Comprehensive molecular dynamics study of the dynamical properties of a dense binary hard-sphere mixture
Abstract
We present an extensive molecular dynamics (MD) study of the dynamical properties of a binary hard-sphere fluid over a wide range of packing fractions, ϕ≈ 0.357−0.582. The self-diffusivity, D, and shear viscosity, η, are computed using an efficient implementation of the Einstein--Helfand method. The finite-size effects in D scale as 1/Nα, with α increasing from approximately 1/3 to 3/4 with increasing ϕ, whereas those in η are negligible except for ϕ≳ 0.554, where they scale as 1/N. The data are then extrapolated to the thermodynamic limit to obtain D∞ and η∞. Both coefficients show a super-Arrhenius dependence on ϕ for dense states, accompanied by a breakdown of the Stokes--Einstein relation. Although both D∞(ϕ) and η∞(ϕ) data are well described by an exponential form, we demonstrate that these fits do not provide reliable estimates of the critical packing fraction, ϕ0, owing to the substantial extrapolation required beyond the accessible equilibrium range. We find the commonly assumed proportionality between η and the structural relaxation time, τα , to not hold for this system. For ϕ≳ 0.570, the van Hove self-correlation function Gs(r, τ) exhibits a spatial exponential decay at intermediate times, τ, signaling dynamic heterogeneity. The characteristic decay length scales as λ∼ τν, with ν≈ 1/3, in contrast to the conventional square-root scaling. We also investigate temporal heterogeneity through the four-point dynamic susceptibility, χ4(τ), and its peak time, τ4. These findings provide rigorous benchmark MD data for computational studies of glassy dynamics and establish a reference for testing theoretical models in dense disordered systems.
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BibTeX
@misc{moustafa2026comprehensive,
title = {{Comprehensive molecular dynamics study of the dynamical properties of a dense binary hard-sphere mixture}},
author = {Sabry G. Moustafa and Andrew J. Schultz},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09532},
eprint = {2609.09532},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09532},
}
RIS
TY - UNPB
TI - Comprehensive molecular dynamics study of the dynamical properties of a dense binary hard-sphere mixture
AU - Sabry G. Moustafa
AU - Andrew J. Schultz
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09532
UR - https://arxiv.org/abs/2609.09532
AB - We present an extensive molecular dynamics (MD) study of the dynamical properties of a binary hard-sphere fluid over a wide range of packing fractions, ϕ≈ 0.357−0.582. The self-diffusivity, D, and shear viscosity, η, are computed using an efficient implementation of the Einstein--Helfand method. The finite-size effects in D scale as 1/N^α, with α increasing from approximately 1/3 to 3/4 with increasing ϕ, whereas those in η are negligible except for ϕ≳ 0.554, where they scale as 1/N. The data are then extrapolated to the thermodynamic limit to obtain D_∞ and η_∞. Both coefficients show a super-Arrhenius dependence on ϕ for dense states, accompanied by a breakdown of the Stokes--Einstein relation. Although both D_∞(ϕ) and η_∞(ϕ) data are well described by an exponential form, we demonstrate that these fits do not provide reliable estimates of the critical packing fraction, ϕ_0, owing to the substantial extrapolation required beyond the accessible equilibrium range. We find the commonly assumed proportionality between η and the structural relaxation time, τ_α , to not hold for this system. For ϕ≳ 0.570, the van Hove self-correlation function G_s(r, τ) exhibits a spatial exponential decay at intermediate times, τ, signaling dynamic heterogeneity. The characteristic decay length scales as λ∼ τ^ν, with ν≈ 1/3, in contrast to the conventional square-root scaling. We also investigate temporal heterogeneity through the four-point dynamic susceptibility, χ_4(τ), and its peak time, τ_4. These findings provide rigorous benchmark MD data for computational studies of glassy dynamics and establish a reference for testing theoretical models in dense disordered systems.
ER -