Effective elastic modulus of isolated gecko setal arrays

Abstract

Conventional pressure sensitive adhesives (PSAs) are fabricated from soft viscoelastic materials that satisfy Dahlquist's criterion for tack with a Young's modulus (E) of 100 kPa or less at room temperature and 1 Hz. In contrast, the adhesive on the toes of geckos is made of beta-keratin, a stiff material with E at least four orders of magnitude greater than the upper limit of Dahlquist's criterion. Therefore, one would not expect a beta-keratin structure to function as a PSA by deforming readily to make intimate molecular contact with a variety of surface profiles. However, since the gecko adhesive is a microstructure in the form of an array of millions of high aspect ratio shafts (setae), the effective elastic modulus (E(eff)) is much lower than E of bulk beta-keratin. In the first test of the E(eff) of a gecko setal adhesive, we measured the forces resulting from deformation of isolated arrays of tokay gecko (Gekko gecko) setae during vertical compression, and during tangential compression at angles of +45 degrees and -45 degrees . We tested the hypothesis that E(eff) of gecko setae falls within Dahlquist's criterion for tack, and evaluated the validity of a model of setae as cantilever beams. Highly linear forces of deformation under all compression conditions support the cantilever model. E(eff) of setal arrays during vertical and +45 degrees compression (along the natural path of drag of the setae) were 83+/-4.0 kPa and 86+/-4.4 kPa (means +/- s.e.m.), respectively. Consistent with the predictions of the cantilever model, setae became significantly stiffer when compressed against the natural path of drag: E(eff) during -45 degrees compression was 110+/-4.7 kPa. Unlike synthetic PSAs, setal arrays act as Hookean elastic solids; setal arrays function as a bed of springs with a directional stiffness, assisting alignment of the adhesive spatular tips with the contact surface during shear loading.