The Physics of Soft Adhesion

TL;DR

This article surveys the physics of soft adhesion, connecting thermodynamics of surfaces with the mechanics of contact between soft solids and substrates. By tracing the progression from Hertzian contact to JKR adhesion and extending into elastocapillary regimes, it explains how surface energy, surface stress, and elasticity compete to determine contact geometry and debonding forces. The review highlights the critical roles of wetting, fracture mechanics, and time-dependent relaxation (viscoelasticity and poroelasticity) in soft materials like gels and elastomers, and it outlines practical methods for measuring adhesion, including JKR tests, tack tests, and peel tests. Collectively, the work provides a unified framework for predicting and tailoring adhesion in soft matter systems and emphasizes the relevance of elastocapillary effects and phase behavior at soft interfaces for future research and applications.

Abstract

This review provides an introduction to the essential physics of soft adhesion, including the thermodynamics of adhesion and wetting, the mechanics of contact with deformable materials, and the material properties that most affect interfacial interactions with soft solid gels and elastomers. Throughout, we emphasize both foundational physics and current experimental and theoretical research in these areas. We conclude with a practical overview of standard experimental test methods for characterizing soft adhesion. The physical understanding developed herein provides the basis for understanding the mechanics of contact with soft materials.

Figures (5)

• Figure 1: Everyday soft adhesion. (a) The adhesive on the back of a sticky note comprises thousands of $\sim 50$-$\mu$m-scale asperities that deform about a millimeter before debonding. (b) Soft adhesive medical bandages, tapes, and similar products revolutionized wound care by replacing stitches. (c) Soft "sticky hands" are popular toys. (d) Large-scale, removable adhesive wallpaper and floor coverings are increasingly used for decoration and advertising. Electron micrograph in Panel a provided by Nancy Piatczyc. Photographs in Panel c provided by Meredith Taghon. All other photographs provided by Katharine E. Jensen.
• Figure 2: Adhesion and wetting both eliminate free surface areas with surface energies per area $\gamma_1$ and $\gamma_2$, respectively, in order to create an interface with interfacial energy per area $\gamma_{12}$. (a) Adhesion between two flat, solid materials. (b) Wetting between a liquid droplet (1) and a flat solid (2) results in partial or total wetting depending on the surface energy balance (Equation \ref{['eqn:YD']}) at the contact line (inset). (c) In contact between a rigid particle (1) and a fluid (2), partial wetting (inset) results in adsorption, which adheres the particle to the liquid surface. (d) Wetting between a fluid droplet (1) and an initially-flat, immiscible fluid (2) results in deformation of both phases to create a Neumann triangle (inset). Illustration created by Roderick W. Jensen.
• Figure 3: Adhesive contact geometries with increasing softness and interface complexity. Relevant parameters are indicated, including applied load $P$, sphere radius $R$, contact radius $a$, indentation depth $d$, Young modulus $E$, Poisson ratio $\nu$, adhesion energy $W$, and surface stress $\Upsilon$. (a-b) Hertzian contact between (a) two spheres or (b) a rigid sphere indenting an initially-flat, compliant elastic half space substrate due to an applied load $P>0$. (c) A positive adhesion energy $W$ at the sphere-substrate interface drives deformation to create additional contact area and spontaneous indentation in JKR contact with or without an applied load. (d) For highly compliant materials, solid surface tension $\Upsilon$ provides an additional restoring force that resists deformation of the substrate, resulting in adhesion that can quantitatively resemble capillary wetting (see also Figure \ref{['fig:adhesion_wetting']}c). Very soft substrates often have significant out-of-plane deformation outside the contact area (dashed line, lightly shaded); such "adhesion ridges" are often neglected in theoretical treatments of soft contact. (e) Adhesion between a rough rigid surface and an initially-flat, compliant substrate that fails to make full conformal contact under the applied load, leaving a small gap. Illustration created by Roderick W. Jensen.
• Figure 4: Static and dynamic properties of soft matter affect adhesive contact. (a) Schematic comparison of elastomer versus gel structure. Both have system-spanning, crosslinked elastic networks (gray lines linked by red circles); in gels, the network is also permeated by a continuous free fluid phase (blue dots). (b) Surface and bulk properties of soft materials can be highly strain-dependent, affected by both fabrication pre-strains and deformations during experiments heyden2024distance. (c) Adhesion and wetting can induce local fluid phase separation in soft gels, modifying both the equilibrium structure and dynamics of making an breaking contact jensen2015wettingcai2024phase; confocal microscopy image (inset) shows the fluorescently-dyed gel fluid phase (yellow) establishing a sharp wetting ridge beyond the surface of the gel elastic network (red dots). (d) Soft rubbery gel materials like silicones typically demonstrate power law rheology. Lines show fit to Equation \ref{['eqn:chasset-thirion']}, with fit parameters noted. Panel a illustration created by Roderick W. Jensen. Panel b reproduced from Reference heyden2024distance with permission from the Royal Society of Chemistry. Panel c adapted from Reference jensen2015wetting; Panel c (inset) data provided by Katharine E. Jensen. Panel d adapted from Reference karpitschka2015droplets.
• Figure 5: Testing soft adhesion. (a) JKR adhesion testing based on Equations \ref{['eqn:JKR-a']} and \ref{['eqn:JKR-d']}. (b) Standard probe-tack test and rolling ball comparative tack measurement. (c) Surface energy measurements using a Surface Forces Apparatus (SFA) or atomic force microscopy (AFM). (d) Tape peel adhesion tests. Different geometries address different intended use cases for the adhesive. Illustration created by Roderick W. Jensen, adapted with permission from a presentation created by Arnaud Chiche.