Rapid and continuous regulating adhesion strength by mechanical micro-vibration

Controlled tuning of interface adhesion is crucial to a broad range of applications, such as space technology, micro-fabrication, flexible electronics, robotics, and bio-integrated devices. Here, we show a robust and predictable method to continuously regulate interface adhesion by exciting the mechanical micro-vibration in the adhesive system perpendicular to the contact plane. An analytic model reveals the underlying mechanism of adhesion hysteresis and dynamic instability. For a typical PDMS-glass adhesion system, the apparent adhesion strength can be enhanced by 77 times or weakened to 0. Notably, the resulting adhesion switching timescale is comparable to that of geckos (15 ms), and such rapid adhesion switching can be repeated for more than 2 × 107 vibration cycles without any noticeable degradation in the adhesion performance. Our method is independent of surface microstructures and does not require a preload, representing a simple and practical way to design and control surface adhesion in relevant applications.

The designed contactor (with a total mass of 45 g) contains three identical vibration elements, i.e., three small electrodynamic/moving coil cone loudspeakers with spacing of 5 cm among each other (each loudspeaker has diameter of 1 inch, rated power of 3 W, and impedance of 4 Ω). The cone side of each loudspeaker is converted to the contact side with a slightly convex surface (curvature radius 80 mm, constructed by a 3D-printed connector and commercial thin PVC anti-slip mats), and the magnet side is glued to a regular triangular plastic frame. A rough test (at a randomly selected actuation frequency of 350 Hz; see Supplementary Movies 1 and 2) indicates that the normal (without additional shear force) and shear (without additional normal force) strengths can be enhanced by 10 and 4 times, respectively, compared with those without vibration.
Switching time (ms) 16 10 33 16 16 Supplementary  15 proposed the relation = 0 + arcsinh , where is the apparent (effective) adhesion work, 0 is the quasi-static (intrinsic) adhesion work, and is the crack propagation speed. However, the parameters and are quite sensitive to material and differ by orders of magnitude for different adhesion systems, which is somewhat inconvenient. At present, for small (> 0), the widely adopted constitutive relation of the apparent adhesion work is 9, 10, 16-24  28 . However, such an approach should be improved because the JKR theory itself is not applicable to dynamic adhesion systems.
Similar to the JKR theory, for a dynamic adhesion contact system, it can be assumed that the contact force is repulsive in the contact region and attractive at the edge of the contact region, i.e. the adhesion is valid only at the edge of the contact region. In addition, considering ≤ ( is a saturation velocity as marked in Fig. 4), we adopted the adhesive work constitutive relation for the dynamic adhesion contact system with the following form: where is the polar radius (the pole is at the centre of the contact interface), = −̇; 0 is the quasi-static (intrinsic) adhesion work of the contact pair; and 0 > 0 is the crack propagation speed, enabling = 2 0 . Eq. (1) and Fig. 4 indicate that the growth and healing of the interface crack have different resistances.
Without loss of generality, we considered a fixed base and a vibrating contactor (Fig.   1b), the kinetic energy of the contactor is ≈̇2 2 ⁄ , the elastic potential energy of the system is ≈ 3 4 ⁄ • ( 2 − 2 3 ⁄ • 3 ⁄ + 5 2 ⁄ 5 ⁄ ) 28 one can obtain the governing equation, where ̅ is the apparent (or average) contact load and = cos (in our experiment, One can then obtain the steady state solution of Eq. (6): which yields Based on Eq. (4b), ̇ can be expressed as (for convenience, we let = 0 in the following discussion, which has no effect on the final results) where = 3 (8 ̅ 0 ) ⁄ • ( − ̅ 2 ⁄ ) 2 . On the one hand, the continuity of ̇ at ̇= 0 requires | − 1| 1⁄ = | −1 − 1| 1⁄ = 0, i.e. |̇= 0 = 1, or The solution to Eq. (10) is The left-hand side of Eq. (12) is the total decrement in the contact radius due to crack growth, and the right-hand side is the total increment in the contact radius due to crack Notably, Eq. (13) includes the limit of → 0, which indicates an infinite crack healing speed and ( , ) → 0( < 0). Such an approximation holds only when the actuation frequency is high enough. Note that → 0 indicates infinite displacement, which is only theoretically feasible. Thus, should be large enough, i.e., ≫ 0 , in actual estimation or theoretical prediction. Substituting Eqs. (8) and (13) into Eq. (5), the apparent contact load (i.e., Eq. (3)) can be obtained as where ≥ 0, ≫ 0, and ≤ . Eq. (14) can also be expressed as the function of the input power, is the input power (Eq. (7) is considered). Eq. (15) reveals a simple relation among ̅ , and and .

Supplementary Note 3. Discussion of the pull-off force.
By determining the minimum value of ̅ for a given combination of and , the pull-off force off can be obtained based on Eq. (14), where off,0 = − 3 0 2 ⁄ is the quasi-static pull-off force predicted by the JKR theory. The minimum value − √1 + 2 2 2 ⁄ can be determined when ̅ = 2( 2 + 2 2 ) (3 ) ⁄ . In addition, by letting max{ } ≤ and referring to Eqs. (8) and (9), one can find that max{ } ≤ is equivalent to ≤ describes the restrictions on the actuation forces to ensure ≤ . In addition, for a given combination of and , = gives the solution of ̅ = ̅ .
For a given combination of and that satisfies max{ } ≥ , the system could lose stability because of the rapid drop in effective adhesive work (Fig. 4) where we consider ≫ 0 .
Alternatively, when the apparent contact load is abruptly changed, such as from ̅ off,0 ⁄ = 6 to 95 (approximately 120% of the maximum theoretical value) under an actuation frequency of 450 Hz and amplitude of 50 μm, and the adhesion is maintained for approximately 1 s, which may be long enough for some extreme working conditions. Supplementary Note 6. Energy consumption analysis.
As defined in Eq. (15), the input power can be calculated as Eq. (20) can be used to calculate the actual power based on the experimental data by integrating within the internal area of a closed loop of the cos~ curves (similar to the those in Supplementary Figure 2). Theoretically, it is readily obtained that (when ≤ ) Eq. (21) can be used to estimate the damping factor . A group of data of the input power and the damping factor are listed in Supplementary Table 2, where ( eff 2 ) ⁄ represents the required input power per unit contact area and is experimentally determined based on Eq. (20) and the corresponding recorded displacement data.