Nematic Tensor Research Articles

Viscoelastic theory for nematic polymer interfaces

Full Paper: A macroscopic theory for the dynamics of compressible nematic polymer-viscous fluid interfaces is developed from first principles. The theory is used to define and characterize the basic interfacial viscoelastic material properties of the ordered interfaces. The theory is based on a decomposition of the kinematic fields and nematic tensor order parameter that takes into account the symmetry breaking of the interface. The interfacial rate of entropy production used to identify the interfacial viscoelastic modes is given in terms of surface rate of deformation tensor and the surface Jaumann derivative of the tangential component nematic tensor order parameter. The derived surface viscous stress tensor is asymmetric and thus describes surface flow-induced changes in the tensor order parameter. Consistency with the Boussinesq surface fluid appropriate for Newtonian interfaces is established. The interfacial material functions are identified as the dynamic surface tension, the interfacial dilational viscosities, and the interfacial shear viscosities. The interfacial material functions depend on the surface tensor order parameter and as a consequence anisotropy is their characteristic feature. Two characteristic interfacial tensions and two dilational viscosities are predicted depending on the director orientation. In addition six interfacial shear viscosities arise as the directors sample the velocity, velocity gradient, and vorticity directions. Finally the theory provides for the necessary theoretical tools needed to describe the interfacial dynamics of nematic polymer interfaces, such as capillary instabilities, Marangoni flows, and wetting phenomena.

Tension gradients and Marangoni flows in nematic interfaces.

This brief report (i) presents equations that govern the balance of tangential forces in interfaces between isotropic viscous fluids and nematic liquid crystals, and (ii) establishes the physical origin of nematic Marangoni flows. It is shown that surface gradients in the orientation dependent surface free energy gives rise to tangential nematic Marangoni forces. Tangential nematic Marangoni forces are caused by surface gradients of the nematic tensor order parameter, and the kinetic coefficient characterizing this interfacial phenomenon is proportional to nematic elastic storage. Expressions of the Marangoni forces using a classical constitutive equation for the surface free energy are given for general and uniaxial nematic ordering states. Nematic Marangoni flows or nematocapillarity augments the class of Marangoni flows present in electrocapillarity, diffusocapillarity, and thermocapillarity.

Symmetry rules and temperature-induced anchoring transitions

A sandwich cell made of two flat glass substrates covered with obliquely evaporated SiO x and filled with a common thermotropic nematic liquid crystal is considered. The two glasses are assembled with their evaporation directions antiparallel to each other in order to provide a uniformly pretilted nematic layer, without any local distortion. By means of a Landau-de Gennes approach, based on the general symmetry properties of the flat glass surface, including the anisotropy induced by the SiO x , and of the nematic tensor order parameter, a temperature variation of the director azimuthal and tilt angle in the nematic phase is predicted. Observations via polarizing microscopy were performed and the fits, made according to the proposed model, compare well with the experimental data presented here.

Flexoelectric polarization and second order elasticity for nematic liquid crystals

The flexoelectric properties of nematic liquid crystals are analysed. It is shown that in the frame of the usual elasticity two coefficients characterize completely the flexoelectric properties of the liquid crystal. These coefficients, in the limit of small scalar order parameter, i.e. near the clearing point, are approximately equal. More precisely they have the same linear term in the scalar order parameter, and differ for terms quadratic in this parameter. Their difference behaves, hence, as the usual nematic liquid crystal elastic constants, whereas their sum depends on the temperature, like the mixed splay-bend elastic constant. It is shown furthermore that in the frame of a second order elastic theory in the flexoelectric polarization there are no terms from the second order spatial derivatives of the nematic director, or the nematic tensor order parameter. Consequently also in the frame of the second order elasticity the flexoelectric polarization is given by the usual expression. This conclusion is important in connection with the surface polarization recently discovered in pretilted nematic liquid crystal samples.

On the tensor vs. the vector character of the director field in a nematic liquid crystal

The description of the director field of the nematic phase of a liquid crystalline material is investigated. It is shown that utilizing a tensor field to represent the director has exactly the same physical consequences as the more commonly used vector field. Furthermore it is proven that a nematic tensor field can always be replaced by the square of a vector field for which the Frank-Oseen expression holds.