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2 Computational Methods in Science and Technology

2 2023

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Isomorph Scaling of Hard Sphere and Lennard-Jones Fluids

Heyes David M., Pieprzyk Sławomir, Brańka Arkadiusz C.

Computational Methods in Science and Technology

2023

Vol. 29, No. 1-4

45--55

The transport coefficients of model monatomic fluids are explored within the context of isomorph theory. An extension of our previous study in this field to the thermal conductivity of Lennard-Jones (LJ) fluids is reported here. The relationship to and comparisons with the behavior of the LJ system and those of hard spheres (HS), which form perfect isomorphs at all densities are made. The HS and LJ transport coefficients obtained by MD simulations when scaled by socalled macroscopic (‘isomorph’) units, and the density is scaled by the freezing density, form curves which are extremely similar, and in near quantitative agreement apart from close to freezing in most cases. It is shown that to a large extent the excellent ‘isomorph’ scaling of the transport coefficients exhibited by the LJ system, even at low densities, can be traced back to the dominance of the repulsive part of this potential for these dynamical quantities, which can reasonably accurately be accounted for by the scaling behavior of hard spheres. Numerical support for this conclusion using molecular dynamics data for the HS and LJ model fluids is presented.

Density Functional Formalism as a Description of the Elastic Behavior of a Hard-Sphere Crystal

Pieprzyk Sławomir, Brańka Arkadiusz C., Heyes David M.

Computational Methods in Science and Technology

2023

Vol. 29, No. 1-4

57--64

The density functional method of Jaric and Mohanty [Phys. Rev. B ´ 37, 4441 (1988)] for calculating the elastic moduli of crystalline solids is considered here from the perspective of some new findings. The very slow convergence of the reciprocal-lattice vector summations and presence of the three body term in the method’s computational scheme identified in [J. Chem. Phys. 118, 6594 (2003)] is confirmed and discussed. The sensitivity of the results to the scheme parameters, such as the width of the Gaussian density profiles and the Percus-Yevick approximation used for the direct correlation function is explored. The calculations are for a hard-sphere crystal but most conclusions can be applicable to model crystalline solids in general.