LIQUID CRYSTALSIntroduction

LIQUID CRYSTALSLIQUID CRYSTALSIntroductionIntroduction

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

AGGREGATION STATES OF MATTERAGAGGREGATIONGREGATION STASTATES OF MATTERTES OF MATTERheatingcooling

Example: H2O molekule

Liquid phaseSolid phase (crystal)

THERMOTROPIC LIQUID CRYSTALSTTHHERMOTROPERMOTROPICIC LIQUID CRYSTALSLIQUID CRYSTALSheatingcooling

Solid phase (crystal) Liquid phaseLiquid crytalline phaseLiquid crytalline phase

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

Disc-shape molecules (discotic LCs)example: triphenylene derivativesTexture of the

LC phase observedby polarization optical microscopy Synthetic materials

LIOTROPIC LIQUID CRYSTALSLIOTROPLIOTROPIC LIQUID CRYSTALSIC LIQUID CRYSTALSdecreasing concentration

increasing concentration

Solid phase (crystal)Liquid crystalline phaseLiquid crystalline phase

100 nm

TM virus

Molecular solutionsMolecular Molecular solutionssolutions

Liquid phase

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

Natural materials

POLYMER 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 LCGENERAL PROPERTIES OF LC--MESOPHASESMESOPHASES1) 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

n1nn11

n2nn22

Example: bend strain

THERMOTROPIC LIQUID CRYSTAL PHASESTHERMOTROPIC LIQUID CRYSTAL PHASESTHERMOTROPIC LIQUID CRYSTAL PHASESof achiral moleculesof achiral molecules

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

smectic C phase (SmC)

nematic phase (N)

smectic A phase (SmA)

columnar phase (2D lattice)

NEMATIC LC PHASE – theoretical descriptionNEMATIC LC PHASE NEMATIC LC PHASE –– theoretical descriptiontheoretical 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, ...)

F = U F = U –– TSTSMicroscopic description: f(θ) angular distribution functionf(θ)dΩ = fraction of the molecules pointing into a solid angle Ωhead to tail invariance of the nematic phase requires f(θ)=f(π-θ)!!

nematic order paramerSN = <((3cos2θ)-1)/2> = ( )∫ Ω− df )(1)cos3(

21 2 θθ

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

( )∫ Ω−= dffkS )(ln)( θθMaier-Saupe theory: U= –u SN2 ,

( )( )[ ]πθθ 4ln)(ln)(2 +Ω+−=∆ ∫− dffkTuSF NNIn=directorˆ

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

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

χz= n(ηII<cos2θ>+ η⊥<sin2θ>) = n(η+(2/3)ηaSN)

χx= χy = n(η–(1/3)ηaSN)SN=(χz–χx)/(nηa)z

xy

η=(ηII+2η⊥)/3, ηa= (ηII-η⊥), n=N/Vwhere molecular parameters

should be known from other measurements.

ELASTIC 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.

F

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

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

Elastic energy density of distortion (continuum theory):

( )23

22

21 ˆˆ(

21)ˆˆ(

21)ˆ(

21 nnKnnKnKFd ×∇×+×∇⋅+⋅∇=

Frank elastic constants: Ki ∼10-12 N

EFFECT OF INTERFACE INTERACTIONSEFFECT OF INTERFACE INTERACTIONSEFFECT OF INTERFACE INTERACTIONSNematic phase between two planar surfaces.

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

Fsurface=f0+Bsin2Φ ∆ϕ

easyaxisn

Φ= angle betweenn and the easy axis^

Rapini-Papoular approximationSurface anchoring energy coefficients: Bθ ≥ Bϕ ∼10-5 N/m

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

Nematic phase cofinedto spherical droplets.

F=Fsurface+Fd=MIN

STANDARD TECHNIQUE TOSTANDARD ACHIEVE PLANAR SURFACE ANCHORING

STANDARD TECHNIQUE TOTECHNIQUE TOACHIEVE PLANAR SURFACE ANCHORINGACHIEVE PLANAR SURFACE ANCHORING

glassglass

LCLCPolyimidePolyimide

glass

glass

Unidirectionalrubbing

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

ALIGNMENT OF LIQUID CRYSTALSON 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 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=ε0χeE, M=χmH).

For dielectric polarization local field corrections are quite important!!zPz= εon(α+(2/3) αaSN)fhEz=εo(ε II-1) Ez

Px= εon(α–(1/3) αaSN) fhEx=εo(ε ⊥-1) Exxy h=3 ε/(2 ε +1) cavity field factor

f reaction field factor

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

in general: ε = ε ⊥1+ εa(n⊗n), where εa=(ε II-ε ⊥) is dielectric anisotropy.^ ^

D= εo(ε⊥E+εa(n·E)n)^ ^

DIELECTRIC ANISOTROPYDIELECTRIC ANISOTROPYDIELECTRIC ANISOTROPY

ε(T)

2020 3030 4040 5050 70706060

DSC

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

FREEDERICKSZ EFFECTFREEDERICKSZ EFFECTFREEDERICKSZ EFFECT

+–

For εa>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+– U U

2a E)n(EED ˆ

21

21

21

02

0 εεεε −−=−= ⊥e

^

Electrostatic free energy density: F

E>EthE<Eth

Reorientation: n=n0+δn(z), n0=ex,, δnIIez, approximation: δn(z)= (δn)sin(πz/d)

Total free energy density: Ft=Fe+Fd= Cznz

zn−−

∂∂ 2

0

2

1 ))((21)(

21 δεεδ 2

a EK

^

ath

Kd

Eεε

π

0

1=( ) 044

02

12

0

<

−

=∫

dd

ndzFd

t

2a EK εεπδ∆

critical field ~ 1V/µm

THERMOTROPIC LIQUID CRYSTAL PHASESTHERMOTROPIC LIQUID CRYSTAL PHASESTHERMOTROPIC LIQUID CRYSTAL PHASESof chiral moleculesof chiral molecules

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

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

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

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

p/2

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

spherulite of the cholesteric phasec>10 wt %

segment of DNA

hexagonal LC phase

OPTIOPTICAL PROPERTIESCAL PROPERTIES

OPTICAL PROPERTIES OF THE NEMATIC PHASEOPTIOPTICAL PROPERTIES OF THE NEMATIC PHASECAL PROPERTIES OF THE NEMATIC PHASE

ε= ε⊥1+εa(n⊗n), εa=(ε –ε⊥)=nSN(α – α⊥)fh

nn--nn ⊥⊥ = = ∆∆nn ∼∼ 0.20.2Dielectric tensor at optical frequencies (~1015 Hz), refractive index n=(ε)1/2

LC phases have very large birefringence:

nbirefringent medium

Optical axis is parallelto the nematic director n.^

tiiEeAtr ω−= krsE ),(

k=(ω/c)n

θ

n(k/k)

extraordinary polarizationordinary polarization

sE

Ordinary beam: no= n⊥Extraordinary beam:

2

2

2

2

2

cossin1

⊥

+=nnne

θθ

II

OPTICAL BIREFRINGENCEOPTIOPTICAL BIREFRINGENCECAL BIREFRINGENCE

NI

Nematic liquid crystals are stronglybirefringent “liquids”!!!

((nnee--nnoo))∝∝ SSNN

Φ=(2π(∆∆nn)d)d))//λλPhase retardation between ordinary and extraordinary rayin d=4λ thick LC layer is 2π !!!

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

Liquid crystal have large electrooptic response!!!

COLORFULL NEMATIC TEXTURESobserved between crossed polarizers

COLORFULL NEMATIC TEXTURESCOLORFULL NEMATIC TEXTURESobserved between crossed polarizersobserved between crossed polarizers

Phase retardation between ordinary and extraordinary ray

Φ=(2π(∆∆nn)d)d))//λλ

Optical polarization microscopy:

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

Analyser

Polariser

TransmittanceTransmittance Τ Τ = ΤΤ (Φ)

OPTICAL PROPERTIES OF THE CHOLESTERIC PHASEOPTIOPTICAL PROPERTIES OF THE CHOLESTERIC PHASECAL PROPERTIES OF THE CHOLESTERIC PHASE

/2

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

n(z)=(cos(qz), sin(qz), 0)^

q=2π/pzx

Dielectric tensor in x,y plane:ε = ε⊥1+εa(n⊗n) =

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

^ ^

a=(ε +ε⊥)/2, b=(ε -ε⊥)/2

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

ImK means strong selective reflection for λ~p.

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

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

Theory versus practice.

• For λ<< 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

n0

q

Fd=(V/2)∑[δn1(q)(K1q⊥2+K3q

2)+δn2(q)(K2q⊥2+K3q

2) ]

1 2

kT

Relaxation rate: (1/τ )≈(K/γ)q2

10-5 cm2/s

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

d

Overdamped relaxation:δδnn

LIGHT 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.

δδnn((rr)=)=∑δ∑δnn((qq))eeiiqrqrn(r)=n0(r)+δn(r)

dFd/dni = -γi∂ni/∂t, i=1,2

δδnn((qq,t,t))==δδnn((qq,0,0))ee--t/t/ττ

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

Laser

Detector (I(t)∝|Es(t) |2)

θ

sample

∝>+><<

>+<=

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

ss

ss(1) ∑ −

l

tl

lSleC )/( τ

H

V

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

g(2)(t)=<I(t’)I(t’+t)>/<I>2

we measure

kkq fS −=ˆfk

ik

2(1)(2) (t))g(1(t)g ⋅+= α

scattered light

transmitted light

Largest scatteringcross section forδδnn((qq= = qs)) ..

LIGHT SCATTERING FROM CONFINED LC STRUCTURES

LIGHT SCATTERING LIGHT SCATTERING FROM CONFINED LC STRUCTURESFROM CONFINED LC STRUCTURES

A) Spherical LC droplets of radius Rqmin≈ π/R, (1/τ )min≈ (K/γ)R-2

qmin≈ π/D, (1/τ )min≈ (K/γ)D-2

B) Thin LC film of thickness D ~ λ.

0 2 4 6 8 10 12

qs=(0,0,qz)1/

τ1/

τ

qsD

qs=(qx,0,0)

0 2 4 6 8 10 12

1/τ

qRs

?

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

APPLICATIONS 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.

Liquid Crystal Display (LCD) PRINCIPLELLiquid iquid CCrystal rystal DDisplay (LCD)isplay (LCD) PRIPRINCIPLENCIPLE

ElectrodesVVoltage ONoltage ON

PolarizPolarized output lighted output light

No output light

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 DISPLAY

Segment-type display Active matrix display

semiconductorplatform

composition of TFT LCDcolour filter

polariser

liquid crystalmaterial

commonelectrode backlight

skupna elektroda

skupna elektrodasegment electrode

(RGB)

colours

SWITCHABLE WINDOWSSWITCHABLE WINDOWSSWITCHABLE WINDOWS

voltage off voltage on

Switchable windowsare made frompolymer dispersedliquid crystals (PDLC)

OTHER APPLICATIONSOTHER APPLICATIONSOTHER APPLICATIONSCar paint fromchiral LCs.

Temperature sensorfrom cholesteric LCs

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

Olenik 2001