Confinement controls the creep rate in soft granular packings.

Flow in soft materials encompasses a wide range of viscous, plastic and elastic phenomena which provide challenges to modelling at the microscopic level. To create a controlled flow, we perform falling ball viscometry tests on packings of soft, frictionless hydrogel spheres. Systematic creep flow is found when a controlled driving stress is applied to a sinking sphere embedded in a packing. Here, we take the novel approach of applying an additional global confinement stress to the packing using an external load. This has enabled us to identify two distinct creep regimes. When confinement stress is small, the creep rate is independent of the load imposed. For larger confinement stresses, we find that the creep rate is set by the mechanical load acting on the packing. In the latter regime, the creep rate depends exponentially on the imposed stress. We can combine the two regimes via a rescaling onto a master curve, capturing the creep rate over five orders of magnitude. Our results indicate that bulk creep phenomena in these soft materials can be subtly controlled using an external mechanical force.

Elongated particles discharged with a conveyor belt in a two-dimensional silo.

The flow of elliptical particles out of a two-dimensional silo when extracted with a conveyor belt is analyzed experimentally. The conveyor belt-placed directly below the silo outlet-reduces the flow rate, increases the size of the stagnant zone, and it has a very strong influence on the relative velocity fluctuations as they strongly increase everywhere in the silo with decreasing belt speed. In other words, instead of slower but smooth flow, flow reduction by belt leads to intermittent flow. Interestingly, we show that this intermittency correlates with a strong reduction of the orientational order of the particles at the orifice region. Moreover, we observe that the average orientation of the grains passing through the outlet is modified when they are extracted with the belt, a feature that becomes more evident for large orifices.

Capillary Flow-MRI: Quantifying Micron-Scale Cooperativity in Complex Dispersions.

Strongly confined flow of particulate fluids is encountered in applications ranging from three-dimensional (3D) printing to the spreading of foods and cosmetics into thin layers. When flowing in constrictions with gap sizes, w, within 102 times the mean size of particles or aggregates, d, structured fluids experience enhanced bulk velocities and inhomogeneous viscosities, as a result of so-called cooperative, or nonlocal, particle interactions. Correctly predicting cooperative flow for a wide range of complex fluids requires high-resolution flow imaging modalities applicable in situ to even optically opaque fluids. To this goal, we here developed a pressure-driven high-field magnetic resonance imaging (MRI) velocimetry platform, comprising a pressure controller connected to a capillary. Wall properties and diameter could be modified respectively as hydrophobic/hydrophilic, or within w ∼ 100-540 µm. By achieving a high spatial resolution of 9 µm, flow cooperativity length scales, ξ, down to 15 µm in Carbopol with d ∼ 2 µm could be quantified by means of established physical models with an accuracy of 13%. The same approach was adopted for a heterogeneous fat crystal dispersion (FCD) with d and ξ values up to an order of magnitude higher than those for Carbopol. We found that for strongly confined flow of Carbopol in the 100 µm capillary, ξ is independent of flow conditions. For the FCD, ξ increases with gap size and applied pressures over 0.25-1 bar. In both samples, nonlocal interactions span domains up to about 5-8 particles but, at the highest confinement degree explored, ∼8% for FCD, domains of only ∼2 particles contribute to cooperative flow. The developed flow-MRI platform is easily scalable to ultrahigh field MRI conditions for chemically resolved velocimetric measurements of, e.g., complex fluids with anisotropic particles undergoing alignment. Future potential applications of the platform encompass imaging extrusion under confinement during the 3D printing of complex dispersions or in in vitro vascular and perfusion studies.

Phase separation in supramolecular and covalent adaptable networks.

Phase separation phenomena have been studied widely in the field of polymer science, and were recently also reported for dynamic polymer networks (DPNs). The mechanisms of phase separation in dynamic polymer networks are of particular interest as the reversible nature of the network can participate in the structuring of the micro- and macroscale domains. In this review, we highlight the underlying mechanisms of phase separation in dynamic polymer networks, distinguishing between supramolecular polymer networks and covalent adaptable networks (CANs). Also, we address the synergistic effects between phase separation and reversible bond exchange. We furthermore discuss the effects of phase separation on the material properties, and how this knowledge can be used to enhance and tune material properties.

Tailorable and Biocompatible Supramolecular-Based Hydrogels Featuring two Dynamic Covalent Chemistries.

Dynamic covalent chemistry (DCC) has proven to be a valuable tool in creating fascinating molecules, structures, and emergent properties in fully synthetic systems. Here we report a system that uses two dynamic covalent bonds in tandem, namely disulfides and hydrazones, for the formation of hydrogels containing biologically relevant ligands. The reversibility of disulfide bonds allows fiber formation upon oxidation of dithiol-peptide building block, while the reaction between NH-NH2 functionalized C-terminus and aldehyde cross-linkers results in a gel. The same bond-forming reaction was exploited for the "decoration" of the supramolecular assemblies by cell-adhesion-promoting sequences (RGD and LDV). Fast triggered gelation, cytocompatibility and ability to "on-demand" chemically customize fibrillar scaffold offer potential for applying these systems as a bioactive platform for cell culture and tissue engineering.

Raman Spectroscopy Reveals Phase Separation in Imine-Based Covalent Adaptable Networks.

The introduction of dynamic covalent bonds into cross-linked polymer networks enables the development of strong and tough materials that can still be recycled or repurposed in a sustainable manner. To achieve the full potential of these covalent adaptable networks (CANs), it is essential to understand-and control-the underlying chemistry and physics of the dynamic covalent bonds that undergo bond exchange reactions in the network. In particular, understanding the structure of the network architecture that is assembled dynamically in a CAN is crucial, as exchange processes within this network will dictate the dynamic-mechanical material properties. In this context, the introduction of phase separation in different network hierarchies has been proposed as a useful handle to control or improve the material properties of CANs. Here we report-for the first time-how Raman confocal microscopy can be used to visualize phase separation in imine-based CANs on the scale of several micrometers. Independently, atomic force microscopy (AFM) confirmed the phase-separated domains inside the polymer. Remarkably, the materials were found to undergo phase separation despite being built up from miscible monomers, which arguably should yield homogeneous materials. We found that the phase separation not only affected the appearance of the material but-more notably-also had a noticeable effect on the thermal-mechanical properties of the material: CANs (of equal aliphatic/aromatic monomer composition) that displayed phase separation had both a higher crossover temperature (T cross, where tan(δ) = 1, and where the material transits from a rubbery to a viscous state) and an increased elastic modulus (G'). By modifying the CAN architecture, we were able to either suppress or enhance the phase separation, and we propose that the phase separation is driven by favorable π-π interactions between the aromatic components. Our work further shows the importance of phase separation in CANs, including in networks built from miscible components, and provides a handle to control the dynamic material properties. Moreover, our work underlines the suitability of Raman imaging as a method to visualize phase separation in CANs.

Creep Control in Soft Particle Packings.

Granular packings display a wealth of mechanical features that are of widespread significance. One of these features is creep: the slow deformation under applied stress. Creep is common for many other amorphous materials such as many metals and polymers. The slow motion of creep is challenging to understand, probe, and control. We probe the creep properties of packings of soft spheres with a sinking ball viscometer. We find that in our granular packings, creep persists up to large strains and has a power law form, with diffusive dynamics. The creep amplitude is exponentially dependent on both applied stress and the concentration of hydrogel, suggesting that a competition between driving and confinement determines the dynamics. Our results provide insights into the mechanical properties of soft solids and the scaling laws provide a clear benchmark for new theory that explains creep, and provide the tantalizing prospect that creep can be controlled by a boundary stress.

Non-Invasive Rheo-MRI Study of Egg Yolk-Stabilized Emulsions: Yield Stress Decay and Protein Release.

A comprehensive understanding of the time-dependent flow behavior of concentrated oil-in-water emulsions is of considerable industrial importance. Along with conventional rheology measurements, localized flow and structural information are key to gaining insight into the underlying mechanisms causing time variations upon constant shear. In this work, we study the time-dependent flow behavior of concentrated egg-yolk emulsions with (MEY) or without (EY) enzymatic modification and unravel the effects caused by viscous friction during shear. We observe that prolonged shear leads to irreversible and significant loss of apparent viscosity in both emulsion formulations at a mild shear rate. The latter effect is in fact related to a yield stress decay during constant shearing experiments, as indicated by the local flow curve measurements obtained by rheo-MRI. Concurrently, two-dimensional D-T2 NMR measurements revealed a decrease in the T2 NMR relaxation time of the aqueous phase, indicating the release of surface-active proteins from the droplet interface towards the continuous water phase. The combination of an increase in droplet diameter and the concomitant loss of proteins aggregates from the droplet interface leads to a slow decrease in yield stress.

Quantifying cooperative flow of fat crystal dispersions.

We quantify the cooperative flow behaviour of fat crystal dispersions (FCDs) upon varying crystallization conditions. The latter enabled altering the multiscale microstructure of the FCDs, from the nanometer-sized platelets, and the dispersed fractal aggregates, up to the strength of the mesoscopic weak-link network. To the goal of characterizing strongly-confined flow in these optically-opaque materials, we acquire high-resolution rheo-magnetic-resonance-imaging (rheo-MRI) velocimetry measurements using an in-house developed 500 µm gap Couette cell (CC). We introduce a numerical fitting method based on the fluidity model, which yields the cooperativity length, ξ, in the narrow-gap CC. FCDs with aggregates sizes smaller than the confinement size by an order of magnitude were found to exhibit cooperativity effects. The respective ξ values diverged at the yield stress, in agreement with the Kinetic Elasto-Plastic (KEP) theory. In contrast, the FCD with aggregates sizes in the order of the gap size did not exhibit any cooperativity effect: we attribute this result to the correspondingly decreased mobility of the aggregates. We foresee that our optimized rheo-MRI measurement and fitting analysis approach will propel further similar studies of flow of other multi-scale and optically-opaque materials.

Validation of temperature-controlled rheo-MRI measurements in a submillimeter-gap Couette geometry.

A temperature-controlled submillimeter-gap (500 µm) rheo-magnetic resonance imaging (MRI) Couette cell has been developed to measure confined flow of soft structured materials under controlled temperature. The proposed setup enables performing rheo-MRI measurements using (i) a spatially uniform temperature control over the range 15°C to 40°C and (ii) a high spatial resolution up to 10 µm, as a consequence of the improved mechanical stability of the in-house developed rotating elements. Here, we demonstrate the performance of the cell for the rheo-MRI velocimetry study of a thixotropic fat crystal dispersion, a complex fluid commonly used in food manufacturing. The submillimeter-gap geometry and variable temperature capability of the cell enable observing the effects of shear- and temperature-induced fat recrystallization on both wall slip and shear banding under strongly confined flow. Our improved rheo-MRI setup opens new perspectives for the fundamental study of strongly confined flow, cooperative effects, and the underlying interparticle interactions and for ultimately aiding optimization of products involved in spreading/extrusion, such as cosmetics and foods.

Rotational diffusion and rotational correlations in frictional amorphous disk packings under shear.

We show here that rotations of round particles in amorphous disk packing reveal various nontrivial microscopic features when the packing is close to rigidification. We analyze experimental measurements on disk packing subjected to simple shear deformation with various inter-particle friction coefficients and across a range of volume fractions where the system is known to stiffen. The analysis of measurements indicates that shear induces diffusive microrotation, that can be both enhanced and suppressed depending upon the volume fraction as well as the inter-particle friction. Rotations also display persistent anticorrelated motion. Spatial correlations in microrotation are observed to be directly correlated with system pressure. These observations point towards the broader mechanical relevance of collective dynamics in the rotational degree of freedom of particles.

Sheared Amorphous Packings Display Two Separate Particle Transport Mechanisms.

Shearing granular materials induces nonaffine displacements. Such nonaffine displacements have been studied extensively, and are known to correlate with plasticity and other mechanical features of amorphous packings. A well known example is shear transformation zones as captured by the local deviation from affine deformation, D_{min}^{2}, and their relevance to failure and stress fluctuations. We analyze sheared frictional athermal disc packings and show that there exists at least one additional mesoscopic transport mechanism that superimposes itself on top of local diffusive motion. We evidence this second transport mechanism in a homogeneous system via a diffusion tensor analysis and show that the trace of the diffusion tensor equals the classic D_{min}^{2} when this second mesoscopic transport is corrected for. The new transport mechanism is consistently observed over a wide range of volume fractions and even for particles with different friction coefficients and is consistently observed also upon shear reversal, hinting at its relevance for memory effects.

Erratum: Obtaining self-similar scalings in focusing flows [Phys. Rev. E 92, 043016 (2015)].

This corrects the article DOI: 10.1103/PhysRevE.92.043016.

Uncovering friction dynamics using hydrogel particles as soft ball bearings.

Rolling ball bearings are widely known and applied to decrease friction between two surfaces. More recently, hydrogel-hydrogel tribopairs have also revealed good but rather complex lubrication properties. Here, we use hydrogels as ball bearings to elucidate that soft spherical particles have nontrivial rate-dependent lubrication behavior. Unlike Newtonian lubrication or dry solid friction, hydrogel particles in suspension transition through four frictional regimes as a function of sliding velocity. We relate the different regimes to the deformation of the particles at different gap sizes, which changes the effective contact area between the sliding surfaces. By systematically varying the particle characteristics and the surface properties of the sliding surfaces, we assign potential mechanisms for each of the different lubricating regimes as a function of velocity: (I) relatively high friction due to particle flattening and direct contact between interacting bodies (II) decrease of friction owing to the presence of rolling particles (III) large inflow of particles in a confined space leading to compressed particles and (IV) the formation of a thick lubricating layer. Using these suspensions with soft, deformable particles as a ball bearing system, we provide new insights into soft material friction with applications in emulsions, powders, pastes or other granular materials.

High Field MicroMRI Velocimetric Measurement of Quantitative Local Flow Curves.

Performing rheo-microMRI velocimetry at a high magnetic field with strong pulsed field gradients has clear advantages in terms of (chemical) sensitivity and resolution in velocities, time, and space. To benefit from these advantages, some artifacts need to be minimized. Significant sources of such artifacts are chemical shift dispersion due to the high magnetic field, eddy currents caused by the pulsed magnetic field gradients, and possible mechanical instabilities in concentric cylinder (CC) rheo-cells. These, in particular, hamper quantitative assessment of spatially resolved velocity profiles needed to construct local flow curves (LFCs) in CC geometries with millimeter gap sizes. A major improvement was achieved by chemical shift selective suppression of signals that are spectroscopically different from the signal of interest. By also accounting for imperfections in pulsed field gradients, LFCs were obtained that were virtually free of artifacts. The approach to obtain quantitative LFCs in millimeter gap CC rheo-MRI cells was validated for Newtonian and simple yield stress fluids, which both showed quantitative agreement between local and global flow curves. No systematic effects of gap size and rotational velocity on the viscosity of a Newtonian fluid and yield stress of a complex fluid could be observed. The acquisition of LFCs during heterogeneous and transient flow of fat crystal dispersion demonstrated that local constitutive laws can be assessed by rheo-microMRI at a high magnetic field in a noninvasive, quantitative, and real-time manner.

Transparent experiments: releasing data from mechanical tests on three dimensional hydrogel sphere packings.

We describe here experiments on the mechanics of hydrogel particle packings from the Behringer lab, performed between 2012 and 2015. These experiments quantify the evolution of all contact forces inside soft particle packings exposed to compression, shear, and the intrusion of a large intruder. The experimental set-ups and processes are presented and the data are concomitantly published in a repository (Barés et al. in Dryad, Dataset 10.5061/dryad.6djh9w0x8, 2019).

Molecular control over vitrimer-like mechanics - tuneable dynamic motifs based on the Hammett equation in polyimine materials.

In this work, we demonstrate that fine-grained, quantitative control over macroscopic dynamic material properties can be achieved using the Hammett equation in tuneable dynamic covalent polyimine materials. Via this established physical-organic principle, operating on the molecular level, one can fine-tune and control the dynamic material properties on the macroscopic level, by systematic variation of dynamic covalent bond dynamics through selection of the appropriate substituent of the aromatic imine building blocks. Five tuneable, crosslinked polyimine network materials, derived from dianiline monomers with varying Hammett parameter (σ) were studied by rheology, revealing a distinct correlation between the σ value and a range of corresponding dynamic material properties. Firstly, the linear correlation of the kinetic activation energy (E a) for the imine exchange to the σ value, enabled us to tune the E a from 16 to 85 kJ mol-1. Furthermore, the creep behaviour (γ), glass transition (T g) and the topology freezing transition temperature (T v), all showed a strong, often linear, dependence on the σ value of the dianiline monomer. These combined results demonstrate for the first time how dynamic material properties can be directly tuned and designed in a quantitative - and therefore predictable - manner through correlations based on the Hammett equation. Moreover, the polyimine materials were found to be strong elastic rubbers (G' > 1 MPa at room temperature) that were stable up to 300 °C, as confirmed by TGA. Lastly, the dynamic nature of the imine bond enabled not only recycling, but also intrinsic self-healing of the materials over multiple cycles without the need for solvent, catalysts or addition of external chemicals.

Mechanics of composite hydrogels approaching phase separation.

For polymer-particle composites, limited thermodynamic compatibility of polymers and particles often leads to poor dispersal and agglomeration of the particles in the matrix, which negatively impacts the mechanics of composites. To study the impact of particle compatibility in polymer matrices on the mechanical properties of composites, we here study composite silica- protein based hydrogels. The polymer used is a previously studied telechelic protein-based polymer with end groups that form triple helices, and the particles are silica nanoparticles that only weakly associate with the polymer matrix. At 1mM protein polymer, up to 7% of silica nanoparticles can be embedded in the hydrogel. At higher concentrations the system phase separates. Oscillatory rheology shows that at high frequencies the particles strengthen the gels by acting as short-lived multivalent cross-links, while at low frequencies, the particles reduce the gel strength, presumably by sequestering part of the protein polymers in such a way that they can no longer contribute to the network strength. As is generally observed for polymer/particle composites, shear-induced polymer desorption from the particles leads to a viscous dissipation that strongly increases with increasing particle concentration. While linear rheological properties as function of particle concentration provide no signals for an approaching phase separation, this is very different for the non-linear rheology, especially fracture. Strain-at-break decreases rapidly with increasing particle concentration and vanishes as the phase boundary is approached, suggesting that the interfaces between regions of high and low particle densities in composites close to phase separation provide easy fracture planes.

Symmetry-reversals in chiral active matter.

We perform experiments on an active granular material composed of individually-driven, spinning disks confined within a circular arena. Small bumps at the outer edges of the disks provide a variable amount of interparticle coupling in the form of geometric friction. The disks each spin counter-clockwise, but undergo a transition in their collective circulation around the center of the arena, from a clockwise orbit to a counter-clockwise orbit, as a function of packing fraction φ. We identify that, unlike for vibrated granular gases, the particles' velocity distributions are Gaussian over a large range of φ. By fitting the speed distribution to a Maxwell-Boltzmann distribution, we identify a temperature-like parameter which is a universal function of φ; this parameter is also equal to the mean translational energy of the particles. We quantify the collective circulation via its solid-body-like rotation rate, and find that this is a universal function centered around a critical packing fraction. In addition, the ratio of orbital kinetic energy to spin kinetic energy is also a universal function for non-zero geometric friction. These findings highlight the important role of both the type of driving and the interparticle interactions (here, geometric friction) in controlling the collective behavior of active granular systems.

Microscopic Origins of Shear Jamming for 2D Frictional Grains.

Shear jamming (SJ) occurs for frictional granular materials with packing fractions ϕ in ϕ_{S}<ϕ<ϕ_{J}^{0}, when the material is subject to shear strain γ starting from a force-free state. Here, ϕ_{J}^{µ} is the isotropic jamming point for particles with a friction coefficient µ. SJ states have mechanically stable anisotropic force networks, e.g., force chains. Here, we investigate the origins of SJ by considering small-scale structures-trimers and branches-whose response to shear leads to SJ. Trimers are any three grains where the two outer grains contact a center one. Branches occur where three or more quasilinear force chain segments intersect. Certain trimers respond to shear by compressing and bending; bending is a nonlinear symmetry-breaking process that can push particles in the dilation direction faster than the affine dilation. We identify these structures in physical experiments on systems of two-dimensional frictional discs, and verify their role in SJ. Trimer bending and branch creation both increase Z above Z_{iso}≃3 needed for jamming 2D frictional grains, and grow the strong force network, leading to SJ.