Physically assembled gels have promising applications in many fields because of their tunable mechanical properties. Here, we report the mechanical properties as a function of polymer volume fraction ($ϕ$) for a physical gel system consists of poly(styrene)-poly(isoprene)-poly(styrene) [PS-PI-PS] in mineral oil. The PI-block molecular weight is higher than the entanglement molecular weight, which leads to the entanglement of PI-blocks at higher $ϕ$. The micellar microstructure for all gels results in a similar stress relaxation mechanism, as captured by the superposition of stress-relaxation results. Tensile testing experiments reveal a strain-rate dependence mechanical response for the entangled gels. To capture the critical energy release rate ($Γ_0$) over a range of $ϕ$, both cavitation rheology and fracture experiments were performed and we obtain $Γ_0\simϕ^{2.0}$. The gel moduli scale with the volume fraction as $ϕ^{2.39}$, where the exponent is likely dictated by the change in loop-to-bridge fraction with increasing $ϕ$.
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 Materials, doi:10.1038/nmat1666 (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.
A droplet of surfactant spreading on an ultrasoft ($E \lesssim 100$ Pa) gel substrate will produce capillary fractures at the gel surface; these fractures originate at the contact-line and propagate outwards in a starburst pattern. There is an inherent variability in both the number of fractures formed and the time delay before fractures form. In the regime where single fractures form, we observe a Weibull-like distribution of delay times, consistent with a thermally-activated process. The shape parameter is close to 1 for softer gels (a Poisson process), and larger for stiffer gels (indicativ…
We analyze the evolution of the mechanical response of a colloidal suspension to an external tensile stress, from fracture to flow, as a function of the distance from the sol-gel transition. We cease to observe cracks at a finite distance from the transition. In an intermediate region where the phenomenon is clearly hysteretic, we observe the coexistence of both flow and fracture. Even when cracks are observed, the material in fact flows over a distance that increases in the vicinity of the transition.
To clarify effects of crack speed and cross-link density on fracture energy of acrylamide gels, we evaluated the roughness of the fracture surface and measured the fracture energy taking into account the roughness. The fracture energy increases linearly with crack speed $V$ in a fast crack speed region, and the increasing rate of fracture energy with $V$ decreases with increasing cross link density in the gels. In a slow crack speed region the fracture energy depends on crack speed more strongly than in the fast crack speed region. This indicates that a qualitative change exists in fracture pr…
The liquid-liquid phase separation of a binary solvent can be arrested by colloidal particles trapped at the interface [K. Stratford et al., Science 309, 5744 (2005)]. We show experimentally that the colloidal network so formed can remain stable after fully remixing the liquids, creating a new type of gel in which colloids in a single-phase solvent have locally planar coordination. We argue that this structure is likely maintained by primary-minimum DLVO bonding of our charged colloids, created under strong compression by capillary forces. We present simulation evidence that the combination of…
We study the nonlinear rheology of a novel class of transient networks, made of surfactant micelles of tunable morphology reversibly linked by block copolymers. We couple rheology and time-resolved structural measurements, using synchrotron radiation, to characterize the highly nonlinear viscoelastic regime. We propose the fluctuations of the degree of alignment of the micelles under shear as a probe to identify a fracture process. We show a clear signature of a brittle-to-ductile transition in transient gels, as the morphology of the micelles varies, and provide a parallel between the fractur…
We have carried out systematic fracture experiments in a single edge notch geometry over a range of stretch rates on dual crosslink hydrogels made from polyvinyl alcohol chains chemically crosslinked with glutaraldehyde and physically crosslinked with borate ions. If the energy release rate necessary for crack propagation was calculated conventionally, by using the work done to deform the sample to the critical value of stretch $λ_c$ where the crack propagates, we found that the fracture energy $Γ$ peaks around $λ\sim 0.001 s^{-1}$ before decreasing sharply with increasing stretch rate, in con…
We explore the Mode I fracture toughness of a polymer gel containing a semi-infinite, growing crack. First, an expression is derived for the energy release rate within the linearized, small-strain setting. This expression reveals a crack tip velocity-independent toughening that stems from the poroelastic nature of polymer gels. Then, we establish a poroelastic cohesive zone model that allows us to describe the micromechanics of fracture in gels by identifying the role of solvent pressure in promoting poroelastic toughening. We evaluate the enhancement in the effective fracture toughness throug…
We have designed a new experimental setup able to investigate fracture of soft materials at small scales. At high crack velocity, where energy is mostly dissipated through viscoelastic processes, we observe an increasingly large high strain domain in the crack tip vicinity. Taking advantage of our ability to determine where linear elasticity breaks down, we derive a simple prediction for the evolution of the energy release rate with the crack velocity.
Fracture of highly stretched materials challenges our view of how things break. We directly visualize rupture of tough double-network (DN) gels at >50\% strain. During fracture, crack tip shapes obey a $x\sim y^{1.6}$ power-law, in contrast to the parabolic profile observed in low-strain cracks. A new length-scale $\ell$ emerges from the power-law; we show that $\ell$ scales directly with the stored elastic energy, and diverges when the crack velocity approaches the shear wave speed. Our results show that DN gels undergo brittle fracture, and provide a testing ground for large-strain fracture …
A liquid droplet resting on a soft gel substrate can deform that substrate to the point of material failure, whereby fractures develop on the gel surface that propagate outwards from the contact-line in a starburst pattern. In this paper, we characterize i) the initiation process in which the number of arms in the starburst is controlled by the ratio of surface tension contrast to the gel's elastic modulus and ii) the propagation dynamics showing that once fractures are initiated they propagate with a universal power law $L\propto t^{3/4}$. We develop a model for crack initiation by treating t…
We investigate the delayed rupture of biopolymer gels under a constant shear load by simultaneous dynamic light scattering and rheology measurements. We unveil the crucial role of normal stresses built up during gelation: all samples that eventually fracture self-weaken during the gelation process, as revealed by a partial relaxation of the normal stress concomitant to a burst of microscopic plastic rearrangements. Upon applying a shear stress, weakened gels exhibit in the creep regime distinctive signatures in their microscopic dynamics, which anticipate macroscopic fracture by up to thousand…
Hydrogels have the ability to undergo large deformations and yet fail like brittle materials. The development of biocompatible hydrogels with high strength and toughness is an ongoing challenge in many applications. We crosslinked bovine gelatin using glutaraldehyde (control) and methylglyoxal (MGO) and assessed changes in their fracture toughness. Swelling experiments show ~710% retention of water in MGO hydrogels as compared to ~450% in control specimens. We used FTIR to identify the presence of chemical groups that may be involved in the crosslinking of gelatin gels. Scanning electron micro…
Imprinting Macroscopic Fracture during Gelation: A Mechanism for Tuning Colloidal Gels
ENSL, CNRS, Laboratoire de physique（法国国家科学研究中心物理实验室）；Department of Polymer Engineering, IPC, University of Minho（米尼奥大学高分子工程系）；Institut Universitaire de France (IUF)（法兰西学院）
Biomaterials such as protein or polysaccharide gels are known to behave qualitatively as soft solids and to rupture under an external load. Combining optical and ultrasonic imaging to shear rheology we show that the failure scenario of a protein gel is reminiscent of brittle solids: after a primary creep regime characterized by a power-law behavior which exponent is fully accounted for by linear viscoelasticity, fractures nucleate and grow logarithmically perpendicularly to shear, up to the sudden rupture of the gel. A single equation accounting for those two successive processes nicely captur…
The resistance to fracture of reversible biopolymer hydrogels is an important control factor of the cutting/slicing and eating characteristics of food gels. It is also critical for their utilization in tissue engineering, for which mechanical protection of encapsulated components is needed. Its dependence on loading rate and, recently, on the density and strength of cross-links has been investigated. But no attention was paid so far to solvent nor to environment effects. Here we report a systematic study of crack dynamics in gels of gelatin in water/glycerol mixtures. We show on this model sys…
The flow behavior of a viscoelastic organogel is investigated using ultrasonic velocimetry combined with rheometry. Our gel presents a decreasing flow curve, i.e., the measured stress decreases as a function of the applied shear rate. Strikingly, we note that the local flow curve calculated from the velocity profiles also exhibits a decreasing part. We attribute this regime to the presence of a fracturing process and three-dimensional motions in the bulk of the sample.
Self-assembled fibrillar network (SAFIN) hydrogels and organogels are commonly obtained by a crystallization process into fibers induced by external stimuli like temperature or pH. The gel-to-sol-to-gel transition is generally readily reversible and the change rate of the stimulus determines the fiber homogeneity and eventual elastic properties of the gels. However, recent work shows that in some specific cases, fibrillation occurs for a given molecular conformation and the sol-to-gel transition depends on the relative energetic stability of one conformation over the other, and not on the rate…
Direct observations of the surface and shape of model nano-colloidal gels associated with measurements of the spatial distribution of water content during drying show that air starts to significantly penetrate the sample when the material stops shrinking. We show that whether the material fractures or not during desiccation, as air penetrates the porous body, the water saturation decreases but remains almost homogeneous throughout the sample. This air-invasion is at the origin of another type of fracture due to capillary effects, these results provide a new insight in the liquid dynamics at th…
Ice-templating, also referred to as freeze-casting, is a process exploiting unidirectional crystallization of ice to structure macroporous materials from colloidal solutions. Commonly applied to inorganic and polymeric materials, we employ it here to cast soft self-assembled matter into spongy solid foams. Use of ice-templating to cast soft matter is generally confined to polymers. In the case of polymeric hydrogels, cross-linking ensures a good stability towards the harsh conditions (fast cooling at temperatures as low as-80{\textdegree}C) employed during ice-templating. However, freeze-casti…
Polymer gels behave as soft viscoelastic solids and exhibit a generic nonlinear mechanical response characterized by pronounced stiffening prior to irreversible failure, most often through macroscopic fractures. Here, we aim at capturing the latter scenario for a protein gel using a nonlinear integral constitutive equation built upon ($i$) the linear viscoelastic response of the gel, here well described by a power-law relaxation modulus, and ($ii$) the nonlinear viscoelastic properties of the gel, encoded into a "damping function". Such formalism predicts quantitatively the gel mechanical resp…
Flexible superparamagnetic filaments are studied under the influence of fast precessing magnetic fields using simulations and a continuum approximation analysis. We find that individual filaments can be made to exert controllable tensile forces along the precession axis. These forces are exploited for microscopic actuation. In bulk, the filaments can be rapidly assembled into different configurations whose material properties depend on the field parameters. The precession frequency affects filament aggregation and conformation by changing the net torques on the filament ends. Using a time-depe…
Entanglement of polymer chains is ubiquitous in elastomers, gels, and biological tissues. While the effects of chain entanglement on elasticity and viscoelasticity of polymer networks have been intensively studied, it remains elusive how chain entanglement affects fracture and fatigue of polymer networks. In this paper, using polyacrylamide hydrogels as a model material, we systematically compare fracture toughness and fatigue threshold of polymer networks with various levels of chain entanglement. We find that the fracture toughness and fatigue threshold of an unentangled polymer network are …
Hydrogels have had a profound impact in the fields of tissue engineering, drug delivery, and materials science as a whole. Due to the network architecture of these materials, imbibement with water often results in uniform swelling and isotropic expansion which scales with the degree of cross-linking. However, the development of internal stresses during swelling can have dramatic consequences, leading to surface instabilities as well as rupture or bursting events. To better understand hydrogel behavior, macroscopic mechanical characterization techniques (e.g.\ tensile testing, rheometry) are of…
In studies of the dynamic failure of brittle hydrogels, a bound has been placed on the process zone scale - the scale where material separation and ultimate failure occur. For the polyacrylamide hydrogel system under study, this bound is set at 20 microns. Thus, any subtle alterations to the material at a \emph{smaller} scale should not in principle alter the dynamic fracture response of the hydrogel. Here we test this directly by embedding sub-micron-scale latex polystyrene microspheres within the brittle polyacrylamide hydrogel at a solids fraction of 0.1 \%. We verify that the spheres are w…
Colloidal nanocrystal gels can be assembled using a difunctional "linker" molecule to mediate bonding between nanocrystals. The conditions for gelation and the structure of the gel are controlled macroscopically by the linker concentration and microscopically by the linker's molecular characteristics. Here, we demonstrate using a toy model for a colloid-linker mixture that linker flexibility plays a key role in determining both phase behavior and structure of the mixture. We fix the linker length and systematically vary its bending stiffness to span the flexible, semiflexible, and rigid regime…
Experimental and theoretical observations have agreed that the onset of cavitation in soft materials requires higher tensile pressure than pure water. The extra tensile pressure is required since the cavitating bubble needs to overcome the elastic energy in soft materials. In this manuscript, we have developed two models to study and quantify the extra tensile pressure. In the first approach, we proposed a strain energy based random fiber network (RFN) failure criteria in which interaction between the cavitating bubble and RFN is considered. Gelatin samples are prepared for different concentra…
We propose a two-body spherically symmetric (isotropic) potential such that particles interacting by the potential self assemble into linear semiflexible polymeric chains without branching. By suitable control of the potential parameters we can control the persistence length of the polymer, and can even introduce a controlled number of branches. Thus we show how to achieve effective directional interactions starting from spherically symmetric potentials. The self assembled polymers have a exponential distribution of chain lengths akin to what is observed for worm-like micellar systems. On incr…
Liquid crystalline polymers are materials of considerable scientific interest and technological value to society [1-3]. An important subset of such materials exhibit rubber-like elasticity; these can combine the remarkable optical properties of liquid crystals with the favourable mechanical properties of rubber and, further, exhibit behaviour not seen in either type of material independently [2]. Many of their properties depend crucially on the particular mesophase employed. Stretchable liquid crystalline polymers have previously been demonstrated in the nematic, chiral nematic, and smectic me…
Materials with network-like microstructure, including polymers, are the backbone for many natural and human-made materials such as gels, biological tissues, metamaterials, and rubbers. Fracture processes in these networked materials are intrinsically multiscale, and it is computationally prohibitive to adopt a fully discrete approach for large scale systems. To overcome such a challenge, we introduce an adaptive numerical algorithm for modeling fracture in this class of materials, with a primary application to polymer networks, using an extended version of the Quasi-Continuum method that accou…
Characterizing emergent multiscale dynamics in colloidal nanoparticle gels
University of Michigan（密歇根大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；University of Washington（华盛顿大学）；Deutsches Elektronen-Synchrotron DESY（德国电子同步辐射中心）
With exquisite precision and reproducibility, cells orchestrate the cooperative action of thousands of nanometer-sized molecular motors to carry out mechanical tasks at much larger length scales, such as cell motility, division and replication. Besides their biological importance, such inherently non-equilibrium processes are an inspiration for developing biomimetic active materials from microscopic components that consume energy to generate continuous motion. Being actively driven, these materials are not constrained by the laws of equilibrium statistical mechanics and can thus exhibit highly…
The synthesis of metal-organic frameworks (MOFs) in a monolithic morphology is a promising way to achieve the transition of this class of materials from academia to industrial applications. The sol-gel process has been widely employed to produce MOF monoliths. It is relatively cheap and simple compared to other techniques (e.g., mechanical densification) and moreover it allows to produce "pure" monoliths, i.e., without the need of using binders or templates that could affect the functional properties of the MOF. Understanding the mechanical properties of these monoliths is crucial for their tr…
