Rate-Dependent Indentation Adhesion of Hydrogels

Hydrogels are important engineering and natural materials. In both nature and engineering applications, hydrogels often involve rate-dependent adhesion interaction. To understand the rate-dependent adhesion mechanism of hydrogels, measuring the adhesion behavior is important, and a theoretical model is required to quantify the rate-dependent adhesion properties. In this work, we apply the indentation test on hydrogel to measure the rate-dependent adhesion behavior. We use atomic force microscope to perform indentation test on polyacrylamide hydrogel using polystyrene spherical indenter (25 um in diameter). The spherical indenter is pressed into the hydrogel and held for a certain time, then retracted in different amounts of pull-off velocity until the indenter is completely separated from the hydrogel. We perform the test across a wide range of pull-off velocity from 1 nm/s to 50 um/s. Additionally, the test is repeated for different indentation depths (0.5 um, 1 um, and 3 um) and holding times (15 s, 25 s, and 50 s) across the same velocity range to study the length-scale and time-scale dependency of hydrogel adhesion. The result shows that for each group of indentation depth and holding time, the pull-off force first decreases then increases with the pull-off velocity. The transition phenomenon has not been observed or modeled in the literature before. Here, this phenomenon is assumed to be due to the competition of two time scales, one is the time for the adhesion to build up and the other is the rate-dependent pulling force. In the indentation test, for larger pull-off velocity, the amount of adhesion sites that has been built is less as total contact time is shorter, but the pull-off stress of the adhesion site is greater due to the faster pulling velocity. These two competing factors provide transition behavior in the pull-off force. To quantify this picture, we adopt the Maugis adhesion theory and the stochastic bonding theory to model the rate-dependent contact problem. Specifically, the hydrogel is modeled as a linear elastic material, and deformation and stress fields of the hydrogel is described by the Maugis contact adhesion theory, in which a cohesive zone is prescribed in the periphery of the contact area. Additionally, we apply the stochastic bonding theory to describe the time-dependent binding of the adhesive site and rate-dependent adhesive stress inside the contact area and in the cohesive zone. The indentation adhesion problem is solved analytically, and the theoretical result predicts the transition behavior in the pull-off force. The experimental rate-dependent pull-off forces for different indentation depths are used to fit the theoretical result. Additionally, we use the same set of adhesive parameters to calculate the pull-off forces for different holding times, and the results predict the experimental data. This study provides a more complete picture of the rate-dependent adhesion behavior of hydrogels and promotes new understandings of the hydrogel adhesion mechanism.