Energy landscapes for diffusion: Analysis of cage-breaking processes

Abstract

A wide spectrum of potential energy barriers exists for binary Lennard-Jones systems. Here we examine the barriers and cage-breaking rearrangements that are pertinent to long-term diffusion. Single-step cage-breaking processes, which follow high-barrier routes, are identified, and different methods and criteria for defining a cage-breaking process are considered. We examine the extent to which a description of cage-breaking within the energy landscape is a description of long-term diffusion. This description includes the identification of cage-breaks that are reversed, and those that are productive towards long-term diffusion. At low temperatures, diffusion is adequately described by productive cage-breaks, or by considering all cage-breaks and accounting for the effect of reversals. To estimate the diffusion constant we require only the mean square displacement of a cage-break, the average waiting time for a cage-break, and a measure of the number of reversed cage-breaks. Cage-breaks can be visualized within the potential energy landscape using disconnectivity graphs, and we compare the use of productive cage-breaks with previous definitions of "megabasins" or "metabasins."

Decoding the energy landscape: extracting structure, dynamics and thermodynamics

“…The disconnectivity graph in this region of configuration space is therefore highly frustrated [66,71], and provides a useful reference for a 'rough' or 'rugged' landscape. This picture has been confirmed in subsequent calculations [132,133], and analysis of rearrangements in terms of cage-breaking events has revealed [132] a further level of hierarchical structure and a possible definition of 'metabasins' [134,135].…”

Anomalous dimensionality dependence of diffusion in a rugged energy landscape: How pathological is one dimension?

“…[1,[39][40][41] In the context of transport in the supercooled liquid, Goldstein and Johari discussed the possible influence of energy landscape in describing slow relaxation in glassy liquids. [16] This pioneering idea was further studied using inherent structure formalism [17][18][19][20][21][22][23]. The latter provides evidence of the migration of a system from one minimum to another minimum.…”

Communications: Comparison of activation barriers for the Johari–Goldstein and alpha relaxations and its implications

“…At that time, we suggested as an explanation of this universality that the basins in the energy landscapes of supercooled liquids had "corrugated bottoms," energy hills, and valleys that are small compared to the hills and valleys that constitute the major features of the landscape. 2 Subsequent calculations of energy landscapes pioneered by Stillinger and Weber [3][4][5] and extended by others [6][7][8][9][10][11][12][13][14] have amply confirmed this complex fine structure and led to the concept of the "metabasin." 4,5 The alpha relaxation was attributed to transitions over large barriers between metabasins and the JG to activated transitions over the lower barriers within a metabasin.…”

“…10,12,14 Such calculations on a Lennard-Jones liquid performed around the critical temperature T c of the mode coupling theory have found barrier heights of about 10 T c , which increase on further cooling. 14 On the other hand, MD calculations of trajectories in Lennard-Jones liquids that visit a long enough sequence of metabasins to enable the alpha relaxation behavior or the diffusion coefficient to be calculated show the typical super-Arrhenius temperature dependence of fragile liquids.…”

“…14 On the other hand, MD calculations of trajectories in Lennard-Jones liquids that visit a long enough sequence of metabasins to enable the alpha relaxation behavior or the diffusion coefficient to be calculated show the typical super-Arrhenius temperature dependence of fragile liquids. Wales and co-workers 7,10 have offered an explanation of this temperature dependence in terms of the gradual kinetic closing off of connections between metabasins on cooling.…”