Single Particle Jumps in a Binary Lennard-Jones Glass
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Single Particle Jumps in a Binary Lennard-Jones Glass K. Vollmayr-Lee1,2 1 Department of Physics, Bucknell University Lewisburg, PA 17837, USA 2 Institute of Physics, Johannes-Gutenberg-University of Mainz, Staudinger Weg 7, 55099 Mainz, Germany ABSTRACT We study a binary Lennard-Jones mixture below the glass transition with molecular dynamics (MD) simulations. To investigate the dynamics of the system we define single particle jumps via their single particle trajectories. We find two kinds of jumps: metastable jumps, where a particle jumps back and forth between two or more states, and real jumps, where a particle does not return to any of its former states. For both the real and metastable jumps we present as a function of temperature the number of jumps, jump size, time between jumps, and energy. INTRODUCTION While glasses are well-studied, there are still many open questions about their static and dynamic behavior [1]. We study here the dynamics of single particles. In a glass each particle is trapped in a cage formed by its neighbors. If one waits long enough a particle may escape its cage [2–6]. In this paper we focus on the event of a particle jumping out of its cage. We systematically identify and analyze such jumps in a binary Lennard-Jones mixture by studying single-particle trajectories. The outline of this paper is as follows. We first describe the model and details of the simulation and follow with our definition of jumps and jump types. We then present the number of jumping particles, time scales, and spatial and energetic jump sizes and their dependence on the temperature, along with conclusions. MODEL AND SIMULATION We use a binary Lennard-Jones mixture of 800 A and 200 B particles with the same mass. The interaction potential for particles i and j at positions ri and rj and of type α, β ∈ {A,B} Vαβ (r) = 4 αβ
σαβ r
12
σαβ − r
6
,
(1)
where r = |ri − rj |, and AA = 1.0, AB = 1.5, BB = 0.5, σAA = 1.0, σAB = 0.8, and σBB = 0.88. We carry out molecular dynamics simulations using the velocity Verlet algorithm with both particle types having mass 48 and a time step of 0.02. The volume is kept constant at V = 831 and we use periodic boundary conditions. To study the microscopic dynamics below the kinetic glass transition, which according to Kob and Andersen is at T ≈ 0.45 [7], we analyze here simulations at T = 0.15, 0.20, 0.25, 0.30, 0.35, 0.38, 0.40, 0.41, 0.42, and 0.43, as they have been described in [8]. For each temperature we use 10 independent initial configurations and run NVE simulations with 5·106 MD steps. For subsequent analysis all
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ri σr R
t
sj e j
Figure 1: This sketch illustrates the trajectory ri (t) of a particle i which undergoes a jump. ri
ri
real jump
t
metastable jump
t
Figure 2: These two sketches show the trajectories of a real jump and of multiple metastable jumps. positions {ri } are printed out every 2000 MD steps. As is well known, it is a nontrivial and unsolved problem to prepare well equilibrated glassy configurations of any mode
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