From creep to flow: Granular materials under cyclic shear.

When unperturbed, granular materials form stable structures that resemble the ones of other amorphous solids like metallic or colloidal glasses. Whether or not granular materials under shear have an elastic response is not known, and also the influence of particle surface roughness on the yielding transition has so far remained elusive. Here we use X-ray tomography to determine the three-dimensional microscopic dynamics of two granular systems that have different roughness and that are driven by cyclic shear. Both systems, and for all shear amplitudes Γ considered, show a cross-over from creep to diffusive dynamics, indicating that rough granular materials have no elastic response and always yield, in stark contrast to simple glasses. For the system with small roughness, we observe a clear dynamic change at Γ ≈ 0.1, accompanied by a pronounced slowing down and dynamical heterogeneity. For the large roughness system, the dynamics evolves instead continuously as a function of Γ. We rationalize this roughness dependence using the potential energy landscape of the systems: The roughness induces to this landscape a micro-corrugation with a new length scale, whose ratio over the particle size is the relevant parameter. Our results reveal the unexpected richness in relaxation mechanisms for real granular materials.

Surface properties of alkali silicate glasses: Influence of the modifiers.

Using large-scale molecular dynamics simulations, we investigate the surface properties of lithium, sodium, and potassium silicate glasses containing 25 mol % 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 competing mechanisms 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.

Topology of vibrational modes predicts plastic events in glasses.

The plastic deformation of crystalline materials can be understood by considering their structural defects such as disclinations and dislocations. Although also glasses are 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 to 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.

Intermediate-range order governs dynamics in dense colloidal liquids.

The conventional wisdom is that liquids are completely disordered and lack nontrivial 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 nontrivial 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.

Structure and elasticity of model disordered, polydisperse, and defect-free polymer networks.

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 cross-linked 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 cross-links 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 cross-link localization length to the shear modulus of the system.

Creating bulk ultrastable glasses by random particle bonding.

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.

Equivalence of Fluctuation-Dissipation and Edwards' Temperature in Cyclically Sheared Granular Systems.

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 agreement between these two temperatures, independent of the type of the tracers, cyclic shear amplitudes, and particle surface roughness, giving therefore the first experimental evidence that the concept of effective temperature is valid in driven frictional granular systems.

Are strongly confined colloids good models for two dimensional liquids?

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.

Cooperative excitations in superionic PbF2.

Links between dynamical Frenkel defects and collective diffusion of fluorides in ß-PbF2 are explored using Born-Oppenheimer molecular dynamics. The calculated self-diffusion coefficient and ionic conductivity are 3.2 × 10-5 cm2 s-1 and 2.4 Ω-1 cm-1 at 1000 K in excellent agreement with pulsed field gradient and conductivity measurements. The calculated ratio of the tracer-diffusion coefficient and the conductivity-diffusion coefficient (the Haven ratio) is slightly less than unity (about 0.85), which in previous work has been interpreted as providing evidence against collective 'multi-ion' diffusion. By contrast, our molecular dynamics simulations show that fluoride diffusion is highly collective. Analysis of different mechanisms shows a preference for direct collinear 'kick-out' chains where a fluoride enters an occupied tetrahedral hole/cavity and pushes the resident fluoride out of its cavity. Jumps into an occupied cavity leave behind a vacancy, thereby forming dynamic Frenkel defects which trigger a chain of migrating fluorides assisted by local relaxations of the lead ions to accommodate these chains. The calculated lifetime of the Frenkel defects and the collective chains is approximately 1 ps in good agreement with that found from neutron diffraction. This article is part of the Theo Murphy meeting issue 'Understanding fast-ion conduction in solid electrolytes'.

Experimental Test of the Edwards Volume Ensemble for Tapped Granular Packings.

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

Effect of Chain Polydispersity on the Elasticity of Disordered Polymer Networks.

Due to their unique structural and mechanical properties, randomly cross-linked 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 (e.g., chain-length and end-to-end distributions), we generate disordered phantom networks with different cross-linker concentrations C and initial densities ρinit 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 ρinit. We rationalize 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 nonmonotonic function of the density of elastically active strands, and that this behavior has a purely entropic origin. Our results show that if short chains are abundant, as it is always the case for randomly cross-linked polymer networks, the knowledge of the exact chain conformation distribution is essential for correctly predicting the elastic properties. Finally, we apply our theoretical approach to literature experimental data, qualitatively confirming our interpretations.

Connecting real glasses to mean-field models.

We propose a novel model for a glass-forming liquid, which allows us 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-neighbors and by means of analytical calculations, and we determine the structural properties related to these additional neighbors. We show that the relaxation dynamics of the system slows down very quickly with the increase in k and that the onset and the mode-coupling temperatures increase. The systems with high values of k follow the mode-coupling theory power law behavior for a larger temperature range compared to the ones with lower values of k. The dynamic susceptibility indicates that the dynamic heterogeneity decreases with the increase in k, whereas the non-Gaussian parameter is independent of it. Thus, we conclude that with the increase in the number of pseudo-neighbors, the system becomes more mean-field-like. By comparing our results with previous studies on mean-field-like systems, 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.

Roughness and Scaling Properties of Oxide Glass Surfaces at the Nanoscale.

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 unravel the crucial role of spatial resolution on surface measurements and conclude that on length scales less than 10 nm FS are not self-affine fractals.

Connecting Packing Efficiency of Binary Hard Sphere Systems to Their Intermediate Range Structure.

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.

Anatomy of cage formation in a two-dimensional glass-forming liquid.

As a glass-forming liquid is cooled, the dynamics of its constituent particles changes from being liquid-like to more solid-like. The solidity of the resulting glassy material is believed to be due to a cage-formation process, whereby the motion of individual particles is increasingly constrained by neighbouring particles. This process begins at the temperature (or particle density) at which the glass-forming liquid first shows signs of glassy dynamics; however, the details of how the cages form remain unclear1-4. Here we study cage formation at the particle level in a two-dimensional colloidal suspension (a glass-forming liquid). We use focused lasers to perturb the suspension at the particle level and monitor the nonlinear dynamic response of the system using video microscopy. All observables that we consider respond non-monotonically as a function of the particle density, peaking at the density at which glassy dynamics is first observed. We identify this maximum response as being due to cage formation, quantified by the appearance of domains in which particles move in a cooperative manner. As the particle density increases further, these local domains become increasingly rigid and dominate the macroscale particle dynamics. This microscale rheological deformation approach demonstrates that cage formation in glass-forming liquids is directly related to the merging of such domains, and reveals the first step in the transformation of liquids to glassy materials1,5.

Structure and vibrational properties of sodium silicate glass surfaces.

Using molecular dynamics simulations, we investigate how the structural and vibrational properties of the surfaces of sodo-silicate glasses depend 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 ≈2.3 Å. The vibrational density of states shows that the presence of the surfaces leads to a decrease in the characteristic frequencies in the system. The two-membered rings give rise to a pronounce band at ≈880 cm-1, which is in good agreement with experimental observations.

Revealing the three-dimensional structure of liquids using four-point correlation functions.

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 probing of the 3D structure of such systems. Using computer simulations, we find that hard sphere-like liquids have on intermediate and large scales a simple 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 nontrivial 3D structure and that this structural information is encoded in nonstandard correlation functions.

New interaction potentials for borate glasses with mixed network formers.

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 reliably reproduce 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 the properties of various boroaluminate and borosilicate glasses.

Friction-Controlled Entropy-Stability Competition in Granular Systems.

Using cyclic shear to drive a two-dimensional granular system, we determine the structural characteristics for different interparticle 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 liquidlike rather than glassy.

New interaction potentials for alkali and alkaline-earth aluminosilicate glasses.

We apply a recently developed optimization scheme to obtain effective potentials for alkali and alkaline-earth aluminosilicate glasses that contain 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 us to reproduce and predict the structure and properties of multicomponent glasses.