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The medium range order (MRO) in amorphous systems has been linked to complex features such as the dynamic heterogeneity of supercooled liquids or the plastic deformation of glasses. However, the nature of the MRO in these materials has remained elusive, primarily due to the lack of methods capable of characterizing this order. Here, we leverage standard two-body structural correlators and advanced many-body correlation functions to probe numerically the MRO in prototypical network glassformers, i.e., silica and sodium silicates, systems that are of importance in natural as well as industrial settings. With increasing Na concentration, one finds that the local environment of Na becomes more structured and the spatial distribution of Na on intermediate length scales changes from blob-like to channel-like, indicating a growing inhomogeneity in the spatial Na arrangement. In parallel, we find that the Si-O network becomes increasingly depolymerized, resulting in a ring size distribution that broadens. The radius of gyration of the rings is well described by a power-law with an exponent around 0.75, indicating that the rings are progressively more crumbled with increasing size. Using a recently proposed four-point correlation function, we reveal that the relative orientation of the tetrahedra shows a transition at a distance around 4 Angstroms, a structural modification that is not seen in standard two-point correlation functions. Furthermore, we find that the length scale characterizing the MRO is non-monotonic as a function of temperature, caused by the competition between energetic and entropic terms. Finally, we demonstrate that the structural correlation lengths as obtained from the correlation functions that quantify the MRO are correlated with macroscopic observables such as the kinetic fragility of the liquids and the elastic properties of the glasses.

Granular materials such as sand, powders, and food grains are ubiquitous in civil engineering, geoscience, agriculture, and medicine. While the influence of friction between the grains on the static structure of these systems is well understood, its impact on the dynamics is an open problem. Here we use particle-based simulations of a granular pack under cyclic shear and discover that the relaxation time of the system is a non-monotonic function of friction. By introducing the concept of dynamic constraints, we reveal that this re-entrant dynamics is due to the competition between increasing frictional coupling and a concurrent change in the structure of the granular pack. Our theoretical approach, which unifies the dynamics of friction-less systems with frictional ones, is applicable to other systems that have a complex free energy landscape and a dynamics which involves time-dependent constraints, thus setting the stage for a description of the dynamic behavior of a large class of complex systems.

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

Using large-scale molecular dynamics simulations, we investigate the surface properties of lithium, sodium, and potassium silicate glasses containing 25 mole % of alkali oxide. The comparison of two types of surfaces, a melt-formed surface (MS) and a fracture surface (FS), demonstrates that the influence of the alkali modifier on the surface properties depends strongly on the nature of the surface. The FS exhibits a monotonic increase of modifier concentration with increasing alkali size while the MS shows a saturation of alkali concentration when going from Na to K glasses, indicating the presence of two competing mechanism that influence the properties of a MS. For the FS, we find that larger alkali ions reduce the concentration of under-coordinated Si atoms and increase the fraction of two-membered rings, implying an enhanced chemical reactivity of the surface. For both types of surfaces, the roughness is found to increase with alkali size, with the effect being more pronounced for the FS than for the MS. The height-height correlation functions of the surfaces show a scaling behavior that is independent of the alkali species considered: The ones for the MS are compatible with the prediction of the frozen capillary wave theory while the ones for the FS show a logarithmic growth, i.e., on the nanoscale these surfaces are not self-affine fractals. The influence of the modifier on the surface properties are rationalized in terms of the interplay between multiple factors involving the size of the ions, bond strength, and charge balance on the surface.

The conventional wisdom is that liquids are completely disordered and lack non-trivial structure beyond nearest-neighbor distances. Recent observations have upended this view and demonstrated that the microstructure in liquids is surprisingly rich and plays a critical role in numerous physical, biological, and industrial processes. However, approaches to uncover this structure are either system-specific or yield results that are not physically intuitive. Here, through single-particle resolved three-dimensional confocal microscope imaging and the use of a recently introduced four-point correlation function, we show that bidisperse colloidal liquids have a highly non-trivial structure comprising alternating layers with icosahedral and dodecahedral order, which extends well-beyond nearest-neighbor distances and grows with supercooling. By quantifying the dynamics of the system on the particle level, we establish that it is this intermediate-range order, and not the short-range order, which has a one-to-one correlation with dynamical heterogeneities, a property directly related to the relaxation dynamics of glassy liquids. Our experimental findings provide a direct and much sought-after link between the structure and dynamics of liquids and pave the way for probing the consequences of this intermediate-range order in other liquid state processes., Comment: 18 pages, and 3 figures

Granular materials such as sand, powders, and grains are omnipresent in daily life, industrial applications, and earth-science [1]. When unperturbed, they form stable structures that resemble the ones of other amorphous solids like metallic and colloidal glasses [2]. It is commonly conjectured that all these amorphous materials show a universal mechanical response when sheared slowly, i.e., to have an elastic regime, followed by yielding [3]. Here we use X-ray tomography to determine the microscopic dynamics of a cyclically sheared granular system in three dimensions. Independent of the shear amplitude $\Gamma$, the sample shows a cross-over from creep to diffusive dynamics, indicating that granular materials have no elastic response and always yield, in stark contrast to other glasses. The overlap function [4] reveals that at large $\Gamma$ yielding is a simple cross-over phenomenon, while for small $\Gamma$ it shows features of a first order transition with a critical point at $\Gamma\approx 0.1$ at which one finds a pronounced slowing down and dynamical heterogeneity. Our findings are directly related to the surface roughness of granular particles which induces a micro-corrugation to the potential energy landscape, thus creating relaxation channels that are absent in simple glasses. These processes must be understood for reaching an understanding of the complex relaxation dynamics of granular systems.

The elasticity of disordered and polydisperse polymer networks is a fundamental problem of soft matter physics that is still open. Here, we self-assemble polymer networks via simulations of a mixture of bivalent and tri- or tetravalent patchy particles, which result in an exponential strand length distribution analogous to that of experimental randomly crosslinked systems. After assembly, the network connectivity and topology are frozen and the resulting system is characterized. We find that the fractal structure of the network depends on the number density at which the assembly has been carried out, but that systems with the same mean valence and same assembly density have the same structural properties. Moreover, we compute the long-time limit of the mean-squared displacement, also known as the (squared) localization length, of the crosslinks and of the middle monomers of the strands, showing that the dynamics of long strands is well described by the tube model. Finally, we find a relation connecting these two localization lengths at high density, and connect the crosslink localization length to the shear modulus of the system., Comment: 37 pages, 12 figures; fixed equation at pag. 24 and typos

Using particle trajectory data obtained from x-ray tomography, we determine two kinds of effective temperatures in a cyclically sheared granular system. The first one is obtained from the fluctuation-dissipation theorem which relates the diffusion and mobility of lighter tracer particles immersed in the system. The second is the Edwards compactivity defined via the packing volume fluctuations. We find robust excellent agreement between these two temperatures, independent of the type of the tracers, cyclic shear amplitudes, and particle surface roughness. We further elucidate that in granular systems the viscous-like drag force is due to the broken symmetry of the local contact geometry., Comment: 19 pages, 6 figures

The plastic deformation of crystalline materials can be understood by considering their structural defects such as disclinations and dislocations. Although glasses are also solids, their structure resembles closely the one of a liquid and hence the concept of structural defects becomes ill-defined. As a consequence it is very challenging to rationalize on a microscopic level the mechanical properties of glasses close to the yielding point and to relate plastic events with structural properties. Here we investigate the topological characteristics of the eigenvector field of the vibrational excitations of a two-dimensional glass model, notably the geometric arrangement of the topological defects as a function of vibrational frequency. We find that if the system is subjected to a quasistatic shear, the location of the resulting plastic events correlate strongly with the topological defects that have a negative charge. Our results provide thus a direct link between the structure of glasses prior their deformation and the plastic events during deformation.

We use large-scale simulations to investigate the dynamic fracture of silica and sodium-silicate glasses under uniaxial tension. The stress-strain curves demonstrate that silica glass is brittle whereas the glasses rich in Na show pronounced ductility. A strong composition dependence is also seen in the crack velocity which is on the order of 1800 m/s for glasses with low Na concentration and decreases to 700 m/s if the concentration is high. We find that during the fracture of Na-rich glasses very irregular cavities as large as 3-4 nm form ahead of the crack front, indicating the presence of nanoductility in these glasses. Before fracture occurs, the local composition, structure, and mechanical properties are heterogeneous in space and show a strong dependence on the applied strain. Further analysis of the correlations between these local properties allows to obtain a better microscopic understanding of the deformation and fracture of glasses and how the local heating close to the crack tip, up to several hundred degrees, permits the structure to relax.

A recent breakthrough in glass science has been the synthesis of ultrastable glasses via physical vapor deposition techniques. These samples display enhanced thermodynamic, kinetic and mechanical stability, with important implications for fundamental science and technological applications. However, the vapor deposition technique is limited to atomic, polymer and organic glass-formers and is only able to produce thin film samples. Here, we propose a novel approach to generate ultrastable glassy configurations in the bulk, via random particle bonding, and using computer simulations we show that this method does indeed allow for the production of ultrastable glasses. Our technique is in principle applicable to any molecular or soft matter system, such as colloidal particles with tunable bonding interactions, thus opening the way to the design of a large class of ultrastable glasses., Comment: 8 pages, 6 figures + supplementary information. Improved version thanks to referees' comments

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.

For small tension the response of a solid to an applied stress is given by Hooke's law. Outside this linear regime the relation between stress and strain is no longer universal and at present there is no satisfactory insight on how to connect for disordered materials the stress-strain relation to the microscopic properties of the system. Here we use atomistic computer simulations to establish this connection for the case of silicate glasses containing modifiers. By probing how in the highly non-linear regime the stress-strain curve depends on composition, we are able to identify the microscopic mechanisms that are responsible for the complex dependence of stress on strain, notably the presence of an unexpected quasi-plateau in the tangent modulus. We trace back this dependence to the mobility of the modifiers which, without leaving their cage or modifying the topology of the network, are able to relieve the local stresses. Since the identified mechanism is general, the results obtained in this study will also be helpful for understanding the mechanical response of other disordered materials.

Using computed x-ray tomography we determine the three dimensional (3d) structure of binary hard sphere mixtures as a function of composition and size ratio of the particles, q. Using a recently introduced four-point correlation function we reveal that this 3d structure has on intermediate and large length scales a surprisingly regular order, the symmetry of which depends on q. The related structural correlation length has a minimum at the composition at which the packing fraction is highest. At this composition also the number of different local particle arrangements has a maximum, indicating that efficient packing of particles is associated with a structure that is locally maximally disordered.

Silica is known as the archetypal strong liquid, exhibiting an Arrhenius viscosity curve with a high glass transition temperature and constant activation energy. However, given the ideally isostatic nature of the silica network, the presence of even a small concentration of defects can lead to a significant decrease in both the glass transition temperature and activation energy for viscous flow. To understand the impact of trace level dopants on the viscosity of silica, we measure the viscosity-temperature curves for seven silica glass samples having different impurities, including four natural and three synthetic samples. Depending on the type of dopant, the glass transition temperature can vary by nearly 300 K. A common crossover is found for all viscosity curves around ~2200-2500 K, which we attribute to a change of the transport mechanism in the melt from being dominated by intrinsic defects at high temperature to dopant-induced defects at low temperatures.

Combining X-ray tomography with simultaneous shear force measurement, we investigate shear-induced granular avalanches using spherical particles with different surface roughness. We find that systems consisting of particles with large surface roughness display quasi-periodic avalanches interrupted by crackling-like small ones. In contrast, systems consisting of particles with small roughness display no detectable avalanches. The stress drop of quasi-periodic avalanche shows a linear relation with the correlation length of particle non-affine displacement, suggesting that roughness enhances inter-particle locking and hence particle-level dynamic correlation length. However, the nonaffine displacement is two orders of magnitude smaller than particle size, indicating that stress is mainly released on the length scale of roughness. The correlation length of non-affine displacements abruptly increases when a quasi-periodic avalanche occurs, suggesting that quasi-periodic avalanches can be interpreted as a spinodal nucleation event in a first-order phase transition., Comment: 22 pages, 7 figures

Using molecular dynamics simulations we study the static and dynamic properties of spherical nanoparticles (NPs) embedded in a disordered and polydisperse polymer network. Purely repulsive (RNP) as well as weakly attractive (ANP) polymer-NP interactions are considered. It is found that for both types of particles the NP dynamics at intermediate and at long times is controlled by the confinement parameter $C=\sigma_N/\lambda$, where $\sigma_N$ is the NP diameter and $\lambda$ is the dynamic localization length of the crosslinks. Three dynamical regimes are identified: i) For weak confinement ($C \lesssim 1$) the NPs can freely diffuse through the mesh; ii) For strong confinement ($C \gtrsim 1$) NPs proceed by means of activated hopping; iii) For extreme confinement ($C \gtrsim 3$) the mean squared displacement shows on intermediate time scales a quasi-plateau since the NPs are trapped by the mesh for very long times. Escaping from this local cage is a process that depends strongly on the local environment, thus giving rise to an extremely heterogeneous relaxation dynamics. The simulation data are compared with the two main theories for the diffusion process of NPs in gels. Both theories give a very good description of the $C-$dependence of the NP diffusion constant, but fail to reproduce the heterogeneous dynamics at intermediate time scales., Comment: 62 pages, 24 figures

Using X-ray tomography, we experimentally investigate granular packings subject to mechanical tapping for three types of beads with different friction coefficients. We validate Edwards volume ensemble in these three-dimensional granular systems and establish a granular version of thermodynamic zeroth law. Within Edwards framework, we also explicitly clarify how friction influences granular statistical mechanics as modifying the density of states, which allows us to determine the entropy as a function of packing fraction and friction subsequently. Additionally, we obtain a granular jamming phase diagram based on geometric coordination number and packing fraction., Comment: 20 pages, 7 figures

Due to their unique structural and mechanical properties, randomly-crosslinked polymer networks play an important role in many different fields, ranging from cellular biology to industrial processes. In order to elucidate how these properties are controlled by the physical details of the network (\textit{e.g.} chain-length and end-to-end distributions), we generate disordered phantom networks with different crosslinker concentrations $C$ and initial density $\rho_{\rm init}$ and evaluate their elastic properties. We find that the shear modulus computed at the same strand concentration for networks with the same $C$, which determines the number of chains and the chain-length distribution, depends strongly on the preparation protocol of the network, here controlled by $\rho_{\rm init}$. We rationalise this dependence by employing a generic stress-strain relation for polymer networks that does not rely on the specific form of the polymer end-to-end distance distribution. We find that the shear modulus of the networks is a non-monotonic function of the density of elastically-active strands, and that this behaviour has a purely entropic origin. Our results show that if short chains are abundant, as it is always the case for randomly-crosslinked polymer networks, the knowledge of the exact chain conformation distribution is essential for predicting correctly the elastic properties. Finally, we apply our theoretical approach to published experimental data, qualitatively confirming our interpretations., Comment: SM appended after the list of references

We use \textit{ab initio} molecular dynamics simulations to investigate the properties of the dry surface of pure silica and sodium silicate glasses. The surface layers are defined based on the atomic distributions along the direction ($z-$direction) perpendicular to the surfaces. We show that these surfaces have a higher concentration of dangling bonds as well as two-membered (2M) rings than the bulk samples. Increasing concentration of Na$_2$O reduces the proportion of structural defects. From the vibrational density of states, one concludes that 2M rings have a unique vibrational signature at a frequency $\approx850$~cm$^{-1}$, compatible with experimental findings. We also find that, due to the presence of surfaces, the atomic vibration in the $z-$direction is softer than for the two other directions. The electronic density of states shows clear the differences between the surface and interior and we can attribute these to specific structural units. Finally, the analysis of the electron localization function allows to get insight on the influence of local structure and the presence of Na on the nature of chemical bonding in the glasses.

We propose a novel model for a glass-forming liquid which allows to switch in a continuous manner from a standard three-dimensional liquid to a fully connected mean-field model. This is achieved by introducing k additional particle-particle interactions which thus augments the effective number of neighbors of each particle. Our computer simulations of this system show that the structure of the liquid does not change with the introduction of these pseudo neighbours and by means of analytical calculations, we determine the structural properties related to these additional neighbors. We show that the relaxation dynamics of the system slows down very quickly with increasing k and that the onset and the mode-coupling temperatures increase. The systems with high values of k follow the MCT power law behaviour for a larger temperature range compared to the ones with lower values of k. The dynamic susceptibility indicates that the dynamic heterogeneity decreases with increasing k whereas the non-Gaussian parameter is independent of it. Thus we conclude that with the increase in the number of pseudo neighbours the system becomes more mean-field like. By comparing our results with previous studies on mean-field like system we come to the conclusion that the details of how the mean-field limit is approached are important since they can lead to different dynamical behavior in this limit., Comment: 19 pages, 21 figures

The solidity of glassy materials is believed to be due to the cage formed around each particle by its neighbors, but in reality the details of cage-formation remain elusive [1-4]. This cage starts to be formed at the onset temperature/density at which the normal liquid begins to show the first signs of glassy dynamics. To study cage-formation we use here focused lasers to produce a local perturbation of the structure on the particle level in 2D colloidal suspensions and monitor by means of video microscopy the system's non-linear dynamic response. All observables we probed show a response which is non-monotonic as a function of the packing fraction, peaking at the onset density. Video microscopic images reveal that this maximum response is due to the buildup of domains with cooperative dynamics that become increasingly rigid and start to dominate the particle dynamics. This proof-of-concept from microrheological deformation demonstrates that in this glass-forming liquid cage formation is directly related to the merging of these domains, thus elucidating the first step in glass-formation [1, 5]., Comment: 29 pages, 8 figures

Using cyclic shear to drive a two dimensional granular system, we determine the structural characteristics for different inter-particle friction coefficients. These characteristics are the result of a competition between mechanical stability and entropy, with the latter's effect increasing with friction. We show that a parameter-free maximum-entropy argument alone predicts an exponential cell order distribution, with excellent agreement with the experimental observation. We show that friction only tunes the mean cell order and, consequently, the exponential decay rate and the packing fraction. We further show that cells, which can be very large in such systems, are short-lived, implying that our systems are liquid-like rather than glassy.

Using atomistic computer simulations we determine the roughness and topographical features of melt-formed (MS) and fracture surfaces (FS) of oxide glasses. We find that the topography of the MS is described well by the frozen capillary wave theory. The FS are significant rougher than the MS and depend strongly on glass composition. The height-height correlation function for the FS shows an unexpected logarithmic dependence on distance, in contrast to the power-law found in experiments. We thus conclude that on length scales less than 10 nm FS are not self-affine fractals.

Disordered systems like liquids, gels, glasses, or granular materials are not only ubiquitous in daily life and in industrial applications but they are also crucial for the mechanical stability of cells or the transport of chemical and biological agents in living organisms. Despite the importance of these systems, their microscopic structure is understood only on a rudimentary level, thus in stark contrast to the case of gases and crystals. Since scattering experiments and analytical calculations usually give only structural information that is spherically averaged, the three dimensional (3D) structure of disordered systems is basically unknown. Here we introduce a simple method that allows to probe the 3D structure of such systems. Using computer simulations we find that hard-sphere-like liquids have on intermediate and large scales an intricate structural order given by alternating layers with icosahedral and dodecahedral symmetries, while open network liquids like silica have a structural order with tetrahedral symmetry. These results show that liquids have a highly non-trivial 3D structure and that this structural information is encoded in non-standard correlation functions., Comment: arXiv admin note: substantial text overlap with arXiv:1904.12447

Using molecular dynamics simulations we investigate the dependence of the structural and vibrational properties of the surfaces of sodo-silicate glasses on the sodium content as well as the nature of the surface. Two types of glass surfaces are considered: A melt-formed surface (MS) in which a liquid with a free surface has been cooled down into the glass phase and a fracture surface (FS) obtained by tensile loading of a glass sample. We find that the MS is more abundant in Na and non-bridging oxygen atoms than the FS and the bulk glass, whereas the FS has higher concentration of structural defects such as two-membered rings and under-coordinated Si than the MS. We associate these structural differences to the production histories of the glasses and the mobility of the Na ions. It is also found that for Na-poor systems the fluctuations in composition and local atomic charge density decay with a power-law as a function of distance from the surface while Na-rich systems show an exponential decay with a typical decay length of $\approx2.3$~\AA. The vibrational density of states shows that the presence of the surfaces leads to a decrease of the characteristic frequencies in the system. The two-membered rings give rise to a pronounce band at $\approx880$~cm$^{-1}$ which is in good agreement experimental observations.

We adapt and apply a recently developed optimization scheme used to obtain effective potentials for aluminosilicate glasses to include the network former boron into the interaction parameter set. As input data for the optimization, we used the radial distribution functions of the liquid at high temperature generated by ab initio molecular dynamics simulations, and density, coordination and elastic modulus of glass at room temperature from experiments. The new interaction potentials are shown to reproduce reliably the structure, coordination and mechanical properties over a wide range of compositions for binary alkali borates. Furthermore, the transferability of these new interaction parameters allows mixing to reliably reproduce properties of various boroaluminate and borosilicate glasses.

We compare the ability of various interaction potentials to predict the structural and mechanical properties of silica and sodium silicate glasses. While most structural quantities show a relatively mild dependence on the potential used, the mechanical properties such as the failure stress and strain as well as the elastic moduli depend very strongly on the potential, once finite size effects have been taken into account. We find that to avoid such finite size effects, samples of at least 75,000 atoms are needed. Finally we probe how the simulation ensemble influences the fracture properties of the glasses and conclude that fracture simulations should be carried out in the constant pressure ensemble., Comment: Minor corrections. An additional figure (current Fig. 3) and correction in Tab. I (interchange of SiO and OO parameters' lines)

In order to characterize the geometrical mesh size $\xi$, we simulate a solution of coarse-grained polymers with densities ranging from the dilute to the concentrated regime and for different chain lengths. Conventional ways to estimate $\xi$ rely either on scaling assumptions which give $\xi$ only up to an unknown multiplicative factor, or on measurements of the monomer density fluctuation correlation length $\xi_c$. We determine $\xi_c$ from the monomer structure factor and from the radial distribution function, and find that the identification $\xi=\xi_c$ is not justified outside of the semidilute regime. In order to better characterize $\xi$, we compute the pore size distribution (PSD) following two different definitions, one by Torquato et al. (Ref.1) and one by Gubbins et al. (Ref.2). We show that the mean values of the two distributions, $\langle r \rangle_T$ and $\langle r \rangle_G$, both display the behavior predicted for $\xi$ by scaling theory, and argue that $\xi$ can be identified with either one of these quantities. This identification allows to interpret the PSD as the distribution of mesh sizes, a quantity which conventional methods cannot access. Finally, we show that it is possible to map a polymer solution on a system of hard or overlapping spheres, for which Torquato's PSD can be computed analytically and reproduces accurately the PSD of the solution. We give an expression that allows $\langle r \rangle_T$ to be estimated with great accuracy in the semidilute regime by knowing only the radius of gyration and the density of the polymers.

In our previous publication (Ref. 1) we have shown that the data for the normalized diffusion coefficient of the polymers, $D_p/D_{p0}$, falls on a master curve when plotted as a function of $h/\lambda_d$, where $h$ is the mean interparticle distance and $\lambda_d$ is a dynamic length scale. In the present note we show that also the normalized diffusion coefficient of the nanoparticles, $D_N/D_{N0}$, collapses on a master curve when plotted as a function of $h/R_h$, where $R_h$ is the hydrodynamic radius of the nanoparticles., Comment: Addition to arXiv:1804.06993, 2 pages, 2 figures

Using the potential energy landscape formalism we show that, in the temperature range in which the dynamics of a glass forming system is thermally activated, there exists a unique set of "basis glass states" each of which is confined to a single metabasin of the energy landscape of a glass forming system. These basis glass states tile the entire configuration space of the system, exhibit only secondary relaxation and are solid-like. Any macroscopic state of the system (whether liquid or glass) can be represented as a superposition of basis glass states and can be described by a probability distribution over these states. During cooling of a liquid from a high temperature, the probability distribution freezes at sufficiently low temperatures describing the process of liquid to glass transition. The time evolution of the probability distribution towards the equilibrium distribution during subsequent aging describes the primary relaxation of a glass., Comment: 19 pages

Disordered systems like liquids, gels, glasses, or granular materials are not only ubiquitous in daily life and in industrial applications but they are also crucial for the mechanical stability of cells or the transport of chemical and biological agents in living organisms [1-3]. Despite the importance of these systems, their microscopic structure is understood only on a rudimentary level, thus in stark contrast to the case of gases and crystals [1,4]. Experimental and theoretical investigations indicate that disordered systems have a structural order on the length scale of a few particle diameters but which then quickly vanishes at larger distances [5]. This conclusion is, however, based mainly on the behavior of two-point correlation functions such as the static structure factor or the radial distribution function [5.6]. Whether or not disordered systems have an order that extents to larger length scales is therefore a highly important question that is still open [7-10]. Here we use computer simulations to show that liquids have an intricate structural order given by alternating layers with icosahedral and dodecahedral symmetries and which extends to surprisingly large distances. We show that the temperature dependence of the corresponding length scale can be detected in the static structure factor, making it directly accessible to scattering experiments. These results, obtained by a novel type of four point correlation function that probes directly the particle density in three dimensions, show that liquids are far more ordered than envisaged so far but that this structural information is encoded in non-standard correlation functions.

The glass is a disordered solid that processes distinct dynamical and elastic properties compared with crystal. How heterogeneous glassy materials can be and to what extent dynamics is encoded with structure and elasticity are long-standing puzzles in glass science. In this experiment, we probed the responses of binary colloidal glasses towards the excitations induced by highly focused laser pulses. We observed very similar excitation patterns when the laser was repeated in the linear region; directly proving that the dynamical heterogeneity is strongly encoded with structure. In the non-linear region, we identified a non-monotonic dynamical length scale as a function of area fraction, resulting from the non-monotonic coupling of momentum transfer in radial and orthogonal directions. Surprisingly, the excitation size and radius of gyration conformed to a universal scaling relation that covered both linear and non-linear regions. Our experiments offered a new strategy of actively probing the response of glassy materials on the microscopic level., Comment: 31 pages, 15 figures

We apply a recently developed optimization scheme to obtain effective potentials for alkali and alkaline-earth aluminosilicate glasses that contains lithium, sodium, potassium, or calcium as modifiers. As input data for the optimization, we used the radial distribution functions of the liquid at high temperature generated by means of ab initio molecular dynamics simulations and density and elastic modulus of glass at room temperature from experiments. The new interaction potentials are able to reproduce reliably the structure and various mechanical and vibrational properties over a wide range of compositions for binary silicates. We have tested these potentials for various ternary systems and find that they are transferable and can be mixed, thus allowing to reproduce and predict the structure and properties of multi-component glasses., Comment: 21 pages

The relaxation dynamics of glass-forming systems shows a multitude of features that are absent in normal liquids, such as non-exponential relaxation and a strong temperature-dependence of the relaxation time. Connecting these dynamic properties to the microscopic structure of the system is very challenging because of the presence of the structural disorder. Here we use computer simulations of a metallic glass-former to establish such a connection. By probing the temperature and wave-vector dependence of the intermediate scattering function we find that the relaxation dynamics of the glassy melt is directly related to the local arrangement of icosahedral structures: Isolated icosahedra give rise to a flow-like stretched exponential relaxation whereas clusters of icosahedra lead to a compressed exponential relaxation that is reminiscent to the one found in a solid. Our results show that in metallic glass-formers these two types of relaxation processes can coexist and give rise to a surprisingly complex dynamics, insight that will allow to get a deeper understanding of the outstanding mechanical properties of metallic glasses.

Upon mechanical loading, granular materials yield and undergo plastic deformation. The nature of plastic deformation is essential for the development of the macroscopic constitutive models and the understanding of shear band formation. However, we still do not fully understand the microscopic nature of plastic deformation in disordered granular materials. Here we used synchrotron X-ray tomography technique to track the structural evolutions of three-dimensional granular materials under shear. We establish that highly distorted coplanar tetrahedra are the structural defects responsible for microscopic plasticity in disordered granular packings. The elementary plastic events occur through flip events which correspond to a neighbor switching process among these coplanar tetrahedra (or equivalently as the rotation motion of 4-ring disclinations). These events are discrete in space and possess specific orientations with the principal stress direction., Comment: 26 pages, 11 figures, 2 tables, to be published in Nature Communications

We use molecular dynamics simulations to study a semidilute, unentangled polymer solution containing well dispersed, weakly attractive nanoparticles (NP) of size ($\sigma_N$) smaller than the polymer radius of gyration $R_g$. We find that if $\sigma_N$ is larger than the monomer size the polymers swell, while smaller NPs cause chain contraction. The diffusion coefficient of polymer chains ($D_p$) and NPs ($D_N$) decreases if the volume fraction $\phi_N$ is increased. The decrease of $D_p$ can be well described in terms of a confinement parameter, while $D_N$ shows a more complex dependence on $\sigma_N$, which results from an interplay between energetic and entropic effects. When $\phi_N$ exceeds a $\sigma_N$-dependent value, the NPs are no longer well dispersed and $D_N$ and $D_p$ increase if $\phi_N$ is increased.

The physical behavior of glass-forming liquids presents complex features of both dynamic and thermodynamic nature. Some studies indicate the presence of thermodynamic anomalies and of crossovers in the dynamic properties, but their origin and degree of universality is difficult to assess. Moreover, conventional simulations are barely able to cover the range of temperatures at which these crossovers usually occur. To address these issues, we simulate the Kob-Andersen Lennard-Jones mixture using efficient protocols based on multi-CPU and multi-GPU parallel tempering. Our setup enables us to probe the thermodynamics and dynamics of the liquid at equilibrium well below the critical temperature of mode-coupling theory, $T_{\rm MCT} = 0.435$. We find that below $T=0.4$ the analysis is hampered by partial crystallization of the metastable liquid, which nucleates extended regions populated by large particles arranged in an fcc structure. By filtering out crystalline samples, we reveal that the specific heat grows in a regular manner down to $T=0.38$. Possible thermodynamic anomalies suggested by previous studies can thus occur only in a region of the phase diagram where the system is highly metastable. Using the equilibrium configurations obtained from the parallel tempering simulations, we perform molecular dynamics and Monte Carlo simulations to probe the equilibrium dynamics down to $T=0.4$. A temperature-derivative analysis of the relaxation time and diffusion data allows us to assess different dynamic scenarios around $T_{\rm MCT}$. Hints of a dynamic crossover come from analysis of the four-point dynamic susceptibility. Finally, we discuss possible future numerical strategies to clarify the nature of crossover phenomena in glass-forming liquids., Comment: 12 pages, 9 figures, contribution to the special issue "Advances in Computational Methods for Soft Matter Systems". Data relevant to this work are available at https://doi.org/10.5281/zenodo.1227830

We propose a new scheme to parameterize effective potentials that can be used to simulate atomic systems such as oxide glasses. As input data for the optimization, we use the radial distribution functions of the liquid and the vibrational density of state of the glass, both obtained from ab-initio simulations, as well as experimental data on the pressure dependence of the density of the glass. For the case of silica, we find that this new scheme facilitates finding pair potentials that are significantly more accurate than previous ones even if the functional form is the same, thus demonstrating that even simple two-body potentials can be superior to more complex three-body potentials. We have tested the new potential by calculating the pressure dependence of the elastic moduli and find a good agreement with the corresponding experimental data.

We use computer simulations to probe the thermodynamic and dynamic properties of a glass-former that undergoes an ideal glass-transition because of the presence of randomly pinned particles. We find that even deep in the equilibrium glass state the system relaxes to some extent because of the presence of localized excitations that allow the system to access different inherent structures, giving thus rise to a non-trivial contribution to the entropy. By calculating with high accuracy the vibrational part of the entropy, we show that also in the equilibrium glass state thermodynamics and dynamics give a coherent picture and that glasses should not be seen as a disordered solid in which the particles undergo just vibrational motion but instead as a system with a highly nonlinear internal dynamics., Comment: Published version

We use X-ray tomography to investigate the translational and rotational dynamical heterogeneities of a three dimensional hard ellipsoids granular packing driven by oscillatory shear. We find that particles which translate quickly form clusters with a size distribution given by a power-law with an exponent that is independent of the strain amplitude. Identical behavior is found for particles that are translating slowly, rotating quickly, or rotating slowly. The geometrical properties of these four different types of clusters are the same as those of random clusters. Different cluster types are considerably correlated/anticorrelated, indicating a significant coupling between translational and rotational degrees of freedom. Surprisingly these clusters are formed already at time scales that are much shorter than the $\alpha-$relaxation time, in stark contrast to the behavior found in glass-forming systems., Comment: 9 pages

Granular materials such as sand, powders, foams etc. are ubiquitous in our daily life, as well as in industrial and geotechnical applications. Although these disordered systems form stable structures if unperturbed, in practice they do relax because of the presence of unavoidable external influences such as tapping or shear. Often it is tacitly assumed that for granular systems this relaxation dynamics is similar to the one of thermal glass-formers, but in fact experimental difficulties have so far prevented to determine the dynamic properties of three dimensional granular systems on the particle level. This lack of experimental data, combined with the fact that in these systems the motion of the particles involves friction, makes it very challenging to come up with an accurate description of their relaxation dynamics. Here we use X-ray tomography to determine the microscopic relaxation dynamics of hard granular ellipsoids that are subject to an oscillatory shear. We find that the distribution function of the particle displacement can be described by a Gumbel law with a shape parameter that is independent of time and the strain amplitude $\gamma$. Despite this universality, the mean squared displacement of a tagged particle shows power-laws as a function of time with an exponent that depends on $\gamma$ and the time interval considered. We argue that these results are directly related to the existence of the microscopic relaxation mechanisms that involve friction and memory effects. These observations demonstrate that on the particle level the dynamical behavior of granular systems is qualitatively different from the one of thermal glass-formers and instead more similar to the one of complex fluids. Thus we conclude that granular materials can relax even when the driving is weak, an insight which impacts our understanding of the nature of granular solids., Comment: Submitted version; final version is here: https://www.nature.com/articles/nature24062

Recent diffraction experiments on metallic glasses have unveiled an unexpected non-cubic scaling law between density and average interatomic distance, which lead to the speculations on the presence of fractal glass order. Using X-ray tomography we identify here a similar non-cubic scaling law in disordered granular packing of spherical particles. We find that the scaling law is directly related to the contact neighbors within first nearest neighbor shell, and therefore is closely connected to the phenomenon of jamming. The seemingly universal scaling exponent around 2.5 arises due to the isostatic condition with contact number around 6, and we argue that the exponent should not be universal., Comment: 24 pages, 8 figures,to be published in Phys. Rev. Lett

We present a class of simple algorithms that allows to find the reaction path in systems with a complex potential energy landscape. The approach does not need any knowledge on the product state and does not require the calculation of any second derivatives. The underlying idea is to use two nearby points in configuration space to locate the path of slowest ascent. By introducing a weak noise term, the algorithm is able to find even low-lying saddle points that are not reachable by means of a slowest ascent path. Since the algorithm makes only use of the value of the potential and its gradient, the computational effort to find saddles is linear in the number of degrees of freedom, if the potential is short-ranged. We test the performance of the algorithm for two potential energy landscapes. For the M\"uller-Brown surface we find that the algorithm always finds the correct saddle point. For the modified M\"uller-Brown surface, which has a saddle point that is not reachable by means of a slowest ascent path, the algorithm is still able to find this saddle point with high probability., Comment: 10 pages, 8 figures