Open Access Article
Ming Jun Lee
a,
Isha Bordawekara and
Rosa M. Espinosa-Marzal
*ab
aDepartment of Materials Science and Engineering, University of Illinois Urbana-Champaign, IL 61801, USA. E-mail: rosae@illinois.edu
bDepartment of Civil and Environmental Engineering, University of Illinois Urbana-Champaign, IL 61801, USA
First published on 11th May 2026
Hydrogels are hydrated polymer networks with promising biomedical applications due to their microstructural similarity to biological tissues at sliding interfaces, such as the articular cartilage. These tissues are highly hydrated, charged, and operate in ionic environments. A fundamental understanding of lubrication at charged hydrogel interfaces is thus essential to advance practical applications. Hydration lubrication has recently been proposed to govern hydrogel lubrication. Here, a thin film of water remains confined under pressure, enabling friction coefficients below 0.01, a condition referred to as superlubricity. Yet, studies of hydration lubrication in hydrogels remain limited. This work investigates positively charged polyvinyl alcohol–chitosan double-network hydrogels as a model system for hydrophilic, positively charged hydrogels. When equilibrated in salt solution, these hydrogels exhibit stronger surface zeta potential and weaker storage modulus. Using atomic force microscopy, we directly image the sliding interface in water and salt solutions while measuring friction with a negatively charged probe. Friction coefficients are highest in water and smallest in NaI solution. The results reveal that hydration (repulsive) forces can dominate over electrostatic attraction and activate superlubricity. This study provides new insights into the mechanisms that govern hydration lubrication in charged hydrogels.
New conceptsSoft material interfaces are ubiquitous in biological tissues. These tissues are hydrated, charged, and immersed in ionic environments. Hydrogels—hydrated polymer networks—closely mimic these characteristics, making them model systems for probing interfacial behavior. Fundamental knowledge of how these surfaces slide in contact is essential to understanding how pain arises from friction or to reduce wear using biocompatible gels. Distinct from prior work, we discover that, despite electrostatic attraction of an oppositely charged hydrogel surface, hydration forces can dominate and endow superlubricity (coefficient of friction <0.01). This effect is enhanced in ionic environments relative to water, with subtle anion-specific effects, as NaI can outperform NaCl. Analysis of the velocity-dependence of friction indicates that hydration lubrication governs hydrogel superlubricity, provided that the hydration repulsion is sufficiently strong. Increasing the ionic strength effectively charges the hydrogels and amplifies this repulsive interaction. Furthermore, the velocity dependence is modulated by the contact size, suggesting a dynamic regulation mechanism of the lubricating film thickness governed by fast rehydration during sliding. |
Numerous studies have explored lubrication mediated by hydrophilic polymers in aqueous environments, with various mechanisms being proposed. Among these, hydration lubrication is widely considered most prevalent and broadly relevant and believed to play a crucial role in achieving superlubricity and minimizing wear in biological systems such as the ocular epithelium and articular joints. Hydration lubrication was originally proposed by Raviv and Klein to explain the lubrication of two negatively charged mica surfaces by a thin film of water containing dissolved salt.5 In aqueous environments, oppositely charged ions–counterions, in this case cations–bind to the charged sites on mica to neutralize the surface charge, while retaining water molecules in their hydration shells. Their results confirmed that the Na-bound water molecules confined between the mica surfaces remain fluid and exhibit low viscosity under shear, leading to friction coefficients µ in the order of 10−3, thereby achieving superlubricity –i.e., µ < 0.01.5,6 This concept was later extended to charged polymers tethered to surfaces–polyelectrolyte brushes– where friction coefficients as low as µ ∼ 6.10−4 were measured under applied pressures up to 0.3 MPa using a surface force balance (SFB). However, multiple mechanisms contributed to the observed low friction, including the repulsive osmotic pressure arising from counterions within the brush film –so called, Donnan osmotic pressure.7 Later, Chen and co-workers studied phosphorylcholine brushes, which contain both positively and negatively charged groups, making them overall neutral in order to eliminate the contribution from Donnan osmotic pressure differences. In this system, friction reduction was attributed solely to shearing the hydration shells surrounding the zwitterionic groups—which was considered to be a manifestation of pure hydration lubrication.8,9 The friction coefficient remained low and approximately constant (µ ∼ 4.10−4) across a range of sliding velocities (2–4000 nm s−1) and pressures (0.3–7.5 MPa), supporting the conclusion that the absence of velocity dependence is a characteristic feature of hydration lubrication. Hydration lubrication has recently been invoked to explain lubrication in hydrogels with incorporated liposomes or grafted polymer brushes,9–11 yet fundamental studies are still scarce.
The velocity-dependence of hydrogel friction is complex. The seminal work by Gong et al.12 proposed that the very strong hydration ability of hydrogels makes it possible to sustain hydrodynamic lubrication, even at low sliding velocity – yet generally higher than in SFB studies – and pressures up to ∼0.5 MPa on repulsive contacts. A prediction based on hydrodynamics led to F ∼ Vn, with n = 1, as in experiments, but underestimated the friction force. Subsequent studies showed the increase of n from 0 to 0.55 with increasing load, and that friction could evolve from velocity-independent to velocity-dependent with increasing velocity.13 According to soft elasto-hydrodynamic lubrication (EHL) theory, friction (F) arises from shear of the interfacial fluid film
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Velocity-independent low friction has been observed for Gemini hydrogel interfaces in tribometer experiments. Gombert et al. showed that polyacrylamide hydrogels molded against a hydrophobic surface terminate in a brush-like layer that is able to retain an interfacial water film even under load.20 When subjected to transient normal load and shear, water is exudated but the interface can easily rehydrate during the out-of-contact phase. This dynamic balance between exudation and rehydration enables the formation of a thick water film. By invoking hydrodynamic lubrication, this thick fluid film reduces shear stress and, consequently, the frictional force, resulting in low, quasi velocity-independent friction. In contrast, when molded against a hydrophilic surface, the hydrogel surface is well crosslinked, and cannot maintain an interfacial fluid film under load. The increase in friction with velocity, F ∼ V0.5–0.7, was associated with the existence of a thin fluid film that yields higher friction based on EHL. Instead, Sawyer's group associated velocity-independent friction with thermal-fluctuation lubrication.16,21 That is the polymer chains create a dynamically blurred interface that can relax the shear stress through random thermal fluctuations, effectively reducing the energy barrier to sliding compared to a rigid interface. The transition to velocity-dependent friction (∝V0.5) at higher velocities could not be rationalized as EHL which predicted much lower friction forces. Here, the dissipation was attributed to the relaxation of strained polymer chains at the contact. Friction measurements by Atomic Force Microscopy have also revealed that the polymer network can contribute to dissipation, particularly at adhesive interfaces, where direct polymer–probe interactions and deformation of the network enhance energy dissipation beyond purely fluid-mediated lubrication.17,22
Pressure-driven fluid flow in hydrogels occurs when the applied pressure exceeds the osmotic pressure of the network, and water is pushed through the polymer network, a condition that generally requires the use of rigid probes.23 The hallmark of poroelastically-driven lubrication is the decrease in friction with increasing sliding velocity, as the time available for fluid drainage is reduced and the contact area gradually decreases. Reale and Dunn's model24 modelled the friction coefficient as a function of the Péclet number and the interfacial energy. Within this framework, decreasing velocity promotes dehydration of the contact, leading to an increase in adhesion energy with the countersurface and, consequently, higher friction. However, pressure-driven fluid flow can also lead to an increase in friction with velocity at sufficiently small sliding velocities, while the contact area remains constant.23
This work focuses on hydrogels composed of uncharged polyvinyl alcohol (PVA), which contains hydroxyl groups that make them highly hydrophilic, combined with chitosan (Cs), which carries amine groups that provide a positive charge in the selected pH range,25 forming a double-network hydrogel. Double-network (DN) hydrogels – pioneered by Gong26– have emerged as an alternative to single-network (SN) hydrogels, because they are stronger and tougher and mimic better the properties of tissues like cartilage, tendon or blood vessels.27 The two networks are usually chemically independent and physically entangled. Entanglement creates a synergistic effect where one network takes on load-bearing while the other provides ductility, together resulting in multifold strengthening over their individual SN hydrogels.26 The charged nature of the double network introduces responsive behavior to added salts, which is leveraged here to probe the underlying lubrication mechanisms. The countersurface (silicon oxide) is negatively charged, resulting in electrostatic attraction between charged hydrogel and the solid surface. This work demonstrates that hydration repulsion can overcome electrostatic attraction and activate superlubricity and reveals subtle anion-specific effects. We further show that hydrogel friction under hydration lubrication can exhibit velocity dependence and propose a regulation mechanism of the film thickness to explain these results.
Water and two salt solutions –NaI and NaCl–were selected for measurements. In hydrogels, salts can cause changes in water content or swelling behavior, which in turn can influence properties like adhesion and friction. Fig. 1d shows the negligible change of the swelling ratio of the hydrogels with salt concentration. The swelling ratio of pure PVA hydrogels (∼50) is much higher than that of chitosan hydrogels (∼15), which suggests that chitosan restricts the swelling of PVA. Hydrogels swell when water diffuses into the network, which results from the competition between (i) a free energy of mixing that includes the affinity between the polymer and water and promotes swelling (Πmix), and (ii) the entropy elasticity (Πel), i.e. the restoring force against polymer stretching, which counters swelling. Counterions in charged hydrogels introduce the so-called (iii) Donnan osmotic pressure difference (ΠDo)–due to the different counterion concentration in the gels and in the surrounding environment–which can both promote and reduce swelling. Additionally, (iv) unscreened charges in the network lead to electrostatic repulsion, which promotes swelling (Πch). The negligible change in swelling ratio indicates a highly entangled structure between the two polymers in the double network.
Although the swelling ratio does not change with salt concentration, the rheological behavior of the hydrogels does, demonstrating the interaction between counterions and polymers; see Fig. 1e and additional experimental results in Fig. S4. The hydrogels behave as viscoelastic solids (G′ > G″) with a rubbery plateau in the range of frequencies between 0.1 Hz and ∼20–30 Hz in water and salt solutions. The loss modulus exhibits only a weak frequency dependence, indicating minimal energy dissipation and suggesting that the physical cross-links remain stable at small deformations under shear. In water, the plateau storage (G′) and loss moduli (G″) of the DN hydrogels are 8.9 ± 2.8 kPa and 0.4 ± 0.1 kPa, respectively. These values are higher than those observed in equilibrium with both NaCl and NaI solutions (G′ ∼ 7.2 ± 2.7 kPa and G″ ∼ 0.2 ± 0.1 kPa), indicating that the double network has been partially weakened. FTIR spectroscopy of the hydrogels in 10 mM NaCl and NaI solutions supports that counterions displace sulfate crosslinkers in the chitosan network (Fig. S5).
Surface charge was indirectly compared via the zeta potential (ζ) measurements using an electrokinetic streaming method. The zeta potential is measured within the electrical double layer (at the slippage plane) rather than directly at the hydrogel surface. Under conditions of conventional electrostatic screening, the surface charge is expected to have the same sign as the zeta potential.34 Zeta potential measurements support the hypothesis that chloride and iodide anions partially substitute the sulfate (SO42−) cross-linkers and weaken the hydrogel; see Fig. 1f. The ζ value in water is close to zero. Upon addition of 0.1 mM NaCl, ζ increases to ∼1 mV and reaches ∼13 mV at 10 mM NaCl. Likewise, ζ increases from ∼4 mV in 0.1 mM NaI to ∼20 mV in 10 mM NaI. Interestingly, the magnitude of ζ in NaI is consistently higher than in NaCl solutions at the same concentration, which may result from differences in the binding affinity of I− and Cl− to chitosan. Indeed, the hydration energy of I− is lower than that of Cl− (−305 kJ mol−1 vs. −381 kJ mol−1),35 which indicates that partial dehydration and substitution of SO4−2 cross-linkers by I− is energetically more favorable. Sulfates are divalent while chloride and iodide are monovalent, and hence, they cannot bridge two amine groups, justifying the partial weakening of the chitosan network and the increase of its positive charge upon addition of salt.
To further investigate the hydrogel interface, a silica microsphere (radius R = 2.1 µm) was glued to the AFM cantilever and used to perform surface force measurements on the hydrogels in a custom-built fluid cell. The surface of the silica microsphere was confirmed to acquire a negative charge in water and in both salt solutions; see Fig. S6.
Fig. 2a and b shows representative force measurements. Fitting the Hertz model to the extension curve at indentation depths of up to 1 µm (black lines), gives elastic moduli of 25.6 ± 7.6 kPa, 20.9 ± 5.6 kPa and 16.4 ± 4.1 kPa, in water, 10 mM NaCl and 10 mM NaI solutions, respectively. The fits deviate from the measurements at low forces, i.e., during compression of the hydrogel's near-surface region, with the discrepancy being much more pronounced in water. The charge of the hydrogel should activate an electrical double layer force,34 which is attractive due to the opposite charge of hydrogel and tip; see estimation in Fig. S7. This is a rough estimate, since the surface potential is unknown, and it neglects potential charge regulation.34 Additional contributions are also expected from the dehydration penalty of the confined counter-ions and from the Donnan osmotic pressure difference, however, an estimation is not possible since the counter-ion number density is unknown. Notably, the near-surface region of the hydrogel is more readily compressed in water; Fig. 2c. This behavior is attributed to stronger net repulsive interaction between the tip and the hydrogel surface in NaCl and NaI solutions. This repulsive surface force is similar to that measured on polymer thin films and brushes that are either charged and/or hydrophilic, i.e. a hydration (polymer-mediated) force.20,36 Here, such repulsion can arise from PVA being strongly hydrophilic, and therefore, strongly hydrated; in addition to the charged chitosan, which also binds strongly to water. Quantitative modeling of the surface force is not feasible, owing both to the complexity of the superposed interactions and to the unknown absolute surface separation in AFM experiments; labeled as “arbitrary zero” in Fig. 2. Furthermore, the higher variability in force–distance curves in water indicates that the surface is more heterogeneous than in NaCl/NaI solution.
Fig. 2d and e also shows representative force curves upon retraction. In this case, the force–distance curves in water show multiple adhesive detachment events, indicating polymer bridge ruptures as the tip retracts from the surface. The pull-off force is estimated to be around −2 nN, though it is not exact due to the multiple detachment events. In 10 mM NaI and 10 mM NaCl, force–distance curves do not show any adhesion, despite the much higher positive zeta potential. Note that the zeta potential accounts for partial screening of surface charge with the counterions. The negligible adhesion in the salt solution than in water supports the action of a repulsive force that dominates over electrostatic attraction.
Friction force measurements were carried out in water, 10 mM NaCl and 10 mM NaI using colloidal tips. Additionally, a Si tip with a nominal radius of 8 nm was thermally annealed and oxidized, resulting in a blunted tip with cap radius R = 107 nm; Fig. S9. The oxidized tip simulates the surface chemistry of the silica microsphere (i.e. SiO2),37 while the smaller radius provides higher spatial resolution than the colloid and applies higher pressures; Table S3. The surface of the blunted tip was also confirmed to acquire a negative charge in water and in both salt solutions; see Fig. S6. As with the colloid, retraction force measurements indicate adhesive interactions in water, while no measurable adhesion was observed in NaCl and NaI solutions; Fig. S8. Loads ranging from 10 nN to 50 nN were applied, corresponding to mean Hertzian pressures between ∼4.7 kPa and ∼9.4 kPa when using the colloid, and between ∼39.9 kPa and ∼68.2 kPa, when using the blunted tip, both in water; Table S2 and S3. Cuccia et al. have demonstrated that hydrogels deformed to a0/R ∼ 0.4 satisfy Hertz contact mechanics.38
In contact mode, the AFM tip slides in forward (trace) and reverse (retrace) direction along a scan line at constant load and velocity before moving to the next scan line, producing trace and retrace height (topographic) images of the sliding interface. Due to the friction force between the sphere and hydrogel surface, the cantilever laterally deflects, and trace and retrace lateral deflection images are concurrently generated. Each friction image results from half of the difference between the lateral deflection images in forward and reverse direction multiplied by the lateral spring constant.33 Comparing friction and topographic images allows us to assess whether the tip probes the polymer network during sliding and deforms it, or loses contact with the surface. Pixel values of all friction images are exported to histograms and fitted by Gaussian distributions to determine the mean friction value and the standard deviation; see details in Materials and methods and SI Text.
Representative friction and topographic images are displayed in Fig. 3 and 4 in function of load and sliding velocity, respectively, while a complete set of images is shown in Fig. S10–S21; note that the color scale of the friction images is the same in all images to facilitate comparison across conditions (see Figure caption). To minimize the variability arising from sample-to-sample differences and examine the influence of the solvent, these friction measurements were performed on multiple pieces sectioned from the same hydrogel sample. First, we describe the results in function of applied load. In water, the colloid appears to track the polymer network and voids (black regions) are visible, where friction is negligible; see also trace and retrace topographic images in Fig. S10. As the load (L) increases to 50 nN, the area covered by voids is reduced, indicating that the tip probes the polymer network better as the pressure increases. The average friction (F) from each image increases linearly from ∼10 pN at L = 10 nN to ∼110 pN at L = 50 nN; Fig. 5a. In 10 mM NaCl, friction is similar at L = 10 nN but there is a noticeable decrease in friction at higher loads, up to a maximum ∼30 pN at L = 50 nN. Similar as in water, the colloidal tip continues to track the polymer network in 10 mM NaCl, but friction images do not change remarkably under an increase in load. In 10 mM NaI, polymer network and voids are not distinguishable, which indicates that the colloidal tip does not track the surface network. This implies that fluid remains between the tip and the hydrogel surface, even under the higher applied load of 50 nN.
With the blunted tip, friction images in water and 10 mM NaCl display a quasi mesh-like pattern, consistent with tracking of the polymer network with higher spatial resolution compared to the colloid. In remarkable contrast, microstructural details are lost in 10 mM NaI, indicating the presence of a fluid film between the tip and the hydrogel surface; see also Fig. S13–S15. Adding salt notably reduces friction at the much higher pressures applied with the blunted tip; Fig. 5c. Note that although the average friction in 10 mM NaCl and 10 mM NaI is similar, the spatial distribution of friction is notably different, and leads to different standard deviations. Friction increases linearly with applied load in the two salt solutions. Deviations from linearity, such as those observed in water, have been reported for hydrogels depending on their composition.39 Among others, they have been attributed to an increase in adhesion,24 which is confirmed here, as well; Fig. 2e and f.
We define a friction coefficient as the slope of the linear regression of F vs. L, consistent with Amonton's law; Fig. 5a and c. In single-asperity friction measurements, the intercept of the linear regression with the Y-axis is attributed to the contribution of adhesion or stiction to friction.40 Note that friction is ≈0 at loads smaller than 20 and 30 nN in NaCl and NaI, respectively. Hence, these results indicate the absence of stiction despite the opposite charge of the two surfaces. The (low-pressure) coefficient of friction (µL) decreases from ≈0.0025 to ≈0.0005, when water is replaced with the salt solution; Fig. 5a. This happens at contact pressures in the range 5.5–9.4 kPa in water and 4.8–8.1 kPa in salt solution; see estimation in Table S2. The high-pressure friction coefficients (µH)–as measured with the blunted tip–are greater than µL and they remain higher in water compared to salt solution (≈0.0082 in water ≈0.0051 in NaCl and 0.0023 in NaI). This is important because, although the electrostatic (electrical double layer) attraction between the hydrogel and the colloid/tip increases in both salt solutions, friction remains higher in water. Indeed, friction measurements suggest that the interaction between the tip and the hydrogel is more repulsive in NaI solution, when the hydrogels are most positively charged. As inferred from Fig. 2, this can be attributed to a strong net (hydration) repulsion that outcompetes the electrostatic attraction. The decrease in friction with added salts cannot be accounted for by the decrease in the elastic modulus; see Fig. S22 for details.
A collection of friction coefficients measured on independent hydrogel samples per condition is shown in Fig. 5e. Hydrogels in water have a highly heterogeneous surface structure, with varying thicknesses of the brushy layer as shown in Fig. 2. This greater variability in surface properties in water is reflected in a larger standard deviation in friction coefficient. Despite this, the reduction in friction coefficient upon addition of salt is robust. In contrast, anion-specific effects (Cl− vs. I−) are smaller than the variability arising from sample-to-sample differences. Such variability is expected in hydrogels and can originate from differences in surface roughness, charge distribution and water content.41
The velocity-dependence of friction was also studied in the range from 5 µm s−1 to 500 µm s−1 under an applied load of 10 nN and 30 nN using a colloid and blunted tip, respectively; see full dataset in Fig. S16–S21 and representative results in Fig. 4. Friction images taken with the colloid poorly display the polymer network, indicating that a fluid film remains confined between the hydrogel surface and the colloid. This can also be inferred from the height channel while sliding (Fig. S16–S18). At lower velocities, the tip resolves taller polymer chains and voids resulting in larger height differences. Upon losing contact the tip, a decrease in height difference is observed in trace and retrace topographic images. Under the higher pressures applied by the blunted tip, the polymer network can be clearly resolved in water. In contrast, the blunt tip loses contact with the hydrogel surface above 20 µm s−1 in NaCl solution, and already at 10 µm s−1 in NaI solution, the most positively charged hydrogel, and despite the negative charge of the tip; see concurrent topographic images in Fig. S19–S21.
Fig. 5b and d shows the average friction (F) as a function of the sliding velocity (V). Under the pressure applied with the colloid (Fig. 5b), the average friction force increases slightly with velocity, remaining within 10–35 pN in all three solutions. We find that F ∝ Vn, where n = 0.33 and 0.38 in water and NaI. The friction force in NaCl seems to be intermediate between the results in water and NaI. Although the standard deviation of the friction measurements is large enough that the data could also be interpreted as velocity-independent, friction measurements on two separate hydrogel samples per solvent condition also display a similar velocity dependence (see Fig. S23, S24 summary of n values in Fig. 5f). Therefore, we assume that this increase in friction with velocity is meaningful, supporting the action of the same underlying lubrication mechanism in water and NaCl/NaI solution if the pressure is sufficiently low.
The decreasing ability to resolve polymer chains and voids in the images with an increase in velocity indicates the presence of a fluid film between the AFM tip and the hydrogel. Furthermore, the fact that hydrogel properties—such as elastic modulus, surface charge (or zeta potential), and the nature of the ions—does not influence the relationship supports that friction is governed by the shear of the fluid. Soft EHL (eqn (1)) predicts F ∝ V0.35, which is close to the fitting parameter, n, (0.33–0.38 in Fig. 5b and 0.36 ± 0.04 in Fig. 5f). The contact area (A) for eqn (1) was estimated based on the Hertz model for small elastic deformation; see details in Table S2. This model neglects viscoelastic deformation of the hydrogel, which is a reasonable approximation based on its rheological behavior under small strains (Fig. 1e). Eqn (1) estimates a film thickness (h) between 2 nm and 30 nm at 10 and 500 µm s−1, respectively, which is smaller than expected based on classical EHL theory. That is, a nanoscopic fluid film—arising from hydration repulsion and consistent with the concept of hydration lubrication—lubricates the contact under small pressures and substantially reduces friction (µL < 0.01), yet exhibits a non-negligible velocity dependence due to the shear of the confined fluid. This analysis assumes that water remains Newtonian and low viscosity (1 mPa s). While this assumption is supported by several studies,5,42 deviations have been also reported: water exhibits viscoelastic behavior under extreme confinement (h < 1.0 nm),43,44 and high shear rates (from 104 to 105 s−1) and oscillation frequencies (5–25 kHz).45 In the present system, the compliant nature of the hydrogel and the comparatively lower frequencies (few Hz) suggest that such conditions are unlikely to be reached.
Concurrently with the increase in the friction coefficient (µL up to ∼0.045, Fig. 5e) when the blunted tip slides on the hydrogel in water under high pressure, friction gradually increases with sliding velocity according to F ∝ Vn, where n ∼ 0.1 in Fig. 5d (n ∼ 0.12 ± 0.08 in Fig. 5f). An estimate of the film thickness based on soft EHL (eqn (1)) for hydrogels in water leads to unreasonably small values of the fluid film (h ∼ 0.017 nm). Friction and topographic images (Fig. 4 and Fig. S19) support the direct contact between the tip and the polymer network, and therefore the absence of a fluid film. As detailed in the SI Text, an adhesive friction model17 also fails to describe the increase in friction with velocity (Fig. S25).
Hydrogels are poroelastic, and as such pressure-driven fluid flow occurs when the applied pressure exceeds the osmotic pressure of the hydrogel. The osmotic pressure of a polymer swollen in equilibrium with a good solvent is close to the shear storage modulus.46 Under the colloid, the estimated mean pressure in water and salt solutions is lower than the hydrogel's shear modulus, suggesting that fluid drainage does not occur; Table S2.46 However, under the load applied by the blunted tip, the estimated mean pressure is higher than the hydrogel's shear modulus (Table S3). This suggests that fluid drainage does occur, if the contact time a/V is greater than the poroelastic relaxation time, τW, which characterizes the pressure-driven fluid flow. Based on the Darcy's law, τW can be roughly estimated from
as a function of mesh size ξ, pressure P, contact radius a, and solvent viscosity ηs (∼1 mPa s). Table S3 estimates the contact mechanics parameters for a blunted tip of different geometries. For example, for a paraboloid shape, under a load of 30 nN, it yields a = 0.41 µm. The mesh size of the hydrogels is ξ ∼ 1 µm (from AFM images), which leads to relaxation times τW ∼ 0.054 µs, much smaller than the contact times, a/V (0.04–0.0008 s), yielding Peclet numbers smaller than 1. There could be a small mesh size that was not visualized in SEM or AFM images, but the largest mesh size will dominate the fluid flow.
Based on the above estimation, poroelastically-driven lubrication is possible.24,46–48 Delavoipière et al.23 used crack growth theory to derive a simple equation for the friction force in function of the poroelastic relaxation time. If
, then
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This model fits the experimental results in water very well (R2 = 0.976, see dashed line in Fig. 5d), considering a low-velocity (static) friction F0, with a fitting parameter τ0 ∼ 0.07 µs, which is a bit larger than the estimated value above. An increase in the viscosity of water under confinement by a factor of 1.5 at most according to ref. 42 or a slightly smaller mesh size would yield a poroelastic relaxation time closer to τ0. The satisfactory agreement between the model parameter and the estimated relaxation time supports the relevance of poroelastically-driven lubrication in this case.
In NaCl and NaI solutions, friction decreases with velocity before leveling off to an approximately constant value, much smaller than in water; Fig. 5d. As described in the Introduction, a decrease in friction with velocity may originate from poroelastically-driven lubrication, if the contact area decreases with increasing velocity.23 However, this requires Peclet numbers greater than 1, which are not reached under the conditions of these experiments
, and therefore, we can exclude poroelastic-driven lubrication in this case. A decrease of friction with increasing velocity can also result from adhesive-dominated friction, either due to an increased interfacial hydration24 and/or from a reduced interfacial strength,12 since bonds between the sliding surfaces cannot form as fast. It is possible that the negative charges on the tip attract positive groups in chitosan at sufficiently slow velocities. However, we refrain from fitting this model to our results because the number of data points is too small, and the contact geometry between the blunted tip and the hydrogel is too complex to be modeled precisely.
More notable is the following quasi plateau (n ∼ 0.04 ± 0.09), which correlates with the absence of direct contact between the blunted tip and the hydrogel network in friction images; Fig. S20 and S21. At Vc ∼ 100 µm s−1, the friction force at small and high pressures in salt solutions reaches approximately the same level, pointing at similar mechanisms. As with the colloid, we propose this is the onset of hydration lubrication, but it is only achieved under high pressure if salt is added to the system. Based on the results from force measurements (Fig. 2), we invoke the action of a strong repulsion that surpasses the effect of the electrostatic attraction and the applied pressure. Such repulsive interaction can thus be justified by (i) the hydrophilic nature of PVA, (ii) the enhanced charge of the hydrogels in salt solution, which binds more water and raises the dehydration penalty under compression,49 and (iii) the Donnan osmotic pressure difference introduced by the higher concentration of counterions at the interface compared to the surrounding solution.
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| Fig. 6 Proposed mechanisms of lubrication. HL denotes hydration lubrication, which occurs with the colloid in water and salt solution, and with the blunted tip in the presence of the salt solution. | ||
The quasi velocity independence of the friction force measured with the blunted tip, in contrast to the velocity-dependent behavior with the colloid probe, is intriguing, given that both are governed by lubrication through a nanoscopic fluid film–originating from hydration forces–that prevents direct contact between the polymer network and the rigid probe. A recent study by Klein et al. attributed the velocity-dependence of friction to the crosslinking characteristics of the interface.9 Specifically, at brushier (vs. more crosslinked) interfaces, self-regulating interpenetration of opposing polymer chains at higher sliding velocities can offset increased energy dissipation, resulting in a weaker dependence of friction on velocity. In the hydrogel-tip configuration, however, an interpenetration zone is not possible, and velocity-independent friction is observed only with the blunt tip. This suggests a different mechanism governing the regulation of the film thickness. We posit that the smaller contact area between the blunted tip and the hydrogel surface enhances rehydration (i.e. the increase in film thickness h with velocity) during sliding relative to the colloidal tip, for the same molecular relaxation process, provided that the hydration repulsion exceeds the applied pressure. This mechanism can account for the observed plateau with the blunted tip, (F ∝ V/h ∼ V0), in contrast to the power law measured with the colloid (F ∝ V0.35). At sufficiently high sliding velocities, a transition to velocity-dependent friction may be expected even for the blunted tip; however, such a transition is not observed within the experimental range explored here (up to 500 µm s−1).
It is possible to estimate the energy required for the dehydration of the protonated amines in chitosan and PVA to support the mechanism of hydrogel hydration lubrication. The dehydration penalty of the hydroxyl groups in PVA should contribute to the repulsive interaction between tip and hydrogel interface. Taking the hydration enthalpy of vinyl alcohol (VA), ΔHhyd ≈ −30 kJ mol−1 (ref. 52) and the VA concentration per unit volume in the hydrogels (c = 454.5 mol m−3), yields a dehydration penalty within a slab of ∼0.4 nm (size of VA) in thickness equal to Ehyd ≈ 0.00544 J m−2. Applying the Derjaguin approximation, the corresponding repulsive barrier or force can be estimated from Fwhyd = 2πREhyd and it is Fwhyd ≈ 68.4 nN in the case of the colloid, which is higher than the applied force in our experiments, supporting the action of a strong hydration repulsion (i). While this is only a rough estimation, it indicates that the order of magnitude of the hydration repulsion is relevant to the forces applied in AFM experiments.
Adding salt activates an additional dehydration penalty (ii). The effective surface charge density σeff of the hydrogels is related to the surface potential ϕ0 by the Grahame equation.34 Since ϕ0 is unknown, we use the zeta potential ζ to get a rough estimate of σeff,53
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When comparing measurements performed on the same hydrogel sample (Fig. 5a–d), hydration lubrication is most effective in NaI solution, revealing subtle anion-specific effects. Based on the considerations above, the smaller magnitude of ζ in NaCl relative to NaI is expected to result in weaker hydration repulsion and a lower osmotic pressure associated with Cl− counterions. This provides a rationale for why the tip can approach closer to the hydrogel surface in NaCl than in NaI, as inferred from AFM images.
Fig. 5e and f compares friction coefficients (µL and µH) and power-law exponents (n) obtained from measurements across different hydrogel samples using multiple tips. While the coefficient of friction is consistently lower in salt solutions than in water, the standard deviation arising from sample-to-sample variability exceeds the effect of the salt composition. Consequently, variations in surface properties among different hydrogel samples obscure the anion-specific effects. The freeze-thawing method to synthesize physically crosslinked PVA-based gels commonly results in a highly heterogeneous surface due to ice crystal formation and melting, creating heterogeneous PVA crystallite distribution and asymmetric large pores during thawing.55 The combination of these processes can result in highly rough and porous hydrogel surface.
Long-term stability is critical for the application of PVA-based hydrogels. Previous studies have reported an initial dissolution of the PVA phase and melting of crystallites over time, followed by recrystallization upon aging, which can lead to solvent exclusion.56 In the investigated double-network hydrogels, chitosan was shown to substantially influence the microstructure, including the formation and stability of PVA crystallites, and may therefore enhance long-term stability. While the conclusions presented here are robust for hydrogels investigated up to 3 weeks after synthesis, the long-term stability and potential wear under extended tribological loading (e.g., hundreds to thousands of cycles) have not yet been evaluated and remain important directions for future investigation.
The data supporting this article have been included as part of the supplementary information (SI). Supplementary information is available. See DOI: https://doi.org/10.1039/d5mh02460a.
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