Direct Observation of Stretched-Exponential Relaxation in Low-Temperature Lennard-Jones Systems Using the Cage Correlation Function

Abstract

We report on the direct observation of stretched exponential relaxation in low-temperature monatomic Lennard-Jones systems which were cooled slowly from the liquid phase to form crystals with a large number of defects. We use the cage correlation function [ E. Rabani, J. D. Gezelter, and B. J. Berne, J. Chem. Phys. 107, 6867 (1997)] which measures changes in atomic surroundings to observe the stretched exponential relaxations. We obtain a distribution of hopping rates assuming that the origin of the Kohlrausch-Williams-Watts law is from static disorder in the distribution of barrier heights.[S0031-9007(99)09049-3]

Energy landscapes for diffusion: Analysis of cage-breaking processes

“…Rabani et al [14][15][16] have developed a link between cages and long-time behavior with the introduction of a cage correlation function. The decay of this function can be examined to obtain estimates of the residence times within different local minima ͑inherent structures͒ on the potential energy surface, and can be used to reproduce the characteristic stretched relaxation of fragile glass formers.…”

Connectivity in the potential energy landscape for binary Lennard-Jones systems

“…A cage correlation function, [18][19][20] which examines changes in nearest neighbors, has been introduced to develop a link between cages and long-time behavior. The function decays as each particle's surroundings change, and the decay can be examined to obtain estimates of the residence times within different local minima ͑inherent structures 21,22 ͒ on the PES.…”

“…Using this function, it is possible to reproduce the characteristic stretched relaxation of fragile glass formers. 19,23 A number of direct studies of the caging process in supercooled liquids have provided information on cage structure and relaxation properties, 24,25 and on the ratio of "reversible" to "irreversible" processes. [26][27][28] The idea of cagebreaking also plays a role in mode-coupling theory 29,30 and is directly applicable in energy landscape studies.…”

Theory of correlated two-particle activated glassy dynamics: General formulation and heterogeneous structural relaxation in hard sphere fluids

“…The stretching exponent associated with C 2 (t), which is relevant to the cage correlation function studied in Rabani et al, 48,62 is far from the value of β k = 0.5 reported. 62 However, interestingly, our value of β k ≈ 0.56 for the full static-and dynamic-disorder averaged generic relaxation function, C 1 (t), is very close to what is observed in dense hard sphere colloidal suspensions for the alpha process on the cage wavevector scale, 66 and also the prediction of ideal MCT. 67 Moreover, this value is close to that observed in the dielectric experiments on TNB, 68 the decoupling behavior for which was discussed in the preceding section.…”

“…A simulation study of this problem 48,62 was based on defining a generalized neighbor list for particle i as a vector with components (l i (t)) j = f (r i j (t)), where f (r i j (t)) is a step function equal to one if particle j is within the first solvation shell of i, and zero otherwise. The cut-off used is g min , the distance from contact to the first minimum of g(r ).…”