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Register a new userHeterogeneous diffusion, viscosity and the Stokes Einstein relation in binary liquids
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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.
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Recent numerical studies on glassy systems provide evidences for a population of non-Goldstone modes (NGMs) in the low-frequency spectrum of the vibrational density of states $D(omega)$. Similarly to Goldstone modes (GMs), i. e., phonons in solids, NGMs are soft low-energy excitations. However, differently from GMs, NGMs are localized excitations. Here we first show that the parental temperature $T^*$ modifies the GM/NGM ratio in $D(omega)$. In particular, the phonon attenuation is reflected in a parental temperature dependency of the exponent $s(T^*)$ in the low-frequency power law $D(omega) sim omega^{s(T^*)}$, with $2 leq s(T^*) leq 4 $. Secondly, by comparing $s(T^*)$ with $s(p)$, i. e., the same quantity obtained by pinning mttp{a} $p$ particle fraction, we suggest that $s(T^*)$ reflects the presence of dynamical heterogeneous regions of size $xi^3 propto p$. Finally, we provide an estimate of $xi$ as a function of $T^*$, finding a mild power law divergence, $xi sim (T^* - T_d)^{-alpha/3}$, with $T_d$ the dynamical crossover temperature and $alpha$ falling in the range $alpha in [0.8,1.0]$.
Using molecular dynamics simulation, we have calculated the pressure dependence of the diffusion constant in a binary Lennard-Jones Glass. We observe four temperature regimes. The apparent activation volume drops from high values in the hot liquid to a plateau value. Near the critical temperature of the mode coupling theory it rises steeply, but in the glassy state we find again small values, similar to the ones in the liquid. The peak of the activation volume at the critical temperature is in agreement with the prediction of mode coupling theory.
This work aims at reconsidering several interpretations coexisting in the recent literature concerning non-linear susceptibilities in supercooled liquids. We present experimental results on glycerol and propylene carbonate showing that the three independent cubic susceptibilities have very similar frequency and temperature dependences, both for their amplitudes and phases. This strongly suggests a unique physical mechanism responsible for the growth of these non-linear susceptibilities. We show that the framework proposed by two of us [BB, Phys. Rev. B 72, 064204 (2005)], where the growth of non-linear susceptibilities is intimately related to the growth of glassy domains, accounts for all the salient experimental features. We then review several complementary and/or alternative models, and show that the notion of cooperatively rearranging glassy domains is a key (implicit or explicit) ingredient to all of them. This paves the way for future experiments which should deepen our understanding of glasses.
A recently published analytical model, describing and predicting elasticity, viscosity, and fragility of metallic melts, is applied for the analysis of about 30 nonmetallic glassy systems, ranging from oxide network glasses to alcohols, low-molecular-weight liquids, polymers, plastic crystals, and even ionic glass formers. The model is based on the power-law exponent lambda representing the steepness parameter of the repulsive part of the inter-atomic or -molecular potential and the thermal-expansion parameter alpha_T determined by the attractive anharmonic part of the effective interaction. It allows fitting the typical super-Arrhenius temperature variation of the viscosity or dielectric relaxation time for various classes of glass-forming matter, over many decades. We discuss the relation of the model parameters found for all these different glass-forming systems to the fragility parameter m and detect a correlation of lambda and m for the non-metallic glass formers, in accord with the model predictions. Within the framework of this model, thus the fragility of glass formers can be traced back to microscopic model parameters characterizing the intermolecular interactions.
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.
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