Microscopic mechanisms of the brittleness of viscoelastic fluids

A Protein-Like Nanogel for Spinning Hierarchically Structured Artificial Spider Silk

Spider dragline silk is draw-spun from soluble, β-sheet-crosslinked spidroin in aqueous solution. This spider silk has an excellent combination of strength and toughness, which originates from the hierarchical structure containing β-sheet crosslinking points, spiral nanoassemblies, a rigid sheath, and a soft core. Inspired by the spidroin structure and spider spinning process, a soluble and crosslinked nanogel is prepared and crosslinked fibers are drew spun with spider-silk-like hierarchical structures containing cross-links, aligned nanoassemblies, and sheath-core structures. Introducing nucleation seeds in the nanogel solution, and applying prestretch and a spiral architecture in the nanogel fiber, further tunes the alignment and assembly of the polymer chains, and enhances the breaking strength (1.27 GPa) and toughness (383 MJ m^-3 ) to approach those of the best dragline silk. Theoretical modeling provides understanding for the dependence of the fiber's spinning capacity on the nanogel size. This work provides a new strategy for the direct spinning of tough fiber materials.

Instabilities in freely expanding sheets of associating viscoelastic fluids

We use the impact of drops on a small solid target as a tool to investigate the behavior of viscoelastic fluids under extreme deformation rates. We study two classes of transient networks: semidilute solutions of supramolecular polymers and suspensions of spherical oil droplets reversibly linked by polymers. The two types of samples display very similar linear viscoelastic properties, which can be described with a Maxwell fluid model, but contrasting nonlinear properties due to different network structures. Upon impact, the weakly viscoelastic samples exhibit a behavior qualitatively similar to that of Newtonian fluids: a smooth and regular sheet forms, expands, and then retracts. By contrast, for highly viscoelastic fluids, the thickness of the sheet is found to be very irregular, leading to instabilities and eventually to the formation of holes. We find that the rheological properties of the material rule the onset of instabilities. We first provide a simple image analysis of the expanding sheets to determine the onset of instabilities. We then demonstrate that the Deborah number related to the shortest relaxation time associated with the sample structure following a high shear is the relevant parameter that controls the heterogeneities in the thickness of the sheet, eventually leading to the formation of holes. When the sheet tears-up, data suggest by contrast that the opening dynamics depends also on the expansion rate of the sheet.

A network model of transient polymers: exploring the micromechanics of nonlinear viscoelasticity

Dynamic networks contain crosslinks that re-associate after disconnecting, imparting them with viscoelastic properties. While continuum approaches have been developed to analyze their mechanical response, these approaches can only describe their evolution in an average sense, omitting local, stochastic mechanisms that are critical to damage initiation or strain localization. To address these limitations, we introduce a discrete numerical model that mesoscopically coarse-grains the individual constituents of a dynamic network to predict its mechanical and topological evolution. Each constituent consists of a set of flexible chains that are permanently cross-linked at one end and contain reversible binding sites at their free ends. We incorporate nonlinear force-extension of individual chains via a Langevin model, slip-bond dissociation through Eyring's model, and spatiotemporally-dependent bond attachment based on scaling theory. Applying incompressible, uniaxial tension to representative volume elements at a range of constant strain rates and network connectivities, we then compare the mechanical response of these networks to that predicted by the transient network theory. Ultimately, we find that the idealized continuum approach remains suitable for networks with high chain concentrations when deformed at low strain rates, yet the mesoscale model proves necessary for the exploration of localized stochastic events, such as variability of the bond kinetics, or the nucleation of micro-cavities that likely conceive damage and fracture.

The relationship between viscoelasticity and elasticity

Soft materials that are subjected to large deformations exhibit an extremely rich phenomenology, with properties lying in between those of simple fluids and those of elastic solids. In the continuum description of these systems, one typically follows either the route of solid mechanics (Lagrangian description) or the route of fluid mechanics (Eulerian description). The purpose of this review is to highlight the relationship between the theories of viscoelasticity and of elasticity, and to leverage this connection in contemporary soft matter problems. We review the principles governing models for viscoelastic liquids, for example solutions of flexible polymers. Such materials are characterized by a relaxation time λ, over which stresses relax. We recall the kinematics and elastic response of large deformations, and show which polymer models do (and which do not) correspond to a nonlinear elastic solid in the limit λ → ∞. With this insight, we split the work done by elastic stresses into reversible and dissipative parts, and establish the general form of the conservation law for the total energy. The elastic correspondence can offer an insightful tool for a broad class of problems; as an illustration, we show how the presence or absence of an elastic limit determines the fate of an elastic thread during capillary instability.

Crack Initiation in Viscoelastic Materials

In viscoelastic materials, individually short-lived bonds collectively result in a mechanical resistance which is long lived but finite as, ultimately, cracks appear. Here, we provide a microscopic mechanism by which a critical crack length emerges from the nonlinear local bond dynamics. Because of this emerging length scale, macroscopic viscoelastic materials fracture in a fundamentally different manner from microscopically small systems considered in previous models. We provide and numerically verify analytical equations for the dependence of the critical crack length on the bond kinetics and applied stress.

Damage in elastomers: healing of internally nucleated cavities and micro-cracks

Following on the work of Poulain et al. (Damage in elastomers: Nucleation and growth of cavities, micro-cracks, and macro-cracks, Int. J. Fract., 2017, 205, 1-21), this paper presents an investigation of the response of cavities/cracks internally nucleated within a transparent PDMS elastomer that is confined between two firmly embedded stiff beads and subjected to quasistatic cyclic loading-unloading. Specifically, it is observed that cracks that nucleate and propagate to reach tens of microns in length during the loading can heal completely upon unloading. They do so autonomously within a time scale of seconds. Furthermore, the regions of the elastomer that experience healing appear to acquire higher strength or toughness.

Impact of Beads and Drops on a Repellent Solid Surface: A Unified Description

We investigate freely expanding sheets formed by ultrasoft gel beads, and liquid and viscoelastic drops, produced by the impact of the bead or drop on a silicon wafer covered with a thin layer of liquid nitrogen that suppresses viscous dissipation thanks to an inverse Leidenfrost effect. Our experiments show a unified behavior for the impact dynamics that holds for solids, liquids, and viscoelastic fluids and that we rationalize by properly taking into account elastocapillary effects. In this framework, the classical impact dynamics of solids and liquids, as far as viscous dissipation is negligible, appears as the asymptotic limits of a universal theoretical description. A novel material-dependent characteristic velocity that includes both capillary and bulk elasticity emerges from this unified description of the physics of impact.

A New 3D Printing Strategy by Harnessing Deformation, Instability, and Fracture of Viscoelastic Inks

Direct ink writing (DIW) has demonstrated great potential as a multimaterial multifunctional fabrication method in areas as diverse as electronics, structural materials, tissue engineering, and soft robotics. During DIW, viscoelastic inks are extruded out of a 3D printer's nozzle as printed fibers, which are deposited into patterns when the nozzle moves. Hence, the resolution of printed fibers is commonly limited by the nozzle's diameter, and the printed pattern is limited by the motion paths. These limits have severely hampered innovations and applications of DIW 3D printing. Here, a new strategy to exceed the limits of DIW 3D printing by harnessing deformation, instability, and fracture of viscoelastic inks is reported. It is shown that a single nozzle can print fibers with resolution much finer than the nozzle diameter by stretching the extruded ink, and print various thickened or curved patterns with straight nozzle motions by accumulating the ink. A quantitative phase diagram is constructed to rationally select parameters for the new strategy. Further, applications including structures with tunable stiffening, 3D structures with gradient and programmable swelling properties, all printed with a single nozzle are demonstrated. The current work demonstrates that the mechanics of inks plays a critical role in developing 3D printing technology.

Force percolation of contractile active gels

Living systems provide a paradigmatic example of active soft matter. Cells and tissues comprise viscoelastic materials that exert forces and can actively change shape. This strikingly autonomous behavior is powered by the cytoskeleton, an active gel of semiflexible filaments, crosslinks, and molecular motors inside cells. Although individual motors are only a few nm in size and exert minute forces of a few pN, cells spatially integrate the activity of an ensemble of motors to produce larger contractile forces (∼nN and greater) on cellular, tissue, and organismal length scales. Here we review experimental and theoretical studies on contractile active gels composed of actin filaments and myosin motors. Unlike other active soft matter systems, which tend to form ordered patterns, actin-myosin systems exhibit a generic tendency to contract. Experimental studies of reconstituted actin-myosin model systems have long suggested that a mechanical interplay between motor activity and the network's connectivity governs this contractile behavior. Recent theoretical models indicate that this interplay can be understood in terms of percolation models, extended to include effects of motor activity on the network connectivity. Based on concepts from percolation theory, we propose a state diagram that unites a large body of experimental observations. This framework provides valuable insights into the mechanisms that drive cellular shape changes and also provides design principles for synthetic active materials.

Polymer liquids fracture like solids

While fracture in brittle solids has been studied for centuries until today, there are few studies on fracture in polymer liquids. Recent developments in experimental techniques, especially the combination of controlled filament stretching rheometry and high speed imaging, have opened new windows into the detailed study of fracture processes for polymer liquids. High speed imaging shows that polymer liquids fracture like solids with initiation and propagation of an edge fracture. However, remarkable features such as highly reproducible critical stress, independent appearance of multiple fractures, and trumpet crack profiles, reveal mechanisms which are significantly different from solids.

Rearrangement Zone around a Crack Tip in a Double Self-Assembled Transient Network

We investigate the nucleation and propagation of cracks in self-assembled viscoelastic fluids, which are made of surfactant micelles reversibly linked by telechelic polymers. The morphology of the micelles can be continuously tuned, from spherical to rodlike to wormlike, thus producing transient double networks when the micelles are sufficiently long and entangled and transient single networks otherwise. For a single network, we show that cracks nucleate when the sample deformation rate involved is comparable to the relaxation time scale of the network. For a double network, by contrast, significant rearrangements of the micelles occur as a crack nucleates and propagates. We show that birefringence develops at the crack tip over a finite length, ξ, which corresponds to the length scale over which micelle alignment occurs. We find that ξ is larger for slower cracks, suggesting an increase of ductility.

Brittle fracture in associative polymers: the case of ionomer melts

Ionomers are interesting due to their applications in coatings, adhesives, films and packaging materials. A study of the underlying mechanisms for fracture in ionomers is consequently of both practical as well as theoretical interest. In this study, we employ high speed imaging coupled with uniaxial extensional rheometry to delineate the mechanics leading to the brittle fracture of ionomer melts. When these ionomers are elongated at a rate higher than the inverse relaxation time of physical crosslinks, an edge fracture occurs at a critical stress. Parabolic fracture profiles provide evidence that the phenomenon is purely elastic and bulk dissipation has little impact on the crack profile. Experimental results are interpreted within the Griffiths theory for linear elastic materials and the de Gennes theory for viscoelastic materials.

Bubble dynamics inside an outgassing hydrogel confined in a Hele-Shaw cell

We report an experimental study of bubble dynamics in a non-Newtonian fluid subjected to a pressure decrease. The fluid is a hydrogel, composed of water and a synthetic clay, prepared and sandwiched between two glass plates in a Hele-Shaw geometry. The rheological properties of the material can be tuned by the clay concentration. As the imposed pressure decreases, the gas initially dissolved in the hydrogel triggers bubble formation. Different stages of the process are observed: bubble nucleation, growth, interaction, and creation of domains by bubble contact or coalescence. Initially bubble behave independently. They are trapped and advected by the mean deformation of the hydrogel, and the bubble growth is mainly driven by the diffusion of the dissolved gas through the hydrogel and its outgassing at the reactive-advected hydrogel-bubble interface. In this regime, the rheology of the fluid does not play a significant role on the bubble growth. A model is proposed and gives a simple scaling that relates the bubble growth rate and the imposed pressure. Carbon dioxide is shown to be the gas at play, and the hydrogel is degassing at the millimeter scale as a water solution does at a smaller scale. Later, bubbles are not independent anymore. The growth rate decreases, and the morphology becomes more anisotropic as bubbles interact because they are separated by a distance smaller than the individual stress field extension. Our measurements show that the interaction distance scales with the bubbles' size.

Multiple Cracks Propagate Simultaneously in Polymer Liquids in Tension

Understanding the mechanism of fracture is essential for material and process design. While the initiation of fracture in brittle solids is generally associated with the preexistence of material imperfections, the mechanism for initiation of fracture in viscoelastic fluids, e.g., polymer melts and solutions, remains an open question. We use high speed imaging to visualize crack propagation in entangled polymer liquid filaments under tension. The images reveal the simultaneous propagation of multiple cracks. The critical stress and strain for the onset of crack propagation are found to be highly reproducible functions of the stretch rate, while the position of initiation is completely random. The reproducibility of conditions for fracture points to a mechanism for crack initiation that depends on the dynamic state of the material alone, while the crack profiles reveal the mechanism of energy dissipation during crack propagation.

Self-organization in suspensions of end-functionalized semiflexible polymers under shear flow

The nonequilibrium dynamical behavior and structure formation of end-functionalized semiflexible polymer suspensions under flow are investigated by mesoscale hydrodynamic simulations. The hybrid simulation approach combines the multiparticle collision dynamics method for the fluid, which accounts for hydrodynamic interactions, with molecular dynamics simulations for the semiflexible polymers. In equilibrium, various kinds of scaffold-like network structures are observed, depending on polymer flexibility and end-attraction strength. We investigate the flow behavior of the polymer networks under shear and analyze their nonequilibrium structural and rheological properties. The scaffold structure breaks up and densified aggregates are formed at low shear rates, while the structural integrity is completely lost at high shear rates. We provide a detailed analysis of the shear- rate-dependent flow-induced structures. The studies provide a deeper understanding of the formation and deformation of network structures in complex materials.

Creep and fracture of a protein gel under stress

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 whose 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 captures the full rheological response. The failure time follows a decreasing power law with the applied shear stress, similar to the Basquin law of fatigue for solids. These results are in excellent agreement with recent fiber-bundle models that include damage accumulation on elastic fibers and exemplify protein gels as model, brittlelike soft solids.

Timescales in creep and yielding of attractive gels

The stress-induced yielding scenario of colloidal gels is investigated under rough boundary conditions by means of rheometry coupled with local velocity measurements. Under an applied shear stress σ, the fluidization of gels made of attractive carbon black particles dispersed in a mineral oil is shown to involve a previously unreported shear rate response γ dot above(t) characterized by two well-defined and separated timescales τc and τf. First γ dot above decreases as a weak power law strongly reminiscent of the primary creep observed in numerous crystalline and amorphous solids, coined the "Andrade creep". We show that the bulk deformation remains homogeneous at the micron scale, which demonstrates that whether plastic events take place or whether any shear transformation zone exists, such phenomena occur at a smaller scale. As a key result of this paper, the duration τc of this creep regime decreases as a power law of the viscous stress, defined as the difference between the applied stress and the yield stress σc, i.e. τc ∼ (σ - σc)(-β), with β = 2-3 depending on the gel concentration. The end of this first regime is marked by a jump of the shear rate by several orders of magnitude, while the gel slowly slides as a solid block experiencing strong wall slip at both walls, despite rough boundary conditions. Finally, a second sudden increase of the shear rate is concomitant with the full fluidization of the material which ends up being homogeneously sheared. The corresponding fluidization time τf robustly follows an exponential decay with the applied shear stress, i.e. τf = τ0 exp(-σ/σ0), as already reported for smooth boundary conditions. Varying the gel concentration C in a systematic fashion shows that the parameter σ0 and the yield stress σc exhibit similar power-law dependences with C. Finally, we highlight a few features that are common to attractive colloidal gels and to solid materials by discussing our results in the framework of theoretical approaches of solid rupture (kinetic, fiber bundle, and transient network models).

Dynamic fracture of nonglassy suspensions

We study the dynamic fracture of thin layers of suspensions of non-Brownian rigid particles. The impact of a projectile triggers a liquid-to-solid transition and a hole opens in the layer. We show that the occurrence of fracture and the spatial and dynamic features of the cracks depend mostly on the thickness of the layer and the particle volume fraction. In contrast, the properties of the fractured material seem independent of volume fraction. Finally, we measure the velocity of the crack tip, from which we estimate an effective value of the shear modulus of the fractured material.

Ultrafast ultrasonic imaging coupled to rheometry: principle and illustration

We describe a technique coupling standard rheology and ultrasonic imaging with promising applications to characterization of soft materials under shear. Plane wave imaging using an ultrafast scanner allows to follow the local dynamics of fluids sheared between two concentric cylinders with frame rates as high as 10 000 images per second, while simultaneously monitoring the shear rate, shear stress, and viscosity as a function of time. The capacities of this "rheo-ultrasound" instrument are illustrated on two examples: (i) the classical case of the Taylor-Couette instability in a simple viscous fluid and (ii) the unstable shear-banded flow of a non-Newtonian wormlike micellar solution.

Failure of film formation of viscoelastic fluid: dynamics of viscoelastic fluid in a partially filled horizontally rotating cylinder

The dynamics of a viscoelastic Maxwell fluid is studied in a partially filled cylinder rotating around a horizontal axis. At low rotational velocity, the fluid behaves in the same manner as a viscous fluid. A thin fluid film is pulled up from the edge of a fluid bump at the bottom of the cylinder, and it covers the inner wall of the cylinder completely. As a result, a steady state is the coexistence of the film and the bump of the fluid. When the rotational velocity of the cylinder is increased, the film formation fails and the bump of fluid rolls steadily at the bottom of the cylinder. This failure of film formation has never been observed in the case of a viscous fluid. At higher rotational velocity, the bump of the fluid starts to oscillate at the bottom of the cylinder. Then, the fluid bump again rolls steadily with a further increase in the rotational velocity. The failure of film formation is explained in terms of the elastic behavior of the viscoelastic fluid near the boundary between the film and the bump regions. The theoretical prediction shows good agreement with the experimental results. We further estimate the condition for which a viscoelastic fluid displays dynamically nonwetting behavior; i.e., the absence of fluid film at any value of rotational velocity.

Extreme strain localization and sliding friction in physically associating polymer gels

Model physically associating gels deformed in shear over a wide range of reduced rates displayed evidence of strain localization. The nonlinear stress responses and inhomogeneous velocity profiles observed during shear rheometry coupled with particle tracking velocimetry were associated with the occurrence of rate-dependent banding and fracture-like responses in the gel. Scaling law analysis from traditional sliding friction studies suggests that, at the molecular level, deformation is confined to a shear zone with thickness comparable to the mesh size of the gel, the smallest structurally relevant length scale in the gel.

Structural signature of a brittle-to-ductile transition in self-assembled networks

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 fracture of solids and the fracture under shear of viscoelastic fluids.

Yielding Behavior in Injectable Hydrogels from Telechelic Proteins

Injectable hydrogels show substantial promise for use in minimally invasive tissue engineering and drug delivery procedures.1,2 A new injectable hydrogel material, developed from recombinant telechelic proteins expressed in E. coli, demonstrates shear thinning by three orders of magnitude at large strains. Large amplitude oscillatory shear illustrates that shear thinning is due to yielding within the bulk of the gel, and the rheological response and flow profiles are consistent with a shear-banding mechanism for yielding. The sharp yielding transition and large magnitude of the apparent shear thinning allow gels to be injected through narrow gauge needles with only gentle hand pressure. After injection the gels reset to full elastic strength in seconds due to rapid reformation of the physical network junctions, allowing self-supporting structures to be formed. The shear thinning and recovery behavior is largely independent of the midblock length, enabling genetic engineering to be used to control the equilibrium modulus of the gel without loss of the characteristic yielding behavior. The shear-banding mechanism localizes deformation during flow into narrow regions of the gels, allowing more than 95% of seeded cells to survive the injection process.

When gel and glass meet: a mechanism for multistep relaxation

We use computer simulations to study the dynamics of a physical gel at high densities where gelation and the glass transition interfere. We report and provide detailed physical understanding of complex relaxation patterns for time-correlation functions which generically decay in a three-step process. For certain combinations of parameters we find logarithmic decays of the correlators and subdiffusive particle motion.