Download Measurement of Elastic Constants of Liquid Crystal Material

Characterization Lab, Liquid Crystal Institute
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 in 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 happen. 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 arranged in twist.
Further study shows:
f=1/2[k11(n)2 +k22(nxn)2 +k33(nxxn)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.
k11, k22,and k33 are called elastic constant of liquid crystal.
K11 corresponds to the deformation of splay;
K22 corresponds to the deformation of twist;
K33 corresponds to the deformation of bend.
.
Fig.1 Three deformations of liquid crystal
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Characterization Lab, Liquid Crystal Institute
Different liquid crystal material has different K11. The unit of K11 is newton or erg.
Let us estimate the magnitude of K11:
U : intermolecular interaction energy (~10-14 ergs);
a: molecular distance (~10-8 cm);
K11 ~U/a~ 10-6 dynes =10-11 newtons.
Present research indicates some new features: a fourth constant K24 maybe more.
K11 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 Creating deformation with field and surface
Our experiment is to determine the dielectric constant and elastic constant of an
unknown material.
The Procedure of the Measurement of Dielectric, Diamagnetic and
Elastic Constant of Liquid Crystal
1. Measure the optical index ne and no by using ABBE refractometer, then obtain
n.
2. 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 K11 from:
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Characterization Lab, Liquid Crystal Institute
K11= (Vthreshold)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 Hc1.
7. Calculate  from:
Δ= K11• 2/ (Hc1)2• d2
8. Make the settlement as Fig.8. To measure the Phase Retardation verses Magnetic
field,.
find the threshold field Hc2
K22 =  • (Hc2)2 • d2/ 2
9. Make the settlement as Fig.9, find Hc3 and calculate K33 from:
K33 = • (Hc3)2 • d2/ 2
Fig. 5, Use Schlumberger-SI1260 to measure the C-V curve and find
the Vthreshold, then to calculate K11
C(pf)
Vthreshold
V(volt)
Fig.3 C-V Curve
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Characterization Lab, Liquid Crystal Institute
Using two cell method to measure dielectricity of LC
C=0• •A/d
C=0• •A/d
=-
Fig.4 Using two-cell method to measure 
Planar cell for ; homeotropic cell for 
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Characterization Lab, Liquid Crystal Institute
K11 ,Splay
N
S
Laser
Analyzer
polarizer
Cell
Compensator
Photo
detector
Dimagnetic Anisotropy:
 =K112/(Hc1)2d2
K11 is known from c-v
measurement
Fig. 5  measurement
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Characterization Lab, Liquid Crystal Institute
Fig.5 K22 Measurement
K22= • (Hc2)2•d2/ 2
Twist
N
Analyzer
Laser
polarizer
Photodetector
S
Compensator
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Characterization Lab, Liquid Crystal Institute
Fig.6 K33 measurement, use homeotropic cell
K33=  • (Hc3)2 • d2/ 2
Bend
N
Laser
Analyzer
polarizer
Photo-detector
S
Compensator
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Characterization Lab, Liquid Crystal Institute
Additional Reading
Further reading, from the website of Lavrentovich’s group
Frank Elastic Properties (by Bo Polak)
The Frank elastic constants* are determined 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 field 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 retardation 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 K11 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 deformation will be a twist
deformation, and the Frank elastic constant K22 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 bend deformation
and K33 can be determined.
The determination of the splay elastic constant (K11) requires a liquid crystal cell with
planar alignment. K11 can be determined by measuring the capacitance of the cell as a
function of voltage (which also can be used to determine the dielectric constants.
With knowledge of the dielectric constants of the liquid crystal and the Frederiks
transition voltage, K11 is then determined. It should be noted that if the cell is not planar
(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 pretilt angle, numerical
analysis can be used to accurately determine the elastic constant.
The measurement of the twist elastic constant (K22) requires a cell with planar alignment.
K22 can be measured by magnetic field or electric field techniques. In the magnetic field
technique, the critical magnetic field Hth 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 magnetic 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
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Characterization Lab, Liquid Crystal Institute
knowledge of the diamagnetic 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 Vs or Vb
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Characterization Lab, Liquid Crystal Institute
The bend elastic constant (K33) can be determined in two ways. It can be determined
simultaneously with K11 and the dielectric constants**, by examining 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
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