S. Toxvaerd

Self-diffusion in n-alkane fluid models

Molecular dynamic simulations of fluid n‐pentane and n‐decane have been performed in order to analyze the self‐diffusion. An isotropic united‐atom (UA) model as well as anisotropic united‐atom (AUA) models have been used to represent the molecular interactions. Self‐diffusion coefficients have been calculated. The sensitivity of the self‐diffusion coefficient to the shape of the intermolecular potential as well as the torsion potential has been analyzed. The simulation results for the diffusion coefficient are in excellent agreement with experimental data when the molecular interaction is represented by an anisotropic United‐Atom model and the internal rotation is governed by a torsion potential proposed in this work.

Algorithms for canonical molecular dynamics simulations

Finite-difference algorithms for Nose-Hoover canonical molecular dynamics (NH-MD) are investigated. In general, NH-MD functions excellently, but it is demonstrated that time symmetry is broken in NH-MD algorithms and that this results in irreversible thermostatting, which can destroy the canonical sampling. However, the traditional ‘leapfrog’ algorithm, extended to NH-MD, works almost perfectly and equilibrates correctly, even for a system of a single butane chain, which is found to be very sensitive to numerical approximations. The MD conserves the total momentum—and for a single molecule also the angular momentum. NH-MD can run with or without these conservation constraints, and it is stable with respect to round-off errors, at least for the first 109 time steps for the present system.

EQUATION OF STATE OF ALKANES II

The pressure in condensed fluids of pentane and decane is calculated by molecular dynamics for temperatures from room temperature to 673 K and pressures up to 350 MPa using the anisotropic united atom (AUA) model [Toxvaerd, J. Chem. Phys. 93, 4290 (1990)], and compared with other recently published united atom models (UA). The pressure for the AUA model agrees well with experimentally obtained pressures whereas the UA model fails outside the region of moderate pressure and density. The impact of the torsion potential and the intermolecular potential on structure, thermodynamics, and self-diffusion is investigated for fluids of decanes at high and moderate densities. A time reversible and numerical stable implementation of Gauss’ principle of least constraint (of bond lengths) is described in the Appendix. The constrained molecular dynamics is performed without any adjustment or rescaling of the bond lengths.

Molecular-dynamics simulation of homogeneous nucleation in the vapor phase

Ten independent quenches of a gas of 40 000 Lennard-Jones particles are followed until the systems exhibit droplet growth. The cluster distributions and the kinetics are determined for the quenched quasi-equilibrium state, at the onset of nucleation and at droplet growth. All the distributions are isomorphic with the particle distribution in the equilibrium gas state and asymptotically given by simple exponentials. The kinetics show detailed balance of particles and clusters which join and which leave the successful critical nuclei. The systems exhibit chaoticlike behavior with respect to the onset of nucleation, so that only marginal changes in a system will change the onset of nucleation.

Molecular dynamics simulations of Langmuir monolayers: A study of structure and thermodynamics

Molecular dynamics (MD) simulations have been performed on Langmuir monolayers of single chain surfactants at the air–water interface using a new anisotropic united atom model (AUA) for chain–chain interactions and a dipolar potential for head–head repulsions. Water–surfactant interactions are modeled using an external potential that does not fix the head group positions. The forces of the skeletal chains involved intramolecular effects of angle bending, and rotation among quartets of adjacent segments. Several molecular dynamics simulations have been performed on monolayers with densities ranging from 18 to 30 A2/molecule. The results show two transitions in the monolayer. The first phase transition is a melting from a triangular lattice state maintained by the carbon chains to a fluidlike state with chain diffusion and lattice defects. The second transition is characterized by a change in molecular conformation, but with no change in lattice defects.

Communication: Shifted forces in molecular dynamics.

Simulations involving the Lennard-Jones potential usually employ a cutoff at r = 2.5σ. This communication investigates the possibility of reducing the cutoff. Two different cutoff implementations are compared, the standard shifted potential cutoff and the less commonly used shifted forces cutoff. The first has correct forces below the cutoff, whereas the shifted forces cutoff modifies Newtons equations at all distances. The latter is nevertheless superior; we find that for most purposes realistic simulations may be obtained using a shifted forces cutoff at r = 1.5σ, even though the pair force is here 30 times larger than at r = 2.5σ.

Hidden scale invariance in molecular van der Waals liquids: A simulation study

We address a recent conjecture according to which the relaxation time τ of a viscous liquid obeys density scaling (τ = F (ρ/T ) where ρ is density) if the liquid is “strongly correlating,” i.e., has almost 100% correlation between equilibrium virial and potential-energy fluctuations [Pedersen et al., PRL 100, 011201 (2008)]. Computer simulations of two model liquids an asymmetric dumbbell model and the Lewis-Wahnström OTP model confirm the conjecture and demonstrate that the scaling exponent γ can be accurately predicted from equilibrium fluctuations.

Statistical mechanical and quasithermodynamic calculations of surface densities and surface tension

The Born-Green-Yvon-Bogolyubov integrodifferential equation for the density in a plane transition zone between liquid and gas in a Lennard-Jones fluid is solved after approximating the pair distribution function by a simple combination of its bulk values. The density profiles so obtained are all monotomic functions in excellent agreement with the profiles obtained from quasithermodynamic models. The surface tension and the stress tensor differences in the interface, calculated from the statistical mechanical model of Kirkwood and Buff are compared with the corresponding quasithermodynamic values and with the experimental values of the surface tension for argon. It is found that the Kirkwood-Buff formula, in the present approach, predicts a much stronger dependence of the surface tension on the curvature of the transition zone than the quasithermodynamic approach.

Surface Structure of a Square‐Well Fluid

The perturbation expansion for fluids is formulated as an expansion of the chemical potential. The interface density profile between the uniform bulk phases of a square‐well fluid is obtained by requiring that the chemical potential is constant in the interface. The profile is compared with the profile obtained from the Born‐Green‐Yvon‐Bogolyubov integrodifferential equation in the density and with the profile obtained by minimizing the excess free energy of the interface. The density profiles obtained from the three different approaches are all in mutual agreement and show that the interface density decreases monotonically and rapidly for temperatures far from the critical point.

The mobile-layer model for adsorption

The adsorption isotherms for Kr monolayers on graphite measured by A. Thomy and X. Duval, J. chim. phys., 67, 1101 (1970) are transformed into the ‘spreading pressure’ as a function of the number density of adsorbed molecules and compared with the pressure of a two-dimensional Lennard-Jones fluid determined by the molecular dynamics technique. The comparison shows that the mobile-layer model for adsorption fails at low temperatures. The liquid-solid phase transitions in the adsorption monolayer appear at lower densities than in a two dimensional Lennard-Jones fluid and the adsorbed liquid layer is compressible in contrast to the two-dimensional Lennard-Jones liquid.