The Effects of Multi-walled Carbon Nanotubes on the Pretilt Angle of a Nematic Liquid Crystal

The Effects of Multi-walled Carbon Nanotubes on the Pretilt Angle of a Nematic Liquid Crystal Matthew Sheffield, Department of Engineering Physics, Ca...
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The Effects of Multi-walled Carbon Nanotubes on the Pretilt Angle of a Nematic Liquid Crystal Matthew Sheffield, Department of Engineering Physics, Case Western Reserve University

A Thesis for the Senior Project Committee, Department of Physics, Case Western Reserve University May 2, 2012

Table of Contents Abstract

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1. Introduction

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1.1. What are liquid crystals?..................................................................................................4 1.2. The pretilt Angle……………………………………………………………………………………………………………5 1.3. Interaction of liquid crystals and Carbon nanotubes…………………………………………………….6 1.4. Interaction of Polymers and CNTs…………………………………………………………………………………6 1.5. Controlling the Pretilt angle………………………………………………………………………………………….7 2. Materials and Methods

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2.1. Setup History……………………………………………………………………………………………………………….9 2.2. Final Cell Setup……………………………………………………………………………………………………………10 2.3. Final Apparatus Setup…………………………………………………………………………………………………14 3. Results and Analysis

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4. Conclusions

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5. Future Work

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Acknowledgements

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References

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Abstract We examine whether the presence of multi-walled carbon nanotubes (CNT) in the nematic liquid crystal pentylcyanobiphenyl (5CB) affects the pretilt angle associated with the liquid crystal. Here, pretilt angle is defined as the angle between the normal to the substrate and the liquid crystal director. We control the pretilt angle by coating a substrate with a polyamic acid, bake at a temperature slightly higher than recommended by the manufacturer, and rubbing the resulting polyimide with a commercial fabric at different rubbing strengths. The increased baking temperature results in an extension of the polyimide’s backbone and partially removes the side chains, which produce competing easy axes for the liquid crystal alignment. The rubbing preferentially aligns the backbone as well as creates a slightly tilted side chain. The pretilt angle is controlled by varying the rubbing strength. Pretilt angle was measured using a HeNe laser setup containing two crossed polarizers, a Babinet-Soleil compensator and a gradiently rubbed cell. We used the compensator to measure the retardation of the sample cells at various positions along the cell (each position corresponds to a different rubbing strength), from which the pretilt angle was extracted. Results appear to indicate that the LC-CNT has a slightly lower pretilt angle than 5CB. Also, the results suggest that the CNT causes a slower rate of increase in the pretilt angle as a function of rubbing strength.

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1. Introduction Liquid Crystals represent a class of fascinating materials that has seen a rise in a variety of applications in recent years. A primary use of liquid crystals is in liquid crystal displays (LCD). Due to the unique tendency of the liquid crystal molecules to align with an applied electric field (some align parallel to the field, others align perpendicular to the field), the liquid crystals can be used to represent individual pixels in a display, varying from black to white depending on the intensity of the applied field. Color LCDs use the same method but employ colored filters over the liquid crystal’s to make up the image. The response time of the liquid crystals with respect to the applied field and the amount of light passing perpendicularly through a cell are directly related to the pretilt angle of the liquid crystal. In our experiment we hope to expand our knowledge of the pretilt angle by examining the effects of multi-walled carbon nanotubes on the pretilt angle of the liquid crystal 5CB. Carbon nanotubes were chosen as the main experimental factor in this experiment because previous experiments have shown that carbon nanotubes do have an effect on certain properties of a liquid crystal (e.g. CNTs dispersed in a LC resulted in an electroclinic effect [9]). Chien’s work on the anchoring strength coefficient W2 raises the question of whether CNTs affect the pretilt angle itself [11]. Thus, we hope this experiment can produce a discernible effect related to the CNT’s presence. 1.1 What are liquid crystals? Liquid Crystals (LC) are a unique phase of matter that exists between the 3D structure of a solid and the random, isotropic state of a liquid. Thus, liquid crystals Solid

exist in a variety of phases, with various orders of

Smectic

Nematic

Liquid

Figure 1: Comparison of solid and liquid order to that of liquid crystals (the Smectic and Nematic phases). 4

alignment (Figure 1). The order of a liquid crystal is related to the temperature of the liquid crystal. As the temperature of the liquid crystal increases, the order decreases until it reaches a critical temperature and crosses into the isotropic phase. In the isotropic phase, the liquid crystal has no long range order and its macroscopic properties behave in a manner similar to plain ordinary liquid. In this experiment, we used the liquid crystal 4-Cyano-4'-pentylbiphenyl (5CB). 5CB has a nematic phase (a phase with long range orientational order but no long range translational order) at room temperatures, making it an easy liquid crystal to handle [8]. The Figure 2. Chemical structure of 4-cyano-4′pentylbiphenyl (5CB).

local average direction of alignment of the liquid crystal is defined as its director. We use this

director to define the pretilt angle of the liquid crystal. The ability to control this pretilt angle is central to controlling the response time of LCD displays. 1.2 The Pretilt Angle

the angle between the director of the liquid crystal (its general alignment) and the normal to the substrate (homeotropic alignment). Pretilt angle can be controlled

Substrate Normal

The pretilt angle, as defined in this experiment, is

θ

through a number of methods, but in this case pretilt resulted from the liquid crystals interaction with a polymer applied to the liquid crystal’s cell. Depending on what type of polymer is applied to the cell, and on

Figure 3. The LC can be approximated as an ellipsoidal structure for clarification. Pretilt angle in this experiment (defined as θ above) takes the above convention mainly because SE1211 is a normally homeotropic polymer.

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how the polymer is treated, the liquid crystal can be directed to be in homeotropic alignment, planar alignment, or at some angle between planar and homeotropic [12]. 1.3 Interaction of liquid crystals and Carbon Nanotubes Carbon nanotubes are essentially rolled up sheets of graphene (a single layer of graphite). Each graphene piece has a benzene-type structure composed solely of carbon atoms. Some liquid crystals also contain benzene rings and this leads to a CNT-LC interaction known as π-π stacking [10], where the benzene rings of the liquid crystal stack on top of the benzene rings of the CNT forming a bond on the order of -2eV. This bond does not affect the liquid crystal director more than a few tens of nanometers from the CNT surface, as the CNT itself tends to align with the orientation of the liquid crystal. The CNTs alignment with the liquid crystal director is held constant even under the application of an applied electric field across the cell, making liquid crystals a good candidate for controlling the axis of CNTs and vice versa [5].

Figure 4: Liquid Crystal exhibits π-π stacking, orienting the CNT in the direction of the liquid crystal director.

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1.4 Interaction of Polymers and CNTs Outside of the world of liquid crystals, CNTs and polymers have their own unique relationship. The unique properties of the CNTs give them a massive tensile strength measured to be approximately 30 GPa and a young’s Modulus of approximately 1 TPa [6] (for single walled CNTs). When mixing CNT and polymers, depending on the structure of the polymer, the polymer may “wrap” around the CNT, imparting some of the CNTs properties to the polymer [7]. The specific monomer structure of the polymer plays a big part in determining the strength of the CNT-polymer bond. Perhaps this “wrapping” effect may manifest even when the CNTs are dispersed in a liquid crystal, but until now there have been no attempts to observe this behavior. 1.5 Controlling the Pretilt angle There are several different methods for achieving a large pretilt angle in a liquid crystal. One method involves dipping a polyimide surface in a solvent either before or after rubbing [3]. Another method irradiates SiC surfaces with an ion beam, inducing a pretilt angle that varies as a function of beam angle when the surface is carbon rich [4]. Doing so has allowed for complete control of the pretilt angle between 0 and 90 degrees to the substrate. Yet another method of controlling pretilt angle, and the principle method used during this research, is to rub a polyimide that has a side chain designed for homeotropic alignment (along with a rigid backbone) at various rubbing strengths [2]. The

Figure 5: Depending on what polymer is used, the liquid crystals can take on a normally homeotropic or planar alignment.

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rubbing of the polyimide induces a tilt in the polymer’s side chains, which translates to the liquid crystal and induces a tilt in the liquid crystal director. Over-baking the polyimide can increase the effects of the pretilt and can even control the pretilt depending on the temperature applied. Over-baking refers to the process of baking above the manufacturer’s recommended baking temperature in order to further imidize the polymer’s backbone, promoting planar alignment, and to remove some of the polymer’s side chains, weakening its vertical alignment tendency [1&13]. Here, we chose to keep the baking temperature constant while varying the rubbing strength of the cell.

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2. Materials and Methods 2.1 Setup History The apparatus itself went through several variations over the course of the research. The first setup implemented a computer controlled system that measured the retardation of the system. By applying an AC signal across the cell we induce a torque on the liquid crystal that causes the liquid crystal directors to tilt in line with the applied field. The intensity of the output beam at the detector, after the beam passes through a polarizer, the sample, and the analyzer, is then a function of the applied field. The function has a complicated shape with the possibility of multiple minima and maxima (depending on cell thickness and the liquid crystal’s birefringence). At high fields, however, the intensity dies out as the applied field becomes strong enough to fix the liquid crystals into Homeotropic alignment. Unfortunately, after multiple tests with cells of varying rubbing strengths, the method proved unable to provide a reliable and reproducible calculable pretilt angle for the lower values of rubbing strength. For the samples that we prepared, the output would just not produce a full intensity range because of the cell’s small retardation, thus preventing us from calculating the pretilt angle. We tried to correct this by increasing the thickness of the cell; however, this only made it easier for the CNTs to aggregate and muddle the results. The sample cell also underwent a few design changes over the course of the experiment. The first thought was to create a number of cells , each of which contained its own unique rubbing strength value. With an assembly time nearing 2 hours for one cell, it soon 9

became apparent that a better method was required. Therefore we switched to a gradiently rubbed cell in order to speed up the research process. The substrates were (described in detail in the next section) rubbed at an angle, creating a cell that contained a gradiently varying rubbing strength. Now, an entire set of data could be taken from one cell and eliminate the error associated with multiple cells. 2.2 Final Cell Setup

Figure 6: Cell diagram. Left side contains the LC-CNT mixture and right side contains plain 5CB. Spacer made of epoxy prevents contamination from each side. Cell assembled antiparallel to ensure proper rubbing alignment.

The cell is composed of two semitransparent Indium-Tin Oxide (ITO) coated glass slides, which allow for an electric field to be applied across the cell. Before spin-coating the polymer onto the slides, we cleaned each slide by submersing it in a series of cleaning agents (soap wash, distilled water, acetone, and ethanol) and then sonicating for 10 min in each solution. Each slide has a layer of SE1211 polymer applied by spin-coating at 3000 rpm for 10 seconds. The slides are then

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pre-baked for 30 minutes at 80⁰C and then “over-baked” at 200 ⁰C for 50 minutes. This overbaking process weakens the side chains of the polymer, decreasing the normally homeotropic tendencies of SE1211. We then rub each slide gradiently by translating it at a constant velocity under a rubbing cloth cylinder rotating at a fixed speed v (Fig 7). The formula for rubbing

1)

strength is:

Here r is the radius of the rubbing cylinder, v is the roller’s rotation frequency, σf is the fiber density of the rubbing cloth, s is the velocity of the slide’s translation stage, and N is the number of passes under the roller. In the gradient rubbing process we varied the rubbing strength by adjusting the δ parameter, which refers to the distance between the rubbing cloth and the zero rubbing strength height

Figure 7: Example of rubbing process for one side of the cell. The height of the roller was controlled by micrometers.

above the test cell (Fig 8). By varying the rubbing strength we were able to control the pretilt angle of the test cell [2]. The slides are arranged in an antiparallel configuration to ensure the alignment angle. We divided each cell into two halves: one half has plain 5CB and the other half has 5CB with 0.05% concentration by weight of multi-walled CNT. This dual-sided cell technique ensured that the main only factor affecting the pretilt of the LC is the CNTs.

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The δ parameter was calculated by using basic geometry, as depicted in Figure 8. The only tricky part was determining the zero point rubbing position on the cell. The zero point is the point where the roller has just touched the surface. We manually measured the zero point Figure 8: Geometrical process used to determine the δ parameter. Typical θ values were around 2 degrees.

by lowering the height of the rubbing cloth until it just made contact with the cell. This sometimes proved quite difficult as we were also trying to avoid disturbing the polymer already applied

to cell. After rubbing, each cell was assembled using two 5 µm mylar spacers placed along the outside edges of the cell. In the center of the cell was a small strand of 5-min epoxy that separated the CNT-LC side from the plain liquid crystal side. Epoxy was also used on the corners of each cell to ensure a firm cell thickness, and then binder clips were used to hold the cell together until the epoxy dried. The mylar spacers proved to be an obstacle because their small size made them prone to wrinkling. Wrinkling added 2-3 µm to the cell thickness and also disrupted uniform thickness along the cell. In order to overcome this problem, I took multiple measurements of the cells thickness at different points along both sides of the cell. The cell’s thickness was measured using a laser setup that rotated the cell from -40 to 40 degrees with respect to the laser beam and then plotting the resulting maxima and minima in a MATLAB program. 4 maxima were chosen (2 adjacent maxima from the negative degree side and 2 adjacent maxima from the positive degree side) and then entered into the following equations to determine the 2 thickness measurements of the cell.

(

)

2)

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(

3)

)

Where θo is just the average of all 4 maxima values (the numbered θ values) and λ is the wavelength of the beam. Theta 1 and 2 refer to the negative degree side measurement and theta 3 and 4 refer to the positive degree side measurement. We used the two thickness measurements to determine an average cell thickness. Eight thickness measurements were made for each cell: 4 per each side at 6mm increments. Next, each cell was filled, with one side containing plain 5CB liquid crystal and the other side containing a 0.05% by weight concentration of multi-walled carbon nanotubes in 5CB. The CNTs had a diameter range from 8-15 nm and a length range from 0.5-2 µm. Assembling the CNT-LC mixture was a challenge because the amount of CNTs needed to create a 0.05% concentration in a typical amount of 5CB (0.25 g) was so small that the measuring scale could not accurately display the mass of the CNTs. Therefore, we created an acetone solution containing a known concentration of CNTs. We then thoroughly mixed the acetone and CNT using a sonicator for an hour before adding the required amount to a vial containing the correct 5CB to create a 0.05% by weight concentration of multi-walled carbon nanotubes in 5CB. After sonicating the CNT-LC mixture once more, we left the vial on a hotplate in order to evaporate the acetone out of the vial. The final result was then sonicated one last time before inserting into the cell by a pipette. The final step in cell construction was to solder wire leads to each side of the cell using InSn solder. These leads would allow the application of an AC voltage across the cell (the

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purpose of which is found in the next section). We first scratched off a small layer of polymer from each side of the cell to ensure proper contacts for the leads. Then I soldered each wire to one side of the cell. The solder proved unwilling to remain attached to the slides a majority of the time, so a small application of epoxy was sometimes necessary to ensure the connections remained stable. However, this did not affect the solder’s ability to conduct electricity because either the solder was firmly held in place, or it fell off. There appeared to be no noticeable level of connection between these two states. 2.3 Final Apparatus Setup Sample

Polarizer

Analyzer

HeNe laser

Detector

Babinet-Soleil Compensator

KDMM

Pinhole Signal Generator

Figure 9: Experimental setup: includes a pinhole to eliminate scattering effects and increase precision of laser on the sample cell.

In this setup, a polarized HeNe laser passes through a polarizer crossed 90 degrees with an analyzer in order to maximize the sample cell’s signal. The analyzer is aligned 90⁰ with the polarizer, and then the sample cell and the Babinet-Soleil compensator are rotated to be 45⁰ with respect to both the polarizer and analyzer. This setup allows for maximum beam intensity at the detector and creates a change in the birefringence of the sample while ensuring that the

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compensator matches that change. A Keithley Digital Multimeter (KDMM) was used to detect and display the detector’s output voltage. A voltage generator was used to apply an AC voltage across the sample cell, and was used only to ensure that only one period of retardation is present in the cell. This is an important step because the compensator can induce only a 2π retardation in the signal, while the sample cell’s retardation is only limited by the length of the cell and its inherent birefringence.

Figure 10: The interior of a Babinet-Soleil Compensator. The Compensator’s wedge is controlled by a micrometer, which changes the effective thickness of the top plate. This results in a retardation applied to the incoming beam. http://www.cvimellesgriot.com/company/Glossary.aspx?Character=S

The Babinet-Soleil Compensator is a device that can impart a user defined retardation to a laser beam. It consists of two birefringent plates of equal thickness with perpendicular ordinary and extraordinary refractive indexes (Fig 10). One of the plates is divided into two wedges, and one of these wedges is then controlled by the user. This allows the user to control the effective thickness of the second plate and therefore the resulting retardation applied to the laser. By placing the compensator in the sample’s path, we can effectively cancel the

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retardation of the sample. The retardation of the compensator is then the retardation of the sample, from which the pretilt angle can be extracted. When using the compensator, a micrometer displays the position of the movable wedge in a value of millimeters. Before it can be used in the experiment it had to be calibrated first. In order to calibrate the compensator, we first remove the sample cell from the beam path and then adjust the compensator’s micrometer (starting from its zero value) until a minimum intensity is reached at the detector. This micrometer value is our zero point. We then increase the micrometer value until another minimum is reached, a total period of 2π in the retardation applied to the signal. The difference between the micrometer’s values at these two minima is defined as Δbo. We then place the sample cell back into the beam path, and return the compensator to the zero point determined previously. Again, we increase the micrometer until the detector hits a minimum value, and then the difference between these two micrometer values is defined as Δb. By taking the ratio of Δb to Δb o and then multiplying by 2π, we can determine the retardation of the sample cell (α o), as shown in the following equation:

4)

The equation for determining the pretilt angle depends on the change in the birefringence of the sample. This change in birefringence creates an effective extraordinary refractive index and an ordinary refractive index. The effective extraordinary refractive index is dependent on the pretilt angle of the cell, and allows us to calculate said pretilt angle, as shown below: 5) 6) 16

By knowing the parameters of the cell (refractive indices n o and ne, and cell length z), we can calculate the retardation

. Then we set

equal to the calculated retardation

and

solve for neeff , the effective extraordinary refractive index (noting that λ is the wavelength of the laser beam in vacuum and the integral is just over the thickness of the cell (z)). Once we know neeff we can solve for the pretilt angle θ (z): ( )

[

√ (

(

) )√

]

7)

Here, no and ne are just the ordinary and extraordinary refractive indices of 5CB, a constant value. We worked under the assumption that the carbon nanotubes contributed little to the inherent refractive indices of the liquid crystal because the quantity of CNT was small enough that it would not have a statistically significant effect on the indices.

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3. Results and Analysis CNT-LC vs. LC Pretilt Angle

40 35

Pertilt Angle (degrees)

30 25 20 15 10 5

LC-CNT 5CB

0 2x105

3x105

4x105

5x105

6x105

Rubbing Strength (1/cm) -1

Figure 11: The pretilt angle of the LC-CNT mixture and 5CB as a function of rubbing strength. All points here taken from a single gradiently rubbed cell.

Of the six gradient cell trials performed, the graph in Figure 11 gave the best set of data. A general curve of a liquid crystal’s pretilt angle as a function of rubbing strength would show a pretilt angle of zero before it reaches it a threshold in rubbing strength, generally corresponding to a yield stress in the polymer. At this point, the pretilt angle increases rapidly with rubbing strength, with the rise eventually tailing off until a certain maximum pretilt angle is reached. In that respect, the measured behavior shown in Figure 11 exhibits this expected behavior. However, it is important to note that the CNT-LC mixture appears to have an arguably slightly smaller pretilt angle than the plain LC mixture, although the variation in the data may cast doubt on this observation. Also, the pretilt angle of the CNT-LC mixture

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seemingly increases at a slower rate than that of the plain liquid crystal. Unfortunately, after these points the points become very scattered, suggesting an error that has not yet been accounted. Error was seen to be found primarily in the thickness measurements of the cell and the micrometer values of the Babinet-Soleil compensator. The thickness measurements were a huge source of error because, as mentioned earlier, the mylar spacers had a huge tendency to wrinkle and cause variances in the thickness along the length of the cell. Even though thickness measurements were done in multiple areas along the cell, thicknesses between measured points tended to vary by 1 micron. Error due to the compensator also was a problem because the micrometer used to control the movable wedge contained a moderate amount of backlash. Therefore, a single measurement of the compensator’s micrometer could vary by 0.2-0.5 mm, which is statistically significant when general measurements were in the neighborhood of 2-10 mm. Error was calculated using the following equation:

√(

)

(

)

8)

Where c refers to the measured compensator value of the sample cell used to determine Δb in equation 8 (typical δc = 0.20mm). The z component of this equation referred to the thickness of the cell with an estimated error of 1µm. This is a huge amount of error for a cell that averaged a thickness of 7µm. However, typical error results were about ±2 degrees in the pretilt angle of each cell. We also note that another possible source of error not accounted for is a large local variation in the supped rubbing strength. The rubbing cloth fibers have a characteristic size of a few hundred micrometers. As the surface passes under the roller, any

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given spot may be “hit” an average of a handful of times by fibers, and thus there could be a statistically large variation of the rubbing strength around some expected local value. This possible error still needs to be quantified further [14].

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4. Conclusions Present data suggest that the presence of CNTs may cause a slight decrease in the pretilt angle of 5CB. Additionally, the CNT-LC mixture data indicates that the CNTs slow down the rate of increase in the pretilt angle as a function of rubbing strength. However, it is important to note that the data acquired are merely the foundations of a hypothesis that needs more results of greater accuracy to be truly proven. An unknown error (possibly local variations in the rubbing strength) has created a widely varying pretilt angle result and therefore these results suffer from it. Also, the fact that the pretilt angle of the CNT-LC mixture does not vary consistently from the pretilt angle of the plain liquid crystal suggests that the CNTs have little effect on the pretilt angle of the liquid crystal. The length of time to create one cell (when everything went right) and the difficulty in achieving a uniform thickness across both sides of the cell were both huge contributing factors to the shortcomings of this experiment. But, in the end, these results do form a solid basis from which future endeavors may be made to better understand the carbon nanotubes relationship with the pretilt angle of a nematic liquid crystal.

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5. Future Work There are several paths this research could take. The most obvious step would be to repeat the experiment multiple times and then average the results with the hope that the increased trial runs would create a clearer result in the effects of the multi-walled CNTs on the pretilt angle of 5CB. Another step would be to vary the concentrations of CNTs in the LC. From the experiment reported herein, we see that a 0.05% by weight concentration of CNTs has little effect on the pretilt angle. Therefore it would be worthwhile to start an incremental increase in the concentration of the carbon nanotubes to see how this affects the pretilt angle of 5CB. Alternatively, we could maintain the concentration of CNTs and then vary the liquid crystal to see how different liquid crystals respond to the presence of CNTs. Finally, one may investigate whether single-walled carbon nanotubes affect the pretilt angle in a manner distinct from that of multi-walled carbon nanotubes. Single-walled and multi-walled carbon nanotubes have shown differing properties in applications outside of the realm of liquid crystals, and these differences may remain when we compare their effects on the pretilt angle of a liquid crystal.

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Acknowledgements I would like to thank my advisor Professor Charles Rosenblatt for all of his help, especially in understanding the physics behind the experiment. I would also like to thank Postdoc Rajratan Basu for his knowledge of carbon nanotubes and the many discussions we had were a great help during my senior project.

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