Q-tensor model for electrokinetics in nematic liquid crystals

Abstract

We use a variational principle to derive a mathematical model for a nematic electrolyte in which the liquid crystalline component is described in terms of a second-rank order parameter tensor. The model extends the previously developed director-based theory and accounts for presence of disclinations and possible biaxiality. We verify the model by considering a simple but illustrative example of liquid crystal-enabled electro-osmotic flow around a stationary dielectric spherical particle placed at the center of a large cylindrical container filled with a nematic electrolyte. Assuming homeotropic anchoring of the nematic on the surface of the particle and uniform distribution of the director on the surface of the container, we consider two configurations with a disclination equatorial ring and with a hyperbolic hedgehog, respectively. The computed electro-osmotic flows show a strong dependence on the director configurations and on the anisotropies of dielectric permittivity and electric conductivity of the nematic, characteristic of liquid crystal-enabled electrokinetics. Further, the simulations demonstrate space charge separation around the dielectric sphere, even in the case of isotropic permittivity and conductivity. This is in agreement with the induced-charge electro-osmotic effect that occurs in an isotropic electrolyte when an applied field acts on the ionic charge it induces near a polarizable surface.

Optical manipulation and defect creation in a liquid crystal on a photoresponsive surface

“…The Fe:LN layer was covered with a layer of LC with a height of h = 30 µm. The physical properties of the LC were modeled with a Q-tensor approach [26][27][28][29], using the dielectric constants and the elastic constant measured in MLC-2087.…”

“…where was Kronecker's delta ( 1, when ; otherwise 0). The total energy per unit volume E of the LC was described by the Landau-de Gennes energy ( , ∇ ) and electric potential [28]:…”

Electrokinetic effects in nematic suspensions: Single-particle electro-osmosis and interparticle interactions

“…In particular, we examine a possible resolution of the discrepancy between the flows observed experimentally in a thin film geometry [13], and the results of the axisymmetric numerical analysis of Ref. [24]. Finally, Sec.…”

“…Either some ad-hoc regularization scheme is introduced on the director representation (as we do in Sec. II B) (still disallowing half degree singularities), or the mesoscale tensor order parameter description is used in which the defect region must be explicitly resolved (at a significant computational cost [24]), and with uncertainty about the structure of the phenomenological gradient terms in the free energy, including boundedness issues [19]. To a significant degree, this is one of the central objectives of this manuscript:…”

“…To extend our earlier calculations in the tensor order parameter representation for a particlehedgehog configuration in three dimensions [24], although in an axisymmetric setup, in order to examine the effects of dimensionality and liquid crystal anchoring on charge separation and hydrodynamic flow in configurations that correspond to recent experiments [1,13].…”