The Problem of Gecko Adhesion

A. Basu
December 7, 2007

(Submitted as coursework for Physics 210, Stanford University, Autumn 2007)

The remarkable adhesive quality of the feet of the gecko has long fascinated people. The earliest records probably go back to Aristotle [1], who in his book on the History of Animals, talks of the remarkable ability of the Gecko to climb along a tree, even with its head downwards. Today, we know that the feet of a gecko are littered with millions of foot hair, which make intimate contact with the surface. Each foot hair, or "setae," made from the protein keratin, ends in hundreds of 200 nm spatular tips. Robert Full and coworkers [2] discovered that a single setae, which is about a 100 microns in length, and 5 microns in diameter, can hold a force of about 20 microNewtons, and the Tokay gecko, with a setae density of about 5000 per square milimeter, can produce a force of about 10N. This is of course several times the weight of the gecko!

Since the 1900s, there has been a large array of scientific work devoted to understanding the mechanism of gecko adhesion. Haase (1900) [3] discovered that adhesion is load dependent, and suggested that geckos stick by intermolecular forces. Dellit in 1934 [4] suggested that setae acts like hooks that grab on to irregular surfaces. Ruibal and Ernst (1965) [5] postulated that the spatulae lie flat against the substrate, thereby increasing contact area and the friction. However, a model simply based on molecular interlocking is insufficient to account for the fact that geckos can climb on almost all types of surfaces, and even upside down (which is something friction simply cannot account for). It was Hiller in 1968 [6], who first suggested that material properties of the setae play an important role in the adhesion of the gecko.

Adhesion based on Cohesive Forces and Surface Tension

One hypothesis that appeared in 1980 by Stork [7], explaining the adhesion of the setae, was based on surface tension. Molecules in a fluid are held together by comparatively long range forces; the force of cohesion. During the 1800s, it was suggested that insects secrete a sticky fluid and that the cohesive action of these forces holds the setae onto the smooth surface. Since the force of adhesion between the solid surface and the fluid is greater than the cohesive forces between the molecules of the fluid, any 'tear' will occur in the fluid when the two surfaces are pulled apart. The surface tehsion of the fluid can then play an important part in preventing this tear from occuring. Stork suggested that the almost all types of surfaces that setae bearing creatures climb on, bear minute traces of adsorbed water, and thus it is not necessary for the gecko to actually secrete a cohesive fluid. The internal pressure P in a film of fluid of thickness r, separated between a circular plate of radius R and a flat surface is given by

P=S(1/R - 1/r)

where S is the surface tension. Since r is much less than R, we can approximate and say that the force generated by surface tension F is given by

F= PxA = (SxA)/r

The surface tension of water is 73 mN/m, and a film of water is of the order of nanometers. Using these numbers, Stork calculated that the maximum adhesive force is 70 N, for an insect C. polita, which also has a setae structure. However, Full and coworkers in 2002 [8] showed that this mechanism of setae adhesion for the C. polita cannot be used to explain the adhesion of the gecko setae.

Adhesion Based on Van Der Waals Interactions

In 2002, Full and coworkers [8] performed experiments that conclsively eliminated the possibility that surface tension and capillarity were responsible for the the adhesion of the gecko setae. Many insects secrete a layer of cohesive fluid, but that the gecko does not have any such glands cannot discredit this hypothesis. This is because even a monolayer of water can cause significant capillary attraction between hydrophilic surfaces. In order to separate the effect of capillary attraction and Van Der Waal's forces, they measured the force of adhesion on two separate surfaces: Galium Arsenide, which is hydrophobic (water contact angle 110 degrees), but highly polarizable, and Silicon Dioxide, which is strongly hydrophilic (water contact angle 0), and polarizable. Van Der Waal forces are the result of dipole - dipole, dipole - induced dipole, and induced dipole - induced dipole interactions. Thus, these forces would increase with increase in polarizability of the surface. Thus, if capillary action dominated the adhesion, then high force of adhesion would be observed in only the hydrophilic case (SiO2), while if Van Der Waal forces dominate, high adheson would be observed for both materials.

Full et al measured parallel stresses on live gecko toes to be 0.213 N/mm2 for GaAs, and 0.218 N/mm2 for Si. They also measured perpendicular forces of adhesion for isolated gecko setae on hydrophobic cantilevers (41.3 microNewton) and hydrophilic cantilevers (40.4 microNewtons), which difer by only 2%. Strong adhesion even in the hydrophobic case demonstrated that the adhesion is owing to Van Der Waal's forces.

Predicting Spatial Dimension from the Van Der Waals Model

Full and coworkers verified their model by using it to estimate the spatial dimensions of a setae, because if Van Der Waals force dominate the setal force, than geometry, and not surface chemistry should dictate setae design. They measured a pull off force of about 40 microNewton per setae, which for the Tokay gecko, translates to about 576,000 N/m2. They modeled the spatulae as a cyllinder with a hemispherical head of radius R. The John - Kendall - Roberts theory of adhesion predicts that the pull off load for a sphere - plane contact is given by

F = (3/2) π RW

where W is the adhesion energy per unit area. On dimensional grounds we can predict the form RW for the pull off force. If the spatula are assumed to be tightly packed, then the pull off stress is given by:

&sigma = (3/2 π RW)/( &pi R2) = (3/2)(W/R)

Using W ~ 50 mJ/m2 (which is typical for Van Der Waals interaction), and the measured value for &sigma, Full et al calculated R to be ~ 0.13 microns. This matches emperical experiments, and though it is only a crude estimate, it shows that the measurements are qualitatvely consistent with a Van Der Waals interaction between setae and substrate.

Patterned Adhesives, or "Gecko Tape"

Although most of the work done so far has been on single setae, or ensemble measurements on the entire live gecko, the very arrangement of setae on the feet of a gecko could have important implications for the adhesive force. Mahadevan and coworkers at Harvard, in 2004 [9], did an experiment where they slowly peeled an elastic film which was originally glued to a substrate. They showed that the normal stress exibits an oscillatory behavior, being maximum at a point slightly away from the edge that is being peeled, and then oscillating, and finally dying down with distance. But they also showed that once a crack initiates, it propagates rapidly, and the entire film gets peeled off. This motivated the idea of making a patterned adhesive instead of a continuous glue. Basically, if the glue is chopped at regular intervals, then a propagating crack will get arrested whenever it hits a non glued region, and then a new crack has to initiate, which requires a much higher stress. And if the wavelength of the oscillations of the stress match the wavelength of patterning the glue, then when one segment is being peeled off, the stress on the adjacent segment is almost zero (because it lies on a node), and so it does not get weekned in the process. On the one hand, this has technological implications - that we may be able to construct "gecko tape" [10], based on this concept of patterned adhesives. On the other hand, it could also potentially motivate further research into how the very pattern and arrangement of setae on the gecko's toe affects it's adhesive quality.

© 2007 A. Basu. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] Aristotle, Historia Animalium, Book IX, trans. by D. A. W. Thompson (Oxford, 1918). []

[2] K. Autumn et al., "Adhesive Force of a Single Gecko Foot Hair," Nature 405, 8 (2000).

[3] A. Haase, "Untersuchungen über den Bau und die Entwicklung der Haftlappen bei den Geckotiden," Archiv. f. Naturgesch. 66, 321 (1900).

[4] W. D. Dellit, "Zur Anatomie und Physiologie der Geckozehe," Jena. Z. Naturw. 68, 613 (1934).

[5] R. Ruibal and V. Ernst, "The Structure of the Digital Setae of Lizards", J. Morph 117, 271 (1965).

[6] U. Hiller, "Untersuchungen zum Feinbau und zur Funktion der Haftborsten von Reptilien," Z. Morph. Tiere 62, 307 (1968).

[7] N. E. Stork, "Experimental Analysis of Adhesion of Chrysolina Polita (Chrysomelidae: Coleoptera) on a Variety of Surfaces," J. Exp. Biol. 88, 91 (1980).

[8] K. Autumn et al., "Evidence for van der Waals adhesion in gecko setae", Proc. Natl. Acad. Sci. 99, 9 (2002).

[9] A. Ghatak et al., "Peeling from a Patterned Thin Elastic Film", Proc. Roy. Soc. Lond. (A) 460, 2725 (2004).

[10] A. K. Geim et al., "Microfabricated Adhesive Mimicking Gecko Foot-Hair", Nat. Mat. 2, (2003).