«UNIVERSITY OF CALIFORNIA Santa Barbara Design and Characterization of Fibrillar Adhesives A Dissertation submitted in partial satisfaction of the ...»
Gecko-inspired adhesives could also be used in industrial manufacturing applications. Transportation of material without surface contamination cannot be used with some traditional adhesives because of the residue left behind when separated. Using suction to hold material can also be diﬃcult when the environment itself is in a vacuum. A gecko-like adhesive would be able to function in both of these environments and has already been used to transport a thin glass substrate Chapter 1. Introduction in a liquid crystal display panel assembly . Other industries such as microfabrication facilities could use gecko adhesives to transport fragile components where vacuum systems risk damage.
Commercial applications oﬀer the most exciting development area. Geckoinspired adhesives could be used as a universal one-piece VelcroTM, with only the adhesive structures applied to a backing layer instead of the two-part hook and loop components. Since van der Waals forces are more size dependent than material dependent , the adhesive would be able to stick to a variety of surfaces while retaining adhesion strength. It would also be reusable due to the ability to remove fouling particles, enabling a long lifetime. An extreme commercial example would be gloves and shoes covered with the synthetic gecko adhesive which would allow humans to climb and cling to surfaces just like the gecko.
The medical ﬁeld is another emerging application area. The replacement of sutures with gecko adhesives capable of holding tissue together has been proposed and experiments using gecko-inspired adhesives have already begun. Using a biocompatible and biodegradable elastomer, an adhesive patch has already been place internally . The pillar structures, coated with the bio-adhesive coating dextran aldehyde, showed shear force improvements over uncoated and unpatterned patches of the same material. PDMS mushroom tipped pillars were also applied externally and their adhesion characteristics were compared with currently used Chapter 1. Introduction acrylic bandages . Although adhesion forces were not as high as the acrylic medical bandage, the PDMS bandage regained its adhesion strength when cleaned whereas the acrylic bandage could not.
While all these applications are mostly in their infant stages, continued work on gecko-inspired adhesives will progress them further. The work presented here is primarily directed toward climbing robot applications and focuses on generating higher force anisotropy through ﬁber geometry and articulation. The anisotropy will allow the adhesive to have a gripping direction with high adhesion and shear forces as well as a releasing direction with low adhesion and friction. The ﬁber geometry and articulation can also have other beneﬁts such as zero detachment force, high lifetime, and non-sticky default state for higher performance.
1.2 Thesis Outline The thesis can be divided into three main parts: background information, ﬁber geometry, and ﬁber articulation. Part one (Chapter 2) provides background information relevant to the developed adhesives. Basic introductions to contact mechanics, adhesion, and friction are ﬁrst presented as a reference for the forces commonly measured on the adhesives. Important properties of the gecko’s adhesive are then introduced as a standard to measure adhesive performance. The Chapter 1. Introduction last part of the background discusses other gecko-inspired adhesives to show the current state of development.
Part two (Chapters 3, 4, and 5) discusses the inﬂuence of ﬁber geometry. The test apparatus, named the Bio-F, is ﬁrst introduced in Chapter 3 and general testing methodology is presented. Initial testing was performed on vertical and angled PDMS rectangular ﬂaps to discern if contact with the side faces of the structures could be made for increased shear and adhesion forces. The results were compared to an established tester, the surface force apparatus (SFA), in order to have conﬁdence in the Bio-F tester. Chapter 4 introduces a new type of asymmetric ﬁber where the ﬁber shape, instead of tilt is used to gain force anisotropy. The vertical PDMS ﬁbers used a semicircular shape with diﬀering amounts of available contact area when sheared along opposing directions of a single axis. Chapter 5 presents a combination of the two previous chapters where both tilt and asymmetric ﬁber shape are used in an angled PDMS semicircular ﬁber. It was unclear if these two components could be combined for increased anisotropy. This design also used a higher ﬁber density for greater force values and was tested over 10,000 cycles to determine the adhesive’s lifetime.
Part three of the thesis (Chapter 6) investigates the inﬂuence of articulation, or how the ﬁbers are moved. Vertical testing procedures have been generally used to characterize gecko-inspired adhesives, although the procedure has not been Chapter 1. Introduction shown to be ideal. An angled testing procedure was introduced as an alternative to vertical testing and vertical PDMS semicircular ﬁbers were characterized using both tests. The results show advantages to using non-vertical adhesive placement strategies for increased performance. The last chapter of the thesis (Chapter 7), oﬀers conclusions to the work as well as directions for future work.
Chapter 2 Background The subject of synthetic adhesives draws upon many diverse areas of science and a comprehensive discussion would require material far beyond the scope of this document. However, an introduction to the main theories regarding the areas of contact mechanics, adhesion, and friction is provided for those unfamiliar with the topics. Subsequent topics will include summaries of the gecko adhesive system and current synthetic adhesives.
Hertz ﬁrst solved the problem of two elastic spheres in contact . In his solution, the following four assumptions were made: (1) contacting surfaces are homogeneous, isotropic, and initial contact is isolated; (2) deformation is small so that linear theory of elasticity is still valid; (3) dimensions of the contact region are small compared to the dimensions of the contacting bodies, allowing the treatment Chapter 2. Background of each body as an elastic half-space; and (4) bodies have smooth contacting surfaces and therefore no friction in the contact zone. From his observations, a classical theory of contact without adhesion was formed with a variety of solutions for simple geometries.
For two spheres of a given radius, R1 and R2, contacting each other to form a circle of contact with radius a, the radius is related to the force, F, by Equation 2.1.
Hertz experimentally veriﬁed his solution using an optical microscope to measure the contact obtained by pressing glass spheres together . Work by Sneddon Chapter 2. Background was later performed to include a cylindrical ﬂat punch pressed into the elastic half-space . Here, the force-distance relationship changes and is given by Equation 2.5 with a being the radius of the cylinder.
Later, experimental results showed divergence from Hertz theory under certain conditions. When the load was high, the results did not diﬀer signiﬁcantly from Hertz theory, but three main diﬀerences were observed at low loads. First, the contact area was larger than that predicted. Second, the contact area was reduced to a ﬁnite value as the load diminished to zero. Third, strong adhesion was seen between spheres if the surfaces were clean and dry.
In 1971, Johnson, Kendall, and Roberts (JKR) built upon Hertz’s theory .
The original Hertzian assumptions were still used but the contact between the spherical surfaces was assumed to be adhesive in JKR theory. The adhesive assumption allows for contact to remain when tension was applied during the unloading cycle. JKR theory assumes that adhesive interactions were conﬁned only to the contact area, unlike the Derjaguin, Muller and Toporov (DMT) discussed later. JKR theory balances energies between deformation of the sphere (elastic energy), displacement of the load (potential energy), and formation/breaking of the adhesive bond (surface energy). The contact radius, aJKR, predicted with the Chapter 2. Background inﬂuence of the adhesive interactions, is given in Equation 2.6.
∆γ is the change in surface energy per unit area and describes the work needed to build a unit area of a particular surface. ∆γ can be calculated using Equation
2.7 where γ1 and γ2 are the surface energies of thew two surfaces and γ12 is the interfacial tension between the two materials.
Diﬀerences from the inclusion of adhesive forces between the Hertz and JKR theories include parts of the JKR contact being in tension and compression, while Hertzian contact has only compression. The tension also causes the JKR case to perpendicularly contact the opposing surface at the edge of the contact zone whereas the surfaces meet tangentially with a Hertzian contact.
Since the radius can only be reduced by applying a negative (tensile) load, the surfaces would separate at the smallest load at which the radicand in Equation
Derjaguin, Muller and Toporov (DMT) took a diﬀerent approach to solve elastic contact deformation’s eﬀect on adhesion . In this model, they assumed that Chapter 2. Background the deformed proﬁle of the sphere remains Hertzian and that the adhesion forces only act outside the area of contact, which is entirely in compression. Equilibrium is achieved when the elastic response is balanced by the sum of the external load and surface attraction forces. The contact radius for DMT contact is given by
The diﬀerences between the JKR and DMT models was resolved by Tabor in 1977  where it was shown that both analyses are correct for diﬀerent types of contact. The non-dimensional parameter θT is a measure of the elastic deformation magnitude compared to the surface force range and z0 is the equilibrium spacing
As general rule, DMT analysis provides a good approximation when θ ≤ 0.1 and JKR analysis provides a good approximation when θ ≥ 5. For values between the
0.1 and 5, Maugis has developed an alternative analysis .
Chapter 2. Background It is noteworthy that these analysis are for ideally elastic materials which are smooth enough to be able to make molecular contact across the entire contact area.
In experimental testing, both the testing surface (RMS roughness up to 160 nm) as well as the adhesive ﬁbers/structures (asperity size 100 nm for angled rectangular ﬂaps) were seen to have roughness signiﬁcantly exceeding molecular contact. Therefore, the forces found using the analyses presented in this section will be much greater than those found experimentally.
Among the most important forces responsible for the adhesion seen in adhesives mimicking the gecko are van der Waals (vdW) forces. These forces are always seen in atoms and molecules of macroscopic bodies. To avoid confusion, the van der Waals forces here are referring to London dispersion interactions which come about due to ﬂuctuations in dipole moments. Even materials without permanent dipole moments can have instantaneous dipole moments due to these ﬂuctuations.
At very small separations, the force becomes repulsive due to overlapping of the electron clouds. As the separation is increased, the force becomes attractive with the maximum attractive force often being found around a separation of a few nanometers. Above this distance, the attraction falls oﬀ quickly. The van der Waals interaction is often described in terms of the Hamaker constant, AH, and the separation distance, D. For two ﬂat surfaces, the force, FvdW per unit area of contact is given by Equation 2.12. Typical Hamaker constants vary between Chapter 2. Background
Since vdW forces are small for single contacts, many contacts are needed in order to generate forces large enough to support macroscopic objects. These objects, however, often contain signiﬁcant surface roughness compared to the distances over which the vdW forces act. The roughness results in small contact areas and prevents any signiﬁcant attractive forces.
An analysis using Equation 2.12 to calculate the adhesion force due to vdW interactions was performed for the gecko’s terminal structures, spatulae, assuming contact between two planar surfaces . Using a Hamaker constant within the range stated above and a separation distance of 0.4–0.8 nm, the adhesion force of the 100–1,000 spatulae was found to agree with experimental adhesion forces . Similar approaches at modeling the adhesion forces of natural and synthetic adhesives have also been taken using JKR [120, 37] and DMT  theories.
Friction can be described as the force resisting the relative motion of two material surfaces sliding against each other. Although diﬀerent types of friction exist depending on the state of the materials, dry friction, or the friction between Chapter 2. Background two solid surfaces, will be the only topic covered. The two types of dry friction are static friction, between surfaces without movement, and kinetic friction, between moving surfaces. For many cases, dry friction is approximated using Coulomb friction, Equation 2.13, where Ff is the friction force, µ is the coeﬃcient of friction, and Fn is the normal force between the two surfaces.
The friction force always acts parallel to the surface in the direction opposite to the net force. The coeﬃcient of friction is an empirical value and depends on the properties of the system. Generally, a distinction is made for the coeﬃcient depending on if the surfaces are static, µs, or kinetic, µk. Most values for dry friction fall between 0.3–0.6 depending on the materials, although they can be as low as 0.04 with Teﬂon or higher than 1 with rubber.