Journal of Modern Physics, 2013, 4, 517-521
http://dx.doi.org/10.4236/jmp.2013.44073 Published Online April 2013 (http://www.scirp.org/journal/jmp)
Optical Measurements and Speckle Photography for
Thermotropic Liquid Crystals Mixtures
Ayman A. Zaki
Physics Department, Faculty of Science, Benha University, Benha, Egypt
Received October 22, 2012; revised November 22, 2012; accepted December 2, 2012
Copyright © 2013 Ayman A. Zaki. This is an open access article distributed under the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
In this work, an experimental approach of speckle photography was used for measuring birefringence of thermotropic
liquid crystals mixtures at different wavelengths in the visible region. Also the dispersion relations were investigated.
The values of the refractive indices were measured for these mixtures of thermotropic liquid crystals in isotropic and
liquid crystal phase at different wavelengths. The effect of the end group of these LCs used on the values of birefrin-
gence was investigated and discussed.
Keywords: Thermotropic Liquid Crystals Mixtures; Interference; Birefringence; Speckle Photography
1. Introduction
Liquid crystal technology has a major effect on many
fields of science and engineering, as well as devices tech-
nology. Applications for this special kind of material are
still being discovered and continued to provide effective
solutions to many different problems.
The complex optical properties of thin films of poly-
mer dispersed liquid crystals, and their refractive indices,
have been determined [1]. Birefringence measurements
at the wavelength 0.6328 μm for some common nematic
liquid crystal cells were presented [2]. Refractive indices
(ne, no) and birefringence (Δn) for cholesteric and iso-
tropic phases of cholesteryl carbonate, cholesteryl stea-
rate at varying temperature were measured [3]. Transmit-
tance spectra of a mica film and 4-cyano 49-pentyl bi-
phenyl liquid crystal were acquired in the visible spectral
region, and the dispersion curves of the refractive index
and the birefringence were deduced [4]. New guidelines
for selecting or synthesizing the liquid crystals with the
desired birefringence were established [5]. The thermo-
tropic liquid crystal (N-4-methoxybenzilidene-4butylani-
line), entrapped on hydrogels, based on crosslinked poly-
acrylamide was studied [6]. The birefringence of the liq-
uid crystal as functions of the temperature was measured
with and without the power supply [7]. The voltage de-
pendence of the birefringence, for a nematic liquid crys-
tal mixture doped with two anthraquinone derivatives
were predicted [8]. The temperature dependence of the
two indices ne, no and of the optical activity for uniaxial
liquid crystals was reported [9]. The processes of meso-
gen ordering in nematic and cholesteric sidechain poly-
mer systems were studied [10]. Properties of anodic alu-
minum oxide film as a liquid crystal alignment material
were studied [11].
This work deals with four thermotropic LCs com-
pounds locally prepared and the structure of thermotropic
liquid crystal materials used is 4-substituted phenyl-4-
alkoxy benzoates [12] which have the following struc-
ture:
4-C
l
H
2l+1
O- -X-4 -COO-
where l is an integer number, and X is the extension
group which is the electron-withdrawing NO2. In this
work l took the numbers of 6, 8, 14, and 16 respectively.
After that a mixture of liquid crystal of l equal 6 and 14,
and of l equal 6, 14 and 16 and other of 6, 8, 14 and 16
were used, where the composition per percentage mole
was as in Table 1. Each material used is represented by
the value of l with a symbol “e” after each number refer-
ring to the end group NO2. Table 1 shows transition
temperatures in Celsius degree for the compounds used
in this work. The symbols C-A, C-N, A-N, A-I, and N-I
mean the transition from, solid crystal to semictic A,
solid crystal to nematic, semictic A to nematic, semictic
to isotropic and nematic to isotropic respectively. A
C
opyright © 2013 SciRes. JMP

A. A. ZAKI 518
Table 1. Composition and transition temperatures (˚C) for compounds ClH2l+1O-C6H4-COO-C6H4-NO2. Values between pa-
rentheses are those determined by the extrapolation method.
Composition (mol%) Transition Temp. (˚C)
Mixture
l = 6 l = 8 l = 14 l = 16 TC-A T
C-N T A-A T A-I T N-I
6e pure - - - - - - - (71.2)
8e - pure - - 53.1 - 62.6 - 69.2
14e - - pure - - - - - (76.2)
6/14e 60.0 - 37.5 - 50 - 68.0 - -
6/14/16e 47.03 - 30.73 22.22 45.99 - - 72.50 -
6/8/14/16e 33.08 28.55 21.12 17.22 - 69.0 - - (78.0)
2. Refractive Index Measurements
Two different methods were used for measuring refractive
indices of the materials used; one was Abbe refractometer
equipped with hot water bath around the prisms with
different wavelengths at different degrees of temperature.
The temperature of water was controlled by a thermostat
within ±0.1˚C. A white light source was used with inter-
ference filters of wavelengths (640 nm, 577 nm, 546 nm,
435.8 nm), and a sodium lamp of wavelength (589.3 nm).
The dispersion relations between refractive indices and
wavelengths at certain temperature in isotropic and liquid
crystal phase were shown in Figures 1-6, for (6e), (8e),
(14e), (6/14e), (6/14/16e) and (6/8/14/16e).
Another method for measuring the values of refractive
indices of the thermotropic LC materials used was by us-
ing the spectrophotometer device at different wavelengths
of white light source. The value of refractive index was
determined by measuring the reflectance values of mate-
rial [13]. A slight difference in the accuracy of the values
of refractive indices was noticed between ≈0.001 to ≈0.01
when comparing results between the measurements ob-
tained from Abbe refractometer and the spectrophoto-
metric technique.
3. Birefringence Measurement
Birefringence of the liquid crystals was measured by us-
ing speckle interferometry technique. The optical setup
used is shown in Figure 7. The samples were put into an
electric oven for measuring birefringence at a certain de-
grees of temperature in order to obtain the LC phase as
shown in Table 1. The interference pattern for both or-
dinary and extraordinary components were magnified by
(q/p), where p was the distance from the lens (L3) to the
diffuser (D), and q is the distance from the lens (L3) to
the image (H); t was the thickness of the liquid crystal
whose refractive index is n. The photographs were taken
while the samples temperatures were heated and when
they cooled. The setup of the optical arrangement in
Figure 1. The relation between refractive index (n) and
wavelength (λ) at certain temperature, T = 65˚C in isotropic
phase, and 55˚C in LC phase for (6e) liquid crystal.
Figure 2. The relation between refractive index (n) and
wavelength (λ) at certain temperature, T = 73˚C in isotropic
phase, and 66˚C in LC phase for (8e) liquid crystal.
Fourier plane for observing the Young fringes from the
specklegram was used [14]. Plate 1 shows the interfere-
ence Young’s fringes from the specklegram of (6e, 14e,
6/14e and 6/14/16e) thermotropic liquid crystals at wave-
length 632.8 nm.
The relationship of the shift D between ordinary and
extraordinary images and the spacing of the Young’s
fringes  is given by [15]:
p
Df q





(1)

A. A. ZAKI 519
Figure 3. The relation between refractive index (n) and
wavelength (λ) at certain temperature, T = 85˚C in isotropic
phase, and 75˚C in LC phase for (14e) liquid crystal.
Figure 4. The relation between refractive index (n) and
wavelength (λ) at certain temperature, T = 78˚C in isotropic
phase, and 70˚C in LC phase for (6/14e) liquid crystal.
Figure 5. The relation between refractive index (n) and
wavelength (λ) at certain temperature, T = 78˚C in isotropic
phase, and 65˚C in LC phase for (6/14/16e) liquid crystal.
Figure 6. The relation between refractive index (n) and
wavelength (λ) at certain temperature, T = 78˚C in isotropic
phase, and 69˚C in LC phase for (6/8/14/16e) liquid crystal.
6e 14e
6/14e 6/8/14/16e
Plate 1. The interference Young’s fringes from specklegram
for 6e, 14e, 6/14e and 6/8/14/16e thermotropic liquid crys-
tals with laser source of wavelength 632.8 nm.
O
L
1
C
L
2
D
L
3
S H
Pq
Figure 7. Optical set-up for measuring the birefringence of an anisotropic optical material. O: monochromatic source, L1, L2
& L3: converging lenses, C: diaphragm, D: diffuser, S: liquid crystal inside the oven and H: holographic plate.

A. A. ZAKI 520
Table 2. Shows the values of birefringence n at different wavelengths for the thermotropic liquid crystals used.
n
Sample (λ) (632.8 nm) (λ) (543.5 nm) (λ) (514.5 nm) (λ) (488 nm)
6e 0.21 ± 0.01 0.23 ± 0.01 0.24 ± 0.01 0.25 ± 0.01
8e 0.23 ± 0.01 0.24 ± 0.01 0.256 ± 0.01 0.26 ± 0.01
14e 0.27 ± 0.01 0.28 ± 0.01 0.29 ± 0.01 0.30 ± 0.01
6/14e 0.20 ± 0.01 0.21 ± 0.01 0.22 ± 0.01 0.24 ± 0.01
6/14/16e 0.16 ± 0.01 0.18 ± 0.01 0.19 ± 0.01 0.21 ± 0.01
6/8/14/16e 0.14 ± 0.01 0.15 ± 0.01 0.17 ± 0.01 0.19 ± 0.01
where, f is the focal length of the Fourier transform lens
and λ is the wavelength of light used. In order to calcu-
late birefringence n, the following equation was used
[15]:
. (2)
sin 2
nfp
nt q






where n is the refractive index of the LCs; t is the thick-
ness of the sample and θ is the angle between the optic
axis and the normal to the surface of the sample. The
angle θ was determined by using the conoscopic meas-
urement system [16]. Table 2 shows the measuring data
for LCs used where birefringence was calculated with
laser sources of wavelengths, 632.8 nm, 543.5 nm, 514.5
nm, and 488 nm, and the thickness of each sample is
(150 m).
The dispersion curves for birefringence of four LCs
used in the visible region are shown in Figure 8. We
noted from Figure 8 that the increase of the number of
carbon and hydrogen atoms in the single chemical struc-
ture, the value of birefringence as in LCs (6e), (8e) and
(14e) increases. Besides, the mixture of LCs makes in-
crease in the end group NO2 which decreases the value of
birefringence as in LCs (6/14e), (6/14/16e) and (6/8/14/
16e). These results show that in order to increase bire-
fringence, the number of carbon and hydrogen atoms in
the single chemical structure must be increased, which
can be used in many applications such as liquid crystal
displays. But the mixture of these liquid crystals de-
creases the birefringence which isn’t preferable.
4. Conclusion
The experimental approach of speckle interferometry
technique for measuring birefringence of liquid crystals
and the dispersion relation was described. Also the val-
ues of refractive indices for these thermotropic liquid
crystal materials were obtained with a high degree of
accuracy. The experimental data shows that the values of
birefringence increase by increasing the number of car-
bon and hydrogen atoms in the chemical structure and
Figure 8. The dispersion relation between birefringence (Δn)
and the wavelength λ at a certain temperature, in LC phase
for 6e, 14e, 6/14e, 6/14/16e and 6/8/14/16e, liquid crystals.
decrease by increasing the end group NO2 in the mixture
of liquid crystals. The end group NO2 is an electrophile
which is a species having electron deficient atom, so that
it is a positive charged and accepting or withdrawing
electron, which decreases the stability of the chemical
structure compound and then decreases the directionality
of the molecules which decrease birefringence. These
results become opposite when the end group is donating
electrons called monotropic or nucleophiles which is a
species having electrons rich atom, such as OCH3 group
[17]. The experimental errors in measuring birefringence
of the liquid crystal materials used were within ±1% to
±2%, which are acceptable according to others [15,17].
5. Acknowledgements
I wish to express my sincere thanks to Prof. Dr. T. A. El-
Dessouki, Faculty of Science, Ain Shams University and
Prof. Dr. M. Roushdy, Physics Department, with Prof. Dr.
M. Naoum, Chemistry Department, Faculty of Science,
Cairo University for their facilities and guidance.
REFERENCES
[1] L. McKenna, L. S. Miller and I. R. Peterson, “Polymer
Dispersed Liquid Crystal Films for Modulating Infra-Red

A. A. ZAKI 521
Radiation,” Polymer, Vol. 45, No. 20, 2004, pp. 6977-
6984. doi:10.1016/j.polymer.2004.07.033
[2] B.-E. Benkelfata, E.-H. Horachea, Q. Zoua and B. Vinou-
zeb, “An Electro-Optic Modulation Technique for Direct
and Accurate Measurement Of Birefringence,” Optics Com-
munication, Vol. 221, No. 4-6, 2003, pp. 271-278.
doi:10.1016/S0030-4018(03)01539-6
[3] R. Manohar and J. P. Shukla, “Refractive Indices, Order
Parameter and Principal Polarizability of Cholesteric Liq-
uid Crystals and Their Homogeneous Mixtures,” Journal
of Physics and Chemistry of Solids, Vol. 65, No. 10, 2004,
pp. 1643-1650.
[4] S. Brugioni and R. Meucci, “Mid-Infrared Interferometric
Measurement of Liquid Crystal Anisotropy,” Optics Com-
munication, Vol. 230, No. 1, 2004, pp. 19-22.
[5] M. Manaia, A. Gharbia, J. P. Marceroub, H. T. Nguyenb
and J. C. Rouillonb, “Optic and Electro-Optic Investiga-
tions on Smq, Smc_A and L Phases in Highly Chiral Com-
pounds,” Physica B, Vol. 368, No. 1-4, 2005, pp. 168-
178.
[6] F. A. Aouada , M. R. de Moura, P. R. G. Fernandes, A. F.
Rubira and E. C. Muniz, “Optical and Morphological
Characterization of Polyacrylamide Hydrogel and Liquid
Crystal Systems,” European Polymer Journal, Vol. 41,
No. 9, 2005, pp. 2134-2141.
doi:10.1016/j.eurpolymj.2005.03.020
[7] Z. L. Cao, L. Xuan, L. F. Hu, X. H. Lu and Q. Q. Mu,
“Temperature Effect on the Diffraction Efficiency of the
Liquid Crystal Spatial Light Modulator,” Optics Commu-
nications, Vol. 267, No. 1, 2006, pp. 69-73.
doi:10.1016/j.optcom.2006.06.003
[8] A. Jafari, A. Ghanadzadeh, H. Tajalli and M. Yeganeh,
“Linear Optical Parameters of a Dyed Nematic Mixture in
the Presence of an AC Voltage,” Optical Materials, Vol.
29, No. 8, 2007, pp. 1004-1009.
doi:10.1016/j.optmat.2006.03.034
[9] N. Bitri, A. Gharbi and J. P. Marcerou, “Scanning Cono-
scopy Measurement of the Optical Properties of Chiral
Smectic Liquid Crystals,” Physica B: Condensed Matter,
Vol. 403, No. 21-22, 2008, pp. 3921-3927.
doi:10.1016/j.physb.2008.07.033
[10] Al. Bobrovsky, A. Ryabchun, A. Medvedev and V. Shi-
baev, “Ordering Phenomena and Photoorientation Proc-
esses in Photochromic Thin Films of LC Chiral Azoben-
zene-Containing Polymer Systems,” Journal of Photoche-
mistry and Photobiology A: Chemistry, Vol. 206, No. 1,
2009, pp. 46-52. doi:10.1016/j.jphotochem.2009.05.010
[11] T.-T. Tang, C.-Y. Kuo, R.-P. Pan, J.-M. Shieh and C.-L.
Pan, “Strong Vertical Alignment of Liquid Crystal on Po-
rous Anodic Aluminum Oxide Film,” Journal of Display
Technology, Vol. 5, No. 9, 2009, pp. 350-354.
[12] R. I. Nessim, “Phase Behaviour of Binary Mixture of 4-
Substituted Phenyl 4’-N-Alkoxybenzoates,” Liquid Crys-
tals, Vol. 30, No. 2, 2003, pp. 211-218.
doi:10.1080/0267829021000060241
[13] E. Hecht and A. Zajac, “Optics,” Addison-Wesley, Read-
ing, Vol. 378, 1990, p. 282.
[14] M. Francon, “Information Processing Using Speckle Pat-
terns,” In: J. C. Dainty, Ed., Laser Speckle and Related
Phenomena, Springer-Verlag, New York, 1975.
doi:10.1007/BFb0111439
[15] L. M. Bernardo and O. D. D. Soares, “Birefringence Mea-
surements by Double Speckle Photography,” Applied Op-
tics, Vol. 26, No. 5, 1987, pp. 769-772.
doi:10.1364/AO.26.0769_1
[16] W. A. Crossland, J. H. Morrissy and B. Needham, “Tilt
Angle Measurements of Nematic Phases of Cyano-Bi-
phenyls Aligned by Obliquely Evaporated Films,” Jour-
nal of Physics D: Applied Physics, Vol. 9, No. 14, 1976, p.
2001. doi:10.1088/0022-3727/9/14/010
[17] T. A. El-Dessouki, N. I. Hendawy and A. A. Zaki, “Meas-
uring Birefringence of Curved Sheet and Single Crystals
by Double-Exposure Speckle Photography,” Optics and
Lasers in Engineering, Vol. 47, No. 6, 2009, pp. 622-628.
doi:10.1016/j.optlaseng.2008.12.006