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Voyles, Andrew000442-067
Modeling the Variation in Specific Heat of a 4’-
Octyl-4-Biphenyl-Carbonitrile Liquid Crystal due
to Phase Transition
Andrew Voyles
000442-067
Chemistry
3968 words
Voyles, Andrew000442-067
Abstract
The intent of this paper is to investigate how the specific heat of a 4’-Octyl-4-Biphenyl-Carbonitrile (8CB) liquid crystal changes as the crystal undergoes phase transitions as it is heated, and to subsequently model the variation in specific heat in the various liquid crystal phases. I undertook this investigation as a result of a suggestion by a local professor at a demonstration he gave at our school, as well as out of a great passion for chemistry. A molecular-level discussion of the mechanisms behind specific heat for conventional and the structure of and interactions between the molecules as the crystals are heated and undergo phase transition provides a solid theoretical base for the analysis. This was approached experimentally, by collecting specific heat capacity data over a range of temperatures in all of the liquid crystal mesophases of a particular liquid crystal, 8CB, using a differential scanning calorimeter to calculate the thermodynamic properties of the sample as it was heated, a procedure suggested to me by my supervisor, Dr. Timothy Royappa. From this data, I attempted to construct rational functions to model the specific heat as it rapidly changed due to the multiple transitions of structure that the liquid crystal experiences as it is heated, as it undergoes phase transition. This function was statistically analyzed, using the coefficient of determination, R2, in order to determine how well the original data fit the constructed functions. By comparing the generated data to the molecular-level structure and interactions of the crystals as they are heated, it was possible to theorize a possible mechanism for the variation in specific heat as the crystals undergo phase transition. While I was able to construct relatively accurate models for each phase, no reviewed literature values exist to compare my results to.
Voyles, Andrew000442-067
Table of Chapters
I: Introduction.............................................................1
II: A Brief History of Liquid Crystals.............................3
III: Thermotropic Liquid Crystal Mesophases...............5
IV: Specific Heat........................................................16
V: Investigation.........................................................20
VI: Analysis...............................................................33
VII: Bibliography........................................................36
Voyles, Andrew000442-067
Modeling the Variation in Specific Heat of a 4’-Octyl-4-Biphenyl-
Carbonitrile Liquid Crystal due to Phase Transition
I: Introduction
Perhaps one of the biggest developments of the 20th century, the
discovery of the liquid crystal, a so-called “fourth state of matter”, in
1888 by the Austrian botanist and chemist Friedrich Reinitzer has
greatly impacted modern technology. Many modern devices utilize the
most common application of these crystals, the liquid crystal display
(LCD). This use creates a very profitable market for these crystals, as
the LCD uses very little power, making them ideal for use in handheld
electronic devices. The potential uses for liquid crystals make a
seemingly endless list, one that has yet to begin to be tapped.
One major division is that of thermotropic liquid crystals, those
which undergo a phase transition and thermal property changes as a
result of changes in temperature. In this investigation, the particular
liquid crystal in use is 4’-Octyl-4-Biphenyl-Carbonitrile (8CB), also
known as 4-Cyano-4'-Octylbiphenyl or 4-Octyl-4’-Cyanobiphenyl, a
common thermotropic liquid crystal. The structural formula of the 8CB
liquid crystal is CH3(CH2)7C6H4C6H4CN, and its molecular formula is
C21H25N. The structural diagram of this liquid crystal is seen here
Voyles, Andrew000442-067
below. The decidedly rod-like shape plays a large role in phases that
8CB transitions through, as the close packing of the molecules allows
for greater potential for intermolecular forces.
Fig. 1. Structural diagram of 8CB liquid crystal
Sigma Aldrich, 338680 4′-Octyl-4-biphenylcarbonitrile.
http://www.sigmaaldrich.com/catalog/search/ProductDetail/ALDRICH/33
8680
The intent of this paper is to investigate how the specific heat of
a 4’-Octyl-4-Biphenyl-Carbonitrile (8CB) liquid crystal changes as the
crystal undergoes phase transitions as it is heated, and subsequently
model the specific heat in the various liquid crystal phases. An
understanding of this change allows one to create new technologies
that are capable of bettering society, utilizing the change as an
innovation behind new technologies.
Voyles, Andrew000442-067
II: A Brief History of Liquid Crystals
In the brief time period since their discovery, the field of liquid
crystals has been full of important discoveries. In 1888, Friedrich
Reinitzer, an assistant at the German University of Prague’s Institute of
Plant Physiology, was working on determining the chemical formulas of
cholesterol derivatives extracted from carrots. Reinitzer noticed that
one particular cholesterol, cholesteryl benzoate, had two melting
points: at 145.5°C, the cholesterol melted into a cloudy liquid up to
178.5°C, at which point it melted again, giving rise to a clear liquid, a
reversible process (Sluckin, 2004; Reinitzer, 1888). After this, Reinitzer
would contribute no more to this field.
Otto Lehmann, a German physicist and friend of Reinitzer, who
had been frequently contacted via letters by Reinitzer during his
investigations, carried on the research. Over the next year, Lehmann
studied cholesteryl benzoate and other chemically similar compounds,
noticing that they, too, possessed the double melting points, and the
ability to polarize light (Lehmann, 1889).
No more major advances in the field of liquid crystals would
occur until 1969, when Hans Kelker synthesized MBBA (p-
Methoxybenzyliden-p’-n-butylanilin), which exhibited the cloudy liquid
state at room temperature, re-starting liquid crystal research in the
20th century. This compound would prove to be vastly important in
liquid crystal research (Kelker, 1969). Exhibiting the cloudy state at
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room temperature made it much easier to work with, as others at the
time exhibited this state only at high temperature and pressure.
Because of this, MBBA has become known as the “fruit fly” of liquid
crystal research (de Gennes, 1974).
A final obstacle to commercial applications was resolved in 1973,
when George W. Gray synthesized cyanobiphenyl liquid crystals,
extremely stable liquid crystals with low melting points, ideal for use in
LCDs (Gray, 1973). Since then, research into applications has
continued to abound, creating a very large market for this technology,
which has shown such promise as a future technology that, as a result
of his work in the field of ordered liquid crystal systems, Pierre-Gilles
de Gennes received the Nobel Prize in physics in 1991 (The Nobel
Foundation, 2008).
Voyles, Andrew000442-067
III: Thermotropic Liquid Crystal Mesophases
As stated previously, thermotropic liquid crystals, including 4’-
Octyl-4-Biphenyl-Carbonitrile, undergo a phase transition as they are
either heated or cooled, through the crystalline solid, smectic, nematic,
and the isotropic liquid phases, known more accurately as
mesophases, and can be determined by analyzing the degree of
system order that the individual molecules exhibit. Unless otherwise
noted, order will be defined as both positional order and orientational
order.
Positional order is “the extent to which… an average molecule or
group of molecules shows… arrangement in space”, and orientational
order is the “measure of the tendency of the molecules to align along
the director [the larger axis of an individual molecule] on a long-range
basis” (Case Western Reserve University, 2008). Crystalline solids have
three degrees of positional order (all constituent molecules being fixed
in place with an x, y, and z coordinate), and conventional liquids have
no positional order at all. As heat is added, in the case of liquid
crystals, positional order is lost before orientational order, as
orientational order forces are stronger (Johnston, 2008; Vertogen,
1988).
All matter, including liquid crystals, undergoes phase transitions
in accordance with the second law of thermodynamics, which states
that entropy (a measure of the disorder of a system) is constantly
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increasing. As matter is heated, it assumes states of minimized
chemical potential and order, resulting in an increase in entropy. These
states are the various conventional phases of solid, liquid, and gas
(Atkins, 1986; de Gennes, 1974)
The most orderly mesophase of liquid crystals is that of the
crystalline, anisotropic (directionally dependent, due to molecular
shape and alignment).solid, a regular lattice of millions of molecules
bonded together. The smallest unit of a crystalline solid is called a unit
cell, consisting of that specific crystal’s empirical formula. Individual
unit cells with identical surroundings repeat endlessly in a periodic
pattern, called a lattice, forming crystals. As the solid is heated, the
individual molecules become more disorderly, and transition into the
liquid state of matter at their melting point, as the added heat
overcomes the forces locking the molecules in their fixed positions.
Many organic molecules, notably liquid crystals, do not exhibit
this single, clear transition. Since many organic molecules are long,
polar, rod-like chains, there exists the possibility for many more
intermolecular forces than in inorganic compounds. As they are
heated, the intermolecular attractions create intermediate states of
organization, not seen in conventional matter. These are mesophases,
intermediate states of low chemical potential and order that are
formed as liquid crystals are heated, before finally transitioning to a
conventional isotropic (directionally uniform, as opposed to
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anisotropic) liquid, where the order of particles is uniform in all
directions, and any orientation is indistinguishable from any alternative
orientation (de Gennes, 1974). As the crystals proceed from solid to
liquid, they transition through intermediate (mesomorphic) phases.
Which and how many the crystals transition through depends on the
properties and structure of the individual crystal. For many, however,
the transition to the first liquid crystalline mesophase, at the melting
point, produces a turbid (cloudy) and birefringent fluid, as seen by
Reinitzer. The phenomenon of birefringence is caused by an imbalance
in the refractive indices of an optical medium (classically seen in
calcite crystals), which rotates polarized light, producing the colorful
show (Templer, 1991). As the sample is further heated, it may pass
through other mesophases, until it reaches the “clearing point”, the
“second melting point” observed by Reinitzer, at which the liquid
crystal “melts” again, into an optically clear, isotropic liquid (Vertogen,
1988). This transition can be visualized below.
Fig. 2. The liquid crystalline phases on a temperature scale (Vertogen,
1988)
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The most orderly mesophase is the smectic phase, in which there
are many distinct phases, given capital identification letters. This
system was introduced by the Halle research group, and, as of 2004,
phases A-L have been identified. The placement in a specific phase is
based upon the miscibility (solubility) of the phase: two samples are
classified as being in the same smectic phase if they are miscible in all
proportions (Case Western Reserve University, 2008). The three most
common mesophases, are the Smectic A, B, and C mesophases.
In the smectic mesophase, long-range orientational order is
preserved and short-range positional order is greatly reduced, but still
present, resulting in the individual molecules aligning themselves in
layers (Atkins, 1986; de Gennes, 1974). The word smectic is derived
from the Greek word for soapy, as the soap scum is a common type of
smectic liquid crystal (Case Western Reserve University, 2008). The
centers of mass of every molecule arrange themselves in distinct
planes, whose symmetry distinguishes the different phases from each
other (Vertogen, 1988).
Of the different smectic phases, the simplest, least ordered, and
first to be discovered is that of the smectic A mesophase.
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Fig. 3. Example photo of the smectic A phase displaying its
characteristic fan-like texture (using microscope, under crossed
polarizing lenses)
(Case Western Reserve University, 2008)
Fig 4. Schematic picture of the smectic A phase
(Case Western Reserve University, 2008)
In the smectic A mesophase, more like a liquid than a solid,
molecules form flat planes, normal to the director, whose thicknesses
are approximately the length of the molecules themselves. The
molecules show no positional order (de Gennes, 1974; de Vries, 1971).
A liquid crystal in the smectic A phase is optically uniaxial, that is,
plane-polarized monochromatic light is only capable traveling through
a sample in one direction, referred to as the crystal’s optical axis (Case
Western Reserve University, 2008).
The A phase always occurs at the highest temperature of any
other smectic phase, as a higher temperature would be needed to
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achieve a greater state of disorder (de Vries, 1971). In the case of the
4’-Octyl-4-Biphenyl-Carbonitrile liquid crystal, the A phase is the first
mesophase, upon being heated from the solid state.
The next primary smectic phase is that of the smectic B. Of the
three major smectic phases, the B has the greatest order, so it is the
first to possibly emerge with increasing temperature, as it requires the
least amount of added heat to overcome the intermolecular forces (de
Gennes, 1974). Unlike the A and C phases, the layers of the B phase
are more like a two-dimensional solid, due to their rigidity and
periodicity, confirmed through x-ray diffraction, which reveals definite
positional and orientational order (de Vries, 1971).
Fig. 5. Example photo of the smectic B phase displaying its
characteristic mosaic-like texture (using microscope, under crossed
polarizing lenses)
(Kent State University, 2008)
In the layers of the B phase, molecules align in tightly packing
cyclic, hexagonal rings, as opposed to the linear orientation seen in the
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A phase. As a combined result of the tight packing and the strength of
the hexagonal shape, the enthalpy change for this phase is much
greater than that seen in the A and C phases, nearly fivefold that of its
A phase, in the case of N’-terephthalylidene-bis-(4-n-butylaniline)
(TBBA) (Petrie, 1971).
The final primary smectic phase is that of the smectic C phase.
The C phase possesses some orientational order, and more positional
order than the A phase. These crystals are optically biaxial, allowing
plane-polarized monochromatic light to pass in two directions, the
optical axis lying between these directions (de Gennes, 1974). There is,
on average, a constant tilt angle away from the normal to the plane of
the molecules, caused by dipole-dipole intermolecular attractions
between polar molecules, so that the distance between layers is
approximately equal to d=l * cos(ω), where l is the molecule’s length,
and ω is the constant tilt angle. This creates a distinctive texture,
called schlieren (Vertogen, 1988).
Fig. 6. Example photo of the smectic C phase displaying its
characteristic schlieren texture (using microscope, under crossed
polarizing lenses)
Voyles, Andrew000442-067
University of Cambridge, DoITPoMS TLP - Liquid Crystals.
http://www.doitpoms.ac.uk/tlplib/liquid_crystals/printall.php
Fig 7. Schematic picture of the smectic C phase
(Case Western Reserve University, 2008)
This holds true when the liquid crystal is optically inactive. When
mixed with a second, optically active, compound, called a chiral
dopant, the periodic structure of the layers becomes distorted,
creating a special case, referred to as the smectic C* phase, which
possesses geometrical asymmetry. Like the normal C phase, the
director is at a constant tilt angle to the normal to the smectic plane,
but, unseen in the C phase, the constant tilt angle rotates about a
central axis by a constant angle between each layer, giving a helical
structure, which can reflect one specific wavelength of circularly-
polarized light (Petrie, 1971; Case Western Reserve University, 2008).
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Fig. 8. Schematic picture of the smectic C* phase
(Case Western Reserve University, 2008)
The final mesophase of liquid crystals, possessing the least
positional and orientational order, is that of the nematic mesophase,
first observed as Reinitzer’s cloudy, birefringent liquid. This occurs
immediately before the liquid phase, as temperature increases.
Weaker positional order is completely lost, including the smectic
layered structure, while stronger orientational order is preserved, to a
notable degree, causing the molecules to retain a rough parallel
arrangement, like strands of string, as nematic is the Greek word for
“thread” (Atkins, 1986).
For nematic mesophases, the orientational order arises from all
of the liquid crystal molecules arranged so that a common axis of all of
the constituent molecules is aligned parallel in one direction (the
director), labeled with a unit vector, n. Around the director, there is
nearly complete rotational symmetry. Nematic crystals flow almost
exactly like conventional fluids (de Gennes, 1974).
Fig. 9. A schematic diagram of the nematic phase
Voyles, Andrew000442-067
Wikimedia Commons, Schematic of mesogen alignment in a liquid
crystal nematic phase.
http://commons.wikimedia.org/wiki/Image:LiquidCrystal-MesogenOrder-
Nematic.jpg
Fig. 10. Example photo of the nematic phase (using microscope, under
crossed polarizing lenses)
(Kent State University, 2008)
There also exists a chiral, or, geometrically asymmetrical,
molecule in the nematic mesophase. This special case is referred to as
the chiral nematic (cholesteric) phase. Like the smectic C* phase, the
chiral nematic consists of repeating nematic planes, rotated by a
constant angle from the previous one, capable of reflecting specific
circularly-polarized wavelengths of light. The wavelength reflected
depends upon the distance it takes for one complete revolution of the
helix, called the pitch, so that light of wavelength equal to the pitch will
be completely reflected. While the C* is produced by the addition of a
chiral dopant, the cholesteric phase may exist as a naturally chiral
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material, or by the addition of a chiral dopant. Unlike the smectic, the
cholesteric and the nematic phases are completely miscible. Also, if
equal amounts of samples with opposite chirality are mixed together,
referred to as a racemic mixture, a normal nematic results, with no
changes in any physical property. (Vertogen, 1988; Saeva, 1971).
Fig 11. Structural diagram of the chiral nematic phase
(Case Western Reserve University, 2008)
Finally, upon sufficient heating, as a result of multiple transitions
of structure, the liquid crystal sample will overcome the intermolecular
forces creating orientational and positional order, transitioning to a
conventional isotropic liquid. As stated previously, in an isotropic
liquid, particle order is uniform in all directions, and any orientation of
the liquid is indistinguishable from any other alternative orientation.
Voyles, Andrew000442-067
IV: Specific Heat
One of the most important tasks for classifying and investigating
a new compound is to determine its thermal properties, one of the first
experiments classically performed in determining the identity of the
compound, but replaced in modern times with more advanced
techniques such as mass spectrometry. Nonetheless, it still remains a
highly important task in research, especially in new types of
compounds, including liquid crystals, metamaterials, polymers, and
composites. One of the simplest thermal properties to determine for a
compound is its melting point, the temperature at which a compound
begins the transition from the solid to the liquid state, at constant
pressure.
A second, related property is the specific heat capacity of the
compound. The specific heat capacity, c, is defined as “the quantity of
heat required to raise the temperature of 1 gram of a substance by 1°
Celsius (or one Kelvin) at constant pressure” (Ebbing, 2005).
Mathematically, this relationship can be expressed as c=Δq/mΔt, where
Δq represents the change in heat of the substance, m represents the
mass of the substance, and Δt represents the change in temperature
of the substance. The greater the specific heat capacity of a given
substance, the more thermal energy is needed to raise the
temperature of that substance by 1° Celsius, and vice versa.
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Many methods exist to experimentally determine the specific
heat of a given substance. The simplest method is that of the
calorimeter, where a heated compound is dropped into an insulating
container of liquid, and, based upon the given masses, specific heat of
the liquid, and initial and final temperatures of the two substances
(assuming that no heat is lost to the surroundings), the specific heat of
the heated compound is determined. However, this is a very loose
assumption; more accurate and precise values can be determined
through the use of a differential scanning calorimeter (DSC).
A solid grasp of the molecular-level theory of specific heat is
required to accurately understand the variation, as liquid crystals
undergo phase transitions, discussed in the analysis. At the molecular
level, what is it that causes molecules to be able to store thermal
energy? Due to the unique characteristics of liquid crystals, let’s first
look at conventional matter to understand what causes the change in
heat capacity.
One fundamental concept of thermodynamics has been
neglected: temperature. Temperature is a measure of the average
kinetic energy of an object, the energy of an object due to its motion,
calculated by the equation KE=mv2, where m is the mass of an object
and v is the object’s linear velocity. The average kinetic energy of an
object can also be related to temperature, in the form of the equation,
KEavr=3/2kT, where k is the Boltzmann constant, 1.380 6504×10−23 J×
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ºC-1 and T is the temperature of the object. Thus, an object at high
temperature has a high degree of kinetic energy and, subsequently,
motion (Georgia State University, 2008).
As a molecule gains kinetic energy, it requires a place to “store”
it. This is in the form of internal motion, the result of the agitation of
chemical bonds, through what is referred to as internal degrees of
freedom. An internal degree of freedom is any way that the molecule
or its atoms are capable of moving. There are three forms:
translational freedom (rigid movement or collisions of the whole
molecule in three-dimensional space), rotational freedom (the rotation
of the entire molecule or an atom around an axis), and vibrational
freedom (rapid shaking and contraction of bond lengths). Molecules
maintain minimized chemical potential by converting this excess
kinetic energy into temperature, as discussed above. Small molecules,
such as diatomic gases, have fewer degrees of freedom as they are
made up of fewer atoms. Larger molecules, notably the long, chain
structures seen in many organic molecules, consist of many atoms,
and have dozens of degrees of internal freedom, and a large heat
capacity.
As a result, a heated object will gain kinetic energy and begin to
vibrate and twist extremely vigorously. Two particular bonds capable
of storing a large quantity of thermal energy are the Carbon-Hydrogen
bond seen in the vast majority of organic compounds, and the
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hydrogen bond, a strong special case of dipole-dipole attractions
between a hydrogen atom and a nitrogen, oxygen, or fluorine atom
(University of Cincinnati, 2008; Tim Royappa, PhD., personal interview,
August 11, 2008). Indeed, the number of degrees of internal freedom
of a molecule and that molecule’s molar heat capacity (the specific
heat of 1 mole, 6.022×1023 molecules) are connected by the relation
c=g/2 R, where g is the number of internal degrees of freedom, and R is
the universal gas constant, 8.314 472 J mol-1 C-1 (or K-1) (Fitzpatrick,
2008).
For conventional matter, the specific heat of the compound will
remain approximately constant inside a phase. There will also be a
sharp spike in the values of heat capacity at the compound’s phase
transition, followed by a more or less constant value. In the liquid
crystal mesophases, strength and stability is achieved in these
temporary stable states, causing the sharp peak at the phase
transition; once more heat is added, the heat overcomes more forces,
and so the heat capacity rapidly falls again. A typical example of a
specific heat curve for a conventional compound, sulfapyridine
(C11H11N3O2S), with a single, clear melting point can be seen below.
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Fig 12. Typical DSC specific heat curve
(Mettler Toledo, 2008)
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V: Investigation
For this investigation, a Mettler Toledo DSC823e DSC was used to
obtain specific heat data over a range of temperatures. This machine is
capable of generating extremely accurate and precise results for
specific heat capacity. It works by heating two crucibles, an empty
reference crucible and the crucible containing the sample. The two
crucibles are cooled to some arbitrary initial temperature set by the
user, are heated identically, and a platinum thermometer located
beneath each crucible independently records the temperature of each.
Using a coolant gas, in this case, nitrogen, allows the taking of
measurements below room temperature. Based on the difference
between the final temperatures, knowing that heat was applied to each
at the same rate, it is then possible for the calorimeter to determine
the molar specific heat capacity of the sample (Bonvallet, 1999; Tim
Royappa, PhD., personal interview, August 11, 2008)
Fig 13. Mettler Toledo DSC823e
(Mettler Toledo, 2008)
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I believe that the model for specific heat capacity inside the
mesophase will be of the type of a rational function. I manipulated the
temperature of the sample in order to see how it affects the specific
heat of the sample, which I then measured. By using a calibration run
with the iridium sample, the resulting graphs with much systematic
error taken out acts as a control run.
Materials
Mettler Toledo DSC823e
4’-Octyl-4-Biphenyl-Carbonitrile Sample
Analytic Balance
Aluminum microcrucible
Iridium calibration sample
Nitrogen gas coolant
Table 1. List of materials used
The procedure for this investigation was suggested to me by my
supervisor, Dr. Timothy Royappa, of the University of West Florida. I
first calibrated the DSC using the iridium sample. I then measured out
the mass of the 8CB sample, recorded in the data table below, in a
microcrucible, using an analytic balance. I sealed the crucible shut,
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poking a small hole in the top to allow the pressurized hot air to escape
during the heating process, as per DSC procedure. I placed the
crucibles inside the DSC and cooled the samples to an initial
temperature of 0.0 ± .1 ºC and then heated at 10 ºC min-1 to a final
temperature of 60.0 ± .1 ºC. The transition temperatures were
determined by averaging the temperature at which the peaks in the
specific heat graphs occurred, which indicate phase transitions. This
process was repeated for another sample. As the molar heat capacity
is measured, the mass of the sample has no effect. The general
formula describing the shape of the data that was obtained is y=A(|x-
xc|/xc)-α. By taking the natural logarithm of this equation and plotting a
graph of ln(y) versus ln(|x-xc|/xc), a straight-line graph is produced, with a
slope of α and y-intercept of (0, eA), and a vertical asymptote at xc,
which the DSC rounds off as a sharp peak. From this, I constructed the
rational function for each mesophase, as seen below.
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Data Table
DSC Specific Heat Error Maximum of ± 4%
Solid-Smectic A Smectic A-Nematic Nematic-Isotropic Liquid
Literature Phase Transition
Temperature(Thoen, 1982)
22.2 ºC 34.0 ºC 41.0 ºC
Sample 1 Sample 2 Sample 3 Sample 4 Sample 5
Mass (± .0001 g)
.0255 g .0257 g .0259 g .0263 g .0268 g
Initial Temperatur
e (± .1 ºC)
0.0 ºC 0.0 ºC 0.0 ºC 0.0 ºC 0.0 ºC
Heating Rate
(± .2 ºC)
10 ºC min-1 10 ºC min-1 10 ºC min-1 10 ºC min-1 10 ºC min-1
Final Temperatur
e (± .1 ºC)
60.0 ºC 60.0 ºC 60.0 ºC 60.0 ºC 60.0 ºC
Table 2. Data table
Results TableSolid-Smectic A Smectic A-Nematic Nematic-Isotropic
LiquidAverage Phase
Transition Temp22.2 ºC
([Thoen, 1982] value used, as no transition
peak appeared in data)
33.20 ºC 40.58 ºC
% Error (Thoen, 1982)
n/a -2.35% -1.02%
Mesophase Modeling Function R2 Value
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Smectic A Cp(t)=e6.241 *(|t-33.2|/33.2)-.0482 .3325R2 Value Cp(t)=e6.0975 *(|t-40.58|/40.58)-.169 .673
Isotropic Liquid Cp(t)=e6.188 *(|t-40.58|/40.58)-.1049 .4642Table 3. Results table
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Fig. 14. DSC Specific heat capacity curve for sample 1
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Fig. 15. DSC Specific heat capacity curve for sample 2
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Fig. 16. DSC Specific heat capacity curve for sample 3
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Fig. 17. DSC Specific heat capacity curve for sample 4
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Fig. 18. DSC Specific heat capacity curve for sample 5
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Specific Heat vs. Temperature: Smectic A Phase
0
100
200
300
400
500
600
700
800
0 5 10 15 20 25 30 35
Temperature (oC) (± .1 ºC)
Sp
ecif
ic H
eat
(J/m
ol/
ºC)
Fig. 19. Smectic A mesophase data plot
y = -0.0482x + 6.241
R2 = 0.3325
5.8
5.9
6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
-7 -6 -5 -4 -3 -2 -1 0
ln (|T – Tc|/Tc)
ln c Linear (Series1)
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Fig 20. Smectic A mesophase logarithmic function plot, with best fit
line
Specific Heat vs. Temperature: Nematic Phase
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30 35 40 45
Temperature (oC) (± .1 ºC)
Sp
ecif
ic H
eat
(J/m
ol/
ºC)
Fig. 21. Nematic mesophase data plot
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y = -0.169x + 6.0975
R2 = 0.673
5.8
6
6.2
6.4
6.6
6.8
7
7.2
7.4
-6 -5 -4 -3 -2 -1 0
ln (|T – Tc|/Tc)
ln c Linear (Series1)
Fig 22. Nematic mesophase logarithmic function plot, with best fit line
Specific Heat vs. Temperature: Isotropic Liquid Phase
0
200
400
600
800
1000
1200
0 10 20 30 40 50 60
Temperature (oC) (± .1 ºC)
Sp
ecif
ic H
eat
(J/m
ol/
ºC)
Fig. 23. Isotropic liquid data plot
Voyles, Andrew000442-067
y = -0.1049x + 6.188
R2 = 0.4642
5
5.5
6
6.5
7
7.5
-7 -6 -5 -4 -3 -2 -1 0
ln (|T – Tc|/Tc)
ln c Linear (Series1)
Fig 24. Isotropic liquid logarithmic function plot, with best fit line
Specific Heat vs. Temperature: Full Range
0
200
400
600
800
1000
1200
0 10 20 30 40 50 60
Temperature (oC) (± .1 ºC)
Sp
ecif
ic H
eat
(J/m
ol/
ºC)
Fig 25. Full range of specific heat data
Voyles, Andrew000442-067
Fig 26. Full range of specific heat data, graphed on TI-84 Plus Silver Edition
graphing calculator, alongside the mesophase modeling function for
the domain of each mesophase
Voyles, Andrew000442-067
VI: Analysis
The theory behind the specific heat change for conventional
matter is known. While there is a general idea, the exact mechanisms
behind the specific heat change for liquid crystals are not currently
known. In fact, the topic is currently researched at the forefront of
science, by numerous groups. As a result, a complete understanding of
how the specific heat changes due to the phase transitions cannot be
obtained. However, it is still possible for us to try to qualitatively
theorize just why the heat capacity changes the way it does.
As compared to the graph of a normal compound (see Fig. 12),
the graph of the crystal’s heat capacity shares the same large spikes
at the phase transitions. However, inside the difference mesophases,
it does not remain constant, but varies with temperature as a rational
function. In the smectic A phase, there is not a major difference in the
specific heat capacity from the solid mesophase, as not much heat is
required to break the positional order forces. The nematic mesophase
displays a much larger jump in heat capacity, since the stronger
orientational order forces were overcome.
A quantitative analysis is required for an accurate understanding
of the significance of these results. Rational functions were fit to the
data for each phase, which were separated using the measured
average transition temperatures as the cutoffs between mesophases.
These models were average fits for the data, which is to be expected
Voyles, Andrew000442-067
due to the fact that relatively little data was collected. The lower
values seen in the smectic and liquid phases as well as the moderate
value of the nematic mesophase indicate that the specific heat offset
between each trial prevented the functions from being even better fits.
However, the measured average transition temperatures were
extremely accurate (Thoen, 1982) .This could be improved by
collecting more data and reanalyzing the results, based on the R2
coefficient of determination values, an indicator of how well a function
fits its data, where a value closest to 1 indicates a better fit.
Despite the fact that results were not very great, this
investigation has provided valuable insight into the phenomenon of the
specific heat capacity changes in 4’-Octyl-4-Biphenyl-Carbonitrile liquid
crystals, for which no reviewed literature could be found. The main
sources of error for this investigation included the random error of
impurities in the 8CB sample and the systematic error of inaccurate
calibration of the calorimeter. Due to the effect of hysteresis, the
tendency of a system to display results out of phase in the forward and
reverse directions, melting data is generally preferred over freezing
data, due to the fact that orienting the molecules while freezing is
much more unpredictable then disorienting them while melting. In
DSC curves, this appears as a transition spike appearing at a lower
temperature while freezing than while melting (Bonvallet, 1999), but
was not discussed. Nonetheless, this investigation has produced very
Voyles, Andrew000442-067
important results. Further analysis in this subject should be done in the
near future, as the possibilities for using this change in new
technologies have vast possibilities, which could greatly enhance the
quality of everyday life.
PHS IB Honor Code
“Students shall be honor bound to truthful conduct.”
On my honor, I pledge that I have neither given nor received any
unacknowledged aid on this paper.
Voyles, Andrew000442-067
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