Numerical determination of the exponents controlling the relationship between time, length and temperature in glass-forming liquids

There is a certain consensus that the very fast growth of the relaxation time $\tau$ occurring in glass-forming liquids on lowering the temperature must be due to the thermally activated rearrangement of correlated regions of growing size. Even though measuring the size of these regions has defied scientists for a while, there is indeed recent evidence of a growing correlation length $\xi$ in glass-formers. If we use Arrhenius law and make the mild assumption that the free-energy barrier to rearrangement scales as some power $\psi$ of the size of the correlated regions, we obtain a relationship between time and length, $T\log\tau \sim \xi^\psi$. According to both the Adam-Gibbs and the Random First Order theory the correlation length grows as $\xi \sim (T-T_k)^{-1/(d-\theta)}$, even though the two theories disagree on the value of $\theta$. Therefore, the super-Arrhenius growth of the relaxation time with the temperature is regulated by the two exponents $\psi$ and $\theta$ through the relationship $T\log\tau \sim (T-T_k)^{-\psi/(d-\theta)}$. Despite a few theoretical speculations, up to now there has been no experimental determination of these two exponents. Here we measure them numerically in a model glass-former, finding $\psi=1$ and $\theta=2$. Surprisingly, even though the values we found disagree with most previous theoretical suggestions, they give back the well-known VFT law for the relaxation time, $T\log\tau \sim (T-T_k)^{-1}$.Comment: 9 pages, 8 figure

Patch-repetition correlation length in glassy systems

We obtain the patch-repetition entropy Sigma within the Random First Order Transition theory (RFOT) and for the square plaquette system, a model related to the dynamical facilitation theory of glassy dynamics. We find that in both cases the entropy of patches of linear size l, Sigma(l), scales as s_c l^d+A l^{d-1} down to length-scales of the order of one, where A is a positive constant, s_c is the configurational entropy density and d the spatial dimension. In consequence, the only meaningful length that can be defined from patch-repetition is the cross-over length xi=A/s_c. We relate xi to the typical length-scales already discussed in the literature and show that it is always of the order of the largest static length. Our results provide new insights, which are particularly relevant for RFOT theory, on the possible real space structure of super-cooled liquids. They suggest that this structure differs from a mosaic of different patches having roughly the same size.Comment: 6 page

Surface Tension in Kac Glass Models

In this paper we study a distance-dependent surface tension, defined as the free-energy cost to put metastable states at a given distance. This will be done in the framework of a disordered microscopic model with Kac interactions that can be solved in the mean-field limit.Comment: 13 pages, 6 figure

Surface tension fluctuations and a new spinodal point in glass-forming liquids

The dramatic slowdown of glass-forming liquids has been variously linked to increasing dynamic and static correlation lengths. Yet, empirical evidence is insufficient to decide among competing theories. The random first order theory (RFOT) links the dynamic slowdown to the growth of amorphous static order, whose range depends on a balance between configurational entropy and surface tension. This last quantity is expected to vanish when the temperature surpasses a spinodal point beyond which there are no metastable states. Here we measure for the first time the surface tension in a model glass-former, and find that it vanishes at the energy separating minima from saddles, demonstrating the existence of a spinodal point for amorphous metastable order. Moreover, the fluctuations of surface tension become smaller for lower temperatures, in quantitative agreement with recent theoretical speculation that spatial correlations in glassy systems relax nonexponentially because of the narrowing of the surface tension distribution.Comment: 6 pages, 5 figure

A phase-separation perspective on dynamic heterogeneities in glass-forming liquids

We study dynamic heterogeneities in a model glass-former whose overlap with a reference configuration is constrained to a fixed value. The system phase-separates into regions of small and large overlap, so that dynamical correlations remain strong even for asymptotic times. We calculate an appropriate thermodynamic potential and find evidence of a Maxwell's construction consistent with a spinodal decomposition of two phases. Our results suggest that dynamic heterogeneities are the expression of an ephemeral phase-separating regime ruled by a finite surface tension

TESTING THE EFFICIENCY OF FENTONS REAGENT IN TREATMENT OF PETROLEUM-CONTAMINATED SAND

The removal of petroleum of beach sand after an oil spill in Guanabara Bay, Rio de Janeiro (Brazil) was studied using Fentons reagent (Fe2+ + H2O2) with H2O2 concentrations of 0.4 M and 4.0 M and Fe2+ concentrations of 2.7 g/L and 27.2 g/ L. The initial Oil & Grease (O&G) content in the contaminated sand was 32 g/kg sand. The maximum O&G removal obtained was 97 % after Fentons reaction. An analysis of the supernatant after the reaction showed that it was biodegradable. Chromatographic analysis indicated that Fentons reaction favored the modification and reduction of the fractions of saturated and aromatic hydrocarbons in the oil

An experimental study of the behaviour of two rockfills accounting for the effects of degree of saturation

Rockfill dams have become more and more recognized for their safety, economy and adaptability to widely varying site conditions. As a contribution to the understanding of the main factors affecting the rockfill behaviour, the paper reports and discusses experimental data on several aspects relevant to the interpretation and analysis of their in-situ response. The experimental programme involved three series of oedometric tests on specimens of two different gravels having the same grading, reconstituted at the same initial relative density. Experimental observations on rockfills compressibility are presented and discussed: attention is paid to the role of degree of saturation (Sr) through the analysis of "driest", "fully saturated"conditions, and the transition from one to the other. Grain crushing tests on dry and saturated soil particles are also reported. Grain size distributions of the specimens, both after compaction and after the oedometer tests, are compared in the paper. The results show that the effect of Sr cannot be overlooked in the mechanical characterization of the material, especially in rockfill/stress conditions prone to crushin