Flexoeffect in Smectic C liquid crystals

1
Flexoeffect in Smectic C liquid crystals
M.A.Osipov Department of
Mathematics, University of Strathclyde, 26
Richmond Str. Glasgow

• 1. Various contributions to the flexoelectric
  polarization
• n smectics,
• Flexoelectric contribution to the spontaneous
  polarization
• in chiral smectics and its order of
  magnitude,
• 3. Discrete flexoelectric effect in the
  intermediate phases.

2
General Phenomenological Theory
P.G. de Gennes, J.Prost, The Physics of Liquid
Crystals, p. I.Dahl, S.T.Lagerwall,
Ferroelectrics, 58, 215 (1984)
Incompressible layers
Layer bending director
gradients
c
Only gradients along z-axis
3
Tilt Order Parameter approach
Flexoelectric polarization
----------
--------------
--------------
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Only 4 flexocoefficiients
4
Major flexoelectric contributions
Linear terms in
Tilted membranes and Langmuir-Blodgett films
5
Conventional flexoelectric effect in Smectics C
R.Meyer 1977, S.Pikin and V.Imdenbom, 1978
n
Flexoelectric polarisation in the helical
structure
P
n
P
Spontaneous polarization
z
Order parameter
6
Measurements of the flexocoefficients
Total polarization
Ostrovski et.al. 1978 Ostrovski, Pikin,
Chigrinov, 1984 Durand, Martinot-Lagarde, 1980
Beresnev, Baikalov, Blinov, 1984 Chigrinov
et.al., 1985 Kuzchinski, Hoffman, PRE, 2005
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Measurements of flexocoefficients. W.Kuczynski,
J.Hoffman, PRE,

72, 041701 (2005)
Tilt
Tilt
Flexoelectric contribution
8
Sign inversion of the flexoelectric coefficiient
k
Biaxial (secondary) order parmeter of the Sm C
Phase
a
n
c
Perfect nematic order
b
Biaxial molecules
Flexoelectric polarization
Biaxiality induced by tilt
May possess opposite signs
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Discrete flexoelectric effect
Low (polar) symmetry of the layer i
n
Two-fold symmetry axes
Internediate Phase
Sm C Phase
A
c
c
Flexoelectric polarisation in the central
layer due to a difference in director
rientation in the two adjacent layers
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Discrete Flexoelectric Effect. General Theory
-- order parameter tensor
Flexoelectric polarisation
No biaxiality, ?i ? const
Continuous limit
Conventional flexoeffect In Smectics C
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Flexoelectric Origin of the
Nonplanar Structure of
Intermediate Phases
Total Polarisation
Spontaneous Polarisation
Discrete Flexoelectric Polarization
Electrostatic Energy
Coupling term
Creates the torque and destabilises the planar
structure
12

• Coworkers
• Dr. A.V.Emelyanenko
• Acknowledgements
• L.M.Blinov and H.Kuchinski for
• Valuable discussions
• EPSRC for funding.