Transcript Dielectric Constants (@20 C, 1kHz) De e

Dielectric Constants (@20oC, 1kHz)
*Mixture
Application
De
e
e
BL038
MLC-6292
ZLI-4792
TL205
18523
95-465
PDLCs
TN AMLCDs
TN AMLCDs
AM PDLCs
Fiber-Optics
-De material
16.7
7.4
5.2
5
2.7
-4.2
21.7
11.1
8.3
9.1
7
3.6
5.3
3.7
3.1
4.1
4.3
7.8
*EM Materials
Materials
Vacuum
Air
Polystyrene
Polyethylene
Nylon
Water
Dielectric Constant
1.0000
1.0005
2.56
2.30
3.5
78.54
Dielectric Constants:
Temperature Dependence
e
16
CH3-(CH2)4
De  S(T )
14
Dielectric Constant
4’-pentyl-4-cyanobiphenyl
12
Temperature Dependence
Extrapolated from isotropic phase
10
8
eis
1
De   2e   e // 
3
e
30
T-TNI (°C)
De  S(T )
Average Dielectric Anistropy
6
25
C N
35
1
De   2e   e // 
3
Magnetic Anisotropy: Diamagnetism
Diamagnetism: induction of a magnetic moment in opposition
to an applied magnetic field. LCs are diamagnetic due to the
dispersed electron distribution associated with the electron
structure.
Delocalized charge makes
the major contribution to
diamagnetism.
Ring currents associated with
aromatic units give a large
negative component to c for
directions  to aromatic ring
plane. Dc is usually positive since:
Dc  c ll  c   0
c ll  c 
Magnetic Anisotropy: Diamagnetism
Dc /10 9 m3 kg 1
Compound
C5H11
CN
1.51
C7H15
CN
1.37
CN
0.46
CN
0.42
C5H11
C7H15
CN
C7H15
-0.38
Optical Anisotropy: Birefringence
ordinary ray (no, ordinary index of refraction)
extraordinary ray (ne, extraordinary index
of refraction)
Optical Anisotropy: Birefringence
n  no
ordinary wave
extraordinary wave
1 cos2 q sin2 q


2
2
n
no
ne2
optic
axis
q
For propagation along the optic
axis, both modes are no
Optical Anisotropy: Phase Shift
analyzer
liquid
crystal
f = 2pdno,e/l
Df  fe  fo=2pdDn/l
Dn = ne - no
0 < Dn < 0.2
polarizer
depending on deformation
380 nm < l < 780 nm
light
visible light
Birefringence (20oC @ 589 nm)
EM Industry
Mixture
BL038
TL213
TL205
ZLI 5400
ZLI 3771
ZLI 4792
MLC-6292
ZLI 6009
MLC-6608
95-465
MLC-6614
MLC-6601
18523
ZLI 2806
Dn
0.2720
0.2390
0.2175
0.1063
0.1045
0.0969
0.0903
0.0859
0.0830
0.0827
0.0770
0.0763
0.0490
0.0437
ne
1.7990
1.7660
1.7455
1.5918
1.5965
1.5763
1.5608
1.5555
1.5578
1.5584
----------------1.5089
1.5183
no
1.5270
1.5270
1.5270
1.4855
1.4920
1.4794
1.4705
1.4696
1.4748
1.4752
----------------1.4599
1.4746
Application
PDLC
PDLC
AM PDLC
STN
TN
AM TN LCDs
AM TN LCDs
AN TN LCDs
ECB
-De devices
IPS
IPS
Fiber Optics
-De device
Birefringence: Temperature
Dependence
Average Index
ne
1.8
Index of Refraction
n
1.7
n

1
 ne 2  2n02
3
2
2


1 2
 ne  2n02
3
niso
Extrapolated from isotropic phase
1.6
no
Temperature
Dependence
1.5
Dn  S(T )
1.4
50
40
30
T-TNI (°C)
20
10
0

Birefringence Example: 1/4 Wave Plate
What is minimum d for
liquid crystal 1/4 wave plate ?
circular polarized
linear polarized
Unpolarized
d LC: Dn=0.05
polarizer
1
Ne  No 
4
Takes greater number of e-waves
ned nod 1
than o-waves to span d, use


Dn=0.05
l
l
4
1 l
589nm
d

 2,950 nm  2.95  m
4 Dn 4  0.05 
Nematic Elasticity: Frank Elastic Theory
1
2
2
2










{
K
(
n
)
K
(
n
n
)
K
(
n
n
)
} dV
11
22
33

2V
1
  { K 24  ( n    n + n   n )  K 13   ( n   n )} dV
2V
Dc
1
1
2
Fe    e o D e ( E  n ) dV   o
( B  n ) 2 dV
2V
2 V co
Fd 
1
Fs  W0  sin 2 q  q 0  dS
2
s
Splay, K 11
Twist, K 22
Bend, K33
Surface Anchoring
Alignment at surfaces propagates over macroscopic distances
microgrooved surface homogeneous alignment (//)
rubbed polyimide
ensemble of chains homeotropic alignment ()
surfactant or silane
Surface Anchoring
N
q
n
polar
anchoring
Wq
f
azimuthal
anchoring
Wf
Strong anchoring
Weak anchoring
10-4 J/m2
10-7 J/m2
Wq,f 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
Mixture
K11
(pN)
K22
(pN)
K33
(pN)
Application
BL038
TL205
ZLI 4792
ZLI 5400
ZLI-6009
13.7
17.3
13.2
10
11.5
----------6.5
5.4
5.4
27.7
20.4
18.3
19.9
16.0
PDLC
AM PDLC
TN AM LCD
TN
AM LCD
Order of magnitude estimate of elastic constant
1014 ergs
6
11
Kii  

10
dynes

10
N  10 pN
8
a
10 cm
U
U: intermolecular interaction energy
a: molecule distance
Elastic Constant K22:
Temperature Dependence
K  S2 (T )
K22 (x 10-12 Newton)
7
P-a
zox
yp
6
he
ne
tol
e
5
P-a
z
4
oxy
ani
sol
e (P
AA
3
)
2
-30
-20
-10
T-TNI (°C)
0
The Flexoelectric Effect
+
Undeformed
state of banana
and pear shaped
molecules
Polar structure
corresponds to
closer packing
of pear and
banana molecules
Bend
Splay
Polar Axis
+
Effects of an Electric Field
n
E
q
y
x
e
n  sinq x  cos q y
E  Eo y
e
1
1
2
2
fe  e o De  E  n   e o De Eo cos2 q Electric Free Energy Density
2
2
df
1
2
Electric Torque Density
e  e  e o De Eo sin  2q 
dq 2
Using De = 5 and E=0.5 V/m
2
1
1
2
12
2
2
6
e o De Eo   8.85  10 C / N  m   5   0.5  10 V / m   5.5 N / m 2
2
2
Effects of an Magnetic Field
n
B
q
y
n  sinq x  cos q y
B  Bo y
x
c
c
1 Dc
1 Dc 2
2
fe 
Bo cos2 q
B  n  
2 o
2 o
dfb 1 Dc 2
e 

Bo sin  2q 
dq 2 o
Magnetic free energy density
Magnetic torque density
Using Dc = 10-7 m3kg-1 and B= 2 T = 20,000 G
1 Dc 2 1
2
7
7
3
1
Bo   4p  10 N / A 10 m  kg   2T   0.2 N / m 2
2 o
2
Deformation Torque
Surface
q
x
q p 
 2p
tan     exp 
2 4
d
1  q 
fd  K   cos2 q
2  x 

x

d
Orientation of molecules obeys this eq.
2
dfd 1  2p 
 2p 
 K   sin  2q   K   q
dq 2  d 
d 
2
d 
Free energy density from elastic theory
2
Torque density
Surface
Deformation Torque
 2p 
d  K   q
d 
2
q
x
d
3
8
 2p  10 N   2p 
2
K  

15
N
/
m
 15Pa
2
6
 d 
5

10


2
Material
Steel
Silica
Nylon
11
2
Shear Modulus
3
100 GPa
Shear modulus  Young’s modulus
40 GPa
8
1 GPa
Coherence Length: Electric or Magnetic
Surface
E
q
1  2p 
1
d  e  K   sin  2q   e o De E 2 sin  2q 
2  d 
2
2
 K 1
d  2p 

e
D
e
 o E

Balance torque
Find distance d
 K 1
d
p 

2
e
D
e
 o E
10
d
x
Coherence length 
N
Using E = 0.5 V/m
1
 p
 1.5  m
6
12 2
2
and De = 20
8.85  10 C / N  m   20  0.5  10 V / m
11
Viscosity: Shear Flow Viscosity Coefficient
h11
h22
h33
v
n
n
n  v
n  v
shear stress ( )
h
velocity gradient (v )
n
n v
n v
Typically h22 > h33 >h11
Viscosity: Flow Viscosity Coefficient
LC specification sheets give
kinematic viscosity in mm2/s
h
n 

Dynamic Viscosity h
1 kg/m·s = 1 Pa·s
0.1 kg/m·s = 1 poise
Kinematic Viscosity n
1 m2/s
Approximate density
kg
  1000 3
m
Viscosity: Flow Viscosity Coefficient
2
 1m 
3
3
hii  20 mm2 / s      20 mm 2 / s   3
10
kg
/
m
 0.02 kg / ms  0.2 poise



 10 mm 
Typical
Flow
Viscosity
Conversion
EM Industry
MIXTURE
CONFIGURATION
ZLI-4792
ZLI-2293
MLC-6610
MLC-6292
18523
TL205
BL038
TN AM LCDs
STN
ECB
TN AM LCDs (Tc=120oC)
Fiber Optics (no=1.4599)
PDLC AM LCD
PDLCs (Dn=0.28)
Density

Conversion
0.1 kg/ms = 1 poise
Kinematic (n)
(mm2/s)
Dynamic (h)
(Poise)
15
20
21
28
29
45
72
0.15
0.20
0.21
0.28
0.29
0.45
0.72
Viscosity: Temperature Dependence
N
H3CO
C4H9
Viscosity (poise)
1.0
For isotropic liquids
h2
 E 

K
T
 B 
0.7
0.4
0.2
hiso  h0 exp 
E is the activation energy for
diffusion of molecular motion.
h3
h1
TNI
0.1
20
30
40
50
Temperature (°C)
60
Viscosity: Rotational Viscosity Coefficient
n
Time
n
n
Rotation of the director n bv external
fields (rotating fields or static).
Viscous torque's v are exerted on a liquid
crystal during rotation of the director n
and by shear flow.
dq
v   1
dt
1: rotational viscosity coefficient
Viscosity: Rotational Viscosity Coefficient
n
n
EM Industry
MIXTURE
ZLI-5400
ZLI-4792
ZLI-2293
95-465
MLC-6608
CONFIGURATION
TN LCDs
TN AM LCDs
STN
-De Applications
TN AM LCD

n
Viscosity
(mPas)
109
123
149
185
186
Viscosity
(Poise)
1.09
1.23
1.49
1.85
1.86
1 Pa 
 0.109 Pa  s  0.109 kg / m  s  1.09 poise

3
 10 mPa 
 1  109 mPa  s  109 mPa  s 
Viscosity: Comparisons
Material
Viscosity (poise)
Air
Water
Light Oil
Glycerin
10-7
10-3
10-1
1.5
LC-Rotational (1)
LC-Flow (hii)
1< 1 < 2
0.2< hii<1.0
Relaxation from Deformation
field on state
Surface
E
x
Surface
Relaxation when field is turned off
Relaxation time 
zero field
state
x
d  visc
Balance viscous/deformation torque
dq
 2p 
K
q   1

dt
 d 
2
q  q o exp  t /  
10


10


1
 1d 2
where  
2
K  2p 
kg / ms 10 m 
(10
1
Assume small deformations
4
11
N )  2p 
2
(10
N )  2p 
2
Solution
2
 2.5 s
kg / ms  5  10 m 
6
11
Surface
Relaxation from Deformation
For 100 m cell
2
 6 ms
For 5 m cell
x
Freedericksz Transition The Threshold I
y
z
E
x
d

E
n
q
Ec
x
y
n
At some critical E
field, the director
rotates, before Ec
nothing happens

n  cos q  z  ,sin q  z  ,0
1
2
2
2
Fd   K11    n   K 22  n    n   K33  n    n  dV
2 VOL


0
 dq 
K 22  

 dz 
2
0
Freedericksz Transition The Threshold II
2
2
1
1
Fe   e o De E  n dV   e o De E sin2 q dV
2 VOL
2 VOL
2


1 
 dq 
2
2 
F  Fd  Fe   K 22 
 e o De E sin q  dz

2 0 
 dz 

E-field
free energy
d


F d  F 

0

q dz   dq  
   dz  

 
Minimize free energy with
‘Euler’ Equation
total
free energy
Freedericksz Transition The Threshold III
ETH

2

e
D
e
E
sinq cos q  0
 o

p


K 22
p


d e o De  5  10 6 m 
soln.
10 11 N
12
2
2
8.85

10
C
/
Nm

 (10) small q
V
V
 200,000  0.2
m
m
VTH
differential equation

V 
 ETH d   0.2
 5  m   1volt

m 

mid-layer tilt (deg)
 d 2q
K 22  2
 dz
threshold
1.0
E/Ec
Defects
s=1/2
s=+1
s=3/2
s=-1/2
s=+1
s=+2
s=-1
s=+1
The singular line
(disclination) is pointing
out of the page, and director
orientation changes by
2ps on going around the
line (s is the strength)
Estimate Defect Size
The simplest hypothesis is that the core or defect
or disclination is an isotropic liquid, therefore the
core energy is proportional to kBDTc. Let M be the
molecular mass, N Avogadadro’s number and 
the density of the liquid crystal.
l 2p R
R
R 
1
dr
2
Fe     K11    n  rdrdf dz  p lK11 
 p lK11 ln  
2 z 0 f 0 r rc
r
 rc 
rc
F  Fe  Fcore
R 
 N 
 p lK11 ln    k B DTc p rc2l  

r
M


 c
F
 0  rc 
rc
1  M   K11 




2   N   k B DTc 


1
1011 N
26
2

10 m  

23
 10 J / K  10K  
2


 rc  3  108 m  30 nm
Microscopic Fluttering and Fluctuations
• Characteristic time  of
Fluctuations:
1
1


2
2
Kq
 2p 
K

l



Thermally induced
Deformations
0.1kg / m  s
2p


11
10
N

  589  109 m 
2
 100  s
• Can see fluctuations with
microscope:
• Responsible for opaque
appearance of nematic LC
General Structure
Z’
Z
Y
A
X
• Aromatic or saturated ring core
• X & Y are terminal groups
• A is linkage between ring systems
• Z and Z’ are lateral substituents
CH3 - (CH2)4
C N
4-pentyl-4’-cyanobiphenyl (5CB)
Common Groups
Mesogenic Core
Ring Groups
Linking Groups
phenyl
N
pyrimidine
N
cyclohexane
biphenyl
terphenyl
diphenylethane
stilbene
tolane
schiffs base
azobenzene
azoxybenzene
phenylbenzoate
(ester)
phenylthiobenzoate
 CH2  CH2 
 CH  CH 
 CH  CH 
 CH  N 
N N
O
N N
O
CO
O
CS 
Nomenclature
Mesogenic Core
terphenyl
biphenyl
phenyl
benzyl
benzene
phenylcyclohexane (PCH)
3’
2’
2
3
1’ 1
4’
5’
6’
cyclohexane
cyclohexyl
4
6
5
Ring Numbering
Scheme
Terminal Groups
(one terminal group is typically an alkyl chain)
CH2
CH2
CH2
CH3
CH2
CH2
CH3
C*H
straight chain
branched chain
(chiral)
CH3
Attachment to mesogenic ring structure
Direct
alkyl (butyl)
Ether
-O- alkoxy (butoxy)
Terminal Groups
CH3-
methyl
CH3-O-
methoxy
CH3-CH2-
ethyl
CH3-CH2-O-
ethoxy
CH3-(CH2)2- propyl
CH3-(CH2)2-O- propoxy
CH3-(CH2)3- butyl
CH3-(CH2)3-O- butoxy
CH3-(CH2)4- pentyl
CH3-(CH2)4-O- pentoxy
CH3-(CH2)5- hexyl
CH3-(CH2)5-O- hexoxy
CH3-(CH2)6- heptyl
CH3-(CH2)6-O- heptoxy
CH3-(CH2)7- octyl
CH3-(CH2)7-O- octoxy
Second Terminal Group and
Lateral Substituents (Y & Z)
H
F
Cl
Br
I
CH3
CH3(CH2)n
CN
NH2
N(CH3)
NO2
flouro
chloro
bromo
iodo
methyl
alkyl
cyano
amino
dimethylamino
nitro
phenyl
cyclohexyl
Odd-Even Effect
Clearing point versus alkyl chain length
O
CH3-(CH2)n-O
C-O
O-(CH2)n-CH3
clearing point
18
16
14
12
10
0 1 2 3 4 5 6 7 8 9 10 11
carbons in alkyl chain (n)
Nomenclature
Common molecules which exhibit a LC phase
CH3-(CH2)4
C N
4’-pentyl-4-cyanobiphenyl
CH3-(CH2)4-O
C N
4’-pentoxy-4-cyanobiphenyl
Structure - Property
vary mesogenic core
CH3-(CH2)4
A
A
C N
C-N (oC)
N-I(oC)
Dn
De
22.5
35
0.18
11.5
71
52
0.18
19.7
31
55
0.10
9.7
N
N
Structure - Property
vary end group
COO
CH3-(CH2)4
X
H
F
Br
CN
CH3
C 6H 5
X
C-N (oC)
N-I (oC)
87.5
92.0
115.5
111.0
106.0
155.0
114.0
156.0
193.0
226.0
176.0
266.0
Lateral Substituents (Z & Z’)
Z’
Z
X
A
Y
• Z and Z’ are lateral substituents
• Broadens the molecules
• Lowers nematic stability
• May introduce negative dielectric anisotropy
Why Liquid Crystal Mixtures
Melt Temperature:
Liquid Crystal-Solid
Temperature
Isotropic Liquid
ln ci = DHi(Teu-1 - Tmi-1)/R
Liquid
Crystal
DH: enthalpies
Teu: eutectic temperature
Tmi: melt temperature
R: constant
E
eutectic
point
Solid
0
50
Concentration (c2), %
100
Nematic-Isotropic
Temperature: TNI
TNI = S ciTNIi
EM Industry Mixtures
S-N
<-40 C
solid nematic transition (< means supercools)
Clearing
+92 C
nematic-isotropic transition temperature
Viscosity (mm2 /s)
+20 C
0C
15
40
flow viscosity, some materials may stipulate the
rotational viscosity also. May or may not give
a few temperatures
K33/K11
1.39
ratio of the bend-to-splay elastic constant
De
5.2
dielectric anisotropy
Dn
0.0969
optical birefringence (may or may not give ne, no)
dDn (m)
0.5
product of dDn (essentially the optical path length)
dV/dT (mV/oC)
2.55
how drive voltage changes as temperature varies
V(10,0,20)
V(50,0,20)
V(90,0,20)
2.14
2.56
3.21
threshold voltage (% transmission, viewing angle,
temperature)
EM Industry Mixtures
Property
S-N
ZLI 4792
<-40 C
MLC 6292/000
<-30 C
MLC 6292/100
<-40 C
Clearing
+92 C
+120 C
+120 C
Viscosity (mm2 /s)
+20 C
0C
-20 C
-40 C
15
40
160
2500
28
95
470
7000
25
85
460
7000
K33/K11
1.39
-------
------
De
Dn
5.2
0.0969
7.4
0.0903
6.9
0.1146
dDn (m)
dV/dT (mV/C)
0.5
2.55
0.5
1.88
0.5
1.38
V(10,0,20)
V(50,0,20)
V(90,0,20)
2.14
2.56
3.21
1.80
2.24
2.85
1.38
2.25
2.83
Summary of Fundamentals
• Thermotropic Liquid Crystal
• Anisotropy
• Nematic phase
• Chirality
• Order parameters
• Dielectric Anisotropy
• Diamagnetism
• Birefringence
• Elastic constants
• Surface Anchoring
• Viscosity
• Threshold
• Defects
• Eutectic Mixture