Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture I: The van Hove correlation function

Abstract

We report the results of a large scale computer simulation of a binary supercooled Lennard-Jones liquid. We find that at low temperatures the curves for the mean squared displacement of a tagged particle for different temperatures fall onto a master curve when they are plotted versus rescaled time tD(T ), where D(T ) is the diffusion constant. The time range for which these curves follow the master curve is identified with the α-relaxation regime of modecoupling theory (MCT). This master curve is fitted well by a functional form suggested by MCT. In accordance with idealized MCT, D(T ) shows a powerlaw behavior at low temperatures. The critical temperature of this power-law is the same for both types of particle and also the critical exponents are very similar. However, contrary to a prediction of MCT, these exponents are not equal to the ones determined previously for the divergence of the relaxation times of the intermediate scattering function [Phys. Rev. Lett. 73, 1376]. At low temperatures the van Hove correlation function (self as well as distinct part) shows hardly any sign of relaxation in a time interval that extends over about three decades in time. This time interval can be interpreted as the β-relaxation regime of MCT. From the investigation of these correlation functions we conclude that hopping processes are not important on the time scale of the β-relaxation for this system and for the temperature range investigated. We test whether the factorization property predicted by MCT holds and find that this is indeed the case for all correlation functions investigated. The distance dependence of the critical amplitudes are in qualitative accordance with the ones predicted by MCT for some other mixtures. The non-gaussian parameter for the self part of the van Hove correlation function for different temperatures follows a master curve when plotted against time 1 t.

V-T theory for the self-intermediate scattering function in a monatomic liquid

“…Diverse and valuable reviews are available [20][21][22][23]. For normal and supercooled liquids, MD data for the MSD time evolution [24] has a well established interpretation in terms of the atomic motion [25]. Here we apply the same interpretation to the SISF, as shown in figure 8.…”

Universal glassy dynamics at noise-perturbed onset of chaos: a route to ergodicity breakdown

“…This behavior is displayed by molecular dynamics simulations [3] and successfully reproduced by mode coupling (MC) theory [4]. Another important feature of the dynamic properties of glasses is the loss of time translation invariance.…”

“…This consists of time t power-law decays towards and away from a plateau, the duration t x of which diverges also as a power law of the difference T − T g as the temperature T decreases to a critical value T g [1] [2]. This behavior is displayed by molecular dynamics simulations [3] and successfully reproduced by mode coupling (MC) theory [4]. Another important feature of the dynamic properties of glasses is the loss of time translation invariance.…”

Local polymer dynamics under strong connectivity constraints: The dendrimer case

“…At longer length scales and/or later times near the late-␤/early-␣ dynamic range, the so-called "decaging" ͑i.e., escape from the cage͒ process takes place. In this regime, a common feature detected in liquids, 7,13 colloids, 14,15 and polymers 16,17 is the existence of mobility contrast among the glass-forming units. The observed dynamic heterogeneity is characterized by a non-Gaussian distribution in the particle/ monomer displacements r͑t͒ at the relevant spatial and temporal scales, which can be quantified by means of the nonGaussian parameter ͑NGP͒, 18 ␣ 2 ͑t͒ = 3 5 ͓͗r͑t͒ − r͑0͔͒ 4 ͘/͓͗r͑t͒ − r͑0͔͒ 2 ͘ 2 − 1.…”

“…[3][4][5][6] At such subnanometer scale and in the dynamic range of the ␤-relaxation where the glass-forming units are moving within a "cage" formed by their immediate neighbors, [7][8][9][10] polymer specific effects are seemingly not directly involved. Notwithstanding, even at these very short spatial dimensions indirect effects such as the modification of local packing characteristics due to the applied intramolecular potentials in polymeric models, 4 or even correlation of motion within the cage 11,12 should properly be taken into account.…”