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Register a new userKovacs effect and the relation between glasses and supercooled liquids
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In this note we revisit the Kovacs effect, concerning the way in which the volume of a glass-forming liquid, which has been driven out of equilibrium, changes with time while the system evolves towards a metastable state. The theoret- ical explanation of this phenomenon has attracted much interest even in recent years, because of its relation with some subtle aspects of the still elusive nature of the glass transition. In fact, even if there is a rather general consensus on the fact that what is experimentally observed on cooling is the dramatic effect produced by the dynam- ical arrest of slower degrees of freedom over the experimental time scale, it is not yet clear whether this phenomenology can be justified upon assuming the existence of an underlying (possibly, high order) phase transition at lower temperatures.
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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.
In this work we revisit the description of dynamics based on the concepts of metabasins and activation in mildly supercooled liquids via the analysis of the dynamics of a paradigmatic glass former between its onset temperature $T_{o}$ and mode-coupling temperature $T_{c}$. First, we provide measures that demonstrate that the onset of glassiness is indeed connected to the landscape, and that metabasin waiting time distributions are so broad that the system can remain stuck in a metabasin for times that exceed $tau_alpha$ by orders of magnitude. We then reanalyze the transitions between metabasins, providing several indications that the standard picture of activated dynamics in terms of traps does not hold in this regime. Instead, we propose that here activation is principally driven by entropic instead of energetic barriers. In particular, we illustrate that activation is not controlled by the hopping of high energetic barriers, and should more properly be interpreted as the entropic selection of nearly barrierless but rare pathways connecting metabasins on the landscape.
We show experimentally that in a supercooled liquid composed of molecules with internal degrees of freedom the internal modes contribute to the frequency dependent shear viscosity and damping of transverse phonons, which results in an additional broadening of the transverse Brillouin lines. Earlier, only the effect of internal modes on the frequency dependent bulk viscosity and damping of longitudinal phonons was observed and explained theoretically in the limit of weak coupling of internal degrees of freedom to translational motion. A new theory is needed to describe this new effect. We also demonstrate, that the contributions of structural relaxation and internal processes to the width of the Brillouin lines can be separated by measurements under high pressure.
Particle motion of a Lennard-Jones supercooled liquid near the glass transition is studied by molecular dynamics simulations. We analyze the wave vector dependence of relaxation times in the incoherent self scattering function and show that at least three different regimes can be identified and its scaling properties determined. The transition from one regime to another happens at characteristic length scales. The lengthscale associated with the onset of Fickian diffusion corresponds to the maximum size of heterogeneities in the system, and the characterisitic timescale is several times larger than the alpha relaxation time. A second crossover lengthscale is observed, which corresponds to the typical time and length of heterogeneities, in agreement with results from four point functions. The different regimes can be traced back in the behavior of the van Hove distribution of displacements, which shows a characteristic exponential regime in the heterogeneous region before the crossover to gaussian diffusion and should be observable in experiments. Our results show that it is possible to obtain characteristic length scales of heterogeneities through the computation of two point functions at different times.
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