Velocity autocorrelation function in supercooled liquids: Long-time tails and anomalous shear-wave propagation

Fast crystal growth in deeply undercooled ZrTi melts

We investigate the growth of crystals in Zr50Ti50 melts by classical molecular-dynamics simulations with an embedded atom method and a Stillinger-Weber potential model. Both models display fast solidification rates that can be captured by the transition state theory or the Ginzburg-Landau theory at small undercoolings. Fast crystal-growth rates are found to be affected by the pre-existing ordering in liquids, such as the body-centered cubic-like and icosahedral-like structures. The interface-induced ordering unveiled by the crystal-freezing method can explain the rate difference between these two models. However, these orderings fail to rationalize the temperature evolution of the growth rate at deep undercoolings. We correlate the growth kinetics with the detailed dynamical processes in liquids, finding the decoupling of hierarchic relaxation processes when collective motion emerges in supercooled liquids. We find that the growth kinetics is nondiffusive, but with a lower activation barrier corresponding to the structural relaxation or the cage-relative motion in ZrTi melts. These results explore a new relaxation mechanism for the fast growth rate in deeply undercooled liquids.

Crystal growth in deeply undercooled Ni50Al50: Signature of the ordering sequence at the interface

Crystal growth of the intermetallic alloy, Ni₅₀Al₅₀, is investigated by molecular dynamics simulations with two different interatomic potentials. The calculated growth rate can be captured by the Wilson-Frenkel or Broughton-Gilmer-Jackson model at small undercoolings but deviates from the theory at deep undercoolings. Failure of the theory is found to be correlated with the dynamic processes that emerged at the interface, but not apparently with the static interface structure. The chemical segregation of Ni and Al atoms occurs before the geometrical ordering upon crystallization at small undercoolings. In contrast, the geometrical ordering precedes the chemical one at deep undercoolings. These two ordering processes show a collapsed time evolution at the crossover temperature consistent with the onset of the theoretical deviation. We rationalize the delayed chemical segregation behavior by the collective atomic motion, which is characterized by the super-Arrhenius transition of the temperature-dependent diffusivity and structural relaxation time at the crossover point.

Molecular-dynamics simulations on the mesophase transition induced by oscillatory shear in imidazolium-based ionic liquid crystals

Molecular dynamics simulations were performed on a 1-dodecyl-3-methylimidazolium hexafluorophosphate ([C₁₂mim][PF₆]) ionic liquid crystal (ILC) with the application of an oscillatory shear. We found that the oscillatory shear can both accelerate and suppress mesophase formation depending on shear amplitude. A small amplitude shear can speed up the mesophase transition dynamics and result in a more ordered mesomorphic structure than that without shear, i.e., an effect of accelerated aging. The mesophase is destabilized when the shear amplitude is large enough, resulting in a smectic A (SmA) to liquid or a smectic B (SmB) to SmA transition, with the mesophase behaviour summarized in an out-of-equilibrium phase diagram. Inside the layer plane a medium-range hexatic order was observed, with the correlation length extending to several nanometres in the shear-induced SmA phase. We rationalize the nonequilibrium mesophase behaviour from the rheology of isotropic liquids, finding a temperature-independent critical relaxation time for the mesophase transition in the translational or rotational dynamics. This finding can be used to predict the mesophase behaviour in the sheared ILCs from the rheology of isotropic liquids.

Oscillations and negative velocity autocorrelation emerging from a Brownian particle model with hydrodynamic interactions

We study the dynamics of a particle in a fluid from a generalized Langevin equation (GLE) with a frictional exponential memory kernel and hydrodynamic interactions. By using Laplace analysis we obtain the analytical expressions for the velocity autocorrelation function (VACF) and mean square displacement (MSD) of the particle. Our results show that, in the strictly asymptotic time limit, the dynamics of the particle correspond to a particle ruled by a GLE with a Dirac delta friction memory kernel and hydrodynamic interactions. However, at intermediate times the dynamical behavior is qualitatively different due to the presence of a characteristic time in the frictional exponential memory kernel. Remarkably, the VACF exhibits oscillations and negative correlation regimes which are reminiscent of features already observed in pioneering works of molecular dynamics simulations. Moreover, ripples in the MSD appear as an emerging behavior associated with the mentioned regimes.

Local Density Fluctuation Governs the Divergence of Viscosity Underlying Elastic and Hydrodynamic Anomalies in a 2D Glass-Forming Liquid

If a liquid is cooled rapidly to form a glass, its structural relaxation becomes retarded, producing a drastic increase in viscosity. In two dimensions, strong long-wavelength fluctuations persist, even at low temperature, making it difficult to evaluate the microscopic structural relaxation time. This Letter shows that, in a 2D glass-forming liquid, relative displacement between neighbor particles yields a relaxation time that grows in proportion to the viscosity. In addition to thermal elastic vibrations, hydrodynamic fluctuations are found to affect the long-wavelength dynamics, yielding a logarithmically diverging diffusivity in the long-time limit.

Persistent Anti-Correlations in Brownian Dynamics Simulations of Dense Colloidal Suspensions Revealed by Noise Suppression

Transport properties of a hard-sphere colloidal fluid are investigated by Brownian dynamics simulations. We implement a novel algorithm for the time-dependent velocity-autocorrelation function (VACF) essentially eliminating the noise of the bare random motion. The measured VACF reveals persistent anti-correlations manifested by a negative algebraic power-law tail t^{-5/2} at all densities. At small packing fractions the simulations fully agree with the analytic low-density prediction, yet the amplitude of the tail becomes dramatically suppressed as the packing fraction is increased. The mode-coupling theory of the glass transition provides a qualitative explanation for the strong variation in terms of the static compressibility as well as the slowing down of the structural relaxation.

Isolating long-wavelength fluctuation from structural relaxation in two-dimensional glass: cage-relative displacement

It has recently been revealed that long-wavelength fluctuation exists in two-dimensional (2D) glassy systems, having the same origin as that given by the Mermin-Wagner theorem for 2D crystalline solids. In this paper, we discuss how to characterise quantitatively the long-wavelength fluctuation in a molecular dynamics simulation of a lightly supercooled liquid. We employ the cage-relative mean-square displacement (MSD), defined on relative displacement to its cage, to quantitatively separate the long-wavelength fluctuation from the original MSD. For increasing system size the amplitude of acoustic long wavelength fluctuations not only increases but shifts to later times causing a crossover with structural relaxation of caging particles. We further analyse the dynamic correlation length using the cage-relative quantities. It grows as the structural relaxation becomes slower with decreasing temperature, uncovering an overestimation by the four-point correlation function due to the long-wavelength fluctuation. These findings motivate the usage of cage-relative MSD as a starting point for analysis of 2D glassy dynamics.