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Register a new userDynamic heterogeneity in two-dimensional supercooled liquids: comparison of bond-breaking and bond-orientational correlations
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We compare the spatial correlations of bond-breaking events and bond-orientational relaxation in a model two-dimensional liquid undergoing Newtonian dynamics. We find that the relaxation time of the bond-breaking correlation function is much longer than the relaxation time of the bond-orientational correlation function and self-intermediate scattering function. However, the relaxation time of the bond-orientational correlation function increases faster with decreasing temperature than the relaxation time of the bond-breaking correlation function and the self-intermediate scattering function. Moreover, the dynamic correlation length that characterizes the size of correlated bond-orientational relaxation grows faster with decreasing temperature than the dynamic correlation length that characterizes the size of correlated bond-breaking events. We also examine the ensemble-dependent and ensemble-independent dynamic susceptibilities for both bond-breaking correlations and bond-orientational correlations. We find that for both correlations, the ensemble-dependent and ensemble-independent susceptibilities exhibit a maximum at nearly the same time, and this maximum occurs at a time slightly shorter than the peak position of the dynamic correlation length.
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Recent computational studies have reported evidence of a metastable liquid-liquid phase transition (LLPT) in molecular models of water under deeply supercooled conditions. A competing hypothesis suggests, however, that non-equilibrium artifacts associated with coarsening of the stable crystal phase have been mistaken for an LLPT in these models. Such artifacts are posited to arise due to a separation of time scales in which density fluctuations in the supercooled liquid relax orders of magnitude faster than those associated with bond-orientational order. Here, we use molecular simulation to investigate the relaxation of density and bond-orientational fluctuations in three molecular models of water (ST2, TIP5P and TIP4P/2005) in the vicinity of their reported LLPT. For each model, we find that density is the slowly relaxing variable under such conditions. We also observe similar behavior in the coarse-grained mW model of water. Our findings therefore challenge the key physical assumption underlying the competing hypothesis.e find that density relaxes significantly faster than bond-orientational order, as incorrectly predicted by this competing hypothesis.
A theoretical treatment of deeply supercooled liquids is difficult because their properties emerge from spatial inhomogeneities that are self-induced, transient, and nanoscopic. I use computer simulations to analyse self-induced static and dynamic heterogeneity in equilibrium systems approaching the experimental glass transition. I characterise the broad sample-to-sample fluctuations of salient dynamic and thermodynamic properties in elementary mesoscopic systems. Findings regarding local lifetimes and distributions of dynamic heterogeneity are in excellent agreement with recent single molecule studies. Surprisingly broad thermodynamic fluctuations are also found, which correlate well with dynamics fluctuations, thus providing a local test of the thermodynamic origin of slow dynamics.
Glasses are solid materials whose constituent atoms are arranged in a disordered manner. The transition from a liquid to a glass remains one of the most poorly understood phenomena in condensed matter physics, and still no fully microscopic theory exists that can describe the dynamics of supercooled liquids in a quantitative manner over all relevant time scales. Here we present such a theoretical framework that yields near-quantitative accuracy for the time-dependent correlation functions of a supercooled system over a broad density range. Our approach requires only simple static structural information as input and is based entirely based on first principles. Owing to this first-principles nature, the framework offers a unique platform to study the relation between structure and dynamics in glass-forming matter, and paves the way towards a systematically correctable and ultimately fully quantitative theory of microscopic glassy dynamics.
The statistics of critical spin-spin correlation functions in Ising systems with non-frustrated disorder are investigated on a strip geometry, via numerical transfer-matrix techniques. Conformal invariance concepts are used, in order to test for logarithmic corrections to pure power-law decay against distance. Fits of our data to conformal-invariance expressions, specific to logarithmic corrections to correlations on strips, give results with the correct sign, for the moments of order $n=0-4$ of the correlation-function distribution. We find an interval of disorder strength along which corrections to pure-system behavior can be decomposed into the product of a known $n$-dependent factor and an approximately $n$-independent one, in accordance with predictions. A phenomenological fitting procedure is proposed, which takes partial account of subdominant terms of correlation-function decay on strips. In the low-disorder limit, it gives results in fairly good agreement with theoretical predictions, provided that an additional assumption is made.
The scaling of the bond-bond correlation function $C(s)$ along linear polymer chains is investigated with respect to the curvilinear distance, $s$, along the flexible chain and the monomer density, $rho$, via Monte Carlo and molecular dynamics simulations. % Surprisingly, the correlations in dense three dimensional solutions are found to decay with a power law $C(s) sim s^{-omega}$ with $omega=3/2$ and the exponential behavior commonly assumed is clearly ruled out for long chains. % In semidilute solutions, the density dependent scaling of $C(s) approx g^{-omega_0} (s/g)^{-omega}$ with $omega_0=2-2 u=0.824$ ($ u=0.588$ being Florys exponent) is set by the number of monomers $g(rho)$ contained in an excluded volume blob of size $xi$. % Our computational findings compare well with simple scaling arguments and perturbation calculation. The power-law behavior is due to self-interactions of chains on distances $s gg g$ caused by the connectivity of chains and the incompressibility of the melt. %
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