Shear stress relaxation and diffusion in simple liquids by molecular dynamics simulations: Analytic expressions and paths to viscosity
File(s)
Accepted version
Author(s)
Heyes, David
Smith, ER
Dini, D
Type
Journal Article
Abstract
The results are reported of an equilibrium molecular dynamics simulation study of the shear viscosity, η, and self-diffusion coefficient, D, of the Lennard-Jones liquid using the Green-Kubo (GK) method. Semiempirical analytic expressions for both GK time correlation functions were fitted to the simulation data and used to derive analytic expressions for the time dependent diffusion coefficient and shear viscosity, and also the correlation function frequency transforms. In the case of the shear viscosity for a state point near the triple point, a sech function was found to fit the correlation function significantly better than a gaussian in the ballistic short time regime. A reformulation of the shear GK formula in terms of a time series of time integrals (“viscuits”) and contributions to the viscosity from components based on the initial stress (“visclets”) enable the GK expressions to be recast in terms of probability distributions which could be used in coarse grained stochastic models of nanoscale flow. The visclet treatment shows that stress relaxation is statistically independent of the initial stress for equilibrium and metastable liquids, suggesting that shear stress relaxation in liquids is diffusion controlled. By contrast, the velocity autocorrelation function is sensitive to the initial velocity. Weak oscillations and a plateau at intermediate times originate to a greater extent from the high velocity tail of the Maxwell-Boltzmann velocity distribution. Simple approximate analytic expressions for the mean square displacement and the self Van Hove correlation function are also derived.
Date Issued
2019-05-07
Date Acceptance
2019-04-08
Citation
The Journal of Chemical Physics, 2019, 150 (17)
ISSN
0021-9606
Publisher
AIP Publishing
Journal / Book Title
The Journal of Chemical Physics
Volume
150
Issue
17
Copyright Statement
© 2019 Author(s). Published under license by AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in J. Chem. Phys. 150, 174504 (2019) and may be found at https://dx.doi.org/10.1063/1.5095501
Sponsor
Engineering & Physical Science Research Council (E
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EPSRC Fellowship Smith
EP/N025954/1
Subjects
Chemical Physics
02 Physical Sciences
03 Chemical Sciences
09 Engineering
Publication Status
Published
Article Number
174504
Date Publish Online
2019-05-07