Sliding on Slide-Ring Gels

All reagents were used as received except where noted. Pseudo-rotaxane crosslinkers were synthesized from PEG-diacrylate and α-cyclodextrin-acrylate through adaptations of literature protocols [17, 19, 20]. In a representative protocol, 6 g (1 equiv.) of 20 kDa PEG (Sigma-Aldrich Product #81,300) was dried under high vacuum at 35 °C overnight. The dried PEG was dissolved in 15 mL of anhydrous dichloromethane (Sigma-Aldrich Product #270,997) with 0.17 mL (4 equiv.) triethylamine (Sigma-Aldrich Product #471,283) under nitrogen with stirring. This solution was cooled to 0 °C before the addition of 0.15 mL (6 equiv.) acryloyl chloride (Sigma-Aldrich Product #549,797). The reaction then proceeded at room temperature for 24 h. The PEG-diacrylate product was collected by precipitation in cold diethyl ether.

To prepare α-cyclodextrin-acrylate, 8.56 g (1 equiv.) of α-cyclodextrin (Sigma-Aldrich Product #778,788) was dissolved in 125 mL of DI water with 2.97 g (6 equiv.) of potassium hydroxide (Sigma-Aldrich Product #484,016) with stirring. The reaction flask was cooled to 0 °C, and 7.15 mL (10 equiv.) of acryloyl chloride was added dropwise over 15 min. The reaction flask was brought to 40 °C for 6 h. The α-cyclodextrin-acrylate was collected by precipitation in acetone following Ding et al. [19].

Both PEG-diacrylate and α-cyclodextrin-acrylate were dried under high vacuum overnight after precipitation. PEG-diacrylate and α-cyclodextrin-acrylate were dissolved in water individually at concentrations of 1 g per 5 mL and 1 g per 7 mL, respectively. The solutions were mixed at room temperature, then stirred at 70 °C for 90 min. The initially clear, slightly gray solutions appeared white and cloudy after equilibrating at 4 °C for one week, indicating the complexation of PEG-diacrylate and α-cyclodextrin-acrylate [21] (Fig. S1). Additional evidence of complexation was the shifting and broadening of ¹H NMR resonances of the complex prepared in D₂O (Fig. S2). This mixture was used directly as a pseudo-rotaxane stock solution. This ratio of α-cyclodextrin-acrylate to PEG-diacrylate corresponds to a ratio of 1 α-cyclodextrin-acrylate molecule per 10 PEG repeat units. The maximum density possible of α-cyclodextrin molecules on a PEG chain is 1 α-cyclodextrin molecule per two PEG repeat units [12]. Thus, a pseudo-rotaxane with one α-cyclodextrin-acrylate ring per 10 PEG repeat units had a ‘coverage’ of 20% because it had 20% of the maximum possible amount of cyclodextrin. The inherent softness and high swelling of slide-ring gels necessitated a high coverage pseudo-rotaxane at high loading to obtain hydrogel networks that permitted reproducible and reliable measurements of their mechanical and tribological properties.

Hydrogels were formed by polymerizing the pseudo-rotaxane crosslinker with acrylamide monomer. It has been previously shown that copolymerizing PEG and α-cyclodextrin-based pseudo-rotaxane with acrylamide traps the α-cyclodextrin rings on PEG chains, creating sliding crosslinks within the gel [17, 18]. The formation of sliding crosslinks was supported by gelation tests with varying crosslinker identities (Fig. S3). These tests showed an increase in crosslinking density resulting from the combination of PEG and α-cyclodextrin-acrylate, providing evidence for the existence of sliding crosslinks in the gel. Ammonium persulfate (APS) (Sigma-Aldrich, Product #A3678) was used as a water soluble free-radical initiator with N,N,N′,N′-tetramethylethylenediamine (TEMED) (Sigma-Aldrich Product #T9281) as a catalyst. Briefly, stock solutions of 50 wt.% acrylamide, 50 mg/mL APS, and 50 mg/mL TEMED were prepared in ultrapure water. The pseudo-rotaxane solution was prepared as previously described with a concentration of 154 mg/mL. Stock solutions were combined to achieve the compositions listed in Table 1. The order of addition of the stock solutions was acrylamide, water, TEMED, pseudo-rotaxane, then APS. Gels were polymerized under nitrogen (< 300 ppm O₂) with the top surface exposed to the atmosphere to create an unmolded surface for testing. Gels were equilibrated in ultrapure water for at least one week prior to testing with multiple exchanges of the swelling media for fresh ultrapure water. All slide-ring gels increased in diameter from 12 mm initially to 20–22 mm, which corresponds to a volume increase of approximately 5 × assuming isotropic swelling (Table S1). Two duplicates of each formulation were synthesized and tested. Hydrogel samples with 0.5 wt.% crosslinker were synthesized but were too soft to be accurately measured with our experimental configuration.

Since our slide-ring hydrogel system was predominantly composed of polyacrylamide, covalently crosslinked (“fixed-crosslink”) polyacrylamide hydrogels were selected as chemically similar controls. Polyacrylamide control samples were synthesized in ultrapure water at initial acrylamide concentrations of 7.5 wt.%, 12.5 wt.%, and 17.5 wt.% following the methods in Urueña et al. [22]. N,N′-Methylenebisacrylamide (MBAAm) was used as a crosslinker with the molar ratio of AAm:MBAAm equal to 200:1, and the concentrations of APS and TEMED were both 0.15 wt.%. As with the slide-ring gels, fixed-crosslink gels were polymerized under nitrogen with the top surface of the sample exposed to the atmosphere, and all samples equilibrated in ultrapure water for at least 24 h prior to testing.

A custom-built linear reciprocating tribometer was used to indent the slide-ring gels following methods previously described in Chau et al. [23] using a hemispherical borosilicate glass probe (Type 1 Class A; radius of curvature, R = 2.6 mm) attached to a titanium double-leaf cantilever with normal and tangential spring constants k_n = 222.7 µN/µm and k_f = 91.6 µN/µm to indent two flat gel disks of each formulation in three unique sites. Reduced modulus values reported for each formulation are the average and standard deviation of these repeated measurements. During indentation measurements, the hydrogel and probe were completely submerged in ultrapure water. Indentation measurements for determining E* had constant velocity of v_indent = 10 µm/s and a targeted normal force of F_n = 1.0 mN. This force corresponds to contact pressures (p_max ≈ 1 to 2 kPa) as calculated with Eq. 1:where F_n is the normal force and E* is the reduced elastic modulus. We used Eq. 2 from Hertzian contact mechanics to fit the approach curves up to F_n = 0.5 mN to calculate E*:where d is the depth which the probe has pushed into the gel surface. Since the instrument records F_n and d, and R is known, E* can be calculated. To measure the contact area, the contact radius a was estimated using Eq. 3:

For fixed-crosslink gels, reduced modulus values were determined using the same protocol as for slide-ring gels but with a different probe and cantilever. The hemispherical borosilicate glass probe had a radius of curvature of R = 3.2 mm and the normal and tangential spring constants of the cantilever used for indentation measurements were k_n = 61.36 µN/µm and k_t = 75.8 µN/µm. Five indents were conducted on one location per sample. The reduced elastic modulus, E*, used to calculate the minimum fluid film thickness, h_min, for fixed-crosslink polyacrylamide gels, was the averages and standard deviations of these five indentation measurements.

To investigate adhesion between the slide-ring gels and glass probe, modified indentation measurements with varying hold times at the maximum F_n = 1.0 mN were conducted. Indentation and retraction speeds were equal at v_indent = 5 µm/s. After reaching the prescribed force, the probe position was held constant for maximum dwell times of t_dwell = 0, 10, 60, or 600 s. The work of adhesion, W_ad, was calculated from the area above the retraction curve and below F_n = 0 N using Eq. 4:where z is the height of the glass probe in units of µm. The surface of the gel was set to z = 0. The probe location above the gel surface corresponds to z > 0, and the probe indenting the gel corresponds to z < 0. One slide-ring gel sample of each formulation was indented three times in three different sites with the average and standard deviation reported for these measurements.

Sliding experiments were conducted using a custom-built linear reciprocating tribometer. Hydrogels were secured in a custom polyetheretherketone (PEEK) dish and submerged in ultrapure water for the duration of the experiment. The glass probes used for evaluating tribological behavior were identical in geometry to those used in the indentation measurements. Hydrogel samples were mounted to a motorized stage (Physik Instruments, L-509.20DG10, 52 mm travel range). Slide-ring gel friction was measured at sliding velocities of v_slide = 10, 50, or 100 µm/s across a sliding path of 6 mm (1/2) cycle. An applied normal load of F_n = 0.5, 1, or 1.5 mN was maintained for at least 10 sliding cycles. The average friction coefficient of one cycle was calculated by taking the average ratio of the friction force F_f and normal force F_n in the forward and reverse directions as shown in Eq. 5:where µ_cycle is the average friction coefficient in the free-sliding regime, which here was set to the middle 1 mm of the sliding path, F_f,fwd is the friction force in the forward sliding direction, and F_f,rev is the friction force in the reverse sliding direction. Since the tribometer is configured with only one side-mounted capacitance probe to record cantilever displacements in the tangential direction, the friction force in the reverse direction is recorded as negative values. µ_cycle for 10 cycles was recorded for each sample and all values of µ_cycle from the same formulation and testing conditions were grouped and used to calculate the reported averages and standard deviations of friction coefficients.

Friction coefficients of the fixed-crosslink polyacrylamide gels were determined by the same procedure as the slide-ring gels except with a different probe geometry and cantilever stiffness as previously described. All tribological measurements of fixed-crosslink gels were conducted at a constant sliding velocity of 100 µm/s. Measurements were performed at normal forces, F_n = 100 µN, 500 µN, 1,000 µN, 1,500 µN, or 2,000 µN. The sliding path for each fixed-crosslink gel measurement was 700 µm. Data were collected only from experiments in which the estimated contact radius was less than 300 µm, so that there was at least 100 µm of free sliding in the middle of the sliding path. One measurement of the slide-ring gels resulted in a coefficient of friction below the noise floor µ_noise of the instrument, calculated from Eq. 6:where k_f is the tangential stiffness of the cantilever (k_f = 437.8 µN/µm) and x_min is the minimum displacement detectable by the capacitance probes (x_min = 5 nm). With this configuration, the experimental noise floor in friction coefficient measurements was µ_noise = 0.001.

We determined the reduced elastic moduli of the 1.0 wt.% and 1.5 wt.% crosslinked slide-ring gel formulations to be E* = 10 ± 0.9 kPa and E* = 15 ± 0.4 kPa, respectively, from microindentation measurements without dwell (Fig. 2a). The 1.5 wt.% crosslinked sample exhibited a greater modulus than the 1.0 wt.% crosslinked gel, which suggests that at least some of the additional pseudo-rotaxane added to the 1.5 wt.% formulation with respect to the 1.0 wt.% formulation did incorporate into the network, and the two formulations resulted in mechanically distinct samples.

Both slide-ring formulations exhibited negligible work of adhesion, W_ad, during indentation measurements conducted without dwelling in contact at maximum normal load, t_dwell = 0 s (Fig. 2a). Increasing dwell time resulted in significant increases in the work of adhesion for both formulations. In most cases—notably for t_dwell = 60 and 600 s—the 1.0 wt.% crosslinked sample exhibited greater W_ad than the 1.5 wt.% crosslinked sample (Fig. 2b,c). At maximum dwell time, t_dwell = 600 s (10 min), the work of adhesion of the 1.0 wt.% crosslinked gel (W_ad = 51.7 ± 12.9 nJ) was approximately five times that of the 1.5 wt.% sample (W_ad = 11.6 ± 3.1 nJ). Such sensitivity to dwell time for the 1.0 wt.% crosslinked gel suggests greater chain mobility at the surface.

Friction-force traces and friction coefficients were very similar for the 1.5 wt.% crosslinked slide-ring gels when sliding velocity, v_slide, increased from 10 to 100 µm/s (Fig. 3a). The friction coefficients were µ = 0.029 ± 0.006 at v_slide = 10 µm/s and µ = 0.022 ± 0.004 at v_slide = 100 µm/s. Friction-force traces exhibited clear separation between the forward and reverse directions for both sliding velocities, which indicated that contact was maintained between the probe and the gel surface. In contrast, the 1.0 wt.% crosslinked slide-ring gels evaluated at F_n = 500 µN exhibited velocity-dependent friction behavior. At low sliding velocity, v_slide = 10 µm/s, the friction coefficient was relatively high (µ = 0.070 ± 0.009) and the presence of stick–slip in the friction-force trace was evident (Fig. 3b).

Increased adhesion at longer dwell times may provide insight into the high friction and stick–slip behavior exhibited by the 1.0 wt.% crosslinked slide-ring gels at v_slide = 10 µm/s. Slow-speed sliding and quasi-static indentations both involve probes spending significant time in contact. For hydrogels, time in persistent contact could greatly exceed the polymer relaxation time and thus lead to high adhesion and hysteresis. The observations that 1.0 wt.% crosslinked gels exhibit the highest W_ad at the longest dwell time t_dwell = 600 s and the highest friction coefficients at the slowest sliding speeds v_slide = 10 µm/s are consistent with the hypothesis that slide-ring crosslink concentration is inversely correlated with network relaxation time. Similarly, W_ad was only moderately sensitive to dwell time (Fig. 2c) and friction coefficients appeared mostly insensitive to sliding velocity (Fig. 3c) for the 1.5 wt.% crosslinked gel. At the slowest sliding velocity, v_slide = 10 µm/s, the 1.5 wt.% crosslinked samples exhibited lower friction coefficients than the 1.0 wt.% crosslinked samples. This agrees with adhesion trends: the 1.5 wt.% crosslinked sample moderately increased W_ad at longer dwell times but increased to a much lesser extent than the 1.0 wt.% crosslinked sample. Differences in the work of adhesion and slow-speed friction may be related to changes in reduced elastic moduli, E*, between the 1.0 wt.% and 1.5 wt.% crosslinked samples. The projected contact area (estimated from Eq. 3) of the moderately softer 1.0 wt.% sample under an applied load of F_n = 1,000 µN is about 130% of the contact area of the 1.5 wt.% crosslinked sample. However, contact area differences likely do not fully account for the roughly 500% difference in adhesion at the highest dwell time or the significant difference in friction coefficient at the slowest sliding speed.

Slide-ring gels represent a class of materials with low modulus and potentially greater capacity for energy dissipation than conventional (fixed-crosslink) polyacrylamide hydrogels. Both slide-ring gel formulations exhibited E* < 20 kPa. The 7.5 wt.%, 12.5 wt.%, and 17.5 wt.% fixed-crosslink polyacrylamide gels spanned reduced elastic moduli of E* = 40 ± 1 kPa, E* = 136 ± 8 kPa, and E* = 226 ± 9 kPa, respectively. The friction coefficient, µ, generally increased with reduced elastic modulus, E*, for both slide-ring and covalently (fixed) crosslinked hydrogels (Fig. 4a). The incorporation of sliding crosslinks is one route to increase mobility in hydrogel networks and achieve both low modulus and low friction. The possibility of dangling chains at the sliding interface may also contribute to lubricity as well as higher adhesion at long dwell times [24].

At the highest sliding velocity and lowest applied force, v_slide = 100 µm/s and F_n = 500 µN, the average friction coefficient was µ = 0.003 ± 0.003 for the 1.0 wt.% crosslinked sample (Fig. 3c). This calculation included data points at the noise floor of friction coefficient measurements, µ ≈ 0.001. Trends in adhesion measurements do not explain the extremely low friction of the 1.0 wt.% crosslinked samples at the highest sliding speed, v_slide = 100 µm/s; both slide-ring gel formulations exhibited similarly low work of adhesion, W_ad, for short dwell times (t_dwell = 0 s or 10 s) yet resulted in significant differences in friction coefficient, µ, for the highest sliding speed, which suggests another mechanism dominates. In the fast-sliding velocity measurement for the 1.0 wt.% crosslinked slide-ring gel, there was no apparent separation between the forward and reverse directions of the friction-force traces, which may be evidence of fluid film entrainment.

To investigate the extent to which low friction coefficients could be due to fluid film lubrication, Eq. 7 was used to calculate the minimum fluid film thickness, h_min [25, 26] to achieve soft elasto-hydrodynamic lubrication (EHL).where η₀ is the viscosity of the fluid (water, η₀ = 8.9 × 10^–4 Pa·s) across the interface, v_slide is the sliding velocity, E* is the reduced elastic modulus of the sample, and F_n is the applied normal force.

Increasing fluid film layer thickness with increasing sliding velocity, v_slide, is a reasonable explanation for the failure of adhesion measurements to predict the difference in friction between the 1.0 wt.% and 1.5 wt.% crosslinked slide-ring gels. Fluid films may have partially separated the sliding interfaces at high v_slide, but not for brief dwell times, t_dwell. Slide-ring gels generally showed decreasing friction coefficients, µ, with increasing h_min, the estimated minimum fluid film thickness (Fig. 4b). The 1.0 wt.% crosslinked formulation had a stronger dependence on h_min than the 1.5 wt.% crosslinked formulation. In contrast, covalently crosslinked hydrogels exhibited increased friction coefficients with larger h_min.

If the combined surface roughness of the probe and gel is less than h_min then the probe may slide on a fluid film layer rather than the gel itself. However, friction-force traces were evaluated for all experiments, and in all but one case (the 1.0 wt.% slide-ring crosslinker at highest sliding velocity), there was clear separation between F_f,fwd and F_f,rev as well as symmetric lateral contact stiffness at the reversals, all which suggest that physical contact was maintained between the probe and gel surfaces for the duration of each sliding cycle. For the single measurement below the noise floor that was previously discussed, no separation was observed between F_f,fwd and F_f,rev. The lack of separation between forward and reverse friction-force traces is evidence that the probe may have been sliding on a fluid film. The corresponding h_min = 65 nm for this measurement (indicated by a dashed green square in Fig. 4b) was the largest h_min estimated across all experiments, which supports the idea that fluid film lubrication is beginning to occur.

Although the soft EHL calculations in this investigation only provide theoretical estimates, h_min remains a valuable parameter that helps describe situations in which fluid film lubrication is more likely to occur (increased v_slide, decreased E*, and decreased F_n). The use of h_min conveniently encompasses all the changes in sliding conditions applied to the slide-ring gels in this study. The stronger dependence of friction on h_min in the 1.0 wt.% crosslinked slide-ring gels with respect to the 1.5 wt.% crosslinked gels can be understood in the context of the adhesion measurements in Fig. 3. Compared to the 1.5 wt.% crosslinked gel, the 1.0 wt.% crosslinked gel was more adhesive at long dwell times and had higher friction at v_slide = 10 µm/s. Increasing h_min by increasing v_slide, decreasing E*, or decreasing F_n would have removed some of these adhesive contacts between the probe and the gel in exchange for contact between the probe and a lubricating layer of water. This likely had a greater impact on the friction of the 1.0 wt.% crosslinked gel due to the increased adhesion between the 1.0 wt.% gel and the glass probe. Furthermore, for high values of h_min, in which there was low contact area between the gel and probe, an incremental increase in h_min would result in a greater percentage reduction in contact area.

Friction between the glass probe and the pseudo-rotaxane gels may proceed through mechanisms of polymer relaxation leading to interfacial drainage (Fig. 5). Dunn et al. hypothesized that friction of hydrogels with soft surface gel layers (E* ≈ 25 kPa) increased with increasing force because the probe crushed the surface gel layer, forcing water out of the contact interface and creating a region of high polymer density at the surface of the gel [27]. In this work, it is unlikely that the applied normal loads led to contact pressures sufficient to collapse the gels. Instead of drainage due to increased force, drainage may proceed due to increased time, facilitating greater adhesion between the probe and gel. As the polymer network remained in persistent contact with the probe, relaxations in the polymer may have preferentially drive water away from regions of higher osmotic pressure to regions of lower osmotic pressure, away from the contacting or sliding interface. Higher polymer density may thus have led to higher friction at slower sliding speeds and lower values of h_min. This hypothesis is supported by the work of Schulze et al. which showed that the increase in adhesion with longer dwell times was due to polymer network relaxations when the applied pressure was less than the osmotic pressure of the gel [28].