Environmental Nanoparticle-Induced Toughening and Pinning of a Growing Crack in a Biopolymer Hydrogel.

We study the interplay between a crack tip slowly propagating through a hydrogel and nanoparticles suspended in its liquid environment. Using a proteinic gel enables us to tune the electrostatic interaction between the network and silica colloids. Thereby, we unveil two distinct, local toughening mechanisms. The primary one is charge independent and involves the convective building of a thin particulate clog, hindering polymer hydration in the crack process zone. When particles and network bear opposite charges, transient adhesive bonding superimposes, permitting the remarkable pinning of a crack by a liquid drop.

Preferential hydration fully controls the renaturation dynamics of collagen in water-glycerol solvents.

Glycerol is one of the additives which stabilize collagen, as well as globular proteins, against thermally induced denaturation --an effect explained by preferential hydration, i.e. by the formation, in water/glycerol solvents, of a hydration layer whose entropic cost favors the more compact triple-helix native structure against the denatured one, gelatin. Quenching gelatin solutions promotes renaturation which, however, remains incomplete, as the formation of a gel network gives rise to growing topological constraints. So, gelatin gels exhibit glass-like dynamical features such as slow aging of their shear modulus and stretched exponential stress relaxation, the study of which gives us access to the re(de)naturation dynamics of collagen. We show that this dynamics is independent of the bulk solvent viscosity and controlled by a single parameter, the undercooling [Formula: see text] below the glycerol-concentration-dependent denaturation temperature. This provides direct proof of i) the presence of a nanometer thick, glycerol-free hydration layer, ii) the high locality of the kinetically limiting process governing renaturation.

Glass-like dynamics of the strain-induced coil/helix transition on a permanent polymer network.

We study the stress response to a step strain of covalently bonded gelatin gels in the temperature range where triple helix reversible crosslink formation is prohibited. We observe slow stress relaxation towards a T-dependent finite asymptotic level. We show that this is assignable to the strain-induced coil → helix transition, previously evidenced by Courty et al. [Proc. Natl. Acad. Sci. U. S. A. 102, 13457 (2005)], of a fraction of the polymer strands. Relaxation proceeds, in a first stage, according to a stretched exponential dynamics, then crosses over to a terminal simple exponential decay. The respective characteristic times τK and τf exhibit an Arrhenius-like T-dependence with an associated energy E incompatibly larger than the activation barrier height for the isomerisation process which sets the clock for an elementary coil → helix transformation event. We tentatively assign this glass-like slowing down of the dynamics to the long-range couplings due to the mechanical noise generated by the local elementary events in this random elastic medium.

Two-step build-up of a thermoreversible polymer network: From early local to late collective dynamics.

We probe the mechanisms at work in the build-up of thermoreversible gel networks, with the help of hybrid gelatin gels containing a controlled density of irreversible, covalent crosslinks (CLs), which we quench below the physical gelation temperature. The detailed analysis of the dependence on covalent crosslink density of both the shear modulus and optical activity evolutions with time after quench enables us to identify two stages of the physical gelation process, separated by a temperature-dependent crossover modulus: (i) an early nucleation regime during which rearrangements of the triple-helix CLs play a negligible role, and (ii) a late, logarithmic aging one, which is preserved, though slowed down, in the presence of irreversible CLs. We show that aging is fully controlled by rearrangements and discuss the implication of our results in terms of the switch from an early, local dynamics to a late, cooperative long-range one.

Microstructuration stages during gelation of gelatin under shear.

We study gelation under shear of aqueous gelatin by measuring the evolution of the apparent viscosity, thus extending the previous study by de Carvalho and Djabourov (W. de Carvalho, M. Djabourov, Rheol. Acta 36, 591 (1997)). From a set of experiments under constant stress, we deduce that the microstructure evolves through the following succession of regimes: i) nucleation and growth until crowding of a microgel suspension; ii) coalescence into strata parallel to the flow; iii) gradual thickening of these strata via transverse cross-linking until the flow finally localizes into two interfacial sliding bands which close sequentially. The transition between these regimes occurs at characteristic viscosity values. This scenario is fully confirmed by experiments performed at constant shear rates. We expect it to be relevant for all materials forming thermoreversible gels.

Cooperative effect of stress and ion displacement on the dynamics of cross-link unzipping and rupture of alginate gels.

We study the effect of nonbinding Na(+) ions on the kinetics of rupture of alginate gels cross-linked by Ca(2+). Wetting a crack tip with a saline solution at physiological concentrations is found to be able to induce a quasi-instantaneous, 10-fold velocity jump. This effect is analyzed with a phenomenological model for the rate-dependent fracture energy in physical gels, extended here to account for the role of ions on the rate of cross-link "unzipping". Ionic interaction is found to act cooperatively with mechanical tension, leading to an enhanced rate of rupture. The kinetics turns out to be second order in counterion concentration. The definition of the reference state requires to take into account counterion condensation due to long-range interactions in the polyelectrolyte gel. Surprisingly, the contribution of the Na(+) ions to the free energy of the activated state is essentially entropic, suggesting that the displacement of Ca(2+) is primarily a steric process, electrostatic interactions being reduced to the constraint of charge conservation. This phenomenon may have important consequences on the rate of degradation of alginate based scaffolds for in vivo tissue regeneration.

A convective instability mechanism for quasistatic crack branching in a hydrogel.

Experiments on quasistatic crack propagation in gelatin hydrogels reveal a new branching instability triggered by wetting the tip opening with a drop of aqueous solvent less viscous than the bulk one. We show that the emergence of unstable branches results from a balance between the rate of secondary crack growth and the rate of advection away from a non-linear elastic region of size G/E , where G is the fracture energy and E the small strain Young modulus. We build a minimal, predictive model that combines mechanical characteristics of this mesoscopic region and physical features of the process zone. It accounts for the details of the stability diagram and lends support to the idea that non-linear elasticity plays a critical role in crack front instabilities.

Interplay between shear loading and structural aging in a physical gelatin gel.

We show that the aging of the mechanical relaxation of a gelatin gel exhibits the same scaling phenomenology as polymer and colloidal glasses. In addition, gelatin is known to exhibit logarithmic structural aging (stiffening). We find that stress accelerates this process. However, this effect is definitely irreducible to a mere age shift with respect to natural aging. We suggest that it is interpretable in terms of elastically aided elementary (coil --> helix) local events whose dynamics gradually slows down as aging increases geometric frustration.

From thermally activated to viscosity controlled fracture of biopolymer hydrogels.

We report on rate-dependent fracture energy measurements over three decades of steady crack velocities in alginate and gelatin hydrogels. We evidence that irrespective of gel thermoreversibility, thermally activated "unzipping" of the noncovalent cross-link zones results in slow crack propagation, prevailing against the toughening effect of viscous solvent drag during chain pull-out, which becomes efficient above a few mm s(-1). We extend a previous model [T. Baumberger et al., Nat. Mater. 5, 552 (2006)] to account for both mechanisms and estimate the microscopic unzipping rates.

Magic angles and cross-hatching instability in hydrogel fracture.

The full 2D analysis of roughness profiles of fracture surfaces resulting from quasistatic crack propagation in gelatin gels reveals an original behavior characterized by (i) strong anisotropy with maximum roughness at V-independent symmetry-preserving angles and (ii) a subcritical instability leading, below a critical velocity, to a cross-hatched regime due to straight macrosteps drifting at the same magic angles and nucleated on crack-pinning network inhomogeneities. Step height values are determined by the width of the strain-hardened zone, governed by the elastic crack blunting characteristic of soft solids with breaking stresses much larger than low strain moduli.

Fracture of a biopolymer gel as a viscoplastic disentanglement process.

We present an extensive experimental study of mode-I, steady, slow crack dynamics in gelatin gels. Taking advantage of the sensitivity of the elastic stiffness to gel composition and history we confirm and extend the model for fracture of physical hydrogels which we proposed in a previous paper (Nature Mater. 5, 552 (2006)), which attributes decohesion to the viscoplastic pull-out of the network-constituting chains. So, we propose that, in contrast with chemically cross-linked ones, reversible gels fracture without chain scission.

Non-Amontons behavior of friction in single contacts.

We report on the frictional properties of a single contact between a glassy polymer lens and a flat silica substrate covered either by a disordered or by a self-assembled alkylsilane monolayer. We find that, in contrast to a widely spread belief, the Amontons proportionality between frictional and normal stresses does not hold. Besides, we observe that the velocity dependence of the sliding stress is strongly sensitive to the structure of the silane layer. Analysis of the frictional rheology observed on both disordered and self-assembled monolayers suggests that dissipation is controlled by the plasticity of a glass-like interfacial layer in the former case, and by pinning of polymer chains on the substrate in the latter one.

Self-healing slip pulses and the friction of gelatin gels.

We present an extensive experimental study and scaling analysis of friction of gelatin gels on glass. At low driving velocities, sliding occurs via propagation of periodic self-healing slip pulses whose velocity is limited by collective diffusion of the gel network. Healing can be attributed to a frictional instability occurring at the slip velocity V=Vc. For V>Vc, sliding is homogeneous and friction is ruled by the shear-thinning rheology of an interfacial layer of thickness of order the (nanometric) mesh size, containing a solution of polymer chain ends hanging from the network. In spite of its high degree of confinement, the rheology of this system does not differ qualitatively from known bulk ones. The observed ageing of the static friction threshold reveals the slow increase of adhesive bonding between chain ends and glass. Such structural ageing is compatible with the existence of a velocity-weakening regime at velocities smaller than Vc, hence with the existence of the healing instability.

Rheological aging and rejuvenation in solid friction contacts.

We study the low-velocity (0.1-100 microm s(-1)) frictional properties of interfaces between a rough glassy polymer and smooth silanized glass, a configuration which gives direct access to the rheology of the adhesive joints in which shear localizes. We show that these joints exhibit the full phenomenology expected for confined quasi-2D soft glasses: they strengthen logarithmically when aging at rest, and weaken (rejuvenate) when sliding. Rejuvenation is found to saturate at large velocities. Moreover, aging at rest is shown to be strongly accelerated when waiting under finite stress below the static threshold.

Jamming creep of a frictional interface.

We measure the displacement response of a frictional multicontact interface between identical polymer glasses to a biased shear force oscillation. We evidence the existence, for maximum forces close below the nominal static threshold, of a jamming creep regime governed by an aging-rejuvenation competition acting within the micrometer-sized contacting asperities. The time dependence of the creep process deviates from the standard Rice-Ruina [J. R. Rice and A. L. Ruina, J. Appl. Mech. 50, 343 (1983)] phenomenology at early times; this suggests the possibility of an aging-rejuvenation competition at much smaller scales, within the nanometer-thick adhesive junctions.

Shear response of a frictional interface to a normal load modulation

We study the shear response of a sliding multicontact interface submitted to a harmonically modulated normal load, without loss of contact. We measure, at low velocities (V<100 &mgr;m s(-1)), the average value &Fmacr; of the friction force and the amplitude of its first and second harmonic components. The excitation frequency (f=120 Hz) is chosen much larger than the natural one, associated with the dynamical aging of the interface. We show the following: (i) In agreement with the engineering thumb rule, even a modest modulation induces a substantial decrease of &Fmacr;. (ii) The Rice-Ruina state and rate model, though appropriate to describe the slow frictional dynamics, must be extended when dealing with our "high" frequency regime. That is, the rheology which controls the shear strength must explicitly account not only for the plastic response of the adhesive junctions between load-bearing asperities, but also for the elastic contribution of the asperities bodies. This "elastoplastic" friction model leads to predictions in excellent quantitative agreement with all our experimental data.