Inertial effects in anomalous dielectric relaxation of symmetrical top molecules

Sergey V. Titov, Yuri P. Kalmykov, and William T. Coffey
Phys. Rev. E 69, 031114 – Published 31 March 2004
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Abstract

The linear dielectric response of an assembly of noninteracting symmetrical top molecules (each of which is free to rotate in space) is evaluated in the context of fractional dynamics. The infinite hierarchy of differential-recurrence relations for the relaxation functions appropriate to the dielectric response is derived by using the underlying inertial fractional Klein-Kramers equation. On solving this hierarchy in terms of matrix continued fractions (as in the normal rotational diffusion), the complex dynamic susceptibility is obtained and is calculated for typical values of the model parameters. For the limiting case of spherical top molecules, the solution is obtained in terms of an ordinary continued fraction. It is shown that the model can reproduce nonexponential anomalous dielectric relaxation behavior at low frequencies (ωτ<~1, where τ is the Debye relaxation time) and the inclusion of inertial effects ensures that optical transparency is regained at very high frequencies (in the far infrared region) so that Gordon’s sum rule for integral dipolar absorption is satisfied.

  • Received 23 October 2003

DOI:https://doi.org/10.1103/PhysRevE.69.031114

©2004 American Physical Society

Authors & Affiliations

Sergey V. Titov

  • Institute of Radio Engineering and Electronics of the Russian Academy of Sciences, Vvedenskii Square 1, Fryazino, Moscow Region, 141190, Russian Federation

Yuri P. Kalmykov

  • MEPS, Groupe de Physique Moléculaire, Université de Perpignan, 52, Avenue Paul Alduy, 66860 Perpignan Cedex, France

William T. Coffey

  • Department of Electronic and Electrical Engineering, Trinity College, Dublin 2, Ireland

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Vol. 69, Iss. 3 — March 2004

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