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
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 ・・・
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
+
+
-
-
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-
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-
-
-
Ez
n
-
V
+
+
+
+
-
-
-
-
-
-
-
-
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-
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-
-
-
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
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Ez
n
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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 );
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E
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Ex +
Jx
vz
n
Et
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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
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102
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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