Rate-dependent frictional adhesion in natural and synthetic gecko setae

Abstract

Geckos owe their remarkable stickiness to millions of dry, hard setae on their toes. In this study, we discovered that gecko setae stick more strongly the faster they slide, and do not wear out after 30,000 cycles. This is surprising because friction between dry, hard, macroscopic materials typically decreases at the onset of sliding, and as velocity increases, friction continues to decrease because of a reduction in the number of interfacial contacts, due in part to wear. Gecko setae did not exhibit the decrease in adhesion or friction characteristic of a transition from static to kinetic contact mechanics. Instead, friction and adhesion forces increased at the onset of sliding and continued to increase with shear speed from 500 nm s(-1) to 158 mm s(-1). To explain how apparently fluid-like, wear-free dynamic friction and adhesion occur macroscopically in a dry, hard solid, we proposed a model based on a population of nanoscopic stick-slip events. In the model, contact elements are either in static contact or in the process of slipping to a new static contact. If stick-slip events are uncorrelated, the model further predicted that contact forces should increase to a critical velocity (V*) and then decrease at velocities greater than V*. We hypothesized that, like natural gecko setae, but unlike any conventional adhesive, gecko-like synthetic adhesives (GSAs) could adhere while sliding. To test the generality of our results and the validity of our model, we fabricated a GSA using a hard silicone polymer. While sliding, the GSA exhibited steady-state adhesion and velocity dependence similar to that of gecko setae. Observations at the interface indicated that macroscopically smooth sliding of the GSA emerged from randomly occurring stick-slip events in the population of flexible fibrils, confirming our model predictions.

Figure 1.

The tokay gecko (approx. 30 cm in length) possesses adhesive pads on the undersides of its toes (approx. 1 cm in length). Arrays of branched setae (approx. 110 µm in length) achieve intimate contact with surfaces to engage intermolecular van der Waals forces. Setae are adhesive only under the application of a shear force. Setae are first applied vertically to a surface and then sheared parallel to the surface. The setal shafts load elastically until the elastic component is saturated, at which point the setae slide across the substrate while remaining in adhesion. As the adhesive begins to slide (300 ms), friction and adhesion forces remain constant and do not exhibit any notable decrease, uncharacteristic of solid contact mechanics. The solid line represents friction and the dashed line adhesion. Note that for normal force, adhesion is negative while compression is positive.

Figure 2.

Steady-state contact forces increased in magnitude as a function of drag speed over drag distances of 10⁻³ mm (open circles), 10⁻² mm (filled circles), 10⁻¹ mm (open squares), 10⁰ mm (filled squares), and 10¹ mm (open triangles). (a) Friction forces increased 3.3× over the velocity range. (b) Adhesion forces increased 10.3× over the test velocity range. Line fits are F_shear = (0.018 N)(1 + v/(1.11 × 10³ mm s⁻¹))⁻¹ × sinh⁻¹(v/(0.972 mm s⁻¹)) + 0.044 N (R² = 0.99) and F_normal =−(0.009 N)(1 + v/(1.11 × 10³ mm s⁻¹))⁻¹ sinh⁻¹(v/(0.751 mm s⁻¹)) − 0.009 N (R² = 0.99).

Figure 3.

Steady-state contact forces of the GSA as a function of drag speed over drag distances of 10⁻¹ mm (open circles), 10⁰ mm (filled circles), 10¹ mm (open squares) and 3× 10¹ mm (filled squares). (a) Friction forces increased with speed until approximately 10 mm s⁻¹ at which point friction decreased with speed. (b) Adhesion force followed the friction force. Line fits are F_shear = (0.020 N)(1 + v/(52.4 mm s⁻¹))⁻¹sinh⁻¹(v/(1.5 × 10⁻⁶ mm s⁻¹)) + 0.511 N (R² = 0.96) and F_normal = (−0.014 N)(1 + v/(52.4 mm s⁻¹))⁻¹ sinh⁻¹(v/(1.5 × 10⁻⁶ mm s⁻¹)) − 0.025 N (R² = 0.91).

Figure 4.

Stick–slip frequency analysis of the GSA. (a) The averaged FFT magnitude from high-speed video shows dominant stick–slip frequencies that increase in proportion to velocity. The 0.05, 0.10, 0.50, 1.00 and 1.50 mm s⁻¹ FFT traces are highlighted with arrows from left to right in increasing order. (b) The dominant stick–slip frequencies (arrows) varied linearly with speed as f = (25.3 µm)v. Using equation (4.4), the fit predicts a stick–slip displacement of λ = 25.3 µm.

Figure 5.

Fibrillar geometry of (a) natural gecko setae and (b) GSA.