«UNIVERSITY OF CALIFORNIA Santa Barbara A Micro/Nano-Fabricated Gecko-Inspired Reversible Adhesive A Dissertation submitted in partial satisfaction of ...»
As with any adhesive, in order for the adhesive to work it has to come into contact with the adhering surface. For an ideally smooth surface making contact is relatively straight forward. However, the gecko does not have the luxury of ideal surfaces in nature. Imagine a gecko running up a tree trunk trying to maximize contact with the tree. The first thing the gecko is able to do is bend its legs, adjusting for the curvature of the trunk, putting the pads into contact with the surface. Depending on the surface, the toes are then able to bend and wrap around any centimeter scale roughness. Next the blood sinuses in the pad are able to deform to millimeter scale roughness in the surface. The setae are then able to bend and nestle into milli- to micro-scale roughness, which then puts the spatulas into contact with the surface. The thin, compliant spatulas are then able to conform to nanoscale roughness and make intimate contact with the surface. As will be discussed in the adhesion mechanics section, this intimate contact is necessary to enhance the van der Waals interactions responsible for adhesion.
Although in literature, and in this document, this phenomenon of a gecko sticking to a surface will be called “adhesion,” in fact it is a combination of friction and adhesion, arguably the more important contributor being friction. Observing a gecko, immediately one becomes aware of the directionality of the toes and feet, and how their orientation can change depending on the orientation of the gecko and surface. While on a vertical surface a gecko tends to have a greater number of toes point upwards, and toes on opposing legs tend to face away from each other. The toes facing upwards tend to create a friction in an optimal direction for the gecko (creating friction on the spatulas by dragging them along a surface instead of peeling them away from the surface). Meanwhile the toes on opposing legs, by pointing away from each other, tend to induce a squeezing action, again creating a frictional component in the system. On an inverted surface the gecko relies on this squeezing action.
To understand this concept imagine for a second holding a balloon with one hand. If you simply take a rigid flat hand and press it against a balloon and pull away, there should be no ‘adhesion,’ the non-compliant situation. Now take a limp hand and allow it to wrap around the balloon and pull away – probably a slight sense of adhesion, but the balloon is left behind. Now, place a hand around the balloon and squeeze slightly. The balloon should easily be manipulated. The gecko uses a similar strategy, employing friction via a squeezing action, to enhance its ability to stick to surfaces.
Prior work in this area has focused solely on fabricating nanostructured surfaces (10-13). However, it is clear that the hierarchical nature of the gecko adhesive serves many other purposes as well – e.g. enhancing surface conformation and inducing a frictional component. In this work, efforts have been focused on creating the first two levels of the hierarchical structure. That is creating an analogue to the spatular/setal structure by integrating similar nano/micro-scale structures.
The gecko adhesive system may open the door for a variety of new adhesives with niche applications, i.e. tape for high vacuum environments and highly reusable tape. However, the system is of real interest because it presents the opportunity for creating an adhesive that can stick and then be caused to unstick. Thus, it is important to understand a bit about the unsticking mechanism of the gecko.
Figure II-4 Image of Dude the Gecko peeling his tarsus from the surface (Image by Jeff Clark).
To unstick its foot from a surface the gecko uses a peeling action, starting from the tip of the toe and rolling inwards, Fig. II-4. From a macroscale understanding of how tape works, peeling is much easier than trying to pull off the entire piece of tape at the same time. However there is more to the story with the gecko. The specific shape of the spatulas and the setae allow for maximum adhesion (actually a combination of adhesion and friction) when the pull-off force is directed at a 30° angle from the surface (6, 14, 15). This angle is the point where both the frictional force and adhesion forces are highest; the frictional force due to the larger component of lateral force, but with still enough normal force to maintain contact;
and the adhesion force due to the geometry of the spatula creating a compressive force at the base of the stalk inhibiting crack initiation (14). As the pull-off angle moves above 30° the adhesion (and friction) decreases rapidly facilitating the removal of the pad from the surface.
In order to mimic the biological adhesive system, it is helpful to understand a little bit more about fundamental adhesion mechanics. In this section a brief and concise overview of a few of the fundamental theories, as well as a few specialized theories, applicable to the multiple contact adhesion phenomenon is presented.
The simplest relevant case to consider is a sphere contacting a flat surface.
Hertz found that a sphere contacting a flat, smooth surface (assuming the materials
to be homogeneous and isotropic) has a contact area of (16):
where Ei and νi are the Young’s moduli and Poisson ratios of the two materials respectively.
In this case Hertz assumes that the sphere is pushed into the surface, deforms, and then when the force is removed returns back to original configuration without hysteresis. While this theory explains the contact mechanics it does not predict adhesion between the sphere and the flat surface.
Johnson-Kendall-Roberts considered the surface energies of the contacting surfaces and found that the contact area increases due to a reduction in interfacial
where γ is the interfacial energy and responsible for the mechanism of adhesion.
The interesting outcome is that in the absence of a normal force there is still a
contact area and an adhesive force. The radius of contact is given by:
The Derjaguin-Muller-Toporov Model (20-22) is a variation of the JKR Model of above and also takes into account long range forces. The attractive force is approximated by Leonard-Jones potentials. The model also considers that surfaces in contact deform due to attractive forces, calculated using a Hertzian approach.
Modifying the JKT model accordingly a new pull-off force is derived:
for the case of an undeformable flat surface and considering both surfaces to have equal surface energies.
This gives a radius of contact with no normal load of:
As it turns out in some instances it is better to use the JKR method and in other cases to use the DMT method. To determine whether or not to use JKR or DMT
where s is the separation between the two solids with strongest attraction. If β is much greater than unity then the JKR model is valid.
A helpful way to interpret adhesion is the change in surface energy associated
with separation of two surfaces, described by the Dupré equation(23):
where Wa is the work of adhesion, γ1 and γ2 are the surface energies of the contacting surfaces, and γ12 is the interfacial energy associated with the two surfaces.
This concept is revisited in chapter V.
From the above, it is clear that adhesion is related to the amount of contact area between surfaces. A few general rules can be made about adhesion accordingly.
1. Adhesion increases with decreasing surface roughness.
2. Soft, flexible and conformal surfaces increase adhesion.
3. Deformable surfaces conform to surface roughness making intimate contact and enhancing adhesion.
4. Surface conformation can also be enhanced by increasing the normal loading force (24).
Thus far nothing has been said about the actual interactions responsible for adhesion. In the case of the multiple contact biological system, the interaction forces and role of forces is still a debated question. Strong evidence suggests that van der Waals forces are operative (10). Other evidence suggests that humidity plays a significant role (25). However, the introduction of water between two surfaces (due to a more humid atmosphere) can introduce capillary forces, but may also affect the van der Waals interactions (23).
Considered a short-range molecular interaction force, van der Waals forces arise from temporarily induced dipoles between two neutral molecules. The momentary shift in the electron cloud of one molecule induces the shift of a neighboring molecule’s cloud of electrons. The two dipoles then attract each other. These London dispersion forces operate over a short range, typically 10 nm, and can be
described using a Leonard-Jones potential ψ (d ) (23):
where ψ o is the strength of the interaction, d* the range of the interaction and d the distance of the two molecules. The positive portion of the equation denotes the repulsive energy associated with two molecules not being able to penetrate each other. The force is very strong, but also very short ranged.
Using Derjaguin approximation (21) a force relationship for a sphere on a flat
surface can be developed (26):
where A is the Hamaker Constant, R the radius of the sphere, do is a characteristic interaction distance, and d is the distance between sphere and surface.
Capillary forces are a result of the interaction of a wetting fluid with a surface.
In capillary action a wetting agent is pulled up a capillary. This force can also act between two surfaces when a wetting agent is present. If one of the surfaces is not wettable by the liquid, capillary forces are not relevant. A brief treatise will be given to the relation between capillary forces and a sphere contacting a flat surface.
Taking the Laplace pressure:
where r1 and r2 are the curvatures of the hyperbolic paraboloid produced by the meniscus about a sphere. For the case of the sphere and flat Scherge and Gorb (26)
have derived the relation:
where θ i are the contact-angles. If the two surfaces are made of identical materials then these angles will be equal. Also for the case of r2 r1 the Laplace
pressure reduces to:
It is noted that this relationship does not hold for increasingly rough surfaces. In the case of rough surfaces asperities act like local spheres causing a reduction in the large meniscus radius rendering the assumption r2 r1 invalid. Also, capillary forces dominate when large smooth surfaces are in contact in the presence of atmosphere. Van der Waals interactions become significant when a sharp probe penetrates the liquid interface and allows for short range interactions.
The concept of contact splitting in the gecko adhesive system offers a direct explanation for the increase in adhesion observed when many small contacts are made as opposed to one large contact. A theory developed by Arzt et al. (27) shows how the size of the final termini of an animal’s contacts is inversely related to the mass of the animal, Fig. II-5. For example the largest animal to use this adhesion system, the Tokay Gecko, also has the smallest termini, ~200 nm. Whereas a fly has termini of order 2 μm.
Figure II-5 Illustration of the contact splitting phenomenon in nature. Plot shows that as the animal’s mass increases then so does the necessary density of termini in the adhesion system. Figure from reference (27).
The basic concept of contact splitting is that adhesion decreases linearly with the radius of contact, while the number of contacts increases by the square of the radius, or a higher packing density. This means that the net increase in adhesion per unit area is the square root of the number of contacts in the total contact area. This can
accordingly modify the JKR model above so that:
This concept of contact splitting offers an explanation for the fine terminal structure of the fine hair attachment system. There is however much more to the structure of the adhesive system. The fine hairs are located at the end of long, 130 μm, slender, 20 μm, setal stalks. These stalks are attached to the foot of the gecko via an undulated surface cushioned by blood sinuses. In view of contact mechanics, this hierarchical system seems to aid in increasing surface contact with non-ideal surfaces.
In the case of rough surfaces, it is no longer possible to assume that a single large contact will make perfect contact with a surface. In addition it is not possible to assume that if a large contact is split into many smaller contacts they will all make contact. For a rough surface it becomes very important to consider the roughness and the ability of the two surfaces to make intimate contact. Thus, the mechanical properties of the underlying substrate become important. If one substrate is highly compliant then the surfaces will mate better and adhesion will be increased (28).
The long slender setae aid in surface conformation increasing contact area without increasing the repulsive push-off force. This push-off force can be modeled as an
elastic restoring force (29):
The concept of reducing the elastic restoring force and enhancing surface conformation was a driving force for the work presented here. This work was the first effort to create a hierarchical structure; the first work to integrate two different scales of structures (micro and nano) for enhanced adhesion.