Fewer polymer chains but higher adhesion: How gradient-stiffness hydrogel layers mediate adhesion through network stretch.

The presence of gradient softer outer layers, commonly observed in biological systems (such as cartilage and ocular tissues), as well as synthetic crosslinked hydrogels, profoundly influences their interactions with opposing surfaces. Our prior research demonstrated that gradient-stiffness hydrogel layers, characterized by increasing elasticity with depth, control contact mechanics, particularly in proximity to the layer thickness. We postulate that the distribution of polymers within these gradient layers imparts extraordinary stretch and adhesion characteristics due to network adaptability and stress-induced reorganization. To investigate this phenomenon, we utilized Atomic Force Microscopy nanoindentation to assess the depth-dependent adhesion behavior of polyacrylamide hydrogels with varying gradient layer thicknesses. Two gradient layer thicknesses were achieved by employing different molding materials: glass and polyoxymethylene (POM). Glass-molded hydrogels exhibited a thinner gradient layer alongside a stiffer bulk layer compared to their POM-molded counterparts. In indentation experiments, the POM-molded hydrogel had larger adhesion compared to glass-molded hydrogel. We find that indenting within the gradient layer engenders increased load-unload hysteresis due to heightened fluid transport in the sparse outer polymer network. Consequently, this led to augmented adhesion and work of separation at shallow depths. We suggest that the prominent stretching capability of the sparse outer polymer network during probe retraction contributes to enhanced adhesion. The Maugis-Dugdale adhesive model only fits well to indentations on the thin layer or indentations which engage significantly with the bulk. These results facilitate a comprehensive characterization of adhesion mechanics in gradient-stiffness hydrogels, which could foster their application across emerging contexts in health science and environmental domains.

Composition controls soft hydrogel surface layer dimensions and contact mechanics.

Hydrogels are soft hydrated polymer networks that are widely used in research and industry due to their favorable properties and similarity to biological tissues. However, it has long been difficult to create a hydrogel emulating the heterogeneous structure of special tissues, such as cartilage. One potential avenue to develop a structural variation in a hydrogel is the "mold effect," which has only recently been discovered to be caused by absorbed oxygen within the mold surface interfering with the polymerization. This induces a dilute gradient-density surface layer with altered properties. However, the precise structure of the gradient-surface layer and its contact response have not yet been characterized. Such knowledge would prove useful for designs of composite hydrogels with altered surface characteristics. To fully characterize the hydrogel gradient-surface layer, we created five hydrogel compositions of varying monomer and cross-linker content to encompass variations in the layer. Then, we used particle exclusion microscopy during indentation and creep experiments to probe the contact response of the gradient layer of each composition. These experiments showed that the dilute structure of the gradient layer follows evolving contact behavior allowing poroelastic squeeze-out at miniscule pressures. Stiffer compositions had thinner gradient layers. This knowledge can potentially be used to create hydrogels with a stiff load-bearing bulk with altered surface characteristics tailored for specific tribological applications.

Soft Contact Mechanics with Gradient-Stiffness Surfaces.

The stiffness in the top surface of many biological entities like cornea or articular cartilage, as well as chemically cross-linked synthetic hydrogels, can be significantly lower or more compliant than the bulk. When such a heterogeneous surface comes into contact, the contacting load is distributed differently from typical contact models. The mechanical response under indentation loading of a surface with a gradient of stiffness is a complex, integrated response that necessarily includes the heterogeneity. In this work, we identify empirical contact models between a rigid indenter and gradient elastic surfaces by numerically simulating quasi-static indentation. Three key case studies revealed the specific ways in which (I) continuous gradients, (II) laminate-layer gradients, and (III) alternating gradients generate new contact mechanics at the shallow-depth limit. Validation of the simulation-generated models was done by micro- and nanoindentation experiments on polyacrylamide samples synthesized to have a softer gradient surface layer. The field of stress and stretch in the subsurface as visualized from the simulations also reveals that the gradient layers become confined, which pushes the stretch fields closer to the surface and radially outward. Thus, contact areas are larger than expected, and average contact pressures are lower than predicted by the Hertz model. The overall findings of this work are new contact models and the mechanisms by which they change. These models allow a more accurate interpretation of the plethora of indentation data on surface gradient soft matter (biological and synthetic) as well as a better prediction of the force response to gradient soft surfaces. This work provides examples of how gradient hydrogel surfaces control the subsurface stress distribution and loading response.

Nonlinear elasticity and damping govern ultrafast dynamics in click beetles.

Many small animals use springs and latches to overcome the mechanical power output limitations of their muscles. Click beetles use springs and latches to bend their bodies at the thoracic hinge and then unbend extremely quickly, resulting in a clicking motion. When unconstrained, this quick clicking motion results in a jump. While the jumping motion has been studied in depth, the physical mechanisms enabling fast unbending have not. Here, we first identify and quantify the phases of the clicking motion: latching, loading, and energy release. We detail the motion kinematics and investigate the governing dynamics (forces) of the energy release. We use high-speed synchrotron X-ray imaging to observe and analyze the motion of the hinge's internal structures of four Elater abruptus specimens. We show evidence that soft cuticle in the hinge contributes to the spring mechanism through rapid recoil. Using spectral analysis and nonlinear system identification, we determine the equation of motion and model the beetle as a nonlinear single-degree-of-freedom oscillator. Quadratic damping and snap-through buckling are identified to be the dominant damping and elastic forces, respectively, driving the angular position during the energy release phase. The methods used in this study provide experimental and analytical guidelines for the analysis of extreme motion, starting from motion observation to identifying the forces causing the movement. The tools demonstrated here can be applied to other organisms to enhance our understanding of the energy storage and release strategies small animals use to achieve extreme accelerations repeatedly.

Cartilage-like tribological performance of charged double network hydrogels.

A synthetic hydrogel material may offer utility as a cartilage replacement if it is able to maintain low friction in different sliding environments and achieve bulk mechanical properties to withstand the severe environment of the joint. In this work, we compared the tribological behavior of four double network (DN) hydrogels to that of fresh porcine cartilage in both water and fetal bovine serum (FBS). The DN hydrogels were comprised of a negatively charged 1st network and a 2nd network wherein comonomers of varying charge (i.e. neutral, positive, negative, and zwitterionic) were introduced at 10 wt% to an otherwise neutral network. A steel ball probe was used to perform microindentation tests to determine the surface elastic modulus of the samples and estimate their contact areas during sliding. Friction tests using a stationary probe with a stage that reciprocated at a range of speeds were performed to develop lubrication curves in both water and FBS. We found that the DN hydrogels with a neutral or zwitterionic 2nd network had the lowest friction and shear stresses, notably below that of cartilage. The differences in charge and structure of the samples were more evident in water than in FBS, as the lubrication responses for all the hydrogels spanned a wider range of values. In FBS, the lubrication responses were pushed towards elasto-hydrodynamics with nearly all friction coefficient values falling below 0.3. This indicates that the FBS interacts with the hydrogels and cartilage samples in a similar manner as that of cartilage by maintaining a robust layer of solution at the interface during sliding. These DN hydrogels prove to fulfill, and in some cases surpass, the lubrication demands for cartilage replacement in load bearing joints.

Precise Correlation of Contact Area and Forces in the Unstable Friction between a Rough Fluoroelastomer Surface and Borosilicate Glass.

Stick-slip friction of elastomers arises due to adhesion, high local strains, surface features, and viscous dissipation. In situ techniques connecting the real contact area to interfacial forces can reveal the contact evolution of a rough elastomer surface leading up to gross slip, as well as provide high-resolution dynamic contact areas for improving current slip models. Samples with rough surfaces were produced by the same manufacturing processes as machined seals. In this work, a machined fluoroelastomer (FKM) hemisphere was slid against glass, and the stick-slip behavior was captured optically in situ. The influence of sliding velocity on sliding behavior was studied over a range of speeds from 1 µm/s to 100 µm/s. The real contact area was measured from image sequences thresholded using Otsu's method. The motion of the pinned region was delineated with a machine learning scheme. The first result is that, within the macroscale sticking, or pinned phase, local pinned and partial slip regions were observed and modeled as a combined contact with contributions to friction by both regions. As a second result, we identified a critical velocity below which the stick-slip motion converted from high frequency with low amplitude to low frequency with high amplitude. This study on the sliding behavior of a viscoelastic machined elastomer demonstrates a multi-technique approach which reveals precise changes in contact area before and during pinning and slip.

An indentation-based approach to determine the elastic constants of soft anisotropic tissues.

Characterization of the mechanical properties of tissue can help to understand tissue mechanobiology, including disease diagnosis and progression. Indentation is increasingly used to measure the local mechanical properties of tissue, but it has not been fully adapted to capture anisotropic properties. This paper presents an indentation-based method to measure elastic constants of soft anisotropic tissues without additional mechanical tests. The approach uses measurement of the indentation modulus and the aspect ratio of the elliptical contact introduced by anisotropic mechanical properties of tissue to determine the elastic constants from finite element analysis. The imprinted area imparted by a fluorescent bead-coated spherical indenter showed the aspect ratio of the contact area, giving a generalized sense of the level of anisotropy, and instrumented indentation determined the indentation modulus. A parametric study using finite element simulation of the indentation tests established the relationship between the aspect ratio of contact and the non-dimensional ratios, Ex/Ey and Gxy/Ey; here, Ex and Ey are the Young's moduli (Ex > Ey) and Gxy is the shear modulus in the xy plane. For strongly anisotropic materials (Ex/Ey > 150), aspect ratio and indentation modulus are sufficient to determine Gxy and Ey. For weakly anisotropic materials, indentation modulus in the transverse direction, Ey, and the aspect ratio of contact in the anisotropic plane can be used to determine the elastic constants. The proposed approach improves the elastic characterization of soft, anisotropic biological materials from indentation and helps to elucidate the complex mechanical behavior of soft anisotropic tissues.

Self-regenerating compliance and lubrication of polyacrylamide hydrogels.

Pristine hydrogel surfaces typically have low friction, which is controlled by composition, slip speeds, and immediate slip history. The stiffness of such samples is typically measured with bulk techniques, and is assumed to be homogeneous at the surface. While the surface properties of homogeneous hydrogel samples are generally controlled by composition, the surface also interfaces with the open bath, which distinguishes it from the bulk. In this work, we disrupt as-molded polyacrylamide surfaces with abrasive wear and connect the effects on the surface stiffness and lubrication to the wear events. At both the nanoscale and the microscale, quasistatic indentations reveal a stiffer surface by up to two times following wear events, even considering roughness. Longitudinal experiments with a series of wear episodes interposed with periods of re-equilibration show that increased stiffness is reversible: more compliant surfaces regenerate within 24 hours. The timescale suggests an osmotic swelling mechanism, and we postulate that abrasive wear removes a swollen surface layer, revealing the stiffer bulk. The newly-revealed bulk becomes the surface, which re-swells over time. We quantify the effects on the self-lubricating ability of these surfaces following abrasive wear using micro-tribometry. The lubrication curve shows that robust low friction is maintained, and that the friction becomes less dependent upon the sliding speed. The unique ability of these materials to regenerate swollen surfaces and maintain robust low friction following abrasive wear is promising for designing their slip behavior into aqueous soft robotics components or biomedicine applications.

Latching of the click beetle (Coleoptera: Elateridae) thoracic hinge enabled by the morphology and mechanics of conformal structures.

Elaterid beetles have evolved to 'click' their bodies in a unique maneuver. When this maneuver is initiated from a stationary position on a solid substrate, it results in a jump not carried out by the traditional means of jointed appendages (i.e. legs). Elaterid beetles belong to a group of organisms that amplify muscle power through morphology to produce extremely fast movements. Elaterids achieve power amplifications through a hinge situated in the thoracic region. The actuating components of the hinge are a peg and mesosternal lip, two conformal parts that latch to keep the body in a brace position until their release, the 'click', that is the fast launch maneuver. Although prior studies have identified this mechanism, they were focused on the ballistics of the launched body or limited to a single species. In this work, we identify specific morphological details of the hinges of four click beetle species - Alaus oculatus, Parallelostethus attenuatus, Lacon discoideus and Melanotus spp. - which vary in overall length from 11.3 to 38.8 mm. Measurements from environmental scanning electron microscopy (ESEM) and computerized tomography (CT) were combined to provide comparative structural information on both exterior and interior features of the peg and mesosternal lip. Specifically, ESEM and CT reveal the morphology of the peg, which is modeled as an Euler-Bernoulli beam. In the model, the externally applied force is estimated using a micromechanical experiment. The equivalent stiffness, defined as the ratio between the applied force and the peg tip deflection, is estimated for all four species. The estimated peg tip deformation indicates that, under the applied forces, the peg is able to maintain the braced position of the hinge. This work comprehensively describes the critical function of the hinge anatomy through an integration of specific anatomical architecture and engineering mechanics for the first time.

Compliant and stretchable thermoelectric coils for energy harvesting in miniature flexible devices.

With accelerating trends in miniaturization of semiconductor devices, techniques for energy harvesting become increasingly important, especially in wearable technologies and sensors for the internet of things. Although thermoelectric systems have many attractive attributes in this context, maintaining large temperature differences across the device terminals and achieving low-thermal impedance interfaces to the surrounding environment become increasingly difficult to achieve as the characteristic dimensions decrease. Here, we propose and demonstrate an architectural solution to this problem, where thin-film active materials integrate into compliant, open three-dimensional (3D) forms. This approach not only enables efficient thermal impedance matching but also multiplies the heat flow through the harvester, thereby increasing the efficiencies for power conversion. Interconnected arrays of 3D thermoelectric coils built using microscale ribbons of monocrystalline silicon as the active material demonstrate these concepts. Quantitative measurements and simulations establish the basic operating principles and the key design features. The results suggest a scalable strategy for deploying hard thermoelectric thin-film materials in harvesters that can integrate effectively with soft materials systems, including those of the human body.

Mechanically-Guided Deterministic Assembly of 3D Mesostructures Assisted by Residual Stresses.

Formation of 3D mesostructures in advanced functional materials is of growing interest due to the widespread envisioned applications of devices that exploit 3D architectures. Mechanically guided assembly based on compressive buckling of 2D precursors represents a promising method, with applicability to a diverse set of geometries and materials, including inorganic semiconductors, metals, polymers, and their heterogeneous combinations. This paper introduces ideas that extend the levels of control and the range of 3D layouts that are achievable in this manner. Here, thin, patterned layers with well-defined residual stresses influence the process of 2D to 3D geometric transformation. Systematic studies through combined analytical modeling, numerical simulations, and experimental observations demonstrate the effectiveness of the proposed strategy through ≈20 example cases with a broad range of complex 3D topologies. The results elucidate the ability of these stressed layers to alter the energy landscape associated with the transformation process and, specifically, the energy barriers that separate different stable modes in the final 3D configurations. A demonstration in a mechanically tunable microbalance illustrates the utility of these ideas in a simple structure designed for mass measurement.

Poroelasticity-driven lubrication in hydrogel interfaces.

It is widely accepted that hydrogel surfaces are slippery, and have low friction, but dynamic applied stresses alter the hydrogel composition at the interface as water is displaced. The induced osmotic imbalance of compressed hydrogel which cannot swell to equilibrium should drive the resistance to slip against it. This paper demonstrates the driving role of poroelasticity in the friction of hydrogel-glass interfaces, specifically how poroelastic relaxation of hydrogels increases adhesion. We translate the work of adhesion into an effective surface energy density that increases with the duration of applied pressure from 10 to 50 mJ m-2, as measured by micro-indentation. A model of static friction coefficient is derived from an area-based rules of mixture for the surface energies, and predicts the friction coefficient changes upon initiation of slip. For kinetic friction, the competition between duration of contact and relaxation time is quantified by a contacting Péclet number, PeC. A single length parameter on the scale of micrometers fits these two models to experimental micro-friction data. These models predict how short durations of applied pressure and faster sliding speeds, do not disrupt interfacial hydration; this prevailing water maintains low friction. At low speeds where interface drainage dominates, the osmotic suction works against slip for higher friction. The prediction of friction coefficients after adhesion characterization by micro-indentation makes use of the interplay between poroelasticity, adhesion, and friction. This approach provides a starting point for prediction of, and design for, hydrogel interfacial friction.

Publisher's Note: Multicellular density fluctuations in epithelial monolayers [Phys. Rev. E 92, 032729 (2015)].

This corrects the article DOI: 10.1103/PhysRevE.92.032729.

Soft hydrated sliding interfaces as complex fluids.

Hydrogel surfaces are biomimics for sensing and mobility systems in the body such as the eyes and large joints due to their important characteristics of flexibility, permeability, and integrated aqueous component. Recent studies have shown polymer concentration gradients resulting in a less dense region in the top micrometers of the surface. Under shear, this gradient is hypothesized to drive lubrication behavior due to its rheological similarity to a semi-dilute polymer solution. In this work we map 3 distinct lubricating regimes between a polyacrylamide surface and an aluminum annulus using stepped-velocity tribo-rheometry over 5 decades of sliding speed in increasing and decreasing steps. These regimes, characterized by weakly or strongly time-dependent response and thixotropy-like hysteresis, provide the skeleton of a lubrication curve for hydrogel-against-hard material interfaces and support hypotheses of polymer mechanics-driven lubrication. Tribo-rheometry is particularly suited to uncover the lubrication mechanisms of complex interfaces such as are formed with hydrated hydrogel surfaces and biological surfaces.

Kinetics of aqueous lubrication in the hydrophilic hydrogel Gemini interface.

The exquisite sliding interfaces in the human body share the common feature of hydrated dilute polymer mesh networks. These networks, especially when they constitute a sliding interface such as the pre-corneal tear film on the ocular interface, are described by the molecular weight of the polymer chains and a characteristic size of a minimum structural unit, the mesh size, ξ. In a Gemini interface where hydrophilic hydrogels are slid against each other, the aqueous lubrication behavior has been shown to be a function of sliding velocity, introducing a sliding timescale competing against the time scales of polymer fluctuation and relaxation at the surface. In this work, we examine two recent studies and postulate that when the Gemini interface slips faster than the single-chain relaxation time, chains must relax, suppressing the amplitude of the polymer chain thermal fluctuations.

Multicellular density fluctuations in epithelial monolayers.

Changes in cell size often accompany multicellular motion in tissue, and cell number density is known to strongly influence collective migration in monolayers. Density fluctuations in other forms of active matter have been explored extensively, but not the potential role of density fluctuations in collective cell migration. Here we investigate collective motion in cell monolayers, focusing on the divergent component of the migration velocity field to probe density fluctuations. We find spatial patterns of diverging and converging cell groups throughout the monolayers, which oscillate in time with a period of approximately 3-4 h. Simultaneous fluorescence measurements of a cytosol dye within the cells show that fluid passes between groups of cells, facilitating these oscillations in cell density. Our findings reveal that cell-cell interactions in monolayers may be mediated by intercellular fluid flow.

A novel method for low load friction testing on living cells.

A low load tribology technique for studying the effects of friction on living cells was developed. Results show a direct relationship between the coefficient of friction (COF) and the extent of cell damage. The COF, mu, for a glass pin on an intact layer of human corneal epithelial cells is determined to be on the order of mu = 0.05 +/- 0.02 (n = 16). The correlations between applied normal load and extent of cell damage, as well as between number of reciprocation cycles and cell damage, are reported. It is also found that cell damage can occur when a loading force as low as 0.5 mN is applied, although the cells appear to be intact.

A biphasic model for micro-indentation of a hydrogel-based contact lens.

The stiffness and hydraulic permeability of soft contact lenses may influence its clinical performance, e.g., on-eye movement, fitting, and wettability, and may be related to the occurrence of complications; e.g., lesions. It is therefore important to determine these properties in the design of comfortable contact lenses. Micro-indentation provides a nondestructive means of measuring mechanical properties of soft, hydrated contact lenses. However, certain geometrical and material considerations must be taken into account when analyzing output force-displacement (F-D) data. Rather than solely having a solid response, mechanical behavior of hydrogel contact lenses can be described as the coupled interaction between fluid transport through pores and solid matrix deformation. In addition, indentation of thin membranes ( approximately 100 microm) requires special consideration of boundary conditions at lens surfaces and at the indenter contact region. In this study, a biphasic finite element model was developed to simulate the micro-indentation of a hydrogel contact lens. The model accounts for a curved, thin hydrogel membrane supported on an impermeable mold. A time-varying boundary condition was implemented to model the contact interface between the impermeable spherical indenter and the lens. Parametric studies varying the indentation velocities and hydraulic permeability show F-D curves have a sensitive region outside of which the force response reaches asymptotic limits governed by either the solid matrix (slow indentation velocity, large permeability) or the fluid transport (high indentation velocity, low permeability). Using these results, biphasic properties (Young's modulus and hydraulic permeability) were estimated by fitting model results to F-D curves obtained at multiple indentation velocities (1.2 and 20 microm/s). Fitting to micro-indentation tests of Etafilcon A resulted in an estimated permeability range of 1.0 x 10(-15) to 5.0 x 10(-15) m(4)N s and Young's modulus range of 130 to 170 kPa.