1
GENERAL INTRODUCTION
______________________________________________ 1.1 Introduction
In the Early 1960’s the pioneering research efforts at RCA and Xerox brought
attention to possibility of using a relatively unknown class of organic materials, i.e.,
liquid crystals (LC’s), for modulating electro-optic properties of light for fabricating a
revolutionary new flat panel display. Today the flat panel liquid crystal display
devices, (LCD’s) have replaced the bulky and power-hungry cathode ray tubes
(CRTs) and thus changed the face of the modern office.
Liquid-crystalline material research has contributed significantly both to the
development of liquid-crystalline display (LCD) technology and also to the better
understanding of the phase behavior of soft condensed matter systems. Quantitative
knowledge of the physical properties is necessary, so that improved materials may be
devised for applications. Thus, attempts are continuously being made to study the
material properties of both pure compounds as well as their mixtures for a better
insight into the basic understanding of liquid crystalline behavior so that a newer and
more acceptable class of materials suitable for display devices emerges.
Any material, if the temperature is raised more and more, it generally changes
its state from solid to liquid and to gaseous. An Austrian botanist, Friedrich Reinitzer1
first observed liquid crystals in 1888. He discovered a strange material that exhibited
a mesophase between solid state and liquid state1. At a temperature of 145
OC, it
melted, becoming cloudy white and viscous. At a temperature of 179 OC, it became
isotropic and clear. The material he discovered was cholesteryl benzoate. On March
14, 1889, he wrote a letter to Otto Lehmann2, telling him about the two melting
points. Lehmann studied the material and discovered that the liquid at the mesophase
exhibited a double refraction effect, characteristic of a crystal. Because it shared
characteristics of both liquid and crystal, he named it “fliessende krystalle”and the
name “liquid crystal” was born2.
Liquid crystal is a state of matter that is neither a solid crystal nor an isotropic
liquid. The basic difference between crystals and liquids is that the molecules in a
2
crystal are ordered whereas in a liquid they are not. The existing order in a crystal is
usually both positional and orientational, i.e., the molecules are constrained both to
occupy specific sites in a lattice and to point their molecular axes in specific
directions. Contrary to this, the molecules in liquids diffuse randomly throughout the
sample container with the molecular axes tumbling wildly. The states of matter whose
symmetric and mechanical properties are intermediate between those of a crystalline
solid and an isotropic liquid are called `liquid crystals3-6
(LC). Liquid crystals exhibit
anisotropy in their mechanical, electrical, and optical properties, behaving in this
sense as solid crystal. Nevertheless, they have no ability to support shearing, and thus
they flow like ordinary liquids7.
This is why liquid crystals attain their importance in technological
applications, especially in electro optic switches and in liquid-crystal displays8.
Therefore, thermal stability of liquid-crystalline mesophase and its molecular ordering
are of great importance.
1.2 Chemical structure of liquid crystals
The role of molecular structure or geometry in liquid crystals is extensively
studied by Gray9. In order to exhibit the mesomorphism, the molecules should
possess highly geometrical anisotropy in shape, namely it should be either rod like or
disc like. The mosomorphic molecule mainly consists of three units such as core,
linking groups and terminal groups. The core should be highly rigid to form liquid
crystalline phases because it makes the interaction with other molecules anisotropic.
In addition to the core rigidity, there is a need to have certain flexibility for the
molecule in order to ensure reasonable low melting points and stability. This
flexibility can be obtained by attaching the terminal groups.
3
The general molecular structure is given as below
where R and R” are flexible terminal groups, while A and B are aromatic groups and
Z is the linking group. This part including aromatic rings and linking group together is
called as central rigid core. Z represents a linkage of the type –A=B- between two
benzene or hexane rings. The aromatic rings linked through a central group Z which
often involves a double bond or a triple bond to preserve the rigidity and linearity of
the molecules.
R and R” may be same or different and represent groups example, R = n-alkyl and R”
= n-alkoxy or viceversa, R and R” = n-alkyl
Generally the linking group used is as follows
Saturated groups, such as ethylene (C2H4), ester (-COO-)
Unsaturated groups containing double bonds, such as stilbene (-CH=N-),
azoxy (–N=N-) and schiff’s base (–CH=N-).
Unsaturated groups containing triple bond such as acetylene (-C≡C-), and
diacetylene (-C≡C-C≡C-) 10-13
.
1.3 Classification of liquid crystals
The Liquid crystal nature is exhibited by many number of different classes of
materials which includes organic compounds, amphiphilic organic compounds,
polymeric liquid crystals and colloidal dispersion of inorganic materials14, 15
.
The transitions to the mesophases may be obtained in two different ways
either by the change of temperature or by the change of concentration of a solvent,
usually water
Z R” A B R
4
1.3.1. Thermotropic liquid crystals
Thermotropic liquid crystal phases are observed due to the change in
temperature. Thermotropic liquid crystals in which the transitions takes place
reversibly on both heating and cooling are the thermotropic liquid crystals which are
stable above the melting point of the compound are called enantiotropic. In certain
cases the phases are observed only on cooling, and the liquid crystalline state is stable
at temperature below the melting point. The phases are called monotropic.
Thermochronic liquid crystals are thermotropic in origin and have chiral (twisted)
structures16, 17
.
1.3.2. Lyotropic liquid crystals
Lyotropic phases are formed in the presence of a suitable solvent and also
concentration. The molecules that make up lyotropic liquid crystals are amphiphilic
or surfactants consisting of two distinct parts: a polar (often ionic) head and a non-
polar (often a hydrocarbon) tail. Following the rule of the like dissolve like, the head
is attached to water (or hydrophilic) and the tail is repelled by water (hydrophobic).
These amphiphilic molecules of material form liquid crystals on dissociation in
solvent18-20
. Deoxyribonucleic acid (DNA), certain viruses like tobacco mosaic virus
(TMV) form lyotropic mesophases when dissolved in an appropriate solvent (usually
water) in suitable concentration. Soaps and detergents when used with water form
liquid crystals.
1.3.3. Polymeric liquid crystals
Liquid crystalline polymers combine the self organization of the mesogenic
groups into the ordered structure of liquid crystalline phases with some typical
polymer properties such as freezing of the disordered polymer chain at glass transition
temperature. These can be prepared by incorporation of the anisotropic mesogenic
groups into polymeric systems. These are classified either as main chain liquid
crystalline polymers [MCLCP] or polymers with mesogenic side groups [SCLCP] or
as liquid crystalline elastomers21-24
.
5
Liquid crystalline materials in general may have various types of molecular
structure. Basing on the geometrical structure, the thermotropic liquid crystals can be
divided into rod like9, disc like
25, sanidic or brick-like or lath-like
26 and bowlic for
bowl-like27
. The liquid crystals derived from the rod-like molecules are called
calamitics. The liquid crystals formed from disc-shape molecules are known as
discotics. Intermediate between rod-like and disc-like molecules are the lath-like
species. The symmetry-based classification of liquid crystals was first made by
Friedel28
.
Liquid Crystals may be broadly classified as follows
Liquid Crystals
Thermotropic Lyotropic
Calamitic Discotic Sanidic bowlic
Nematic Cholestric Smectic
Cybotactic
Normal skewed SA SD SC SB (h) SI SF SL=B(cl) SJ SG SE S SM SO SQ SX
Nematics:
The first phase that condenses when isotropic liquid is cooled is called nematic
and also is known as high temperature liquid crystal phase. This phase possesses long
range orientational order. The phase is fluid and there is no long-range correlation of
the molecular centre of mass position. The long axis of the molecules on an average
are aligned about a specific direction, which is denoted by a unit vector, called the
director, . Nematic phase is apolar in nature i.e. and - are physically
equivalent. Thus the material is still anisotropic29-32
. In thermal equilibrium it has
6
∞/mm symmetry and is uniaxial. The important variable in nematic liquid crystal is
the order parameter, which measures how the molecules are aligned with the director.
The usual measure of this order is,
S = ½<3 cos2θ-1>
where S represents the thermal fluctuations of the individual molecular long axis and
the brackets <> denote a thermal averaging and θ is the angle between the molecule
(molecular long axis) and the director .
If the classical nematic has an additional short range smectic like ordering,
then it is called cybotactic nematic. The short range smectic like layers are either
orthogonal or tilted to the layer planes and they are denoted as normal cybotactic, Nnc
and skewed cybotactic, Nsc phases respectively. Biaxial nematics are also reported32,
33. The nematics exhibit schlieren, threaded marble, pseudo isotropic textures when
the sample is observed through crossed polarizers.
Cholesteric or spontaneously twisted nematic
Cholesteric LC’s are regarded as special kind of nematics. The nematic phase
exhibited by an optically active compound is called spontaneously twisted nematic or
cholesteric. The name cholesteric is given to these compounds as the first materials
exhibiting this phase are from cholesterol derivatives. In this phase, the molecules
prefer to lie next to each other in a slightly skewed orientation. This induces helical
director configuration in which the director rotates through the material. These are
composed of helical aggregation of the molecules. Such a structure is envisaged as
being composed of sheets of molecules and within each sheet the molecules behave as
in nematic phase and has an average direction defined by a director . To quantify
7
the degree of twist, the pitch length, P of the helix is defined by convention as the
longitudinal distance in which the director has made one complete 360o revolution.
The pitch length varies with time. Each molecule is skewed at some average angle
with respect to its neighbors in a sheet above and below. Two such helical
arrangements are possible one right-handed, other left-handed, but one will have a
lower energy than the other34-37
. These are uniaxial (both positive and negative).
These exhibit focal conic with Grandjean, homogeneous and pseudo isotropic
textures. The molecular arrangement is shown below.
Smectics
Smectic is the name coined by G.Friedel for certain mesophases with
mechanical properties reminiscent of soaps. From a structural point of view, all the
smectics are layered structures, with well defined inter-layer spacing which can be
measured by X-ray diffraction technique28
. Smectic phases are characterized by both
long range orientational order as well as short range positional order. With simple
changes in mutual arrangement of the layers and with changes (in the state of order)
inside the layers, a variety of smectic phases can be obtained38-41
. The smectics
exhibit subtle polymorphism than nematics. No single compound is found to exhibit
all the smectic phases (SA to SX) so far.
There are various modifications of the smectic phases, each with different
combination of in-plane order and tilt angle. These have been named as the smectic A,
B, C, D, E, F, G, H, I, J and K phases designated as, Smectic-A42-47
, Smectic-B48-49
,
Smectic-C50-53
, Smectic-D54-55
, Smectic-E55-59
, Smectic-F60-64
, Smectic-G, Smectic-
8
H65-66
, Smectic-I44
, Smectic-J44
and Smectic-K44
or SA, SB, SC, SD, SE, SF, SG, SH, SI,
SJ, and SK, with the letters denoting the chronological order of their discovery. The
thermal sequence of their occurrence is SA, SD, SC, SB, SE, SI, SF, SG, SG (SJ), SH and
SH (SK) with decreasing temperature. SB, SG, SJ, SE, SH and SK are found to be more
crystalline than remaining liquid crystalline phases
The structural characteristics of smectic phases of classic liquid crystalline
compounds is given in Table 1.1.
Table 1.1 The structural characteristics of smectic phases of classic liquid crystalline
compounds
Phase Phase
type
Molecular
Packing
Molecular
Orientation
In-plane
Correlation
Layer
correlation
Bond-
orientation
order
Dimensionality
A fluid random orthogonal Short-range None Short-range -----------------
B
(Hexatic) hexatic hexagonal orthogonal Short-range None Long- range 3D hexatic
Crystal
B
crystal Hexagonal orthogonal long-range long-range long-range
3D
C fluid random tilted Short-range None Long-range -----------------
D Plastic rods ----------- long-range ------------- ------------- isotropic
E crystal orthorhom
bic orthogonal long-range long-range long-range 3 D
F hexatic Pseudo
hexagonal Tilt to side Short-range None long-range 3D hexatic
G crystal Pseudo
hexagonal Tilt to side long-range long-range long-range 3 D
H crystal
Herringbon
e Tilted* long-range long-range long-range 3 D
Monoclinic
I Pseudo
hexagonal Tilt to apex
Possibly long
range None long-range
Stacked 2D
crystal & 3D
hexatic
J(G’) crystal
Pseudo
hexagonal Tilt to apex long-range long-range long-range 3 D
K(H’) crystal
Herringbon
e Tilted* long-range long-range long-range 3 D
Monoclinic
9
Discotics
Mesogens with disc-like molecules are called discotics. The existence was
theoretically predicted in 1970 and mesomorphism in discotic materials (hexa
alkonoyl benzenes) was first reported in 1977 by Chandrasekhar et al25
. The
molecules of these classes are flat and disc-like in shape and able to be packed in
different structures. The classification of columnar phase is given below.
The tilted variants are also possible. Similar to rod shaped molecules the disc-
shaped molecules can also form a nematic phase characterized by a long range
orientational order, but no positional order with the director parallel to the disc
normal. In chiral compounds, the discotic nematic exhibits a twisted structure67-70
.
Sanidic
These are characterized by boards. Depending up on the relative size of the
main axes, these molecules can be derived from either rod-like or disc-like molecules.
Derived from Greek word for board, these phases are called sanidic. The rod-like and
disc-like liquid materials are characterized by the rotational symmetry of the
molecular models, which means the anisotropy of the models can be described by two
main axes. The more general case would be the consideration of molecular models
with three different main axes. The structure of sanidic phases can be characterized
by three translational periods (in accordance with length, breadth and thickness) of
scattering maxima, which cause three molecular units by investigation with X-rays71
.
10
Bowlics
Mesogens with bowl-like molecules forms the bowlic liquid crystal. These
contain molecules, which are three dimensional in a physical sense and can exhibit
mesophases as the one-dimensional rod-like and two-dimensional disc-like bowlic
compounds. Lin first proposed72
these bowl like molecules. Pyramidal73
shape and
cone-shaped74
are later reported. X-ray diffraction studies75
performed to investigate
the structure of these phases showed either classical columnar or a hexagonal or
oblique lattice in a two dimensional array with a disordered array in three dimensions.
11
1.4. Statement of the problem
The research on materials is mainly directed towards the design, fabrication and synthesis
of novel systems and the study of the physical properties of these for the usage in fundamental
and applied research for their applications which are useful for the society. These include the
fascinating and novel liquid crystal materials also. These systems function as both ordered
crystalline solids and isotropic liquids. That is they have the flow as well as anisotropic nature.
The research interest in these materials is two fold. On one hand new properties are expected and
on the other hand the study of interaction of different systems (namely the effect of end chains,
rigidity of the core, position of certain polar atoms like N, O, Cl etc, in the molecule) is
fascinating and interesting. Now the research is mainly directed towards the design and
fabrication of such materials for their use in chronological and scientific interest, which involve
the characterization and study of their properties with different experimental techniques
including density and optical measurements.
In recent years, liquid crystals have become lucrative and alternative candidates for the
electro optic displays in the place of conventional inorganic materials, as they are easy to design
and also for synthesis. However, these materials underline much importance to an experimental
solid-state chemist and condensed matter physicist, as they are representative of low-dimensional
systems, workable at ambient temperatures. On the other side, if the information of these phase
transitions is systematically studied in the domain of fundamental molecular forces and the
higher archive of fundamental scaling laws, it gives totality of understanding in exploitation of
their application viabilities. Moreover, these materials exhibit polymorphism involving phase
transitions of rare occurrence and far awaited theoretical expectations at the inter phase one, two,
and three –dimensional melting.
The Schiff’s base N-(p-n-alkoxybenzylidene)-p-n-alkoxy anlines popularly known as
nO.Om’s where the chain number on both sides can be varied from 1 to 18 to realize a variety of
phase sequences (variants). The quenching of oxygen atom in the molecular moiety on either
side or on both sides will provide a variety of changes in phases or the clearing temperatures or
both. That is, the electro negative oxygen atom plays an important role in deciding the clearing
temperature as well as the phase variants. It is well established that the oxygen atom in the
molecular moiety enhances the clearing temperatures as well as the nematic phase abundance in a
homologous series.
12
The earlier systematic studies are carried out at CLCRE, Acharya Nagarjuna University
and the literature survey on a number of nO.Om, nO.m, n.Om and n.m compounds regarding the
phase transitions across different LC phases and the molecular polarizability studies which
includes the estimation of molecular polarizability anisotropy of a liquid crystal material
employing the modified Lippincott - δ function and molecular vibrational models, motivated the
author to synthesize N-(p-n-heptyloxybenzylidene)-p-n-alkoxy anlines with alkoxy chain
number, m = 3, 5, 6, 7, and 9 with the molecular formula.
These liquid crystal materials show different phase variants namely N, N-C, N-C-I giving
rise to different phase transformations, such as isotropic to nematic, nematic to smectic-C, and
smecti-C to smectic-I phases.
The order of phase transitions can be studied by number of experimental techniques. The
author used the density studies to arrive at the order of the phase tansformation.
These experimental and semi empirical theoretical calculations enabled for the study of
temperature variation of orientational nematic order parameter, S in the nematic phase.
In the estimation of order parameter, S the author used different methods and field
models. The author used the birefringence data along with density results to understand the
nature of phase transformations and for the determination of molecular polarizabilities of the
molecule employing different local field models which the molecule experiences in the nematic
phase. Further, the author studied the variation of order parameter, S with temperature in all the
compounds and able to discuss the results with the body of the data available. The comparative
study of S from different methods on these compounds and the compounds available in literature
is studied.
Further, different thermodynamic parameters are estimated from the density data for these
compounds and compared the results with the other compounds available in literature.
C7H15O OCmH2m+1 CH = N
13
1.5. References
1. F. Reinitzer, “Beiträge zur Kenntniss des Cholesterins,” Wiener Monatschr,
Für Chem., 9, 421, 1888.
2. O. Lehmann, “Über fliessende Krystalle,” Z. Phys. Chem., 4, 462,
1889.
3. P.G. de Gennes, The Physics of Liquid Crystals, Clarendon Press, Oxford,
1974; (b) P.G. de Gennes, J. Prost, The Physics of Liquid Crystals,
Clarendon Press, Oxford, 1993.
4. S. Chandrasekhar, Liquid Crystals, Cambridge Univ. Press, Cambridge, 1977, 1992.
5. D. Demus, L. Richter, Texture of Liquid Crystals, Leipzig, 1978.
6. G.R. Luckhurst, G.W. Gray (Eds.), The Molecular Physics of Liquid
Crystals, Academic Press, New York, 1979.
7. P. J. Collings, & M. Hird, Introduction to Liquid Crystals Chemistry
and Physics, Taylor & Francis. UK (London) USA (Philadephia) 1998.
8. G. P. Crawford, & S. Zumer, (Liquid Crystals in Complex m Geomeries, Taylor &
Francis, 1996.
9. G.W.Gray, “Molecular structures and the properties of Liquid crystals”, Academic
press, Newyork, 1962.
10. W.R.Young, I.Haller and A.Aviram, Mol.Cryst., 15, 311, 1972.
11. H. Kelker and B. Scheurle, Angew.Chem.(Int.Ed), 8, 884, 1969.
12. J. Malthete, M.Leclerq, J.Gabard, J. Billard and J. Jacques, Mol.Cryst., 23,
133, 1973.
13. B. Flannery and W.Haas, J.phy.Chem., 74, 361,1970.
14. F. C. Bawden, and N.W. Pirie, Proc. R. Soc. Lond, B 123, 274. 1937.
15. G. Oster, J. Gen.Physiol, 33, 445, 1950.
16. A.L.Tsykalo, “Thermo Physical Properties of Liquid Crystals”, Gordon and Breach,
New York, 1991.
17. G.Vertogen and W.H. de Jeu, “Thermotropic Liquid Crytals, Fundamentals”,
Springer-Verlag, Berlin, 1988.
14
18. T.A.Harroun, M.P.Nieh, M.J.Watson, V.A.Raghunathan, G.Pabst, M.R.Morrow and
J.Katsaras, Phy.Rev.E., 69, 3109, 2004.
19. C.Tanford,”The Hydrophobic effect”, John Wiley and Sons, New York, 1973.
20. S. Safran, “Statistical Thermodynamics Surfaces, Interfaces and Membranes”,
Addison Wesley, 1994.
21. J. L.White, J.appl.Polym.Sci., Appl.Polym.symp., 41, 3, 1985.
22. J.Torre, M.Cortazar, M.Gomez, G.Eills and C.Marco, J.Polym.sci., 42, 1949, 2004.
23. J.W.Daone, N.A.Vaz, B.G.Wu and S.Zumer, Appl.Phys.Lett., 48, 269,1986.
24. P.S. Drzaic, J.appl.Phys., 60, 2142, 1986.
25. S.Chandrasekhar, B.K.Sadasiva and K.A.Suresh, Pramana, 9, 471,1977.
26. K.Praefcke, B.Kohne, D.Singer, D.Demus, G.Pelzl and S.Diele, Liq.Cryst, 7,
589,1990.
27. T.Sekine, T.Niori, M.Sone, J.Watanabe, S.W.Choi, Y.Takanishi and H.Takezoe,
Jpn.J.Appl.Phys, 36, 6455, 1997.
28. G. Friedel, Ann. Phys. 18, 273, 1922
29. V.Freedericksz and V.Zolina, Trans Faraday.Soc., 29, 919, 1933.
30. A.de Vries, Pramana, 1, 93, 1975.
31. S.Chandrasekhar, B.K.Sadasiva and B.srikanta, Mol. Cryst. Liq. Cryst., 151, 93,1987.
32. S.Chandrasekhar, B.K.Sadasiva, B.R.Ratna and V.N.Raja, Pramana.J.Phys., 30, L-
491,1988.
33. L.V.Azaroff, S.Bhattacharjee, Z.Kristallografiya., 179, 249, 1987.
34. A.Walf, J.Chem.Phy., 59, 1487, 1973
35. R.G.Priest and T.C.Lubensky, Phys.Rev., A9, 893, 1974.
36. M.Marcus and J.W.Goodby, Mol. Cryst. Liq. Cryst. Lett., 72, 297, 1982.
37. H.Stegmeyer, Th.Blumel, K.Hiltrop, H.Onussiet and F.Porsch, Liq.Cryt., 1, 3, 1986.
38. P.G.de Genne, Mol. Cryst. Liq. Cryst., 21, 49, 1973.
39. H.Sackmann and D.Demus, Mol. Cryst. Liq. Cryst., 21, 239, 1973.
15
40. G.W.Smith and Z.G.Gardlund, J.chem.Phys., 59, 3214, 1973.
41. D.Coates and G.W.Gray, The Microscope, 24, 117, 1976.
42. J.Prost, ”Advances in Physics”, 33, 1, 1984.
43. G.W.Gray, Mol. Cryst. Liq. Cryst., 66, 270, 1981.
44. G.W.Gray and J.W.Goodby in “Smectic Liquid Crystals – Textures and structures”,
Leonard Hill., London, 1984.
45. F.Hardouin, A.M.Levelut, M.F.Achard and G.Sigaud J.Phys.(Paris)., 42, 71, 1981.
46. J.Prost and P.Borois, J.Chem.Phys., 80, 65, 1983.
47. P.Borois, J.Prost and T.C.Lubensky, J.Phys., 46, 391, 1985.
48. J.W.Goodby, G.W.Gray, A.J.Leadbetter and M.A.Mazid in “Liquid Crystals of one
and two dimensional order”.Ed: W.Helfrich and G.Heppke, Springer Verlag.,
Newyork, 1980.
49. G.Poeti, E.Fanelli and D.Guillon, Mol. Cryst. Liq. Cryst, 82, 107, 1982.
50. R.Bartoline, J.Doucet and G.Durand, Ann.Phys., 3, 389, 1978.
51. T.R.Taylor, J.C.Fergason and S.L.Arora, Phys. Rev.Lett, 24, 359, 1970.
52. E.Fanelli, S.Melone, G.Torquati, V.G.K.M.Pisipati and N.V.S, .Rao, Mol.Cryst.Liq.
Cryst ., 146, 151, 1987.
53. G.R.Luckhurst, B.A.Timmi, V.G.K.M.Pisipati and N.V.S.Rao, Mol. Cryst. Liq.
Cryst.Lett., 1, 45, 1985.
54. D.Demus, G.Kunicke, J.Nelson and H.Sackmann, Z.Naturfosch., 23a, 84, 1968.
55. S.Diele, P.Brand and H.Sackmann, Mol. Cryst. Liq. Cryst., 17, 163, 1972.
56. J.W.Goodby and G.W.Gray, Mol. Cryst. Liq. Cryst., 56, 43,1979.
57. A.deVries, Mol. Cryst. Liq. Cryst., 24, 337, 1973.
58. D.Coates, K.J.Harrison and G.W.Gray, Mol. Cryst. Liq. Cryst., 22, 99,1973
59. A.Biering, D.Demus, G.W.Gray and H.sackmann, Mol.Cryst.Liq.Cryst., 28, 275,
1974.
60. S.Kumar and P.Patel, Con.Matt.News., 2, 9, 1993.
16
61. H.Sackmann, “Advances in Liquid Crystals and Applications” (Ed.L.Bata), Pergamon
press, Oxford, 1981.
62. P.BhaskaraRao, N.V.S.Rao and V.G.K.M.pisipati, Mol.Cryst.Liq.Cryst.Lett., 6, 95,
1989.
63. N.K.Sharma, W.Weissflog, L.Richter, S.Diele, D.Walther, H.Sackmann and
D.Demus., Mol.Cryst. Liq. Cryst., 28, 275, 1974.
64. P.R.Alapati, P.Bhaskara Rao, N.V.S.Rao, V.G.K.M.Pisipati., Mol. Cryst. Liq. Cryst.,
5, 73, 1988.
65. S.Sakagami, A.Takase and M.Nakamizo, Mol. Cryst. Liq. Cryst., 36, 261,1976.
66. E. Arun, Mol. Cryst. Liq. Cryst., 4, 189,1987
67. J.C.Dubois, Annls.Phys., 3, 131, 1978.
68. C.Destrade, M.C.Mondon and N.h.Tinh, Mol. Cryst. Liq. Cryst. Lett., 49, 169,
1979.
69. A.M.Levelut, J. Chem. Phys., 80, 149, 1983.
70. A.R.Berardi, M.Cecchini and C.Zanoni, J.Chem.phys, 199, 9933, 2003.
71. O.H.Schonherr, J.H.Wendroff, H.Ringsdorff and P.Tschirner, Macrmol.
Chem.Rapid.Commui., 7, 791, 1986.
72. Lei Lin, Mol.Cryst. Liq. Cryst., 146, 41, 1987.
73. H.Zimmermann, R.Poupko, Z.Luz and J.Billard, Z.Naturforsch.,40a, 149,
1985.
74. J.Malthete and A.collet, J. Chem., 9, 151, 1985.
75. A.M. Levelut, J.Malthete and A.Collet, Ann.Phys. (Paris), 47, 351, 1986.