In Situ Measurements of Contact Dynamics in Speed-dependent Hydrogel Friction
Introduction
Aqueous lubrication with soft hydrogels, tissues, cartilage, and biopolymers frequently reveals a friction dependence on sliding speed. A number of different mechanisms have been suggested to explain this dependence, including a hypothesis of viscoelasticity in which a “plowing” component of friction is sensitive to sliding speed. As discussed by Bonnevie et al., the plowing contribution of friction is attributed to the integrated pressure distribution having a component parallel to the sliding vector but in the opposite direction [1]. Bonnevie et al. also discussed that these plowing contributions, “cannot be determined without known pressure distributions”. The prevailing theory is that viscoelastic effects lead to an asymmetry in the pressure distributions – viscoelasticity is frequently measured and modeled for cartilage, tissues, and high-water content gels [2], [3], [4], [5], [6].
A recent finding using self-mated contacts of identical hydrogel samples (Gemini hydrogels) revealed a surprising speed independence in friction coefficient that spanned over 2 orders of magnitude in sliding speed [7], which was notable as the majority of healthy biological sliding interfaces are in Gemini configurations. This study raised questions as to whether or not in vivo biological interfaces experienced speed-dependent friction, or if they were effectively constant friction interfaces. In an effort to tease out the fundamental mechanisms underlying the friction behavior of biological interfaces, high-water content hydrogels have been used as convenient surrogates for in vitro studies [7], [8], [9]. The optical clarity, tunable mechanical and transport properties through changes in the mesh size (ξ), wide range of water content, and ease of fabrication have made these hydrogels nearly ideal experimental samples for studies of aqueous lubrication. One recent, and perhaps surprising, discovery was that friction coefficient decreased with increasing mesh size, and that this could continue into the regime of superlubricity (μ < 0.005) [9], [10]. As elastic modulus falls rapidly as mesh size increases (E proportional to ξ− 1/3) [11]. These superlubricious hydrogels were almost “slime-like” in their mechanics as elastic modulus falls rapidly with increasing mesh size (E ~ ξ− 1/3) [11], suggesting that the softest surface gels in bio-lubrication may be responsible for the low friction coefficients that rival values found under hydrodynamic lubrication.
Physiological sliding speeds span a wide range from nm/s for cell migration to over 100 mm/s for blinking and joint movements. Gemini hydrogel experiments performed over a range in speed, 30 μm/s to 100 mm/s, revealed a critical transition speed at which friction coefficient rises with increasing sliding speed, and this transition may be related to the polymer relaxation time [8], [9]. Speed-dependent friction behavior has also been observed in cartilage systems [12], and the hypothesis for this behavior was a form of viscoelasticity in which fluid depressurization in the cartilage matrix due to fluid exudation in the wake of contact resulted in a time-dependent recovery following deformation. Bonnevie et al. argued that in a contact configuration of a rigid sphere sliding against a flat countersample of cartilage, the trailing half of the contact could not provide meaningful load support and thus only the front half supported the load. This concept was consistent with simulations by Kusche [13] that modeled the sliding of a probe over an indented viscoelastic half-space at sufficiently high sliding speeds (Fig. 1).
The hypothesis of a viscoelastic effect on friction for soft biomaterials is essentially one of leading/trailing edge contact asymmetry. Earlier studies have investigated the deformed surface profile of flat transparent elastomers loaded under a clean glass hemispherical probe and used Newton's rings to determine contact area in static and dynamic conditions [14]. Barquins and Courtel directly observed an asymmetric contact patch of a soft elastomer under hemispherical contact develop as sliding speed increased but were unable to image the surface profile. Schulze et al. [15] observed a complex speed-dependent folding and contact patch evolution when sliding soft rubber spheres against smooth glass countersurfaces. Krick et al. and Persson et al. used similar methods under liquid-lubricated conditions to resolve changes in contact area during the sliding of soft hemispherical probes against smooth glass surfaces [16], [17]. The insight provided by these experiments for understanding elastomer tribology suggests that direct visualization of the contact patch and adjacent regions during sliding may also be necessary to elucidate the mechanisms of speed-dependent friction at hydrogel surfaces. Further, direct observations and measurements of hydrogel surface profiles during loading and sliding may reveal insights into the nature of biological sliding contacts, such as those found in cartilaginous joints or the cornea-eyelid interface.
Here we describe in situ experiments measuring the surface profile of a deforming hydrogel sample sliding against a spherical glass probe. These experiments were performed and imaged using 3D confocal laser-scanning microscopy under a condition of dynamic equilibrium where fluorescent particle dispersions were used to delineate the borders between the hydrogel surface, water, and the glass probe. Imaging was performed relative to the stationary spherical probe that was loaded into contact with a submerged hydrogel countersurface spinning under steady angular speed. The deformation profiles over a range of sliding speeds from 0.1 mm/s to 100 mm/s were analyzed and compared to changes in friction coefficient as a function of sliding speed.
Section snippets
Hydrogel Preparation and Characterization
Polyacrylamide (pAAm) hydrogel disks (~ 10 mm thick) were polymerized at room temperature from a precursor solution, reported as weight-solute per weight-total percentages: 3.75% acrylamide monomer, 0.15% N,N′-methylenebisacrylamide cross-linker, 0.15% ammonium persulfate initiator, 0.15% tetramethylethylenediamine catalyst in ultrapure water (18 MΩ). FluoroMax green fluorescent microspheres (5 μm diameter) were included in the precursor composition at 0.002 wt% in solution. To ensure flatness and
Results and Discussion
The motivation of this study was to quantitatively measure in situ deformations of hydrogels during steady sliding experiments over a wide range of sliding speeds. The scanning speed of the available confocal microscope was too slow to follow high-speed deformations in situ. For example, at sliding speeds of 100 mm/s and a contact radius of approximately 1 mm, the deformation through the contact would take place over 20 ms. Therefore, the approach was to perform relatively slow confocal scans
Concluding Remarks
A method to perform slow confocal scans through a dynamic equilibrium in situ was established. Fluorescent microbeads in the hydrogel and solution were used to produce images of the dynamic contact interface and reveal local and bulk deformations during sliding. An asymmetric contact was measured using a 3.75 wt% polyacrylamide gel, and asymmetric deformation between the inlet and exit increased with increasing sliding speed. Changes in friction with sliding speed correlated with the tangent of
Acknowledgements
This work was supported by Alcon Laboratories.
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