Metallic glass-formers in 2D exhibit the same scaling as in 3D between vibrational dynamics and structural relaxation.

Glass-forming systems approaching their glass transition exhibit universal correlations between picosecond vibrational dynamics and long-time structural relaxation, which can be described by the same master curve in the bulk or confined conditions. In this work, we study at a fundamental level the effects of the reduction of spatial dimensionality on this phenomenon. We perform molecular dynamics simulations of a metallic glass-formers in two dimensions (2D). We show that in the supercooled regime particle localization in the cage and structural relaxation are blurred by long-wavelength fluctuations specific to low-dimensional systems. Once these effects are properly removed, we demonstrate that the fast dynamics and slow relaxation comply, without any adjustment, with same scaling between the structural relaxation time and the Debye-Waller factor, originally observed in three-dimensions (3D).

Communication: Fast dynamics perspective on the breakdown of the Stokes-Einstein law in fragile glassformers.

The breakdown of the Stokes-Einstein (SE) law in fragile glassformers is examined by Molecular-Dynamics simulations of atomic liquids and polymers and consideration of the experimental data concerning the archetypical ortho-terphenyl glassformer. All the four systems comply with the universal scaling between the viscosity (or the structural relaxation) and the Debye-Waller factor ⟨u2⟩, the mean square amplitude of the particle rattling in the cage formed by the surrounding neighbors. It is found that the SE breakdown is scaled in a master curve by a reduced ⟨u2⟩. Two approximated expressions of the latter, with no and one adjustable parameter, respectively, are derived.

Dynamical, structural and chemical heterogeneities in a binary metallic glass-forming liquid.

As it approaches the glass transition, particle motion in liquids becomes highly heterogeneous and regions with virtually no mobility coexist with liquid-like domains. This complex dynamic is believed to be responsible for different phenomena including non-exponential relaxation and the breakdown of the Stokes-Einstein relation. Understanding the relationships between dynamical heterogeneities and local structure in metallic liquids and glasses is a major scientific challenge. Here we use classical molecular dynamics simulations to study the atomic dynamics and microscopic structure of [Formula: see text] alloy in the supercooling regime. Dynamical heterogeneities are identified via an isoconfigurational analysis. We demonstrate the transition from isolated to clustering low mobility with decreasing temperature. These slow clusters, whose sizes grow upon cooling, are also associated with concentration fluctuations, characterized by a Zr-enriched phase, with a composition [Formula: see text]. In addition, a structural analysis of slow clusters based on Voronoi tessellation evidences an increase with respect of the bulk system of the fraction of Cu atoms having a local icosahedral order. These results are in agreement with the consolidated scenario of the relevant role played by icosahedral order in the dynamic slowing-down in supercooled metal alloys.

Thermodynamic scaling of relaxation: insights from anharmonic elasticity.

Using molecular dynamics simulations of a molecular liquid, we investigate the thermodynamic scaling (TS) of the structural relaxation time [Formula: see text] in terms of the quantity [Formula: see text], where T and ρ are the temperature and density, respectively. The liquid does not exhibit strong virial-energy correlations. We propose a method for evaluating both the characteristic exponent [Formula: see text] and the TS master curve that uses experimentally accessible quantities that characterise the anharmonic elasticity and does not use details about the microscopic interactions. In particular, we express the TS characteristic exponent [Formula: see text] in terms of the lattice Grüneisen parameter [Formula: see text] and the isochoric anharmonicity [Formula: see text]. An analytic expression of the TS master curve of [Formula: see text] with [Formula: see text] as the key adjustable parameter is found. The comparison with the experimental TS master curves and the isochoric fragilities of 34 glassformers is satisfying. In a few cases, where thermodynamic data are available, we test (i) the predicted characteristic exponent [Formula: see text] and (ii) the isochoric anharmonicity [Formula: see text], as drawn by the best fit of the TS of the structural relaxation, against the available thermodynamic data. A linear relation between the isochoric fragility and the isochoric anharmonicity [Formula: see text] is found and compared favourably with the results of experiments with no adjustable parameters. A relation between the increase of the isochoric vibrational heat capacity due to anharmonicity and the isochoric fragility is derived.

Thermodynamic scaling of vibrational dynamics and relaxation.

We investigate by thorough molecular dynamics simulations the thermodynamic scaling (TS) of a polymer melt. Two distinct models, with strong and weak virial-energy correlations, are considered. Both evidence the joint TS with the same characteristic exponent γts of the fast mobility-the mean square amplitude of the picosecond rattling motion inside the cage-and the much slower structural relaxation and chain reorientation. If the cage effect is appreciable, the TS master curves of the fast mobility are nearly linear, grouping in a bundle of approximately concurrent lines for different fragilities. An expression of the TS master curve of the structural relaxation with one adjustable parameter less than the available three-parameter alternatives is derived. The novel expression fits well with the experimental TS master curves of thirty-four glassformers and, in particular, their slope at the glass transition, i.e., the isochoric fragility. For the glassformer OTP, the isochoric fragility allows to satisfactorily predict the TS master curve of the fast mobility with no adjustments.

Plastic response and correlations in athermally sheared amorphous solids.

The onset of irreversible deformation in low-temperature amorphous solids is due to the accumulation of elementary events, consisting of spatially and temporally localized atomic rearrangements involving only a few tens of atoms. Recently, numerical and experimental work addressed the issue of spatiotemporal 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 fourfold 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.

The kinetic fragility of liquids as manifestation of the elastic softening.

We show that the fragility m , the steepness of the viscosity and relaxation time close to the vitrification, increases with the degree of elastic softening, i.e. the decrease of the elastic modulus with increasing temperature, in a universal way. This provides a novel connection between the thermodynamics, via the modulus, and the kinetics. The finding is evidenced by numerical simulations and comparison with the experimental data of glassformers with widely different fragilities (33 ≤ m ≤ 115), leading to a fragility-independent elastic master curve extending over eighteen decades in viscosity and relaxation time. The master curve is accounted for by a cavity model pointing out the roles of both the available free volume and the cage softness. A major implication of our findings is that ultraslow relaxations, hardly characterised experimentally, become predictable by linear elasticity. As an example, the viscosity of supercooled silica is derived over about fifteen decades with no adjustable parameters.

Weak links between fast mobility and local structure in molecular and atomic liquids.

We investigate by molecular-dynamics simulations, the fast mobility-the rattling amplitude of the particles temporarily trapped by the cage of the neighbors-in mildly supercooled states of dense molecular (linear trimers) and atomic (binary mixtures) liquids. The mixture particles interact by the Lennard-Jones potential. The non-bonded particles of the molecular system are coupled by the more general Mie potential with variable repulsive and attractive exponents in a range which is a characteristic of small n-alkanes and n-alcohols. Possible links between the fast mobility and the geometry of the cage (size and shape) are searched. The correlations on a per-particle basis are rather weak. Instead, if one groups either the particles in fast-mobility subsets or the cages in geometric subsets, the increase of the fast mobility with both the size and the asphericity of the cage is revealed. The observed correlations are weak and differ in states with equal relaxation time. Local forces between a tagged particle and the first-neighbour shell do not correlate with the fast mobility in the molecular liquid. It is concluded that the cage geometry alone is unable to provide a microscopic interpretation of the known, universal link between the fast mobility and the slow structural relaxation. We suggest that the particle fast dynamics is affected by regions beyond the first neighbours, thus supporting the presence of collective, extended fast modes.

Time-dependent elastic response to a local shear transformation in amorphous solids.

The elastic response of a two-dimensional amorphous solid to induced local shear transformations, which mimic the elementary plastic events occurring in deformed glasses, is investigated via molecular-dynamics simulations. We show that for different spatial realizations of the transformation, despite relative fluctuations of order one, the long-time equilibrium response averages out to the prediction of the Eshelby inclusion problem for a continuum elastic medium. We characterize the effects of the underlying dynamics on the propagation of the elastic signal. A crossover from a propagative transmission in the case of weakly damped dynamics to a diffusive transmission for strong damping is evidenced. In the latter case, the full time-dependent elastic response is in agreement with the theoretical prediction, obtained by solving the diffusion equation for the displacement field in an elastic medium.

Competition of the connectivity with the local and the global order in polymer melts and crystals.

The competition between the connectivity and the local or global order in model fully flexible chain molecules is investigated by molecular-dynamics simulations. States with both missing (melts) and high (crystal) global order are considered. Local order is characterized within the first coordination shell (FCS) of a tagged monomer and found to be lower than in atomic systems in both melt and crystal. The role played by the bonds linking the tagged monomer to FCS monomers (radial bonds), and the bonds linking two FCS monomers (shell bonds) is investigated. The detailed analysis in terms of Steinhardt's orientation order parameters Ql (l = 2 - 10) reveals that increasing the number of shell bonds decreases the FCS order in both melt and crystal. Differently, the FCS arrangements organize the radial bonds. Even if the molecular chains are fully flexible, the distribution of the angle formed by adjacent radial bonds exhibits sharp contributions at the characteristic angles θ ≈ 70°, 122°, 180°. The fractions of adjacent radial bonds with θ ≈ 122°, 180° are enhanced by the global order of the crystal, whereas the fraction with 70° ~/< θ ~/< 110° is nearly unaffected by the crystallization. Kink defects, i.e., large lateral displacements of the chains, are evidenced in the crystalline state.

Scaling between relaxation, transport and caged dynamics in a binary mixture on a per-component basis.

The universal scaling between the average slow relaxation/transport and the average picosecond rattling motion inside the cage of the first neighbors has been evidenced in a variety of numerical simulations and experiments. Here, we first show that the scaling does not need information concerning the arbitrarily-defined glass transition region and relies on a single characteristic length scale a(2)(1/2) which is determined even far from that region. This prompts the definition of a novel reduced rattling amplitude (1/2) which has been investigated by extensive molecular-dynamics simulations addressing the slow relaxation, the diffusivity, and the fast cage-dynamics of both components of an atomic binary mixture. States with different potential, density, and temperature are considered. It is found that if two states exhibit coinciding incoherent van Hove function on the picosecond timescale, the coincidence is observed at long times too, including the large-distance exponential decay--a signature of heterogeneous dynamics--observed when the relaxation is slow. A major result of the present study is that the correlation plot between the diffusivity of the two components of the binary mixtures and their respective reduced rattling amplitude collapse on the same master curve. This holds true also for the structural relaxation of the two components and the unique master curve coincides with the one of the average scaling. It is shown that the breakdown of the Stokes-Einstein law exhibited by the distinct atomic species of the mixture and the monomers of a chain in a polymer melt is predicted at the same reduced rattling amplitude. Finally, we evidence that the well-known temperature/density thermodynamic scaling of the transport and the relaxation of the mixture is still valid on the picosecond timescale of the rattling motion inside the cage. This provides a link between the fast dynamics and the thermodynamic scaling of the slow dynamics.

Communication: Fast and local predictors of the violation of the Stokes-Einstein law in polymers and supercooled liquids.

The violation of the Stokes-Einstein (SE) law is investigated in a melt of linear chains by extensive molecular-dynamics simulations. It is found that the SE breakdown is signaled (with 5% uncertainty) by the monomer mean-square displacement on the picosecond time scale. On this time scale the displacements of the next-next-nearest neighbors are uncorrelated. It is shown that: (i) the SE breakdown occurs when is smaller than the breadth of the distribution of the square displacements to escape from the first-neighbors cage, (ii) the dynamical heterogeneity affects the form of the master curve of the universal scaling between the structural relaxation and .

Spatial displacement correlations in polymeric systems.

The spatial correlations of the monomer displacements are studied via molecular-dynamics simulations of a melt of fully flexible, unentangled polymer chains with different length, interacting potential, density, and temperature. Both the scalar and the vector characters of the correlations are considered and their extension quantified in terms of suitable dynamical correlation lengths. Displacements performed at both short, i.e., vibrational, and long times, i.e., comparable to the structural relaxation time, are investigated. On both time scales the spatial correlations are modulated according to the radial distribution function g(r) to an extent which is determined by the character of the correlations, the time scale of the displacements and the structural slowing down. The spatial correlations of the short-time displacements have clear directional character. The modulus correlations of the long-time displacements are more marked, especially for sluggish states. Analogous findings are found by experiments on colloids. By inspecting the dynamical heterogeneities of states with slowed-down dynamics, it is observed that fast monomers exhibit correlations which are stronger and more differing from the bulk than the slow ones. It is shown that states with identical average vibrational monomer displacement exhibit identical spatial correlations of the monomer displacements pertaining to the subsets of the fast and the slow monomers characterizing both the short-time and the long-time dynamical heterogeneities.

Communication: correlation of the instantaneous and the intermediate-time elasticity with the structural relaxation in glassforming systems.

The elastic models of the glass transition relate the increasing solidity of the glassforming systems with the huge slowing down of the structural relaxation and the viscous flow. The solidity is quantified in terms of the instantaneous shear modulus G(∞), i.e., the immediate response to a step change in the strain. By molecular-dynamics simulations of a model polymer system, one shows the virtual absence of correlations between the instantaneous elasticity and the structural relaxation. Instead, a well-defined scaling is evidenced by considering the elastic response observed at intermediate times after the initial fast stress relaxation. The scaling regime ranges from sluggish states with virtually pure elastic response on the picosecond time scale up to high-mobility states where fast restructuring events are more apparent.

Scaling between relaxation, transport, and caged dynamics in polymers: from cage restructuring to diffusion.

The slow relaxation, the diffusivity, and the fast cage-dynamics of a melt of fully flexible unentangled polymer chains is studied by molecular-dynamics simulations. States with different nonbonding potential, chain length, density and temperature are considered. The scaling between the slow dynamics and the fast dynamics, as characterized by the amplitude of the rattling motion inside the cage, is evidenced. The analysis carried out in terms of the van Hove function shows that: (i) the scaling does not depend on the specific quantity used to quantify both the relaxation times and the amplitude of the rattling motion; (ii) it holds on the length scale of the jump-like dynamics; (iii) it also holds on the time scale of the diffusive regime if the chain-length effect is taken into proper account, thus extending analogous results already known for atomic liquids.