Search

This review presents the state of the art on the theory, molecular simulation, and coarse-grained strategies applied to the transport of gases and liquids in nanoporous materials (pore size in the range 1 - 100 nm). Recent advances in the understanding of molecular diffusion and transport under thermodynamic gradients in nanoporous adsorbents are discussed with special emphasis on small molecules in zeolites, active carbons, metal organic frameworks, but also in nanoporous materials with larger pores such as ordered and disordered mesoporous oxides. We provide a description of the fundamentals and principles of the different atom-scale and mesoscopic methods as well as of the theoretical formalisms that can be used to address such an important problem. Special attention is paid to the investigation of different molecular transport coefficients - including the so-called self, collective and transport diffusivities - but also to the determination of free energy barriers and their role in overall adsorption/separation process rates. We also introduce other available approaches such as hierarchical simulations and upscaling strategies.

Soft amorphous materials are viscoelastic solids ubiquitously found around us, from clays and cementitious pastes to emulsions and physical gels encountered in food or biomedical engineering. Under an external deformation, these materials undergo a noteworthy transition from a solid to a liquid state that reshapes the material microstructure. This yielding transition was the main theme of a workshop held from January 9 to 13, 2023 at the Lorentz Center in Leiden. The manuscript presented here offers a critical perspective on the subject, synthesizing insights from the various brainstorming sessions and informal discussions that unfolded during this week of vibrant exchange of ideas. The result of these exchanges takes the form of a series of open questions that represent outstanding experimental, numerical, and theoretical challenges to be tackled in the near future., Comment: 21 pages, 7 figures, perspective on the workshop 'Yield stress and fluidization in brittle and ductile amorphous systems' held from January 9 to 13, 2023 at the Lorentz Center in Leiden

Creating amorphous solid states by randomly bonding an ensemble of dense liquid monomers is a common procedure which is applied to create a variety of materials such as epoxy resins, colloidal gels, and vitrimers. The properties of the resulting solid do, however, {\it a priori} strongly depend on the preparation history. This can lead to substantial aging of the material, i.e., properties such as mechanical moduli and transport coefficients depend on the time elapsed since solidification, which can lead to a slow degradation of the material in technological applications. It is therefore important to understand under which conditions random monomer bonding can lead to stable solid states, i.e., long-lived metastable states whose properties do not change over time. In this work, we present a theoretical and computational analysis of this problem, and introduce a random bonding procedure that guarantees the proper equilibration of the resulting amorphous states. Our procedure also provides a new route to investigate the fundamental properties of glassy energy landscapes by producing translationally-invariant ultrastable glassy states of simple particle models., Comment: 25 pages, 15 figures

Beyond well-documented confinement and surface effects arising from the large internal surface and severely confining porosity of nanoporous hosts, the transport of nanoconfined fluids remains puzzling by many aspects. With striking examples such as memory, \textit{i.e.} non-viscous, effects, intermittent dynamics and surface barriers, the dynamics of fluids in nanoconfinement challenges classical formalisms (\textit{e.g.} random walk, viscous/advective transport) -- especially for molecular pore sizes. In this context, while molecular frameworks such as intermittent brownian motion, free volume theory and surface diffusion are available to describe the self-diffusion of a molecularly confined fluid, a microscopic theory for the collective diffusion (\textit{i.e.} permeability) -- which characterizes the flow induced by a thermodynamic gradient -- is lacking. Here, to fill this knowledge gap, we invoke the concept of `De Gennes narrowing' which relates the wavevector-dependent collective diffusivity $D_0(q)$ to the fluid structure factor $S(q)$. First, using molecular simulation for a simple yet representative fluid confined in a prototypical solid (zeolite), we unravel an essential coupling between the wavevector-dependent collective diffusivity and the structural ordering imposed on the fluid by the crystalline nanoporous host. Second, despite this complex interplay with marked Bragg peaks in the fluid structure, the fluid collective dynamics is shown to be accurately described through De Gennes narrowing. Moreover, in contrast to the bulk fluid, departure from De Gennes narrowing for the confined fluid in the macroscopic limit remains small as the fluid/solid interactions in severe confinement screen collective effects and, hence, weaken the wavevector dependence of collective transport.

The process of crystal nucleation can be accelerated or retarded by ultrasonic vibration, which is particularly attractive for the addictive manufacture and thermoplastic forming of metallic glasses, however, the effect and mechanism of oscillatory loading on the nucleation process are still elusive. By using molecular dynamics simulation, the changes in the time-temperature-transformation (TTT) curve under oscillatory external loading are systematically investigated in two typical binary alloys. A glass forming ability dependent response to the external loading is found, and the shortest incubation time is insensitive to the external loading, while the corresponding temperature can be significantly shifted. Within the framework of classical nucleation theory, a fitting formula is proposed to describe the simulation data quantitatively. In contrast to stationary shear, the elastic stress, rather than the strain rate, is the key parameter to control the evolution of TTT curve under oscillatory loading. Furthermore, the model shows that oscillatory loading can decouple the mobility and nucleation in the deeply supercooled liquid, hence the formation ability can be enhanced while the nucleation is suppressed, which is particularly helpful for the forming and manufacturing of metallic glasses.

We provide an overview of the different types of computational techniques developed over the years to study supercooled liquids, glassy materials and the physics of the glass transition. We organise these numerical strategies into four broad families. For each of them, we describe the general ideas without discussing any technical details. We summarise the type of questions which can be addressed by any given approach and outline the main results which have been obtained. Finally we describe two important directions for future computational studies of glassy systems., Comment: 16 pages, 1 figure. Submitted to the French Academy of Sciences to celebrate International Year of Glass 2022

We investigate the temperature dependence of thermodynamic (density, isobaric heat capacity), dynamical (self-diffusion coefficient, shear viscosity), and dielectric properties of several water models, the commonly employed TIP3P water model, well-established 4-point water model TIP4P-2005, and recently developed 4-point water model TIP4P-D. We focus on the temperature range of interest for the field of computational biophysics and soft matter (280-350 K). The 4-point water models lead to a spectacularly improved agreement with experimental data, strongly suggesting that the use of more modern parametrizations should be favored compared to the more traditional TIP3P for modeling temperature-dependent phenomena in biomolecular systems., Comment: 4 pages, 3 figures

Quasi-two-dimensional (quasi-2D) colloidal hard-sphere suspensions confined in a slit geometry are widely used as two dimensional (2D) model systems in experiments that probe the glassy relaxation dynamics of 2D systems. However, the question to what extent these quasi-2D systems indeed represent 2D systems is rarely brought up. Here, we use computer simulations that take into account hydrodynamic interactions to show that dense quasi-2D colloidal bi-disperse hard-sphere suspensions exhibit much more rapid diffusion and relaxation than their 2D counterparts at the same area fraction. This difference is induced by the additional vertical space in the quasi-2D samples in which the small colloids can move out of the 2D plane, therefore allowing overlap between particles in the projected trajectories. Surprisingly, this difference in the dynamics can be accounted for if, instead of using the surface density, one characterizes the systems by means of a suitable structural quantity related to the radial distribution function. This implies that in the two geometries the relevant physics for glass-formation is essentially identical. Our results provide not only practical implications on 2D colloidal experiments but also interesting insights into the 3D-to-2D crossover in glass-forming systems.

The quantum harmonic oscillator is the fundamental building block to compute thermal properties of virtually any dielectric crystal at low temperatures in terms of phonons, extended further to cases with anharmonic couplings, or even disordered solids. In general, Path Integral Monte Carlo (PIMC) or Molecular Dynamics (PIMD) methods are powerful tools to determine stochastically thermodynamic quantities without systematic bias, not relying on perturbative schemes. Addressing transport properties, for instance calculating thermal conductivity from PIMC, however, is substantially more difficult. Although correlation functions of current operators can be determined by PIMC from analytic continuation on the imaginary-time axis, Bayesian methods are usually employed for the numerical inversion back to real-time response functions. This task not only strongly relies on the accuracy of the PIMC data, but also introduces noticeable dependence on the model used for the inversion. Here, we address both difficulties with care. In particular, we first devise improved estimators for current correlations which substantially reduce the variance of the PIMC data. Next, we provide a neat statistical approach to the inversion problem, blending into a fresh workflow the classical stochastic maximum entropy method together with recent notions borrowed from statistical learning theory. We test our ideas on a single harmonic oscillator and a collection of oscillators with a continuous distribution of frequencies, and provide indications of the performance of our method in the case of a particle in a double well potential. This work establishes solid grounds for an unbiased, fully quantum mechanical calculation of transport properties in solids.

Mechanical deformation of amorphous solids can be described as consisting of an elastic part in which the stress increases linearly with strain, up to a yield point at which the solid either fractures or starts deforming plastically. It is well established, however, that the apparent linearity of stress with strain is actually a proxy for a much more complex behavior, with a microscopic plasticity that is reflected in diverging nonlinear elastic coefficients. Very generally, the complex structure of the energy landscape is expected to induce a singular response to small perturbations. In the athermal quasistatic regime, this response manifests itself in the form of a scale free plastic activity. The distribution of the corresponding avalanches should reflect, according to theoretical mean field calculations (Franz and Spigler, Phys. Rev. E., 2017, 95, 022139), the geometry of phase space in the vicinity of a typical local minimum. In this work, we characterize this distribution for simple models of glass forming systems, and we find that its scaling is compatible with the mean field predictions for systems above the jamming transition. These systems exhibit marginal stability, and scaling relations that hold in the stationary state are examined and confirmed in the elastic regime. By studying the respective influence of system size and age, we suggest that marginal stability is systematic in the thermodynamic limit.

Amorphous materials have a rich relaxation spectrum, which is usually described in terms of a hierarchy of relaxation mechanisms. In this work, we investigate the local dynamic modulus spectra in a model glass just above the glass transition temperature by performing a mechanical spectroscopy analysis with molecular dynamics simulations. We find that the spectra, at the local as well as on the global scale, can be well described by the Cole-Davidson formula in the frequency range explored with simulations. Surprisingly, the Cole-Davidson stretching exponent does not change with the size of the local region that is probed. The local relaxation time displays a broad distribution, as expected based on dynamic heterogeneity concepts, but the stretching is obtained independently of this distribution. We find that the size dependence of the local relaxation time and moduli can be well explained by the elastic shoving model.

In this work we develop a theoretical framework for the localization of flow in the steadily flowing regime of sheared disordered solids with inertial dynamics on a microscopic scale. To this aim we perform rheology studies at fixed shear rate on a 3D model of dense disordered solid. Our particle based simulations reveal the existence of heterogeneous shear-profiles in the stationary flow under homogeneous driving conditions. To rationalize this result, we propose a continuum model that couples the dynamics of the local flow to the evolution of a kinetic temperature field. A linear stability analysis of this theory predicts the minimum system size necessary for the flow instability to develop. This prediction as well as the velocity profiles obtained from this continuum model are in good agreement with the results from the particle based simulations., Comment: 27 pages, 5 main figures, 7 Supplementary figures

We report simulation results on melts of entangled linear polymers confined in a free-standing thin film. We study how the geometric constraints imposed by the confinement alter the entanglement state of the system compared to the equivalent bulk system using various observables. We find that the confinement compresses the chain conformation uniaxially, decreasing the volume pervaded by the chain, which in turn reduces the number of the accessible inter-chain contact that could lead to entanglements. This local and non-uniform effect depends on the position of the chain within the film. We also test a recently presented theory that predicts how the number of entanglements decreases with geometrical confinement., Comment: 28 pages, 10 figures

Yield stress fluids display complex dynamics, in particular when driven into the transient regime between the solid and the flowing state. Inspired by creep experiments on dense amorphous materials, we implement mesocale elasto-plastic descriptions to analyze such transient dynamics in athermal systems. Both our mean-field and space-dependent approaches consistently reproduce the typical experimental strain rate responses to different applied steps in stress. Moreover, they allow us to understand basic processes involved in the strain rate slowing down (creep) and the strain rate acceleration (fluidization) phases. The fluidization time increases in a power-law fashion as the applied external stress approaches a static yield stress. This stress value is related to the stress over-shoot in shear start-up experiments, and it is known to depend on sample preparation and age. By calculating correlations of the accumulated plasticity in the spatially resolved model, we reveal different modes of cooperative motion during the creep dynamics., Comment: 12 pages, 11 figures. To appear in Soft Matter

Cryogenic rejuvenation in metallic glasses reported in Ketov et al 's experiment (Nature(2015)524,200) has attracted much attention, both in experiments and numerical studies. The atomic mechanism of rejuvenation has been conjectured to be related to the heterogeneity of the glassy state, but the quantitative evidence is still elusive. Here we use molecular dynamics simulations of a model metallic glass to investigate the heterogeneity in the local thermal expansion. We then combine the resulting spatial distribution of thermal expansion with a continuum mechanics calculation to infer the internal stresses caused by a thermal cycle. Comparing the internal stress with the local yield stress, we prove that the heterogeneity in thermomechanical response has the potential to trigger local shear transformations, and therefore to induce rejuvenation during a cryogenic thermal cycling.

Self-consistent field approach is used to model a single end-tethered polymer chain on a substrate subject to various forces in three dimensions. Starting from a continuous Gaussian chain model, the following perturbations are considered: (i) hydrodynamic interaction with an externally imposed shear flow for which a new theoretical framework is formulated; (ii) excluded volume effect in a good solvent, treated in a mean field approximation; (iii) monomer-substrate repulsion. While the chain stretches along the flow, the change of the density profile perpendicular to the substrate is negligible for any reasonable simulation parameters. This null effect is in agreement with multiple neutron scattering studies.

Recent experiments (Le Bouil et al., Phys. Rev. Lett., 2014, 112, 246001) have analyzed the statistics of local deformation in a granular solid undergoing plastic deformation. Experiments report strongly anisotropic correlation between events, with a characteristic angle that was interpreted using elasticity theory and the concept of Eshelby transformations with dilation; interestingly, the shear bands that characterize macroscopic failure occur at an angle that is different from the one observed in microscopic correlations. Here, we interpret this behavior using a mesoscale elastoplastic model of solid flow that incorporates a local Mohr-Coulomb failure criterion. We show that the angle observed in the microscopic correlations can be understood by combining the elastic interactions associated with Eshelby transformation with the local failure criterion. At large strains, we also induce permanent shear bands at an angle that is different from the one observed in the correlation pattern. We interpret this angle as the one that leads to the maximal instability of slip lines.

The deformation and flow of disordered solids, such as metallic glasses and concentrated emulsions, involves swift localized rearrangements of particles that induce a long-range deformation field. To describe these heterogeneous processes, elastoplastic models handle the material as a collection of 'mesoscopic' blocks alternating between an elastic behavior and plastic relaxation, when they are too loaded. Plastic relaxation events redistribute stresses in the system in a very anisotropic way. We review not only the physical insight provided by these models into practical issues such as strain localization, creep and steady-state rheology, but also the fundamental questions that they address with respect to criticality at the yielding point and the statistics of avalanches of plastic events. Furthermore, we discuss connections with concurrent mean-field approaches and with related problems such as the plasticity of crystals and the depinning of an elastic line., Comment: review article

We develop an elasto-plastic description for the transient dynamics prior to steady flow of athermally yielding materials. Our mean-field model not only reproduces the experimentally observed non-linear time dependence of the shear-rate response to an external shear-stress, but also allows for the determination of the different physical processes involved in the onset of the re-acceleration phase after the initial critical slowing down and a distinct well defined fluidization phase. The evidenced power-law dependence of the fluidization time on the distance of the applied to an age dependent static yield stress is not universal but strongly dependent on initial conditions., Comment: 8 pages, 4 figures

We present a computer simulation of entangled polymer solutions at equilibrium. The chains repel each other via a soft Gaussian potential, appropriate for semi-dilute solutions at the scale of a correlation blob. The key innovation to suppress chain crossings is to use a pseudo-continuous model of a backbone which effectively leaves no gaps between consecutive points on the chain, unlike the usual bead-and-spring model. Our algorithm is sufficiently fast to observe the entangled regime using a standard desktop computer. The simulated structural and mechanical correlations are in fair agreement with the expected predictions for a semi-dilute solution of entangled chains.

Mechanical signaling plays a key role in biological processes like embryo development and cancer growth. One prominent way to probe mechanical properties of tissues is to study their response to externally applied forces. Using a particle-based model featuring random apoptosis and environment-dependent division rates, we evidence a crossover from linear flow to a shear-thinning regime with increasing shear rate. To rationalize this non-linear flow we derive a theoretical mean-field scenario that accounts for the interplay of mechanical and active noise in local stresses. These noises are respectively generated by the elastic response of the cell matrix to cell rearrangements and by the internal activity., Comment: 6 pages, 4 figures

By means of a finite elements technique we solve numerically the dynamics of an amorphous solid under deformation in the quasistatic driving limit. We study the noise statistics of the stress-strain signal in the steady state plastic flow, focusing on systems with low internal dissipation. We analyze the distributions of avalanche sizes and durations and the density of shear transformations when varying the damping strength. In contrast to avalanches in the overdamped case, dominated by the yielding point universal exponents, inertial avalanches are controlled by a non-universal damping dependent feedback mechanism; eventually turning negligible the role of correlations. Still, some general properties of avalanches persist and new scaling relations can be proposed., Comment: 10 pages, 9 figures

The onset of irreversible deformation in low-temperature amorphous solids is due to the accumulation of elementary events, consisting of spacially and temporally localized atomic rearrangements involving only a few tens of atoms. Recently, numerical and experimental work addressed the issue of spatio-temporal correlations between these plastic events. Here, we provide further insight into these correlations by investigating, via molecular dynamics (MD) simulations, the plastic response of a two-dimensional amorphous solid to artificially triggered local shear transformations. We show that while the plastic response is virtually absent in as-quenched configurations, it becomes apparent if a shear strain was previously imposed on the system. Plastic response has a four-fold symmetry which is characteristic of the shear stress redistribution following the local transformation. At high shear rate we report evidence for a fluctuation-dissipation relation, connecting plastic response and correlation, which seems to break down if lower shear rates are considered.

In crystals, molecules thermally vibrate around the periodic lattice sites. Vibrational motions are well understood in terms of phonons, which carry heat and control heat transport. The situation is notably different in disordered solids, where vibrational excitations are not phonons and can be even localized. Recent numerical work has established the concept of elastic heterogeneity: disordered solids show inhomogeneous local mechanical response. Clearly, the heterogeneous nature of elastic properties strongly influences vibrational and thermal properties, and it is expected to be the origin of anomalous features, including boson peak, vibrational localization, and temperature dependence of thermal conductivity. These are all crucial long-standing problems in materials physics, which we address in the present work. We have considered a toy model able to stabilize different states of matter, by introducing an increasing amount of size disorder. The phase diagram generated by molecular dynamics simulations encompasses the perfect crystalline state with a spatially homogeneous elastic moduli distribution, multiple defective phases with increasing moduli heterogeneities, and eventually a series of amorphous states. We have established clear correlations among the heterogeneous local mechanical response, vibrational states, and thermal conductivity. We provide evidence that elastic heterogeneity controls both vibrational and thermal properties, and is a key concept to understand the anomalous puzzling features of disordered solids.

We study the finite-shear-rate rheology of disordered solids by means of molecular dynamics simulations in two dimensions. By systematically varying the damping magnitude $\zeta$ in the low-temperature limit, we identify two well defined flow regimes, separated by a thin (temperature-dependent) crossover region. In the overdamped regime, the athermal rheology is governed by the competition between elastic forces and viscous forces, whose ratio gives the Weissenberg number $Wi= \zeta \dot\gamma$ (up to elastic parameters); the macroscopic stress $\Sigma$ follows the frequently encountered Herschel-Bulkley law $\Sigma= \Sigma\_0 + k \sqrt{Wi}$, with yield stress $\Sigma\_0\textgreater{}0$. In the underdamped (inertial) regime, dramatic changes in the rheology are observed for low damping: the flow curve becomes non-monotonic. This change is not caused by longer-lived correlations in the particle dynamics at lower damping; instead, for weak dissipation, the sample heats up considerably due to, and in proportion to, the driving. By suitably thermostatting more or less underdamped systems, we show that their rheology only depends on their kinetic temperature and the shear rate, rescaled with Einstein's vibration frequency., Comment: Accepted for publication in Phys. Rev. Lett

We present a computer simulation study of glassy and crystalline states using the standard Lennard-Jones interaction potential that is truncated at a finite cut-off distance, as is typical of many computer simulations. We demonstrate that the discontinuity at the cut-off distance in the first derivative of the potential (corresponding to the interparticle force) leads to the appearance of cut-off nonlinearities. These cut-off nonlinearities persist into the very-low-temperature regime thereby affecting low-temperature thermal vibrations, which leads to a breakdown of the harmonic approximation for many eigen modes, particularly for low-frequency vibrational modes. Furthermore, while expansion nonlinearities which are due to higher order terms in the Taylor expansion of the interaction potential are usually ignored at low temperatures and show up as the temperature increases, cut-off nonlinearities can become most significant at the lowest temperatures. Anharmonic effects readily show up in the elastic moduli which not only depend on the eigen frequencies, but are crucially sensitive to the eigen vectors of the normal modes. Whereas, those observables that rely mainly on static structural information or just the eigen frequencies, such as the vibrational density of states, total potential energy, and specific heat, show negligible dependence on the presence of the cut-off. Similar aspects of nonlinear behavior have recently been reported in model granular materials, where the constituent particles interact through finite-range, purely-repulsive potentials. These nonlinearities have been ascribed to the nature of the sudden cut-off at contact in the force-law, thus we demonstrate that cut-off nonlinearities emerge as a general feature of ordered and disordered solid state systems interacting through truncated potentials., Comment: 20 pages, 16 figures, 2 tables

We obtain, using semi-analytical transfer operator techniques, the Edwards thermodynamics of a one-dimensional model of blocks connected by harmonic springs and subjected to dry friction. The theory is able to reproduce the linear divergence of the correlation length as a function of energy density observed in direct numerical simulations of the model under tapping dynamics. We further characterize analytically this divergence using a Gaussian approximation for the distribution of mechanically stable configurations, and show that it is related to the existence of a peculiar infinite temperature critical point., Comment: 5 pages, 3 figures and Supplementary Material (5 pages, 3 figures)

We study stress time series caused by plastic avalanches in athermally sheared disordered materials. Using particle-based simulations and a mesoscopic elasto-plastic model, we analyze size and shear-rate dependence of the stress-drop durations and size distributions together with their average temporal shape. We find critical exponents different from mean-field predictions, and a clear asymmetry for individual avalanches. We probe scaling relations for the rate dependency of the dynamics and we report a crossover towards mean-field results for strong driving., Comment: 5 pages, 3 figures, 1 table, supplementary material to be found at http://www-liphy.ujf-grenoble.fr/pagesperso/martens/documents/liu2015-sm.pdf

The value measured in the amorphous structure with the same chemical composition is often considered as a lower bound for the thermal conductivity of any material: the heat carriers are strongly scattered by disorder, and their lifetimes reach the minimum time scale of thermal vibrations. An appropriate design at the nano-scale, however, may allow one to reduce the thermal conductivity even below the amorphous limit. In the present contribution, using molecular-dynamics simulation and the Green-Kubo formulation, we study systematically the thermal conductivity of layered phononic materials (superlattices), by tuning different parameters that can characterize such structures. We discover that the key to reach a lower-than-amorphous thermal conductivity is to block almost completely the propagation of the heat carriers, the superlattice phonons. We demonstrate that a large mass difference in the two intercalated layers, or weakened interactions across the interface between layers result in materials with very low thermal conductivity, below the values of the corresponding amorphous counterparts.

Shear transformations (i.e., localised rearrangements of particles resulting in the shear deformation of a small region of the sample) are the building blocks of mesoscale models for the flow of disordered solids. In order to compute the time-dependent response of the solid material to such a shear transformation, with a proper account of elastic heterogeneity and shear wave propagation, we propose and implement a very simple Finite-Element (FE) -based method. Molecular Dynamics (MD) simulations of a binary Lennard-Jones glass are used as a benchmark for comparison, and information about the microscopic viscosity and the local elastic constants is directly extracted from the MD system and used as input in FE. We find very good agreement between FE and MD regarding the temporal evolution of the disorder-averaged displacement field induced by a shear transformation, which turns out to coincide with the response of a uniform elastic medium. However, fluctuations are relatively large, and their magnitude is satisfactorily captured by the FE simulations of an elastically heterogeneous system. Besides, accounting for elastic anisotropy on the mesoscale is not crucial in this respect. The proposed method thus paves the way for models of the rheology of amorphous solids which are both computationally efficient and realistic, in that structural disorder and inertial effects are accounted for., Comment: Submitted to the Journal of Mechanics and Physics of Solids

We show that, at least at a mean-field level, the effect of structural disorder in sheared amorphous media is very dissimilar depending on the thermal or athermal nature of their underlying dynamics. We first introduce a toy model, including explicitly two types of noise (thermal versus athermal). Within this interpretation framework, we argue that mean-field athermal dynamics can be accounted for by the so-called H{\'e}braud-Lequeux (HL) model, in which the mechanical noise stems explicitly from the plastic activity in the sheared medium. Then, we show that the inclusion of structural disorder, by means of a distribution of yield energy barriers, has no qualitative effect in the HL model, while such a disorder is known to be one of the key ingredients leading kinematically to a finite macroscopic yield stress in other mean-field descriptions, such as the Soft-Glassy-Rheology model. We conclude that the statistical mechanisms at play in the emergence of a macroscopic yield stress, and a complex stationary dynamics at low shear rate, are different in thermal and athermal amorphous systems.

Physical parameters characterising electrokinetic transport in a confined electrolyte solution are reconstructed from the generic transport coefficients obtained within the classical non-equilibrium statistical thermodynamic framework. The electro-osmotic flow, the diffusio-osmotic flow, the osmotic current, as well as the pressure-driven Poiseuille-type flow, the electric conduction, and the ion diffusion, are described by this set of transport coefficients. The reconstruction is demonstrated for an aqueous NaCl solution between two parallel charged surfaces with a nanoscale gap, by using the molecular dynamic (MD) simulations. A Green-Kubo approach is employed to evaluate the transport coefficients in the linear-response regime, and the fluxes induced by the pressure, electric, and chemical potential fields are compared with the results of non-equilibrium MD simulations. Using this numerical scheme, the influence of the salt concentration on the transport coefficients is investigated. Anomalous reversal of diffusio-osmotic current, as well as that of electro-osmotic flow, is observed at high surface charge densities and high added-salt concentrations., Comment: 6 pages with 6 figures

We study consequences of long-range elasticity in thermally assisted dynamics of yield stress materials. Within a two-dimensinal mesoscopic model we calculate the mean-square displacement and the dynamical structure factor for tracer particle trajectories. The ballistic regime at short time scales is associated with a compressed exponential decay in the dynamical structure factor, followed by a subdiffusive crossover prior to the onset of diffusion. We relate this crossover to spatiotemporal correlations and thus go beyond established mean field predictions., Comment: 5 pages, 2 figures, to appear in PRL

Electrokinetic flows of an aqueous NaCl solution in nanochannels with negatively charged surfaces are studied using molecular dynamics (MD) simulations. The four transport coefficients that characterise the response to weak electric and pressure fields, namely the coefficients for the electrical current in response to the electric field ($M^{jj}$) and the pressure field ($M^{jm}$), and those for the mass flow in response to the same fields ($M^{mj}$ and $M^{mm}$), are obtained in the linear regime using a Green--Kubo approach. Nonequilibrium simulations with explicit external fields are also carried out, and the current and mass flows are directly obtained. The two methods exhibit good agreement even for large external field strengths, and Onsager's reciprocal relation ($M^{jm} = M^{mj}$) is numerically confirmed in both approaches. The influence of the surface charge density on the flow is also considered. The values of the transport coefficients are found to be smaller for larger surface charge density, because the counter-ions strongly bound near the channel surface interfere with the charge and mass flows. A reversal of the streaming current and of the reciprocal electro-osmotic flow, with a change of sign of $M^{mj}$ due to the excess co-ions, takes places for very high surface charge density., Comment: 28 pages

In the recent years, much attention has been devoted to the inhomogeneous nature of the mechanical response at the nano-scale in disordered solids. Clearly, the elastic heterogeneities that have been characterized in this context are expected to strongly impact the nature of the sound waves which, in contrast to the case of perfect crystals, cannot be completely rationalized in terms of phonons. Building on previous work on a toy model showing an amorphisation transition [Mizuno H, Mossa S, Barrat JL (2013) EPL {\bf 104}:56001], we investigate the relationship between sound waves and elastic heterogeneities in a unified framework, by continuously interpolating from the perfect crystal, through increasingly defective phases, to fully developed glasses. We provide strong evidence of a direct correlation between sound waves features and the extent of the heterogeneous mechanical response at the nano-scale.

The slow flow of amorphous solids exhibits striking heterogeneities: swift localised particle rearrangements take place in the midst of a more or less homogeneously deforming medium. Recently, experimental as well as numerical work has revealed spatial correlations between these flow heterogeneities. Here, we use molecular dynamics (MD) simulations to characterise the rearrangements and systematically probe their correlations both in time and in space. In particular, these correlations display a four-fold azimuthal symmetry characteristic of shear stress redistribution in an elastic medium and we unambiguously detect their increase in range with time. With increasing shear rate, correlations become shorter-ranged and more isotropic. In addition, we study a coarse-grained model motivated by the observed flow characteristics and challenge its predictions directly with the MD simulations. While the model captures both macroscopic and local properties rather satisfactorily, the agreement with respect to the spatiotemporal correlations is at most qualitative. The discrepancies provide important insight into relevant physics that is missing in all related coarse-grained models that have been developed for the flow of amorphous materials so far, namely the finite shear wave velocity and the impact of elastic heterogeneities on stress redistribution.

We study the two-dimensional (2D) shear flow of amorphous solids within variants of an elastoplastic model, paying particular attention to spatial correlations and time fluctuations of, e.g., local stresses. The model is based on the local alternation between an elastic regime and plastic events during which the local stress is redistributed. The importance of a fully tensorial description of the stress and of the inclusion of (coarse-grained) convection in the model is investigated; scalar and tensorial models yield very similar results, while convection enhances fluctuations and breaks the spurious symmetry between the flow and velocity gradient directions, for instance when shear localisation is observed. Besides, correlation lengths measured with diverse protocols are discussed. One class of such correlation lengths simply scale with the spacing between homogeneously distributed, simultaneous plastic events. This leads to a scaling of the correlation length with the shear rate as $\dot{\gamma}^{\frac{-1}{2}}$ in 2D in the athermal regime, regardless of the details of the model. The radius of the cooperative disk, defined as the near-field region in which plastic events induce a stress redistribution that is not amenable to a mean-field treatment, notably follows this scaling. On the other hand, the cooperative volume measured from the four-point stress susceptibility and its dependence on the system size and the shear rate are model-dependent., Comment: 17 pages