Microscopic dynamics of thin hard rods

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dc.creatorOtto, Matthias
dc.creatorAspelmeier, Timo
dc.creatorZippelius, Annette
dc.date2005-10-18
dc.date2006-10-11
dc.date.accessioned2026-07-07T06:44:31Z
dc.date.available2026-07-07T06:44:31Z
dc.descriptionBased on the collision rules for hard needles we derive a hydrodynamic equation that determines the coupled translational and rotational dynamics of a tagged thin rod in an ensemble of identical rods. Specifically, based on a Pseudo-Liouville operator for binary collisions between rods, the Mori-Zwanzig projection formalism is used to derive a continued fraction representation for the correlation function of the tagged particle's density, specifying its position and orientation. Truncation of the continued fraction gives rise to a generalised Enskog equation, which can be compared to the phenomenological Perrin equation for anisotropic diffusion. Only for sufficiently large density do we observe anisotropic diffusion, as indicated by an anisotropic mean square displacement, growing linearly with time. For lower densities, the Perrin equation is shown to be an insufficient hydrodynamic description for hard needles interacting via binary collisions. We compare our results to simulations and find excellent quantitative agreement for low densities and qualtitative agreement for higher densities.
dc.description21 pages, 6 figures, v2: clarifications and improved readability
dc.identifierhttps://arxiv.org/abs/cond-mat/0510474
dc.identifierhttp://arxiv.org/abs/cond-mat/0510474
dc.identifierJ. Chem. Phys. 124, 154907 (2006)
dc.identifierdoi:10.1063/1.2186325
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/102801
dc.subjectSoft Condensed Matter
dc.titleMicroscopic dynamics of thin hard rods
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