Effects of surface roughness and film thickness on the adhesion of a bioinspired nanofilm

Inspired by the gecko's climbing ability, adhesion between an elastic nanofilm with finite length and a rough substrate with sinusoidal roughness is studied in the present paper, considering the effects of substrate roughness and film thickness. It demonstrates that the normal adhesion force of the nanofilm on a rough substrate depends significantly on the geometrical parameters of the substrate. When the film length is larger than the wavelength of the sinusoidal roughness of the substrate, the normal adhesion force decreases with increasing surface roughness, while the normal adhesion force initially decreases then increases if the wavelength of roughness is larger than the film length. This finding is qualitatively consistent with a previously interesting experimental observation in which the adhesion force of the gecko spatula is found to reduce significantly at an intermediate roughness. Furthermore, it is inferred that the gecko may achieve an optimal spatula thickness not only to follow rough surfaces, but also to saturate the adhesion force. The results in this paper may be helpful for understanding how geckos overcome the influence of natural surface roughness and possess such adhesion to support their weights.

Figure 1

Schematic of a finite-size nanofilm in adhesive contact with a sinusoidal rough substrate. (a) Wavelength $\lambda$ of the surface roughness smaller than the length $b$ of the nanofilm; (b), (c), and (d) $\lambda$ larger than $b$ but with increasing amplitudes.

Figure 2

Schematic of obtaining the interaction energy between a finite-size nanofilm and a semi-infinite space. (a) A molecule near a semi-infinite body with distance $D$; (b) a finite-size nanofilm with thickness $h$ near a semi-infinite body with distance $D$. Adopted from Ref. [31].

Figure 3

The relation between the normalized effective interfacial energy $\Delta {\gamma }_{\mathrm{eff}}/\Delta \gamma$ and the surface roughness $a/\lambda$ for cases with different wavelengths $\lambda$, where $\Delta \gamma$ is the interfacial energy for a flat surface case and $a$ is the amplitude of the sinusoidal profile of the surface.

Figure 4

Peelingforce of a spatula pad adhering to a rough surface as a function of the effective interfacial energy at a peeling angle of $\theta ={90}^{°}.$

Figure 5

The relation between the normalized effective interfacial energy $\Delta {\gamma }_{\mathrm{eff}}/\Delta \gamma$ and the surface roughness $a/\lambda$ for cases with different wavelengths $\lambda$ and different film thicknesses $h$.

Figure 6

(a) The effect of film thickness on adhesion energy. (b) The relation between the normalized effective interfacial energy $\Delta {\gamma }_{\mathrm{eff}}/\Delta {\gamma }_0$ and the surface roughness $a/\lambda$ for the case with size-dependent adhesion energy and the one with constant adhesion energy.

Figure 7

The effect of film thickness on (a) the adhesion energy and (b) the corresponding adhesion force in a model of a finite-size nanofilm in adhesive contact with a flat semi-infinite space. The distance between them is 0.3 nm. The inset is given in order to find the critical thickness after which the adhesion force will saturate.