Electrohydrodynamic instability in nematic liquid crystals

(액정의 전기유체역학적 불안성정)

Prof. Jong-Hoon, Huh, 許 宗焄 （허 종훈）

Fac. of Computer Science and Systems Engineering,

Kyushu Institute of Technology, Fukuoka, Japan

（九州工業大学・情報工学研究院）

物質の状態

Gas

Solid

Plasma

Liquid

Dep

osi

tion

Su

bli

mati

on

En

thalp

y o

f sy

stem

H = U + PV

固体

液体

Liquid Crystal

液晶

柔らかい結晶

固体と液体の間では・・・以下の可能性は？

固体 液体

温度

配列

秩序

Positional order

配向

秩序

Orientational order

固体

液晶の出現

ネマティック液晶

温度

配向

秩序

配列

秩序

液体

温度転移型の液晶（Thermotropic LCs）

濃度転移型の液晶もある

Hydrophilic (親水性)

Hydrophobic (疎水性)

濃度増加

Qt. of water

Solid Gel Liquid Crystal Isotropic Liquid

Tk :krafft point (in soap industry)

TNI :clearing point Tc :Gel-LC transition point

ライオトロピック液晶(Lyotropic LCs)

温度転移型液晶に戻って・・・

温度 Tm Tc

固体 液体

液晶

Tm TSN* TN*N Tc

スメチック コレステリック

SC SA

ネマティック

SA1, SA2 ・・・

Cholesteric LC タイプのコガネムシ

左円偏光板下での撮影 右円偏光板下での撮影

この虫のラセン構造は左ラセン！

液晶の電気光学的性質

明 暗

Applications in Liquid Crystals

•Main applications :Formation of optical image by external fields

•New fields :Mechanical deformation, ???

orientational order

electric

field

magnetic

field heat

light

mechanical

stress

chemical

stimulus

compressibility

conductivity

electric susceptibility

magnetic susceptibility

refractive index

elastic modulus

viscosity

responsivity: result of coupling via orientational order

many possibilities to explore!

History of liquid crystals (1850-1888) Precursory discovery of liquid crystals

R. Virchow, C. Mettenheimer, G. Valentin, O. Lehmann, P. Planer, W. Lobisch, B. Raymann, W. Heintz

: Polarizing effects in biological matters (i.e., nonsolid matters)

1888 F. Reinitzer（Austrian botanist and chemist）: discovered a strange behavior in botanical cholesterol

（chiral nematic LC） “soft crystals”

1889-1910 O. Lehmann : Primary theory for liquid crystals, 1889 “flowing crystals”

1922 G. Freidel : Classification of liquid crystals（nematic, smectic, cholesteric）

1922-1940 C. Oseen, F. C. Frank : Viscoelastic theory for liquid crystals

1960 W. Maier, A. Saupe : Molecular theory for liquid crystals

1963 R. Williams（RCA Lab,US）: Discovery of electro-optical effect in Liquid crystals Electrohydrodynamics

1968 G. Heilmeier, J. Fergason（ RCA Lab, US ）: Trial production of LCD（DS-type, GH-type）

1969 H. Kelker : succeeded in synthesizing a nematic phase at room temperature(MBBA)

1971 M. Scbadt & W. Helfrich（Swiss）: TN-type LCD

1973 DS-type desktop calculator（Sharp）

1980 Trial production of TFT-LCD（UK）

1982 Commercial viability of B&W LCD-TV（Seiko, Casio）

1984 Color LCD-TV（Seiko）

1991 P. G. de Gennes(France): The Nobel Prize in Physics

2007 LCD TV surpassed CRT units in worldwide sales

EL-805

Electrohydrodyanmics in Liquid Crystals

●Applications

•Synthesis of liquid crystal materials

•Controlling alignment of molecules

•Electro-optical effects

•Thermo-optical effects

Optical device ・Polarization prism

・Welding mask

・Lamella-light-guiding device

・Focus-variable lens

・

Measurement/sensor ・IC-nondestructive test

・Ultrasound detector

・Thermo-sensing

・Infrared-light detector

・

Display ・Home electric appliances such as TV, PC

・medical instrumentation system

・Transportation system

・Electric measurement system

•Driving systems

•Measurements and Evaluation

•Electro-hydro effects

•Electro-mechanical effects

●Pure physics on EHC in LCs

Dissipative structure,

Amplitude Equations,

Phase dynamics, …

＋

V

＋

＋

－

－

－

－

－

－

－

－

Ez

n

－

V

＋

＋

＋

＋

－

－

－

－

－

－

－

－

－

－

－

－

－

－

－

－

Ex

ｘ

E

＋

＋

Top-view patterns

Lens effect

by Carr-Helfrich

mechanism

Electrohydrodyanmics in Liquid Crystals

Far from equilibrium

● Non-linear dissipative system

Variety of nature

Vari

ety

Degree far from equilibrium

・Soliton

・Spatiotemporal chaos

・Chaos & Fractal

・Turing pattern

・Limit cycle

・Relaxation

phenomena

（NoneqEq） ・World of

death

Brown motion

(macroscopic eq.)

Equilibrium sys. T

T+DT DT<Tc

T

T+DT DT=0

Linear nonequilibrium sys.

Conduction Homogeneous

Into uniformity

T

T+DT DT> DTc

Nonlinear nonequilibrium sys.

Convection

Into nonuniformity

NNES induce

patterns or

rhythm !

Far from equilibrium

● Non-linear dissipative system

・ Equilibrium system (microscopic structure)

・Phase transition

・Statical stability

・Dissipative system

(macroscopic structure)

・Bifurcation

・Dynamical stability

Mechanism from non-structure to structure

Crystal LC Isotropic

Ferromagnet Paramagnet

Temp

RBC：thermal conduction steady rolls

oscillation・・・turbulence

EHC：electric conductionsteady rolls？ DSM

T, V ・Phases

・Minimization of free energy

(double minimum potential)

・Patterns (spatial and/or periodic rhythm)

= Self-organization

= Dissipative system

・What is the fundamental principle ?

Thermal equilibrium system Nonequilibrium dissipative system

Ex.

Far from equilibrium

● Non-linear dissipative system

・Landau’s 2nd order transition for equilibrium system

2 4

0

1 1

2 4F F A C 　

2

2

( ), 0 ( )

0,

(

0

)

0

c

c

ccA a T

A a T T C

F F

T T

TC C

TT

　

　

　

　　　

　

e.g., para, isotropic

e.g., ferro, nematic

F-F0

T>Tc T=Tc

T<Tc

0

0

para, isotropic

nerro, nematic

-M M

Consider order parameter in general case

near Tc

We can average of ;

( )

0

0

cF T T T

unstable

stable

　:

　： 　

　： 　　

In the case of

Nonequilibrium

system

？

What is the

fundamental

principle ?

Electrohydrodynamics

● EHC vs RBC

>Vc

＋

V

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－

－

－

－

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Ez

n

－

V

＋

＋

＋

＋

－

－

－

－

－

－

－

－

－

－

－

－

－

－

－

－

Ex

E

＋

＋

Electrohydrodynamic convection(EHC) Reyleigh-Benard convection (RBC)

T

T+DT DT> DTc

flow

velocity

buoyancy

thermal distribution

Temperance

(DT)

angle distribution of the director n

inner

electric

field (Ex) external

electric

field (Ez)

spatial

charge

flow

velocity

Coulomb force

Electrohydrodynamics

● Carr-Helfrich instability for anisotropic fluids

With coupling q and y due to application of E (in the case of AC);

c 0osMH

qE tq y

2

0

2 2( ) 0cos cosM M

qEE t E ty y

Assuming y independent of t (if, d>>) and

put ; cos sinq A t B t

( / )sin ( / )cos 0HA B t B A t y

2 2

2 2

2 2

( 1)

( 1)

H M

H M

EA

EB

y

y

2 2( ) (cos sin )

( 1)

H MEq t t t

y

(i) for conductive regime ( c );

＋

V

＋

＋ －

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－

E

－

V

＋

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＋ －

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Ex ＋

Jx

vz

n

Et

＋

V

＋

＋ －

－

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－

－

－

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V

＋

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－ －

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－

Electrohydrodynamics

● Carr-Helfrich instability for anisotropic fluids

We can revised the critical voltage (not simplest case) (i) for conductive regime (c);

)1(

)1()(

222

222

02

VVc : relaxation

time of charge

0

a

//

1

2//

//

2 11

: Helfrich parameter //////

2

)//(

95)(

dVc

(ii) for dieletric regime (c);

From the fundamental equations, we obtain a space charge distribution

and a critical field for instability;

d

x

d

Ex m

ael

sin

4)(

//

a

cc

KVdE

)(

4)(

2

1//33

322

V

c

( )cV

Electrohydrodynamics

Frequency [Hz]

Voltage

[V] Prewavy mode

Dielectric mode

Inertia mode

Williams

domains

Isotropic (injection) mode

Isotropic (electrolytic) mode

What are their

mechanisms ?

How to Observe Electrohydrodynamic Patterns

Normal Rolls Abnormal Rolls

Huh, PRE (1998)

k k

(C // k) (C // k)

How to Observe Electrohydrodynamic Patterns

n0

Williams

Domain

Flexoelectric

Domain (n0 ┴ k)

P. Tadapatri, Soft Matter (2012)

Prewavy

Huh, PRE (2002)

n0

Carr-Helfrich instability (n // k)

k

k

How to Observe Electrohydrodynamic Patterns and How to Understand Them as Experimentalist

●光学測定

► Focus（実像２，虚像１） ► 偏光板（Cross-Polarizers)‐director n

●物性測定

► 誘電率，導電率（Anisotropy D, D） ●基本測定値

► 閾値の周波数依存性

► 特性周波数（導電－誘電領域） ●その他

► 配向

► セル厚さ（d）とPattern特性長の関係

Williams domain

Response of Dynamical Dissipative System (EHC)

to External Noise

Patterns or Rhythms

(Dissipative structures)

◆ What happens in external noise ?

・Threshold ?

・Structures ?

・Noise can make order ?

・Stochastic Resonance

(neural networks，electric circuits)

V Noise effects on nonlinear dissipative systems

chaos cosmos

uniformity Patterns,

rhythms

・Noise-induced phase transitions

・Noise-induced pattern formations

noise, fluctuation

Response of Dynamical Dissipative System (EHC)

to External Noise

If the external field is

deterministic, EHC occurs.

)1(

)1()(

222

222

02

VVc

If an additional stochastic field is applied to the EHC,

what happens?

+

Consequently, a fluctuating

sinusoidal field is applied to

the system.

V

c

What

change ?

Response of Dynamical Dissipative System (EHC)

to External Noise

●Expanded Carr-Helfrich mechanism

By adding an electric noise into the EHC system, we obtain

charge distribution and motion of the director ;

cos( )

[ ] ( ) 0( )H MEq

q ttt

t

y

2 2

0 { cos }[ ]( ) [ ]co ) 0(sM M

qE tE Ett ty y

( )t

2

02

2

2( 1( )

) 2

H M tE

E

y

y

From the instability condition ( ) ,

We obtain a critical field;

0 exp( ); 0st sy y 　

2 2 2 2 2 22 0 0

2 2 2

2

2

(1 (1 ) (1 )

2 (1 ) (1 )

)Mc

H H

E tEE

2 2 2

0c c NV V bV

Response of Dynamical Dissipative System (EHC)

to External Noise

●Expanded Carr-Helfrich mechanism

0

50

100

150

200

0 50 100 150 200 250

200kHz

50kHz

20kHz

10kHz

5kHz

2kHz

1kHz

500Hz

200Hz

VW

D

2 [

V2]

VN

2 [V

2]

101

102

103

104

105

106

107

102

103

104

105

f c* [

Hz]

fcd

[Hz]

Y = M0*XM1

0.08031M0

1.3908M10.99818R

fc*= hfcd

( = 1.4, h = 0.1)

The noise with fc > fc* plays a role in stabilization effects for the onset of EHC (i.e., an

upward threshold-shift), whereas the noise with fc < fc* plays a role in destabilization effects

(i.e., a downward threshold-shift). The noise with fc = fc* gives rise to no threshold shift (i.e.,

neutral to the onset of EHC).

fc*

JPSJの2014年の注目論文！

Response of Dynamical Dissipative System (EHC)

to External Noise

Topics of Current Interest

◆ Oscillation of candle flame

・What makes in-phase and antiphase Synchronization?

・Noise light intensity enhance or damage the Calvin system ?

◆ Photosynthesis in fluctuating light intensity

500

1000

1500

2000

2500

0 4000 8000 12000 16000

CO 2 [ppm]

t [s]

明暗 暗明 明