Electromechanical effects in liquid crystals

A. JákliLiquid Crystal Institute, Kent State University, Kent,

OH 44242

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Crystals of a solid

organic compound

Nematic liquid

crystal phase looks like milk

Isotropic liquid

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Crystals of a solid

organic compound

Smectic liquid

crystal gooey material

Isotropic liquid

Liquid crystals

1850:W. Heintz, 1888: Reinitzer, O. Lehmann

isotropic nematic smectic crystal

Flat panel displays: TN-LCD (use nematics)

Thermotropic Liquid crystals

I. Rod-shape molecules (calamitics)

SmAorthogonal

SmCtilted

(synclinic)

SmCAtilted

(anticlinic)

Smectic sub-phases with fluid layers(2D fluid)

II. Disc-shape molecules

nematic columnar smectic

Chiral liquid crystals from chiral molecules

Cholesteric (N*)(thermometer, etc)CN*

Transfer of molecularchirality to mesoscopic level

helical structure

Tilt + molecular chirality polarityR.B. Meyer, 1974

Smectic C*

Tokyo Inst. Tech. [Niori et al., J. Mater. Chem., 6, 1231 (1996)]

Polarity + tilt layer chirality

III. Bent-shape (“banana”) molecules

Lyotropic liquid crystals

Biology: cell membranes, DNA, cholesterol, etc

Right-handed B-DNA(Watson and Crick, 1953)

Left-handed Z-DNA(Wang and Rich, 1979)

bacteriofag fdl: 880 nm; D: 7 nm; ξ: 2.2 µm

In aqueous solutions they form cholesteric and smectic phases

Liquid crystal forms of Biopolymers

Spider fiber have liquid crystal structure during formation flow alignment decrease spinning energy

By weight stronger than steel and tougher than Kevlar: 1.1GPa…(2’’ thick silk would withstand a full-size jet)

F. Vollrath, D.P. Knight, Nature, 410, 541 (2001); D.P. Knight, F. Vollrath, Proc. R. Soc. Lond. B, 266, 519 (1999)

Stages of the fiber extrusion. (a) The thick cuticle of the funnel (350mm), (b) The thinner inside duct, that allows surfactants and lubricants into the lumen (40mm); (c) valve (300mm); spigot (190mm)

Piezoelectricity (No inversion symmetry)

Curie brothers, 1880Direct effect:Direct effect:

• Electric polarization produced by mechanical stress

Converse effect:•Mechanical strain due to electric fields

i oi ijk jkjk

P P d T= + ∑

jk ojk ijk ii

S S d E= + ∑

λ=1/2(i+j)δij+[9-(i+j)](1-δij)

Conventions:

Stress: Tij Tλ

Strain: Sij Sλ

11 1; 22 2; 33 3; 23=32 4; 13=31 5; 12=21 6

Polar axis: 3

A.) Linear effect

Crystals, ceramics, polymers

Ferroelectric (e.g. Rochelle salt):

Non-polar (e.g. quartz)

A3+B3- (B3- at vertex)

Piezoelectric-type couplings in liquid crystals

No elastic restoring force in N*, within smectic layers and along columns.

Steady energy conversion in columnars, elastomers, glasses

N/Ad3,11; d3,22; d3,33, d1,13; d2,23; d1,23; d2,13; d3,12

d3,33; d3,11=d3,22d3,33; d3,11; d3,22

d3,11; d3,22; d3,33, d1,13; d2,23; d1,23; d2,13; d3,12

D6hC2

C∞νC∞C2

CylinderChiral cylinder

Bowl shapeChiral bowlTilted bowl

Colh; H1, H2Col*tilt

PhP*hPtilt

N/Od3,11; d3,22; d3,33, d1,13; d2,23; d1,23; d2,13; d3,12d3,11; d3,22; d3,33, d1,13; d2,23; d1,23; d2,13; d3,12

all di,jk

C2hC2C2C1

Cylinder Chiral cylinder

Bent shapeBent shape

SmCSmC*SmCPSmCG

N/Od1,23 = - d2,13

d3,11; d3,22; d3,33, d1,13; d2,23

D∞hD∞C2ν

CylinderChiral cylinder

Bent shape

N, SmA, LαN*, SmA*

SmAP,

Non-zero piezoelectric constantsSymmetryMolecular shape

Phase

Experimentsd~400pC/N

Meyer et al., 1997

Cholesteric elastomers

Shear-induced SmC* structure

TheoryTerentjev, Warner

1999

SmC*

A. Goldstone mode (∝sinφ) backflow: shear mode

B .Electroclinic mode (∝cosφ) piezoelectric-type: d33

( ) oE c E Pθ θ= + ⋅ ⋅ cP

=∂∂θ

331 sin2 o

Pd P∂ θ∂θ

= ⋅ ⋅ ⋅

Layer thickness varies, but volume is constant film thickness changesVibration normal to substrates

2 1/ 1ˆ2

E Pγ γσ += ×

Viscous stress:

(Jákli, Saupe, 1993)

E

x

y

z

homeotropic vertical bookshelf tilted bookshelf

Acting forces

Shapes of free volume elements

Piezoelectricity of ferroelectric SmC*

In some directions electric fields induce flows, in others induce elastic deformation

with the frequency of the fields.

Fluid SmC*

frequency (kHz)

displacement(nm)

10

20

1 2 3

Y

X

normal to plates

along plates

Vibration of SmC* films between glasses

Polymeric SmC*

33 ~ 500 /d pC N

Resonance frequencies determined by the bending modes of the cover plates.

Note:1mg FLC makes 10g cover glass

to move by 10nm at 1kHz!This corresponds to 106W/kg,

i.e. 104 times larger specific power than of strongest bio muscles

(Jákli, Saupe,Liq. Cryst., 1991)

Free-standing SmC* filmsYablonski et al, 1999

Effect based on backflow

electro-clinic mode

SmC* elastomersKremer et al., 1999

O

O

OO

OO

O

O

OO

CnH2n+1

OO

CnH2n+1

OO CnH2n+1

O

OCnH2n+1

OO

H2n+1Cn

OO

H2n+1Cn

OO

H2n+1Cn

O

OCnH2n+1

Linear electromechanical effects in ferroelectric columnar liquid crystals

AJ et al. Liq. Cryst.(1998)

Audio application

Bio - piezoelectricity

FlexoelectricityR.B. Meyer, 1969

This does not require lack of inversion symmetry

Possible role in cell membranes

Freestanding fibers (in air)calamitic smectics form films, bananas form fibers

0.1mm

Shape: cylindrical cross section with 2-10 micrometers (similar to spider silk)

0.1mm±100V

Electric field effectsThick bridge Single fiber

Push-pull Transversal vibration

V=500V@1mm; D=1.5μm

a b

(a): Proposed structure of banana fibers (ΔP=-ρ) (b): Myelinated nerve in the frog retina.

(insulating myelin sheath surround conducting axon)

PROPOSED STRUCTURE

Perspectives

2 7max ~ 10 5 10 ~ 0.5sP E MPa−⋅ ⋅ ⋅

This is similar to the bio muscle cells.

Elastic modulus is low liquid crystal – polymer compositesare needed.

FLC Elastomer electrostrictor: ~0.1MPaFLC ‘banana’ systems:

Power per weight of FLC-s are orders of magnitude higherthan of bio-muscles

They have high polarization: Ps~10-2C/m2

and can stand high fields: E~50MV/m

Bio muscle cellsSimilar structure (sarcomeres have cylindrical shape,

~10 micron diameter, 1 cm length)

O

O

N+O O

O

P

O-

O

O

H

O

O

O O

OH

HO OH

OH

HOHO OH

Glycolipid

Phospholipid +oleic acid-based magnetite (Fe3O4)

Ongoing study:magnetic effect of a model system

H=0 H~100G

Homing pigeons use magnetismMora et al., Nature, 432, 508 (2004)

Mineral magnetites in beaks and head as the navigation aid

Unreasolved puzzle: how the brain receives signals from the magnetite?

Idea: piezoelectricity and flexoelectricity

Nonlinear effects in SmC*

Pumping

Quadratic effect Transient vibration

U>Uk U=0

x~1nm, due to Goldstone mode

film thickness increases by 0.3μm

Due to electroclinic (50kp/A4size)

Electrostriction in FLC elastomers(Lehmann et al, 2001)

S~4% @ 1.5MV/m @ elastic modulus~3MPaElectrostriction coefficient ~104 nm2V-2.

4) LIQUID CRYSTALS & DNAA Proof of the Formation of 2 Types of Liquid Crystal Microphases of Low Molecular Weight DNA. By: Evdokimov, Skuridin, Badaev.In: Dokl Akad Nauk SSSR, 19865) LIQUID CRYSTALS & HUMAN PHOSPHOLIPIDSRole of Hydration in the Gel-to-Liquid Crystal Transition of Phospholipids.By: Kreissler, Lemaire, BothorelIn: Biochim Biophys Acta, 1983 Oct.6) LIQUID CRYSTALS & LOWERING CHOLESTEROLLiquid Crystal Solubilization of Cholesterol: Potential Method for Gallstone Dissolution.By: BogardusIn: Journal of Pharmaceutical Science 1983 Apr.7) LIQUID CRYSTALS & CELL MEMBRANEOscillation of Lipid Bi-Layer Membranes Induced by the Gel-Liquid Crystal Phase Transitions.By: Yagisawa, Naito, Gondaira, Kambara.At: Department of Applied Physics and Chemistry, University of Electro-Communications, Tokyo.In: Biophysical Journal 1993 May.8) IMPROVING LIPOSOMES WITH LIQUID CRYSTALSLiposome Interaction with Cells. Liposomes with a Liquid-Crystal Membrane. By: Margolis, NeifakhIn: Usp Sovrem Biol 1982 Mar-Apr.9) LIQUID CRYSTALS & BIOLOGICAL MEMBRANESPhase Transitions in Biological Membranes and Model Liquid Crystal Systems.By: SeleznevIn: Biofizika 1981 Mar-Apr.10) LIQUID CRYSTALS & HUMAN LIPIDSEvaluation of Certain Structural Models of Pre-Transition Phenomena in Liquid-Crystal Systems.By: Seleznev, MineevIn: Biofizika 1980 Sep-Oct.11) LIQUID CRYSTALS & CHIRALITYAsymmetric Synthesis in Liquid Crystals: Independence of Stereochemistry on Handedness of Liquid Crystals. By: Martin, MartinIn: Journal of American Chemical Society 1977 May.12) LIQUID CRYSTALS & BONE COLLAGENBone Stiffness Explained by the Liquid Crystal Model for the Collagen Fibril.By: HukinsIn: Molecular Biology 1992 Sep-Oct.13) LIQUID CRYSTALS & DNAEnzymatic Cleavage of Superhelical DNA in a Liquid Crystal State. By: Salianov, Palumbo, EvdokimovIn: Molecular Biology 1992 Sep-Oct.14) LIQUID CRYSTALS & CELL MEMBRANEChain-Length Dependence of Lipid Bilayer Properties Near the Liquid Crystal-to-Gel Phase Transition... By: Morrow, Whitehead, LuAt: Department of Physics, Memorial University of Newfoundland, St. John's, Canada.In: Biophysical Journal 1992 Jul.15) LIQUID CRYSTALS & PLANT CELLS