Electrohydrodynamic instability in nematic liquid crystals
( )
Prof. Jong-Hoon, Huh,
Fac. of Computer Science and Systems Engineering,
Kyushu Institute of Technology, Fukuoka, Japan
Gas
Solid
Plasma
Liquid
Dep
osi
tion
Su
bli
mati
on
En
thalp
y o
f sy
stem
H = U + PV
Liquid Crystal
Positional order
Orientational order
Thermotropic LCs
Hydrophilic ()
Hydrophobic ()
Qt. of water
Solid Gel Liquid Crystal Isotropic Liquid
Tk :krafft point (in soap industry)
TNI :clearing point Tc :Gel-LC transition point
(Lyotropic LCs)
Tm Tc
Tm TSN* TN*N Tc
SC SA
SA1, SA2
http://upload.wikimedia.org/wikipedia/commons/e/ec/Nematische_Phase_Schlierentextur.jpghttp://upload.wikimedia.org/wikipedia/commons/6/67/Smectic_nematic.jpg
Cholesteric LC
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. ReinitzerAustrian 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 crystalsnematic, 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. WilliamsRCA Lab,US: Discovery of electro-optical effect in Liquid crystals Electrohydrodynamics
1968 G. Heilmeier, J. Fergason RCA Lab, US : Trial production of LCDDS-type, GH-type
1969 H. Kelker : succeeded in synthesizing a nematic phase at room temperature(MBBA)
1971 M. Scbadt & W. HelfrichSwiss: TN-type LCD
1973 DS-type desktop calculatorSharp
1980 Trial production of TFT-LCDUK
1982 Commercial viability of B&W LCD-TVSeiko, Casio
1984 Color LCD-TVSeiko
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
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 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
RBCthermal conduction steady rolls oscillationturbulence
EHCelectric 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
Landaus 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
Electrohydrodynamics
EHC vs RBC
>Vc
V
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 0osMHq
E tq y
2
0
2 2( ) 0cos cosM Mq
EE 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
E
V
Ex
Jx
vz
n
Et
V
V
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
http://www.google.co.jp/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&ved=0ahUKEwjW08HF7IPOAhVFsJQKHSn9ADEQjRwIBw&url=http%3A%2F%2Fpubs.rsc.org%2Fen%2FContent%2FArticleHtml%2F2012%2FSM%2Fc1sm06870a&psig=AFQjCNE1Sl23dc-VQenw9nsh0W9nkBN_vg&ust=1469166122439916
How to Observe Electrohydrodynamic Patterns and How to Understand Them as Experimentalist
Focus Cross-Polarizers)director n Anisotropy D, D dPattern
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 networkselectric 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 th
