Adhesion paradox: Why adhesion is usually not observed for macroscopic solids

The adhesion paradox refers to the observation that for most solid objects no adhesion can be detected when they are separated from a state of molecular contact. The adhesion paradox results from surface roughness, and we present experimental and theoretical results that show that adhesion in most cases is “killed” by the longest-wavelength roughness. In addition, adhesion experiments between a human finger and a clean glass plate were carried out, and for a dry finger no macroscopic adhesion occurred. We suggest that the observed decrease in the contact area with increasing shear force results from nonadhesive finger-glass contact mechanics, involving large deformations of complex layered material.

Figure 1

The Jülich experimental setup for measuring adhesion.

Figure 2

The green, red, and blue lines shows the wave number $q$ (and wavelength $\lambda =2\pi /q$) dependency of the 1D surface roughness power spectra for the smooth, sandblasted 1, and sandblasted 2 surfaces, respectively (log-log scale).

Figure 3

The interaction force between the glass ball and the three PDMS surfaces. The green, red, and blue lines are for the smooth, sandblasted 1, and sandblasted 2 surfaces, respectively. Note that no adhesion can be detected on approach, and for the sandblasted 2 surface also not during pull-off (retraction).

Figure 4

The work of adhesion as a function of time, where each data point is obtained from the pull-off force in each sequential contact cycles. Here, we show data for the smooth PDMS surface (green squares) and for the PDMS replica of the sandblasted surface 1 (red squares).

Figure 5

The calculated effective interfacial binding energy (per unit surface area), or work of adhesion, as a function of the magnification (lower scale) or the wave number (upper scale). Note that $\gamma \left(\zeta \right)$ at the magnification $\zeta$ is the interfacial binding energy including only the roughness components with $q>\zeta q_0$ (where $q_0$ is the smallest wave number). The red and green line is for the roughness on the elastic solid and rigid solid, respectively. In the calculation we used $\mathrm{\Delta }\gamma =0.1\mathrm{J}/{\mathrm{m}}^2$ and $E^{*}=1.0\mathrm{MPa}$.

Figure 6

The projected area of real contact $A$, normalized by the nominal contact area $A_0$, as a function of the nominal applied (squeezing) pressure. The red and green lines are for the roughness on the elastic solid and rigid solid, respectively. The black line is the result without adhesion.

Figure 7

The green, red, and blue lines shows the wave-number dependency of the 2D surface roughness power spectra for the smooth, sandblasted 1, and sandblasted 2 surfaces, respectively (log-log scale). The dashed vertical line indicates the lower cutoff wave number used in the adhesion calculations.

Figure 8

The effective interfacial binding energy (per unit surface area), or work of adhesion, as a function of the magnification (lower scale) or the wave number (upper scale). Note that $\gamma \left(\zeta \right)$ at the magnification $\zeta$ is the interfacial binding energy including only the roughness components with $q>\zeta q_0$ (where $q_0$ is the smallest wave number). The green, red, and blue lines are for the smooth, sandblasted 1, and sandblasted 2 surfaces, respectively. In the calculation we used $\mathrm{\Delta }\gamma =0.2\mathrm{J}/{\mathrm{m}}^2$ and $E=2.3\mathrm{MPa}$, $\nu =0.5$.

Figure 9

The interaction force between a human finger and a dry glass plate cleaned by acetone and isopropanol. Case (a) (red curve) is for a not cleaned finger, (b) (green curve) for a finger cleaned with soap and water, and (c) (blue curve) for a clean wet finger. In cases (a) and (b), no (macroscopic) adhesion is observed, while in case (c) do we observe adhesion with a pull-off force $F_{\mathrm{c}}\approx 5.5\mathrm{mN}$. The results are qualitatively the same for different fingers on different persons. The glass surface is very smooth (rms roughness $\approx 20\mathrm{nm}$ when measured over $1\mathrm{mm}$ line track). The finger roughness was not studied, but other studies (see Ref. [27]) have shown the roughness amplitude to be of order $0.1\mathrm{mm}$, thus (as expected) much larger than that of the glass plate.