Measurement of Elastic Constants of Liquid Crystal Material

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Oct 18, 2013 (3 years and 5 months ago)

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Characterization Lab, Liquid Crystal Institute


1

Measurement of Dielectric, Dimagnetic, and Elastic Constants of

Liquid Crystal Material


By Liou Qiu,


Under certain external forces such as electric field or magnetic field, some deformation
will be happen within the liquid crystal.


Just as we learnt i
n general physics: when a force exerts onto a spring, the spring would
become extended or suppressed. The spring was described as being deformed.

In the case of liquid crystal, when the external force exert and exceed a certain value,
deformation will ha
ppen. The relative position of the LC molecules will be changed.
They were forced to splay, twist and bent until equilibrium. When the system is in
equilibrium, it is in minimum energy status.

Generally speaking, There are three deformations: splay, twist

and bent. ( see Fig1.) Not
only external field can cause these deformations. The alignment of the substrates also can
cause these deformations. For example, wedged cells makes the LC molecules arrange
themselves in splay and TN cell makes the molecule arr
anged in twist.

Further study shows:



f=1/2[k
11
(


n
)
2

+k
22
(
n


x
n
)
2

+k
33
(
n
x

x
n
)
2
]

Where
n
is the unit director of the liquid crystal;

f is the free energy density; Free energy density was defined as the free energy in a unit
volume of LC.

k
11
, k
22
,
and k
33

are called elastic constant of liquid crystal.

K
11
corresponds to the deformation of splay;

K
22

corresponds to the deformation of twist;

K
33

corresponds to the deformation of bend.

.

Fig.1 Three deformations of liquid crystal


Characterization Lab, Liquid Crystal Institute


2

Different liquid cry
stal material has different K
11
. The unit of K
11

is newton or erg.

Let us estimate the magnitude of K
11
:

U : intermolecular interaction energy (~10
-
14
ergs);

a: molecular distance (~10
-
8

cm);

K
11

~U/a~ 10
-
6

dynes =10
-
11

newtons.

Present research indicate
s

some new features: a fourth constant K
24
maybe more.

K
11

of 5cb that is one of a common used LC material, is 6.65x10
-
12 newton at 24

C.


Fig 2. Shows creating deformation with field and surface:




Fig.2

C
reating deformation with field and surface



Ou
r experiment is to determine the dielectric constant and elastic constant of an
unknown material.





The Procedure of the Measurement of Dielectric, Di
a
magnetic and
Elastic Constant of Liquid Crystal


1.

Measure the optical index n
e

and n
o

by using ABBE refr
actometer, then obtain





Use
two cell method to measure the
Δε
;


please see the two cells method;

3.

Use Schlumbuger SI1260 Impedance/Gain Phase Analyzer to measure C
-
V
curve, (Fig.5) then find the threshold voltage, Calculate K
11
from:

Characterization Lab, Liquid Crystal Institute


3



K
11
= (V
threshold
)
2



0





/

2


4.

Make planar cells and homeotropic cells
, measure d by using Perkin Elmer
spectrometer to measure the cell thickness d.

5.

Use Magnetic Null method (Fig. 6) to measure the pretilt angle for each cell.
Choose best cells for experiments.

6.

Make the settlement as Fig.7, use Minimum Angle Seeking Program

to find
phase retardation verses magnetic field. Find the threshold field H
c1
.

7.

Calculate



fr潭:


†††
Δ

= K
11




2
/ (H
c1
)
2


d
2


8. Make the settlement as Fig.8. To measure the Phase Retardation verses Magnetic
field,
.


find the threshold field H
c2



K
22
=





(H
c2
)
2



d
2
/

2


9.

Make the settlement as Fig.9, find H
c3

and calculate K
33

from:




K
33
=




(H
c3
)
2



d
2
/

2

























C(pf)

V(volt)



V
threshold

Fig.3 C
-
V
Curve

Fig. 5,

Use Schlumberger
-
SI1260 to measure the C
-
V curve and find
the V
threshold,
then to calculate K
11

Characterization Lab, Liquid Crystal Institute


4









Fig.4

Using two
-
cell method to measure





Planar cell for


;

homeotropic cell for



















C

=

0



•A/d

C


=

0




•A/d





=



-



U
sing two cell method to measure dielectricity of LC







Characterization Lab, Liquid Crystal Institute


5









Photo
detector

K
11 ,
Splay









Laser


polarizer

N

S

Compensator

An
alyzer

Cell

Dimagnetic Anisotropy:






=K
11

2
/(H
c1
)
2
d
2


K
11

is known from c
-
v
measurement

Fig.
5




measurement


Characterization Lab, Liquid Crystal Institute


6















































N

S

Laser


polarizer

Compensator

Analyzer

Photo
-
detector

Twist

K
22
=



• (H
c2
)
2

d
2
/

2


Fig.
5

K
22

Measurement




Characterization Lab, Liquid Crystal Institute


7









N

S

Laser


polarizer

Com
pensator

A
nalyzer

Photo
-
detector

Bend

Fig.6
K
33
measurement, use homeotropic cell

K
33
=





(H
c3
)
2



d
2
/

2


Characterization Lab, Liquid Crystal Institute


8



Additional Reading


Further reading, from the website of Lavrentovich’s group

Frank Elastic Properties (by Bo Polak)


The Frank elastic constants* are determi
ned by applying an external field to the liquid
crystal cell in a direction perpendicular to the director orientation fixed by surface
anchoring forces. When the field is small, the liquid crystal will not deform because the
torque caused by the external f
ield is not large enough to overcome the energetic cost of
the elastic distortion; however, at some point, the field becomes large enough to
overcome the elastic energetic barrier, and any measured properties of the cell will
change (i.e., optical retardat
ion or capacitance). This point is called the Frederiks
transition, and is used to determine elastic constants.


If the preferred direction is planar (perpendicular to the substrate normal) and the external
field is parallel to the substrate normal, then
the elastic deformation will be a splay
deformation, and the Frank elastic constant K
11

can be determined.



If the preferred direction is planar and the external field is perpendicular to both the
substrate normal and the planar orientation, then the defo
rmation will be a twist
deformation, and the Frank elastic constant K
22

can be determined.



If the preferred direction is homeotropic (parallel to the substrate normal) and the
external field is parallel to the substrate, then the deformation will be a be
nd deformation
and K33 can be determined.


The determination of the splay elastic constant (K
11
) requires a liquid crystal cell with
planar alignment. K
11

can be determined by measuring the capacitance of the cell as a
function of voltage (which also can b
e used to determine the
dielectric constants
.


With knowledge of the dielectric constants of the liquid crystal and the Frederiks
transition voltage, K
11

is then determined. It should be noted that if the cell is not pla
nar
(i.e., the pretilt angle is not 0°), the change in any measured property of the liquid crystal
cell will be gradual, instead of sudden, and will occur at any field strength smaller than
the true Frederiks transition. However, with knowledge of the pret
ilt angle, numerical
analysis can be used to accurately determine the elastic constant.


The measurement of the twist elastic constant (K
22
) requires a cell with planar alignment.
K
22

can be measured by magnetic field or electric field techniques. In the m
agnetic field
technique, the critical magnetic field H
th

is measured by probing the liquid crystal cell for
changing in optical properties. This measurement can require a thick cell since Hth is
inversely proportional to the thickness. Typically, a magneti
c field of 10,000 Gauss is
required for a cell 10 mm thick. The Liquid Crystal Institute Characterization Laboratory
is capable of creating magnetic fields of 10,000 Gauss. This technique requires
Characterization Lab, Liquid Crystal Institute


9

knowledge of the
diamag
netic anisotropy
. The electric field technique requires that wires
be placed in the planar cell perpendicular to the rubbing direction. The threshold voltage
which causes in
-
plane switching is then determined, which allows for


determination of K22 with
knowledge of the dielectric properties of the liquid crystal.
The former method is easier to employ and more accurate.




Fig.3 Friderick transition. (a) Homogeneous and (b) homeotropic nematic cells with (a)
positive and (b) negative values of dielectric

anisotropy. The transition take place when

the applied field V exceeds certain threshold values V
s

or V
b




Characterization Lab, Liquid Crystal Institute


10


The bend elastic constant (K
33
) can be determined in two ways. It can be determined
simultaneously with K
11

and the dielectric constants**, by ex
amining the slope of the line
when C is plotted against V/Vth. It also can be determined by using a homeotropic cell
with an external electric field parallel to the substrate to determine the Frederiks
transition. In this case, knowledge of the
diamagnetic anisotropy

is needed.

The accuracy of each measurement is 5% and they can be performed over a temperature
range of
-
20° C to 200° C.

The client need only provide the liquid crystal to have this experiment performed.


*
W. H. DeJeu,
Physical Properties of Liquid Crystals
, Gordon and Breach, New York,
1980, Chapter 6.

**Y. Zhou Y. and S. Sato,
Jpn. J. Appl. Phys.
,
36
, 4397 (1997