Denis J. Evans

The Nose–Hoover thermostat

We derive equilibrium fluctuation expressions for the linear response of many body systems thermostated by the Nose–Hoover thermostat. We show that in the thermodynamic limit this response is the same as that of the corresponding Gaussian isothermal system. Numerical comparisons for shear flow show however that the Gaussian methods provide a significantly more efficient means of calculating the shear viscosity coefficient.

Computer ‘‘experiment’’ for nonlinear thermodynamics of Couette flow

Nonequilibrium computer simulations reveal that the equation of state of fluids undergoing shear flow, varies with strain rate. This observation prompted the development of a nonlinear generalization of irreversible thermodynamics to describe steady planar Couette flow, very far from equilibrium. In this paper we use computer simulation to perform a quantitative test of a prediction of this thermodynamics. The prediction tested is: fluids which exhibit positive shear dilatancy for isothermal shear flow should also cool as the strain rate is increased while keeping the internal energy constant. To perform calculations of this effect a new nonequilibrium molecular dynamics algorithm was developed to simulate Couette flow at constant internal energy.

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  ρ=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.

Comparison of constant pressure and constant volume nonequilibrium simulations of sheared model decane

We present the results of nonequilibrium molecular dynamics simulations of a model decane fluid performed at constant pressure and compare them with results previously obtained from simulations performed at constant volume. The strain rate dependence of the viscosity at constant pressure is found to differ from that obtained previously at constant volume. The shear thickening at high strain rates observed in constant volume simulations vanishes when the simulations are performed at constant pressure. We also investigate the question of how our low strain rate data for decane can be accurately extrapolated to zero strain rate. We find a well defined first Newtonian region in which the viscosity is independent of strain rate to within errors. The value of the viscosity that we obtain in this region agrees well with the zero strain rate viscosity calculated from the Green–Kubo formula at equilibrium.

Homogeneous NEMD algorithm for thermal conductivity—Application of non-canonical linear response theory

Abstract We develop an extension of linear response theory for non-canonical, classical systems. This theory allows the design of a translationally invariant non-equilibrium simulation algorithm for calculating the thermal conductivity of dense fluids. When applied to the Lennard-Jones representation of argon, excellent agreement with experiment is obtained.

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.

Configurational temperature: Verification of Monte Carlo simulations

A new diagnostic that is useful for checking the algorithmic correctness of Monte Carlo computer programs is presented. The check is made by comparing the Boltzmann temperature, which is input to the program and used to accept or reject moves, with a configurational temperature kBTconfig=|∇qΦ|2/∇q2Φ. Here, Φ is the potential energy of the system and ∇q represents the dimensionless gradient operator with respect to the particle positions q. We show, using a simulation of Lennard-Jones particles, that the configurational temperature rapidly and accurately tracks changes made to the input temperature even when the system is not in global thermodynamic equilibrium. Coding and/or algorithm errors can be detected by checking that the input temperature and Tconfig agree. The effects of system size and continuity of Φ and its first derivative on Tconfig are also discussed.

Microscopic expressions for the thermodynamic temperature

We show that arbitrary phase space vector fields can be used to generate phase functions whose ensemble averages give the thermodynamic temperature. We describe conditions for the validity of these functions in periodic boundary systems and the molecular dynamics (MD) ensemble, and test them with a short-ranged potential MD simulation.

On the structure of liquid benzene

Monte Carlo calculations of the structure of liquid benzene are reported. The benzene pair potential is represented as a sum of Lennard-Jones (12, 6) interactions acting between six sites on each molecule, giving a total of 36 terms. Results are given for the centre-of-mass radial distribution function, for CH group/CH group distributions and for the centre-of-mass/CH group distribution function. Angular correlation functions are examined in terms of the axial symmetry vector of the benzene ring. It is shown that the liquid-state structure resembles that of the crystalline solid, and in particular that the nearest-neighbour distribution can be interpreted using this similarity.

Shear viscosities away from the melting line: A comparison of equilibrium and nonequilibrium molecular dynamics

Doubts about the validity of the nonequilibrium molecular dynamics (NEMD) methods of computing shear viscosity have persisted, partly because of the apparent disagreement (∼25%) between NEMD and equilibrium Green–Kubo (GK) results for the Lennard‐Jones system near its triple point. This region of the phase diagram near the melting line is the so‐called ‘‘molasses’’ regime where the tail of the shear‐stress autocorrelation function is quite large, deviating from ‘‘exponential’’ decay at a level of about 10%. In order to see whether the effects of the ‘‘molasses tail’’ might be obscuring a more profound difference between NEMD and GK results, we have carried out independent NEMD and GK calculations for a state in the LJ fluid far away from this troublesome molasses region, namely at a temperature twice critical and a density between the triple and critical points. We find the NEMD and GK results for the linear shear viscosity to be in good agreement.