low pressure adhesion performance of biomimetic mushroom-shaped dry adhesives," J Adhes Sci Technol, vol. Gajasinghe et al., “Experimental study of PDMS bonding to various substrates for monolithic microfluidic applications,” J Micromech Microeng, vol.
Hwang et al., "Multifunctional Smart Skin Adhesive Patches for Advanced Health Care," Adv Healthc Mater, vol. Yi et al., “Ultra-adaptable and wearable photonic skin based on a shape-memory, responsive cellulose derivative,” Adv Funct Mater, vol. Zhu et al., “Rapidly switchable water-sensitive shape memory cellulose/elastomer nanocomposites,” Soft Matter, vol.
