Dry adhesives and methods for making dry adhesives

Abstract

A dry adhesive and a method of forming a dry adhesive. The method includes forming an opening through an etch layer and to a barrier layer, expanding the opening in the etch layer at the barrier layer, filling the opening with a material, removing the barrier layer from the material in the opening, and removing the etch layer from the material in the opening.

Claims

1. A dry adhesive fiber array, comprising: a plurality of fibers, wherein each fiber of the plurality of fibers includes: a tip having a cross-sectional area and a height, wherein the tip is compliant; a stem having a first end and a second end, wherein the stem is stretchable along an axis extending from the first end to the second end, wherein a cross-sectional area of the stem is smaller than the tip cross-sectional area, wherein the second end comprises a base; and wherein the first end of the stem is connected to the tip, forming a junction between the tip and the stem, and a backing layer, wherein the base of each fiber of the plurality of fibers is connected to the backing layer at an angle of 90 degrees, wherein the cross-sectional area of the stem of the plurality of fibers further comprises a plurality of cross-sectional areas along a longitudinal length, wherein the plurality of cross-sectional areas comprise a first cross-sectional area smaller than a second cross-sectional area to form a non-uniform stem diameter along the longitudinal length, wherein the second cross-sectional area is directly adjacent to the tip of the each fiber of the plurality of fibers and the first cross-sectional area is directly adjacent to the backing layer.

2. The dry adhesive fiber array according to claim 1, wherein the tip further comprises a flat surface.

3. The dry adhesive fiber array according to claim 1, further comprising: a second plurality of fibers, wherein each fiber of the second plurality of fibers includes: a tip having a cross-sectional area; a stem having a cross-sectional area smaller than the tip cross-sectional area; and wherein the second plurality of fibers is connected to the tip of the plurality of fibers.

4. The dry adhesive fiber array according to claim 3, wherein the tip of the each fiber of the second plurality of fibers further comprises a flat surface.

5. The dry adhesive fiber array according to claim 3, wherein the each fiber of the second plurality of fibers further comprises a base, and wherein the tip of the fiber of the plurality of fibers is connected to the base of the fiber of the second plurality of fibers.

6. The dry adhesive fiber array according to claim 1, wherein the base further comprises a plurality of cross-sectional areas along a longitudinal length, wherein the plurality of cross sectional areas comprise two or more cross sectional areas having different areas forming a non-uniform diameter base.

7. The dry adhesive fiber array according to claim 1, further comprising an angle between the tip and the stem equal to 90 degrees.

8. The dry adhesive fiber array according to claim 1, further comprising an angle between the tip and the stem not equal to 90 degrees.

9. The dry adhesive fiber array according to claim 3, further comprising an angle between the secondary plurality of fibers and tip of the plurality of fibers being equal to 90 degrees.

10. The dry adhesive fiber array according to claim 3, further comprising an angle between the secondary plurality of fibers and tip of the plurality of fibers not being equal to 90 degrees.

11. The dry adhesive fiber array according to claim 3, further comprising an angle between the tip of the each fiber of the secondary plurality of fibers and the stem of the each fiber of the secondary plurality of fibers being equal to 90 degrees.

12. The dry adhesive fiber array according to claim 3, further comprising an angle between the tip of the each fiber of the secondary plurality of fibers and the stem of the each fiber of the secondary plurality of fibers not being equal to 90 degrees.

13. The dry adhesive fiber array according to claim 1, wherein the stem of the each fiber of the plurality of fibers further comprises a surface having a hydrophobic and low surface energy layer on the surface of the stem.

14. The dry adhesive fiber array according to claim 1, wherein the surface of the tip of the each fiber of the plurality of fibers comprises a layer of fluorocarbon.

15. The dry adhesive fiber array according to claim 3, wherein the stem of the each fiber of the second plurality of fibers further comprises a surface having a hydrophobic and low surface energy layer on the surface of the stem.

16. The dry adhesive fiber array according to claim 3, wherein the surface of the tip of the each fiber of the second plurality of fibers comprises a layer of fluorocarbon.

17. The dry adhesive fiber array of claim 1, further comprising a stem-fiber angle that ranges between 1-180 degrees.

18. The dry adhesive fiber array of claim 1, further comprising a tip wedge angle that ranges between 1-179 degrees.

19. The dry adhesive fiber array of claim 3, further comprising a stem-fiber angle that ranges between 1-180 degrees.

20. The dry adhesive fiber array of claim 3, further comprising a tip wedge angle that ranges between 1-179 degrees.

21. The dry adhesive fiber array of claim 1, wherein the backing layer has a thickness that allows equal adhesive load sharing between adjacent fibers of the plurality of fibers, wherein the adhesive load is a force between the tips of the plurality of fibers and a surface in contact with the tips of the plurality of fibers.

22. The dry adhesive fiber array of claim 1, wherein the plurality of fibers form a constant fiber density.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Embodiments of the present invention will now be described, by way of example only, with reference to the accompanying drawings for the purpose of illustrating the embodiments, and not for purposes of limiting the invention, wherein:

(2) FIG. 1 illustrates one embodiment of a dry adhesive fiber according to the present invention;

(3) FIG. 2 illustrates one embodiment of a dry adhesive including a plurality of fibers attached to a backing layer;

(4) FIGS. 3A-D is a Schematic illustration of process flow steps for the fabrication of microfiber arrays according to one embodiment of the present invention;

(5) FIGS. 4a-4h illustrate one embodiment of a method of forming a two layer fiber array 30 according to the present invention;

(6) FIG. 5. is a scanning electron microscope image of the isometric view of a polyurethane elastomer microfiber array illustrated in FIG. 3 with 4.5 m fiber diameter, nine m tip diameter, 20 m length, and 44% fiber density (Scale bar: 50 m);

(7) FIG. 6 is a graph of macroscale adhesion (upper plot) and overall work of adhesion (lower plot) of polyurethane microfibers and flat polyurethane flat control surface on a six mm diameter glass hemisphere for varying preloads;

(8) FIG. 7(a) illustrates a scanning electron microscope image of the profile view of a polyurethane elastomer microfiber array with spatulate tips with around 5 m fiber stem diameter, 9 m tip diameter, 20 m length, and 44% fiber density;

(9) FIG. 7(b) illustrates experimental pull-off force (adhesion) (F.sub.ad) data for elastomer microfiber arrays on a silicon disk with 0.43 mm radius with four different normalized backing layer thicknesses (h/a) for a 10 mN preload (four data points were plotted for each backing thickness on different fiber array locations);

(10) FIGS. 8a and 8b illustrates schematics of the force analysis in two different backing layer thickness cases under constant displacement: (a) fibers on an infinitesimal thick backing layer; (b) fibers on a very thick backing layer;

(11) FIG. 9 illustrates the stem-fiber angle and the tip wedge angle;

(12) FIG. 10 illustrates the stem being angled obligue to the backing layer and tip;

(13) FIGS. 11A and 11B illustrate where the cross sectional area of the stem of the plurality of fibers includes a plurality of cross sectional areas along the longitudinal length;

(14) FIG. 12 illustrates the stem being angled oblique to the backing layer and tip; and

(15) FIG. 13 illustrates the second plurality of fibers having oblique angles relative to the tip of the first and second plurality of fibers.

DETAILED DESCRIPTION OF THE INVENTION

(16) The present invention is directed to dry adhesives and methods for making dry adhesives. The term dry adhesive, as used herein, refers generally to individual dry adhesive fibers and also to materials including a plurality of dry adhesive fibers connected together. The present invention will also be described in terms of micro- and nanofibers, although the present invention is applicable to a wide variety of sizes and is not necessarily limited to a particular size range.

(17) FIG. 1 illustrates one embodiment of a dry adhesive fiber 10 according to the present invention. In that embodiment, the fiber 10 includes a tip 12, a base 14, and a stem 16. The shape of the fiber 10 and the relative size of the various parts of the fiber 10 can vary from that shown in the figure. Different applications and materials, for example, can make different shapes and sizes desirable, and such variations are within the scope of the present invention.

(18) The tip 12 includes a flat surface 20. A layer of fluorocarbon 22 may be on the flat surface 20, as described hereinbelow. The layer of fluorocarbon 22 may be of varying thickness, and is not necessarily shown to scale in FIG. 1. In this particular illustration, the layer of fluorocarbon 22 is shown as being relatively thick for the purpose of illustration.

(19) The base 14 is opposite the tip 12 and is often attached to a backing layer, as is described in more detail with respect to FIG. 2. The base 14 is illustrated as being thicker than the stem 16 and is also illustrated as including a curved surface 24 extending outward from the stem 16 to the edge of the base 14. The relatively large, curved shape of the base 14 allows the base 14 to better withstand strain causes by the bending of the fiber 10, thereby providing for greater durability of the fiber 10. However, in other embodiments the base 14 may have different shapes and sizes. For example, the base 14 may be thinner than the stem or of the same thickness as the stem 16. For example, the base 14 may be indistinguishable from the stem 16 in size and shape, although it is still the base 14 because it represents the end of the fiber 10 that is typically attached to another structure, such as a backing layer.

(20) The stem 16 connects the tip 12 and the base 14. The stem 16 may also include a hydrophobic layer 26 as will be described in more detail hereinbelow. The stem 16 is shown as being at right angles to both the tip 12 and the base 14 in FIG. 2. However, in other embodiments the stem 16 may be oriented differently, such as at an oblique angle (acute or obtuse) with respect to one or both of the tip 12 and the base 14 (see FIGS. 10, 12, and 13). In addition, the stem 16 is illustrated as being straight, although the stem 16 may be made to be curved or to have other non-straight characteristics. The angular orientation of the end 16a of the fiber 16 with tip 12 is tangent with a point along the curvature of tip 12. FIG. 13 also illustrates the second layer of fibers 110 at an oblique angle (acute or obtuse) with respect to one or both of the tip 112 and the base 114 (not shown) or tip 12 (when there is no base 114). FIGS. 10, 12, and 13 are illustrations and are not meant to limit the invention with regards to uniform and non-uniform cross-sectional areas, and orientation of fibers 16, 110 relative to base 14 or tip 12 or tip 112.

(21) FIG. 2 illustrates one embodiment of a dry adhesive structure 30 including a plurality of fibers 10 attached to a backing layer 32. The combination of a plurality of fibers 10 connected to a backing layer 32 will sometimes also be referred to herein as an array 30 or a fiber array 30. The backing layer 32 is connected to the bases 14 of the fibers 10. The dry adhesive structure 30 is not limited to the specifics illustrated in FIG. 2. On the contrary, a dry adhesive 30 according to the present invention may be made in different sizes, with different numbers of fibers 10 having different spacings and different shapes and dimensions. The number of fibers 10, their spacing, dimensions, and other characteristics of the dry adhesive 30 may be uniform or may vary (non-uniform). For example, the dry adhesive 30 may have alternating patterns of fiber sizes and spacings, or the shape of the fibers 10 may be different in different parts of the dry adhesive 30. Many other variations are also possible.

(22) The backing layer 32 may be the same as the material used to make the fibers 10, or the backing layer 32 may be made from a different material. The thickness of the backing layer 32 can have a significant effect on the performance of the fiber array 30, and this is discussed in more detail hereinbelow.

(23) FIGS. 3a-3d illustrate a method of making a dry adhesive according to one embodiment of the present invention.

(24) FIG. 3a illustrates the basic structure in which a dry adhesive is formed. The structure includes an etch layer 40 and a barrier layer 42, as well as a substrate 44 on which the etch 40 and barrier 42 layers are formed. The etch layer 40 and the barrier layer 42 are adjacent to each other and are made from different materials. FIG. 3a is not necessarily to scale, and the dimensions and shapes of the various parts of the structure may vary depending on the particular application.

(25) The etch layer 42 may be a single, homogenous layer, or it may be formed from and include more than one layer of the same or different materials. As used herein, etch layer 40 means one or more layers which are etched or from which material is otherwise removed so as to form the structure described herein. In the illustrated embodiment, the etch layer 40 is changed so as to form a mold for use in manufacturing the dry adhesive fibers 10 and the dry adhesive fiber array 30.

(26) The barrier layer 42 may also be made from one or several layers of the same or different materials. The barrier layer 42 is made from a different material having different properties than the etch layer 40. Unlike the etch layer 40, the barrier layer 42 acts as a stop and does not dramatically change its shape during the manufacturing process. The barrier layer 42 maintains a relatively constant-flat shape that is used to form the flat surfaces 20 on the tips 12 of the fibers 10.

(27) In practice, the barrier layer 42 will lose some material during the formation of the openings, which are described below. However, this loss of material is very small compared to that of the etch layer 40, and the concept of barrier materials is well understood in the art. As used herein, barrier layer 42 generally means the one or more layers which form a border of the openings 50 (described below) but which are not significantly etched or from which significant material is not otherwise removed during the formation of the openings 50, which are described below.

(28) The barrier layer 42 is generally described as having a flat shape, although in other embodiments the barrier layer 42 may be formed otherwise so as to form different shapes for the tips 12 of the fibers 10. For example, the barrier layer 42 may be formed with a curved shape, or with a surface having other features such as recesses or protrusions.

(29) The substrate 44 may be used in connection with the etch 40 and barrier 42 layers. However, in methods where the substrate 44 is not required to form and/or to support the etch 40 and barrier 42 layers, the substrate layer 44 may be omitted.

(30) With reference to FIG. 3b, openings 50 are formed in the etch layer 40. The openings 50 are formed through the etch layer 40 and to the barrier layer 42. The openings 50 may be created, for example, by forming a patterned layer 52 on the surface of the etch layer 40 and then exposing the structure to an etching process or to other processes for removing the exposed material from the etch layer 40. The patterned layer 52 may be photoresist, a contact mask, or some other material used to selectively expose portions of the etch layer 40. In other embodiments, the patterned layer 52 may be omitted and the openings may be formed directly, such as through e-beam processes.

(31) After the openings 50 are formed, the openings 50 are expanded in the etch layer 40 at the barrier layer 42 to form expanded openings 54 which will shape the tip 12 of the fibers 10. The process of forming the expanded openings 54 will be described in more detail hereinbelow.

(32) The openings 50 may also be expanded 56 near the top surface 58 of the etch layer 40, on the surface 58 opposite the barrier layer 42. This expanded opening 56 will shape the base 14 of the fibers 10. By expanding 56 the opening 50, the base 14 will be thicker than the stem 16. Furthermore, if the expanded opening 56 is given a rounded shape, it will cause the base 14 to be formed with a rounded shape, as described herein. The formation of this expanded opening 56 may, for example, be performed with an isotropic etch prior to the formation of the opening 50 and may be performed in the portions of the etch layer 40 not covered by the patterning layer 52.

(33) The process of forming the openings 50 may, under some processes, form a layer of hydrophobic material 60 on the side walls of the openings. Similarly, under some processes, a fluorocarbon layer 62 may be formed on the barrier layer 42 where the flat surface 20 of the tip 12 will be formed. This fluorocarbon layer 62 has been found to cause increased adhesion at the flat surface 20 of the tip 12. The hydrophobic layer 60 is a smooth, non-stick surface which is also advantageous. The formation of these layers 60 and 62 will be described in more detail hereinbelow.

(34) After the openings 50, 54, 56 are formed, the photoresist or other patterned layer 52 may be removed.

(35) With reference to FIG. 3c, after the openings 50 are formed, they are filled with a material 70. The material 70 may be a polymer, a metal, or any other material from which the fibers 10 can be made. After the openings 50 are filled with the material 70, the backing layer 32 may be formed over the openings 50 and on the surface 58 of the etch layer 40 opposite the barrier layer 42. The material 70 in the openings 50 is connected together via the backing layer 32, forming a single structure including a plurality of fibers 10 and the backing layer 32.

(36) The backing layer 32 may be formed in several ways. The backing layer 32 may be formed separately from the material 70 filling the openings 50 and applied over the openings 50 and on the surface 58 of the etch layer 40. Alternatively, the backing layer 32 may be formed from the same material 70 as that used in the openings 50, in which case, for example, the process of filling the openings 50 may be allowed to continue after the openings 50 are filled, so that the material 70 fills the surface 58 over the openings 50 to form the backing layer 32. A mold (not shown) may be formed on top 58 of the etching layer 40 to contain the extra material 70 used to form the backing layer 32. In addition, a step of compressing or squeezing the material forming the backing layer 32 may also be performed so that the backing layer 32 is formed to a desired thickness. Other methods of controlling the thickness of the backing layer 32 are also possible, such as by trimming or cutting excessive backing layer 32 material. The thickness of the backing layer 32 can have a significant effect on the performance of the fiber array 30, and will be discussed in more detail hereinbelow

(37) With reference to FIG. 3d, after the material 70 in the openings 50 has cured or otherwise achieves a desired state, the etch layer 40 and barrier layer 42 may be removed from the material 70, leaving the molded dry adhesive fibers 10 and backing later 32. In addition, the substrate layer 44 may also be removed if it was used.

(38) The use of wet etch processes for the removal of the etch layer 40 tend to cause clumping of, or an attraction between, adjacent fibers 10. This is caused by hydrostatic pressure from the liquid remaining from the wet etching. It has been found that dry etch processes are particularly advantageous for removing the etch layer 40 and reducing or eliminating the clumping or lateral or vertical collapsing of fibers. However, the use of a dry etch process is not required with the present invention, and other processes may be used. For example, supercritical carbon dioxide (CO.sub.2) drying can be used to release the fibers without clumping or collapsing issues where after wet etching of the etch layer, released fibers can be soaked in liquid CO.sub.2, heated and applied pressure over the supercritical point to remove CO.sub.2.

(39) Although this embodiment of the method has been described in terms of making several fibers 10 attached to a backing layer 32, the present invention may also be used to make a single fiber 10, or to make a plurality of fibers 10 that are not connected to a backing layer 32. Furthermore, the present invention may also include two or more layers of fibers 10 or fiber arrays 30 having two or more layers of fibers 10.

(40) FIGS. 4a-4h illustrate one embodiment of a method of forming a two layer fiber array 30 according to the present invention. In this embodiment, the two layers of fibers are different sizes. The smaller fibers 110 (shown in FIGS. 4g and 4h) may be smaller in volume, or smaller in their dimensions. Alternatively, it is also possible to form a multi-layer fiber array 30 in which the different layers of fibers are the same size.

(41) FIGS. 4a and 4b are analogous to FIGS. 3a and 3b and they illustrate the first structure in which the openings 50 are created and in which the first layer of fibers 10 will be formed.

(42) FIGS. 4c and 4d illustrate the second structure in which the second layer of fibers 110 is formed. In the illustrated embodiment, the second structure includes an etch layer 140 and a barrier layer 142, as well as a substrate 144 on which the etch 140 and barrier 142 layers are formed. The etch layer 140 and the barrier layer 142 are adjacent to each other and are made from different materials. The second structure may include the same or different elements as those described hereinabove with respect to FIGS. 3a and 3b. In other words, the openings 150 in the second structure may have the same features as the openings 50 in the first structure, although they differ in their size. FIG. 4a is not necessarily to scale, and the particular dimensions of the various parts of the structure may vary depending on the particular application.

(43) FIGS. 4c and 4d are similar to FIGS. 4a and 4b, except that the fibers 110 to be formed in the process of FIGS. 4c and 4d are smaller than those formed in the process of FIGS. 4a and 4b. For example, FIG. 4a may represent a process with a twenty m thick etch layer 40, three m diameter openings 50, and twelve m spacing between opening 50 centers. In contrast, FIG. 4c may represent a process with a two m thick etch layer 140, a 300 nm diameter openings 150, and 800 nm spacing between opening 150 centers.

(44) Similarly, the etching process of both FIGS. 4b and 4d may be, for example, a dry etching process. That process may include isotropic etching, followed by deep reactive ion etching, and then expanding the opening 50, 150 near the barrier layer 42, 142 to form a desired shape for the base 14, 114 of the fibers 10, 110.

(45) However, variations are also possible with this aspects of the present invention and, for example, the second fibers 110 may be larger than the first fibers 10.

(46) FIG. 4e illustrates the structures of FIGS. 4b and 4d being connected together. The dashed line illustrates where the two structures are joined together. When connected, the structures are oriented so that the openings 50, 150 correspond to or engage with each other. In other words, the exposed openings 50 in the first structure corresponding to or engage with exposed openings 150 in FIG. 4d. This orientation is accomplished in FIG. 4e by rotating the top structure 180 degrees before connecting the two together.

(47) This connection may be formed, for example, by silicon fusion bonding or by other processes. In one embodiment, the bonding is accomplished with ten minutes of piranha cleaning to remove photoresist and anti-reflective coating. Followed by ten minutes of oxygen plasma etching to remove the film that is natively generated in the openings 50, 150 during deep reactive ion etching. Followed by ten minutes of piranha cleaning for final surface cleaning. After the final cleaning, the two structures are pressed to each other and annealed at 1,000 degrees Celsius in a quartz furnace to bond them.

(48) FIG. 4f illustrates the bonded structure after the top layers (the barrier layer 42 and substrate 44) are removed. This may be done, for example, with a buffered oxide etching process. The resulting structure is a two layer mold open at the top where the barrier layer 42 and substrate 44 used to be.

(49) FIG. 4g illustrates the two layer structure after being filled with a material 70. As described above, the material 70 may by any of many different materials, and this process may be, but is not required to be, performed in a vacuum chamber.

(50) FIG. 4g also illustrates that not all of the second openings 150 are necessarily utilized. In this embodiment, one of the second openings 180 is not connected to the first openings 50 and, therefore, that opening 180 is not filled with material 70.

(51) FIG. 4h illustrates the resulting two layer fiber array 30 after the surrounding structure or mold (the remaining etch layers 40, 140, the second barrier layer 142, and the second substrate 144) has been removed. The removal may be performed, for example, with a XeF.sub.2 etch to remove the bottom silicon layer and a buffered oxide etch to remove the oxide layer, as described above with respect to FIGS. 3a-3d. A further XeF.sub.2 etch may be used to remove the upper silicon layer.

(52) Although the present invention has been described in terms of a two layer fiber array 30, the present invention may also be used to produce a fiber array 30 having more than two layers. Furthermore, the present invention is not limited to multilayer fiber arrays 30, and it may also be used, for example, to make multilayer individual fibers and to make other structures.

(53) The theory related to the present invention will now be presented. Flat and larger diameter (also referred to as cross-sectional area) spatulate tips 12 are postulated to enhance the adhesion and work of adhesion significantly due to the increased tip contact area at the fiber-surface interface [H. Gao and H. Yao, PNAS, 101, 7851 (2004)]. In order to model the work of adhesion enhancement approximately, a single polymer fiber 10 is assumed to be stretched while its volume is conserved. In addition, if pull-off of each fiber tip 12 is assumed to happen simultaneously where overall pull-off force per unit area is a constant value (c.sub.1) and the elastic deformation is assumed to happen at the fiber stem 16 only where the polymer Young's modulus (E) is assumed to be constant. Then, the maximum stretched length (x.sub.c) and work of adhesion (W) of a single fiber 10 during separation can be computed as

(54) $\begin{array}{cc}{x}_c=x_0\frac{{\mathrm{Ed}}_0^2}{{\mathrm{Ed}}_0^2-c_1{D}^2}& \left(1\right)\\ W={}_{x_0}^{x_c}Fdx=E\frac{d_0^2{x}_0}{4}\left[\frac{c_1{D}^2}{{\mathrm{Ed}}_0^2-c_1{D}^2}-\ln \frac{{\mathrm{Ed}}_0^2}{{\mathrm{Ed}}_0^2-c_1{D}^2}\right]& \left(2\right)\end{array}$

(55) where x.sub.0 is the initial stem 16 length, D is the fiber spatulate tip 12 diameter, and d.sub.0 is the fiber stem 16 diameter. From (1) and (2), elastomer fibers 10 with larger diameter tips 12 elongate and dissipate energy significantly, and thus the work of adhesion per fiber 10 is increased. Moreover, adhesion is also increased by a fiber array 30 with larger flat spatulate tips 12 since: (1) The fracture mechanics of the microfibers is flaw insensitive [M. Murphy, B. Aksak, and M. Sitti, Langmuir, under review (2006)] (the stress at the interface is uniform and equal to the intrinsic adhesion strength at the instant of pull-off) and thus enables the maximum possible adhesion pressure; (2) Flat and compliant spatulate tips 12 enable easier contact to a smooth surface with almost no alignment problem; (3) Fiber stretching enables larger number of fibers 10 staying in contact with a smooth surface during pull-off. Therefore, this invention is focused on fabrication of polymer microfibers 10 with flat and larger spatulate tips 12 for fibrillar adhesives with improved adhesion capability.

(56) One embodiment of the fabrication process according to the present invention will now be provided. The present invention is not limited to the specifics details of this embodiment, and these details are illustrative of the present invention, and not limiting. FIG. 3a-d illustrates one embodiment of the fabrication process of polymer microfibers with flat and larger diameter spatulate tips 12. FIG. 3a illustrates a silicon-on-insulator (SOI) wafer (purchased from Addison Engineering) which is used as a substrate 44 which has 20 M thick top silicon layer as the etch layer 40 and 0.5 m thick SiO.sub.2 layer as the barrier layer 42. After an optical lithography step forms a desired pattern 52 on the top 58 of the etch layer 40, the negative fiber array template is formed in FIG. 3(b). The required fiber profile shape is obtained in two steps. At first, isotropic etching is used for forming the circular supporting shape 56 of the base 14 of each fiber 10 to reduce the stress concentration for preventing the fracture of fibers 10 at their bases 14. Next, deep reactive ion etching (DRIE) is followed for forming vertical high aspect ratio microchannels 50. Isotropic etching and DRIE were carried out consecutively in STS Multiplex ICP RIE with 20 mT pressure, 130 sccm SF.sub.6, 20 sccm O.sub.2, 600 W coil power, and 120 W platen power. When the vertical etching reaches to the silicon oxide layer 42, it cannot proceed vertically anymore and then starts to expand laterally 54 on the oxide interface between the etch layer 40 and the barrier layer 42. This effect is called the notching effect [M. E. McNie, D. O. King, V. Nayar, M. C. L. Ward, J. S. Burdess, C. Quinn, and S. Blackstone, Proc. of IEEE International SOI Conference, 60 (1997)]. By controlling the lateral etching 54 time, the spatulate tip 12 diameter is determined. Then, in FIG. 3(c), the template is filled with a liquid polymer 70 under vacuum to remove not only the trapped air but also the native gas in the liquid polymer 70, and then the polymer 70 is cured. Here, any polymer 70 (e.g. Parylene C) or any other fiber material 70 can be also gas phase deposited inside to the template 50. In FIG. 3(d), the polymer fiber array 30 with a backing layer 32 is released by three step etching: At first, the bottom silicon layer 44 is etched away by XeF.sub.2 dry etching; The thin oxide layer 42 is removed by buffered oxide etching (BOE); Finally, the 20 m thick top silicon layer 40 is etched away by XeF.sub.2 etching in around 30 minutes to release the fibers 10 with a backing layer 32. Here, the final etching step is particularly important. Since using a wet etching technique such as KOH etching would result in clumped fibers 10 due to capillary forces during drying, XeF.sub.2 dry etching is used to prevent any clumping issues. Moreover, since the DRIE process natively creates a hydrophobic thin submicron film 60 on the template microchannel 50 side walls during the process [A. A. Ayon, R. Braff, C. C. Lin, H. H. Sawin, and M. A. Schmidt, J. of Electrochemical Society, 146(1), 339 (1999)], each released polymer fiber 10 is expected to be coated with this hydrophobic and low surface energy thin film 26 on their side walls 16 (not at the spatulate tip 12 surface 20). The film 60 on the side walls of the openings 50 and the fibers 10 can be characterized as a passivation film or a fluorocarbon thin film. This very low surface energy coating 26 could reduce the cohesion of microfibers 10 significantly, and thus it could minimize any clumping during the mechanical contact of neighboring fibers 10.

(57) Besides forming the flat spatulate tips 12, the above fabrication process has other advantages with respect to previous fibrillar adhesive fabrication methods: (1) Fiber material can be fabricated from any polymer 70 which can be in a liquid solution form or can be gas phase deposited; (2) Array 30 of fibers 10 can be fabricated in large areas up to 8 inch wafer size cost effectively using a single mask; (3) The yield is almost 100%; (4) This method can be extended to the fabrication of hundreds of nanometer diameter fibers 10 easily by using a higher resolution lithography step in FIG. 3a by using phase masks or interference lithography.

(58) High tensile strength elastomer polyurethane (ST-1060, BJB Enterprise) with Young's modulus of around 3 MPa was selected as the fiber adhesive material. FIG. 5 illustrates a scanning electron microscope (SEM) (Hitachi 2460N) image of the resulting microfiber array 30 with 4.5 m fiber diameter, 9 m tip diameter, 4.5 m base supporter diameter, 20 m length, and 12 m spacing between each fiber center (44% fiber tip area density). These geometries are held by 80 sec isotropic etching for the fiber base supporter structures and by 21 min 20 sec vertical etching for the fiber and spatulate tips 12.

(59) Performance of a fibrillar adhesive is characterized by its macroscale adhesion (P) and overall work of adhesion (W). To characterize these parameters for the fabricated fiber arrays 30 during adhering to a glass hemisphere, a custom tensile macroscale adhesion measurement setup was built. A glass hemisphere instead of a flat glass surface was selected as the test surface in order to have no alignment errors during the measurements. A 6 mm diameter very smooth glass hemisphere (ISP Optics, QU-HS-6) attached to a load cell (Transducer Techniques, GSO-25) was moved vertically by a motorized stage (Newport, MFA-CC) with 100 nm resolution. The hemisphere was contacted to and retracted from the fiber array sample with a pre-specified preload force and a very slow speed (1 m/s) to minimize any viscoelastic effects. The maximum tensile force during the glass hemisphere and fiber array separation (pull-off force) gave the adhesion, and the hysteresis area between the loading and unloading curves gave the dissipated energy between the loading and unloading of the fiber array. Dividing this dissipated energy by the maximum circular contact area during loading gave W.sup.10. During the force measurements, an inverted microscope (Nikon Eclipse TE200) is used to measure the real circular maximum contact area between the hemisphere and the fiber array 30.

(60) Adhesion and overall work of adhesion of 1515 mm.sup.2 area and one mm thick ST-1060 polyurethane fiber array 30 samples and a 1 mm thick flat and smooth ST-1060 surface were measured on the glass hemisphere using the above setup. The flat polyurethane surface was used as a control substrate to show the relative enhancement of P and W by structuring the same material as a cylindrical microfiber with flat spatulate tips. Since ST-1060 is also etched slightly during the final XeF.sub.2 dry etching step in FIG. 1(d), flat sample was also exposed to XeF.sub.2 for about 30 minutes to have the same surface roughness with the flat spatulate tip surface.

(61) Using the above setup, the fiber array 30 and the glass hemisphere interface adhesion and overall work of adhesion are measured as shown in FIG. 6. Plots show the error bars measured from the force-distance data at two different locations on the fiber array 30 for preloads up to 25 mN. Adhesion values saturate as preload increases, and the array of fibers has around 4 times higher adhesion than the flat surface. Dividing the adhesion to the optically measured maximum circular contact area during loading, maximum adhesion pressure for the fiber array 30 can be computed as 18 N/cm.sup.2 at a preload pressure of 12 N/cm.sup.2. Overall work of adhesion of the fibers 10 is five times higher than the one from the flat elastomer surface. This energy dissipation enhancement is due to the lost energy during separating the elastic and highly stretched fibers 10 from the adhered glass surface as given in (2). ST-1060 fibers stretched up to 500% strain in the experiments (observed by profile view optical imaging) which would show the reason of the enhancement of the elastic energy loss during unloading of the fibers 10.

(62) Macroscale adhesion data from the fiber array 30 in this work are compared with the previous works as given in Table 1. Table 1 is a comparison of adhesive strength among various natural and synthetic gecko inspired micro/nanofibers [Y. Zhao, T. Tong, L. Delzeit, A. Kashani, M. Meyyappan, and A. Majumdar, J. Vac. Sci. Techno. B, 24(1), 331 (2006)]. The polymer fibers 10 with spatulate tips 12 show better adhesion pressure than other synthetic gecko inspired fibrillar adhesives with no spatulate tips 12 although the single fiber 10 in this work is over 20 times thicker than the single fibers 10 which were fabricated in other works. In order to even increase the adhesion performance in this work, microfibers with tips 12 can be scaled down to hundreds of nanometers in diameter using phase mask type of sub-micron lithography techniques. In addition, N times self-similar scaling down in fiber diameter will generate {square root over (N)} times higher adhesion [E. Arzt, S. Gorb, and R. Spolenak, PNAS, 100, 10603 (2003)], and smaller fibers will need less preload than larger fibers to obtain the same adhesion.

(63) TABLE-US-00001 TABLE 1 Materials & Structures Macroscale Adhesion (N/cm.sup.2) Gecko (Tokay) foot-hairs with 10 [Autumn, Nature, 405, 681 spatulate tips (2000)] Silicone rubber fibers with 60 m 0.003 [Sitti, J. Adhesion Science length and 200 nm diameter and Technology, 17(5), 1055 (2003) Polyurethane fibers 20-60 m 0.5 [D. Campolo, S. Jones, and R. S. length and 200 nm diameter Fearing, Proc. of the IEEE Nanotechnology Conf., 12 (2003)] Polyimide fibers with 2 m 3 [A. K. Geim, S. V. Dubnos, I. V. length and 500 nm diameter Grigorieva, K. S. Novoselov, A. A. Zhukov, and S. Y. Shapoval, Nature Materials, 2, 461 (2003)] Polyurethane fibers with 100 m 3.8 [M. Murphy, B. Aksak, and M. length and 25 m diameter Sitti, Langmuir, under review (2006)] Multi-walled carbon nanotubes 11.7 [Y. Zhao, T. Tong, L. Delzeit, with 40 m length and 20-30 A. Kashani, M. Meyyappan, and A. nm diameter Majumdar, J. Vac. Sci. Techno. B, 24(1), 331 (2006)] Polyurethane fibers with 20 m 18 length, 4.5 m diameter, and 9 m spatulate tips

(64) The Effect of the Backing Layer Thickness.

(65) It has also be found that the thickness of the backing layer 32 has a greater effect on the performance of dry adhesives than was previously known. The effect of the backing layer 32 thickness on adhesion was investigated for single-level elastomer fibrillar adhesives 30. Polyurethane microfiber arrays 30 with spatulated tips 12 on a 160 m thick backing layer 32 show nine times greater adhesion strength (around 22 N/cm.sup.2) than those with a 1120 m thick backing 32. A theoretical model is proposed to explain this difference in which very thin backing layers 32 promote equal load sharing, maximizing adhesion, while very thick backings can lead to reduced adhesion due to edge stress concentration. Therefore, backing layer 32 thickness should be considered as a significant parameter for design of high performance fibrillar adhesives.

(66) As discussed above, the adhesion of biologically inspired fibrillar dry adhesive has been studied extensively in combination with developments of various fabrication methods. Based on dominant forces of van der Waals [K. Autumn, M. Sitti, Y. A. Liang, A. M. Peattie, W. R. Hansen, S. Sponberg, T. W. Kenny, R. Fearing, J. N. Israelachvili, and R. J. Full, PNAS, 99, 12252 (2002)] and possibly capillary [G. Huber, H. Mantz, R. Spolenak, K. Mecke, K. Jacobs, S. N. Grob, and E. Artz, PNAS, 102(45), 16293 (2005)] forces, vertical cylindrical micro/nanofiber arrays [A. K. Geim, S. V. Dubnos, I. V. Grigorieva, K. S. Novoselov, A. A. Zhukov, and S. Y. Shapoval, Nature Materials, 2, 461 (2003)] were proposed as fibrillar adhesives at first. Design parameters for these fibers were proposed as the fiber radius, aspect ratio [C. Greiner, A. del Compo, and E. Arzt, Langmuir, 23, 3495 (2007)], tip shape [H. Gao and H. Yao, PNAS, 101, 7851 (2004)], and material properties [K. Autumn, C. Majidi, R. E. Groff, A. Dittmore, and R. Fearing, J. Exp. Biol., 209, 3558 (2006)]. Inspired by footpads of various animals in nature such as insects and geckos, spatulated tips on single-level cylindrical [S. Kim and M. Sitti, Applied Physics Letters, 89, 261922 (2006)][N. J. Glassmaker, A. Jagota, C-Y. Hui, & J. Kim, J. R. Soc. Interface, 1, 22 (2004)], angled [B. Aksak, M. P. Murphy, and M. Sitti, Langmuir, 23, 3322 (2007)] and hierarchical [N. J. Glassmaker, A. Jagota, C-Y. Hui, W. L. Noderer, M. K. Chaudhury, PNAS, 104, 10786 (2007)][A. del Campo and E. Arzt, Molecular Bioscience, 7(2), 118 (2007)] fibers were introduced for developing high performance fibrillar adhesives. In addition, one of the recent findings demonstrates that the real contact perimeter is a more important geometrical factor governing adhesion than the real contact area [M. Varenberg, A. Peressadko, S. Gorb, and E. Arzt, Applied Physics Letters, 89, 121905 (2006)]. However, the role of backing layer 32 thickness on adhesion has not been investigated in detail so far.

(67) The backing layer 32 thickness effect on adhesion of elastomeric single-level microfiber structures 30 will now be described. Although a thick backing layer 32 improves the roughness adaptation and fiber 10 contact abilities due to increased effective compliance, this study shows that a thick backing layer 32 could reduce the macroscale adhesion of the fibers 10 on smooth surfaces significantly.

(68) We measured the pull-off force of single-level elastomer fiber array 30 samples with different backing layer 32 thicknesses and developed a theoretical model to explain the observed results. Polyurethane (ST-1060, BJB Enterprise) fiber array 30 samples with spatulated tips 12 are fabricated using the procedure reported in S. Kim and M. Sitti, Applied Physics Letters, 89, 261922 (2006). Briefly, we first fabricate negative silicon fiber array templates using deep reactive ion etching as described hereinabove. Liquid polyurethane 70 is filled into these silicon negative templates 50 and cured. The silicon templates 50 are then etched using XeF.sub.2, and the fibers 10 are released. The final backing layer 32 thickness of each sample is determined by regulating the gap between the negative template and a glass slide on it.

(69) All fiber arrays 30 in the samples have a stem 16 diameter of around five m and a tip 12 and base 14 support diameter of nine m. The total length of a fiber 10 is 20 m and the minimum spacing between fiber centers is 12 m as displayed in FIG. 7(a). A custom tensile setup was built to measure the adhesion of the samples. The measure of adhesion in this work is the pull-off load. A silicon disk with 0.43 mm radius and nanometer scale surface roughness was fabricated by patterning a polished silicon (100) wafer using optical lithography and deep reactive ion etching. The silicon disk was attached to a load cell (Transducer Techniques, GSO-25), and moved vertically by a motorized stage (Newport, MFA-CC) with 100 nm resolution. The disk was contacted to and retracted from the fiber array sample with specified preload forces and a slow speed (1 m/s) to minimize viscoelastic effects. The maximum pull-off force was recorded. In addition, the contact area and the deformation of fiber array 32 during loading and unloading was recorded using a camera (Dage-MT1, DC330) attached to an inverted optical microscope (Nikon, Eclipse TE200).

(70) Adhesion of four samples with 160, 280, 630, and 1120 m backing layer 32 thicknesses was measured and is shown in FIG. 7(b). Pull-off forces were measured at five different locations on each fiber array 30 for a preload of ten mN. The sample with the thinnest backing layer 32 (160 m) showed the highest adhesion, with average pull-off force about nine times greater than that of the 1120 m layer 32.

(71) Our interpretation of this surprising finding, that reduced compliance enhances adhesion, lies in the idea that a thinner backing layer 32 promotes equal sharing of the load by the fibers 10. As shown schematically in FIG. 8(a), if a displacement 8 were applied to three fibers 10 on an infinitesimally thin backing layer 32, each one would experience the same vertical tension, F.sub.y1. If the fiber pulled-off at a characteristic force F.sub.f=k.sub.f.sub.f where k.sub.f is the stiffness of the fiber 10 and .sub.f is the fiber 10 elongation at pull-off, then the pull-off force of the system would be 3F.sub.f. If the thin layer 32 were replaced by a very thick backing 32 (FIG. 8(b)), the y-direction forces would be F.sub.y1=k.sub.f and F.sub.y2=k.sub.f+F.sub.B where F.sub.B is the additional force required to keep the tip 12 attached to the disk due to non-uniform deformation of the backing layer 32. Because the backing layer 32 is elastic, F.sub.B=k.sub.f for some positive . The two fibers 10 on the side will pull-off when k.sub.f+F.sub.B=F.sub.f and the total force at pull-off would be (3)F.sub.f.

(72) To quantify this idea for a large number of fibers 10 in contact, we note that the spacing of the fibers 10 are typically very small in comparison with the contact radius a and the thickness of the elastic layer h. Hence, we can treat these fibers 10 as a foundation consisting of elastic springs between the rigid indenter and the backing layer 32. The foundation can support a normal stress , which is related to the displacement of foundation, d by =kd where k is the stiffness of the foundation. Note that d is the difference in normal displacement between the surface of the indenter and the backing layer 32. The stiffness can be determined by assuming that the fibers 10 are bars with height L and effective cross-sectional area A.sub.eff, k=EA.sub.eff/L where is the number of fibrils per unit area. From the known geometry and stiffness of the fibers, k=2.3710.sup.10 N/m.sup.3

(73) where =1/(1210.sup.6).sup.2 fibers/m.sup.2, E=3 MPa, A.sub.eff=r.sup.2, r=2.5 m, and L=14 m.

(74) The maximum pull-off force occurs in the equal load sharing (ELS) regime, where all the fibers in adhesive contact with the indenter bear the same load. To see how ELS depends on the backing layer thickness and the contact area, assume that all the fibers in contact are in this regime, so at pull-off, we have
.sub.fk.sub.f(3)

(75) In the ELS limit, the maximum pull-off force F.sub.max is directly proportional to the contact area,
F.sub.max=.sup.2.sub.f(4)

(76) where a is the radius of the disk. The ELS limit is strictly valid if the backing layer thickness h is very small compared to a. Another limit is a very thick backing layer with very stiff fibers, that is, when h/a and ka/2G is very large where G is the shear modulus. In this limit, the interfacial displacement is dominated by the deformation of the elastic layer and the stress distribution is given by the classical solution of a rigid punch in contact with a half space [K. L. Johnson, Contact Mechanics, Cambridge University Press (1985)]. The normal stress at the punch edge has a square root singularity characteristic of an opening crack. For >>1 and h/a>>1, the pull-off force F.sub.ad in this limit can be derived as
F.sub.ad=4F.sub.max/(2).sup.1/2(5)

(77) This equation shows that, given F.sub.max, the maximum extent of strength reduction can be predicted. The data in FIG. 7(b) show a decrease in pull-off force with increasing thickness. Theoretically, in the limit of very small thickness, pull-off force should asymptotically approach the ELS limit, which depends on the unknown fiber pull off stress, .sub.f. In this limit, the pull-off load is significantly affected by variability in .sub.f. This is reflected in the scatter of the pull-off force data associated with the sample with the smallest h/a.

(78) The theoretical problem of determining pull-off forces as a function of and h/a is more involved and will be addressed in a future work.

(79) In summary, polyurethane microfiber arrays 30 with spatulated tips 12 on 160 m thick backing layer 32 show adhesion strength (around 22 N/cm.sup.2), nine times greater than fiber arrays 30 with thickness of 1120 m. A theoretical model is proposed to explain this difference in which very thin backing layers 32 promote equal load sharing, maximizing adhesion. In the other extreme, very thick backings 32 can lead to reduced adhesion, because of edge stress concentration similar to a rigid punch in adhesive contact with a half space. This work shows the significance of backing layer 32 thickness on equal load sharing of single-level microfiber arrays 30 on smooth surfaces.

(80) The present invention describes a method for fabrication of polyurethane elastomer microfiber arrays with flat spatulate tips. For a preload pressure of around 12 N/cm.sup.2, adhesion pressures up to 18 N/cm.sup.2 and overall work of adhesion up to 11 J/m.sup.2 are demonstrated for polyurethane fibers with 4.5 m fiber diameter, 9 m tip diameter, 20 m length, and 44% fiber tip area density on a 6 mm diameter glass hemisphere. These repeatable fibrillar adhesives would have wide range of applications as space, biomedical, sports, etc. adhesives.

(81) Although the present invention has generally been described in general terms and in terms of specific embodiments and implementations, the present invention is applicable to other methods, apparatuses, systems, and technologies. For example, the present invention can be used with a variety of materials, such as metals, ceramics, other polymers, Paralyne, carbon, crystals, liquid crystals, Teflon, semiconductors, piezoelectric materials, conductive polymers, shape memory alloy materials, and organic materials, and these and other materials could be deposited or molded inside the etch layer 40 as described hereinabove. Furthermore, the base 14 of the fibers 10 may not be necessary in some cases, in which case the base may be omitted or it may be considered to be the part of the fiber 10 attached to another structure. The spatulate tip fibers 10 with or without a hydrophobic surface coating can be used as a superhydrophobic surface where the water contact angle could be increased more due to spatulate tip geometry and fiber spacing. During the fiber tip formation (etching), if the etching time is long enough the tip endings could combine and fibers with a continuous flat thin-film can be formed as another type of fiber based adhesives or materials. Different fiber cross-section geometry (square, ellipsoid, triangle, etc.), base geometry (pyramid, etc.), tip diameter, fiber packing geometry (hexagonal or square), high or low aspect ratio, and constant or variable fiber density is possible with the present invention. Although the etch layer removal has generally been described in terms of a dry etch process, it is still possible to use a wet etching method according to the present invention. The spatulate fibers 10 can be used as static friction enhancing materials in addition to enhanced adhesion materials. Micro or nanoscale patterning methods such as interference lithography, electron-beam lithography, nanoimprinting, directed self-assembly, dip pen lithography, laser micro- or nano-machining, micro/nano-milling, and extreme UV lithography can be used to pattern the etch layer for fabricating micro- or nanoscale fibers with spatulate tips.

(82) FIG. 9 illustrates the stem-fiber angle and the tip wedge angle . The stem-fiber angle and the tip wedge angle are controlled angles during the silicon removal process. The range of these angles is 1-180 degrees and 1-179 degrees, respectively. Stem-fiber angle is the angle between the stem outer surface 16b and the tip outer surface 12b, which varies depending on the location of the point along the tip outer surface 12b. Tip wedge angle is the angle between the tip outer surface 12b and the tip flat surface 20, which varies depending on the location of the point along the tip outer surface 12b. The three illustrations of the fiber 10 show tips 12 with different tip heights (h.sub.1, h.sub.2, h.sub.3) and tip diameters or cross sections (d.sub.2, d.sub.3, d.sub.4) relative to stems 16 with the same stem diameter or cross section (d.sub.1). Any ratio of diameters to height are acceptable. The tips 12 can have a curvature (as shown in the figures) or a straight line (not shown) between the tip flat surface edge (or outer perimeter of the tip diameter) 20a and the junction 16a of tip 12 and stem 16. The angles are controlled during the silicon removal process. After the vertical removal process reaches to the silicon oxide (barrier) layer, these angles could be controlled by specifically tuning and controlling the silicon removal step duration, removal ion type, and removal ion energy level parameters.

(83) FIGS. 11A and 11B illustrate where the cross sectional area of the stem of the plurality of fibers includes a plurality of cross sectional areas along the longitudinal length, where the plurality of cross sectional areas comprise a first cross sectional area smaller than a second cross sectional area to form a non-uniform stem diameter along the longitudinal length. FIG. 11B illustrates the first cross sectional area is adjacent to the backing layer 14 and the second cross sectional area is adjacent to the tip 12 of the each fiber 16 of the plurality of fibers. FIG. 11A illustrates the first cross sectional area is adjacent to the tip 12 of the each fiber 16 of the plurality of fibers and the second cross sectional area is adjacent to the backing layer 14. FIGS. 11A and 11B provide examples and are not meant to limit the present invention. The non-uniform cross-sectional areas can also be applied to single-level fiber embodiments (shown in FIGS. 1, 2, 8, and 10), and to second layer smaller fibers 110.

(84) FIG. 13 illustrates the second plurality of fibers having oblique angles relative to the tip including an angle between the tip of the each fiber of the secondary plurality of fibers and the stem of the each fiber of the secondary plurality of fibers not being equal to 90 degrees.

(85) The examples provided herein are illustrative and not limiting, and other variations and modifications of the present invention are contemplated. Those and other variations and modifications of the present invention are possible and contemplated, and it is intended that the foregoing specification and the following claims cover such modifications and variations.