Dynamics of a Supercooled Lennard-Jones System: Qualitative and Quantitative Tests of Mode-Coupling Theory
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Introduction
In the last few years it has been shown that the mode-coupling theory (MCT) of the glass transition is able to give a quite accurate description of the dynamics of certain supercooled liquids. An introduction to the theory can be found in the review articles of Ref. [1] and a collection of many investigations that have been done in order to test the validity of the theory is compiled in Ref. [2]. Although it has convincingly been shown that there are systems for which MCT gives a good description of the dynamics [2], a few questions remain still open: i) So far it is still not clear for what type of systems the theory is valid. Is it only for glass formers that are basically simple liquids or does MCT also describe more complex liquids? ii) Since so far many of the predictions of the theory are of an asymptotic nature, i.e. are valid only very close to the critical temperature T,, it is not clear how important the corrections to these asymptotic results are if one is at a finite distance from T,. iii) To what extend are also the non-universal predictions of the theory correct, e.g. is the theory able to predict quantitatively the critical temperature or the wave-vector dependence of the nonergodicity parameter? Partial answers to these questions can be found in the above mentioned articles and in Ref. [3] but it is clear that quite a bit of work is left to be done. The goal of this paper is to address the question whether MCT is able to describe the dynamics of a supercooled binary Lennard-Jones system on a qualitative and quantitative basis. In order to study this question we determined the dynamics of such a system by means of a molecular dynamics computer simulation and compared the so obtained dynamics with the (universal) predictions of the theory. From this simulation we also obtained the temperature dependence of the partial structure factors, the crucial input to the theory to make non-universal predictions and then solved the mode-coupling equations in the limit of long times. The so obtained solutions could then be compared with the results from the molecular dynamics simulation.
59 Mat. Res. Soc. Symp. Proc. Vol. 455 01997 Materials Research Society
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Model and Details of the Simulation
The system we consider is a binary mixture of Lennard-Jones particles. Both types of particles (type A and B) have the same mass m and interact with the potential V, =: {(ca,9/r)12 - (u.0/r)6 } with a, /3 E {A, B}. The parameters of the potential are 6AA = 1.0, aAA = 1.0, EAB = 1.5, UAB = 0.8, EBB = 0.5, and OrBB = 0.88. In the following we will measure length in units of aAA, energy in units of EAA (setting kB = 1) and time in units of (maAA/48CAA) 1/ 2 . The resulting equations of motion were integrated with the velocity form of the Verlet algorithm with a time step of 0.01 for T > 1.0 and 0.02 for T < 1.0. The length of the runs were chosen such that they always exceeded the typical a-relaxation time of the system at the corresponding temperature. The temperatures we studied were T = 5.0, 4.0, 3.0
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