Liquid Crystals by imran aziz

Embed Size (px)

Citation preview

  • 8/8/2019 Liquid Crystals by imran aziz

    1/90

  • 8/8/2019 Liquid Crystals by imran aziz

    2/90

    ContentsContents

    Properties of liquidProperties of liquid

    crystalscrystals

    Types of liquid crystalsTypes of liquid crystals

    ThermotropicThermotropic

    nematicnematic

    smecticsmectic cholestericcholesteric

    LyotropicLyotropic

    structuresstructures

    applicationapplication

    NIOSOMESNIOSOMES

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    3/90

    Synergistic Effects of Surfactants

    Observed when surfactants having relatively similarstructure or ionic property are mixed

    Resulted in the formation of liquid crystal structures or

    complexes at the interface by intermolecular

    interactions between surfactants

    Examples

    Anionic and nonionic in synthetic latex emulsion

    polymerisation,

    Mixture of a dispersant and a hydrating agent to

    increase dispersion stability in agricultural chemicals

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    4/90

    STATES OF MATTER

    Common states:

    solid

    liquid

    gas

    Matter can exist in

    other states

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    5/90

    LIQUID CRYSTALS

    A state that occurs between a solid & a liquid

    Possess properties characteristics of both liquids

    & crystalline solids

    Also possess properties not found in either

    liquids or solids

    May response to external perturbations & some

    changes colour with temperature

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    6/90

    A crystal is a highly ordered structure which possesseslong-range positional & orientational order

    For many substances these two types of order are

    destroyed simultaneously when the crystal melts to form

    a liquid

    For some substances, these orders are destroyed in

    stages. These are liquid crystals. E.g. Slide 17

    Crystals vs Liquid Crystals

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    7/90

    Liquid crystal can flow like a liquid, due to loss of positional order Liquid crystal is optically birefringent, due to its orientational order

    Transition from crystalline solids to liquid crystals caused by a change of

    temperature gives rise to THERMOTROPIC liquid crystals

    substances that are most likely to form a liquid crystal phase at a certaintemperature are molecules that are ELONGATED & have some degree

    of RIGIDITY. Try slide 29

    Properties of liquid crystals

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    8/90

    Typical chemical structures

    cholesterol ester

    phenyl benzoates

    surfactants such aspolyethylene-oxides, alkali

    soaps, ammonium salts,lecithin

    paraffins

    glycolipids

    cellulose derivatives

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    9/90

    Typical applications

    LCD displays

    dyes (cholesterics)

    advanced materials (Kevlar)

    membranes temperature measurement (by changing colours)

    solvents for GC, NMR, reactions, etc.

    Drug delivery

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    10/90

    Types of liquid crystals

    Thermotropic Phase transition depends on temperature

    Nematic

    Smectic

    Cholesteric

    Lyotropic

    Phase transition depends on temperature &

    concentration

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    11/90

    As temperature increases..

    The first liquid crystal phase is the smecticA, where thereis layer-like arrangement as well as translational and

    rotational motion of the molecules.

    A further increase in temperature leads to the nematic

    phase, where the molecules rapidly diffuse out of the initial

    lattice structure and from the layer-like arrangement as well.

    At the highest temperatures, the material becomes an

    isotropicliquid where the motion of the molecules changes

    yet again.

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    12/90

    Nematic

    Simplest form is anematic liquid crystal

    i.e. long-rangeorientational order

    but no positionalorder

    The preferred directionis known as director

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    13/90

    NematicNematic

    Despite the high degree of orientational order, nematic phaseas a whole is in disorder i.e. NO MACROSCOPIC ORDER

    (orientation within a group is similar but not from one group to

    another)

    Structure of nematic phase can be altered in a number of ways.E.g. electric or magnetic field or treatment of surfaces of the

    sample container

    Thus, possible to have microscopic order & macroscopic order

    Nematic liquid crystals are widely used in electro-optic displaydevices

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    14/90

    Cholesteric

    The first liquid crystal that was observed through a polarising microscope is

    cholesteryl benzoate. Thus, CHOLESTERIC liquid crystal OR chiral nematic liquid

    crystal

    E.g. cholesteryl benzoate: LC @ 147C, isotropic @ 186C

    Cholesteric liquid crystals have great potential uses as

    - sensors

    - Thermometer

    - fashion fabrics that change colour with temperature

    - display devices

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    15/90

    - In CHOLESTERIC phase, there is

    orientational order & no positional order,

    BUT, director is in HELICAL ORDER.

    The structure of cholesteric depends onthe PITCH, the distance over which the

    director makes one complete turn One pitch - several hundred nanometers

    Pitch is affected by:-

    Temperature

    Pressure

    Electric & magnetic fields

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    16/90

    Smectic SMECTIC phase occurs at temperature below

    nematic or cholesteric

    Molecules align themselves approx. parallel & tend

    to arrange in layers

    Not all positional order is destroyed when a

    crystal melts to form a smectic liquid crystal

    Chiral smectic C liquid crystals are useful in LCDS

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    17/90

    LIQUID CRYSTAL POLYMERS

    Can form nematic, cholesteric, smectic

    When liquid crystal polymers solidify, the liquid

    crystal structure freeze in

    This results in materials of high tensile strength

    & in some cases unusual electro-optical

    behaviour

    E.g. Kevlar aramid fibre bullet-proof vest &airplane bodies (aromatic polyamide)

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    18/90

    Examples of phase changes

    Cholesteryl myristate

    solid smectic A71C

    cholesteric isotropic79C 85C

    4, 4-di-heptyloxyazoxybenxene

    solid

    74C 94C 124C

    smectic C nematic isotropic

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    19/90

    Thermotropic vs Lyotropic

    THERMOTROPIC Absence of solvent

    Rigid organic molecules

    Depends on Temperature

    Structures: Smectic

    Nematic

    Cholesteric

    LYOTROPIC In solvent

    Surfactants Depends on Temperature,

    Concentration, salt, alcohol

    Structures: Lamellar

    Hexagonal etc

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    20/90

    Structure formation in surfactant solution

    micelle rodhexagonal

    monolayer

    bilayerReverse micelleFormation of MICROEMULSION

    REVERSE

    HEXAGONAL

    Oil/alcohol

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    21/90

    Effect of temperature and concentration on the

    structure of lyotropic liquid crystals

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    22/90

    SURFACTANT VESICLES

    [A] Phospholipids (e.g. lecithin) + H2O ---->phospholipid vesicles or liposomes

    [B] Liposomes + (long chain) stearylamine ------->

    tve charge liposome (carriers for DNA)

    [C] Liposomes + dicetyl phosphate -----

    - ve charge liposome

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    23/90

    Vesicles

    Bilayers that fold into a 3D structure

    Vesicles form because they get rid of

    the edges of bilayers, protecting the

    hydrophobic chains from the water, but

    they still allow for relatively small

    layers.

    Lipids found in biological membranes

    spontaneously form vesicles insolution.

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    24/90

    Application of Liposomes

    can encapsulate: drugs,

    proteins,

    enzymes

    administered intravenously, orally or intramuscularly

    decrease toxicity

    increase specificity of drug uptake

    enable slow release

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    25/90

    Problems with phospholipids

    phospholipids undergo oxidative

    degradation

    handling & storage must be under nitrogenexpensive

    [email protected][email protected]

    f f

  • 8/8/2019 Liquid Crystals by imran aziz

    26/90

    Formation of liquid crystals using surfactants

    [A] Anionic

    e.g. alkane sulfonates

    [B] Cationic

    e.g. hexadecyl trimethyl ammonium bromide

    [C] Amphoteric

    e.g. alkyl betaines

    Due to toxicity of ionic surfactants, the vesicles are not used for drug delivery

    [D] Non-ionic

    e.g. alcohol ethoxylates R-O-(CH2CH2O) m H m: 2-20, R :

    mixed; alkyl group C8C18

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    27/90

    Non-ionic + cholesterol -> NIOSOMES

    These vesicles prolong the circulation of entrapped

    drug

    Properties depend on

    1. Composition of bilayer

    2. Method of production

    e.g. cholesterol & single alkyl-chain non-ionicsurfactant with a glyceril head group

    Niosomes

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    28/90

  • 8/8/2019 Liquid Crystals by imran aziz

    29/90

    The three states of mater?The three states of mater?

    solid liquid gas

    Which state is a soap bubble in?

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    30/90

    The fourth state of materThe fourth state of mater

    e.g.: ice -> water

    e.g.: cholesteryl benzoate

    heat

    0oC

    heat heat

    145.5oC 178.5oC

    Fredrich Reinitzer, Otto Lehmann, 1888

    The new liquid state showed birefringence!

    Orientational order but no positional order!

    [email protected][email protected]

    Is liquid crystal more like solid ors qu crys a more e so or

  • 8/8/2019 Liquid Crystals by imran aziz

    31/90

    Is liquid crystal more like solid ors qu crys a more e so or liquid?liquid?

    Latent heat: the energy required to cause phase transition.

    H2O

    80 cal/g of ice -> water,

    540 cal/g water -> steam.

    Cholesteryl myristate:

    65 cal/g of solid -> LC, 7 cal/g LC- liquid.

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    32/90

    The structure of LCThe structure of LC

    solid liquidliquid crystal

    Director

    If random, = 57o

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    33/90

    Types of liquid crystalsTypes of liquid crystals

    Discotic

    Chiral nematic

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    34/90

    LC in an electric fieldLC in an electric field

    Orientation of a dipole inan electric field

    LC film in an electric field

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    35/90

    Light & polarizationLight & polarization

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    36/90

    Interaction of light with LCInteraction of light with LC

    Ex Ey

    Ex Ey Ex EyReflected

    beam

    Incoming

    beam

    Refracted beam

    ExEy

    Ex Ey Ex EyReflected

    beam

    Incoming

    beam

    Refracted beam

    Birefringence

    [email protected][email protected]

    LCs under a polarizationLCs under a polarization

  • 8/8/2019 Liquid Crystals by imran aziz

    37/90

    LCs under a polarizationLCs under a polarization

    microcopemicrocope

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    38/90

    Aligning liquid crystalsAligning liquid crystals

    rubbing

    polishing

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    39/90

    Liquid crystal displayLiquid crystal display

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    40/90

    The operation of a pixel in LCDThe operation of a pixel in LCD

    [email protected][email protected]

    O h l d f LC

  • 8/8/2019 Liquid Crystals by imran aziz

    41/90

    Other cool gadgets from LCsOther cool gadgets from LCsThermochromic Ink

    Polymeric LC

    Interactive art using

    iridescent coloringOptoelectronic computers

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    42/90

    Oth li id t l i tOth li id t l i t

  • 8/8/2019 Liquid Crystals by imran aziz

    43/90

    Other liquid crystals in natureOther liquid crystals in nature

    Iridescent color

    [email protected][email protected]

    I t d tiI t d ti

  • 8/8/2019 Liquid Crystals by imran aziz

    44/90

    IntroductionIntroduction

    Liquid crystals are very important in the study of optics,Liquid crystals are very important in the study of optics,chemistry and polymer science. The discovery of the liquidchemistry and polymer science. The discovery of the liquid

    crystal happened over a century and since this time thecrystal happened over a century and since this time the

    phenomena has been applied to many products in ourphenomena has been applied to many products in our

    society. This presentation will cover the properties, differentsociety. This presentation will cover the properties, different

    phases and uses of liquid crystals. It will also give illustrationsphases and uses of liquid crystals. It will also give illustrationsof liquid crystals from the micro perspective.of liquid crystals from the micro perspective.

    [email protected][email protected]

    What are liquid crystals ?

  • 8/8/2019 Liquid Crystals by imran aziz

    45/90

    What are liquid crystals ?Liquid crystals form from organic compounds and is thought of

    as the phase of matter between the solid and liquid state of acrystal.This phenomena was discovered in 1888 by Austrian

    chemist Frederich Reinitzer.

    [email protected][email protected]

    PhPh

  • 8/8/2019 Liquid Crystals by imran aziz

    46/90

    PhasesPhases

    [email protected][email protected]

    http://en.wikipedia.org/wiki/Image:Shilirren_texture.jpg
  • 8/8/2019 Liquid Crystals by imran aziz

    47/90

    Nematic PhaseNematic Phase

    Molecules in this phaseMolecules in this phase

    are long and rod-like inare long and rod-like in

    shape. They are free toshape. They are free to

    move in space.move in space.

    [email protected][email protected]

    Chi l N tiChiral Nematic

    http://en.wikipedia.org/wiki/Image:Shilirren_texture.jpg
  • 8/8/2019 Liquid Crystals by imran aziz

    48/90

    Chiral NematicChiral Nematic

    This phase is composedThis phase is composed

    of nematic molecules inof nematic molecules in

    a helical structure abouta helical structure about

    the layer normal.the layer normal.

    The distance that it takesThe distance that it takes

    for the molecules tofor the molecules to

    complete one turn iscomplete one turn is

    called the pitch.called the pitch.

    = n*p*[email protected][email protected]

    Smectic PhaseSmectic Phase

  • 8/8/2019 Liquid Crystals by imran aziz

    49/90

    Smectic PhaseSmectic Phase

    This phase can beThis phase can bereached at lowerreached at lowertemperatures than thetemperatures than thenematic phase.nematic phase.

    Molecules alignMolecules alignthemselves in layers.themselves in layers.(They are restricted to(They are restricted totheir plane.)their plane.)

    More order and higherMore order and higher

    viscosityviscosity

    [email protected][email protected]

    Columnar PhaseColumnar Phase

  • 8/8/2019 Liquid Crystals by imran aziz

    50/90

    Columnar PhaseColumnar Phase

    Characterized by its stacked columns of molecules.Characterized by its stacked columns of molecules. Discovered in 1977 by ChandrasekharDiscovered in 1977 by Chandrasekhar

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    51/90

    Order ParameterOrder Parameter

    S = S =

    The order parameter in a liquid crystalThe order parameter in a liquid crystal

    range from 0.3 to 0.9range from 0.3 to 0.9

    [email protected][email protected]

    Electric field EffectsElectric field Effects

  • 8/8/2019 Liquid Crystals by imran aziz

    52/90

    Electric field EffectsElectric field Effects

    If an electric field isIf an electric field isapplied to a liquidapplied to a liquid

    crystal the moleculescrystal the molecules

    will align in the samewill align in the same

    direction as the field.direction as the field.

    [email protected][email protected]

    Twisted NematicTwisted Nematic

  • 8/8/2019 Liquid Crystals by imran aziz

    53/90

    Twisted NematicTwisted Nematic

    This is called theThis is called thetwisted nematic liquidtwisted nematic liquid

    crystal and the spacingcrystal and the spacing

    between the planesbetween the planes

    change withchange withtemperature. Thetemperature. The

    spacing is associatedspacing is associated

    with the wavelengths ofwith the wavelengths of

    light.light.

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    54/90

    [email protected][email protected]

    Uses of Liquid CrystalsUses of Liquid Crystals

  • 8/8/2019 Liquid Crystals by imran aziz

    55/90

    Uses of Liquid CrystalsUses of Liquid Crystals

    Flat screen televisionFlat screen televisionWristwatchesWristwatches

    Laptop screensLaptop screens

    Digital clocksDigital clocksThermometersThermometers

    Switchable windowsSwitchable windows

    [email protected][email protected]

    ConclusionConclusion

    http://shopper.howstuffworks.com/products/Hewlett+Packard+f2105+%28Black%2C+Silver%29+21+inch+LCD+Monitor/SF-1/PID-25727430
  • 8/8/2019 Liquid Crystals by imran aziz

    56/90

    We know today that many chemical compounds can existWe know today that many chemical compounds can existin the liquid crystal state, such as cholesteryl benzoate.in the liquid crystal state, such as cholesteryl benzoate.

    Thanks to the scientists that worked so diligently towardThanks to the scientists that worked so diligently towardunderstanding this phenomenon, the world can focus onunderstanding this phenomenon, the world can focus onways to make this product useful in society. Over the lastways to make this product useful in society. Over the lastcentury many applications such as the detection of hotcentury many applications such as the detection of hotpoints in microcircuits, the findings of fractures or tumorspoints in microcircuits, the findings of fractures or tumorsin humans and the conversion of infared images havein humans and the conversion of infared images have

    become accessible due to the understanding of pitch in abecome accessible due to the understanding of pitch in aliquid crystal.liquid crystal.

    [email protected][email protected]

    Liquid Crystal Materials

  • 8/8/2019 Liquid Crystals by imran aziz

    57/90

    y

    CN

    [email protected][email protected]

    Broad Classification

  • 8/8/2019 Liquid Crystals by imran aziz

    58/90

    Lyotropics Thermotropicsamphiphilic molecules, polar and non-polar

    parts form liquid crystal phases over certain

    concentration ranges when mixed with a

    solvent

    molecules consisting of a rigid core and

    flexible tail(s) form liquid crystal phases

    over certain temperature ranges.

    +

    -hydrophilic

    polar head

    hydrophobic

    non-polar tail flexible tail

    rigid [email protected][email protected]

    The LyotropicPhases

  • 8/8/2019 Liquid Crystals by imran aziz

    59/90

    micelle

    reversemicelle

    cross section

    cross [email protected][email protected]

    The ThermotropicLiquid Crystal Molecule

  • 8/8/2019 Liquid Crystals by imran aziz

    60/90

    CN

    Chemists

    View

    Physicists

    EngineersView

    Shape Anisotropy

    Length > Width

    The molecule above (5CB) is ~2 nm 0.5 [email protected][email protected]

    Geometrical Structures of

    M i M l l

  • 8/8/2019 Liquid Crystals by imran aziz

    61/90

    Mesogenic Molecules

    Low Molecular Weight High Molecular Weight

    (polymers)

    ( ) n

    ( )n

    disk-like

    rod-like

    most practical [email protected][email protected]

    The Liquid Crystal Phase

  • 8/8/2019 Liquid Crystals by imran aziz

    62/90

    n

    TemperatureCrystal Nematic LC Isotropic

    [email protected][email protected]

    The Nematic Director n

  • 8/8/2019 Liquid Crystals by imran aziz

    63/90

    Long

    Molecular

    Axis

    H H

    H H

    H H

    H H

    C NO

    C CH

    H

    HH

    C C

    HH

    H

    H

    H

    n

    The local average axis

    of the long molecular axis

    director

    [email protected][email protected]

    Other Liquid Crystal Phases

  • 8/8/2019 Liquid Crystals by imran aziz

    64/90

    n

    Temperature Smectic C Smectic A Nematic

    nz

    n

    [email protected][email protected]

    Chirality

  • 8/8/2019 Liquid Crystals by imran aziz

    65/90

    left-handed right-handed

    mirror images

    non-superimposable

    H-C-C-C-C-C C N

    H H H H H

    H H H H H

    H-C-C-C-C-C C N

    H H HCH3

    H

    H H H

    H

    H

    non-chiral

    chiral (RH)

    The methyl group on the 2nd carbon atom

    on the alkyl chain of the molecules extends

    out of the plane of the paper and the hydro-

    gen atom extends into the plane of the paper.Therefore the 2nd carbon can be thought of

    as a right or left handed coordinate system

    [email protected][email protected]

    O di N ti

    The Chiral Nematic

  • 8/8/2019 Liquid Crystals by imran aziz

    66/90

    CN

    pitc

    P

    CN

    Ordinary Nematic Chiral Nematic

    director

    n

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    67/90

    The Chiral Smectic: TGB

    T i t d G i B d (TGB)

  • 8/8/2019 Liquid Crystals by imran aziz

    68/90

    Twisted Grain Boundary (TGB)

    A twisted grain boundary smectic A phase (frustrated) - TGBA*

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    69/90

    Discotics Liquid Crystals

    n

  • 8/8/2019 Liquid Crystals by imran aziz

    70/90

    Columnar, columns of molecules

    in hexagonal lattice

    Nematic discotic phase

    n

    n

    [email protected][email protected]

    Polymer Liquid Crystals

    Combining the properties of liquid crystals and polymers

  • 8/8/2019 Liquid Crystals by imran aziz

    71/90

    Combining the properties of liquid crystals and polymers

    Main Chain Side Chain

    mesogenic moieties are

    connected head-to-tail

    mesogenic moieties

    attached as side chains

    on the polymer backbone

    rigid

    semi-flexible

    [email protected][email protected]

    Polymer Liquid Crystals

    forming nematic liquid crystal phases

  • 8/8/2019 Liquid Crystals by imran aziz

    72/90

    o g e a c qu d c ys a p ases

    n

    main-chainside-chain

    [email protected][email protected]

    Example of Side-Chain Polymer LCs

  • 8/8/2019 Liquid Crystals by imran aziz

    73/90

    O C-O-(CH2)n-O R2C-O

    O-(-CH2-C-)X-

    R1

    Too slow for display applications (switching times ~ 0.5-1 s Useful for other applications such as: Optical filters Optical memory Alignment layers for low molecular weight LCs Non-linear optic devices (optical computing)

    [email protected][email protected]

    n

    The Order Parameter

    1

  • 8/8/2019 Liquid Crystals by imran aziz

    74/90

    n

    n

    2

    2

    1(cos ) (3 cos 1)

    2

    = = S P

    2

    2

    2

    cos1

    cos3

    cos ( 0 ) 1

    = =

    = =

    o

    d

    dno order

    perfect order

    2

    2

    (cos ) 1

    (cos ) 0

    = =

    = =

    S P

    S P

    perfect crystal

    isotropic [email protected][email protected]

    I t ti b t i di id l l l t d b

    Maier-Saupe Theory - Mean Field Approach

  • 8/8/2019 Liquid Crystals by imran aziz

    75/90

    Interactions between individual molecules are represented by a

    potential of average force

    ( ) ( )2 2cos cosV vP P = < >

    From Statistical Mechanics (Self Consistency)

    ( ) ( ) ( )( )

    ( )( ) ( )

    1

    2 2 2

    02 1

    2 2

    0

    cos exp cos ) cos

    exp cos cos

    < >

    < >=< >

    P vP P d

    P

    vP P d

    {V: minimum} when phase is ordered (-P2(cos ))

    {V: V=0} when phase is disordered ()

    factor for intermolecular strength ( )

    =(kT)-1

    n

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    76/90

    Landau-de Gennes TheoryLandau-de Gennes Theory

    2 3 4 21 1 1 1

  • 8/8/2019 Liquid Crystals by imran aziz

    77/90

    2 3 4 2

    0

    1 1 1 1( ) ( )

    2 3 4 2

    = + + + f f aS bS cS L S GS z

    a= (T-T*), , b, c, T*, L are phenomenological constants

    G is a surface interaction strength

    OrderPara

    meter,S

    Temperature

    Good near NI transition

    surfac

    e

    Predicts order near

    [email protected][email protected]

    Optical Anisotropy: Birefringence

    ordinary ray (no, ordinary index of refraction)

  • 8/8/2019 Liquid Crystals by imran aziz

    78/90

    y y ( o, y )

    extraordinary ray (ne, extraordinary index

    of refraction)

    [email protected][email protected]

    Optical Anisotropy: Birefringenceordinary wave

    on n=

  • 8/8/2019 Liquid Crystals by imran aziz

    79/90

    extraordinary wave

    o

    2 2

    2 2 2

    1 cos sin

    o en n n

    = +

    For propagation along the optic

    axis, both modes are no

    optic

    axis

    [email protected][email protected]

    Birefringence Example: 1/4 Wave Plate

    circular polarizedWhat is minimum d for

  • 8/8/2019 Liquid Crystals by imran aziz

    80/90

    Unpolarized

    linear polarized

    polarizer

    LC: n=0.05d

    liquid crystal 1/4 wave plate ?

    ( )

    1

    4

    1

    41 589

    2,950 2.954 4 0.05

    e o

    e o

    N N

    n d n d

    nmd nm m

    n

    = +

    = += = = =

    Takes greater number of e-waves

    than o-waves to span d, use

    n=0.05

    [email protected][email protected]

    Creating Deformations with aField and Surface - Bend Deformation

  • 8/8/2019 Liquid Crystals by imran aziz

    81/90

    E orB

    [email protected][email protected]

    Creating Deformations with aField and Surface - Splay Deformation

  • 8/8/2019 Liquid Crystals by imran aziz

    82/90

    E orB

    [email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    83/90

    Elastic Constant K22 :Temperature Dependence

    2

  • 8/8/2019 Liquid Crystals by imran aziz

    84/90

    7

    6

    5

    4

    3

    2

    -30 -20 -10 0T-TNI (C)

    K22

    (x10-12N

    ewton)

    P-azoxyphenetole

    P-azoxyanisole(PAA)

    2( )K S T

    [email protected][email protected]

    y

    n

    Effects of an Electric Field

  • 8/8/2019 Liquid Crystals by imran aziz

    85/90

    x

    yE

    n

    sin cos

    oE

    = +=

    n x

    y

    y

    E

    ( )

    ( )

    ( ) ( ) ( )

    2 2 2

    2

    22 12 2 2 6 2

    1 1cos

    2 2

    1sin 2

    2

    1 18.85 10 / 5 0.5 10 / 5.5 /

    2 2

    e o o o

    e

    e o o

    o o

    f E

    dfE

    d

    E C N m V m N m

    = =

    = =

    = =

    E n Electric Free Energy Density

    Electric Torque Density

    Using = 5 and E=0.5 V/ m

    [email protected][email protected]

    Freedericksz Transition -The Threshold I

  • 8/8/2019 Liquid Crystals by imran aziz

    86/90

    Ec

    z

    y

    E

    xAt some critical E

    field, the director

    rotates, before Ecnothing happens

    n

    y

    x

    nE

    ( ) ( )( )

    ( ) ( ) ( ){ }2 2 2

    11 22 33

    cos ,sin ,0

    1

    2dVOL

    z z

    F K K K dV

    =

    = + +

    n

    n n n n n

    0 02

    22

    dK

    dz

    d

    [email protected][email protected]

    Freedericksz Transition -The Threshold II

  • 8/8/2019 Liquid Crystals by imran aziz

    87/90

    ( )

    2 221 1

    sin2 2e o o

    VOL VOLF dV E dV = = E n

    2

    2 2

    220

    1sin

    2

    0

    d

    d e o

    dF F F K E dz

    dz

    F d F

    ddzdz

    = + = =

    E-field

    free energy

    total

    free energy

    Minimize free energy with

    Euler Equation

    [email protected][email protected]

    Freedericksz Transition -The Threshold III

  • 8/8/2019 Liquid Crystals by imran aziz

    88/90

    ( )

    ( )

    2

    222 2

    11

    22

    6 12 2 2

    sin cos 0

    10

    5 10 8.85 10 / (10)

    200,000 0.2

    0.2 5 1

    o

    TH

    o

    TH TH

    dK E

    dz

    K NE

    d m C Nm

    V V

    m m

    VV E d m volt

    m

    + =

    = =

    =

    = = =

    1.0 E/Ec

    mid-lay

    ertilt(deg)

    differential equation

    soln.

    small

    threshold

    [email protected][email protected]

    Defects

  • 8/8/2019 Liquid Crystals by imran aziz

    89/90

    s=+1 s=+1 s=+1

    s=1/2s=-1/2

    s=-1

    s=3/2 s=+2

    The singular line

    (disclination) is pointing

    out of the page, and directororientation changes by

    2 s on going around the

    line (s is the strength)[email protected][email protected]

  • 8/8/2019 Liquid Crystals by imran aziz

    90/90

    [email protected][email protected]