Brownian Motion in a Periodic Potential: Application to Dielectric Relaxation

Marchesoni, F. and Vij, Jagdish K. (1984) Brownian Motion in a Periodic Potential: Application to Dielectric Relaxation. (Preprint)

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The relaxational dynamics of a planor rotator in an M-fold cosine potential subject to a random torque is investigated in detail. For the case of a periodic potential with large barrier height, the numerical results of the relaxation dynamics are in complete agreement with an approximate analytical solution. The latter is derived on assuming a harmonic potential at the bottom of the potential minima and a large time-scale separation between the short-time libration inside each potential minima and long-time hopping phenomenon over the potential barriers. For M ≥ 2, the hopping phenomenon is found to be the dominant feature of the orientational auto-correlation function. The average hopping time is explained satisfactorily in terms of the Kramers activation rate theory. In particular a complete agreement is found between the numerical results of the escape rate and those obtained from the modified Kramers predictions valid for low friction coefficient. The cosine model is applied to the study of dielectric spectroscopy. The particle mobility and the complex permittivity of a dielectric material are calculated by numerical solutions for rotational velocity and orientational auto-correction functions, respectively. The main features of the experimental observables are determined analytically and compared to the corresponding numerical results. The applicability of the plane rotator model to dielectric spectroscopy is also discussed.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 10 Jul 2018 14:59
Last Modified: 24 Jul 2018 13:29

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