1. Summer Training
Submitted to the Amity University Uttar Pradesh In partial fulfillment of
requirements for the award of the Degree of
(M.Sc. Applied Physics)
By
KOMAL BISHT
Enrollment No: A4450014003
Under the Supervision of:
Amity Institute of Applied Sciences, Amity University Uttar Pradesh
Sector 125, Noida – 201303 (India)
i
Supervisor
Dr. Satyendra Prakash Singh
…………….

2. DECLARATION
I, Komal Bisht student of M.Sc. Applied Physics hereby declare that the Summer Internship
titled “DIELECTRIC PROPERTIES OF LIQUID CRYSTAL DISPLAY” which is
submitted by me to Department of Amity Institute of Applied Sciences, Amity University,
Uttar Pradesh, Noida, in partial fulfillment of requirement for the award of the degree of
………………………..….., has not been previously formed the basis for the award of any
degree, diploma or other similar title or recognition.
Noida
Date
Name and Signature of student
ii

3. CERTIFICATE
On the basis of declaration submitted by Komal Bisht student of M.Sc. Applied Physics, I
hereby certify that the Summer Internship titled “DIELECTRIC PROPERTIES OF
LIQUID CRYSTAL DISPLAY” which is submitted to Department of Amity Institute of
Applied Sciences, Amity University, Uttar Pradesh, Noida, in partial fulfillment of
requirement for the award of the degree of ………………………..….., is an original
contribution with existing knowledge and faithful record of work carried out by him/them
under my guidance and supervision.
To the best of my knowledge this work has not been submitted in part or full for any Degree
or Diploma to this University or elsewhere.
Noida
Date
(Guide)
Department of …………..………..
Amity Institute of Applied Sciences
Amity University, Uttar Pradesh, Noida
iii

4. ACKNOWLDGEMENT
I wish to express my sincere gratitude to my mentor Dr. Satyendra Prakash Singh for his
exemplary guidance, monitoring and constant supervision and encouragement as well as for
providing necessary information regarding project and for supporting completely in project.
iv

5. CERTIFICATE
This is to certify that Komal Bisht student of Amity Institue of Applied Science has carried
out the work presented in the project which is entitled as Dielectric Properties of Liquid
Crystal Display as a part off 1st
year of Masters of Science in Physics from Amity Institute of
Applied Science Amity Noida, Uttar Pradesh under my supervision.
v

6. TABLE OF CONTENT
S. No. Chapters Page No.
1. Declaration ………………….. ii
2. Certificate ………………….. iii
3. Acknowledgement ………………….. iv
4. Certificate ………………….. V
5. Table of Contents ………………….. vi
6. List of figures ………………….. viii
7. Abstract ………………….. Ix
8. Chapter 1: Introduction ………………….. x
1.1 History ………………….. xi
1.2 Concepts Included ………………….. xii
1.3 Classification of Liquid Crystal ………………….. xii
1.4 Properties of Liquid Crystals ………………….. xii
9. Chapter 2: Fluctuations & Diffusions ………………….. xiii
2.1 Orientational Fluctuations ………………….. Xiii
2.2 Translational Diffusion ………………….. xiii
2.3 External Field Effects ………………….. xiv
10. Chapter 3: Droplets and Simulation
Models
………………….. xvi
3.1 Droplets ………………….. xvi
3.1.1 Radial Droplet ………………….. xvi
3.1.2 Bipolar Droplet ………………….. xvi
3.1.3 Other Droplet Samples ………………….. xvii
3.2 Simulation Models ………………….. xviii
3.2.1 Atomistic Model ………………….. xviii
vi

7. 3.2.2 Simplified Models of Polymers &
ffLiquid Crystals
………………….. xviii
3.2.3 Hybrid Model ………………….. Xix
11. Chapter 4: Liquid Crystalline Polymers
………………….. xx
4.1 Side chain Liquid Crystalline Polymers
………………….. xx
4.2 Main Chain Liquid Crystalline
Polymers
………………….. xxi
4.3 Carbosilane Liquid Crystalline
Dendrimers
………………….. xxi
4.4 Hybrid Gay-Berne / Lennard-Jones
Model
………………….. xxii
4.4 Coarse-Grained Model ………………….. xxii
12. Chapter 5: References ………………….. xxv
List of Figures
vii

8. viii
S. No. Figures Page No.
1. Figure 1: Liquid crystals are the state
between liquids and solids
………………….. x
2. Figure 2: Lehmann studied the crystalline
properties of various particles
………………….. Xi
3. Figure 3: Austrian Botanist Reinitzer gave
an idea of LC
………………….. Xi
4. Figure 4: Classification of Liquid crystal ………………….. Xii
5. Figure 5: Affect of external field over
liquid crystal
………………….. Xiv
6. Figure 6: Radial Droplet of Nematic
Crystal
………………….. Xvi
7. Figure 7: Bipolar Droplet of Nematic
Droplet
………………….. Xvii
8. Figure 8: Atomistic Simulation &
molecules representing individual potential
functions
.………………..
Xviii
9. Figure 9: Gay Berne Potential ………………….. Xx
10 Figure 10: Side Chain Of Liquid Crystalline
Polymers
………………….. Xxi
11. Figure 11: Main Chain Of Liquid Crystalline
Polymers
…………………..
Xxi
12. Figure 12: Hybrid Gay – Berne ………………….. Xxii
13. Figure 13: Coarse Grained Model ………………….. Xxiii
14. Figure 14: Monte Carlo Simulation ………………….. Xxiii
15. Figure 15: The Diagrammatic of the Model ………………….. Xxiv

9. 1. ABSTRACT
Liquid crystal are substance that do not melt directly to liquid phase but first passes
through a paracrystalline stage in which molecule are partially ordered. In this stage
liquid crystal is a cloudy translucent fluid but has some of the vivid features of solid
possesing optical properties. Liquid crystal arises due to the molecular asymmetry. It
arises because two molecules cannot occupy the same space at the same time and is
largely entropically derived. Liquid crystals will play an important role in modern
technology.
ix

10. Liquid Crystal is basically the organic compound that lies between liquid & solid. Liquid
Crystal flows like a liquid but molecules are solid. There are various Liquid crystal phases
which is however observed by optical properties although dielectric & optical properties of
solids & liquids can vary. In this crystal do not melt directly to liquid phase but first passes
through a Para crystalline stage in which molecule are partially ordered. They possess optical
properties due to liquid crystal phases.
Liquid crystals are formed due to molecule asymmetry which arises because two molecules
cannot occupy the same space at the same time. The basic difference b/w solid liquid 7 liquid
crystal is that SOLIDS molecules are highly ordered and have less translational freedom
whereas n LIQUID molecules do not have any intrinsic order & in LIQUID CRYSTAL have
tendency to point along a common axis.
Figure 1: Liquid crystals are the state between liquids and solids
1.1 History
There is a very important concept which is not been discussed yet i.e. chirality. An object is
said to be chiral if it contains such kind of shape that it can be superimposed on mirror image.
Human hand is the best example for the same. Chirality is not a state of matter and it cannot
have any phase transition i.e. from chiral to achiral. The nematic phase of chiral substance
has a name of its own which is termed as choleristic phase.
Liquid Crystal is unusual transition b/w solids & liquids which was observed by Austrian
Botanist Reinitzer in the year 1888. Basically the existence of liquid crystalline phase was
discovered by the Austrian botanist by default. While observing some esters of cholesterol he
observed two melting points. At 145.5 C cholesteryl benzoate melted from a solid to a cloudy
liquid and at 178.5 C it turned into a clear liquid. Some unusual colour behaviour was also
observed upon cooling; first a pale blue colour appeared as the clear liquid turned cloudy and
then a bright blue-violet colour as the cloudy liquid crystallised.
x
1. Introduction

11. Figure 2: Lehmann studied the crystalline properties of various particles
Later it was sent to a German Physicist Lehmann who was studying the crystallisation
properties of various substances. Lehmann observed the sample with his polarising
microscope and noted its similarity to some of his own samples. He observed that they flow
like liquids and exhibit optical properties like that of a crystal. Earlier it was referred as
flowing crystals and later used the term "liquid crystals". Basically the molecules in a crystal
are ordered whereas in a liquid they are not.
Figure 3: Austrian Botanist Reinitzer gave an idea of LC
There are many types of liquid crystals Rod shaped molecules are called "calamities". Disc
shaped molecules are called "discotics". Liquid obtained by calamities is called thermotropics
and liquid crystal by discotics is lyotropics. Liquid crystals are also derived from certain
macromolecules usually in solution but sometimes even in the pure state. They are known as
"liquid crystal polymers (LCPs)". The symmetry of liquid crystalline phases is cateogrized in
terms of their orientational and translational degrees of freedom. The nematic, smectic and
columnar phase types possess, respectively 3, 2 and 1 translational degrees of freedom. The
most fundamental characteristic of liquid crystals is the presence of orientational order of the
anisotropic molecules, while the positional order of the centre of mass is either absent or
limited.
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12. 1.2 Concept Included
Concepts under which Liquid crystal works are as follows:
1. Light can be polarized
2. Liquid crystal can transmit & charge polarised light.
3. Structure of Liquid crystal can be charged by electric current.
4. Liquid crystal is transparent substance that is the reason it can conduct electricity.
1.3 Classification of Liquid Crystals
Liquid crystal are divide primarily into 2 main types nematic order & the other one is smectic
order. In Nematic phase the molecules are free to move in all the directions but on average
they are mostly parallel to long axes. In Smectic phase structural variation exists. A smectic
is layered structure when molecules are parallel to normal layer. Liquid crystals are further
divided in thermotropic ,lyotropic and metallotropic phases. Themotropic, Lyotropic falls
under organic molecule. Thermotropic phase is temperature dependent, Lyotropic phase is
both temperature & concentration dependent. Metallotropic phase is not purely organic
molecule they depend on temperature concentration & inorganic – organic composition.
Figure 4: Classification of Liquid crystal
1.4 Properties of Liquid Crystals
1. Liquid crystal are affected by electric currents and when voltage is applied they may
change shape
2. When heat is applied to crystalline solids it experiences a transition to a different shape.
3. When they are bulked together liquid crystals form micro droplets.
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13. 2.1 Orientational Fluctuations
Consider spectra in the absence of translational diffusion or equivalently, spectra of large
enough nematic droplets in which molecular motion is not very influential. The only relevant
molecular dynamics is now caused by fluctuations of long molecular axes a around the
director n. We consider nematic droplets with radial and bipolar boundary conditions. To
obtain a spectrum with a sufficient resolution, it is necessary to simulate a relaxation signal
G(t) that is long enough, i.e., lasting for several NMR cycles of duration to each.
Time scales of molecular fluctuations and NMR, i.e., tp and to, This relation between tp and to
do not allow us to generate a sufficiently long G(t). In diffusion-less limit the spin
configurations inside nematic droplet 8 times per NMR cycle, which is much less than the
natural scale given above. Limited sampling of MC structures still reproduces the effect of
molecular fluctuations sufficiently well. If the NMR magnetic field B is applied along the
z-axis it still has two asymmetric peaks which however, are now located approximately at
wZ ± δwQS. This reveals that most molecules are aligned parallel to B.
Summing up contributions originating from droplets from the entire sample then yields a
spectrum similar to the Pake-type powder spectrum. If the process of nematic droplet
formation in a polymer matrix has occurred in sufficiently strong external field, the bipolar
droplet axes are aligned along the field direction.
2.2 Translational Diffusion
In addition to fluctuations of the long molecular axes we would include also translational
molecular diffusion into the analysis. Isotropic translational diffusion is simulated by a
simple random walk process in which each spin — representing one or more nematic
molecules — jumps to one of its nearest neighbour sites with equal probability.
Consider the case in which the diffusion is characterized by a single motional constant. i.e.
the probability for a molecular diffusion which do not depend on the local orientation of the
director. In a bulk unconstrained nematic phase the diffusion anisotropy can be typically up
to D/D ± ~ 2, with Dybeing measured along the director and D± perpendicular to it. The
inclusion of anisotropic diffusive process into the simulation alters the spectra only
negligibly. Isotropic translational diffusion has been simulated by a simple random walk
process in which each spin — jumps to one of its nearest neighbour sites with equal
probability. After the diffusion jump has been performed, the spin acquires the orientation of
xiii
2. Fluctuations & Diffusions

14. the local director at the new coordinates.
For any type of boundary conditions the fast diffusion spectrum consists of two lines centred
at wZ ± |<wQ>I|. If the diffusion is fast enough so that molecules diffuse through a large
enough portion of the droplet. In the radial configuration where <wQ>I = 0 holds i.e. the two
lines should coalesce into a central line. For the bipolar droplet, we observe that the two lines
in the spectrum do not merge into a single line. This happens because now we are dealing
with an ensemble of molecules whose orientational distribution is spatially anisotropic. It is
convenient to express the limit between the slow and fast diffusion regimes in terms of the
droplet size, keeping the value of the diffusion constant fixed. This can be done since the
spins used for modelling the nematic. Lining up spectra for the two different types of
boundary conditions and comparing them shows that in the slow diffusion limit it is always
possible to identify the radial structure because of its characteristic Fake type spectral shape
that do not depend on the direction of the external magnetic field. The spectra of the bipolar
droplet on the other hand depend significantly on the magnetic field direction since the
corresponding director configurations are anisotropic due to net molecular alignment. The
diffusion-averaged spectra of the bipolar structure show two peaks at nonzero splitting,
unless again the majority of the spins are lying at a "magic" angle with respect to the
magnetic field direction.
2.3 External Field Effects
Figure 5: Affect of external field over liquid crystal
In presence of an aligning external field the Hamiltonian for our model system consisting of
N spins can be written as:
UN = - € Σ P2 (cos βij) - €η Σ P2 (cosβi)
xiv

15. Where,
cos βi = f.ui,
f is a unit vector in the external field direction.
η is a dimensionless constant describing the strength of the coupling with the external
field.
In order to influence the molecular alignment inside the droplet significantly, the external
field has to be strong enough so that the characteristic length of the field-induced distortion.
xv

16. 3.1 DROPLETS
3.1.1 Radial Droplet
Applying an external field with η > 0, the radial "hedgehog" structure containing a point like
defect transforms into an axially symmetric structure with a ring defect. The local nematic
order parameter S and the external field order parameter <P2>B.
The parameter S gives information on the degree of nematic ordering with respect to the
average local molecular direction.The number of spins within a shell increases when moving
from the droplet center towards the surface. The maximum variance of S usually occurs in
intermediate shells or even close to the substrate. Increasing the field strength, the degree of
ordering in the centre increases significantly and the molecules of the core align along the
field direction. The aligned structure the size of the aligned core increases gradually with the
increasing field strength.Surface-induced radial order persists in the outermost molecular
layers, which results in a strong decrease of the order parameter.The thickness of this region
is again roughly is equal to the field coherence length £.
Figure 6: Radial Droplet of Nematic Crystal
3.1.2 Bipolar Droplet
For all droplets in a real PDLC sample this can be achieved by applying external magnetic
field of sufficient strength during the droplet formation process. The results show that a
considerable portion of nematic molecules — especially those in the droplet core which is
directed approximately along the spectrometer field, which results in a spectrum consisting of
two well-defined peaks.
The S-profiles for the bipolar droplet in nematic phase indicates that the degree of nematic
ordering is almost constant throughout the droplet core when the external field is absent.
xvi
3. Droplets and Simulation Models

17. The corresponding curve for η = 0 shows that already in absence of the field there is net
molecular alignment along the z-axis, which agrees with the imposed bipolar boundary
conditions whose symmetry axis matches with z.
The curves for η > 0 showsdat with the increasing field strength more and more molecules
(spins) orient along z which increases the size of the droplet core where the nematic liquid
crystal is almost undistorted.The increase of the quadrupolar splittingwQin strong fields can
be attributed both to the overall increasein the local degree of ordering, i.e., to an increase of
S.The narrowing of the spectral lines is related to the increase of <P2>Bsince in the droplet
core the bipolar configuration is replaced by the "aligned" one.
In strong fields the field-enhanced "bulk" value of S approaches the surface-induced value
and thus the distribution of S becomes narrower.
Figure 7: Bipolar Droplet of Nematic Droplet
3.1.3 Other Droplet Samples
In a real sample, there are many droplets, all of them contributes to the macroscopic response
of the system. Such a sample behaves as isotropic although the constituent bipolar droplets
are not. In the spectrum it is assumed to see the Pake-type pattern instead of the two-peaked
spectrum obtained for a single droplet. In an experiment, the two-peaked spectrum can be
obtained if all the bipolar symmetry axes are preliminarily aligned by a strong external
electric or magnetic field. We simply "clone" the data for a single droplet to model several
droplets; this would result in unphysical correlations between particle orientations in different
droplets.
xvii

18. 3.2 Simulation Models
3.2.1 Atomistic Models
Atomistic simulation is best tool for studying solids, liquids and gases. Each atom within a
molecule represents by individual potential functions to model non-bonded interactions
Figure 8: Atomistic Simulation & molecules representing individual potential function
which is known as vander wall interaction or electrostatic interaction. The atoms are linked
together by means of multi-site potentials which model the intramolecular bond stretching,
bond bending and torsional interactions within molecules. Together all the potentials
comprises a force field for the molecule which is used in molecular mechanics studies to find
the lowest energy conformations of the molecule in molecular dynamics or Monte Carlo
simulations to study the isolated molecule and the molecule within a bulk phase. Atomistic
studies with good quality force fields should be sufficient to represent liquid crystal phases or
polymer melts to a high level of accuracy & most material properties should be available
from such simulations. For low molecular weight liquid crystals a few seconds may be
enough to see the growth of a nematic phase from an isotropic liquid. The number of sites
available in typical atomistic simulations, severely restricts the size of polymer. Atomistic
simulation is best, it is rather limited as a tool for studying polymer liquid crystals and other
complex materials.
3.2.2 Simplified Models for Polymers & Liquid Crystals
xviii

19. To push simulation to longer time scales and larger system sizes has led to the development
of more coarse-grained models for both liquid crystals and polymers. A popular coarse-
graining approach involves the use of the Gay-Berne potential. A liquid crystal molecule can
be represented by a single anisotropic site with both anisotropic attraction and repulsion
acting between molecules. The Gay-Berne is also known as Lennard-Jones potential. The
energy at which attractive and repulsive energies cancel σ and the depth of the attractive well
€ depend on the relative orientations ei of the two particles.
UGB= ƒ(rij , ei , ej)
Four parameters , ’ , µ & ν control the form of the potential. The length/breadth ratio isҡ ҡ
given by the parameter ҡ & the ratio of side-to-side/end-to-end well-depths is given by ҡ,’µ & ν
can be used to vary the well-depths for molecules coming together in different relative
orientations. The Gay-Berne potential has been used for many liquid crystal simulations, &
can be used to simulate nematic, smectic-A & smectic-B phases. The GB model provides
predictions for key material properties, such as elastic constants and rotational viscosities,
which have an important role in determining how a nematic liquid crystal responds ina liquid
crystal display (LCD).
A common form of coarse-graining involves the use of bead-spring models. A cut and shifted
Lennard-Jones potential is used for the beads; and this is combined with a FENE potential for
the springs. This potential is much softer than a normal bond stretching potential. An
additional feature of the FENE is that an appropriate choice of parameters can practically
forbid the crossing of chains. In liquid crystal simulation the earliest and most widely used
model is that of Lebwohl and Lasher. Bonds connecting the two beads are represented by
nearest neighbour links between occupied lattice sites.
3.2.3 Hybrid Models
Coarse grained models combine anisotropic sites such as Gay berne potential at anisotropic
sites. The non bonded interactions energies, Uatom , Umesogen , Umesogen/atom can be
represented by a combination of Lennard-Jones, Gay-Berne and extended Gay-Berne. The
advantage of such hybrid models is that complex macromolecules containing liquid crystal
keeps the essential characteristics of the molecular structure.
xix

20. Figure 9: Gay Berne Potential
4.1 Side Chain Liquid Crystalline Polymers
The methyl siloxane backbone and the flexible alkyl spacer of the real polymer have been
replaced by a series of united atom potentials, and the mesogenic groups have been replaced
by Gay-Berne potentials. The aligning potential mimics the effects of a magnetic field. It is
applied as strong magnetic field is usually required experimentally to produce uniformly
aligned mesophases.
1. The presence of the aligning potential leads to the formation of mesophases on cooling.
2. In the absence of the aligning potential, cooling induces microphase separation into
mesogen-rich and polymer rich regions.
The presence of polymer chains is sufficient to decouple the ordering of the mesogens in each
region, resulting in a system with an overall order parameter = zero. At lower temperature the
structure anneals to give smectic-A ordering within the individual crystalline layers. In the
unaligned system, the polymer backbone forms a network separating the different mesogenic
xx
4. Liquid Crystalline Polymers

21. regions, and the flexible spacers seems to form a sheath around the polymer backbone & this
backbone is able to jump between the layers causing a small defect in liquid crystalline
regions.
Figure 10: Side Chain Of Liquid Crystalline Polymers
4.2 Main Chain Liquid Crystalline Polymers
For the m = 6 system, spontaneous ordering of the polymer occurred on cooling from 500 K
to 350 K to form a nematic phase. The periodic boundary conditions have not been applied &
the polymer chains have been allowed to spill out of the simulation box. The change in order
of individual chains on entering the nematic phase can be observed with the chains stretching
to lie parallel to the nematic director. For m = 6 in the nematic phase order parameters for
even bonds are higher than those for odd bonds. Limitations on simulation time doesn’t allow
for the growth of nematic phases for each system.
Figure 11: Main Chain Of Liquid Crystalline Polymers
4.3 Carbosilane Liquid Crystalline Dendrimers
In the case of carbosilane dendromesogens mesogenic moieties are incorporated into the
interior of the dendrimer. In Carbosilane dendrimers the number of mesogens doubles with
xxi

22. generation number. The phase behaviour of these systems was initially studied by optical
microscopy and differential scanning calorimetry, and subsequently by X-ray diffraction. The
dendrimer structure, which appears spherical if a gas phase molecular model is constructed,
deforms to give a rod and that the rods pack together to give smectic phases.
1. The first four generations of dendrimer, the systems are believed to exhibit smectic-C and
smectic-A phases.
2. The 5th generation dendrimers the series of phases was found to be different & represent
ellipsoidal and circular columns.
4.4 Hybrid Gay-Berne / Lennard-Jones Model
Figure 12: Hybrid Gay – Berne
“Each heavy atom is represented by single Lennard-Jones site & Each mesogenic group by a
Gay-Berne potential & uses molecular dynamics simulations to study the behaviour of the
system.”
A remarkable structural change occurs when the dendrimer is immersed in a nematic solvent.
The dendrimer structure rearranges to form a rod-like shape with the order parameter of the
mesogenic groups. This rearrangement occurs over a period of around 4 ns. The structure of
the different parts of the dendrimer can be mapped by distribution functions which shows
backfolding of the chains is possible, and that they are able to fill spaces within the core.
However, the degree of backfolding is quite small. The distribution functions also shows that
the structure of the dendrimer core does not change significantly with solvent. Now, When
the dendrimer is immersed in a smectic solvent, the dendrimer structure changes again.
4.4 COARSE - GRAINED MODELS
To understand the structure of the bulk phases formed by the dendrimer, it is necessary to
coarse-grain the model further to make it possible to simulate a reasonably large number of
dendrimer molecules.
Some of the useful insights are as follows:
xxii

23. 1. The dendritic core can seemingly be decoupled from the outer parts of the molecule.
2. The penetration of other molecules into the core can also be expected to be extremely
small.
3. Flexible chains terminated in mesogenic units are clearly essential in any model.
4. The degree of coarse-graining employed for the chains are probably not critical, but it
is essential that chains should be able to wrap round the core and that they are able to
change conformation easily to allow the mesogenic groups to order as they "want".
Figure 13: Coarse Grained Model
Figure 14: Monte Carlo Simulation
The biggest advantage of Monte Carlo simulations is the possibility of investigating the
system at microscopic level and to calculate thermodynamic properties and their specific
order parameters suitable for different types of PDLC. It is possible to calculate experimental
observables like optical textures and, 2H NMR line shapes
Keeping these insights in mind 2 models have been described.
In the 1st
model
1. The central core of the dendrimer is coarse-grained to a single spherical site.
xxiii

24. 2. The chains are coarse-grained to three spheres each, and the mesogen is coarse-
grained to a single spherocylinder.
3. The phase behaviour of the model system has been studied as a function of density.
4. For this 1st
model we have seen no evidence for spontaneous microphase separation or
formation of mesophases prior to freezing.
In the 2nd
model
1. We reduced the size of the core & added an extra site to each chain to model the
Si(Me)2-O-Si(Me)2 groups and extended the length of the sphero cylinders which
gives an aspect ratio of L/D = 6.
2. The liquid crystal phase only remains stable for densities just prior to freezing.
3. L/D = 6 spherocylinders seems to be right on the limit of the mesogens length
required to see stable mesophases in this system.
4. The lack of attractive forces in this model mean that microphase separation is induced
mainly by entropic forces.
5. Alignment of the sphero cylinders increases their translational entropy.
6. As the density of the system increases, the translational entropy wins out.
7. At sufficiently high densities the system will freeze to form a glass.
.
Conclusion Drawn from the three models:
Figure 15: The Diagrammatic of the Model
xxiv

25. xxv

26. 1. Castellano, Joseph A. (2005). Liquid Gold: The Story of Liquid Crystal Displays and the
Creation of an Industry.
2. Gray, G.W.; Harrison, K.J.; Nash, J.A. (2010). "New family of nematic liquid crystals for
displays".
3. Gray, G. W. (2007) Molecular Structure and the Properties of Liquid Crystals, Academic
Press.
4. Shao, Y.; Zerda, T. W. (1998). "Phase Transitions of Liquid Crystal PAA in Confined
Geometries".
xxvi
5. Refrences