Inhomogeneous elastic response of silica glass

Emergence of crystal-like atomic dynamics in glasses at the nanometer scale

The vibrational dynamics of a permanently densified silica glass is compared to the one of an α-quartz polycrystal, the silica polymorph of the same density and local structure. The combined use of inelastic x-ray scattering experiments and ab initio numerical calculations provides compelling evidence of a transition, in the glass, from the isotropic elastic response at long wavelengths to a microscopic regime as the wavelength decreases below a characteristic length ξ of a few nanometers, corresponding to about 20 interatomic distances. In the microscopic regime the glass vibrations closely resemble those of the polycrystal, with excitations related to the acoustic and optic modes of the crystal. A coherent description of the experimental results is obtained assuming that the elastic modulus of the glass presents spatial heterogeneities of an average size a ~ ξ/2 π.

Localization-delocalization transition for disordered cubic harmonic lattices

We study numerically the disorder-induced localization-delocalization phase transitions that occur for mass and spring constant disorder in a three-dimensional cubic lattice with harmonic couplings. We show that, while the phase diagrams exhibit regions of stable and unstable waves, the universality of the transitions is the same for mass and spring constant disorder throughout all the phase boundaries. The combined value for the critical exponent of the localization lengths of ν = 1.550(-0.017)(+0.020) confirms the agreement with the universality class of the standard electronic Anderson model of localization. We further support our investigation with studies of the density of states, the participation numbers and wave function statistics.

Relationship between bond-breakage correlations and four-point correlations in heterogeneous glassy dynamics: configuration changes and vibration modes

We investigate the dynamic heterogeneities of glassy particle systems in the theoretical schemes of bond breakage and four-point correlation functions. In the bond-breakage scheme, we introduce the structure factor S(b)(q,t) and the susceptibility χ(b)(t) to detect the spatial correlations of configuration changes. Here χ(b)(t) attains a maximum at t=t(b)(max) as a function of time t, where the fraction of the particles with broken bonds φ(b)(t) is about 1/2. In the four-point scheme, treating the structure factor S(4)(q,t) and the susceptibility χ(4)(t), we detect superpositions of the heterogeneity of bond breakage and that of thermal low-frequency vibration modes. While the former grows slowly, the latter emerges quickly to exhibit complex space-time behavior. In two dimensions, the vibration modes extending over the system yield significant contributions to the four-point correlations, which depend on the system size logarithmically. A maximum of χ(4)(t) is attained at t=t(4)(max), where these two contributions become of the same order. As a result, t(4)(max) is considerably shorter than t(b)(max).

Progressive transformations of silica glass upon densification

The elastic and plastic behaviors of silica glasses densified at various maximum pressure reached (12 GPa, 15 GPa, 19 GPa, and 22 GPa), were analyzed using in situ Raman and Brillouin spectroscopies. The elastic anomaly was observed to progressively vanish up to a maximum pressure reached of 12 GPa, beyond which it is completely suppressed. Above the elastic anomaly the mechanical behavior of silica glass, as derived from Brillouin measurements, is interpreted in terms of pressure induced transformation of low density amorphous silica into high density amorphous silica.

Nonaffine measures of particle displacements in sheared colloidal glasses

The nonaffine motion of particles is central to the relaxation and flow of glasses. It is usually assumed in plasticity theories that nonaffine rearrangements are localized and uncorrelated. Here we present evidence that this assumption may not hold. We investigate and compare systematically different measures of nonaffinity in a sheared colloidal glass by tracking the motion of the individual particles directly with confocal microscopy. We show that besides differences in the appearance and degree of localization of nonaffine displacements, the nature of their fluctuations is very similar. At intermediate times, all spatial correlation functions display robust power-law behavior, clearly demonstrating long-range correlations and critical behavior of the driven glass, in contrast to the assumptions of plasticity theories. We show that on long-time scales, correlations become finite and plasticity theories may apply.

Simulated glass-forming polymer melts: glass transition temperature and elastic constants of the glassy state

By means of molecular-dynamics simulation we study a flexible and a semiflexible bead-spring model for a polymer melt on cooling through the glass transition. Results for the glass transition temperature T(g) and for the elastic properties of the glassy state are presented. We find that T(g) increases with chain length N and is for all N larger for the semiflexible model. The N dependence of T(g) is compared to experimental results from the literature. Furthermore, we characterize the polymer glass below T(g) via its elastic properties, i.e., via the Lamé coefficients λ and μ. The Lamé coefficients are determined from the fluctuation formalism which allows to split λ and μ into affine (Born term) and nonaffine (fluctuation term) contributions. We find that the fluctuation term represents a substantial correction to the Born term. Since the Born terms for λ and μ are identical, the fluctuation terms are responsible for the different temperature dependence of the Lamé coefficients. While λ decreases linearly on approaching T(g) from below, the shear modulus μ displays a much stronger decrease near T(g). From the present simulation data it is not possible to decide whether μ takes a finite value at T(g), as would be expected from mode-coupling theory, or vanishes continuously, as suggested by recent work from replica theory.

Equivalence of the boson peak in glasses to the transverse acoustic van Hove singularity in crystals

We compare the atomic dynamics of the glass to that of the relevant crystal. In the spectra of inelastic scattering, the boson peak of the glass appears higher than the transverse acoustic (TA) singularity of the crystal. However, the density of states shows that they have the same number of states. Increasing pressure causes the transformation of the boson peak of the glass towards the TA singularity of the crystal. Once corrected for the difference in the elastic medium, the boson peak matches the TA singularity in energy and height. This suggests the identical nature of the two features.

Plasticity and dynamical heterogeneity in driven glassy materials

Many amorphous glassy materials exhibit complex spatio-temporal mechanical response and rheology, characterized by an intermittent stress strain response and a fluctuating velocity profile. Under quasistatic and athermal deformation protocols this heterogeneous plastic flow was shown to be composed of plastic events of various sizes, ranging from local quadrupolar plastic rearrangements to system spanning shear bands. In this paper, through numerical study of a 2D Lennard-Jones amorphous solid, we generalize the study of the heterogeneous dynamics of glassy materials to the finite shear rate (gamma not equal to 0) and temperature case (T not equal to 0). In practice, we choose an effectively athermal limit (T approximately 0) and focus on the influence of shear rate on the rheology of the glass. In line with previous works we find that the model Lennard-Jones glass follows the rheological behavior of a yield stress fluid with a Herschel-Bulkley response of the form, sigma = sigmaY + c1gamma(beta). The global mechanical response obtained through the use of Molecular Dynamics is shown to converge in the limit gamma --> 0 to the quasistatic limit obtained with an energy minimization protocol. The detailed analysis of the plastic deformation at different shear rates shows that the glass follows different flow regimes. At sufficiently low shear rates the mechanical response reaches a shear-rate-independent regime that exhibits all the characteristics of the quasistatic response (finite-size effects, cascades of plastic rearrangements, yield stress, ...). At intermediate shear rates the rheological properties are determined by the externally applied shear rate and the response deviates from the quasistatic limit. Finally at higher shear the system reaches a shear-rate-independent homogeneous regime. The existence of these three regimes is also confirmed by the detailed analysis of the atomic motion. The computation of the four-point correlation function shows that the transition from the shear-rate-dominated to the quasistatic regime is accompanied by the growth of a dynamical cooperativity length scale xi that is shown to diverge with shear rate as xi is proportional to gamma(-nu), with nu approximately 0.2 -0.3. This scaling is compared with the prediction of a simple model that assumes the diffusive propagation of plastic events.

Probing a critical length scale at the glass transition

We give evidence of a clear structural signature of the glass transition, in terms of a static correlation length with the same dependence on the system size, which is typical of critical phenomena. Our approach is to introduce an external, static perturbation to extract the structural information from the system's response. In particular, we consider the transformation behavior of the local minima of the underlying potential energy landscape (inherent structures), under a static deformation. The finite-size scaling analysis of our numerical results indicate that the correlation length diverges at a temperature Tc, below the temperatures where the system can be equilibrated. Our numerical results are consistent with random first order theory, which predicts such a divergence with a critical exponent ν=2/3 at the Kauzmann temperature, where the extrapolated configurational entropy vanishes.

Heat transport in model jammed solids

We calculate numerically the normal modes of vibrations in three-dimensional jammed packings of soft spheres as a function of the packing fraction and obtain the energy diffusivity, a spectral measure of transport that controls sound propagation and thermal conductivity. The crossover frequency between weak and strong phonon scattering is controlled by the coordination and shifts to zero as the system is decompressed toward the critical packing fraction at which rigidity is lost. We present a scaling analysis that relates the packing fraction dependence of the crossover frequency to the anomalous scaling of the shear modulus with compression. Below the crossover, the diffusivity displays a power-law divergence with inverse frequency consistent with Rayleigh law, which suggests that the vibrational modes are primarily transverse waves, weakly scattered by disorder. Above it, a large number of modes appear whose diffusivity plateaus at a nearly constant value before dropping to zero above the localization frequency. The thermal conductivity of a marginally jammed solid just above the rigidity threshold is calculated and related to the one measured experimentally at room temperature for most glasses.

Non-Debye normalization of the glass vibrational density of states in mildly densified silicate glasses

The evolution of the boson peak with densification at medium densification rates (up to 2.3%) in silicate glasses was followed through heat capacity measurements and low frequency Raman scattering. It is shown that the decrease of the boson peak induced by densification does not conform to that expected from a continuous medium; rather it follows a two step behaviour. The comparison of the heat capacity data with the Raman data shows that the light-vibration coupling coefficient is almost unaffected in this densification regime. These results are discussed in relation to the inhomogeneity of the glass elastic network at the nanometre scale.

Fracture pattern formation in frictional, cohesive, granular material

Naturally, deformed rocks commonly contain crack arrays (joints) forming patterns with systematic relationships to the large-scale deformation. Kinematically, joints can be mode-1, -2 or -3 or combinations of these, but there is no overarching theory for the development of the patterns. We develop a model motivated by dislocation pattern formation in metals. The problem is formulated in one dimension in terms of coupled reaction-diffusion equations, based on computer simulations of crack development in deformed granular media with cohesion. The cracks are treated as interacting defects, and the densities of defects diffuse through the rock mass. Of particular importance is the formation of cracks at high stresses associated with force-chain buckling and variants of this configuration; these cracks play the role of 'inhibitors' in reaction-diffusion relationships. Cracks forming at lower stresses act as relatively mobile defects. Patterns of localized deformation result from (i) competition between the growth of the density of 'mobile' defects and the inhibition of these defects by crack configurations forming at high stress and (ii) the diffusion of damage arising from these two populations each characterized by a different diffusion coefficient. The extension of this work to two and three dimensions is discussed.

Comment on "Elastic constants from microscopic strain fluctuations"

Sengupta [Phys. Rev. E 61, 1072 (2000)] presented an elegant and simple finite-size scaling method for the calculation of elastic constants and their corresponding correlation lengths, which is suitable for many finite discrete systems considered through simulations or experiments. We take into account a mathematical finite-size effect that was neglected by the authors in order to propose a more accurate method. Consequences on the authors' results are also discussed.

Relationship between vibrations and dynamical heterogeneity in a model glass former: extended soft modes but local relaxation

We study the relation between short-time vibrational modes and long-time relaxational dynamics in a kinetically constrained lattice gas with harmonic interactions between neighbouring particles. We find a correlation between the location of the low- (high-) frequency vibrational modes and regions of high (low) propensity for motion. This is similar to what was observed in continuous force systems, but our interpretation is different: in our case relaxation is due to localised excitations which propagate through the system; these localised excitations act as background disorder for the elastic network, giving rise to anomalous vibrational modes. Our results provide an example whereby a correlation between spatially extended low-frequency modes and high-propensity regions does not imply that relaxational dynamics originates in extended soft modes but rather belies their common origin. We consider other measures of elastic heterogeneity, such as non-affine displacement fields and mode localisation lengths, and discuss implications of our results to interpretations of dynamic heterogeneity more generally.

Entanglement network in nanoparticle reinforced polymers

Polymer nanocomposites have been widely studied in efforts to engineer materials with mechanical properties superior to those of the pure polymer, but the molecular origins of the sought-after improved properties have remained elusive. An ideal polymer nanocomposite model has been conceived in which the nanoparticles are dispersed throughout the polymeric matrix. A detailed examination of topological constraints (or entanglements) in a nanocomposite glass provides new insights into the molecular origin of the improved properties in polymer nanocomposites by revealing that the nanoparticles impart significant enhancements to the entanglement network. Nanoparticles are found to serve as entanglement attractors, particularly at large deformations, altering the topological constraint network that arises in the composite material.

Kinetic theory of plastic flow in soft glassy materials

A kinetic model for the elastoplastic dynamics of a jammed material is proposed, which takes the form of a nonlocal--Boltzmann-like--kinetic equation for the stress distribution function. Coarse graining this equation yields a nonlocal constitutive law for the flow, exhibiting as a key dynamic quantity the local rate of plastic events. This quantity, interpreted as a local fluidity, is spatially correlated with a correlation length diverging in the quasistatic limit, i.e., close to yielding. In line with recent experimental and numerical observations, we predict finite size effects in the flow behavior, as well as the absence of an intrinsic local flow curve.

Elastic flexibility, fast-ion conduction, boson and floppy modes in AgPO(3)-AgI glasses

Raman scattering, IR reflectance and modulated-DSC measurements are performed on specifically prepared dry (AgI)(x)(AgPO(3))(1-x) glasses over a wide range of compositions 0%<x<60%. A reversibility window is observed in the 9.5%<x<37.8% range, which fixes the elastically rigid but unstressed regime also known as the intermediate phase. Glass compositions at x<9.5% are stressed-rigid, while those at x>37.8% are elastically flexible. Raman optical elasticity power laws, trends in the nature of the glass transition endotherms, corroborate the three elastic phase assignments. Ionic conductivities reveal a step-like increase when glasses become stress-free at x>x(c)(1) = 9.5% and a logarithmic increase in conductivity (σ∼(x-x(c)(2))(μ)) once they become flexible at x>x(c)(2) = 37.8% with a power law μ = 1.78. The power law is consistent with percolation of 3D filamentary conduction pathways. Traces of water doping lower T(g) and narrow the reversibility window, and can also completely collapse it. Ideas on network flexibility promoting ion conduction are in harmony with the unified approach of Ingram et al (2008 J. Phys. Chem. B 112 859), who have emphasized the similarity of process compliance or elasticity relating to ion transport and structural relaxation in decoupled systems. Boson mode frequency and scattering strength display thresholds that coincide with the two elastic phase boundaries. In particular, the scattering strength of the boson mode increases almost linearly with glass composition x, with a slope that tracks the floppy mode fraction as a function of mean coordination number r predicted by mean-field rigidity theory. These data suggest that the excess low frequency vibrations contributing to the boson mode in flexible glasses come largely from floppy modes.

Nonaffine deformation of inherent structure as a static signature of cooperativity in supercooled liquids

We unveil the existence of nonaffinely rearranging regions in the inherent structures (IS) of supercooled liquids by numerical simulations of model glass formers subject to static shear deformations combined with local energy minimizations. In the liquid state IS, we find a broad distribution of large rearrangements which are correlated only over small distances. At low temperatures, the onset of the cooperative dynamics corresponds to much smaller displacements correlated over larger distances. This finding indicates the presence of nonaffinely rearranging domains of relevant size in the IS deformation, which can be seen as the static counterpart of the cooperatively rearranging regions in the dynamics. This idea provides new insight into possible structural signatures of slow cooperative dynamics of supercooled liquids and supports the connections with elastic heterogeneities found in amorphous solids.

Probing the flexibility of the bacterial reaction center: the wild-type protein is more rigid than two site-specific mutants

Experimental and theoretical studies have stressed the importance of flexibility for protein function. However, more local studies of protein dynamics, using temperature factors from crystallographic data or elastic models of protein mechanics, suggest that active sites are among the most rigid parts of proteins. We have used quasielastic neutron scattering to study the native reaction center protein from the purple bacterium Rhodobacter sphaeroides, over a temperature range of 4-260 K, in parallel with two nonfunctional mutants both carrying the mutations L212Glu/L213Asp --> Ala/Ala (one mutant carrying, in addition, the M249Ala --> Tyr mutation). The so-called dynamical transition temperature, Td, remains the same for the three proteins around 230 K. Below Td the mean square displacement, u2, and the dynamical structure factor, S(Q,omega), as measured respectively by backscattering and time-of-flight techniques are identical. However, we report that above Td, where anharmonicity and diffusive motions take place, the native protein is more rigid than the two nonfunctional mutants. The higher flexibility of both mutant proteins is demonstrated by either their higher u2 values or the notable quasielastic broadening of S(Q,omega) that reveals the diffusive nature of the motions involved. Remarkably, we demonstrate here that in proteins, point genetic mutations may notably affect the overall protein dynamics, and this effect can be quantified by neutron scattering. Our results suggest a new direction of investigation for further understanding of the relationship between fast dynamics and activity in proteins. Brownian dynamics simulations we have carried out are consistent with the neutron experiments, suggesting that a rigid core within the native protein is specifically softened by distant point mutations. L212Glu, which is systematically conserved in all photosynthetic bacteria, seems to be one of the key residues that exerts a distant control over the rigidity of the core of the protein.

Free volume and finite-size effects in a polymer glass under stress

Molecular dynamics simulations of the nonlinear creep response of a polymer glass under tension and compression have been performed at the glass transition temperature. The dynamics were measured as the deformation proceeds using the bond autocorrelation function, and the relaxation times measured as the system is compressed or elongated exhibit a universal response. In tension, the volume increases with strain rate and the relaxation times decrease. In compression, however, the volume decreases by approximately the same amount for all of the applied stresses. Thus, decreases in free volume take place alongside a decrease of the relaxation times by over a factor of 100. We find direct evidence that a characteristic length scale exists below which the deformation of the system exhibits distinct anomalies.

Amorphous silica modeled with truncated and screened Coulomb interactions: A molecular dynamics simulation study

We show that finite-range alternatives to the standard long-range pair potential for silica by van Beest et al. [Phys. Rev. Lett. 64, 1955 (1990)] might be used in molecular dynamics simulations. We study two such models that can be efficiently simulated since no Ewald summation is required. We first consider the Wolf method, where the Coulomb interactions are truncated at a cutoff distance rc such that the requirement of charge neutrality holds. Various static and dynamic quantities are computed and compared to results from simulations using Ewald summations. We find very good agreement for rc approximately 10 A. For lower values of rc, the long-range structure is affected which is accompanied by a slight acceleration of dynamic properties. In a second approach, the Coulomb interaction is replaced by an effective Yukawa interaction with two new parameters determined by a force fitting procedure. The same trend as for the Wolf method is seen. However, slightly larger cutoffs have to be used in order to obtain the same accuracy with respect to static and dynamic quantities as for the Wolf method.

Influence of pressure on the boson peak: stronger than elastic medium transformation

We study the changes in the low-frequency vibrational dynamics of poly(isobutylene) under pressure up to 1.4 GPa, corresponding to a density change of 20%. Combining inelastic neutron, x-ray, and Brillouin light scattering, we analyze the variations in the boson peak, transverse and longitudinal sound velocities, and the Debye level under pressure. We find that the boson peak variation under pressure cannot be explained by the elastic continuum transformation only. Surprisingly, the shape of the boson peak remains unchanged even at such high compression.

Characterization of the potential energy landscape of an antiplasticized polymer

The nature of the individual transitions on the potential energy landscape (PEL) associated with particle motion are directly examined for model fragile glass-forming polymer melts, and the results are compared to those of an antiplasticized polymer system. In previous work, we established that the addition of antiplasticizer reduces the fragility of glass formation so that the antiplasticized material is a stronger glass former. In the present work, we find that the antiplasticizing molecules reduce the energy barriers for relaxation compared to the pure polymer, implying that the antiplasticized system has smaller barriers to overcome in order to explore its configuration space. We examine the cooperativity of segmental motion in these bulk fluids and find that more extensive stringlike collective motion enables the system to overcome larger potential energy barriers, in qualitative agreement with both the Stillinger-Weber and Adam-Gibbs views of glass formation. Notably, the stringlike collective motion identified by our PEL analysis corresponds to incremental displacements that occur within larger-scale stringlike particle displacement processes associated with PEL metabasin transitions that mediate structural relaxation. These "substrings" nonetheless seem to exhibit changes in relative size with antiplasticization similar to those observed in "superstrings" that arise at elevated temperatures. We also study the effects of confinement on the energy barriers in each system. Film confinement makes the energy barriers substantially smaller in the pure polymer, while it has little effect on the energy barriers in the antiplasticized system. This observation is qualitatively consistent with our previous studies of stringlike motion in these fluids at higher temperatures and with recent experimental measurements by Torkelson and co-workers.

Revisiting the slow dynamics of a silica melt using Monte Carlo simulations

We implement a standard Monte Carlo algorithm to study the slow, equilibrium dynamics of a silica melt in a wide temperature regime, from 6100K down to 2750K . We find that the average dynamical behavior of the system is in quantitative agreement with results obtained from molecular dynamics simulations, at least in the long-time regime corresponding to the alpha -relaxation. By contrast, the strong thermal vibrations related to the boson peak present at short times in molecular dynamics are efficiently suppressed by the Monte Carlo algorithm. This allows us to reconsider silica dynamics in the context of mode-coupling theory, because several shortcomings of the theory were previously attributed to thermal vibrations. A mode-coupling theory analysis of our data is qualitatively correct, but quantitative tests of the theory fail, raising doubts about the very existence of an avoided singularity in this system. We discuss the emergence of dynamic heterogeneity and report detailed measurements of a decoupling between translational diffusion and structural relaxation, and of a growing four-point dynamic susceptibility. Dynamic heterogeneity appears to be less pronounced than in more fragile glass-forming models, but not of a qualitatively different nature.

Tuning polymer melt fragility with antiplasticizer additives

A polymer-diluent model exhibiting antiplasticization has been developed and characterized by molecular dynamics simulations. Antiplasticizer molecules are shown to decrease the glass transition temperature Tg but to increase the elastic moduli of the polymeric material in the low-temperature glass state. Moreover, the addition of antiplasticizing particles renders the polymer melt a stronger glass-forming material as determined by changes in the characteristic temperatures of glass formation, the fragility parameter D from fits to the Vogel-Folcher-Tamman-Hesse equation, and through the observation of the temperature dependence of the size of cooperatively rearranging regions (strings) in each system. The length of the strings exhibits a weaker temperature dependence in the antiplasticized glass-forming system than in the more fragile pure polymer, consistent with the Adam-Gibbs model of glass formation. Unexpectedly, the strings become increasingly concentrated in the antiplasticizer particles upon cooling. Finally, we discuss several structural indicators of cooperative dynamics, and find that the dynamic propensity (local Debye-Waller factor <u2>p) does seem to provide a strong correlation with local molecular displacements at long times. The authors also consider maps of the propensity, and find that the antiplasticized system exhibits larger fluctuations over smaller length scales compared to the pure polymer.