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The objective of the research is to study the frictional behavior of surfaces covered with soft polymer gels. To this end, we introduced a mesoscale computational model for gels, i.e. cross-linked polymer networks immersed in Newtonian fluids (Fig. 1). The gel model is based on dissipative particle dynamics (DPD), a coarse-grained molecular dynamics approach. Our three-dimensional, fully-coupled model not only captures the micromechanics of deformable polymer networks, but also accurately simulates the relevant hydrodynamic effects.

We have validated our methodology by comparing our results for transport through isotropic polymer networks with previously reported theoretical and experimental data. We found that your model can accurately describe the transport properties in gel networks. We have used the model to examine how the transport changes when the network undergoes mechanical deformations typical for rubbing surfaces. We found that the change of the transport properties can be described in terms of filament re-orientation due to network deformation.

We have also demonstrated that our computational approach to capture swelling and deswelling volume transitions in polymer gels. To model the change in the network's swellability, we dynamically vary the length of network filaments which allows us to effectively simulate the internal stresses that cause the network to shrink or expand, and in this fashion, to capture the volume transition in polymer networks. We have verified the swelling kinetics of our model network by calculating the evolution of spherical gel capsules during a swelling process (Fig. 2). We found good agreement between our simulations and Tanaka's model for swelling kinetics of spherical gels.¹ Thus, our gel model not only correctly describes the transport in polymer networks but also effectively captures the kinetics of volume transition.

We consider two cases of rubbing surfaces. In the first case, we examine the sliding motion of a gel-coated surface over a smooth rigid substrate (Fig. 3a). We also investigate how two surfaces covered with thin layers of polymer gels rub against each other (Fig. 3b). To evaluate the amount of friction between two sliding surfaces, we apply normal and tangential forces to the opposite surfaces and measure the relative velocities. We examine the effects of gel compliance and thickness, surfaces interactions, and applied pressure on the resulting friction forces. Below, we describe these studies in more detail.

To examine how the material compliance affects the friction and force distribution between the surfaces, we systematically vary the gel stiffness by alerting the elasticity of network filaments and by changing the layer thickness. We compare our simulation results with relevant experimental data from the literature.^2-4 This comparison indicates that our approach can reproduce the typical force-velocity dependence for rubbing surfaces for both dry and wet friction. We apply our model to establish the parameters controlling the friction, which can be than used to guide future experiments.

Moreover, in our studies, we probe how attractive and repulsive interactions between sliding surfaces modify the friction forces. Previous investigations show that there is a distinct difference in the sliding motion of surfaces with repulsive and attractive interaction. While the hydrodynamic lubrication prevails in the former, our simulations indicate that friction mode undergoes a transition from the elastic friction to hydrodynamic lubrication at a critical sliding velocity in the latter. Thus, altering the interaction enables a means for regulating surface friction forces. In our simulations, we investigate how the critical velocity changes depending on the system temperature, gel elasticity and solvent viscosity. Our simulations reveal the complex interplay among, short-range surface interactions, gel elasticity, and hydrodynamic forces. A journal publication describing these results is currently in preparation. Finally, we examine how the use of nanoscopic particles with different geometries can be harnessed to regulate the friction. We test solvents that include spherical and rod-like particles to establish their tribological behavior. Our simulations indicate that there is a profound effect of the additives on the friction between soft surfaces. The exact contribution of solutes when sliding surfaces are separated by a layer of lubricating fluid, however, still remains unclear and requires further studies. We speculate that the colloidal solution reorganizes as the sliding velocity changes and, in this manner, affects the frictional behavior the system. We will carry out additional simulations to test this hypothesis.

References:

1. T. Tanaka and D. J. Fillmore, "Kinetics of Swelling of Gels," J. Chem. Phys. 70 (3), 1214-1218 (1979).

2. J. P. Gong, "Friction and lubrication of hydrogels - its richness and complexity," Soft Matter 2 (7), 544-552 (2006).

3. A. Casoli, M. Brendle, J. Schultz, P. Auroy and G. Reiter, "Friction of an elastomer sliding on polymeric model surfaces," Tribology Letters 8 (4), 249-253 (2000).

4. J. P. Gong, M. Higa, Y. Iwasaki, Y. Katsuyama and Y. Osada, "Friction of gels," J. Phys. Chem. B 101 (28), 5487-5489 (1997).