Akihiko Sugimura1 and Geoffrey R. Luckhurst2

1Osaka Sangyo University, Japan2Southampton University, U.K.

1. Background of the investigation

2. Advantages of Deuterium NMR spectroscopy

3. General and curious director alignments

4. Discussion on the curious director alignment

Layout of the talk

Director dynamics for a low molar mass nematic liquid crystal

Director dynamics for a low molar mass nematic liquid crystal

Int. Conf. on the Hierarchical Structures in Complex FluidsBeijing, 4-8th of July, 2011 　 (presented on 7th of July)

Thin nematic liquid crystal cell

Glass substrate Glass substrate

L.C. bulk

Bulk surface

Basic interest is in understanding the nature

of the spatial director distribution.

For this aim the field-induced director

alignments are investigated.

Methodology?

Aim of the investigationAim of the investigation

A sample is low molar mass nematics confined in a thin sandwich cell.

How to produce a non-equilibrium state of the director orientation in the strong magnetic field.

Spinningas used for polymer nematics

Spinning the sample tube

Magnetic field

Electric fieldField-induced director alignment by the electric and magnetic fields

Nematic cell B

E

NMR spectroscopyNMR spectroscopy

The quadrupolar splitting ratio, 　 ()/0, gives the angle made by the director with the magnetic field.

=0

/kHz

=54.7

=90 2

0

3cos 1

2

Bn～

B

q～ nDn

Dn0

( )ii

I I

Advantages of Deuterium NMR spectroscopyAdvantages of Deuterium NMR spectroscopy

B

SCM

LC cell

Ultra Sonic Motor

Receiver Coil

E

U.S.M

Glass plateB

n

TURN-ON

TURN-OFF

E

NCCCCCCH D

D

HHH

HH HH

H

4 42 n pentyl d cyanobiphenyl , 'Time-resolved and -averaged measurements during the director relaxation processes are possible.

[1] G. R. Luckhurst, T. Miyamoto, A. Sugimura, T. Takashiro, B. A. Timimi, Journal of Chemical Physics, 114, 10493 (2001).

Experimental geometry [1]Experimental geometry [1]

Static properties of

the director alignments

Static properties of

the director alignments

E

B n

E

Bn

n

E

B

α=85.1°T=20C

0V

200V

138.5V

130V

140V

155V

144V

175V

(kHz)

125V

135V

=85.1o

d0=194.7m

-40 -20 0 20 40

Voltage dependence of the NMR spectra (1)Voltage dependence of the NMR spectra (1)

Uniform director alignmentUniform director alignment

E

B n

E

Bn

n

E

B

α=89.1°T=20C

136V

0V

134.5V

(kHz)

139V

133V

200V

137.5V

137V

160V

130V

140V

-40 -20 0 20 40

Voltage dependence of the NMR spectra (2)Voltage dependence of the NMR spectra (2)

Uniform director alignment

Broadening of the spectral line-shape

Uniform director alignment

Broadening of the spectral line-shape

Uniform director alignment

can be generally described

by the continuum theory

for < 90.

Uniform director alignment

can be generally described

by the continuum theory

for < 90.

General understandingGeneral understanding

Voltage dependence of the static NMR spectra

α=89.9°T=20C

E

B

n

E

B n

E

B

n

n

0V

200V

135.7V

135.6V

135.9V

135.8V

136.1V

136V

136.2V

136.3V

136.4V

(kHz)-40 -20 0 20 40

Voltage dependence of the NMR spectra for 90Voltage dependence of the NMR spectra for 90

1 E

M

U

U

2D powder pattern2D powder pattern

Non-uniform director alignmentNon-uniform director alignment

What causes a non-uniform

static director alignment?

What causes a non-uniform

static director alignment?

The cell used in the measurements has an inhomogeneity of the film thickness with 0.25%

( )d d d x d d

( )x

( )d x

at one sided d

at middle

at the other sided d

x

z

No director deformation along the z-axis,

No surface anchoring effect for a thicker cell without any surface treatments

( ), ( ), ( )x d x E x are a function of x.

( )E x

Linear change of the film thickness along the x-axis causes an electric field gradient. That is,

d=d 0.33%

/o

V/V

=9.26x106

d=195.7m

VTH=136.1V=1

: =89.99o

: =89.9o

: =89.1o

: =88.0o

125 130 135 140 1450

30

60

90

Inhomogeneity of the film thickness causes aspread of the range of the director orientation. Inhomogeneity of the film thickness causes aspread of the range of the director orientation.

Inhomogeneity of the film thicknessInhomogeneity of the film thickness

: Top: Middle: Bottom

y - position

Thi

ckne

ss/

m

0 10 20 30196

198

200

202

Thi

ckne

ss/

m

196

198

200

202

y-axis

top

middle

bottom

Measured 90 points of the cell

Top line

Middle line

Bottom line

Measurement of the film thicknessMeasurement of the film thickness

g()

=(d-(d0-d))/(2d)

=0.2d0=196md=d0/200m

d=d0d=d0-d d=d0+d

0 0.5 1

0

0.5

1

1.5

2

2

2

( 0.5)

21( ) ,

2g e

Gaussian variation for the inhomogeneity of the film thickness is assumed.

d0=199.8 m

Num

ber

of P

oint

s

Thickness (m)196 198 200 2020

2

4

6

8

10

Profile of the film thickness in the bulkProfile of the film thickness in the bulk

d d 0

0.5%,

It is clear that the inhomogeneity of the film thickness is a dominant factor to cause uniform and non-uniform director alignments.

It is clear that the inhomogeneity of the film thickness is a dominant factor to cause uniform and non-uniform director alignments.

It is also apparent that there are some other factors influencing the director alignment.

It is also apparent that there are some other factors influencing the director alignment.

As a basic idea, let’s return to the continuum theory to understand the curious director distribution.

As a basic idea, let’s return to the continuum theory to understand the curious director distribution.

Cell structure

Elastic deformation induced by Teflon spacersElastic deformation induced by Teflon spacers

Cross section of the cell

5CB-d2

6mmW

200 midx

z

e

2

22

0

( )sin 2 sin 2( ) ,

2

d zK B

dz

00

sin 2( ),2 p

z

d A

dz K

22 20E

0 0 MM 0

, , ,2 2E

U EU B U E

U B

1

2 2 2

0

1 2 cos2 ,2

C BK

Torque balance equations

Coordinate system

In the bulk

at the surface [2]

1

2(2 ) sin( ). d

Cdz

at the middle of the bulk

2

0

W

z

d

dz

0

21 ( 0, , ),id d i d i N

N

Teflon spacer

B

n

E

z

e min

W

y

x

Glass substrate

Sliced piece

2

0i

i N

id

[2] A. Sugimura, G. R. Luckhurst, and Z. Ou-Yang, Physical Review E, 52, 681 (1995).

Torque Balance EquationsTorque Balance Equations

2( )

dzf

W d

Conservation of the director density

0( ) f d C dz

min

/20

00

0

( ) 1,2

2 / .

W WC

f d C dz

C W

Torque balance equations

2 sin( ) d

Cdz

Director distribution function

1 2 1( ) .

sin( )f

W C

MIN

1

2min min(2 ) sin( ) sin 2 .

2

AC

K

2

1 cos 2cos2 .

1 2 cos2

at the boundary

at the middle of the bulk

A=1x10-5J/m2

A=5x10-6J/m2

A=5x10-5J/m2

A=5x10-7J/m2

A=5x10-4J/m2

V=160V=89.1o

MIN=-0.074o

INF=86.7o

d=196m=1.27

z/m

(z)

/o

0 2 4

0

30

60

90

5CB-d2

Cross section of the cell

Director probability density function

is analytically derived for

our experimental geometry.

Director probability density function

is analytically derived for

our experimental geometry.

Director probability density functionDirector probability density function

(a) (b)=89.1 =89.9

( )1 2( ) .

sin( ( ) )

Ni

i i

gdf

NW C d 12( ) , ( ), ( ) ( )sin .I G T f

V=200VV=0V

130V

145V

/o

f()

=89.1o

=0.2d=0.5

133V

137V135V138V

142V

140V

136V

0 30 60 900

0.2

0.4

0.6

0.8

1V=200V

V=0V

135.0V

137.0V

/of()

=89.96o

=0.2d=0.5

135.4V

135.6V

135.8V136.0V 136.2V

136.8V

136.6V136.4V

0 30 60 900

0.2

0.4

0.6

Voltage dependence of the director distributionVoltage dependence of the director distribution

136V

0V

134.5V

/kHz

139V

133V

200V

137.5V

137V

160V

130V

140V

-40 -20 0 20 40

T=20C, α=89.1°

0V

200V

135.7V

135.6V

135.9V

135.8V

136.1V

136V

136.2V

136.3V

136.4V

/kHz-40 -20 0 20 40

T=20C, α=89.9°

Comparison of the recorded spectra with those simulated

Comparison of the recorded spectra with those simulated

1. A preliminary model has been proposed to understand the factors influencing the nature of the director distribution for a low molar mass nematic.

2. It has been found that the director alignment by Teflon surfaces is essential in order to account for some subtle features of the NMR spectra as the angle between the two fields approaches 90.

3. In addition some of the major spectral features are found to result from the inhomogeneity in the cell thickness.

1. A preliminary model has been proposed to understand the factors influencing the nature of the director distribution for a low molar mass nematic.

2. It has been found that the director alignment by Teflon surfaces is essential in order to account for some subtle features of the NMR spectra as the angle between the two fields approaches 90.

3. In addition some of the major spectral features are found to result from the inhomogeneity in the cell thickness.

[3] H. Hamasuna, G. R. Luckhurst, A. Sugimura, B. A. Timimi, H. Zimmermann, Phys. Rev. E, in the press.

Summary for the static properties [3]Summary for the static properties [3]

1. The static and dynamic director distributions of 5CB-d2 were investigated using a combination of deuterium NMR spectroscopy and the continuum theory.

2. The experimental results can be understood in terms of the intrinsic director distribution affected by the external fields.

3. The challenge now is to see what kinds of features such as director fluctuation or deformation are responsible for the intrinsic distribution and how this is created during the director relaxation process.

1. The static and dynamic director distributions of 5CB-d2 were investigated using a combination of deuterium NMR spectroscopy and the continuum theory.

2. The experimental results can be understood in terms of the intrinsic director distribution affected by the external fields.

3. The challenge now is to see what kinds of features such as director fluctuation or deformation are responsible for the intrinsic distribution and how this is created during the director relaxation process.

CONCLUSIONS OF THE TALKCONCLUSIONS OF THE TALK

1. Graduate students of my group (Osaka Sangyo University)2. Dr. Bakir A Timimi (University of Southampton, UK)3. Dr. Herbert Zimmermann (Max-Planck-Institute, Heidelberg, Germany )4. Prof. Edward T. Samulski (University of North Carolina, USA)5. Prof. Jim W. Emsley (University of Southampton, UK)6. Dr. Tetsuo Miyamoto (JEOL)7. Dr. Anu Kantola (University of Oulu, Finland) 8. Dr. Peter J. Le Masurier (Kodak)9. Dr. Christopher J Dunn (Merck UK)10. Dr. Mario Cifelli (University of Pisa, Italy)11. The Ministry of Education, Culture, Sports, Science and Technology of Japan 12. The Japan Society for the Promotion of Science13. The Royal Society, UK14. JEOL

AcknowledgementsAcknowledgements