LIQUID CRYSTALSLIQUID CRYSTALSIntroductionIntroduction

LIQUID CRYSTALSLIQUID CRYSTALSIntroductionIntroduction

• LC mesophases• LCs in the bulk and in confined geometries • optical properties of LCs• fluctuations and light scattering• applications of LCs

AGAGGREGATIONGREGATION STA STATES OF MATTERTES OF MATTERAGAGGREGATIONGREGATION STA STATES OF MATTERTES OF MATTER

Solid phase (crystal) Liquid phase

heating

cooling

Example:

H2O molekule

TTHHERMOTROPERMOTROPICIC LIQUID CRYSTALSLIQUID CRYSTALSTTHHERMOTROPERMOTROPICIC LIQUID CRYSTALSLIQUID CRYSTALSheating

cooling

Solid phase (crystal) Liquid phaseLiquid crytalline phaseLiquid crytalline phase

Rod-like molecules (calamatic LCs) example: alkhyl-cianobiphenyls

Synthetic materials

Texture of theLC phase observedby polarization optical microscopy

Disc-shape molecules (discotic LCs)example: triphenylene derivatives

LIOTROPLIOTROPIC LIQUID CRYSTALSIC LIQUID CRYSTALSLIOTROPLIOTROPIC LIQUID CRYSTALSIC LIQUID CRYSTALSdecreasing concentration

increasing concentration

Solid phase (crystal) Liquid phaseLiquid crystalline phaseLiquid crystalline phase

Examples: soaps, lipids, viruses, DNA...

Molecular Molecular solutionssolutionsMolecular Molecular solutionssolutions

100 nm

TM virus

Natural materials

POLYMER LIQUID CRYSTALSPOLYMER LIQUID CRYSTALSPOLYMER LIQUID CRYSTALSPOLYMER LIQUID CRYSTALS

main chain polymer LCs

Examples: Kevlar (du Pont), solutions of biopolymers

side chain polymer LCs

Kevlar

GENERAL PROPERTIES OF LC-MESOPHASESGENERAL PROPERTIES OF LC-MESOPHASESGENERAL PROPERTIES OF LC-MESOPHASESGENERAL PROPERTIES OF LC-MESOPHASES

1) They flow and form surface level(similar to liquids)

2) They exhibit anisotropic material properties(similar to crystals)

3) In some cases they can transmitt mechanical stress (similar to crystals)

Example: optical birefringence

nn11nn11

nn22nn22

Example: bend strain

THERMOTROPIC LIQUID CRYSTAL PHASESTHERMOTROPIC LIQUID CRYSTAL PHASESTHERMOTROPIC LIQUID CRYSTAL PHASESTHERMOTROPIC LIQUID CRYSTAL PHASES

Parameters describing the liquid crystalline phase:•Orientational order •Positional order •Bond orientational order

smectic A phase (SmA)

nematic phase (N)

smectic C phase (SmC)

columnar phase (2D lattice)

of achiral moleculesof achiral molecules

NEMATIC LC PHASE – theoretical descriptionNEMATIC LC PHASE – theoretical descriptionNEMATIC LC PHASE – theoretical descriptionNEMATIC LC PHASE – theoretical descriptionBasic thermodynamic argument for the I-N phase transition:Although orientational alignment of the molecules results in the loss of the entropy S, this loss is compensated by a decrease of the interaction energy U (because Van der Waals attractive forces are increased, molecular packing is optimized, ...)

n=directorˆ

Microscopic description: f() angular distribution functionf()d = fraction of the molecules pointing into a solid angle head to tail invariance of the nematic phase requires f()=f(-)!!

F = U – TSF = U – TS

nematic order paramer

SN = <((3cos2)-1)/2> = df )(1)cos3(2

1 2

Maier-Saupe theory: U= –u SN2 ,

Isotropic phase: SN = 0, totally aligned N phase SN = 1.

dffkS )(ln)(

4ln)(ln)(2 dffkTuSF NNI

NEMATIC - ISOTROPIC PHASE TRANSITIONNEMATIC - ISOTROPIC PHASE TRANSITIONNEMATIC - ISOTROPIC PHASE TRANSITIONNEMATIC - ISOTROPIC PHASE TRANSITION

SN can be measured via anisotropy of the material properties.example: diamagnetic susceptibility

x

z

y

z= n(II<cos2>+ <sin2>) = n(+(2/3)aSN)

x= y = n(–(1/3)aSN)SN=(z–x)/(na)

=(II+2)/3, a= (II-), n=N/Vwhere molecular parameters

should be known from other measurements.

ELASTIC DEFORMATIONS IN NEMATICSELASTIC DEFORMATIONS IN NEMATICSELASTIC DEFORMATIONS IN NEMATICSELASTIC DEFORMATIONS IN NEMATICSNematic phase can transmit forces in casesin which the corresponding deformation perturbs the long-range orientational order.

For example: shear stress will produce usual viscous liquid flow,

F

F

while splay, twist and bend deformations will produce elastic response.

Elastic energy density of distortion (continuum theory):

Frank elastic constants: Ki 10-12 N

23

22

21 ˆˆ(

2

1)ˆˆ(

2

1)ˆ(

2

1nnKnnKnKFd

EFFECT OF INTERFACE INTERACTIONSEFFECT OF INTERFACE INTERACTIONSEFFECT OF INTERFACE INTERACTIONSEFFECT OF INTERFACE INTERACTIONS

Nematic phase between two planar surfaces.

Surface forces generally induce bulk aligment in some preferential direction (easy axis).

Approximation of infinitely strong anchoring (B =) is often reasonable.

Fsurface=f0+Bsin2

Surface anchoring energy coefficients: B B 10-5 N/m

Rapini-Papoular approximation

Nematic phase cofinedto spherical droplets.

F=Fsurface+Fd=MIN

easy axis

n̂= angle betweenn and the easy axis^

glassglass

LCLC

Polymer surface is melted due to applied force and melted polymer molecules align in the direction of the rubbing.

STANDARD STANDARD TECHNIQUE TOTECHNIQUE TO ACHIEVE PLANAR SURFACE ANCHORINGACHIEVE PLANAR SURFACE ANCHORING

STANDARD STANDARD TECHNIQUE TOTECHNIQUE TO ACHIEVE PLANAR SURFACE ANCHORINGACHIEVE PLANAR SURFACE ANCHORING

PolyimidePolyimide

glass

glass

Unidirectionalrubbing

ALIGNMENT OF LIQUID CRYSTALSALIGNMENT OF LIQUID CRYSTALSON RUBBED POLYMER SURFACEON RUBBED POLYMER SURFACE

ALIGNMENT OF LIQUID CRYSTALSALIGNMENT OF LIQUID CRYSTALSON RUBBED POLYMER SURFACEON RUBBED POLYMER SURFACE

Anisotropic interaction between the polymer substrate and the rod-shape liquid crystal molecules induces orientational ordering of the LC layer.

1 mm

Nematic LC texture in a cell without and with the alignment layer.

EFFECT OF EXTERNAL FIELDSEFFECT OF EXTERNAL FIELDSEFFECT OF EXTERNAL FIELDSEFFECT OF EXTERNAL FIELDSDue to head-tail invariance of the molecular arrangement, the nematic phase has no spontaneous macroscopic electric polarization P and magnetization M. External electric and magnetic fields produce induced polarization/magnetization (P=0eE, M=mH).

For dielectric polarization local field corrections are quite important!!

Pz= on(+(2/3) aSN)fhEz=o( II-1) Ez

Px= on(–(1/3) aSN) fhEx=o( -1) Exx

z

y h=3 /(2 +1) cavity field factor

f reaction field factor

Dielectric tensor in case of zIIn:^ = , 0 , 00 , , 00 , 0 , II

in general: = 1+ a(nn), where a=( II- ) is dielectric anisotropy.

^ ^

D= o(E+a(n·E)n)^ ^

DIELECTRIC ANISOTROPYDIELECTRIC ANISOTROPYDIELECTRIC ANISOTROPYDIELECTRIC ANISOTROPY

2020 3030 4040 5050 70706060

Temperature dependenceof the dielectric constant and the DSC response of the liquid crystal 5CB.

(T) DSC

+–

FREEDERICKSZ EFFECTFREEDERICKSZ EFFECTFREEDERICKSZ EFFECTFREEDERICKSZ EFFECT

Electrostatic free energy density:

For a>0 electric field tends to align the LC director n along the field direction.In confined geometries this tendency is opposed by surface anchoring. Competition

results in the threshold behaviour. Example: nematic cell with planar anchoring:

z

x

E<Eth E>Eth

+– U U

Reorientation: n=n0+n(z), n0=ex,, nIIez, approximation: n(z)= (n)sin(z/d)

Total free energy density: Ft=Fe+Fd=

2a E)n(EED ˆ

2

1

2

1

2

10

20 eF

Cznz

zn

2

0

2

1 ))((2

1)(

2

1 2a EK

ath

K

dE

0

1

critical field ~ 1V/m

044

02

12

0

d

dndzF

d

t

2a EK

^

^

THERMOTROPIC LIQUID CRYSTAL PHASESTHERMOTROPIC LIQUID CRYSTAL PHASESTHERMOTROPIC LIQUID CRYSTAL PHASESTHERMOTROPIC LIQUID CRYSTAL PHASES

Via intramolecular interactions chirality is transmitted from the microscopic to the macroscopic scale.

Chiral smectic A phase (SmA*)Similar to achiral SmA,but exhibits optical activity

Chiral nematic phase (N*), known also as cholesteric phase (Ch)Spontaneously twisted

Chiral smectic C phase (SmC*)Tilted and spontaneously twisted(exhibits ferroelectricity)

of chiral moleculesof chiral molecules

p/2

Example: LC phases ofExample: LC phases of DN DNA in aqueous solutionsA in aqueous solutionsExample: LC phases ofExample: LC phases of DN DNA in aqueous solutionsA in aqueous solutions

spherulite of the cholesteric phasec>10 wt %

hexagonal LC phase

segment of DNA

OPTIOPTICAL PROPERTIESCAL PROPERTIES

OPTIOPTICAL PROPERTIES OF THE NEMATIC PHASECAL PROPERTIES OF THE NEMATIC PHASEOPTIOPTICAL PROPERTIES OF THE NEMATIC PHASECAL PROPERTIES OF THE NEMATIC PHASE

nn--nn = = nn 0.2 0.2LC phases have very large birefringence:

= 1+a(nn), a=( –)=nSN( – )fh

Dielectric tensor at optical frequencies (~1015 Hz), refractive index n=()1/2

n^

Optical axis is parallelto the nematic director n.^

birefringent medium

n̂(k/k)

extraordinary polarizationordinary polarization

Ordinary beam: no= n

Extraordinary beam:

2

2

2

2

2

cossin1

nnne

II

k=(/c)n

tiiEeAtr krsE ),(

sE

OPTIOPTICAL BIREFRINGENCECAL BIREFRINGENCEOPTIOPTICAL BIREFRINGENCECAL BIREFRINGENCE

NI

Nematic liquid crystals are stronglybirefringent “liquids”!!!

((nnee-n-noo)) S SNN

=(2nn)d)d))//Phase retardation between ordinary and extraordinary ray

in d=4 thick LC layer is 2

Phase retardation can be mediated by relatively low external voltages (Freedericksz effect).

Liquid crystal have large electrooptic response!!!

COLORFULL NEMATIC TEXTURESCOLORFULL NEMATIC TEXTURESobserved between crossed polarizersobserved between crossed polarizers

COLORFULL NEMATIC TEXTURESCOLORFULL NEMATIC TEXTURESobserved between crossed polarizersobserved between crossed polarizers

Analyser

Polariser

Optical polarization microscopy:

=(2nn)d)d))//

Phase retardation between ordinary and extraordinary ray

TransmittanceTransmittance= (

depends on local orientation of the director field n(r)^

OPTIOPTICAL PROPERTIES OF THE CHOLESTERIC PHASECAL PROPERTIES OF THE CHOLESTERIC PHASEOPTIOPTICAL PROPERTIES OF THE CHOLESTERIC PHASECAL PROPERTIES OF THE CHOLESTERIC PHASE

Cholesteric LCs are natural 1D photonic band-gap media !!

Spatial periodicity (pitch p) of the director field n(r) is typically in the range of optical wavelengths.

ImK means strong selective reflection for ~p.

n(z)=(cos(qz), sin(qz), 0)/2

z

^

Spiralling index ellipsoid.(Analytical solutions of WE for kIIz and d=)

q=2/px

Dielectric tensor in x,y plane: = 1+a(nn) =

a+bcos(2qz), bsin(2qz) bsin(2qz), a-bcos(2qz)

a=( +)/2, b=( -)/2

^ ^

SELECTIVE REFLECTION and MSELECTIVE REFLECTION and MAUGUINAUGUIN LIMIT LIMITSELECTIVE REFLECTION and MSELECTIVE REFLECTION and MAUGUINAUGUIN LIMIT LIMIT• For ~p circularly polarized beam which matches the chirality of the structure is totally reflected. The width of the reflection (forbidden) band ~n·p.

Theory versus practice.

• For << p the polarization plane of the linearly polarized light is rotated synchro-nously with the spontaneous twist of the structure (Mauguin limit). The material acts as a strongly optically active medium.

LIGHT SCATTERINGLIGHT SCATTERING

LIGHT SCATTERING IN THE NEMATIC PHASELIGHT SCATTERING IN THE NEMATIC PHASELIGHT SCATTERING IN THE NEMATIC PHASELIGHT SCATTERING IN THE NEMATIC PHASEOne of the most profound optical manifestations of the thermal fluctuations.

n0

q

Fd=(V/2)n1(q)(K1q2+K3q 2)+n2(q)(K2q

2+K3q 2)

1 2

kT

dFd/dni = -ini/t, i=1,2

Relaxation rate: (1/ )(K/)q2

10-5 cm2/s

n(r)=n0(r)+n(r) nn((rr)=)=nn((qq)e)eiiqrqr

2 2

q

kT

Fluctuations of the director field n(r) produce increase of the elastic energy Fd

Ki 10-12 N

10-6 –1 s

nn((qq,t,t))==nn((qq,0,0))ee-t/-t/

d

Overdamped relaxation:

nn

Laser

Detector (I(t)|Es(t) |2)

sample

t)(t'E)(t'E

t)(t')E(t'E(t)g

ss

ss(1)

l

tl

lSleC )/(

H

V

DLS provides information on of different fluctuation modes nn((qq,t).,t).This gives the values of (Ki/) for different types of deformations.

EKSPERIMENTAL ANALYSISEKSPERIMENTAL ANALYSISEKSPERIMENTAL ANALYSISEKSPERIMENTAL ANALYSISPhoton correlation spectroscopy (known as PCS or DLS): probing range 10-9 –103 s

Largest scatteringcross section for

nn((qq= = qs)) . .

g(2)(t)=<I(t’)I(t’+t)>/<I>2

we measure

kkq fS ˆfk

ik

2(1)(2) (t))g(1(t)g

scattered light

transmitted light

LIGHT SCATTERING LIGHT SCATTERING FROM CONFINED LC STRUCTURESFROM CONFINED LC STRUCTURES

LIGHT SCATTERING LIGHT SCATTERING FROM CONFINED LC STRUCTURESFROM CONFINED LC STRUCTURES

A) Spherical LC droplets of radius R qmin/R, (1/ )min (K/)R-2

B) Thin LC film of thickness D ~ .

DLS gives information on cavity size (R or D)and surface anchoring koefficient B.

0 2 4 6 8 10 12

1/

qR

0 2 4 6 8 10 12

qs=(0,0,qz)1/

1/

qsD

qs=(qx,0,0)

?

qmin/D, (1/ )min (K/)D-2

s

APPLICATIONS OF LIQUID CRYSTALSAPPLICATIONS OF LIQUID CRYSTALSAPPLICATIONS OF LIQUID CRYSTALSAPPLICATIONS OF LIQUID CRYSTALS

Most important comercial productsbased on LCs are LCDs.

Other applications:•optical switching devices, •optical filters, •temperature and stress sensors, •special paints and colorants, •cosmetics, •etc.

Present top LCD:WUXGA (wide ultra extended graphics array) 1920 x 1200 pixels.

ElectrodesVVoltage ONoltage ON

PolarizPolarized output lighted output light

No output light

LLiquid iquid CCrystal rystal DDisplay (LCD)isplay (LCD) PRI PRINCIPLENCIPLELLiquid iquid CCrystal rystal DDisplay (LCD)isplay (LCD) PRI PRINCIPLENCIPLE

Picture element is whitePicture element is white Picture element is blackPicture element is black

PolariserPolariser

Analyser Analyser

FROM PICTURE ELEMENT to THE DISPLAYFROM PICTURE ELEMENT to THE DISPLAYFROM PICTURE ELEMENT to THE DISPLAYFROM PICTURE ELEMENT to THE DISPLAY

Segment-type displayActive matrix display

semiconductorplatform

composition of TFT LCDcolour filter

polariser

liquid crystalmaterial

commonelectrode backlight

skupna elektroda

skupna elektrodasegment electrode

(RGB)

colours

SWITCHABLE WINDOWSSWITCHABLE WINDOWSSWITCHABLE WINDOWSSWITCHABLE WINDOWS

voltage off voltage on

Switchable windowsare made frompolymer dispersedliquid crystals (PDLC)

OTHER APPLICATIONSOTHER APPLICATIONSOTHER APPLICATIONSOTHER APPLICATIONS

LCs in ART: Art-painting made by use ofthe polysiloxane LC paint.left: in reflected lightright: in transmitted light

Car paint from chiral LCs.

Temperature sensorfrom cholesteric LCs

Olenik 2001