Dong-A University DDisplay isplay DDevice evice LLabab1/16

Surface Anchoring EnergySurface Anchoring Energy 가 추가된 가 추가된 FFast Q-tensor Mothodast Q-tensor Mothod 를 이용한 를 이용한 pi-cell pi-cell

시뮬레이션시뮬레이션

강완석 *, 허승열 *, 윤형진 **, 이기동 *

* 동아대학교 전자공학과 , ** ㈜ 사나이시스템

E-mail : gdlee@dau.ac.kr

Dong-A University DDisplay isplay DDevice evice LLabab2/16

▷ Introduction

▷ Fast Q-tensor method

▷ The Results of Simulation

▷Conclusion

Contents

Dong-A University DDisplay isplay DDevice evice LLabab3/16

▣ Next generation of LCD

▶ Large size Display, TV, Mobile Display, etc.

1) Wide viewing for family use

Multi-domain Technology

2) Fast response timefor moving pictures

Dynamics simulator

Defects

Introduction

Dong-A University DDisplay isplay DDevice evice LLabab4/16

1) non uniform electric field distribution (ex. PVA, S-IPS, FFS)

2) Phase transition (ex. Pi cell)

Fig 2. Defects in a PVA cell Fig 4. Defects in a FFS cellFig 3. Defects in a S-IPS cellFig 1. Defects in a pi cell

▣ The generation of the Defect

Introduction

Liquid crystal samples may contain defects where the director n is undefined,that is, where there is a discontinuity in the orientation of n.

⇒ We focus on dynamics simulator which can show the defects.

Dong-A University DDisplay isplay DDevice evice LLabab5/16

Vector Method Q-tensor MethodFast Q-tensor

Method

In real nematics, n and –n are equivalent and give the same free energy

density.

-. Vector : different free energies for n and –n.

-. Q tensor : same free energies for n and –n. Fast Q-tensor method can calculate order parameter S (can show the defects).

▣ Comparison

Introduction

Dong-A University DDisplay isplay DDevice evice LLabab6/16

Vector methodDickman’s Q-ten

sor methodFast Q-tensor

method

Normal Dynamics

O O O

Phase Transition X O O

Defect X X O

commercial use O O Is going

etc. easy calculation simple,

short time for calculation

▪ LC Dynamics : Vector method, Q-tensor method, Fast Q-tensor method

Introduction

Dong-A University DDisplay isplay DDevice evice LLabab7/16

Fast Q-tensor Method

2

)2(4

2203

)3(6

11332

)2(3

24

2

)2(2

2422112

)2(1

221133

9

4)(

27

2

9

2

)3(9

2)3(

27

1

S

GKq

S

GKK

S

GK

S

GKKK

S

GKKKfs

j

VV

S

QVVVf

j

jkkjje

,

,,2

,0

,,3

2

)(2

1

▪ Q-tensor form of electric free energy

▪ Q-tensor form of strain free energy

Dong-A University DDisplay isplay DDevice evice LLabab8/16

▣ What is a Fast Q-tensor method?

Fast Q-tensor Method

질서도 질서도 SS 는 온도에 직접으로 관련되기 때문에 온도의 함수로써 질서도 는 온도에 직접으로 관련되기 때문에 온도의 함수로써 질서도 SS 를 결정를 결정

2 5

1 1( ) ( ) ( )

2 31

( )( ) ( )4

t ij ji ij jk ki

ij ij

f T fo A T Q Q B T Q Q Q

C T Q Q O Q

온도 에너지 밀도를 간단한 다항식의 전개를 사용하여 아래의 식으로 표현온도 에너지 밀도를 간단한 다항식의 전개를 사용하여 아래의 식으로 표현

Dong-A University DDisplay isplay DDevice evice LLabab9/16

[f[fgg]]QQjkjk = strain term([f = strain term([f

gg]]SS) + voltage term([f) + voltage term([fgg]]VV) + temperature term([f) + temperature term([f

gg]]TT))

Fast Q-tensor Method

11 2211 22 33 , ,2 2

24, 33 11 , , , , ,2 3

, , , 0 22 ,2

0 , ,

1 2 3

( )2 1 1 1[ ] ( )

12 4 121

( )(4

2)

1[ ]

2

[ ] ( )

g S jk ll jl lk

jl lk lm j lm k lm l jk m lm jk ml

lm m jk l lm jk lm jlm mk l

g V e j k

g Tni

K Kf K K K Q Q

S SKQ K K Q Q Q Q Q Q

S S

Q Q Q Q q K e QS

f e DV V

Tf A A Q Q A Q Q

T

4

, ( )jkjk ll

Q A Q Q Q Q

QQ

l l

Dong-A University DDisplay isplay DDevice evice LLabab10/16

QQS

S

nnS

nnnnnnnS

nnnnnnnnnnnnS

nnnnnn

nnnnnn

nnnnnn

nnnnnn

nnnnnn

nnnnnn

SQQ

nnnI

nnSQ

3

2

2

3

)3

1221(

4

9

}3

1)(2){(

4

9

}3

1)(

3

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4

9

3

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13

1

3

13

13

1

4

9

1 }3

{2

3

2

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23

2

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22

21

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222

21

2

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21

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22

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21

22

21

43

42

41

2

333231

322221

312111

333231

322221

312111

2

23

22

21

Fast Q-tensor Method

Dong-A University DDisplay isplay DDevice evice LLabab11/16

W : anchoring strengthQjk : Q with strong anchoringQ’

jk: Q of a LC director

zjk

sur

yjk

sur

xjk

sur

jk

sursur dQ

df

dz

d

dQ

df

dy

d

dQ

df

dx

d

dQ

dff

,'

,'

,''

][

)'(][ jkjkQsur QQWfjk

)(2

3][][][ jikkijQsur

i

jkQsurnisur nn

Sf

n

Qff

jkjk

• Rapinni-Papular Equation

2)'(2

1jkjksurface QQWf

Fast Q-tensor Method

Dong-A University DDisplay isplay DDevice evice LLabab12/16

l

Qjk

lllQjk

QQWfg

QQQQAQQQAQQT

TAAfg

VVDefg

QeKqS

QQQQQQQQQQ

KKS

QS

K

QS

KKQKKK

Sfg

jkjkSur

inT

kjeV

lmkjlm

lmjklmljkmlmmljklmmjkllmklmjlm

lkjl

lkjllljkS

,

)'(][

)(][

2

1][

2

)(4

1

)()

12

1

4

1

12

1(

2][

4321

,,0

,2202

,,,,,,,,

11333,224

,22211

,3322112

[f[fgg]]QQjkjk = strain term([f = strain term([fgg]]SS) + voltage term([f) + voltage term([fgg]]VV) + temperature term([f) + temperature term([fgg]]TT) )

+ surface term([f+ surface term([fgg]]sursur))

Fast Q-tensor Method

Dong-A University DDisplay isplay DDevice evice LLabab13/16

m10

m100

m20 m50 m30

ElectrodesElectrodes

K11 14.4pN 10.7

K22 6.9pN 3.7

K33 18.3pNPretilt angle

5

< Liquid Crystal Parameter >< Liquid Crystal Parameter >

< A Simulated Structure >< A Simulated Structure >

The Results of Simulation

Dong-A University DDisplay isplay DDevice evice LLabab14/16

(a) 1.53V (a) 1.55V

(a) 1.6V (a) 1.8V

< 강한 고정에너지를 고려한 pi-cell 의 모델링 결과 >

The Results of Simulation

Dong-A University DDisplay isplay DDevice evice LLabab15/16

(a) 1.53V (a) 1.55V

(a) 1.6V (a) 1.8V

< 약한 고정에너지를 고려한 pi-cell 의 모델링 결과 >

The Results of Simulation

Dong-A University DDisplay isplay DDevice evice LLabab16/16

기존의 Fast Q-tensor method 에 Rapinni – Papoular 방정식을

기반으로 하는 고정에너지항을 추가

고정에너지항이 추가된 Fast Q-tensor method 를 이용하여

pi-cell 의 defect 의 생성 위치와 표면 영역의 질서도 S 값 계산

표면 영역에서 약한 고정에너지를 고려하여 pi-cell 을 시뮬레이션

한 결과 , 정확한 defect 위치 및 표면 영역의 질서도 S 값을

계산할

수 있음

Multi-domain 을 가지고 있는 액정 모드에 고정에너지를 고려한

fast Q-tensor method 를 이용할 경우 더욱 정확한 액정의

동특성을

확인 할 수 있을 것으로 판단됨

Conclusion