Transition state theory and the dynamics of hard disks

Abstract

The dynamics of two and five disk systems confined in a square has been studied using molecular dynamics simulations and compared with the predictions of transition state theory. We determine the partition functions Z and Z^\ddagger of transition state theory using a procedure first used by Salsburg and Wood for the pressure. Our simulations show this procedure and transition state theory are in excellent agreement with the simulations. A generalization of the transition state theory to the case of a large number of disks N is made and shown to be in full agreement with simulations of disks moving in a narrow channel. The same procedure for hard spheres in three dimensions leads to the Vogel-Fulcher-Tammann formula for their alpha relaxation time.

1 new author, new simulations and figures, less speculation. Now 6 pages, 6 figures, 1 animation. Animation may be viewed at http://www.theory.physics.manchester.ac.uk/~godfrey/supplement/activated_dynamics2.html

References in corpus (3)

• Theoretical perspective on the glass transition and amorphous materials
• Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transition
• The Inherent Structure Landscape Connection Between Liquids, Granular materials and the Jamming Phase Diagram

Cited by in corpus (6)

• Understanding the ideal glass transition: Lessons from an equilibrium study of hard disks in a channel
• Static and dynamical properties of a hard-disk fluid confined to a narrow channel
• Glass-like behavior of a hard-disk fluid confined to a narrow channel
• The potential energy landscape and inherent dynamics of a hard-sphere fluid
• Visualizing Free Energy Landscapes for Four Hard Disks
• How the overlap of excluded volume determines the configurational energy landscape and "thermodynamics" in the "one to five hard disks in a box" system