liquid crystal materials. lyotropics thermotropics amphiphilic molecules, polar and non-polar parts...

Liquid Crystal Materials

CN

Lyotropics Thermotropicsamphiphilic molecules, polar and non-polarparts form liquid crystal phases over certainconcentration ranges when mixed with a solvent

molecules consisting of a rigid core and flexible tail(s) form liquid crystal phasesover certain temperature ranges.

+-

hydrophilic polar head

hydrophobic non-polar tail flexible tail

rigid core

Broad Classification

The Lyotropic Phases

micelle

reverse micelle

cross section

cross section

CNChemist’s View

Physicist’sEngineer’s View

• Shape Anisotropy

• Length > Width

The molecule above (5CB) is ~2 nm × 0.5 nm

The Thermotropic Liquid Crystal Molecule

Geometrical Structures of Mesogenic Molecules

Low Molecular Weight High Molecular Weight (polymers)

( )n

( )n

disk-like

rod-like

most practical applications

n

Temperature Crystal Nematic LC Isotropic

The Liquid Crystal Phase

The Nematic Director n

LongMolecular

Axis

H H

H H

H H

H H

C NOC C

H HHH

C C

H H

HH

H

n

The local average axis

of the long molecular axis

director

n

Temperature Smectic C Smectic A Nematic

nz

n

Other Liquid Crystal Phases

left-handed right-handedmirror 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 atomon the alkyl chain of the molecules extendsout 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 ofas a right or left handed coordinate system

Chirality

CN

pitch

P

CN

Ordinary Nematic Chiral Nematic

director

n

The Chiral Nematic

The Chiral Doped Nematic

You can create a cholesteric material by doping a conventionalnematic with a chiral dopant.

1HTP

Pc For dilute solutions

Chiral Dopant HTP (m)-1

S-811 -14 IS-4651 -13.6

- indicates left twist sense 1

1

10.71

14 0.1

PHTP c

mm

For a 10% doping of S-811

The Chiral Smectic C: Ferroelectrics

Eye- dipole moment fin - chiral

ferroelectric LC has adipole moment perp-endicular to its longaxis, and is chiral.

C10H21 ON

COO CH2 CH C2H5

CH3

The Chiral Smectic: TGB

Twisted Grain Boundary (TGB)

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

O

C

R C

O

CR

O

O

C

O

R

OC

O

R

O

C

OR

O

C

O

R

Discotic Liquid Crystal

example: R=OCOC11H23

Columnar, columns of molecules in hexagonal lattice

Nematic discotic phase

n

Discotics Liquid Crystalsn

Polymer Liquid Crystals

Combining the properties of liquid crystals and polymers

Main Chain Side Chain

mesogenic moieties are connected head-to-tail

mesogenic moietiesattached as side chainson the polymer backbone

rigid

semi-flexible

Polymer Liquid Crystalsforming nematic liquid crystal phases

n

main-chainside-chain

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

O

Example of Side-Chain Polymer LCs

-(-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)

n

The Order Parameter

n

22

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 fluid

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

Maier-Saupe Theory - Mean Field Approach

• {V: minimum} when phase is ordered (-P2(cos))• {V: V=0} when phase is disordered (<P2(cos)>)• factor for intermolecular strength ( )

=(kT)-1

n

Maier-Saupe Theory - Mean Field Approach

Temperature

Nematic LiquidCrystal

Isotropic Fluid

-0.6

0.0

1.0

Ord

er P

aram

eter

, S

n

n

Landau-de Gennes TheoryLandau-de Gennes Theory

2 3 4 20

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

Ord

er P

aram

eter

, S

Temperature

Good near NI transition

surf

ace

Predicts order nearsurface

The Order Parameter: How does it affects display performance ?

The order parameter, S, is proportional to a number of importantparameters which dictate display performance.

Parameter Nomenclature Elastic Constant Kii S2

Birefringence n SDielectric Anisotropy SMagnetic Anisotropy SViscosity Anisotropy S

Example: Does the threshold switching voltage for a TN increase or decrease as the operating temperature increases.

Scales as the square root of S therefore lowers with increasing temperature

2

TH

K SV S

S

proportional to

Anisotropy: Dielectric Constant

Off-axis dipole moment, angle with molecular axis

2

23cos 12o B

NhFS F

k T

N: number densityh,f: reaction field, reaction

cavity parametersS: order parameter: anisotropy in polarizability: molecular dipole momentkB: Boltzman constantT: Temperature

For values of the angle , thedipolar term is positive, and forvalues , the dipolar term isnegative, and may result in a materials with an overall -.

Anisotropy: Dielectric Constant

+++++

- -- --

E

E

++++

----

positive

negative

all angles inthe plane to E arepossible for the- materials

E

Anisotropy: Duel Frequency

MLC-2048 (EM Industries), Duel Frequency Material Frequency (kHz) 0.1 1.0 10 50 100Dielectric Anisotropy () 3.28 3.22 0.72 -3.0 -3.4

low frequency, >0 high frequency, <0

Dielectric Constants (@20oC, 1kHz)

*Mixture Application

BL038 PDLCs 16.7 21.7 5.3MLC-6292 TN AMLCDs 7.4 11.1 3.7ZLI-4792 TN AMLCDs 5.2 8.3 3.1TL205 AM PDLCs 5 9.1 4.118523 Fiber-Optics 2.7 7 4.395-465 - material -4.2 3.6 7.8

Materials Dielectric ConstantVacuum 1.0000Air 1.0005Polystyrene 2.56Polyethylene 2.30Nylon 3.5Water 78.54

*EM Materials

Dielectric Constants: Temperature Dependence

1 6

1 4

1 2

1 0

8

62 5 3 0 3 5

T - T N I ( ° C )

/ /1

23

( )S T

Die

lect

ric C

ons

tant

i s

E x t r a p o l a t e d f r o m i s o t r o p i c p h a s e

4’-pentyl-4-cyanobiphenyl

CH3-(CH2)4 C N

( )S T

//1

23

Temperature Dependence

Average Dielectric Anistropy

Magnetic Anisotropy: Diamagnetism

Diamagnetism: induction of a magnetic moment in opposition to an applied magnetic field. LCs are diamagnetic due to thedispersed electron distribution associated with the electron structure.

Delocalized charge makesthe major contribution to diamagnetism.

Ring currents associated witharomatic units give a largenegative component to for directions to aromatic ringplane. is usually positive since:

0ll ll

Magnetic Anisotropy: Diamagnetism

C 5 H 1 1

C 7 H 1 5

C N

C N

C N

C 5 H 1 1

C N

C 7 H 1 5

C 7 H 1 5

C N

9 3 1/ 1 0 m k g

1 . 5 1

1 . 3 7

0 . 4 6

0 . 4 2

- 0 . 3 8

Compound

Optical Anisotropy: Birefringenceordinary ray (no, ordinary index of refraction)

extraordinary ray (ne, extraordinary index of refraction)

Optical Anisotropy: Birefringenceordinary wave

extraordinary wave

on n2 2

2 2 2

1 cos sin

o en n n

For propagation along the opticaxis, both modes are no

optic axis

Optical Anisotropy: Phase Shift

analyzer

polarizer

liquid crystal

light

= 2dno,e/

e=2dn/

n = ne - no

0 < n < 0.2depending on deformation

380 nm < < 780 nm visible light

Birefringence (20oC @ 589 nm)

EM Industry n ne no Application Mixture BL038 0.2720 1.7990 1.5270 PDLCTL213 0.2390 1.7660 1.5270 PDLCTL205 0.2175 1.7455 1.5270 AM PDLCZLI 5400 0.1063 1.5918 1.4855 STNZLI 3771 0.1045 1.5965 1.4920 TNZLI 4792 0.0969 1.5763 1.4794 AM TN LCDsMLC-6292 0.0903 1.5608 1.4705 AM TN LCDsZLI 6009 0.0859 1.5555 1.4696 AN TN LCDsMLC-6608 0.0830 1.5578 1.4748 ECB95-465 0.0827 1.5584 1.4752 - devicesMLC-6614 0.0770 --------- --------- IPSMLC-6601 0.0763 --------- --------- IPS18523 0.0490 1.5089 1.4599 Fiber OpticsZLI 2806 0.0437 1.5183 1.4746 - device

Birefringence: Temperature Dependence

1 . 8

1 . 7

1 . 6

1 . 5

1 . 4

5 0 4 0 3 0 0

T - T N I ( ° C )

Inde

x of

Ref

ract

ion

2 0 1 0

n e

n o

n i s o

2 220

12

3 en n n

E x t r a p o l a t e d f r o m i s o t r o p i c p h a s e

2 220

12

3 en n n

Average Index

TemperatureDependence

( )n S T

Birefringence Example: 1/4 Wave Plate

Unpolarized

linear polarized

circular polarized

polarizerLC: n=0.05d

What is minimum d forliquid crystal 1/4 wave plate ?

1

41

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

Nematic Elasticity: Frank Elastic Theory Nematic Elasticity: Frank Elastic Theory

11 Splay, K Twist, K22 Bend, K33

F K K K dV

K K dV

F dV dV

dV

V

e oV

oV o

12

12

12

12

112

222

332

24 13

2 2

{ ( ) ( ) ( ) }

{ ( ) ( )}

( ) ( )

n n n n n

n n n n n n

E n B n

+

20 0

1sin

2s

s

F W dS

Surface Anchoring

microgrooved surface -homogeneous alignment (//)rubbed polyimide

ensemble of chains -homeotropic alignment ()surfactant or silane

Alignment at surfaces propagates over macroscopic distances

Surface Anchoring

N

n

polar anchoring W

azimuthalanchoring W

surfa

ce

Strong anchoring 10-4 J/m2

Weak anchoring 10-7 J/m2

W, is energy needed to move director n from its easy axis

Creating Deformations with a Field and Surface - Bend Deformation

E or B

Creating Deformations with a Field and Surface - Splay Deformation

E or B

Creating Deformations with a Field and Surface - Twist Deformation

E or B

Magnitudes of Elastic Constants

EM Industry K11 K22 K33

Mixture (pN) (pN) (pN) Application

BL038 13.7 ------ 27.7 PDLCTL205 17.3 ------ 20.4 AM PDLCZLI 4792 13.2 6.5 18.3 TN AM LCDZLI 5400 10 5.4 19.9 TNZLI-6009 11.5 5.4 16.0 AM LCD

Order of magnitude estimate of elastic constant

U: intermolecular interaction energy: molecule distance

146 11

8

1010 10 10

10ii

U ergsK dynes N pN

cm

Elastic Constant K22: Temperature Dependence

7

6

5

4

3

2

-30 -20 -10 0T-TNI (°C)

K22

(x

10

-12

Ne

wto

n)

P-azoxyphenetole

P-azoxyanisole (PAA)

2( )K S T

The Flexoelectric Effect

-

+

-

+

Polar Axis

Undeformedstate of bananaand pear shapedmolecules

Splay

Bend

Polar structure corresponds tocloser packingof pear and banana molecules

x

yE

n

Effects of an Electric Field

sin cos

oE

n x

y

y

E

2 2 2

2

22 12 2 2 6 2

1 1cos

2 21

sin 22

1 18.85 10 / 5 0.5 10 / 5.5 /

2 2

e o o o

ee 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

x

y

Bn

Effects of an Magnetic Field

2 2 2

2

22 7 7 3 1 2

1 1cos

2 2

1sin 2

2

1 14 10 / 10 2 0.2 /

2 2

e oo o

be o

o

oo

f B B

dfB

d

B N A m kg T N m

n

sin cos

oB

n x

y

y

B

Magnetic free energy density

Magnetic torque density

Using = 10-7 m3kg-1 and B= 2 T = 20,000 G

Deformation Torque

Sur

face

dx

22

2 2

2tan exp

2 4

1cos

2

1 2 2sin 2

2

d

dd

xd

f Kx

dfK K

d d d

Orientation of molecules obeys this eq.

Free energy density from elastic theory

Torque density

Sur

face

Deformation Torque

dx

22

d Kd

21122

26

10 2215 / 15

5 10

NK N m Pa

d

Material Shear Modulus Steel 100 GPa Silica 40 GPa Nylon 1 GPa

Shear modulus Young’s modulus

3

8

3

8

Sur

face

dx

Coherence Length: Electric or Magnetic

E

22

11

612 2 2

1 2 1sin 2 sin 2

2 2

12

1

2

10 11.5

0.5 10 /8.85 10 / 20

d e o

o

o

K Ed

Kd

E

d K

E

Nm

V mC N m

Balance torque

Find distance d

Coherence length

Using E = 0.5 V/mand = 20

Viscosity: Shear Flow Viscosity Coefficient

n

v

v n v nvn v

Typically > >

( )

( )

shear stress

velocity gradient

v

n nn

Viscosity: Flow Viscosity Coefficient

Dynamic Viscosity 1 kg/m·s = 1 Pa·s 0.1 kg/m·s = 1 poise

Kinematic Viscosity 1 m2/s

31000

kg

m

LC specification sheets givekinematic viscosity in mm2/s

Approximate density

Viscosity: Flow Viscosity Coefficient

2

2 2 3 33

120 / 20 / 10 / 0.02 / 0.2

10ii

mmm s mm s kg m kg ms poise

mm

Typical Conversion Density Conversion Flow 0.1 kg/ms = 1 poiseViscosity

EM Industry Kinematic () Dynamic () MIXTURE CONFIGURATION (mm2/s) (Poise)

ZLI-4792 TN AM LCDs 15 0.15ZLI-2293 STN 20 0.20MLC-6610 ECB 21 0.21MLC-6292 TN AM LCDs (Tc=120oC) 28 0.28

18523 Fiber Optics (no=1.4599) 29 0.29

TL205 PDLC AM LCD 45 0.45BL038 PDLCs (n=0.28) 72 0.72

Viscosity: Temperature Dependence

For isotropic liquids

0 expisoB

E

K T

E is the activation energy for diffusion of molecular motion.

H3CON C4H9

1.0

0.7

0.4

0.2

0.120 30 40 50 60

2

3

1

TNI

Vis

cosi

ty (

pois

e)

Temperature (°C)

n

Viscosity: Rotational Viscosity CoefficientT

ime

n

n

Rotation of the director n bv externalfields (rotating fields or static).

Viscous torque's v are exerted on a liquidcrystal during rotation of the director n and by shear flow.

1v

d

dt

rotational viscosity coefficient

n

Viscosity: Rotational Viscosity Coefficient

nn

EM Industry Viscosity Viscosity MIXTURE CONFIGURATION (mPas) (Poise)

ZLI-5400 TN LCDs 109 1.09ZLI-4792 TN AM LCDs 123 1.23ZLI-2293 STN 149 1.4995-465 - Applications 185 1.85MLC-6608 TN AM LCD 186 1.86

1 3

1109 109 0.109 0.109 / 1.09

10

PamPa s mPa s Pa s kg m s poise

mPa

Viscosity: Comparisons

Material Viscosity (poise)

Air 10-7

Water 10-3

Light Oil 10-1

Glycerin 1.5

LC-Rotational (1) 1< 1 < 2LC-Flow (ii) 0.2< ii<1.0

Sur

face

x

Relaxation from Deformation

E

Sur

face

x

field on state

zero field state

Relaxation when field is turned off Relaxation time

Relaxation from Deformation

2

1

21

2

21 4

211

21 6

211

2

exp /2

10 / 102.5

(10 ) 2

10 / 5 106

(10 ) 2

d visc

o

dK

d dt

dt where

K

kg ms ms

N

kg ms mms

N

Sur

face

x

Balance viscous/deformation torque

Assume small deformations

Solution

For 100 m cell

For 5 m cell

Freedericksz Transition - The Threshold I

Ec

z

y

E

xAt some critical E field, the director rotates, before Ec

nothing happens

n

y

x

nE

2 2 2

11 22 33

cos ,sin ,0

1

2d

VOL

z z

F K K K dV

n

n n n n n

0 02

22

dK

dz

d

Freedericksz Transition - The Threshold II

2 2 21 1

sin2 2e o o

VOL VOL

F dV E dV E n

22 2

22

0

1sin

2

0

d

d e o

dF F F K E dz

dz

F d Fddzdz

E-fieldfree energy

totalfree energy

Minimize free energy with ‘Euler’ Equation

Freedericksz Transition - The Threshold III

22

22 2

1122

6 12 2 2

sin cos 0

10

5 10 8.85 10 / (10)

200,000 0.2

0.2 5 1

o

THo

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

-laye

r til

t (d

eg)

differential equation

soln.small

threshold

Defects

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

s=1/2 s=-1/2 s=-1

s=3/2 s=+2

The singular line(disclination) is pointing out of the page, and director orientation changes by2s on going around the line (s is the strength)

Estimate Defect Size

The simplest hypothesis is that the core or defector disclination is an isotropic liquid, therefore thecore energy is proportional to kBTc. Let M be themolecular mass, N Avogadadro’s number and the density of the liquid crystal.

22

11 11 11

0 0

211

1126 211

23

8

1ln

2

ln

1 1 100 10

2 2 10 / 10

3 10 30

c c

l R R

ecz r r r

e core B c cc

cc B c

c

dr RF K rdrd dz lK lK

r r

R NF F F lK k T r l

r M

F M K Nr m

r N k T J K K

r m nm

n

core

R

rc

radius of core

planar radial alignment

l

Microscopic Fluttering and Fluctuations

Thermally induced Deformations

• Characteristic time of Fluctuations:

• Can see fluctuations with microscope:• Responsible for opaque appearance of nematic LC

1 122

211

9

2

0.1 /100

210

589 10

KqK

kg m ss

Nm

AX Y

Z Z’

• Aromatic or saturated ring core• X & Y are terminal groups• A is linkage between ring systems• Z and Z’ are lateral substituents

CH3 - (CH2)4C N

4-pentyl-4’-cyanobiphenyl (5CB)

General Structure

Mesogenic Core Linking Groups Ring Groups

N

N

phenyl

pyrimidine

cyclohexane

biphenylterphenyldiphenylethanestilbenetolaneschiffs baseazobenzeneazoxyben-zenephenylbenzoate(ester)phenylthio-benzoate

CH CH2 2

CH CH CH CH CH N

N N

N N

O

C O

C S

O

O

Common Groups

NomenclatureMesogenic Core

phenylbenzylbenzene

biphenyl terphenyl

phenylcyclohexane (PCH)cyclohexane cyclohexyl

Ring Numbering Scheme

3’ 2’

1’

6’5’

4’

32

1

6 5

4

Terminal Groups

(one terminal group is typically an alkyl chain)

CH3

CH2

CH2

CH2

CH3

CH2

C*H

CH2

CH3

straight chain

branched chain (chiral)

Attachment to mesogenic ring structureDirect - alkyl (butyl)Ether -O- alkoxy (butoxy)

CH3-

CH3-CH2-

CH3-(CH2)2-

CH3-(CH2)3-

CH3-(CH2)4-

CH3-(CH2)5-

CH3-(CH2)6-

CH3-(CH2)7-

methyl

ethyl

propyl

butyl

pentyl

hexyl

heptyl

octyl

CH3-O-

CH3-CH2-O-

CH3-(CH2)2-O-

CH3-(CH2)3-O-

CH3-(CH2)4-O-

CH3-(CH2)5-O-

CH3-(CH2)6-O-

CH3-(CH2)7-O-

methoxy

ethoxy

propoxy

butoxy

pentoxy

hexoxy

heptoxy

octoxy

Terminal Groups

Second Terminal Group andLateral Substituents (Y & Z)

H -F flouroCl chloroBr bromoI iodoCH3 methylCH3(CH2)n alkylCN cyanoNH2 aminoN(CH3) dimethylaminoNO2 nitro

phenyl

cyclohexyl

Odd-Even EffectClearing point versus alkyl chain length

0 1 2 3 4 5 6 7 8 9 10 11 carbons in alkyl chain (n)

cle

arin

g po

int

18

16

14

12

10

CH3-(CH2)n-O O-(CH2)n-CH3C-O

O

CH3-(CH2)4C N

CH3-(CH2)4-O C N

4’-pentyl-4-cyanobiphenyl

4’-pentoxy-4-cyanobiphenyl

Nomenclature

Common molecules which exhibit a LC phase

Structure - Property

N

N

CH3-(CH2)4C N

vary mesogenic core

A

A C-N (oC) N-I(oC) n

22.5 35 0.18 11.5

71 52 0.18 19.7

31 55 0.10 9.7

Structure - Property

CH3-(CH2)4COO

vary end group

X

X C-N (oC) N-I (oC)

HFBrCNCH3

C6H5

87.592.0115.5111.0106.0155.0

114.0156.0193.0226.0176.0266.0

Lateral Substituents (Z & Z’)

AX Y

Z Z’

• Z and Z’ are lateral substituents • Broadens the molecules• Lowers nematic stability • May introduce negative dielectric anisotropy

E

Solid

Liquid Crystal

Isotropic Liquid

Concentration (2), %

0 50 100

Why Liquid Crystal MixturesMelt Temperature:Liquid Crystal-Solid

ln i = Hi(Teu-1 - Tmi

-1)/R

H: enthalpiesTeu: eutectic temperature

Tmi: melt temperatureR: constant

Nematic-IsotropicTemperature: TNI

TNI = iTNIi

Tem

per

atu

re

eutecticpoint

S-N <-40 C solid nematic transition (< means supercools)

Clearing +92 C nematic-isotropic transition temperature

Viscosity (mm2 /s) flow viscosity, some materials may stipulate the+20 C 15 rotational viscosity also. May or may not give 0 C 40 a few temperatures

K33/K11 1.39 ratio of the bend-to-splay elastic constant

5.2 dielectric anisotropy

n 0.0969 optical birefringence (may or may not give ne, no)

dn (m) 0.5 product of dn (essentially the optical path length)

dV/dT (mV/oC) 2.55 how drive voltage changes as temperature varies

V(10,0,20) 2.14V(50,0,20) 2.56 threshold voltage (% transmission, viewing angle,V(90,0,20) 3.21 temperature)

EM Industry Mixtures

Property ZLI 4792 MLC 6292/000 MLC 6292/100S-N <-40 C <-30 C <-40 C

Clearing +92 C +120 C +120 C

Viscosity (mm2 /s)+20 C 15 28 25 0 C 40 95 85 -20 C 160 470 460 -40 C 2500 7000 7000

K33/K11 1.39 ------- ------

5.2 7.4 6.9n 0.0969 0.0903 0.1146

dn (m) 0.5 0.5 0.5dV/dT (mV/C) 2.55 1.88 1.38

V(10,0,20) 2.14 1.80 1.38V(50,0,20) 2.56 2.24 2.25V(90,0,20) 3.21 2.85 2.83

EM Industry Mixtures

• Thermotropic Liquid Crystal• Anisotropy• Nematic phase• Chirality• Order parameters• Dielectric Anisotropy• Diamagnetism• Birefringence• Elastic constants• Surface Anchoring• Viscosity• Threshold• Defects• Eutectic Mixture

Summary of Fundamentals