title: Tensorial conservation law for nematic polymers.
abstract: We derive the "conservation law" for nematic polymers in tensorial form valid for quadrupolar orientational order, in contradistinction to the conservation law in the case of polar orientational order. Due to microscopic differences in the coupling between the orientational field deformations and the density variations for polar and quadrupolar order, we find that the respective order parameters satisfy fundamentally distinct constraints. Being necessarily scalar in its form, the tensorial conservation law is obtained straightforwardly from the gradients of the polymer nematic tensor field and connects the spatial variation of this tensor field with density variations. We analyze the differences between the polar and the tensorial forms of the conservation law, present some explicit orientational fields that satisfy the tensorial constraint, and discuss the role of singular "hairpins," which do not affect the local quadrupolar order of polymer nematics, but nevertheless influence its gradients.
authors: Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia.
authors: Daniel
authors: D
authors: Svenšek
authors: Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA.
authors: Gregory M
authors: GM
authors: Grason
authors: Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia and Department of Theoretical Physics, J. Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia and Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA.
authors: Rudolf
authors: R
authors: Podgornik