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Register a new userTheory of heterogeneous viscoelasticity
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We review a new theory of viscoelasticity of a glass-forming viscous liquid near and below the glass transition. In our model we assume that each point in the material has a specific viscosity, which varies randomly in space according to a fluctuating activation free energy. We include a Maxwellian elastic term and assume that the corresponding shear modulus fluctuates as well with the same distribution as that of the activation barriers. The model is solved in coherent-potential approximation (CPA), for which a derivation is given. The theory predicts an Arrhenius-type temperature dependence of the viscosity in the vanishing-frequency limit, independent of the distribution of the activation barriers. The theory implies that this activation energy is generally different from that of a diffusing particle with the same barrier-height distribution. If the distribution of activation barriers is assumed to have Gaussian form, the finite-frequency version of the theory describes well the typical low-temperature alpha relaxation peak of glasses. Beta relaxation can be included by adding another Gaussian with center at much lower energies than that responsible for the alpha relaxation. At high frequencies our theory reduces to the description of an elastic medium with spatially fluctuating elastic moduli (heterogeneous elasticity theory), which explains the occurrence of the boson-peak-related vibrational anomalies of glasses.
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In this letter we report {it in situ} small--angle neutron scattering results on the high--density (HDA) and low-density amorphous (LDA) ice structures and on intermediate structures as found during the temperature induced transformation of HDA into LDA. We show that the small--angle signal is characterised by two $Q$ regimes featuring different properties ($Q$ is the modulus of the scattering vector defined as $Q = 4pisin{(Theta)}/lambda_{rm i}$ with $Theta$ being half the scattering angle and $lambda_{rm i}$ the incident neutron wavelength). The very low--$Q$ regime ($< 5times 10^{-2}$ AA $^{-1}$) is dominated by a Porod--limit scattering. Its intensity reduces in the course of the HDA to LDA transformation following a kinetics reminiscent of that observed in wide--angle diffraction experiments. The small--angle neutron scattering formfactor in the intermediate regime of $5 times 10^{-2} < Q < 0.5$ AA$^{-1}$ HDA and LDA features a rather flat plateau. However, the HDA signal shows an ascending intensity towards smaller $Q$ marking this amorphous structure as heterogeneous. When following the HDA to LDA transition the formfactor shows a pronounced transient excess in intensity marking all intermediate structures as strongly heterogeneous on a length scale of some nano--meters.
The present work deals with the behavior of fiber bundle model under heterogeneous loading condition. The model is explored both in the mean-field limit as well as with local stress concentration. In the mean field limit, the failure abruptness decreases with increasing order k of heterogeneous loading. In this limit, a brittle to quasi-brittle transition is observed at a particular strength of disorder which changes with k. On the other hand, the model is hardly affected by such heterogeneity in the limit where local stress concentration plays a crucial role. The continuous limit of the heterogeneous loading is also studied and discussed in this paper. Some of the important results related to fiber bundle model are reviewed and their responses to our new scheme of heterogeneous loading are studied in details. Our findings are universal with respect to the nature of the threshold distribution adopted to assign strength to an individual fiber.
Spatial heterogeneity in the elastic properties of soft random solids is examined via vulcanization theory. The spatial heterogeneity in the emph{structure} of soft random solids is a result of the fluctuations locked-in at their synthesis, which also brings heterogeneity in their emph{elastic properties}. Vulcanization theory studies semi-microscopic models of random-solid-forming systems, and applies replica field theory to deal with their quenched disorder and thermal fluctuations. The elastic deformations of soft random solids are argued to be described by the Goldstone sector of fluctuations contained in vulcanization theory, associated with a subtle form of spontaneous symmetry breaking that is associated with the liquid-to-random-solid transition. The resulting free energy of this Goldstone sector can be reinterpreted as arising from a phenomenological description of an elastic medium with quenched disorder. Through this comparison, we arrive at the statistics of the quenched disorder of the elasticity of soft random solids, in terms of residual stress and Lame-coefficient fields. In particular, there are large residual stresses in the equilibrium reference state, and the disorder correlators involving the residual stress are found to be long-ranged and governed by a universal parameter that also gives the mean shear modulus.
We investigate the origin of the breakdown of the Stokes-Einstein relation (SER) between diffusivity and viscosity in undercooled melts. A binary Lennard-Jones system, as a model for a metallic melt, is studied by molecular dynamics. A weak breakdown at high temperatures can be understood from the collectivization of motion, seen in the isotope effect. The strong breakdown at lower temperatures is connected to an increase in dynamic heterogeneity. On relevant timescales some particles diffuse much faster than the average or than predicted by the SER. The van-Hove self correlation function allows to unambiguously identify slow particles. Their diffusivity is even less than predicted by the SER. The time-span of these particles being slow particles, before their first conversion to be a fast one, is larger than the decay time of the stress correlation. The contribution of the slow particles to the viscosity rises rapidly upon cooling. Not only the diffusion but also the viscosity shows a dynamically heterogeneous scenario. We can define a slow viscosity. The SER is recovered as relation between slow diffusivity and slow viscosity.
The recent theoretical treatment of irreversible jumps between inherent states with a constant density in shear space is extended to a full theory, attributing the shear relaxation to structural Eshelby rearrangements involving the creation and annihilation of soft modes. The scheme explains the Kohlrausch exponent close to 1/2 and the connection to the low temperature glass anomalies. A continuity relation between the irreversible and the reversible Kohlrausch relaxation time distribution is derived. The full spectrum can be used in many ways, not only to describe shear relaxation data, but also to relate shear relaxation data to dielectric and bulk relaxation spectra, and to predict aging from shear relaxation data, as demonstrated for a very recent aging experiment.
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