«UNIVERSITY OF CALIFORNIA Santa Barbara Design and Characterization of Fibrillar Adhesives A Dissertation submitted in partial satisfaction of the ...»
The ﬁrst study of friction can be attributed to Leonardo da Vinci in the 15th century where he found that the friction between two smooth surfaces was equal to a certain fraction of its weight. Although there was no knowledge of a coeﬃcient of friction, this seems to be the ﬁrst description of it. Amontons and Coulomb furthered the study of friction and came up with three empirical laws describing sliding friction. The laws stated that the friction force was directly proportional to the applied load, the friction force was independent of contact area, and kinetic friction was independent of sliding velocity.
Chapter 2. Background Amontons also attempted to explain friction on a microscopic scale reasoning that the two contacting surfaces were tilted when viewed at a small scale.
In order to generate lateral movement, a certain lateral force is needed to lift the surface against the loading force. From a geometrical viewpoint and assuming no friction between the surfaces, the lateral force necessary to initiate movement, Flat, can be related to the microscopic tilting angle, α, and the loading force, Fload, as seen in Equation 2.14.
By replacing tan (α) in Equation 2.14 with µ, it becomes the same as Equation
2.13. In this manner, tan (α) can be thought of as the geometric equivalent of coeﬃcient of friction.
These historical equations are an oversimpliﬁcation to fully explain friction and have exceptions where they do not hold. However, they are able to give insight into the basic behavior of friction. Today, we know that surfaces touch each other at many micro-asperities across the surface and it is the behavior of these micro-asperities that is responsible for friction .
It should be noted that when the two surfaces adhere to each other, neither Equations 2.13 or 2.14 can describe the measurable friction forces at zero and negative loads. In these situations, a critical shear stress is needed to initiate movement between the two surfaces. Because the previous equations used to Chapter 2. Background describe friction do not agree with this observation, a modiﬁcation must be made to the original equation. The additional terms include the critical shear stress, Sc, and a real area of contact, Areal, as seen in Equation 2.15.
For situations where the ﬁrst part of Equation 2.15 is much greater than the second part, the friction force is approximately equal to Amontons’ law (Equation 2.13) and is often called load-controlled friction. For situations where the second part of Equation 2.15 is much greater than the ﬁrst part, the friction force is approximately equal to the adhesion component and is often called adhesioncontrolled friction.
An alternative approximation for the friction force based on adhesion theory is given in in Equation 2.16 where τa is the shear strength of the contact and Areal remains the real area of contact.
Two adhering surfaces will contact each other at the roughness asperities with the sum of all the areas of contact being Areal. The real areas of contact can be close enough to each other so that physical or chemical interactions cause adhesive forces. In order to move the surfaces relative to each other, the adhesive bonds between the surfaces must be broken. The force necessary to break these bonds Chapter 2. Background is τa. If the adhesive bonds are strong enough, the material at the surface can broken instead of the bonds and the friction force would depend on the shear strength of the material.
2.3 Kendall Peel Model The Kendall peel model investigates a thin elastic ﬁlm peeling from a rigid substrate . The thin ﬁlm has a width, b, a thickness, d, and a Young’s modulus, E, and is being pulled away from the substrate at an angle, θ, from the substrate and with a constant force, F. By assuming conservation of energy, the energy changes as the ﬁlm is peeled over a length ∆c can be summed and set equal to zero. The three contributions to the energy change are a surface energy term −bw∆c where w is the experimental energy required to fracture a unit are of interface, a potential energy term F (1 − cos θ)∆c due to the movement of the
The elastic ﬁlm is assumed to undergo small, linear elastic strains and there is no bending energy in this analysis. The adhesives presented in this document have bending in the elastic ﬁlm (ﬁbers) and have been modeled using the Kendall peel model, although the model does not account for this energy. The part of ﬁlm attached to rigid substrate is not allowed to move during peeling whereas gecko setal arrays  and gecko-inspired adhesives, both in this document and elsewhere [114, 83], have shown smooth sliding with microscale stick-slip.
Peel models have been applied to the terminal structures of the gecko  and have been extended to include friction , pretension , and frictional sliding . Recent work has investigated peeling models with bending stiﬀness , however, the numerical methods to do so can be quite computationally expensive.
2.4 Gecko Adhesive System The system employed by the gecko is truly remarkable and has received much attention over the past 10 years. During this time, researchers have yet to create a material equal to that of the animal. In this section, the physical characteristics and unique properties of the gecko will be discussed. This introduction aims to Chapter 2. Background give the reader a better understanding of important properties when comparing synthetic adhesives to the gecko.
The impressive climbing ability of the gecko can be attributed to the hierarchical foot pad structure. Each of the ﬁve digits on the four feet of the gecko is comprised of micrometer- and nanometer-sized features composed of β-keratin.
The exact value of the Young’s modulus is unknown at the present time, but features found in two other types of geckos place the value around 1.5 GPa . The β-keratin structures found on the bottom surface of each of the gecko’s toes are arranged in rows producing thin plate-like structures, lamellae. These lamellae contain rows of setae which are initially straight but curve at their ends. The setae are 4.2 µm cylindrical shafts, 110 µm in length , and start at an angle of 45 ◦ with respect to the skin. Each seta then branches out to hundreds of spatulae which form the ﬁnal structure of the gecko adhesive system. The spatulae are roughly triangular shaped with a length of 500 nm, a width of 200 nm, and a thickness of 10 nm .
Because this hierarchical structure is able to conform to roughness asperities, the gecko is able to obtain intimate contact with most opposing surfaces. Close contact is essential for the short-range van der Waals forces, which have been shown to be primarily responsible for the gecko’s impressive climbing and clinging abilities  along with capillary forces  in a secondary role. The van der Chapter 2. Background Waals force is weak for a single small contact such as a spatula, but this force can be substantial when summed over all the available spatulae branching out from approximately 6 million setae.
Measurements on the gecko have shown that the area of the two front feet, 227 mm2, is capable of supporting 20.1 N in the direction parallel to the surface .
With a density of 14,400 setae/mm2 the average shear force per setae for a whole foot measurement would be approximately 6.2 µN. A separate test performed on a single setae showed the shear force could reach as high as 194 µN . Small scale tests often give high pressure values (force/test area), but these levels are often not attainable in larger scale testing because of the inability to make good contact over the entire testing area, even when the testing surface is smooth.
The structures on the feet of the gecko are not sticky by default nor do they stick to each other. Instead, articulation engages their adhesive state. Setae placement using both a perpendicular movement followed by a parallel supported higher adhesion and shear forces than setae applied with only a perpendicular movement . With only a preload applied before removal, the setae generated
0.6 µN of adhesive force. However, they were able to generate 13.6 µN of adhesive force when the setae were sheared after the preload application. The shear forces supported 40 µN without horizontal displacement and with displacement the value increased to 200 µN. In order to separate adhesives that stick well with Chapter 2. Background high preload, such as pressure sensitive adhesives, from those with low preload, such as the gecko, an adhesion coeﬃcient, µ′, has been deﬁned to compare the ratio of pulloﬀ (adhesion) to preload force. Measurements made on the gecko’s structures place the adhesion coeﬃcient between 8 and 16 [12, 10].
The gecko adhesive does not behave in a symmetric manner when the adhesive is articulated along a single axis. Isolated setal arrays moved with the direction of tilt supported high shear and adhesion forces whereas movement against the tilt supported no adhesion forces and smaller shear forces [7, 120]. In this manner, the gecko exhibits anisotropic attachment with vastly diﬀerent behavior depending on whether the adhesive is moved in the gripping or releasing direction.
Measurements of geckos running showed that normal forces during attachment and detachment were small in the roughly 20 ms the animal requires to engage or disengage its adhesive structures . Low force detachment is accomplished via two mechanisms. Digital hyperextension allows small portions of the adhesive to be removed in succession . It was also found that increasing the angle of the setae relative to the substrate above 30◦, as could happen when moved against the tilt direction, caused detachment of the terminal spatulae structures .
Signiﬁcant problems should be presented to the animal in its natural environment where surfaces, such as bark and rock, can contain varying degrees of roughness or can be dirty, degrading the adhesive surface. The gecko, however, is Chapter 2. Background able to move over and cling to almost any surface. The gecko can stick to rough surfaces because of the hierarchy in the system. The foot and toes can adjust to large height diﬀerences and the angled setae are able to adjust to smaller height diﬀerences. This system allows the spatulae to maintain intimate contact across large uneven areas.
Experiments show that the adhesive structures of the gecko are able to selfclean . Experiments were ﬁrst performed by contaminating immobilized toes with 2.5 µm radius microspheres. After 8 simulated steps the toes regained ≈ 35% of their shear force. Isolated setal arrays were also contaminated in the same manner and then tested using a setal array test platform. The setal arrays were able to recover ≈ 51% of the shear forces. Imaging of the setal arrays in a dirty state and after being tested conﬁrmed the self-cleaning property.
2.5 Synthetic Adhesives Many approaches toward creating an adhesive equal to the gecko have been attempted and in this section, some of these gecko-inspired adhesives are introduced. The simplest of these include testing of unpatterned polymers  or a polymer ﬁlms with incisions . More involved approaches utilizing unpatterned ﬁlms involve placing micropillar arrays underneath a thin viscoelastic ﬁlm Chapter 2. Background for increased adhesion and a crack propagation modulation . Using fabric surrounded by a ﬂat elastomer layer to provide stiﬀness in the direction of loading while maximizing contact at smaller length scales was also performed .
The practicality of ﬂat sheets as adhesives is limited to smooth surfaces due to diﬃculty adapting to roughness when the ﬂat surface stiﬀness is too high. Flat sheets lack most gecko adhesive properties, although they have been explored for integration with climbing robots [74, 113].
Molding allows a range of ﬁber geometries to be formed over large adhesive patch areas and has been one of the more popular techniques for fabricating synthetic adhesives. The molding technique allows the ﬁlling material to be diﬀerent from the mold material, enabling materials that would not be suitable for the creation of the mold to be used as the adhesive. Negative molds have been created by atomic force microscopy (AFM) tip indentation of a wax surface , removal of metal from a ﬂat plate by a laser , and machining of a hard wax using customized miniature tooling . Commercially available materials such as track etched membranes can be ordered with diﬀerent feature sizes and have also been used as molds [104, 64]. Microfabrication techniques have also been used to create molds and are discussed in the following paragraph. Common ﬁlling materials used for creation of adhesives are polydimethylsiloxane (PDMS) (E=0.3–2.6 MPa) [36, 117, 83], low and high density polyethylene (PE) (E=0.2–0.9 GPa) , Chapter 2. Background polyurethane (PU) (E=2.9 MPa ) , polyurethane acrylate (PUA) (E=19–320 MPa) , polyvinylsiloxane (PVS) (E=3 MPa) , and polypropylene (PP) (E=1 GPa) . Material selection is important since diﬀerent adhesive characteristics can result from the same adhesive design but diﬀerent materials . The negative mold can be reused multiple times unless the mold must be chemically removed  or damage occurs during the separation of the two materials.
Microfabrication techniques have been also been used to create synthetic adhesives directly with materials such as polyimide , which had high adhesion strength and was one of the ﬁrst ﬁbrillar structures. Nanometer polymer structures atop silicon dioxide  have demonstrated a hierarchy similar to that of the gecko. The design was improved by using nickel instead of silicon which allowed the adhesive to be turned oﬀ or on by using a magnetic ﬁeld to change the orientation of the adhesive structures . In addition to making the gecko structures directly, microfabrication techniques have also been used to create molds in silicon for single level [117, 54] and multiple level  polymer structures. SU-8, an epoxy based photoresist, has also been a popular material for molds with single level [37, 83] and hierarchical  polymer structures.