Effective Elastic Modulus of Structured Adhesives: From Biology to Biomimetics

Abstract

Micro- and nano-hierarchical structures (lamellae, setae, branches, and spatulae) on the toe pads of many animals play key roles for generating strong but reversible adhesion for locomotion. The hierarchical structure possesses significantly reduced, effective elastic modulus (E_eff), as compared to the inherent elastic modulus (E_inh) of the corresponding biological material (and therefore contributes to a better compliance with the counterpart surface). Learning from nature, three types of hierarchical structures (namely self-similar pillar structure, lamella⁻pillar hybrid structure, and porous structure) have been developed and investigated.

Keywords: adhesion; effective elastic modulus; hierarchical structure; lamella–pillar hybrid structure; porous structure; self-similar structure.

Figure 1

Proposed models to describe a pillar array. (a) A composite model of aligned fibers/pillars (A, green) embedded within a matrix (B gray) shows the strain (ε) under the stress (σ) along the long axis of fibers/pillars; (b) Schematic of a pillar array with pillar diameter d, length l and tilting angle θ; (c) Dependence of the effective elastic modulus (E_eff) of the structured adhesive normalized to inherent elastic modulus (E_inh) expressed as a function of the filling ratio (f) for hierarchical levels n = 1–5. Reproduced with permission from [22].

Figure 2

Hierarchical structured adhesives in nature. (a) Toe pad of tokay gecko. Reproduced with permission from [10]; (b) Scanning electron microscopy (SEM) image of gecko’s toe pad hierarchical structure of multi-level setae (green), supported by lamella (orange). Adapted with permission from [12]; (c) Effective elastic modulus (E_eff) during deformation of isolated setal arrays on the gecko’s toe pad. Reproduced with permission from [10]; (d) Attachment (A) and detachment (D) processes of the gecko’s toe pad. Reproduced with permission from [40]; (e) The performance of gecko setae on hydrophilic SiO₂ and hydrophobic GaAs or Si surfaces. Reproduced with permission from [14]; (f) Immature White’s tree frog (Litoria caerulea); (g) SEM images of the toe pad of White’s tree frog at different magnifications. Reproduced with permission from [55]; (h) Effect of indentation depth on the effective elastic modulus of the tree frog smooth adhesive pad during indentation test. Open and filled circles represent data from two mature adult frogs. Reproduced with permission from [60]; (i) Elongated polygonal epithelial cells on the toe pad of the torrent frog (Staurois guttatus); (j–m) Adhesion performance of Staurois guttatus on the rotating platform, with an uneven surface under high flow velocity conditions. Reproduced with permission from [65].

Figure 3

Two-level self-similar pillar arrays fabricated by various techniques. (a) Two-step molding with UV-curable polyurethane acrylate (PUA) resin. Reproduced with permission from [79]; (b) Polydimethylsiloxane (PDMS) replicated from a mold, prepared by two-step photolithography. Reproduced with permission from [80]; (c) Inking technique with polyurethane (PU); (d) Dependence of adhesion on preload for the unstructured, single primary structure (macro), single secondary structure (micro), and two-level structure. Reproduced with permission from [82]; (e) Capillary force-assisted molding from a multi-branched AAO template with grade Lexan polycarbonate (PC). Reprinted with permission from [86]. Copyright (2011) American Chemical Society; (f) Three-dimensional (3D) direct laser writing with acrylic-based negative photoresist (IP-G 780). Reproduced with permission from [89]; (g) Imprinting with carbon nanotube forests (CNTFs). Reproduced with permission from [90].

Figure 4

Three-level self-similar pillar structures. Scanning electron microscopy (SEM) images of (a) three-level polyurethane (PU) pillars with mushroom-shaped tips, and (b) the collapse phenomenon of the third-level. Reprinted with permission from [82]. Copyright (2009) American Chemical Society; (c) Schematic and image of the three-level polydimethylsiloxane (PDMS) macropillar adhesive. Reproduced with permission from [93].

Figure 5

Manipulation of effective elastic modulus (E_eff) by adjusting the structure parameters of pillar arrays. (a) Influence of the aspect ratio (AR) and pillar diameter on E_eff. Reprinted with permission from [94]. Copyright (2007) American Chemical Society; (b) Dependence of E_eff on the AR of micropillars, composed of a vertically aligned carbon nanotube (VA-CNT) array. The inset shows a scanning electron microscopy (SEM) image of the VA-CNT array. Reprinted with permission from [77]. Copyright (2012) American Chemical Society; (c) Adhesive stress capacity vs. elastomer pad modulus for varying roughness surfaces. Reproduced with permission from [101]; (d) Dependence of the E_eff on the tilting angle of polyurethane acrylate (PUA) nanopillar array. The inset shows an SEM image of the slanted PUA nanopillar array. Reproduced with permission from [102].

Figure 6

Adhesion performances of pillars with various tip geometries. (a) Influence of the tip geometry of polystyrene (PS) nanorods on adhesion forces. A scanning electron microscopy (SEM) image of the corresponding tip is shown in the right column. Reproduced with permission from [24]. Copyright (2012) American Chemical Society; (b) Schematic of a pillar array with mushroom-shaped and flat tips of diameter D; (c) Schematic diagram of a spatular tip contacting with a rough surface.

Figure 7

Different lamella–pillar hybrid (LPH) structures. (a,b) High-density polyethylene (HDPE) nanopillar array supported by lamellar flaps (LPH-1); (c) Comparison of shear adhesion strength between the LPH structure (with lamella) and the single pillar array (without lamella), contacted with surfaces of different roughnesses (SS: Stainless steel). (a–c) Reprinted with permission from [115]. Copyright (2009) American Chemical Society; (d,e) Nickel paddle coated with a Photoresist nanorod array. Reproduced with permission from [116]; (f) Thin film-terminated fibrillar arrays (LPH-2). Reproduced with permission from [119]; (g,h) Photoresist nanorod array on top of a SiO₂ platform supported by a single-crystal silicon pillar. Reproduced with permission from [121].

Figure 8

Biological and bioinspired porous pillars for adhesion. (a) Scanning electron microscopy (SEM) image of a single dried seta of tokay gecko (some pores can be found on the stalk). Reproduced with permission from [10]; (b) SEM image of the porous fibrillar polystyrene-b-poly(2-vinyl pyridine) (PS-b-P2VP) adhesive. Reproduced with permission from [124]; (c) Effect of the relative humidity on the E_eff and indentation depth. Reprinted with permission from [123]. Copyright (2013) American Chemical Society.

Figure 9

Polydimethylsiloxane (PDMS) film embedded with microchannels for adhesion. (a) Schematic of the channel structure with textured outer surfaces and scanning electron microscopy (SEM) images of (b) fibrillar and (c) conical pillars. (d) Dependence of the pull-off force (P_po) and (e) the P_po normalized to the preload (P_Δpo=0) on the increase of differential pressure in the microchannels (Δp). Reproduced with permission from [129].