Anisotropic and isotropic electroconvection Collaborators: L.Kramer, W.Pesch (Univ. Bayreuth/Germany and N.Eber (Inst. Solid State Phys./Hungary) OR (low f) NR (high f) I. (anis.)III. (isotr.)II. (interm.) ++ x y H planarhomeotropic

ELECTROHYDRODYNAMICS OF NEMATICS - free energy density - balance of torques - equation of motion - incompressibility - equation of electrostatics -charge conservation STANDARDSTANDARD MODELMODEL (SM)

Material parameters: Boundary conditions: planar or homeotropic Relevant: alignment + sign of  a and  a  8 combinations I.planar,  a 0 anisotropic II.homeotropic,  a 0 intermediate III.homeotropic,  a > 0,  a < 0 isotropic IV. planar,  a < 0,  a < 0 non-standard SM

I. planar,  a 0 anisotropic MBBA: Ginzburg-Landau description works

At threshold, increasing f ( planar,  a > 0,  a < 0 ): ORNR TW (non-stand.) DR n

II. homeotropic,  a 0

NR OR H drives between semi-isotropic and anisotropic - soft patterning mode - direct transition to STC - AR-s - chevron formation - defect glide - 2 LP-s

Homeotropic alignment (standard, semi-isotropic) (A.Rossberg, L.Kramer) theor.exp. OR NR

III. Homeotropic,  a > 0,  a < 0 ( truly isotropic) Direct transition to isotropic EC

Direct transition to EC -> SM

nonlinear regime: hard squares : exp. theo. f At onset: Swift-Hohenberg eq. (W.Pesch, L.Kramer, B.Dressel) soft squares not reproduced

IV. planar,  a < 0,  a < 0: no standard pattern (conductive)

- PR or oblique - n z = 0, no shadowgraph - n y (?) oscillates - U c ~ d, f - q c is d indep. Experimental: Dielectric mode! (LK)

I and II- conductive III and IV - dielectric

1. Dielectric mode for MBBA (planar,  a 0) 2. Dielectric mode for MBBA (planar,  a < 0,  a < 0) - no pattern Flexoelectricity

Effect on the roll angle, only for d.c. (only in conductive)

3. Dielectric mode for MBBA (planar,  a < 0,  a < 0) + flexoelectricity finite threshold! obliqueness! e 1 - e 3 = 1.34 e 1 + e 3 = -7.84

4. Dielectric mode for MBBA (planar,  a < 0,  a < 0) + flexoelectricity e 1 - e 3 = 2.68 e 1 + e 3 = (A.Krekhov, W.Pesch)

- dielectric mode at low f - SM + flexoelectricity - why is DM more sensitive to flexo, than CM? planar,  a < 0,  a < 0: no standard pattern (conductive)