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Register a new userSpontaneous and induced dynamic fluctuations in glass-formers I: General results and dependence on ensemble and dynamics
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We study theoretically and numerically a family of multi-point dynamic susceptibilities that quantify the strength and characteristic lengthscales of dynamic heterogeneities in glass-forming materials. We use general theoretical arguments (fluctuation-dissipation relations and symmetries of relevant dynamical field theories) to relate the sensitivity of averaged two-time correlators to temperature and density to spontaneous fluctuations of the local dynamics. Our theoretical results are then compared to molecular dynamics simulations of the Newtonian, Brownian and Monte-Carlo dynamics of two representative glass-forming liquids, a fragile binary Lennard-Jones mixture and a model for the strong glass-former silica. We justify in detail the claim made in [Science 310, 1797 (2005)], that the temperature dependence of correlation functions allows one to extract useful information on dynamic lengthscales in glassy systems. We also discuss some subtle issues associated to the choice of microscopic dynamics and of statistical ensemble through conserved quantities, which are found to play an important role in determining dynamic correlations.
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We study in detail the predictions of various theoretical approaches, in particular mode-coupling theory (MCT) and kinetically constrained models (KCMs), concerning the time, temperature, and wavevector dependence of multi-point correlation functions that quantify the strength of both induced and spontaneous dynamical fluctuations. We also discuss the precise predictions of MCT concerning the statistical ensemble and microscopic dynamics dependence of these multi-point correlation functions. These predictions are compared to simulations of model fragile and strong glass-forming liquids. Overall, MCT fares quite well in the fragile case, in particular explaining the observed crucial role of the statistical ensemble and microscopic dynamics, while MCT predictions do not seem to hold in the strong case. KCMs provide a simplified framework for understanding how these multi-point correlation functions may encode dynamic correlations in glassy materials. However, our analysis highlights important unresolved questions concerning the application of KCMs to supercooled liquids.
We analytically and numerically characterize the structure of hard-sphere fluids in order to review various geometrical frustration scenarios of the glass transition. We find generalized polytetrahedral order to be correlated with increasing fluid packing fraction, but to become increasingly irrelevant with increasing dimension. We also find the growth in structural correlations to be modest in the dynamical regime accessible to computer simulations.
Fragility, quantifying the rapidity of variation of relaxation times, is analysed for a series of model glass formers, which differ in the softness of their interparticle interactions. In an attempt to rationalize experimental observations in colloidal suspensions that softer interactions lead to stronger (less fragile) glass formers, we study the variation of relaxation dynamics with density, rather than temperature, as a control parameter. We employ density temperature scaling, analyzed in recent studies, to address the question. We find that while employing inverse density in place of temperature leads to the conclusion that softer interactions lead to stronger behaviour, the use of scaled variables involving temperature and density lead to the opposite conclusion, similarly to earlier investigations where temperature variation of relaxation dynamics was analysed for the same systems. We rationalize our results by considering the Adam-Gibbs (AG) fragility, which incorporates the density dependence of the configurational entropy and an activation energy that may arise from other properties of a glass former. Within the framework of the Adam-Gibbs relation, by employing density temperature scaling for the analysis, we find that softer particles make more fragile glasses, as deduced from dynamical quantities, which is found to be consistent with the Adam-Gibbs fragility.
We investigate the general property of the energy fluctuation for the canonical ensemble in Tsallis statistics and the ensemble equivalence. By taking the ideal gas and the non-interacting harmonic oscillators as examples, we show that, when the particle number N is large enough, the relative fluctuation of the energy is proportional to 1/N in the new statistics, instead of square root of 1/N in Boltzmann-Gibbs statistics. Thus the equivalence between the microcanonical and the canonical ensemble still holds in Tsallis statistics.
We examined dynamic heterogeneity in a model tetrahedral network glass-forming liquid. We used four-point correlation functions to extract dynamic correlation lengths xi_4^a(t) and susceptibilities chi_4^a(t) corresponding to structural relaxation on two length scales a. One length scale corresponds to structural relaxation at nearest neighbor distances and the other corresponds to relaxation of the tetrahedral structure. We find that the dynamic correlation length xi_4^{a} grows much slower with increasing relaxation time than for model fragile glass formers. We also find that chi_4^a ~ (xi_4^a)^z for a range of temperatures, but z < 3 at the lowest temperatures examined in this study. However, we do find evidence that the temperature where Stokes-Einstein violation begins marks a temperature where there is a change in the character of dynamically heterogeneous regions. Throughout the paper, we contrast the structure and dynamics of a strong glass former with that of a representative fragile glass former.
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