Signatures of distinct dynamical regimes in the energy landscape of a glass-forming liquid

Abstract

Most materials attain a glassy state at low temperatures under suitable methods of preparation. This state exhibits the mechanical properties of a solid, but shows microscopic structural disorder 1,2 . A comprehensive understanding of the glassy state is, however, still lacking 3 . A widespread assumption is that the nonexponential relaxation processes observed in the dynamics of glasses-and also in protein dynamics, protein folding and population dynamics-are (in common with other manifestations of complex dynamics) strongly influenced by the underlying energy landscape associated with the structural configurations that the system may adopt. But concrete evidence for this in studies of glass formation has been scarce. Here we present such evidence, obtained from computer simulations of a model glassforming liquid. We demonstrate that the onset of non-exponential relaxation corresponds to a well defined temperature below which the depth of the potential-energy minima explored by the liquid increases with decreasing temperature, and above which it does not. At lower temperatures, we observe a sharp transition when the liquid gets trapped in the deepest accessible energy basin. This transition temperature depends on the cooling rate, in a manner analogous to the experimental glass transition. We also present evidence that the barrier heights separating potential-energy minima sampled by the liquid increase abruptly at a temperature above the glass transition but well below the onset of non-exponential relaxation. This identification of a relationship between static, topographic features of the energy landscape and complex dynamics holds letters to nature 554 NATURE | VOL 393 | 11 JUNE 1998 0.0 0.5 1.0 1.5 2.0 Temperature -7.05 -7.00 -6.95 -6.90 Energy Cooling rate = 1.08 ×10 -3 Cooling rate = 2.70 ×10 -4 Cooling rate = 8.33 ×10 -5Cooling rate = 3.33 ×10 -6 a Figure 1 Molecular dynamics simulations of a binary Lennard-Jones mixture 21 . 80% of the particles are of type A, 20% are type B, and Lennard-Jones parameters are e AA ¼ 1:0, e AB ¼ 1:5, e BB ¼ 0:5, j AA ¼ 1:0, j AB ¼ 0:8 and j BB ¼ 0:88. All quantities are in reduced units: length in units of j AA , temperature in units of e AA /k B , and time in units of (j 2 AA m/e AA ) 1/2 , where m is the mass of the particles. The density r in all cases is 1.2. The calculated pressures for the system remain positive except for T Ͻ 0:06, much below temperatures where the system forms a glass in all cases studied. The Lennard-Jones potential, with a quadratic cut-off and shifting of the potential at r ab c ¼ 2:5j ab (ref. 29), a; b ʦ A; B is used. Our cut-off procedure results in a potential minimum value which is ϳ4% smaller than that in ref. 21. The time step is dt ¼ 0:003. Each run was initialized by equilibration at a high temperature, followed by equilibration and data collection runs at a series of temperatures. The run length at each temperature, together with the number of temperatures chosen, determines the cooling rate. Equilibration was done at constant temperat...

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