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Electrohydrodynamic instability in nematic liquid (Korea_YN Univ...Electrohydrodyanmics in Liquid Crystals Applications •Synthesis of •liquid crystal materials •Controlling alignment

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  • 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