Shear-induced mixing of granular materials featuring broad granule size distributions.

Granular flows during a shear-induced mixing process are studied using discrete element methods. The aim is to understand the underlying elementary mechanisms of transition from unmixed to mixed phases for a granular material featuring a broad distribution of particles, which we investigate systematically by varying the strain rate and system size. Here the strain rate varies over four orders of magnitude and the system size varies from ten thousand to more than a million granules. A strain rate-dependent transition from quasistatic to purely inertial flow is observed. At the macroscopic scale, the contact stresses drop due to the formation of shear-induced instabilities that serves as an onset of granular flows and initiates mixing between the granules. The stress-drop displays a profound system size dependence. At the granular scale, mixing dynamics are correlated with the formation of shear bands, which result in significantly different timescales of mixing, especially for those regions that are close to the system walls and the bulk. Overall, our results reveal that although the transient dynamics display a generic behavior, these have a significant finite-size effect. In contrast, macroscopic behaviors at steady states have negligible system size dependence.

Emergence of linear isotropic elasticity in amorphous and polycrystalline materials.

We investigate the emergence of isotropic linear elasticity in amorphous and polycrystalline solids via extensive numerical simulations. We show that the elastic properties are correlated over a finite length scale ξ_{E}, so that the central limit theorem dictates the emergence of continuum linear isotropic elasticity on increasing the specimen size. The stiffness matrix of systems of finite size L>ξ_{E} is obtained, adding to that predicted by linear isotropic elasticity a random one of spectral norm (L/ξ_{E})^{-3/2} in three spatial dimensions. We further demonstrate that the elastic length scale corresponds to that of structural correlations, which in polycrystals reflect the typical size of the grain boundaries and length scales characterizing correlations in the stress field. We finally demonstrate that the elastic length scale affects the decay of the anisotropic long-range correlations of locally defined shear modulus and shear stress.

Frictional active Brownian particles.

Frictional forces affect the rheology of hard-sphere colloids, at high shear rate. Here we demonstrate, via numerical simulations, that they also affect the dynamics of active Brownian particles and their motility-induced phase separation. Frictional forces increase the angular diffusivity of the particles, in the dilute phase, and prevent colliding particles from resolving their collision by sliding one past to the other. This leads to qualitatively changes of motility-induced phase diagram in the volume-fraction motility plane. While frictionless systems become unstable towards phase separation as the motility increases only if their volume fraction overcomes a threshold, frictional systems become unstable regardless of their volume fraction. These results suggest the possibility of controlling the motility-induced phase diagram by tuning the roughness of the particles.

Oscillatory instabilities in three-dimensional frictional granular matter.

The dynamics of amorphous granular matter with frictional interactions cannot be derived in general from a Hamiltonian and therefore displays oscillatory instabilities stemming from the onset of complex eigenvalues in the stability matrix. These instabilities were discovered in the context of one- and two-dimensional systems, while the three-dimensional case was never studied in detail. Here we fill this gap by deriving and demonstrating the presence of oscillatory instabilities in a three-dimensional granular packing. We study binary assemblies of spheres of two sizes interacting via classical Hertz and Mindlin force laws for the longitudinal and tangent interactions, respectively. We formulate analytically the stability matrix in three dimensions and observe that a couple of complex eigenvalues emerge at the onset of the instability as in the case of frictional disks in two dimensions. The dynamics then shows oscillatory exponential growth in the mean-square displacement, followed by a catastrophic event in which macroscopic portions of mechanical stress and energy are lost. The generality of these results for any choice of forces that break the symplectic Hamiltonian symmetry is discussed.

Role of Attractive Forces in the Relaxation Dynamics of Supercooled Liquids.

The attractive tail of the intermolecular interaction affects very weakly the structural properties of liquids, while it affects dramatically their dynamical ones. Via the numerical simulations of model systems not prone to crystallization, both in three and in two spatial dimensions, here we demonstrate that the nonperturbative dynamical effects of the attractive forces are tantamount to a rescaling of the activation energy by the glass transition temperature T_{g}: systems only differing in their attractive interaction have the same structural and dynamical properties if compared at the same value of T/T_{g}.

Transition from Static to Dynamic Friction in an Array of Frictional Disks.

The nature of an instability that controls the transition from static to dynamical friction is studied in the context of an array of frictional disks that are pressed from above on a substrate. In this case the forces are all explicit and Newtonian dynamics can be employed without any phenomenological assumptions. We show that an oscillatory instability that had been discovered recently is responsible for the transition, allowing individual disks to spontaneously reach the Coulomb limit and slide with dynamic friction. The transparency of the model allows a full understanding of the phenomenon, including the speeds of the waves that travel from the trailing to the leading edge and vice versa.

Noise amplification in frictional systems: Oscillatory instabilities.

It was discovered recently that frictional granular materials can exhibit an important mechanism for instabilities, i.e., the appearance of pairs of complex eigenvalues in their stability matrix. The consequence is an oscillatory exponential growth of small perturbations which are tamed by dynamical nonlinearities. The amplification can be giant, many orders of magnitude, and it ends with a catastrophic system-spanning plastic event. Here we follow up on this discovery, explore the scaling laws characterizing the onset of the instability, the scenarios of the development of the instability with and without damping, and the nature of the eventual system-spanning events. The possible relevance to earthquake physics and to the transition from static to dynamic friction is discussed.

Oscillatory Instabilities in Frictional Granular Matter.

Frictional granular matter is shown to be fundamentally different in its plastic responses to external strains from generic glasses and amorphous solids without friction. While regular glasses exhibit plastic instabilities due to the vanishing of a real eigenvalue of the Hessian matrix, frictional granular materials can exhibit a previously unnoticed additional mechanism for instabilities, i.e., the appearance of a pair of complex eigenvalues leading to oscillatory exponential growth of perturbations that are tamed by dynamical nonlinearities. This fundamental difference appears crucial for the understanding of plasticity and failure in frictional granular materials. The possible relevance to earthquake physics is discussed.

Revealing the principal attributes of protein adsorption on block copolymer surfaces with direct experimental evidence at the single protein level.

Understanding protein adsorption onto polymer surfaces is of great importance in designing biomaterials, improving bioanalytical devices, and controlling biofouling, to name a few examples. Although steady research efforts have been advancing this field, our knowledge of this ubiquitous and complex phenomenon is still limited. In this study, we elucidate competitive protein adsorption behaviors sequentially occurring onto nanoscale block copolymer (BCP) surfaces via combined experimental and computer simulation approaches. The model systems chosen for our investigation are immunoglobulin G and fibrinogen introduced in different orders into the self-assembled nanodomains of poly(styrene)-block-poly(methylmethacrylate). We unambiguously reveal the adsorption, desorption, and replacement events of the same protein molecules via single protein tracking with atomic force microscopy. We then ascertain adsorption-related behaviors such as lateral mobility and self-association of proteins. We provide the much-needed, direct experimental proof of sequential adsorption events at the biomolecular level, which was virtually nonexistent before. We determine key protein adsorption pathways and dominant tendencies of sequential protein adsorption. We also reveal preadsorbed surface-associated behaviors in sequential adsorption, distinct from situations involving initially empty surfaces. We perform Monte-Carlo simulations to further substantiate our experimental outcomes. Our endeavors in this study may facilitate a well-guided mechanistic understanding of protein-polymer interactions by providing definite experimental evidence of competitive, sequential adsorption at the nanoscale. Increasingly, biomaterial and biomedical applications rely on systems of multicomponent proteins and chemically intricate, nanoscale polymer surfaces. Hence, our findings can also be beneficial for the development of next-generation nanobiomaterials and nanobiosensors exploiting self-assembled BCP nanodomain surfaces.

Long-range stress transmission guides endothelial gap formation.

In endothelial gap formation, local tractions exerted by the cell upon its basal adhesions are thought to exceed balancing tensile stresses exerted across the cell-cell junction, thus causing the junction to rupture. To test this idea, we mapped evolving tractions, intercellular stresses, and corresponding growth of paracellular gaps in response to agonist challenge. Contrary to expectation, we found little to no relationship between local tensile stresses and gap formation. Instead, we discovered that intercellular stresses were aligned into striking multi-cellular domains punctuated by defects in stress alignment. Surprisingly, gaps emerged preferentially not at stress hotspots, as predicted, but rather at stress defects. This unexpected behavior is captured by a minimal model of the cell layer as a jammed assembly of cohesive particles undergoing plastic rearrangements under tension. Together, experiments and model suggest a new physical picture in which gap formation, and its consequent effect on endothelial permeability, is determined not by a local stress imbalance at a cell-cell junction but rather by emergence of non-local, cooperative stress reorganization across the cellular collective.

Dependence of Ion Dynamics on the Polymer Chain Length in Poly(ethylene oxide)-Based Polymer Electrolytes.

It is known from experiments that in the polymer electrolyte system, which contains poly(ethylene oxide) chains (PEO), lithium-cations (Li(+)), and bis(trifluoromethanesulfonyl)imide-anions (TFSI(-)), the cation and the anion diffusion and the ionic conductivity exhibit a similar chain-length dependence: with increasing chain length, they start dropping steadily, and later, they saturate to constant values. These results are surprising because Li-cations are strongly correlated with the polymer chains, whereas TFSI-anions do not have such bonding. To understand this phenomenon, we perform molecular dynamics simulations of this system for four different polymer chain lengths. The diffusion results obtained from our simulations display excellent agreement with the experimental data. The cation transport model based on the Rouse dynamics can successfully quantify the Li-diffusion results, which correlates Li diffusion with the polymer center-of-mass motion and the polymer segmental motion. The ionic conductivity as a function of the chain length is then estimated based on the chain-length-dependent ion diffusion, which shows a temperature-dependent deviation for short chain lengths. We argue that in the first regime, counterion correlations modify the conductivity, whereas for the long chains, the system behaves as a strong electrolyte.

A multi-scale approach to characterize pure CH4, CF4, and CH4/CF4 mixtures.

In this study, we develop three intermolecular potentials for methane (CH4), tetrafluoromethane (CF4), and CH4/CF4 dimers using a novel ab initio method. The ultimate goal is to understand microscopically the phase-separation in CH4/CF4 systems, which takes place in the liquid states near their freezing points. Monte-Carlo (MC) simulations of the pure CH4 system are performed using the ab initio energies to verify the potential. The simulations reproduce quite well the experimentally known liquid densities, the internal energies, the second virial coefficients, and the radial distribution function. The essentially six-dimensional (6D) ab initio potential is then reduced to a one-dimensional (1D) effective potential using the inverse Monte-Carlo technique. This potential, too, successfully reproduces the experimental results. Interestingly, the MC study cannot be extended to the pure CF4 system and the CH4/CF4 mixed system because the two respective ab initio potentials present very rough potential landscapes. This renders the interpolation of energies for the MC simulations and thus the multi-scale approach unreliable. It suggests, however, a possible driving force for the experimentally observed phase separation of the CH4/CF4 system at low temperatures. Furthermore, we carefully study the determination of 1D effective potentials via inverse MC techniques. We argue that to a good approximation the temperature dependence of the 1D potentials can be estimated via reweighting techniques for a fixed temperature.

Effects of ionic liquids on cation dynamics in amorphous polyethylene oxide electrolytes.

We perform extensive molecular dynamics simulations of a poly(ethylene oxide)-based polymer electrolyte material containing lithium bis(trifluoromethanesulfonyl)imide salt for a wide temperature regime above and below the experimental crystallization temperature with and without N-methyl-N-propylpyrrolidinium bis(trifluoromethanesulfonyl)imide ionic liquid (IL). The impact of the IL-concentration on the cation dynamics is studied. The increase of the cation mobility upon addition of IL is significant but temperature-independent. This can be related to distinct variations of the underlying transport properties as expressed within the previously introduced transport model of polymer electrolytes. Even for the largest IL concentration the transport model perfectly predicts the non-trivial time-dependence of the cationic mean square displacement for all temperatures. Finally, we compare our numerical and theoretical findings with the results of recent nuclear magnetic resonance experiments. In this way we can exclusively relate the strong experimentally observed dependence of the low-temperature Li-diffusivity on the IL concentration to the impact of IL on crystallization.

Elastic signature of flow events in supercooled liquids under shear.

Using numerical simulation of a 2D Lennard-Jones system, we study the crossover from shear thinning to Newtonian flow. We find that the short-time elastic response of our system essentially does not change through this crossover, and show that, in the Newtonian regime, thermal activation triggers shear transformations, i.e., local irreversible shear events that produce Eshelby (long-ranged, anisotropic) deformation fields as previously seen in low-T glasses. Quite surprisingly, these Eshelby fields are found to persist much beyond the α-relaxation time, and shear thinning to coincide with the emergence of correlations between shear relaxation centers.

Robustness of avalanche dynamics in sheared amorphous solids as probed by transverse diffusion.

Using numerical simulations, we perform an extensive finite-size analysis of the transverse diffusion coefficient in a sheared 2D amorphous solid over a broad range of strain rates at temperatures up to the supercooled liquid regime. We thus obtain direct qualitative evidence for the persistence of correlations between elementary plastic events up to the vicinity of the glass transition temperature T(g). A quantitative analysis of the data, combined with a previous study of the T and γ dependence of the macroscopic stress [Phys. Rev. Lett. 105, 266001 (2010)], leads us to conclude that the average avalanche size remains essentially unaffected by temperature up to T ~ 0.75T(g).

Universal additive effect of temperature on the rheology of amorphous solids.

Extensive measurements of macroscopic stress in a 2D Lennard-Jones glass, over a broad range of temperatures (T) and strain rates (γ), demonstrate a very significant decrease of the flowing stress with T, even much below the glass transition. A detailed analysis of the interplay between loading, thermal activation, and mechanical noise leads us to propose that over a broad (γ, T) region, the effect of temperature amounts to a mere lowering of the strains at which plastic events occur, while the athermal avalanche dynamics remains essentially unperturbed. Up to the vicinity of the glass transition, temperature is then shown to correct the athermal stress by a (negative) additive contribution which presents a universal form, thus bringing support to and extending an expression proposed by Johnson and Samwer [Phys. Rev. Lett. 95, 195501 (2005)].