Linking energy loss in soft adhesion to surface roughness

Abstract

A mechanistic understanding of adhesion in soft materials is critical in the fields of transportation (tires, gaskets, and seals), biomaterials, microcontact printing, and soft robotics. Measurements have long demonstrated that the apparent work of adhesion coming into contact is consistently lower than the intrinsic work of adhesion for the materials, and that there is adhesion hysteresis during separation, commonly explained by viscoelastic dissipation. Still lacking is a quantitative experimentally validated link between adhesion and measured topography. Here, we used in situ measurements of contact size to investigate the adhesion behavior of soft elastic polydimethylsiloxane hemispheres (modulus ranging from 0.7 to 10 MPa) on 4 different polycrystalline diamond substrates with topography characterized across 8 orders of magnitude, including down to the angstrom scale. The results show that the reduction in apparent work of adhesion is equal to the energy required to achieve conformal contact. Further, the energy loss during contact and removal is equal to the product of the intrinsic work of adhesion and the true contact area. These findings provide a simple mechanism to quantitatively link the widely observed adhesion hysteresis to roughness rather than viscoelastic dissipation.

Keywords: adhesion; contact mechanics; multiscale surface roughness; soft matter; surface topography.

Fig. 1.

Comprehensive topography characterization for four rough nanodiamond surfaces. The surface topography was measured using a multiresolution approach that combines TEM, AFM, and stylus profilometry. Regions of applicability of each technique are indicated with horizontal bars and are delineated more specifically in SI Appendix, Fig. S2. The nanodiamond surfaces are colored as follows: UNCD is shown in red, NCD in black, MCD in green, and polished UNCD in blue. AFM images (of 5-μm lateral size, Left Inset) and TEM images (Right Inset) are shown. More than 50 measurements for each surface are combined using the PSD, which reveals the contribution to overall roughness from different length scales (wavelengths). These comprehensive descriptions of surface topography enable the determination of true surface area and stored mechanical energy due to the topography, which are necessary to understand adhesion.

Fig. 2.

Adhesion measurements during approach and retraction. Loading and adhesion tests were performed with ultrasmooth PDMS hemispheres of varying stiffness from 0.7 to 10 MPa. Representative curves from one material (with E = 1.9 MPa) are presented in this figure, and those of other materials are shown in SI Appendix, Fig. S5. The load-dependent contact radius (shown in A) was measured using in situ optical microscopy. The apparent work of adhesion upon approach $W_{app}$ was extracted by fitting the loading data (hollow points) using the JKR model (dashed lines). The force-displacement curves (B) were used to calculate the energy loss $E_{loss}$ during contact by performing a closed-circuit integral (Inset). Both approach and retraction experiments were conducted at a very low speed, 60 nm/s.

Fig. 3.

During adhesion, the materials go from the initial state (A) to the final state (C). However, to fully account for the energy change, one must consider the change in area of the soft material, which is represented schematically by including the intermediate state (B). The equations give the expression for the total energy of the system in each of the three states.

Fig. 4.

Comparison of work of adhesion and energy loss with the proposed model of conformal contact. In A, experimental measurements of apparent work of adhesion during approach are well-fit using the balance of adhesive and elastic energy described in the main text (Eqs. 7–9); here the solid line shows y = x. In B, the energy loss is plotted as a function of true contact area (Eq. 10). The solid line is a linear fit to the data and has a slope of 46.2 ± 7.7 mJ/m² (R² = 0.8).