Eur. Phys. J. E (2007) 24: 353-365
https://doi.org/10.1140/epje/i2007-10246-8

Regular Article

Polar nano-rods under shear: From equilibrium to chaos

¹ Institut für Theoretische Physik, Sekr. PN 7-1, Technische Universität Berlin, Hardenbergstraße 36, D-10623, Berlin, Germany
² Stranski-Laboratorium für Physikalische und Theoretische Chemie, Sekr. C7, Technische Universität Berlin, Straße des 17. Juni 115, D-10623, Berlin, Germany

^* e-mail: sabine.klapp@fluids.tu-berlin.de

Received: 17 September 2007
Accepted: 21 November 2007
Published online: 21 January 2008

Abstract

The orientational dynamics of rod-like particles with permanent (electric or magnetic) dipole moments in a plane Couette shear flow is investigated using mesoscopic relaxation equations combined with a generalized Landau free energy. The free energy contribution due to the coupling between average alignment and dipole orientation is derived on a microscopic basis. Numerical results of the resulting eight-dimensional dynamical system are presented for the case of longitudinal dipoles and thermodynamic conditions where the equilibrium state is a (polar or non-polar) nematic. Solution diagrams reveal presence of a large variety of periodic, transient chaotic, and chaotic dynamic states of the average alignment and dipole moment, respectively, appearing as a function of Deborah number and tumbling parameter. Compared to rods without dipoles we observe a significant preference of out-of-plane kayaking-tumbling states and, generally, a higher sensitivity to the initial conditions including bistability. We also demonstrate that the average (electric) dipole moment characterizing most of the observed states yields electrodynamic (magnetic) fields of measurable strength.