Poroelastic indentation of mechanically confined hydrogel layers

Friction through molecular adsorption at the sliding interface of hydrogels: theory and experiments

We report on the frictional properties of thin (≈μm) poly(dimethylacrylamide) hydrogel films within contacts with spherical silica probes. In order to focus on the contribution to friction of interfacial dissipation, a dedicated rotational setup is designed which allows to suppress poroelastic flows while ensuring a uniform velocity field at the sliding interface. The physical-chemistry of the interface is varied from the grafting of various silanes on the silica probes. Remarkably, we identify a velocity range in which the average frictional stress systematically varies with the logarithm of the sliding velocity. This dependency is found to be sensitive to the physical-chemistry of the silica surfaces. Experimental observations are discussed in the light of a molecular model where friction arises from thermally activated adsorption of polymer chains at the sliding interface, their elastic stretching and subsequent desorption. From this theoretical description, our experimental data provide us with adhesion energies and characteristic times for molecular adsorption that are found consistent with the physico-chemistry of the chemically-modified silica surfaces.

Depth profiling via nanoindentation for characterisation of the elastic modulus and hydraulic properties of thin hydrogel layers

The accurate determination of the mechanical properties of hydrogels is of fundamental importance for a range of applications, including in assessing the effect of stiffness on cell behaviour. This is a particular issue when using thin hydrogel layers adherent to stiff substrate supports, as the apparent stiffness can be significantly influenced by the constraint of the underlying impermeable substrate, leading to inaccurate measurements of the elastic modulus and permeability of thin hydrogel layers. This study used depth profiling nanoindentation and a poroelastic model for spherical indentation to identify the elastic moduli and hydraulic conductivity of thin polyacrylamide (PAAm) hydrogel layers (∼27 μm-782 μm thick) on impermeable substrates. The apparent stiffness of thin PAAm layers increased with indentation depth and was significantly greater than those of thicker hydrogels, which showed no influence of indentation depth. The hydraulic conductivity decreased as the geometrical confinement of hydrogels increased, indicating that the fluid became more constrained within the confinement areas. The impact of geometrical confinement on the apparent modulus and hydraulic conductivity of thin PAAm hydrogel layers was then established, and their elastic moduli and intrinsic permeability were determined in relation to this effect. This study offers valuable insights into the mechanical characterisation of thin PAAm hydrogel layers used for the fundamental study of cell mechanobiology.

Mechanical response of a thick poroelastic gel in contactless colloidal-probe rheology

When a rigid object approaches a soft material in a viscous fluid, hydrodynamic stresses arise in the lubricated contact region and deform the soft material. The elastic deformation modifies in turn the flow, hence generating a soft-lubrication coupling. Moreover, soft elastomers and gels are often porous. These materials may be filled with solvent or uncrosslinked polymer chains, and might be permeable to the surrounding fluid, which further complexifies the description. Here, we derive the point-force response of a semi-infinite and permeable poroelastic substrate. Then, we use this fundamental solution in order to address the specific poroelastic lubrication coupling associated with contactless colloidal-probe methods. In particular, we derive the conservative and dissipative components of the force associated with the oscillating vertical motion of a sphere close to the poroelastic substrate. Our results may be relevant for dynamic surface force apparatus and contactless colloidal-probe atomic force microscopy experiments on soft, living and/or fragile materials, such as swollen hydrogels and biological membranes.

Compressive Mechanical Behavior of Partially Oxidized Polyvinyl Alcohol Hydrogels for Cartilage Tissue Repair

Polyvinyl alcohol (PVA) hydrogels are extensively used as scaffolds for tissue engineering, although their biodegradation properties have not been optimized yet. To overcome this limitation, partially oxidized PVA has been developed by means of different oxidizing agents, obtaining scaffolds with improved biodegradability. The oxidation reaction also allows tuning the mechanical properties, which are essential for effective use in vivo. In this work, the compressive mechanical behavior of native and partially oxidized PVA hydrogels is investigated, to evaluate the effect of different oxidizing agents, i.e., potassium permanganate, bromine, and iodine. For this purpose, PVA hydrogels are tested by means of indentation tests, also considering the time-dependent mechanical response. Indentation results show that the oxidation reduces the compressive stiffness from about 2.3 N/mm for native PVA to 1.1 ÷ 1.4 N/mm for oxidized PVA. During the consolidation, PVA hydrogels exhibit a force reduction of about 40% and this behavior is unaffected by the oxidizing treatment. A poroviscoelastic constitutive model is developed to describe the time-dependent mechanical response, accounting for the viscoelastic polymer matrix properties and the flow of water molecules within the matrix during long-term compression. This model allows to estimate the long-term Young's modulus of PVA hydrogels in drained conditions (66 kPa for native PVA and 34-42 kPa for oxidized PVA) and can be exploited to evaluate their performances under compressive stress in vivo, as in the case of cartilage tissue engineering.

Adhesion of fluid infused silicone elastomer to glass

Elastomers swollen with non-polar fluids show potential as anti-adhesive materials. We study the effect of oil fraction and contact time on the adhesion between swollen spherical probes of PDMS (polydimethylsiloxane) and flat glass surfaces. The PDMS probes are swollen with pre-determined amount of 10 cSt silicone oil to span the range where the PDMS is fluid free (via solvent extraction) up to the limit where it is oil saturated. Probe tack measurements show that adhesion decreases rapidly with an increase in oil fraction. The decrease in adhesion is attributed to excess oil present at the PDMS-air interface. Contact angle measurements and optical microscopy images support this observation. Adhesion also increases with contact time for a given oil fraction. The increase in adhesion with contact time can be interpreted through different competing mechanisms that depend on the oil fraction where the dominant mechanism changes from extracted to fully swollen PDMS. For partially swollen PDMS, we observe that adhesion initially increases because of viscoelastic relaxation and at long times increases because of contact aging. In contrast, adhesion between fully swollen PDMS and glass barely increases over time and is mainly due to capillary forces. While the relaxation of PDMS in contact is well-described by a visco-poroelastic model, we do not see evidence that poroelastic relaxation of the PDMS contributes to an increase of adhesion with glass whether it is partially or fully swollen.

Hydroelastomers: soft, tough, highly swelling composites

Inspired by the cellular design of plant tissue, we present an approach to make versatile, tough, highly water-swelling composites. We embed highly swelling hydrogel particles inside tough, water-permeable, elastomeric matrices. The resulting composites, which we call hydroelastomers, combine the properties of their parent phases. From their hydrogel component, the composites inherit the ability to highly swell in water. From the elastomeric component, the composites inherit excellent stretchability and fracture toughness, while showing little softening as they swell. Indeed, the fracture properties of the composite match those of the best-performing, tough hydrogels, exhibiting fracture energies of up to 10 kJ m^-2. Our composites are straightforward to fabricate, based on widely-available materials, and can easily be molded or extruded to form shapes with complex swelling geometries. Furthermore, there is a large design space available for making hydroelastomers, since one can use any hydrogel as the dispersed phase in the composite, including hydrogels with stimuli-responsiveness. These features make hydroelastomers excellent candidates for use in soft robotics and swelling-based actuation, or as shape-morphing materials, while also being useful as hydrogel replacements in other fields.

Lower Critical Solution Temperature Phase Transition of Poly(PEGMA) Hydrogel Thin Films

Surface-attached hydrogel films with well-controlled chemistry are a new approach of polymer thin layers and an actual alternative to polymer brushes and layer-by-layer assemblies. The advantage is that the thickness of hydrogel films can widely range from a few nanometers to several micrometers. Hydrogel films can also remarkably respond to stimuli such as temperature: (i) the thickness change is of great amplitude, fourfold and more, which could not be reached with the geometry of polymer brushes or layer-by-layer assemblies, (ii) the time response is very short (less than 1 s), and (iii) the swelling-to-collapse transition is narrow (a small temperature change of a few degrees may be enough). Poly(N-isopropylacrylamide) (PNIPAM) is the most temperature-responsive polymer investigated with a lower critical solution temperature (LCST) of around 32 °C. However, it is relevant to have the available polymers responding to various transition temperatures with the advantage of keeping the same chemistry. Poly[oligo(ethylene glycol) methacrylate] (PEGMA) meets these specifications since its transition temperature can be finely tuned with the number of oligo ethylene glycol units, while it attractively combines biocompatibility with PEG side chains. Here, we report the synthesis and the temperature-responsive properties of poly(PEGMA) hydrogel thin films. We used a simple, versatile, and well-controlled approach through thiol-ene click reaction, the so-called cross-linking and grafting, to synthesize surface-attached poly(PEGMA) hydrogel films with various thickness. We show that the transition temperature of poly(PEGMA) hydrogel films ranges from 15 to 60 °C if the number of PEG units is from 2 to 5. This transition temperature can also be finely adjusted for hydrogel films containing copolymers or mixing homopolymers of PEGMA with a suitable ratio. Moreover, the LCST properties, swelling-to-collapse amplitude and transition temperature, are not sensitive to salt. In particular, there is no effect on the LCST properties of surface-attached poly(PEGMA) hydrogel films in phosphate saline buffer, which is promising for applications in biology such as injectable hydrogels, drug delivery systems, hydrogel-based microfluidic valves, and flow switches for biotechnologies.

Poroelastic shape relaxation of hydrogel particles

Hydrogels are commonly used in research and energy, manufacturing, agriculture, and biomedical applications. These uses typically require hydrogel mechanics and internal water transport, described by the poroelastic diffusion coefficient, to be characterized. Sophisticated indentation-based approaches are typically used for this purpose, but they require expensive instrumentation and are often limited to planar samples. Here, we present Shape Relaxation (SHARE), an alternative way to assess the poroelastic diffusion coefficient of hydrogel particles that is cost-effective, straightforward, and versatile. This approach relies on first indenting a hydrogel particle via swelling within a granular packing, and then monitoring how the indented shape of the hydrogel relaxes after it is removed from the packing. We validate this approach using experiments in packings with varying grain sizes and confining stresses; these yield measurements of the poroelastic diffusion coefficient of polyacrylamide hydrogels that are in good agreement with those previously obtained using indentation approaches. We therefore anticipate that the SHARE approach will find broad use in a range of applications of hydrogels and other swellable soft materials.

Spinning elastic beads: a route for simultaneous measurements of the shear modulus and the interfacial energy of soft materials

Large deformations of soft elastic beads spinning at high angular velocity in a denser background fluid are investigated theoretically, numerically, and experimentally using millimeter-size polyacrylamide hydrogel particles introduced in a spinning drop tensiometer. We determine the equilibrium shapes of the beads from the competition between the centrifugal force and the restoring elastic and surface forces. Considering the beads as neo-Hookean up to large deformations, we show that their elastic modulus and interfacial energy constant can be simultaneously deduced from their equilibrium shape. Also, our results provide further support to the scenario in which interfacial energy and interfacial tension coincide for amorphous polymer gels.

Poroelasticity of highly confined hydrogel films measured with a surface forces apparatus

The influence of poroelasticity on the contact mechanics of thin polyacrylamide films was investigated with a surface forces apparatus (SFA). A model based on a thin film approximation described compression forces for hydrated gels; polymer scaling theory explained the effects of gel dehydration. The results demonstrate that fluid flow dictates the apparent stiffness of highly confined poroelastic films.

Seeded laser-induced cavitation for studying high-strain-rate irreversible deformation of soft materials

Characterizing the high-strain-rate and high-strain mechanics of soft materials is critical to understanding the complex behavior of polymers and various dynamic injury mechanisms, including traumatic brain injury. However, their dynamic mechanical deformation under extreme conditions is technically difficult to quantify and often includes irreversible damage. To address such challenges, we investigate an experimental method, which allows quantification of the extreme mechanical properties of soft materials using ultrafast stroboscopic imaging of highly reproducible laser-induced cavitation events. As a reference material, we characterize variably cross-linked polydimethylsiloxane specimens using this method. The consistency of the laser-induced cavitation is achieved through the introduction of laser absorbing seed microspheres. Based on a simplified viscoelastic model, representative high-strain-rate shear moduli and viscosities of the soft specimens are quantified across different degrees of crosslinking. The quantified rheological parameters align well with the time-temperature superposition prediction of dynamic mechanical analysis. The presented method offers significant advantages with regard to quantifying high-strain rate, irreversible mechanical properties of soft materials and tissues, compared to other methods that rely upon the cyclic dynamics of cavitation. These advances are anticipated to aid in the understanding of how damage and injury develop in soft materials and tissues.

Transient sliding of thin hydrogel films: the role of poroelasticity

We report on the transient frictional response of contacts between a rigid spherical glass probe and a micrometer-thick poly(dimethylacrylamide) hydrogel film grafted onto a glass substrate when a lateral relative motion is applied to the contact initially at rest. From dedicated experiments with in situ contact visualization, both the friction force and the contact size are observed to vary well beyond the occurrence of a full sliding condition at the contact interface. Depending on the imposed velocity and on the static contact time before the motion is initiated, either an overshoot or an undershoot in the friction force is observed. These observations are rationalized by considering that the transient is predominantly driven by the flow of water within the stressed hydrogel networks. From the development of a poroelastic contact model using a thin film approximation, we provide a theoretical description of the main features of the transient. We especially justify the experimental observation that the relaxation of friction force Ft(t) toward steady state is uniquely dictated by the time-dependence of the contact radius a(t), independently on the sliding velocity and on the applied normal load.

Fractography of poly(N-isopropylacrylamide) hydrogel networks crosslinked with mechanofluorophores using confocal laser scanning microscopy

Employing mechanofluorophores in polymer fractography to obtain new information on force-induced events when analyzed by confocal laser scanning microscopy.

Linking Friction and Surface Properties of Hydrogels Molded Against Materials of Different Surface Energies

Biological tissues subjected to rubbing, such as the cornea and eyelid or articular cartilage, are covered in brushy, hydrated mucous structures in order to reduce the shear stress on the tissue. To mimic such biological tissues, we have prepared polyacrylamide (PAAm) hydrogels with various concentrations of un-cross-linked chains on their surfaces by synthesizing them in molds of different surface energies. The selected molding materials included hydrophilic glass, polyoxymethylene (POM), polystyrene (PS), polyethylene (PE), polypropylene (PP), and polytetrafluoroethylene (PTFE). After synthesis, demolding, and equilibration in water, the elastic modulus at the hydrogel surface decreased with increasing water contact angle of the mold. The softer, brushier surfaces did not completely collapse under compressive pressures up to 10 kPa, remaining better hydrated compared to their denser, cross-linked analogs. The hydrogels with brushier surfaces displayed an order of magnitude lower coefficient of friction than the cross-linked ones, which is attributed to the ability of their near-surface regions to retain larger amounts of liquid at the interface. The characteristic speed-dependent friction of the denser, cross-linked hydrogel surface is compared to the speed-independent friction of the brushy hydrogels and discussed from the perspectives of (elasto)hydrodynamic lubrication, permeability, and shear-induced hydrodynamic penetration depth.

Drying-induced stresses before solidification in colloidal dispersions: in situ measurements

We first report an original setup that enables continuous measurements of stresses induced by the drying of confined drops of complex fluids. This setup is mainly based on a precision scale working with an electromagnetic force compensation technique that provides accurate measurements of forces, while allowing simultaneously controlled evaporation rates, in situ microscopic observations, and thus quantitative estimates of normal stresses. We then performed an extensive study of the drying of a charged colloidal dispersion using this setup. Stress measurements clearly show the emergence of large tensile stresses during drying, well-before the solidification stage evidenced by the invasion of the porous colloidal material by air. Combined measurements of solid deformation and concentration profiles (particle tracking, Raman micro-spectroscopy) help us to demonstrate that these stresses are due to the formation of a solid at a low volume fraction, which further undergoes drying-induced shear deformations up to the colloid close-packing, as also supported by large deformation poroelastic modeling. Above all, our results highlight the importance of repulsive colloidal interactions in the build-up of mechanical stresses during drying.

Swelling Dynamics of Surface-Attached Hydrogel Thin Films in Vapor Flows

Hydrogel coatings absorb water vapor, or other solvents, and, as such, are good candidates for antifog applications. In the present study, the transfer of vapor from the atmosphere to hydrogel thin films is measured in a situation where water vapor flows alongside the coating which is set to a temperature lower than the ambient temperature. The effect of the physico-chemistry of the hydrogel film on the swelling kinetics is particularly investigated. By using model thin films of surface-grafted polymer networks with controlled thickness, varied cross-links density, and varied affinity for water, we were able to determine the effect of the film hygroscopy on the dynamics of swelling of the film. These experimental results are accounted for by a diffusion-advection model that is supplemented with a boundary condition at the hydrogel surface: we show that the latter can be determined from the equilibrium sorption isotherms of the polymer films. Altogether, this paper offers a predictive tool for the swelling kinetics of any hydrophilic hydrogel thin film.

Friction of Poroelastic Contacts with Thin Hydrogel Films

We report on the frictional behavior of thin poly(dimethylacrylamide) hydrogel films grafted on glass substrates in sliding contact with a glass spherical probe. Friction experiments are carried out at various velocities and normal loads applied with the contact fully immersed in water. In addition to friction force measurements, a novel optical setup is designed to image the shape of the contact under steady-state sliding. The velocity dependence of both friction force F_t and contact shape is found to be controlled by a Péclet number, Pe, defined as the ratio of the time τ needed to drain the water out of the contact region to a contact time a/ v, where v is the sliding velocity and a is the contact radius. When Pe < 1, the equilibrium circular contact achieved under static normal indentation remains unchanged during sliding. Conversely, for Pe > 1, a decrease in the contact area is observed together with the development of a contact asymmetry when the sliding velocity is increased. A maximum in F_t is also observed at Pe ≈1. These experimental observations are discussed in the light of a poroelastic contact model based on a thin-film approximation. This model indicates that the observed changes in contact geometry are due to the development of a pore pressure imbalance when Pe > 1. An order-of-magnitude estimate of the friction force and its dependence on normal load and velocity are also provided under the assumption that most of the frictional energy is dissipated by poroelastic flow at the leading and trailing edges of the sliding contact.