StickâSlip Friction Reveals Hydrogel Lubrication Mechanisms

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Stick-slip friction reveals hydrogel lubrication mechanisms Tooba Shoaib, Joerg Heintz, Josue Lopez-Berganza, Raymundo Muro-Barrios, Simon A. Egner, and Rosa M. Espinosa-Marzal Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b02834 • Publication Date (Web): 29 Sep 2017 Downloaded from http://pubs.acs.org on October 2, 2017

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Stick-slip friction reveals hydrogel lubrication mechanisms Tooba Shoaib†‡, Joerg Heintz◊, Josue A. Lopez-Berganza†, Raymundo Muro-Barrios‡, Simon A. Egner‡, Rosa M. Espinosa-Marzal† † Department of Civil and Environmental Engineering, 205 N. Matthews Avenue, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA. ‡ Department of Materials Science and Engineering, 1304 W Green St, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA. ◊Health Care Engineering Systems Center, University of Illinois at Urbana-Champaign, 1206 W. Clark Street, Urbana, Illinois 61801, USA. KEYWORDS: friction, stick-slip, hydrogels, Atomic Force Microscopy, scaling law

ABSTRACT. The lubrication behavior of the hydrated biopolymers that constitute tissues in organisms differs from that outlined by the classical Stribeck curve and studying hydrogel lubrication is a key pathway to understand the complexity of biolubrication. We have investigated the frictional characteristics of polyacrylamide (PAAm) hydrogels of various acrylamide concentrations, exhibiting Young’s moduli (E) that range from 1 to 40 kPa, as a function of applied normal load and sliding velocities by colloid probe lateral force microscopy.

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The speed-dependence of the friction force shows an initial decrease in friction with increasing velocity, while, above a transition velocity ∗ , friction increases with speed. This study reveals two different boundary lubrication mechanisms characterized by distinct scaling laws. An unprecedented and comprehensive study of the lateral force loops reveals intermittent friction or stick-slip above and below ∗ , with characteristics that depend on the hydrogel network, applied load, and sliding velocity. Our work thus provides insight into the closely tied parameters governing hydrogel lubrication mechanisms, and stick-slip friction.

Introduction The tribological behavior of hydrated polymer films has gained immense attention over the past few decades owing to its relevance to understanding biolubrication. Hydrogels, i.e. physically and chemically cross-linked polymeric networks that encompass a large amount of water, have been thus investigated due to their synonymy to biological systems1-6. For instance, human cartilage, corneal stoma and tissues, although exhibiting a complex stratified microstructure, are hydrogel-like multiphasic systems that achieve extremely low friction coefficients7. Lateral force microscopy8 and tribometers6 have shown that neutral and charged hydrogels deliver low coefficients of friction before water is squeezed-out from the contact region. The friction force and its dependence on load and speed vary with chemical composition and mechanical properties of the hydrogel, and with the surface properties of the opposing surface9-12. Various mechanisms have been proposed to explain hydrogel lubrication. Depending on the synthesis method, the hydrogel surface may be composed of dangling chains, which essentially behave like polymer brushes13. Since the pioneering work by Klein and co-workers14, many


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works have shown that water, a low-viscosity lubricant, in combination with surface-grafted (biological and synthetic) polymers with diverse architectures and chemistries, can significantly reduce friction at the sliding interface to the limits of superlubricity14-18. The lubricious performance of polymers brushes in a good solvent –termed hydration lubrication for aqueous solvents - presumes the absence of contact between the polymer-bearing surfaces as a result of osmotic and steric interactions 19, even at the lowest attained speeds, thereby attributing the low friction coefficients to the small viscous force of a thin fluid film20-23. Nevertheless, our own molecular dynamic simulations of the tribological performance of polymer brushes have recently shown a good agreement with experiments at low speeds only after consideration of an effective polymer-wall attraction24. An adsorption-repulsion model has been developed by Gong and co-workers to describe the frictional characteristics of hydrogels against a non-permeable counter-surface10,

12

. In the

attractive regime, there is continuous adsorption and desorption of polymer chains to the opposing surface, and friction thus results from the energy dissipated to detach the adsorbed chains. In the repulsive regime, in contrast, the remaining liquid film between hydrogel and opposing surface serves as the lubricant film, which helps to further reduce friction, thereby reconciling this model with the hydration lubrication mechanism invoked for polymer brushes. The attractive interaction between the polymer chains and the opposing surface is characterized by the lifetime of the adsorbed chain, , and the relaxation time for re-adsorption after detachment, , both of which are related by the adsorption energy per polymer chain. Crosslinking impedes the polymer chains to diffuse freely; instead they cooperatively diffuse with a relaxation time characteristic of an isolated polymer chain with a radius equal to the hydrogel mesh size, . The scaling theory thus predicts = ⁄ 25. If the time that allows


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interactions to happen, = , where is the sliding velocity, is large, so that

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≪ 1, the friction

force is proportional to the number of adsorbed chains , ~ . In this regime, the friction force can increase, decrease and remain constant with increasing speed. If the sliding velocity is so high that

≫ 1, the polymer chains do not have enough time to adsorb. The authors thus

assumed that the absence of adsorption implies elasto-hydrodynamic lubrication occurring at > = ⁄ = ⁄ . A different approach was more recently proposed for Gemini hydrogel interfaces, for which Sawyer and co-workers observed a regime of speed-independent friction before the friction increased with speed above V .5-6 They proposed that random thermal chain fluctuations –of length - at the interface relax the shear stress generated during sliding, and provide a blurred interface over which the barrier to sliding is effectively reduced compared to a hard substrate5-6. The transition to higher friction coefficients above V was not attributed to full-fluid film (hydrodynamic) lubrication, though, but instead, to a non-Newtonian shear behavior of the sliding interface that is not fully understood yet3, 5. In this regime, i.e. when the fluid film is not thick enough to yield full-fluid film (hydrodynamic) lubrication, polymer chains are expected to still interact with the counter surface4, 26. Another important yet complex component of soft matter friction is stick-slip27. As a matter of fact, stick-slip is one of the mechanisms considered to be the cause of damage and wear of articular cartilage and tissues at mild loading conditions28. The existence of transient adhesive bridges has been proposed to be the origin of the observed stick-slip of hydrogels, polymer brushes and cartilage28. Stick–slip behavior of hydrogels has been often observed at high pressures and assumed to be the result of a pressure-induced collapse and dehydration of the


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near-surface hydrogel26. The situation is, however, more complex since such transient adhesive bridges can result from polymer entanglements, interpenetration, and specific chain-surface interactions. Non-crosslinked or dangling chains can cause locally inhomogeneous adhesion profiles and enhance the stick-slip response. In this work, we have studied the frictional characteristics of hydrogels with varying acrylamide and crosslinker concentrations by colloidal probe lateral force microscopy as a function of load and speed, while the stick-slip response has been comprehensively analyzed by statistical tools. The results are first discussed in light of available models for hydrogel lubrication, which are then extended to account for the observed phenomena. Materials and Methods Hydrogel Preparation. Polyacrylamide (PAAm) hydrogels with varying moduli were prepared by mixing different concentrations of acrylamide (monomer), bis-acrylamide (crosslinker) and DI water according to ref.29 (Table S1 in the Supplementary Information). Acrylamide 40% w/v solution and N, N’ Methylenebis(acrylamide) were obtained from Sigma Aldrich (USA). The prepared hydrogels are referred here as 4%-PAAm, 6%-PAAm and 12%-PAAm hydrogels for total concentrations (in weight percentage) of monomer (acrylamide) of 4.4, 6.4 and 12.4 wt%, respectively, and increasing crosslinking degree. We note that the near-surface elastic moduli determined by AFM indentation (see details later) differ from the nominal values given in ref.29, and hence, they were measured for each single sample, in which friction force measurements were conducted. Hydrogels were prepared on silane-treated glass coverslips. For the silane treatment, 500 µL of 0.1 M NaOH were added to UV-ozone cleaned coverslips and allowed to evaporate upon heating


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to 80 ℃. Then, the coverslips were covered with 3-aminopropyltriethoxysilane (APTES) (SigmaAldrich, USA) for five minutes, after which the coverslips were rinsed with DI water and immersed in a 0.5% (v/v) glutaraldehyde in phosphate buffered saline (PBS) solution for half an hour. Glass slides (25mm x 75mm) were prepared by rinsing them first with dichlorodimethylsilane (DCDMS) (Sigma Aldrich, USA) and subsequently with DI water. Coverslips were thus rendered hydrophilic to promote hydrogel wetting and adhesion by using a silane with a amine-terminating group, while glass slides were rendered hydrophobic by using a silane with a methyl end group, to ensure a non-wetting surface for the hydrogel in order to facilitate subsequent removal of the glass slide after gelation. Solutions of monomer, crosslinker and water were degassed for 15 minutes and polymerized via the addition of the initiator, ammonium persulfate (APS) (1/100 of total volume) (Sigma Aldrich, USA) and the accelerator, tetramethylethylenediamine (TEMED) (1/1000 of total volume) (Sigma Aldrich, USA). To prepare hydrogel samples for Atomic Force Microscopy (AFM), 40 µl of this solution were quickly pipetted on the hydrophobic glass slide, and then sandwiched between glass slide and the coverslip. After 30 minutes, the coverslips (carrying the hydrogels) were removed from the hydrophobic glass slides, rinsed with DI water, and stored in DI water at 4°C for 1 day. To prepare hydrogel samples for Dynamic Light Scattering (DLS), 750 µl of solution were pipetted into a microcuvette and also allowed to gel for 1 day. After gelation for 1 day, all hydrogels were immersed in a buffer solution (10 mM Tris buffer) to maintain the pH constant and equal to 8.1 for 30 minutes before AFM and DLS experiments. For imaging with a Scanning Electron Microscopy (SEM), thicker hydrogels (3-4 mm) were prepared in circular hydrophobic glass molds (diameter = 25 mm). The hydrophobic functionalization of the glass molds was carried out following the procedure described above.


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Scanning Electron Microscopy (SEM). Scanning electron microscope (Hitachi S4700, High resolution SEM, USA) was used to image the hydrogel network after their critical drying. PAAm hydrogels were dehydrated progressively by successive immersions of 1 hour in a series of ethanol aqueous solutions (30%, 50%, 70%, 90% and 100%) and finally they were kept in 100% ethanol for 12 hours. The samples were then dried using a critical point dryer (Tousimis, Autosamdri-931), where the ethanol was exchanged with liquid carbon dioxide; they were held at the supercritical point of CO2 for 2 minutes, followed by a slow purge. Prior to imaging, the dried hydrogels were coated with Au/Pd for 30 seconds. A voltage of 10 kV and a current of 10 µA were used while the working distance was maintained at ~12 mm. Dynamic Light Scattering. A particle analyzer (Zetasizer 3000, Malvern, USA) was used to conduct light scattering measurements on hydrogels at a fixed wavelength of 632 nm and a scattering angle

of 90º. Multi-exponential decay functions were fitted to the autocorrelation

function extending Tanaka’s model to multiple relaxation modes30: !"#$ = Σ&' exp "−#/' )

(1)

where ' is the characteristic relaxation time and &' measures the magnitude of each mode. The relaxation time ' is related to a cooperative diffusion coefficient -' = 1/"' . $, with . = 4

401/231 , and 1=1.37931, the refractive index of the solution. The corresponding fluctuation length ξi for each relaxation mode was calculated according to ' = ⁄60-' , where is the Boltzman constant, the temperature, and the solvent viscosity (~1 mPas). Atomic Force Microscopy (AFM). Indentation and lateral force measurements were conducted by colloidal probe AFM using a JPK Nanowizard Ultra (JPK Instruments, Berlin, Germany). A


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silica sphere with a diameter of ~ 5µm (Microspheres-Nanospheres, USA) was attached to the end of a tipless cantilever (nominal spring constant = 0.4 N/m, CSC37-No Al/tipless, Mikromash, USA) using epoxy glue (JB-Weld, Sulphur Springs, TX, USA). The AFM cantilevers were cleaned in an ethanol (Sigma-Aldrich, USA) bath followed by UV ozone for at least 30 minutes before each experiment. RMS roughness and radius of each silica colloid were determined via reverse imaging using a clean test grating (MikroMasch, Spain). The roughness was determined within the area of contact with the hydrogel and varied between 5 and 10 nm, while the colloid radius was 2.4±0.1 µm. Normal stiffness of the cantilevers was determined via the thermal noise method before attaching the colloids, while the normal deflection sensitivities were obtained from forcedisplacement curves taken on a hard glass slide in the buffer. Lateral sensitivities were measured with a vertical linearity calibration grid (Mikromasch, Spain) by applying the wedge calibration method32. Indentation (2D maps, each with 64 indents per selected area) was conducted on hydrogels at a constant approach/separation speed of 2 µm/s and applying a maximum load of 10 nN. The cantilever was retracted immediately after achieving the maximum load, i.e. without any hold time between approach and retraction. The Hertz model relates the applied load (F) to small indentation depths (d) according to: 6

= 7 ∗ 89/ : /

(2)

where R is the radius of the colloid, E* is the contact modulus, 1/7 ∗ = "1 − ;?@A $/7, E is

the elastic modulus of the sample and ν its Poisson’s ratio (~ 0.45 for PAAm hydrogels33). To


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determine the initial elastic modulus of PAAm hydrogels with a thickness ℎ~ 60 µm, an indentation depths of ~ 0.3 µm was used. This results in C/8 (C is the contact radius, C = √8. :$ and :/ℎ ratios of ~ 0.35 and 0.005, respectively, ensuring small deformation and no substrate effects34, thereby justifying the use of the Hertz model. The initial (or smalldeformation) elastic moduli of the hydrogels were determined fitting Equation (2) to the approach force-indentation curves. Adhesion energies were calculated by integrating the area below the X-axis of the force-indentation curves upon retraction35. Friction force measurements were conducted on the same samples in which the 2D indentation maps were measured. Normal loads in the range 10-100 nN were applied at a constant sliding speed of 2 µm/s to study the influence of the normal load on the friction force. Two constant loads (5 nN and 50 nN) were selected to investigate the friction force as a function of the sliding speed, which was varied in the range 0.5 µm/s -200 µm/s. Lateral force loops were collected by acquiring the lateral deflection of the colloid tip in the forward (trace) and reverse (retrace) directions, while the sliding distance was maintained constant and equal to 10 µm. The friction force was calculated by averaging over the half width of the trace and retrace scans 36. Stick-Slip Analysis. To quantify the stick-slip, the lateral force drops ∆G during slip were determine for each applied load and speed by using the statistical software R version 3.4.0 for data ingestion, preprocessing and analytics. A spatial resolution of 512 over a sliding distance of 10 µm was selected and no smoothing was applied. The cutoff for the force drops was determined on lateral force loops measured with the colloid far away from the surface (no contact), which corresponds to the noise of the instrument and is ~0.06 nN. At least ten lateral force loops were analyzed per sliding condition on each single hydrogel. Multimodal Gaussian


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distributions were fitted to the slip histograms. Mean value, variance and frequency of each mode were compared in bubble diagrams. Experimental results Microstructure. To estimate the fluctuation length of the polymer chains at the sliding interface, two different methods, SEM and DLS, were applied. Figure 1 shows SEM images of PAAm hydrogels with an acrylamide concentration of 4%, 6% and 12% at two different magnifications. A small but visible decrease of the hydrogel volume occurred upon critical drying of all hydrogels, which means that the visualized network structure might differ from that of the water saturated hydrogels. Nevertheless, the images agree well with previous reports37. Long and entangled polyamide strands between crosslinks were observed in the images of 4%-PAAm hydrogels. Defects (or large pores) in these hydrogels are shown in Figure S1a. As the acrylamide concentration increases, the mesh size decreases and the length of the polymer strands between crosslinkers becomes smaller. Even though the PAAM-12% hydrogels underwent a more significant collapse upon drying (Figure 1c, see black arrow), some regions retained the original architecture of the hydrogel and were used for the determination of the mesh size distribution. The parameters characteristic of the multimodal mesh size distributions and the average mesh size are summarized in Figure 2a. While the large pores in PAAm-12% and PAAm-6% hydrogels are of similar size (80 and 90 nm, respectively), the smaller pores have a smaller diameter in PAAm-12% hydrogels compared to PAAm-6% hydrogels (32 and 49 nm). The largest pore size (220 nm) is observed in 4%-PAAm hydrogels, clearly demonstrating the smaller crosslinking degree of these hydrogels.


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a) 4%-PAAm

b) 6%-PAAm

c) 12%-PAAm

Collapsed strands

Figure 1: SEM pictures of PAAm-hydrogels with acrylamide concentrations of a) 4 wt%, b) 6 wt% and c) 12 wt% after critical drying. The arrows in a) point to the length of network strands between two crosslinks; the circles in b) and c) show the smallest pore size.

250

a)

b)

200

SEM pore size (nm)

SEM pore size (nm)

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150 100 50 0 0

5 10 15 acrylamide concentration (wt%)

100

10 0.01

4%-PAAm 6%-PAAm 12%-PAAm 0.1 1 10 100 DLS correlation length (nm)

Figure 2: a) Multimodal pore size distribution (mean value, standard deviation and frequency of each mode) of 4%-PAAm, 6%-PAAm and 12%-PAAm hydrogels after critical drying, as imaged by SEM. The size of the black bubbles represents the frequency of the corresponding mesh size. The red circles give the average mesh size. b) Correlation lengths obtained by extending Tanaka’s model to multiple relaxation modes to fit the autocorrelation functions measured by


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DLS. Only 4%-PAAm hydrogels exhibit three relaxation modes, one of which has a correlation length of ~100 nm, which we can relate to the larger pore size of the hydrogel observed in the SEM images. The smallest correlation lengths were obtained for 12%-PAAm hydrogels (see bubble diagrams in the SI), followed by PAAm-6%, in qualitative agreement with the mesh size observed in the SEM images. The correlation lengths obtained by applying Tanaka’s model to the autocorrelation functions obtained by DLS are shown in Figure S1a as a function of the acrylamide concentration. While the correlation length decreases with the increase in polymer concentration, in qualitative agreement with the mesh size imaged by SEM (Figure 2a), there is not quantitative agreement between mesh size and correlation length, as shown in Figure 2b. According to Tanaka’s model30, the relaxation of the hydrogel network is attributed to cooperative diffusion, which is related to the longitudinal fluctuation of the network strands.38 Cooperative diffusion assumes that the motion of the polymer chains is balanced by a restoring force and the friction between polymer and solvent molecules; hence, shorter relaxation times imply a smaller fluctuation length. Multiple decays in the correlation function can be related to distinct fluctuation times and lengths. Two decays were obtained for 6%-PAAm and 12%-PAAm hydrogels, while an additional third decay of much larger fluctuation length was observed for 4%-PAAm hydrogels, which is attributed to the long entangled polymer chains in the latter, as shown in Figure 1a. The second relaxation mode is similar for the three hydrogels (~10 nm), likely representing the fluctuation of polymer fibers forming the pores with a diameter of ~ 100 nm. The fastest relaxation, or smallest correlation length (~ 1 nm) may be related to the smallest pore size or to dangling chains. Remarkably, the correlation lengths of second and third modes are about an order of magnitude smaller than the mesh size observed in the SEM images. Nevertheless,


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despite the lack of quantitative agreement between both experimental methods, SEM and DLS, they agree in that the largest and smallest chain fluctuations are thus expected for 4%-PAAm, and 12%-PAAm hydrogels, respectively. AFM-Indentation. The elastic moduli and adhesion energies of the prepared hydrogels were measured by AFM indentation with a silica colloidal probe. Figure S1b shows an increase in the elastic modulus (2.2 ± 0.9, 6.6 ± 2.2 and 30.3 ± 9.7 kPa) with increase in acrylamide concentration (4%-PAAm, 6%-PAAm and 12%-PAAm hydrogels); average values of the elastic moduli (for each concentration) were determined by averaging the mean elastic moduli calculated for each indentation map, while the given standard deviation was determined for the mean elastic moduli. The high variability of the hydrogel elastic modulus, especially at high crosslinking degrees, has been reported before for PAAm hydrogels and attributed, among others, to the formation of highly crosslinked clusters, causing the global network to be more inhomogeneous and to soften39. Further, there is a significant influence of the hydrogel network on the adhesion energy. Figure S1 shows that the surface energy (adhesion energy normalized by the JKR contact area) increases with acrylamide concentration at the selected load of 10 nN, indicating that the main contribution to the surface energy of the hydrogels is the higher polymer concentration. However, the contact area decreases with increase in elastic moduli, which causes 6%-PAAm hydrogels to exhibit the highest total adhesion energy: (0.14±0.03)·10-14 J, (0.17±0.03)·10-14 J, and (0.13±0.06)·10-14 J, for 4%-PAAm, 6%-PAAm and 12%-PAAm hydrogels, respectively. Load-dependent friction force. Figure 3 shows the friction force as a function of normal load for 4%-PAAm, 6%- PAAm and 12%-PAAm hydrogels, thereby illustrating results for samples with different elastic moduli: 1.1 kPa for 4%-PAAm, 3.8 kPa for 6%-PAAm and 15.5 kPa for


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12%-PAAm hydrogels are shown in Figure 3a, and 3.5 kPa for 4%-PAAm, 5.8 kPa for 6%PAAm and 27 kPa for 12%-PAAm hydrogels are depicted in Figure 3b. Despite the pronounced changes in elastic moduli, the changes in the load-dependent friction force are thus small, except for the softest hydrogels, where a plateau, and even a decrease in the friction force, was observed above loads ~50 nN in some occasions; an example is shown in Figure 3a (see arrow). As discussed later, the origin for this behavior is the extensive deformation of 4%-PAAm hydrogels and pile-up effect upon high normal loads, which (partially) hinders sliding and induces an apparent decrease in the measured friction force. This was never observed in 6%-PAAm and 12%-PAAm hydrogels. 5

5

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• 15.5 ± 0.7 kPa • 3.8 ± 0.2 kPa • 1.1± 0.4 kPa

3 2 1

b)

Friction force (nN)

a) Friction force (nN)

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0

• 27.8 ± 3.8 kPa • 5.4 ± 0.5 kPa • 3.8 kPa ± 0.2 kPa

4 3 2 1 0

0

50 Load (nN)

100

0

50 Load (nN)

100

Figure 3: Friction vs. normal load for 4%-PAAm (blue triangles), 6%-PAAm (yellow diamonds) and 12%-PAAm (red circles) hydrogels. The diagrams a) and b) demonstrate that the elastic modulus has a small influence on the load-dependent friction force, except for 4%-PAAm hydrogels, where deformation and pile-up effects of very soft hydrogels can cause an apparent decrease in friction (see arrow). Friction force measurements were conducted at a sliding speed


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of 2 µm/s and a sliding length of 10 µm. Figure S2 (SI) shows friction force measurements as a function of the applied load for hydrogels with other elastic moduli, for comparison. Speed-dependent friction force. Representative results of the speed-dependent friction force under two selected normal loads (5 and 50 nN) are shown in Figure 4. No clear trend of the friction force with polymer concentration was observed. Importantly, an initial decrease in friction was typically observed for all hydrogels at both 5 and 50 nN below a transition speed ( ∗ ), beyond which friction increased with speed. The transition speed, ∗ , was found to augment with increase in polymer concentration, which caused the regime of increasing friction force with speed to be less obvious for the hydrogels with the highest polymer concentrations under the selected conditions (Figure 4); in fact, this regime was occasionally not attained by 12%-PAAm hydrogels under an applied load of 50 nN (see more results in Figure S3). 3

Friction force (nN)

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2

1

0 0

3

30 Speed (µm/s)

300

Figure 4: Representative speed-dependent friction force for 4%-PAAm (1.84 kPa, triangles), 6%-PAAm (3.8 kPa, diamonds) and 12%-PAAm (15.5 kPa, circles) hydrogels at normal loads of


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5 nN (open symbols) and 50 nN (filled symbols). The sliding speed was varied from 0.5 µm/s to 200 µm/s and the scan length was fixed at 10 µm. Figure 5 shows representative lateral force loops for the three hydrogels at selected conditions: 5 nN at c) low (1 µm/s, below V*) and d) high (100 µm/s, above V*) speed, and e-f) at 50 nN at the same speeds. These loops are generated when the AFM colloid slides on the hydrogel surface 10 µm to the right (trace) and to the left (retrace). An increase in the width loop occurs when the applied load is augmented (compare c with e), which indicates the increase in friction. The loops measured on 4%-PAAm hydrogels at high loads show occasionally a very pronounced tilt (Figure 5e) that deviates from the theoretical lateral force loop (Figure 5b, full line). In fact, this “tilt” phenomenon was recently investigated in detail for polymer brushes 40 and it is caused by extensive deformation of soft films: the tip indents the hydrogel and pushes material to the right or to the left (Figure 5a), which causes the hydrogel to pile-up (Figure 5a), thereby (partially) hindering sliding. This is important because, as demonstrated in ref.

40

and illustrated

in Figure 5b, extensive deformation can cause a remarkable underestimation of the friction force. In fact, the plateau that was sometimes observed in the load-dependent friction force curves for 4%-PAAm hydrogels (see arrow in Figure 3a) coincides with the occurrence of the tilt of the loops, and hence, it is attributed to partial or no sliding due to hydrogel deformation and pile-up. Figure 5b illustrates the possible types of lateral force loops during partial sliding (dash line) and no sliding (round dot line) caused by deformation and pile-up. There are possibilities to avoid this phenomenon, e.g. using a larger colloid to decrease the pressure. However, larger silica colloids are vey rough, which dramatically affects our measurements, in particular, the stick-slip described in the following section. Since deformation and pile-up only occasionally affected the friction force measurements conducted on 4%-PAAm hydrogels at high loads (≥50 nN), these


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data have been removed from the following analysis and discussion to avoid an underestimation of the friction force.


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Figure 5: Cartoon showing a) deformation of hydrogel and pile-up while pulling the colloid laterally before sliding occurs, and b) characteristic lateral force loops upon sliding (full line), deformation and sliding (dash line) and only deformation with no sliding (round dot line). The friction force is calculated as the half of the loop width during sliding, which, in case of extensive deformation, can cause a tremendous underestimation of the friction force. Lateral force loops representative for 4%-PAAm (blue), 6%-PAAm (yellow) and 12%-PAAm (red) hydrogels at c) 5 nN and 1µm/s, d) 5 nN and 100 µm/s, e) 50 nN and 1 µm/s and f) 50 nN and 100 µm/s. Their respective Young’s moduli are 2.5 ± 0.1, 9.3 ± 0.1 and 39.2 ± 3.5 kPa. Note that the Y-axis has different scales. Extensive deformation is only shown in e-f) for 4%-PAAm hydrogels.

Stick-slip analysis. The friction loops reflect the intermittent (sawtooth-like) motion of the colloid, which is reminiscent of an irregular stick-slip (see e.g. Figures 5c, 5e, 5f and S4). To quantitatively evaluate the differences in stick-slip at the investigated sliding conditions, the lateral force drops, ∆G, during a slip were calculated and the distribution was fit by bimodal Gaussian distributions. Average and standard deviations of each mode (or peak) and its frequency were compared via bubble diagrams (Figure 6). We only show the bubble diagrams for the largest peak, for which the major differences were observed. The friction characteristics of the three hydrogels were investigated with colloids of different roughness (RMS ranging from 5 to 10 nm within the area of contact). It is important to note that an increase in roughness caused stick-slip to be more pronounced. Therefore, separate bubble diagrams were constructed for each single colloid. Figure 6 and S5 (in the SI) show representative results corresponding to colloids with different RMS roughness, for comparison.


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0.75

b) 6%-PAAm 100

Load Load (nN) (nN)

Load (nN) (nN) Load

50

50

0

0

1

10

Speed Speed (•(µm/s) m/s)

100

40kpa 616 Max 1

c) 12%-PAAm

100

100

Load(nN) (nN) Load

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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50

0

1

10

100


1

10

100


Figure 6: Bubble charts for the lateral force drop during slip (∆G in nN) for 4%-PAAm (a), 6%PAAm (b) and 12%-PAAm (c) hydrogels as a function of applied load and sliding speed. The color represents the magnitude of the stress drop, while the size of the bubble represents the frequency of occurrence. The lines are boundaries between regions of high (red-orange), medium (yellow) and low (blue) stick-slip events. At the highest normal loads (~100 nN) stick-slip seems to be reduced, especially on 4%-PAAm hydrogels (see arrows), likely due to deformation and pile-up.

Irregular sliding (with associated stress drops larger than 0.06 nN) was observed at most of the conditions on all hydrogels, which reflects the direct interaction between the polymer chains and the colloid surface. Upon an applied load of and above ~20 nN, stick-slip was substantial. Nevertheless, by increasing the speed, the frequency of the stick-slip events and also the magnitude of the stress drop decreased, but it was still present in most of the lateral force loops. Only at low loads and high speeds, smooth sliding was sometimes observed on 4%-PAAm hydrogels (see the small size of the blue bubbles at 5 nN in Figure 6a). At the highest applied


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load (~100 nN, see arrows), the occurrence of stick-slip events apparently decreased, likely because polymer fluctuations were restricted upon applied high loads. In the case of gel-like materials, stick-slip happens when the polymer chains are pulled and stretched while they adhere (stick) to the colloid, until the pulling force is stronger than the adhesion force, which yields a slip28. Stretching of the polymer depends on the degree of entanglement and crosslinking, and hence, it varies across the sliding distance due to the heterogeneous nature of the hydrogel surface (Figure 1), which is consistent with the irregular stick-slip observed in the lateral force loops. The hydrogel microstructure substantially affects the stick-slip frictional response. Across experiments with different colloids, stick-slip was most prominent for 6%-PAAm hydrogels, while 12%-PAAm hydrogels exhibited less pronounced stick-slip than 4%-PAAm hydrogels. This trend agrees with the adhesion energy measured by indentation, and thus, it suggests a trade-off between the surface energy and the contact area to determine the transient adhesive bridges between the colloid and the hydrogel: an increase in polymer concentration and crosslinking enhances adhesive interactions between colloid surface and hydrogel (Figure S1b), however, the larger elastic modulus reduces the contact area and the number of interactions. The overall adhesion energy is thus highest for the 6%-PAAm hydrogels, which is likely the origin for the more pronounced stick-slip. Discussion The energy dissipation mechanisms underlying the frictional characteristics of hydrogels are intrinsically different from those of hard rough substrates. Although hydrogel-liquid interfaces are rough due to the thermal fluctuations of the polymer chains, the large deformation imposed by the applied load, the long relaxation times of macromolecules and the presence of a liquid


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phase, i.e. the poroelastic behavior of the hydrogel, lead to intrinsically different energy dissipation mechanisms that need to be taken into account to predict and explain frictional characteristics of hydrogels and lubrication mechanisms. We use the described experimental results in the previous section to provide more insight into these mechanisms. The friction force gradually increases with load, although deviating from the Amonton’s law (Figures 3 and S2). This is not surprising41, since, first, adhesion, which increases with applied load42, is significant, and, second, friction depends on speed. The tenuous increase in the loaddependent friction force with increase in polymer concentration is consistent with the proposed I

adsorption-desorption model; larger fluctuation amplitudes (~7 HJ ), which are expected for 4%PAAm hydrogels, imply longer times for re-adsorption ( ) to the counter-surface, and hence, smaller friction force compared to more crosslinked hydrogels at the same applied load. We note that the polyacrylamide hydrogel microstructure is complex and cannot be appraised by a single mesh size or correlation length (Figure 1 and 2). Although there is an overall decrease in mesh size and correlation length with increase in polyacrylamide concentration, PAAm hydrogels exhibit, at least, two characteristic lengths (Figure 2). While SEM and DLS cannot characterize mesh size or correlation length of each single hydrogel network used on friction force measurements, the elastic modulus can be easily measured on the same sample and area prior to each friction force measurement, which is an advantage considering the variability of properties across PAAm hydrogels. We thus propose to use the initial elastic modulus, 7, which spans over one order of magnitude in this study (1-40 kPa), to represent the fluctuation characteristics of the near-surface hydrogel region.


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The non-monotonic variation of friction with speed (Figure 4) –first decreasing below a transition value, ∗ , at which friction achieves a minimum value, KLM , and then increasing above ∗ , reveals the action of, at least, two different mechanisms underlying friction at the sliding interface. Figure 7a shows that the transition speed ∗ depends on the elastic modulus of the hydrogels in a non-linear fashion according to ∗ ~79/ upon an applied load of 50 nN, which implies that the increase in friction with speed is facilitated at the sliding interface of softer hydrogels. Figure 7b shows that the minimum friction force KLM increases with elastic I

modulus –approximately as KLM ~7 N – consistent with the adsorption-desorption model12, as described earlier; that is, larger time for re-adsorption allows achieving a lower friction force. The large standard deviation might be caused by hydrogel heterogeneities and by the silica colloid, whose properties (e.g. roughness, hydrophilicity) varied across experiments. Upon a load of 5 nN, there is no clear trend for the transition speed as a function of the elastic modulus, however, the precision of the AFM may not be sufficient to distinguish the minimum friction force due to its small magnitude, and hence, this is not further discussed.

50

a)

b) ~E1/3

5nN

~E1/5

2 Fmin (nN)

V* (µm/s)

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1

50nN 5

0 1

10 elastic modulus (kPa)

1

10 elastic modulus (kPa)


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Figure 7: a) Transition speed, ∗, at which the minimum of the friction force, KLM , is achieved and b) KLM as a function of elastic modulus at the applied normal loads of 5 nN (diamonds) and 50 nN (squares). At 50nN, the transition velocity ∗ scales with ~79/ and the minimum friction force KLM scales with ~79/O, while the trends are not clear at 5 nN, likely because the measurement precision is not sufficient to clearly identify the minimum friction force.

Like in previous works10,

12

, we thus assume that the frictional behavior at speeds below ∗

results from polymer chains continuously adsorbing to and detaching from the colloidal probe with a fluctuation amplitude that is related to the mesh size characteristics. The relaxation time for re-adsorption is given by =

QR S

speed, = ~ PT ~

J P QR

, according to the scaling theory25, which yields a critical

I T

"QR S$J U J P

, at which the polymer fluctuation time is equal to the interaction

time upon sliding = ; note that the constants are missing in this equation. Inspired by ref. 5, Figure 8 shows the normalized friction force by >'V as a function of the dimensionless speed

W

. We emphasize that we refrain from quantifying friction via a friction coefficient due to the

evident deviations from the Amonton’s law in our experiments. A satisfactory collapse of the normalized friction force is obtained as a function of the dimensionless velocity

W

at speeds T

smaller than ∗ , demonstrating that the normalized friction force scales with />'V ~"7 HJ $V , n ≈-0.1. The collapse demonstrates that the relaxation time is a good parameter to describe the influence of the hydrogel network on the normalized friction in this regime.


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A decreasing friction with speed appears if the time allowed for interactions to happen at the sliding interface is too short for the polymer to re-adsorb to the opposing surface after detachment. This yields a decrease in kinetic friction below the static friction, thereby causing stick-slip28. As a matter of fact, we observe significant stick-slip in our measurements (Figure 6), which is a clear evidence for the direct contact between the hydrogel and the colloid surface. The stick-slip is irregular and is influenced by the applied load and the sliding speed: higher load and slower sliding enhance stick-slip. We hypothesize that squeeze-out of the fluid (drainage)42, and thereby, polymer dehydration, which is more significant at high loads and slow sliding, increases the adhesive interaction between polyacrylamide and the colloid surface, and thus, promotes stick-slip in this regime. It is important to note that the normalized transition speed ∗ by is several orders of magnitude smaller than 1, which cannot be justified by missing scaling factors (expected to be ~1). In contrast to this, the results from a previous work6 show that the transition at Gemini hydrogel interfaces occurs at / ~1. Our effort to validate the calculations in this previous work have failed and for the given parameters by the authors, we found that / < 0.001 in ref. 6

, in good agreement with the results presented here. Importantly, this supports that an additional

mechanism hinders the critical speed, , and thus, elasto-hydrodynamic lubrication, to be attained. It is also worth mentioning that previous works have revealed a boundary lubrication regime at even lower speeds, where friction either increased and/or remained constant with rising speed12. Figure 4 shows an example for 4%-PAAm hydrogels, where friction first increased at the lowest speeds, before the decrease of friction with increasing speed was measured. According to Gong’s model this happens if the interaction time is sufficient long for re-adsorption of the polymer


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chains to take place, i.e. at sufficiently slow speeds. Such initial increase of friction with speed was, however, rarely observed in our experiments, and we do not further discuss it here due to the small amount of data.

Figure 8: Normalized friction force as a function of under two applied loads, 5 nN and 50 nN. W

Two scaling laws

Z

Z[\]

V

~ ^ _ were determined: n≈-0.1 for VV*. The W

normalized friction at V>V* on hydrogels of different elastic modulus do not collapse because ∗ W

I

~7 HJ . The symbols correspond to 4%-PAAm (triangles), 6%-PAAm (diamonds) and 12%-

PAAm hydrogels (circles).

Figure 8 shows a notable spread of the normalized friction force as a function of

W

at > ∗ ,

I

which is attributed to the network influence on the transition speed, ∗ ~7 J , which yields ∗ W

I

= 7 HJ , thereby hindering the collapse of the normalized friction force with the selected X-


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axis; note the shift of the data to the left with the increase in elastic modulus. Evidently, this deviation indicates that is not a good scaling parameter in this regime. Instead, Figure S6 shows the normalized friction force as a function of / ∗ . Although the scatter of data is large, the distinction with regard to the elastic modulus vanishes, and it provides an approximate scaling law Z

Z

`ab

I

~"/ ∗ $T in this regime. The origin for the poor collapse might be related to the

surface properties of the colloids, which varied across experiments, and to hydrogel I

heterogeneities. Nevertheless, it is also possible that the selected scaling parameter, ∗ ~7 J , is not appropriate to describe this behavior, and instead, one of the modes of the mesh size distribution, i.e. a single correlation length, dictates the change in friction in this regime; this I

requires further investigation. Furthermore, considering that KLM ~79/O and ∗ ~7 J , this suggests that in this regime, the friction force only depends weakly on the elastic modulus, i.e. on the fluctuation length of the hydrogel network. This is confirmed in Figure 4, which shows a good overlap of the friction force at the sliding interface of the three different hydrogels at > ∗. If elasto-hydrodynamic lubrication would occur in this regime, as claimed before12, the friction force would be expected to be given by ~c/ℎ, where ℎ is the lubricant thickness. According to Hamrock&Dowson’s model in the elasto-hydrodynamic regime T

43

d

T

, ℎ~7 He J , and assuming

T

c~7 HJ , the (viscous) friction force should scale with ~"7 HJ $9/ , which differs from our experimental results (see Figure S7a). Deviations from the original model by Hamrock and Dowson, however, are possible, since the hydrogel surface is permeable and hydrogels are poroelastic, properties that are not accounted for in this model. Nevertheless, it is evident that


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full-fluid film lubrication is not attained in most of our experiments, as evidenced by the stickslip analysis, which demonstrates the occurrence of direct chain-colloid interactions.

A mechanistic explanation for the observed scaling law

Z

I

T ~ ^ ∗_ Z[\]

is proposed based on the

likelihood for re-adsorption: at sufficiently fast sliding ( > ∗ ), when the time allowed for ∗

interaction at the sliding interface is reduced below this critical value, = ∗ ~

I

f U J I

UJ

= 1, re-

T

adsorption is not dictated by the time for re-adsorption ~ ~7 HJ anymore. Instead, it is dominated by the likelihood of attachment, fairly independent on the fluctuation length of the hydrogel network. The increase in the likelihood of interaction with speed yields an increase in the number of chains that are effectively adsorbed at each point of time, thereby causing the friction force to increase, to some extent, independently of the fluctuation length. Our future work will be dedicated to get more insight into this regime by expanding the range of investigated hydrogel networks. A similar trend for the friction force as a function of speed was observed for the speed-dependent friction force for PAAm hydrogels against a glass ball (as countersurface) measured with a tribometer12, and for cartilage-cartilage interfaces, measured with a surface forces apparatus28. The authors attributed it to a transition from boundary to elastohydrodynamic lubrication. Our results suggest that, although a transition to elasto-hydrodynamic could happen at higher speeds, under the investigated conditions in our work there is still direct interaction between the hydrogels and the colloid sphere, which is reflected in stick-slip in our measurements. Hydrogel deformation must play a significant role in the onset of hydrodynamic lubrication, but classical


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models do not account for the permeable and non-linear poroviscoelastic nature of hydrogels, and hence, a prediction of the conditions for the onset of fluid-film lubrication is not possible yet. A first attempt to connect the poroelastic behavior of hydrogels to the lubrication mechanism has been recently reported, however, only in the regime where friction decreased with increasing speed42. The authors showed how short durations of applied pressure and faster sliding speeds do not disrupt interfacial hydration, which maintains low friction, while at low speeds, where interface drainage dominates, an increase in adhesion energy - directly derived from poroelastic relationships- and the osmotic suction work against slip to achieve higher friction. It should be noted that this continuum approach is consistent with the adsorption-desorption model applied here, considering that polymer fluctuations (and low friction) are hindered with hydrogel dehydration or squeezing-out of the liquid phase. It is interesting to compare our results to a previous study of the frictional behavior of Gemini hydrogel interfaces5, which showed a transition from velocity-independent to velocity-dependent friction coefficient. The absence of the initial decrease in friction with speed could be related to the more favorable interactions between the polymer chains compared to the interactions between polymer chains and silica surface. We also note that the velocity-dependent friction coefficient above the transition speed showed an excellent collapse for hydrogels with different mesh size, in contrast to our results. We cannot explain this difference yet, but we assume that the dynamics at the Gemini interface might either affect the likelihood of re-attachment of the polymer chains or the range of investigated hydrogel networks was too narrow to reveal this phenomenon. Nevertheless, the coefficient of friction at Gemini hydrogel interfaces also scales I

with "$T above the transition speed, in excellent agreement with our results.


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In summary, we have shown that boundary lubrication at the hydrogel-colloid interface exhibits a non-monotonic change of friction with speed and intermittent sliding. The scaling laws that predict friction above and below the transition speed ∗ deviate from those found for Gemini interfaces, which seems reasonable since the fluctuation dynamics that lead to re-adsorption are expected to be different at hydrogel-silica interfaces. It is intriguing that beyond the reported transition ( > ∗ $, the hydrogel network has a small influence on the friction force, and our current work is trying to scrutinize the origin of this result. Further, the thermal fluctuations at the colloid-hydrogel interface manifest as irregular stick-slip. Since stick-slip sliding is commonly at the origin of irreversible transformations of soft surfaces, and hence, wear processes, understanding the mechanisms that yield this intermittent frictional response with different relaxation times, thus below and above ∗ , will be also the subject of our future investigations. Conclusions This work has investigated the frictional characteristics of hydrogel-silica interfaces by using colloidal probe AFM. PAAm hydrogels with 4, 6 and 12 wt% acrylamide exhibit a complex microstructure with several correlation lengths and/or mesh sizes, which led us to choose the initial elastic modulus as the material parameter to characterize the hydrogel network. By scrutinizing the speed-dependence of the friction force over three orders of magnitude, two different lubrication mechanisms were discerned, both being explained by the fluctuation dynamics of the polymer chains at the sliding interface. Below a transition speed ∗ that scales I J

H

T J

with 7 , the decrease in friction with speed ~ ^7 _

H

I Ig

supports energy dissipation via


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continuous attachment to and detachment of the polymer chains to the colloid surface. Friction is governed by the amplitude of such fluctuations (or mesh size), while stick-slip reflects the transient adhesive interactions between the polymer and the silica counter-surface. According to our results, less crosslinked hydrogels can mediate lower friction forces due to the longer relaxation times of the polymer chains to re-adsorb on the counter-surface; however, the transition into the regime, where friction increases with speed, is favored on less crosslinked hydrogels. Above the transition speed, ∗ , the occurrence of stick-slip decreases, yet it does not I I

vanish, while the scaling law for the friction force switches approximately to ~"7 HJ $T , both supporting the transition to a different lubrication mechanism. While the stick-slip characteristics of hydrogel-silica interfaces are shown to depend on the hydrogel microstructure and to vary with load and speed, future studies are needed to elucidate the different relaxation mechanisms.

ASSOCIATED CONTENT Supporting Information Additional information about the correlations lengths measured by DLS, elastic modulus and adhesion energy determined by colloidal probe AFM indentation, additional friction force measurements and stick-slip bubble charts are included in the supporting information. This material is available free of charge via the Internet at http://pubs.acs.org AUTHOR INFORMATION Corresponding Author * Rosa M. Espinosa-Marzal†


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[email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding Sources Support to TS by the Fulbright Program, U.S. Department, of State is acknowledged. We also thank financial support by the National Science Foundation under Grant No. CMMI-1435920.

ACKNOWLEDGMENT We would like to acknowledge Mr. Andreas Hofheinz for his contribution in the analysis of the multimodal distributions of force drops during slip, and thank Prof. Helen Nguyen for providing access to DLS. We also acknowledge the facilities provided by Materials Research Laboratory (MRL) at UIUC.

REFERENCES 1. Freeman, M. E.; Furey, M. J.; Love, B. J.; Hampton, J. M., Friction, wear, and lubrication of hydrogels as synthetic articular cartilage. Wear 2000, 241 (2), 129-135. 2. Dunn, A. C.; Urueña, J. M.; Huo, Y.; Perry, S. S.; Angelini, T. E.; Sawyer, W. G., Lubricity of Surface Hydrogel Layers. Tribology Letters 2012, 49 (2), 371-378. 3. Pitenis, A. A.; Uruena, J. M.; Schulze, K. D.; Nixon, R. M.; Dunn, A. C.; Krick, B. A.; Sawyer, W. G.; Angelini, T. E., Polymer fluctuation lubrication in hydrogel gemini interfaces. Soft Matter 2014, 10 (44), 8955-62. 4. Dunn, A. C.; Sawyer, W. G.; Angelini, T. E., Gemini Interfaces in Aqueous Lubrication with Hydrogels. Tribology Letters 2014, 54 (1), 59-66. 5. Urueña, J. M.; Pitenis, A. A.; Nixon, R. M.; Schulze, K. D.; Angelini, T. E.; Gregory Sawyer, W., Mesh Size Control of Polymer Fluctuation Lubrication in Gemini Hydrogels. Biotribology 2015, 1–2, 24-29. 6. Pitenis, A. A.; Manuel Urueña, J.; Nixon, R. M.; Bhattacharjee, T.; Krick, B. A.; Dunn, A. C.; Angelini, T. E.; Gregory Sawyer, W., Lubricity from Entangled Polymer Networks on Hydrogels. Journal of Tribology 2016, 138 (4), 042102-042102.


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7. Dowson, D., Bio-tribology. Faraday Discussions 2012, 156, 9. 8. Kim, S. H.; Marmo, C.; Somorjai, G. A., Friction studies of hydrogel contact lenses using AFM: non-crosslinked polymers of low friction at the surface. Biomaterials 2001, 22 (24), 3285-3294. 9. Gong, J. P., Friction and lubrication of hydrogels-its richness and complexity. Soft Matter 2006, 2 (7), 544-552. 10. Gong, J.; Osada, Y., Gel friction: A model based on surface repulsion and adsorption. J Chem Phys 1998, 109 (18), 8062-8068. 11. Gong, J. P.; Osada, Y., Surface friction of polymer gels. Prog Polym Sci 2002, 27 (1), 3-38. 12. Kurokawa, T.; Tominaga, T.; Katsuyama, Y.; Kuwabara, R.; Furukawa, H.; Osada, Y.; Gong, J. P., Elastic− Hydrodynamic Transition of Gel Friction. Langmuir 2005, 21 (19), 8643-8648. 13. Gong, J. P.; Kurokawa, T.; Narita, T.; Kagata, G.; Osada, Y.; Nishimura, G.; Kinjo, M., Synthesis of hydrogels with extremely low surface friction. J Am Chem Soc 2001, 123 (23), 5582-3. 14. Raviv, U.; Giasson, S.; Kampf, N.; Gohy, J. F.; Jerome, R.; Klein, J., Lubrication by charged polymers. Nature 2003, 425 (6954), 163-165. 15. Kampf, N.; Raviv, U.; Klein, J., Normal and Shear Forces between Adsorbed and Gelled Layers of Chitosan, a Naturally Occurring Cationic Polyelectrolyte. Macromolecules 2004, 37 (3), 1134-1142. 16. Raviv, U.; Giasson, S.; Kampf, N.; Gohy, J. F.; Jerome, R.; Klein, J., Normal and frictional forces between surfaces bearing polyelectrolyte brushes. Langmuir 2008, 24 (16), 8678-8687. 17. Müller, M.; Lee, S.; Spikes, H. A.; Spencer, N. D., The Influence of Molecular Architecture on the Macroscopic Lubrication Properties of the Brush-Like Copolyelectrolyte Poly(L-lysine)-g-poly(ethylene glycol) (PLL-g-PEG) Adsorbed on Oxide Surfaces. Tribology Letters 2003, 15 (4), 395-405. 18. Lee, S.; Müller, M.; Ratoi-Salagean, M.; Vörös, J.; Pasche, S.; De Paul, S. M.; Spikes, H. A.; Textor, M.; Spencer, N. D., Boundary Lubrication of Oxide Surfaces by Poly(L-lysine)-g-poly(ethylene glycol) (PLL-g-PEG) in Aqueous Media. Tribology Letters 2003, 15 (3), 231-239. 19. Rosenberg, K. J.; Goren, T.; Crockett, R.; Spencer, N. D., Load-Induced Transitions in the Lubricity of Adsorbed Poly(L-lysine)-g-dextran as a Function of Polysaccharide Chain Density. ACS Applied Materials & Interfaces 2011, 3 (8), 30203025. 20. Klein, J.; Luckham, P., Forces between 2 Adsorbed Polyethylene Oxide Layers Immersed in a Good Aqueous Solvent. Nature 1982, 300 (5891), 429-431. 21. Klein, J.; Kamiyama, Y.; Yoshizawa, H.; Israelachvili, J. N.; Fredrickson, G. H.; Pincus, P.; Fetters, L. J., Lubrication forces between surfaces bearing polymer brushes. Macromolecules 1993, 26 (21), 5552-5560. 22. Nalam, P. C.; Ramakrishna, S. N.; Espinosa-Marzal, R. M.; Spencer, N. D., Exploring Lubrication Regimes at the Nanoscale: Nanotribological Characterization of Silica and Polymer Brushes in Viscous Solvents. Langmuir 2013, 29 (32), 10149-10158.


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Insert Table of Contents Graphic and Synopsis Here Stick-slip reveals two hydrogel lubrication regimes, where direct adhesive interactions exist between the hydrogel and the colloid.


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StickâSlip Friction Reveals Hydrogel Lubrication Mechanisms

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StickâSlip Friction Reveals Hydrogel Lubrication Mechanisms