Liquid Crystal Materials
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Transcript of Liquid Crystal Materials
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