Gary P. Morriss

Constrained molecular dynamics: Simulations of liquid alkanes with a new algorithm

We present a new algorithm for molecular dynamics simulation involving holonomic constraints. Constrained equations of motion are derived using Gauss’ principle of least constraint. The algorithm uses a fast, exact solution for constraint forces and a new procedure to correct for accumulating numerical errors. We report several simulations of liquid n‐butane and n‐decane performed with the new algorithm. We obtain an average trans population of 60.6±1.5% in liquid butane at T=291 K and u2009ρ=0.583 g/ml. This result essentially agrees with that from an earlier simulation by Ryckaert and Bellemans [Discuss. Faraday Soc. 66, 95 (1978)]. However, our simulations are substantially more precise; our run lengths are typically ∼20 times longer than those of Ryckaert and Bellemans. Our result also agrees with that from a recent simulation by Wielopolski and Smith (following paper). Thermodynamic and structural data from our simulations also agree well with results from the simulations discussed in the above articles.

The isothermal/isobaric molecular dynamics ensemble

Abstract Recently Gauss principle of least constraint has been combined with Dolls tensor methods to generate equations of motion for which the ideal gas temperature and the hydrostatic pressure are constants of the motion. We derive the equilibrium distribution function for these systems.

Rheology of n‐alkanes by nonequilibrium molecular dynamics

We have simulated sheared liquid n‐butane and n‐decane by isothermal nonequilibrium molecular dynamics. Both alkanes exhibit nonlinear rheological behavior. Shear thinning at small shear rates, second Newtonian viscosities at moderate shear rates, normal stresses, dilatancy, and birefringence are observed for both fluids. Zero shear rate viscosities were calculated for both fluids: η(γ=0)=0.24 cp for butane at T=292 K, η(γ=0)=0.159 cp for decane at 481 K. These viscosities agree with experimental data for both fluids. The zero shear rate butane viscosity agrees with the Green–Kubo result of Marechal and Ryckaert, Chem. Phys. Lett. 101, 548 (1983). Shear induced molecular rotation, deformation, and alignment are quantitatively described to give a complete picture of molecular behavior in a sheared fluid. Equilibrium and shear simulations of butane with modified dihedral potentials were performed to investigate the effect of molecular conformation on the rheological properties of butane.

Isothermal-isobaric molecular dynamics

We combine the Dolls tensor hamiltonian for flow deformation with Gauss principle of least constraint to develop classical equations of motion for which the temperature and hydrostatic pressure are constants of the motion. These equations of motion define a molecular dynamics algorithm for which N , T , p are the independent thermodynamic state variables.

Isothermal response theory

We derive expressions for the isothermal response of N-particle systems to a mechanical perturbation. Thermostating is achieved using gaussian isothermal equations of motion. Our theory is ergodically consistent in the sense that ensemble averages over the initial phases of the system are equivalent to time averages of the isothermal steady state response.

On the number dependence of viscosity in three dimensional fluids

We compute the shear viscosity of three dimensional simple fluids using nonequilibrium molecular dynamics. We show that for systems of 256 particles or more, the shear viscosity is, within ½ per cent, independent of the number of particles used in the simulation. We estimate that the zero shear rate viscosity of the triple point Lennard-Jones fluid is 3·41 ± 0·07. We observe small, but statistically significant departures from the square root dependence of viscosity with respect to shear rate. We show that by truncating the Lennard-Jones potential at 2·5σ, changes the viscosity by no more than ∼½ per cent compared to the untruncated fluid.

Nonequilibrium molecular dynamics study of shear flow in soft disks

Nonequilibrium molecular dynamics calculations of homogeneous shear flow in two dimensions have been performed on soft disks close to the freezing transition. Simulations at discrete shear rates, γ, reveal complex phase changes and dynamical behavior during extensive shear thinning and a difference in the values of the diagonal components of the pressure tensor. A shear thickening regime was also found near to γ=10 but it had disappeared at γ=50, in line with recent work by Woodcock. The calculations reveal that there is a change from an amorphous liquid structure at γ=1.0 to a fluid microscopically layered along the stream lines at γ=10 and higher shear rates. An intermediate two‐phase region was observed at γ=5 in which both amorphous and ordered phases coexist within the MD cell, containing 896 disks. In the ordered phase the particle dynamics are dominated by the imposed shear flow and can be reproduced in large part by simple models which exclude thermal motion. The time correlation functions a...

Equilibrium time correlation functions under gaussian isothermal dynamics

Abstract We compare equilibrium time correlation functions for Navier-Stokes transport coefficients calculated using either newtonian or gaussian isothermal equations of motion. By explicitly calculating the first few terms of the respective propagators, we show the equivalence of the two sets of time correlation functions in the thermodynamic limit.

On the nonlinear Born effect

In 1920 Max Born described the coupling of the intrinsic molecular spin to the hydrodynamic vorticity. At small shear rates molecules rotate at an angular velocity ⟨ω⟩ = ½∇ × u. In this paper we report the results of NEMD simulations which show that outside the linear regime, the average angular velocity ⟨ω⟩ is less than 1/2y.

Solution of the SSOZ equation for molecules of arbitrary symmetry

We present a flexible and efficient method of solving site-site integral equations for polar molecular fluids. The numerical method is based on a combination of Newton-Raphson and Picard schemes first proposed by Gillan, together with the Ng method for handling Coulomb potentials. It is completely general and can be used with any closure or potential to solve for molecules of arbitrary symmetry. We apply the method to several model systems and demonstrate its superiority to the usual renormalization technique. For quadrupolar hard dumb-bells we find that, in contrast to the situation for neutral dumb-bells, approximate integral equation results depend strongly on the physically irrelevant hard core diameter associated with the centre of the dumb-bell.