STUDY OF THE MECHANISM OF IRREVERSIBLE ADSORPTION

OF SINGLE-WALLED CARBON NANOTUBES TO SEPHACRYL

HYDROGEL

By

CALEB ROLSMA

A thesis submitted to the Graduate Faculty of the

University of Colorado Colorado Springs

in partial fulfillment of the

requirements for the degree of

Master of Sciences

Department of Chemistry and Biochemistry

2017

ii

This thesis for the Master of Sciences degree by

Caleb Rolsma

has been approved for the

Department of Chemistry and Biochemistry

By

Kevin Tvrdy, Chair

Ronald R. Ruminski

Janel E. Owens

Carlos Diaz

Date 9/27/2017

iii

Rolsma, Caleb (M.Sc., Chemistry)

Study of the Mechanism of Irreversible Adsorption of Single-Walled Carbon Nanotubes to

Sephacryl Hydrogel

Thesis Directed by Assistant Professor Kevin Tvrdy

Abstract

As a class of carbon-based nanomaterials, single-walled carbon nanotubes (SWNT)

have many structural variations, called chiralities, each with different properties. Many

potential applications of SWNT require the properties of a single chirality, but current

synthesis methods can only produce single chiralities at prohibitive costs, or mixtures of

chiralities at more affordable prices. Post-synthesis chirality separations provide a solution

to this problem, and hydrogel separations are one such method.

Despite much work in this field, the underlying interactions between SWNT and

hydrogel are not fully understood. During separation, large quantities of SWNT are

irretrievably lost due to irreversible adsorption to the hydrogel, posing a major problem to

separation efficiency, while also offering an interesting scientific problem concerning the

interaction of SWNT with hydrogels and surfactants.

This thesis explores the problem of irreversible adsorption, offering an explanation

for the process from a mechanistic viewpoint, opening new ways for improvement in

separation. In brief, this work concludes adsorption follows three pathways, two of which

lead to irreversible adsorption, both mediated by the presence of surfactants and limited by

characteristics of the hydrogel surface. These findings stand to increase the general

understanding of hydrogel SWNT separations, leading to improvements in separation, and

iv

bringing the research field closer to the many potential applications of single-chirality

SWNT.

v

To my parents,

who brought me into this world and showed me how to live in it

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ACKNOWLEDGEMENTS

First and foremost, I would like to thank my advisor, Dr. Kevin Tvrdy. Specifically,

the concern he shows for his students and their success, his dedication to a sound scientific

approach, and his endeavor to train the next generation of scientists in a well-rounded

manner, teaching us to ask scientific questions, design experiments, and to communicate

our work to both scientific and general audiences.

Second, I would to thank the Department of Chemistry and Biochemistry for their

financial support through the Graduate Student Assistantship. In addition to the financial

aspect, the experience also gave me an opportunity to improve my teaching and public

speaking skills, both of which are sure to benefit me as I continue my scientific career.

Lastly, I would like to thank my lab partners, Kassy Prescott, Nathan Weeks, Nate

Sundquist, Josh Stoll, and Martin Ruben. Your conversations, scientific insight, and

emotional support were invaluable.

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TABLE OF CONTENTS

CHAPTER

I. INTRODUCTION: SINGLE-WALLED CARBON NANOTUBES, THEIR APPLICATIONS, AND PURIFICATION METHODS……..………………..1

1.1 Single-Walled Carbon Nanotubes: Structures and Properties………….….1

1.1.1 Molecular Structure…………………………..………..….……….1

1.1.2 Electronic Structure…………………………...…...…..…….….…3

1.1.3 Physical Properties……………………………..…….…….……...6

1.1.4 Electrical Properties…………………………………...….……….6

1.1.5 Chemical Properties……………………………..….…….……….7

1.1.6 Optical Properties…………………………………...….....….……7

1.2 Potential Applications……………………………………………………..9

1.2.1 Nanoscale Electronics………………………………….……….....9

1.2.2 Energy Production…………………………………...….………..10

1.2.3 Biomedical Applications………………………………....………10

1.2.4 Other Uses…………………………………………..……………11

1.3 Synthesis……………………………………………..…………...…...…12

1.3.1 Chemical Vapor Deposition………………………………….…..12

1.3.2 Arc Discharge……………………………………..…………...…13

1.3.3 Laser Ablation……………………………………..………...…...14

1.3.4 Other Methods………………..…………………………..………14

1.4 Chirality Separations……………………………..………………………15

1.4.1 Density Gradient Ultracentrifugation…………..…………..…….15

1.4.2 Polymer- and DNA-Wrapping……………………….....………..16

1.4.3 Hydrogel Separations…………………………..…………...……17

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1.5 Thesis Statement…………………………………………..……..………24

II. EXPERIMENTAL METHODS………………………….…………………..25

2.1 Reagents and Experimentation………………………………..………….25

2.2 Reagents……………………………………………………..…………...25

2.2.1 Carbon Nanotubes……………………………………..………....25

2.2.2 Sodium Dodecyl Sulfate Solutions………………...……………..26

2.2.3 Sephacryl S-200 and Gel Preparation…………………...………..27

2.3 Pre-Separation Procedures……………………………………..………...29

2.3.1 Ultrasonication……………………..…………………………….29

2.3.2 Ultracentrifugation…………………..…………………………...33

2.4 Separation Procedures……………………………………..……………..34

2.4.1 Column Separation………………………..……………………...34

2.4.2 Mixed Separation………………..……………………………….36

2.5 Analysis Procedures…………………………………………..………….39

2.5.1 Absorbance Spectrometry………………………..………………39

2.5.2 Optical Microscopy…………………..…………………………..43

III. SDS-SWNT ADSORPTION MORPHOLOGY AND PACKING…..………44

3.1 Adsorbed SWNT-SDS………………………………………………..….44

3.2 Hypothesized SDS-SWNT Adsorption Morphology and Packing……….45

3.2.1 Gel Surface Area…………………………………..……………..47

3.2.2 Close-Packing Model……………………………..……………...49

3.2.3 Circular-Packing Model……………………………..…………...50

3.3 SWNT Saturation Experimental Details………………………….……....51

3.4 Comparison of Predicted and Experimental Results…………….………..54

3.5 Gel Saturation versus Equilibrium…………………………………..…...56

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IV. KINETICS AND MECHANISM OF IRREVERSIBLE ADSORPTION…...58

4.1 Dynamics of Adsorbed SWNT on Sephacryl………………….….……...58

4.2 Proposed Mechanism: SDS Rearrangement…….……………….……….58

4.3 Experimental Design………………………………..……………………62

4.3.1 SWNT Pre-Separation…………………..………………………..63

4.3.2 Kinetics Setup………………………..…………………………..64

4.3.3 Data Interpretation…………...…………...……………………...65

4.4 Comparison of Experimental Results and Predicted Trends……..….…...66

4.4.1 Initial Hypothesis: Weakly Adsorbed SWNT vs Time……...…...67

4.4.2 Revised Hypothesis: Irreversible Adsorption Sites…….......…….69

4.4.3 Rate Constants and SDS Concentration…………………………..73

4.4.4 Multiple Pathways and Overall Mechanism……………...….…...75

4.4.5 Irreversible Sites versus Irreversible SWNT……………………..79

V. CONCLUDING THOUGHTS AND FUTURE WORK………………..……81

5.1 Summary…………………………………………..…….……………….81

5.2 Importance and Implications…………………………….……...………..82

5.3 Shortcomings and Unanswered Questions……………….………...…….83

5.4 Future Work……………………………………………………………...84

5.5 Closing Thoughts…………………………………………....…………...85

REFERENCES…………………………………………………….……..…………..….86

1

CHAPTER I

INTRODUCTION: SINGLE-WALLED CARBON NANOTUBES,

THEIR APPLICATIONS, AND PURIFICATION METHODS

1.1 Single-Walled Carbon Nanotubes: Structure and Properties

Single-walled carbon nanotubes (SWNT) and their properties hold promise for

many applications in such varied fields as medicine, electronics, and energy production,

but without proper separation of different SWNT chiralities, these applications are limited

in efficacy. This thesis studies hydrogel separations as a method for separating different

SWNT chiralities from each other, opening the way for future applications. Before

discussing potential applications and purification methods in more detail, the structure and

properties of SWNT will be examined briefly, providing greater context for the rest of this

thesis.

1.1.1 Molecular Structure

With diameters on the order of 1 nm and lengths usually ranging from hundreds of

nanometers to micrometers or longer, SWNTs exist as tube-like one-dimensional crystals,

composed of repeating sp2-hybridized carbon-based unit cells. Hundreds of structural

variations or chiralities exist, each of which can be grouped into one of three different

categories: armchair, zigzag, and chiral.1 The unit cells of three different SWNT chiralities

are shown below in Figure 1.1, illustrating the different ways that carbon atoms can be

arranged in a tube-like structure.2

2

A common way to describe the SWNT structure is via comparison to graphene, the

structure of which is shown in Figure 1.2.A. As seen in the figure, graphene consists of a

single layer of carbon atoms arranged in a sheet of repeating hexagonal rings. Returning

to the structure of SWNT, one can imagine folding a portion of a graphene sheet into a

tube, joining a hexagonal ring on one part of the sheet with a ring on a different part of the

sheet, forming one unit cell of the SWNT, as shown in Figure 1.2.B.3

Figure 1.1. Unit cells of three different SWNT: armchair, zigzag, and chiral, respectively, where differences in structure are most evident along the top and bottom edges of the nanotube unit cells. Figure taken from reference 2.

Figure 1.2. A) Structure of graphene, showing the repeating pattern of sp2-hybridized carbon atoms, including a chiral vector marked with black, and the two components, n1 and n2. B) The conceptual process of forming a SWNT unit cell by folding a portion of a graphene sheet, with different chiralities determined by the chiral vector. Figure 1.2.B. taken from reference 3.

A B

3

The final SWNT unit cell can be designated with what is called a chiral vector,

written generally as (n1, n2), where n1 and n2 are integers. The two components of this

vector indicate the distance along the sheet from the starting hexagonal ring to the ending

ring used in folding, as illustrated in Figure 1.2.A, showing the direction of the components

along the graphene sheet, along with the net chiral vector.

Given this definition of the chiral vector, different SWNT chiralities are grouped

into the three different categories mentioned earlier: armchair, zig-zag, and chiral. If n1 =

n2, the SWNT is arm-chair; if n1 ≠ 0 and n2 = 0, the SWNT is zig-zag; and if n1, n2 > 0 and

n1 ≠ n2, then the SWNT is chiral. The following section briefly discusses the impact that

the chiral vector has on the resulting SWNT properties, in particular, the electronic band

structure.

1.1.2 Electronic Structure

As the primary determinant for many interesting properties of SWNT, the

electronic band structure of carbon nanotubes (CNTs) requires some explanation. With

such a large number of SWNT chiralities, a similarly large number of different electronic

structures also exist. Despite this large number of different chiralities, all SWNT can be

categorized as either metallic or semiconducting. Just as the SWNT molecular structure

can be described in terms of graphene, the SWNT electronic structure can also be described

in terms of graphene using the “zone-folding approximation,” offering a simple method to

describe carbon nanotube properties.1 As a two-dimensional crystal with a repeating

structure, graphene has a band structure, as depicted in k-space in Figure 1.3.4

4

SWNT also have a repeating molecular structure in one direction, giving rise to

periodic wavefunctions along the nanotube length, the exact form depending on the SWNT

unit cell. Additionally, the wavefunctions also have components along the nanotube

circumference. Since the nanotube circumference is closed in nature, wavefunctions are

required to be continuous along the circumference. Consequently, the complete electronic

wavefunctions – including components from both nanotube circumference and length –

depend heavily on the SWNT chirality. Rather than derive the SWNT band structure ab

initio, the zone-folding approximation derives the SWNT band structure from the graphene

band structure by applying restrictions from the SWNT unit cell. Any graphene

wavefunction that satisfies these requirements is assigned as an allowed SWNT

wavefunction. All other graphene wavefunctions are considered forbidden for that

particular SWNT. One especially interesting and useful result from this approximation

predicts the metallic or semiconducting nature of SWNT in terms of the chiral vector, and

is shown in mathematical form in Equation 1.1.1

Figure 1.3. Predicted first Brillouin zone of the two-dimensional graphene band structure, showing the valence (blue-green) and conduction (red-yellow) bands. Figure modified from reference 4.

5

1 2n n m3−

= (1.1)

If the difference between the two components, n1 and n2, is an integer multiple of

3, then the SWNT is metallic; if not, the SWNT is semiconducting. The explanation for

this relationship between chirality and band structure lies in the fact that graphene is

semimetallic, with no band gap between the valence and conduction bands. Consequently,

if the SWNT chiral vector allows for those two bands to exist in the carbon nanotube, the

resulting SWNT will also have no band gap, and display metallic properties. The band

structures for different SWNT are shown in Figure 1.4.5

Figure 1.4. Predicted first Brillouin zone of the SWNT band structure of four different SWNT chiralities [(5,5), (9,0), (10,0), (8,2)] with corresponding density of states. Figure modified from reference 5.

6

1.1.3 Physical Properties

In addition to their interesting one-dimensional structure, carbon nanotubes have a

variety of useful properties. Because of the heavily delocalized bonding, carbon nanotubes

have great tensile strength along their length, where tensile strength describes the

maximum stress a material can experience while stretched before breaking. With

experimental values up to ~100 GPa for defect free SWNT,6 carbon nanotubes have some

of the greatest tensile strengths of any known material, though nanotubes with defects often

have lower tensile strengths, nearer ~40-70 GPa.3 For comparison, many steels have tensile

strengths in the range of ~500-2000 MPa,8 and diamond has a theoretical tensile strength

of 60 GPa.9 In addition to a strong axial structure, carbon nanotubes are also flexible along

their radius.10

1.1.4 Electrical Properties

Due to their chirality-dependent band gaps, SWNT display a wide range of values

of electrical conductivity. While metallic SWNT have conductivities comparable to

copper, and semiconducting SWNT have conductivities comparable to conventional

semiconducting materials, such as silicon, the exact conductivities can be essentially fine-

tuned by selection of an appropriate chirality.11 SWNT electrical properties also depend

sensitively on their environment; the adsorption of different chemical species onto the

SWNT sidewalls can strongly affect the SWNT electrical conductivity, making them useful

for sensing applications, as will be discussed in section 1.2.3.

7

1.1.5 Chemical Properties

Being structurally similar, SWNT react in many of the same ways as organic

aromatic compounds.12 These chemical properties are not especially unique, but they

facilitate many potential applications. Often, pristine SWNT are oxidized to add sidechains

to the nanotube walls, allowing for furhter functionalization of the SWNT. This allows

one to customize the nanotube properties, such as bandgap and solubility, and this also

allows for SWNT to be specifically linked to target substrates, which further allows for

great control over interactions that SWNT can have with other molecules in a given

system.12

1.1.6 Optical Properties

Single-walled carbon nanotubes also display unique optical properties, the main

focus here being their absorbance and emission properties.

Given the electronic band structure described in section 1.1.2, many transitions can

occur between these different states. These transitions can play a role in some applications,

but for the purposes of this thesis, they also provide a means to identify and study different

SWNT chiralities in solution.13 As with electronic transitions in molecular species,

selection rules exist for SWNT electronic transitions, restricting transitions to only a few

possibilities.14 For semiconducting SWNT, the two lowest energy transitions are the E11

and E22 transition. The E11 corresponds to a transition between the valence (highest-energy

filled) band and the conduction (lowest-energy empty) band, while the E22 corresponds to

a transition between the second highest-energy filled band and the second lowest-energy

empty band.13

8

Most E11 transitions occur in the near IR region, usually in the 800-1300 nm range

for SWNT in this research, but the range for all SWNT is much greater, whereas the E22

transitions often occur in the visible. These transitions can be observed via absorbance

spectroscopy, and one example of the absorbance spectrum of a mixture of carbon

nanotubes in solution is given below in Figure 1.5, with annotated absorbance peaks

showing the E11 and E22 transitions of different chiralities.

In addition to electronic transitions, phonon transitions are also possible.15,16

Phonons are the crystal analog of vibrational states, which contribute additional transitions

for every electronic transition, as also annotated in Figure 1.5 as phonon sidebands. Lastly,

SWNT also exhibit emission in the near IR, an uncommon property present in few

materials.17

Figure 1.5. Absorbance spectra of a mixture of SWNT, with annotated E11, E22, and phonon sideband peaks, plotted in energy space.

9

1.2 Potential Applications

Due to their unique properties, SWNT could serve in a variety of potential

applications. Some applications have reached real-world production, but many have only

been realized in lab settings, held back partly by the prohibitive costs of obtaining single-

chirality SWNT in sufficient volumes and purities.18,19 This section briefly lists several

such applications, highlighting how the properties of SWNT could allow for improvements

in numerous fields.

1.2.1 Nanoscale Electronics

With their nanometer diameters and different electrical conductivities, SWNT

could be used to construct efficient electronics on the nanoscale. Some examples of this

have been accomplished by research labs, such as transistors made of individual SWNT,

as well as more complex electronics components and even simple computers.20–22 These

devices would allow for smaller and more efficient electronics, allowing for continued

improvements in computing and consumer devices.18

These applications require extreme control over SWNT chirality: a metallic SWNT

used in place of a semiconducting SWNT, vice versa, or a semiconducting SWNT of the

wrong chirality would lead to a failure of the electrical component and the overall device.

As a result of this and the great expense of obtaining single-chirality SWNT, such

nanoscale devices face challenges in development, and are far from economic feasibility

at the moment.18

10

1.2.2 Energy Production

SWNT also have potential application in energy production, including in

photovoltaics and energy storage. In photovoltaic devices, the conductivity and one-

dimensional nature of SWNT allow for increased current mobility of excited electrons,

which also reduces the chances of recombination of electrons with lower energy states, or

electron holes, leading to improvements in device efficiency.21,23 While improvements

have been achieved using chiral mixtures of SWNT, greater improvements have been seen

when using single-chirality SWNT for photovoltaics.21

In addition to photovoltaic devices, SWNT also have potential uses in fuel cells,

either as a catalyst support, or in a doped form as a catalyst itself.23–25 SWNT have a large

surface to volume ratio, as well as being chemically inert and electrically conductive,

making them a promising support for loading catalytic nanoparticles, and allowing for

improved fuel cell performance while also decreasing the amount of catalyst particles

needed. Alternatively, SWNT can be doped, e.g., with nitrogen, boron, or other elements,

lending the carbon nanotubes catalytic properties.23,26 As with other applications, SWNT

chirality can play an important part in these applications through the strong effect it has on

nanotube properties, such as the band gap and band structure.

1.2.3 Biomedical Applications

While the discussion so far has leaned towards physical science applications,

SWNT also have potential applications in biomedical fields, such as in imaging and drug

delivery. Because of some chiralities’ strong absorbance and emission in the ~700-1100

nm range, SWNT make good candidates for bioimaging and sensing.27–29 Neither water

11

nor biological molecules absorb strongly in this region, and other materials that do so are

uncommon. This region is effectively an optical window into biological systems, allowing

for easy excitation and measurement of SWNT emission, which can be used for

bioimaging.

SWNT also have potential applications for drug delivery. Due to the ease of

functionalizing their sidewalls, SWNT can be sensitized for interactions with certain

biomolecules, allowing one to target specific locations in an organism. For drug delivery,

the SWNT can be simultaneously loaded with drugs for release upon arrival at the target

location.30,31 Another potential SWNT application involves photothermal therapy, where

SWNT adsorb NIR radiation, allowing for selective heating and destruction of cancer

cells.32

1.2.4 Other Uses

Carbon nanotubes have a variety of other uses: incorporation into metal alloys for

improved strength,33 producing flexible electronics,34 and use in polymer materials to

modify electrical properties,35 as well as many other potential uses. Of the applications

discussed in this chapter that use single-walled carbon nanotubes, some are viable with

mixed-chirality samples, but others require single-chirality samples to function properly.

For example, the above-mentioned nanoscale electronics depend sensitively on SWNT

chirality, where mixtures are unusable for some electronic components. Similarly, energy

production and biomedical applications would benefit from pure chiralities, though they

do no depend on this as much as electronics applications might. Section 1.3 discusses

several carbon nanotube synthesis methods, with special focus given to SWNT synthesis.

12

1.3 Synthesis

Various methods for CNT synthesis exist, each with different advantages and

disadvantages. This section provides a brief overview of three of the most commonly used

methods, giving a better understanding of the need for post-synthesis separations.

1.3.1 Chemical Vapor Deposition

Chemical vapor deposition (CVD) is the most commonly used method for

synthesizing CNTs, and the most economical. As schematically illustrated in Figure 1.6,

CVD uses gas phase carbon precursors in contact with catalytic metal particles at high

temperature and elevated pressure (~700-1000 K, ~1-10 atm).36–40 In contact with the

metal catalyst, the carbon precursors decompose, leaving carbon atoms on the catalyst

surface and dissolved into the crystal structure. As these carbon atoms accumulate, they

begin to form a carbon nanotube, which grows overtime with the addition of the carbon

feedstock.

Figure 1.6. Schematic diagram of CVD synthesis of SWNT, specifically, CoMoCat® synthesis. CO gas is pumped into a reactor chamber with cobalt-based catalyst particles, growing SWNT under a continuous supply of CO. Figure taken from reference 36.

13

Common carbon precursors include carbon monoxide, methane, ethyne, ethene,

and ethanol, and catalyst particles most often consist of nanoscale Fe, Ni, or Co crystals,

though other possibilities exist for both carbon precursor and catalyst. The CNT chiralities

produced via CVD depend sensitively on the size and composition of the catalyst

nanoparticles. In short, the resulting SWNT radius is similar to the catalyst nanoparticle

radius, with larger nanoparticles producing SWNT of a larger radius, and even larger sizes

producing multi-walled carbon nanotubes (MWNTs), with further preference for SWNT

or MWNT depending on catalyst composition.39,41 Many SWNT chiralities have similar

radii, leading to a distribution of chiralities. More exact chirality control has proven

difficult, but has been achieved to some degree via improvements in catalyst design.39 The

CoMoCat® method is one such successful method, utilizing carbon dioxide as the carbon

precursor and cobalt nanoparticles for catalysis,42,43 and the primary source of SWNT used

in this research, due to its success in producing SWNT material enriched in single

chiralities.

1.3.2 Arc Discharge

In addition to the more common CVD method, arc discharge is also used for CNT

synthesis. This method was used in the first widely-recognized CNT synthesis in 1991 by

Iijima,44 and can produce SWNT with fewer defects than other synthesis methods, but is

not widely used today due its less scalable nature.45 As a historical note, many earlier

accounts of carbon nanotubes exist in the literature, dating back to the 1950s, but Iijima’s

1991 publication is often misattributed as the original discovery.46

14

In brief, a high voltage is applied across two graphite or graphite-metal-composite

electrodes, resulting in arc discharge between the two. This discharge produces a plasma

at a high temperature (~1700 K), with electrons flowing towards one electrode and carbon

ions towards the other. Under these conditions, the carbon ions deposit on one electrode,

forming carbon nanotubes; MWNT form when using pure graphite electrodes, whereas

SWNT form when metals, such as iron, nickel, or cobalt, are used in composite graphite-

metal electrodes. Various conditions can be varied, such as voltage, composition of the

ambient atmosphere, etc, resulting in different CNTs produced.41,45

1.3.3 Laser Ablation

Laser ablation is another common CNT synthesis method, offering CNTs with few

defects and high purity, but with less potential to be scaled up for large-scale production.

Synthesis involves the use of a laser directed at graphite-metal pellets, converting portions

of the pellet into a gaseous state, usually in the 1500-3000 K temperature range. In such a

state, nanometer-sized catalyst particles are thought to form, upon which collect gaseous

carbon species. As this continues, CNTs grow from the catalysts.47,48 Despite its ability

to produce quality CNTs, laser ablation is not widely used beyond lab settings.

1.3.4 Other Methods

In addition to the methods described above, other CNT synthesis methods exist,

such as various pyrolysis methods, bottom-up organic approaches, and carbide-derived

CNTs, among others.41,49,50 As stated earlier, CVD is currently the most commonly used

and economical synthesis method, and the source of CNTs used here. Given the limitations

15

of CVD, i.e. production of mixtures of chiralities and impurities, the next section describes

several methods of SWNT separation and purification, with focus on the method studied

in this thesis, hydrogel separations.

1.4 Chirality Separations

Various methods have been developed to separate SWNT based on metallic vs

semiconducting properties,51,52 length,53,54 and chirality.55–57 Metallic vs semiconducting

SWNT separation has proved relatively straightforward, but separation of individual

chiralities has shown to be much more difficult.58 Since properties depend so strongly on

chirality, effective chirality separation methods are of great importance.

Some methods developed for chirality separation included density gradient

ultracentrifugation separation, polymer- and DNA-wrapping, and hydrogel separations, in

addition to other methods not discussed here, such as gel electrophoresis and chemical

functionalization.59,60 This section briefly describes these methods, with the greatest detail

given to hydrogel separations as the primary focus of this work.

1.4.1 Density Gradient Ultracentrifugation

Density gradient ultracentrifugation (DGU) offers one way to separate SWNT

chiralities, while simultaneously removing impurities such as catalyst particles and

amorphous carbon produced during synthesis.61 In a colloidal system, surfactant-

suspended SWNT have different buoyant densities dependent on the chirality and how the

surfactant arranges around each SWNT chirality. With DGU, a solution with a density

gradient is prepared, with increasing density towards the bottom of the solution. When

16

surfactant-coated SWNT are introduced and the system is centrifuged, the different

chiralities settle at different heights within the solution, depending on their density.

Providing that the SWNT buoyant densities differ enough, this procedure allows

for chirality separation, but some difficulties prevent large scale implementation: the

method depends on the use of ultracentrifuges, which are neither inexpensive nor designed

for the large volumes required for large-scale production of pure SWNT chiralities. As

such, DGU does offer a path towards purified SWNT, but not on a scale needed for real

world applications. Furthermore, the surfactant most often used for DGU exhibit strong

attraction to the SWNT sidewalls, hindering separation of the two required for later

applications, though some solutions have been proposed for this problem.62

1.4.2 Polymer- and DNA-Wrapping

Another potential method to separate SWNT chiralities lies in polymer- and DNA-

wrapping, two similar methods that rely on the differential adsorption preference of

synthetic polymer or single-stranded DNA (ssDNA) strands for specific SWNT

chiralities.63–66 With each method, linear polymer or ssDNA strands are designed with a

specific sequence, such as a repeating ssDNA strand of (AT)15, ideally resulting in selective

adsorption to and dispersion of specific SWNT chiralities. Once dispersed, SWNT

chiralities can be further separated, e.g., using ion exchange chromatography to separate

SWNT dispersed with ssDNA.65

Advantages to these methods include the potential for great chiral selectivity, lack

of interaction between polymers and ssDNA with impurities produced during SWNT

synthesis, as well as offering a method to non-covalently modify SWNT sidewalls for use

17

in applications, such as ssDNA wrapping for integration into biological systems.29

Shortcomings include the need to identify the most selective polymer or ssDNA strand for

each SWNT chirality, in addition to the need to produce these specialized polymers and

ssDNA on a large scale, making these methods impractical at larger scales.

1.4.3 Hydrogel Separation

As a solution to the lack of scalability in the previously mentioned separation

methods, hydrogel separations offer a different approach to SWNT purification. Utilizing

hydrogels originally developed for size-exclusion chromatography, suspended SWNT

chiralities in solution can be purified via competitive adsorption to the gel surface, as first

used by Moshammer, and studied in more detail by Kataura.57,67 The following sections

provide an overview of the adsorption mechanism, the experimental setup, and the problem

of irreversible adsorption.

1.4.3.1 Adsorption Mechanism

Interaction between hydrogel and SWNT in solution plays a central role in these

separations, but before considering that, SWNT must be suspended in solution via

surfactants. SWNT have extremely poor solubility in most solvents, especially polar

solvents such as water, rendering them incompatible with hydrogels. With surfactants,

such as sodium dodecyl sulfate (SDS), SWNT can be suspended in solution through the

formation of micelles around each nanotube. These micelles drastically improve the

solubility of SWNT in water, and prevent aggregation of SWNT over time.

18

Once suspended in solution, SWNT can be separated through hydrogel separations.

As previously noted, the process occurs through competitive adsorption to the gel surface,

with different chiralities adsorbing at faster or slower rates. To explain these differential

adsorption rates, Figure 1.7 shows a mechanism developed elsewhere.68,69

In brief, suspended SWNT in solution experience a combination of attractive and

repulsive forces to the gel at various distances. At short ranges, adsorption occurs due to

attractive dispersion forces between the SWNT and amide functional groups on the gel

surface, but at longer distances, repulsive coulombic forces act to keep the SWNT and gel

apart, acting as an activation energy for adsorption, as shown in Figure 1.7.A.

These Coulombic forces arise due to the negative charges on the SWNT, and either

negatively charged groups and/or surfactant molecules on the gel surface. Each SWNT

chirality interacts with SDS molecules to different degrees, resulting in larger or smaller

SDS micelles around different chiralities, as illustrated in Figure 1.7.B. This leads to

Figure 1.7. Mechanism of adsorption of SWNT to Sephacryl hydrogel. A) Different chiralities with different degrees of surfactant coverage. B) Different distance versus energy curves for various chiralities, showing different activation energies depending on surfactant coverage. Figure modified from reference 69.

19

similar differences in the magnitude of charge on each chirality, resulting in different

activation energies and rate constants of adsorption. Given these different rate constants

and the limited surface area of the gel, separation occurs according to whichever chirality

fills the limited surface area fastest. Once in the adsorbed state, SWNT remain on the gel,

while others remain in solution. Addition of a higher concentration surfactant solution

reverses the process, allowing for recovery of the adsorbed SWNT. Further study has also

been dedicated to determining the thermodynamics and other aspects of the separation

mechanism with regard to metal-semiconductor SWNT separation and chirality

separation.70–74

1.4.3.2 Hydrogel Separation Experimental Overview

Given the competitive nature of the adsorption mechanism, hydrogel separations

use an iterative process whereby a SWNT solution passes through multiple gel-containing

columns, as illustrated in Figure 1.8,68 each containing a limiting volume of gel.

20

In particular, S-200 Sephacryl hydrogel is used, while SWNT are suspended in 2.0

wt % SDS. Depending on rate constants and relative concentrations, certain SWNT

chiralities will adsorb, while all other chiralities remain in solution and flow through the

column. This flowthrough solution is collected and passed through a second column, and

so on, with different chiralities adsorbing at each iteration. The hydrogels are then rinsed

with a 2.0 wt % SDS solution to clear out any remaining SWNT solution, leaving only

adsorbed SWNT. After this, addition of a 5.0 wt % SDS solution elutes the adsorb

chiralities, yielding purified SWNT.

Figure 1.8. Overview of the hydrogel purification of SWNT, using an iterative method where SWNT competitively adsorb to the gel in a series of identical columns. Figure taken from reference 68.

21

This iterative process allows for purification and separation of different chiralities

from each other and from non-SWNT material present after synthesis. Figure 1.9 shows

the offset absorbance spectra of a series of elutions from such a process, in addition to the

absorbance spectrum of the original SWNT solution before separation, illustrating the

gradual separation and purification of the solution. To reiterate the optical SWNT

properties introduced in section 1.1.6, SWNT chiralities can be identified via their E11 and

E22 peaks, allowing one to determine the composition of a given SWNT solution. By

examining the spectra in Figure 1.9, one sees that different chiralities are obtained with

further iteration of the separation process. Also note that the first two columns in Figure

1.9 contain negligible amounts of SWNT. This occurs due to the predominant adsorption

of amorphous carbon material to the gel, preventing any adsorption of SWNT.

Figure 1.9. Offset absorbance spectra of hydrogel-separated SWNT elutions, beginning with a 50x dilution pre-separation solution at the top and progressing downwards, with elutions from earlier columns shown towards the top.

0

2

4

6

8

10

350 550 750 950 1150 1350

Abs

orba

nce

(offs

et fo

r cla

rity)

Wavelength (nm)

Pre-SeparationCol 1

Col 2

Col 3

Col 4

Col 5

Col 6

Col 7

Col 8

Col 9

Col 10

22

1.4.3.3 Irreversible Adsorption

While hydrogel separations promise a cost effective and scalable approach to

obtaining pure SWNT chiralities, and much progress has been made towards its continual

improvement and the development of new variations of the method,75–80 at least one

problem has largely been ignored by most investigators: irreversible adsorption of SWNT

to the hydrogel. During elution of SWNT, a sizable portion of SWNT remain adsorbed to

the gel despite the addition of high-concentration surfactant solution. Two observations

indicate the existence of these irreversibly adsorbed SWNT: qualitative observation of

color from adsorbed SWNT remaining on the gel after elution, and from quantitative

comparison of the number of SWNT in the solution before adsorption, the number in the

flowthrough, and the number in the elution, indicating a net loss in SWNT. Both

observations are graphically illustrated in Figures 1.10-1.11, where Figure 1.10 shows how

the gel retains the color of adsorbed SWNT, even after elution, and Figure 1.11

demonstrates the apparent loss of SWNT when comparing absorbance spectra of an

original SWNT solution before separation, the flowthrough, and elution, with the

difference between original solution and flowthrough to emphasize the number of SWNT

irreversibly adsorbed. Given this, the next section provides the thesis statement of this

research.

23

Figure 1.10. The different colors observed on the hydrogel during separation, showing the original gel color, pre-SWNT (1); post-SWNT adsorption (2); and post-elution, after presumably removing all the SWNT (3), where the dark color suggests that SWNT remain adsorbed after elution.

0

0.5

1

1.5

2

2.5

3

350 550 750 950 1150 1350

Scal

ed A

bsor

banc

e

Wavelength (nm)Original Flowthrough Elution Original - Flowthrough

Figure 1.11. The absorbance spectra of an original SWNT solution before separation, the flowthrough after separation, the corresponding elution, and the difference between the original and flowthrough solutions. All spectra are scaled according to their respective volumes, allowing for direct comparisons between peak heights.

24

1.5 Thesis Statement

Proposed adsorption mechanisms describing SWNT hydrogel separations have

assumed some degree of homogeneity in terms of gel-SWNT adsorption sites. This thesis

proposes that rather than being homogenous, the gel adsorption sites fall into three different

categories: types A, B, and C, corresponding respectively to weak adsorption (A), weak

adsorption followed slowly by irreversible adsorption (B), and irreversible adsorption by a

second currently unknown mechanism (C). Together, these proposed types of adsorption

sites explain the irreversible adsorption of SWNT to hydrogels.

25

CHAPTER II

EXPERIMENTAL METHODS

2.1 Reagents and Experimentation

This chapter describes the experimental work used in the rest of the thesis, including

the reagents, preparation, instrumentation, and experimental methods, emphasizing the

details needed to repeat any experiment. While later chapters also discuss relevant

experiments, they do so in context of the information provided in here. As such, this

chapter serves as a reference for all following chapters, including discussion of the theory

behind some procedures.

2.2 Reagents

In this first section, all reagents used in this work are listed, along with the

corresponding manufacturers and purities. Additionally, any preparation methods needed

before further experimentation are also described.

2.2.1 Carbon Nanotubes

Carbon nanotubes were purchased from Southwest Nanotechnologies (Norman,

OK), now owned by Chasm Advanced Materials, Inc (Canton, MA). Specifically, 1 g

quantities of SWNT enriched in (6,5) chirality and synthesized using the CoMoCat®

method were purchased under the product name SG65i. As produced SWNT have an

average length of 1 μm, with a total semiconducting SWNT content of 95%, and 40% (6,5)

content, with a black, powder-like consistency. For reference, carbon nanotube molecular

26

structures are shown in Figures 1.1-1.2 in section 1.1.1. Before separation, SWNT require

preparation, as discussed in sections 2.3.1-2.3.2.

2.2.2 Sodium Dodecyl Sulfate Solutions

For the SDS used in this work, 98.5% pure ReagentPlus SDS intended for use in

gel electrophoresis and molecular biology was purchased from Sigma-Aldrich in 1 kg

quantities, and used in solutions without further preparation. In DI water, SDS has a critical

micelle concentration of ~8 mM at 20 °C,81 and a critical micelle temperature of ~17 °C at

concentrations around 100 mM,82 both of which determine lower boundaries for

experimental conditions. Figure 2.1 shows the molecular structure of SDS, as well an

approximate representation of an SDS micelle, shown in the illustrative style used

elsewhere in the thesis.

Figure 2.1. A) Molecular structure of SDS. B) Representation of an SDS molecule, with the ionic and nonpolar portions indicated. C) Representation of an SDS micelle, illustrating the arrangement of charged sulfate group on the surface, with the nonpolar hydrocarbon chains arranged in the interior.

27

SDS solutions were made by percent weight (wt %), according to Equation 2.1.

2

SDS

SDS H O

mwt% 100m m

=+

(2.1)

Where SDSm is the grams of SDS, and 2H Om is the grams of DI water. In all cases, the

needed quantity of SDS is measured out, and added to the corresponding quantity of DI

water while mixing. The most common concentrations are 2.0 wt % for suspending SWNT

prior to separation, and 5.0 wt % for eluting SWNT from Sephacryl. For the more familiar

milimolarity (mM) unit, the wt % concentration can be converted to mM using Equation

2.2, assuming a low enough SDS concentration that the density of the solution equals that

of DI water. This assumption was shown to be valid for concentrations at least as great as

5.0 wt %.

2H O

SDS

dwt % 1000 mL 1000 mMmM100 MW 1L 1M

= (2.2)

Where 2H Od is the density of water at room temperature (0.998 g/mL), and SDSMW is the

molecular weight of SDS (288.38 g/mol). As an example, 2.0 and 5.0 wt % are 69 and

1.7×102 mM, respectively.

2.2.3 Sephacryl S-200 and Gel Preparation

Sephacryl S-200 hydrogel beads were purchased from GE Healthcare in 750 mL

quantities. The hydrogel beads are composed of crosslinked allyl dextran, using N,N’-

methylene bisacrylamide as a crosslinker, with average bead diameter measured to be

4.0×101 μm with a standard deviation of 1.0×101 μm, determined from optical microscopy

28

images, as described in section 2.5.2. Figure 2.2 illustrates the molecular structure of

dextran, showing the crosslinked nature of the different allyl dextran polymers.

As packaged, Sephacryl is stored as a mixture of 20% ethanol and 80% hydrogel

by volume, where ethanol acts as a preservative. Ethanol prevents SDS micelle formation

and must be removed before any separation. Also, to provide a consistent interaction

between SWNT, gel, and SDS, Sephacryl is equilibrated with an SDS solution prior to

separation, which can be accomplished simultaneously with the ethanol removal. The

procedure for accomplishing this depends on the separation procedure used, as discussed

in sections 2.4.1-2.4.2.

Figure 2.2. Molecular structure of Sephacryl, consisting of allyl dextran crosslinked with N,N’-methylene bisacrylamide.

29

During storage, the gel beads settle to the bottom of the container, and for

measuring purposes, the gel-ethanol mixture is gently mixed by inverting the container,

yielding a more homogenous consistency, where the volume of Sephacryl is defined as the

total volume of gel plus ethanol. Thus, 1.0 mL of Sephacryl contains 0.8 mL of gel and

0.2 mL of ethanol. Special care must be taken not to mix the system so hard that the gel

beads begin to break, which can clog the porous frits used in the columns for separation.

2.3 Pre-Separation Procedures

Prior to SWNT separation, two procedures must be completed to produce

individualized, usable SWNT: 1) ultrasonication to break SWNT aggregates (bundles)

apart as much as possible and to disperse the individual SWNT in solution; and 2)

centrifugation to remove remaining SWNT aggregates and catalyst particles remaining

from synthesis. This section covers these procedures in moderate detail, outlining the

general purpose and procedure for each, along with some relevant theory.

2.3.1 Ultrasonication

Often used to homogenize solutions, ultrasonication applies high-frequency

vibrational waves to a liquid solution, breaking apart SWNT bundles and dispersing the

individual SWNT. As synthesized, SWNT form large aggregates of dozens or more

SWNT, and due to the strong dispersion forces acting between carbon nanotubes, these

bundles do not easily break apart. Figure 2.3 shows SEM images of such bundles,

demonstrating the close packing of many carbon nanotubes.83

30

Larger SWNT bundles do not disperse in solution, and while smaller bundles may

disperse to some degree, they trap SWNT in an unusable state and prove difficult to

separate from individually dispersed SWNT via hydrogel separations. Consequently,

sonication plays a crucial role in separation. The next two subsections explain the theory

behind sonication, followed by the procedure and instrumentation, respectively.

2.3.1.1 Ultrasonication Theory

On a microscopic scale, the vibrational waves produced by sonication lead to

localized areas of high pressure and temperature of around 2000 atm and 5000 °C.84 In the

case of SWNT bundles, one theory predicts that these high pressures and temperatures

gradually separate SWNT from each other, allowing surfactant molecules to move in-

between individual SWNT, dispersing them in solution and preventing reaggregation.85 As

a side effect, sonication also breaks SWNT apart, slowly shortening the nanotube length

and producing large quantities of amorphous carbon material. With the sonication

conditions used here, SWNT material of an average length of 1 μm breaks down to an

average length of approximately 300 nm.68

Figure 2.3. TEM images of ~100 bundled carbon nanotubes, showing the large number of nanotubes in close arrangement, preventing dispersion in solution. Figure modified from reference 83.

31

2.3.1.2 Sonication Procedures and Instrumentation

To disperse SWNT in solution, this procedure utilizes two types of sonication: a

mild bath sonication to first mix SWNT bundles into a SDS solution, and a stronger

ultrasonication to break bundles apart and disperse SWNT. To begin, solid SWNT powder

and 2.0 wt % SDS solution are measured out in a 1:1 mg per mL ratio, the exact amounts

depending on the scale of the SWNT separation; half of the SDS solution is mixed with the

SWNT, while the rest is set aside. A Fisher Scientific FS20D bath sonicator is used to

sonicate the SWNT mixture for 15 minutes or until an opaque black mixture is produced

with no solids visible on the bottom of the container.

After bath sonication, the SWNT mixture is transferred to the ultrasonicator, using

the SDS solution set aside earlier to rinse any remaining SWNT material from the first

container into the beaker. Figure 2.4 portrays the setup of the Branson Digital Sonifier

Model 102C horn tip sonicator with 0.5 inch horn, showing a water-jacketed beaker to hold

the SWNT mixture, a cold water source to counter heat produced during sonication, a

thermocouple, and the ultrasonication horn submerged in solution. Given the power output

of the sonicator horn, special care is taken to ensure that it does not touch any other object.

32

Once ready, sonication and water cooling are started. Given that the SDS critical

micelle temperature is ~17 °C, and that the rate of water evaporation increases with

temperature, the SWNT mixture is kept between ~20-24 °C. The sonication state, amount

of sonication, is defined according to the watts of sonication power, time of sonication, and

volume of solution, as given in Equation 2.3.

p tSv×

= (2.3)

Where S is the sonication state, p is the power output in watts, t is the time in hours,

and v is the volume in milliliters. An unpublished side project found that a sonication state

of 2.6 W×hr/mL produced the greatest number of dispersed SWNT. Lower sonication

states leave many SWNT in a bundled state, while higher sonication states disperse SWNT

but also seem to break many of them into amorphous carbon, leading to fewer dispersed

Figure 2.4. Diagram of the Branson Digital Sonifier setup, with water-jacketed beaker, cold water source, thermocouple, ultrasonication horn, and SWNT mixture.

33

SWNT following centrifugation. As an important note, Equation 2.3 assumes that all

samples sonicated at the same W×hr/mL will produce identical results so long as the ratio

of these variables remains the same. As this assumption lies unproven, iterations of similar

experiments used identical sonication power, time, and solution volume, as appropriate for

the experiment.

After sonication, the solution is returned to its original volume by addition of DI

water to counter any loss due to evaporation. Prior to any further experimentation, 100 μL

of SWNT solution are removed and diluted as needed for spectral analysis, which is

described in section 2.5.1.

2.3.2 Ultracentrifugation

After dispersing SWNT via ultrasonication, many SWNT bundles remain in solution,

as well as metallic catalyst particles from synthesis. Due to their lower colloidal stability,

centrifugation removes these bundles and particles from solution, predominantly leaving

individual SWNT for separation.

Using a ThermoScientific Sorvall mX 120+ Micro-Ultracentrifuge with either a S50-

ST swinging-bucket rotor or a S50-A fixed-angle rotor depending on the volume, the

solution is centrifuged at 50,000 rpm for 2 hours at 25 °C. Longer times can be used to

further remove bundles, but at the cost of also removing additional individualized SWNT.

After sonication, a black-metallic pellet is left on the bottom of the centrifuge tube. The

top 90% of the supernatant is removed and kept for separation, while the remaining bottom

10% is discarded to avoid retaining the large quantity of bundled SWNT near the bottom.

34

Of the solution removed from the centrifugation tube, 100 μL is removed and diluted for

spectral analysis, bringing all SWNT preparation to completion.

2.4 Separation Procedures

After completing the pre-separation procedures, the SWNT separations may proceed

according to one of two different separation methods, both discussed in the following

sections in detail. As first introduced in section 1.4.3.2, column separations loosely

resemble traditional column separations, using small chromatography columns to contain

the hydrogel while SWNT solutions flow through, whereas the so-called ‘mixed method’

involves a well-mixed system of gel and SWNT held in a conical centrifugation tube. Each

method has different advantages, e.g., column separation proves easier in implementation

due to the smaller number of steps, while mixed separation provides greater control over

consistency.

2.4.1 Column Separation

As already stated, this separation procedure utilizes columns to contain the

hydrogel and SWNT solution, and since an overview of the process was already given in

section 1.4.3.2, this section focuses more on the technical details of the procedure. Readers

are directed towards Figure 1.8 for a graphical overview of the procedure. The next section

describes column preparation, followed by the separation procedure.

35

2.4.1.1 Column Preparation

Figure 2.5 demonstrates the general

column setup, fitted with a porous frit on the

bottom to retain gel in the column, followed by

gel, and a second frit gently placed on top to

prevent the gel from being disturbed. Unless

specified otherwise, separations employ Thermo

Scientific disposable polypropylene columns of

inner diameter 13 mm and height of 70 mm, with

porous frits of 30 μm pore size.

For a standard separation, each column

contains 1.40 mL of gel, and special care is taken

to ensure that gel fills the column evenly, with no irregularities in height. After adding gel,

the second frit is placed on top, placed gently such that full contact between gel and frit is

established without compressing the gel. Before any SWNT separation, ethanol must be

removed from the gel, followed by equilibration with SDS, as first mentioned in section

2.2.3. Both processes are accomplished by flowing SDS solution through the gel in a ratio

of 4.0 mL of SDS per 1.40 mL of gel. For all separations, the SDS concentration used for

equilibration and removing ethanol equals the concentration used to disperse the

corresponding SWNT solutions, e.g., 2.0 wt % in a standard separation. For every 10.0

mL of 1 mg/mL SWNT solution to be separated, a minimum of 10 columns are prepared.

Figure 2.5. Column prepared with gel and porous frits.

36

2.4.1.2 Column Separation Procedure

With columns and SWNT solutions prepared, the overall procedure follows four

steps:

1. Flow SWNT solution through first column and collect flowthrough in a vial.

2. Rinse the column of residual SWNT solution by addition of a neat SDS solution,

which is gathered in a waste receptacle.

3. Elute adsorbed SWNT from the gel by addition of 5.0 wt % SDS.

4. Use the SWNT flowthrough from Step 1 to repeat the process with the next column.

For a standard separation using 1.40 mL of gel per column, 10.0 mL of SWNT

solution are used per series of 10 columns for Step 1; rinsing in Step 2 is accomplished

with 4.0 mL of SDS solution of the same concentration used for equilibration of gel; and

4.0 mL of 5.0 wt % SDS is used for elutions, though 3.0 mL can be used if more

concentrated elutions are desired. Most often, 10 columns are enough to separate most of

the SWNT from a 10.0 mL original solution, though more columns may be needed to do

so depending on the sonication settings and resultant SWNT concentration.

2.4.2 Mixed Separation

In a mixed separation, the gist of the procedure follows the same ideas behind a

column separation, but the exact details differ noticeably. With this methodology, conical

centrifugation tubes replace the more conventional columns, where each tube contains a

volume of gel, to which is added the SWNT solution for separation. This method requires

a greater number of steps than a column separation, but allows for greater control over

contact time between gel and SWNT, and consequently more consistency between

37

samples. As before, the following section describes the conical centrifugation tube

preparation, with the separation procedure explained after that. All centrifugation for this

procedure was performed using a ThermoFisher Sorvall Legend XTR centrifuge with

swing-out rotor.

2.4.2.1 Conical Centrifugation Tube Preparation

As with column preparation, conical centrifugation tube preparation emphasizes

removal of ethanol, equilibration with SDS, and consistency between samples. To

accomplish this for a mixed separation, the total volume of needed Sephacryl is measured

into a single tube, diluted by a factor of 4 with SDS of the chosen concentration, and mixed

gently by hand. Centrifugation at 2000 rpm for 30 seconds forces the gel towards the

bottom of the tube, leaving the solution of SDS and ethanol as an easily removed

supernatant. To maintain consistent gel volumes, care is taken not to remove any gel when

removing supernatant. To ensure removal of all ethanol from the gel, this process of

dilution and centrifugation is performed a total of three times. After removing the

supernatant for the third time, the gel is returned to its original volume by addition of SDS

solution. Alternatively, if sub-1 mL volumes of gel are to be measured out, the gel is

diluted by a factor of 4 with SDS, allowing for more accurate measurement of otherwise

small volumes in diluted form.

Equilibrated gel volumes are measured into either 50 mL tubes for standard

separations, or 15 mL tubes when using smaller amounts of gel and SWNT. These are

centrifuged at 2000 rpm for 30 seconds, leaving gel on the bottom and supernatant on the

38

top. The supernatant is removed, again taking care not to remove any gel, leaving the tubes

and gel ready for separation.

2.4.2.2 Mixed Separation Procedure

With the prepared gel, the mixed separation procedure follows 5 steps, analogous to

the column separation:

1. Add SWNT solution to the first tube and mix for 15 minutes using a Thermo

Scientific Tube Revolver running at 20 rpm.

2. Centrifuge the SWNT-gel mixture at 2000 rpm for 30 seconds, and remove the

SWNT supernatant from the tube.

3. Rinse gel of residual SWNT solution by addition of SDS solution of the same

concentration used for equilibration, mix for 5 minutes, centrifuge at 2000 rpm for

30 seconds, and remove supernatant. Repeat a total of three times.

4. Elute adsorbed SWNT via addition of 5.0 wt % SDS solution, mix for 5 minutes,

centrifuge at 2000 rpm for 30 seconds, and remove supernatant for analysis.

5. Repeat process using the supernatant from Step 2 for the next tube in the separation.

This procedure uses identical gel, SWNT solution, and 5.0 wt % SDS volumes as

used in a standard column separation, with the primary differences occurring during the

rinsing step. As such, 1.40 mL of gel are used per tube, with 10 tubes per 10.0 mL of

SWNT solution of a 1 mg/mL concentration, with 4.0 or 3.0 mL of 5.0 wt % SDS used for

elution. With rinsing in Step 3, 4.20 mL of SDS solution are added to sufficiently dilute

any remaining SWNT solution.

39

2.5 Analysis Procedures

All prior procedures described in this chapter focus on the wet chemical methods,

with less focus given to instrumentation. As such, this section describes the

instrumentation and the related standard operating procedures used for quantitation. In

particular, absorbance spectrometry and spectral analysis receive the greatest emphasis as

the primary means for determining SWNT chiralities and concentrations. Some attention

is also given to optical microscopy due to its use in studying gel beads.

2.5.1 Absorbance Spectrometry

Absorbance spectra were gathered over the range from 350-1350 nm on a

PerkinElmer Lambda 1050 double-beam spectrometer, operated with the PerkinElmer UV

WinLab software. A photomultiplier tube was used in the range from 350-860 nm and an

InGaAs detector was used in the range from 860-1350 nm, with a tungsten-halogen lamp

for the entire wavelength range. Quartz cuvettes were used for holding solutions, and

spectrometer slit widths were set at 4 nm for the best combination of resolution and signal-

to-noise ratio, with all other settings at default values. By standard operating procedure,

the spectrometer was powered on 30 minutes prior to gathering data to ensure no change

in lamp output during data acquisition.

2.5.1.1 Absorbance Fitting

Considering that any SWNT absorbance spectrum may contain contributions from

many different chiralities, in addition to amorphous carbon, determining the composition

of each sample requires that the net absorbance be fitted by a sum of different components

40

to determine the contribution from each species. Three general absorbance contributions

are considered for fitting purposes: E11 peaks, phonon sidebands coupled to the E11 peaks,

and an exponential background to account for what is thought to be amorphous carbon.

Additional peaks related to carbon nanotube bundling also occur, but are assumed to add a

negligible contribution due to the short times between centrifugation and analysis. Figure

2.6 illustrates the fitting process via a comparison of an experimental absorbance spectrum

to a best fit composed of the sum of individual peaks and background functions in the E11

region, the exact details of which are described in the following paragraphs. Some

discrepancies exist between the spectrum and best fit in the E11 region, but are assumed to

contribute negligibly to the fitting process.

Figure 2.6. Comparison of an experimental absorbance spectrum to a best fit spectrum, showing the E11 and phonon sideband peaks attributed to each chirality, as well as the background function in the E11 region.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.92 1.02 1.12 1.22 1.32 1.42 1.52 1.62 1.72

Abs

orba

nce

Energy (eV)(7,5) (7,3) (6,5) (6,4)

Sum Background Sum Fit Experimental

41

Given an experimental absorbance spectrum, the fitting process goes as follows:

1) Fit the background absorbance using the sum of two exponential functions

2) Identify SWNT chiralities present in the spectrum

3) Iteratively fit each E11 and phonon sideband peak with a Lorentzian function.

For the entire process, spectra are treated in energy space in units of electron volts.

Beginning with Step 1, the exponential functions used to model the background follow

Equation 2.4, including variables for two amorphous carbon species.86

1.924 3.723x x

1 0,1 2 0,2B(x) A y e A y e− −

= + + +

(2.4)

Where B(x) is the background as a function of x, x is the position in energy space in eV,

A1 and A2 depend linearly on the amorphous carbon concentrations, y0,1 and y0,2 affect the

absorbance as x approaches zero, and the exponential constants, -1.924 eV and -3.723 eV,

depend on the amorphous carbon species.86 For fitting purposes, A and y values are varied

until the magnitude of the differences between spectrum and background function at x

values of 1.00 eV and 2.92 eV are less than or equal 0.01 eV. No SWNT chirality absorbs

at these energies, meaning any absorbance depends purely on the background.

Once the background has been fit, potential SWNT chiralities are identified by

comparing peaks in the E11 region to a table containing E11 and E22 absorbance peak data

for all relevant chiralities.13 These potential chiralities are cross-checked against the

absorbance peaks in the E22 region, verifying which chiralities belong to the E11 peaks.

With chiralities identified, E11 peaks are fit with Lorentzian functions, as given by Equation

2.5, which were determined to accurately fit SWNT peaks by a previous student.87

2

2 20

L(x) I(x x ) γ

= − + γ

(2.5)

42

Where L(x) is the Lorentzian function, x is position in energy space in eV, x0 is the peak

center, I is the peak height at x0, and γ is the half-width at half-maximum. During fitting,

I is adjusted to minimize the peak differences between fit and spectrum to less than or equal

to 0.05 eV, while x0 and γ may be varied by a few percent if needed, but are generally left

untouched from default values, where x0 is taken from the aforementioned table of SWNT

absorbance peaks,13 and γ is usually given a value of 0.018 eV. For each of these E11 peaks,

there are accompanying phonon sideband peaks. These are modelled using the same

lineshape, but with an additive shift to peak center of 0.21 eV towards higher energies, and

multiplicative changes to peak height and width of 0.08 and 2.6, respectively.87 Phonon

sidebands occur due to the coupling of electronic transitions with phonon, or vibrational,

transitions. All spectra are fit manually, meaning some subjectivity may be present in

analysis. Consequently, the author of this thesis fit all spectra to avoid inter-person

differences.

2.5.1.2 SWNT Concentration

With a fitted spectrum, the concentrations of different SWNT chiralities can be

determined by analyzing the respective E11 peak heights with Beer’s Law, given in

Equation 2.6.

A lc= ε (2.6)

Where A is the absorbance at the SWNT peak center, ε is the absorption cross section per

carbon nanotube of the corresponding chirality, l is the optical path length with a value of

1 cm, and c is the SWNT concentration in units of number per mL. Values of ε at the E11

peaks can be estimated using Equation 2.7 in units of cm2.1,68

43

( ) ( )1/217 2 2

1 1 2 21/20

10 4L 1.7 10 n n n na 3

−ε = × + + (2.7)

Where L is the SWNT length in nm (estimated as 300 nm here), 1.7×10-17 cm2 is the

estimated absorption cross section per carbon atom in a nanotube, a0 is the SWNT carbon-

carbon bond length in angstroms (2.461 Å), and n1 and n2 are the chiral indices. Using

values of ε from Equation 2.7, and values of A equal to the peak heights, I, from Equation

2.5, allows one to solve Beer’s Law for the concentration of each SWNT chirality.

2.5.2 Optical Microscopy

The average gel bead diameter and the diameter distribution were determined using

a Leica DM 750 microscope with Leica ICC50 HD microscope camera, with the

accompanying Leica Application Suite LAS EZ software for visualizing microscope

camera images in real time and saving images in electronic format. After acquiring images,

Gwyddion software was used to determine the bead diameters.

For the experimental measurement of bead diameter, a volume of Sephacryl S-200

was diluted by a factor of 10, yielding a low enough concentration of beads to avoid major

overlap between beads on the microscope slide, and to allow sufficient light to be

transmitted. A few drops of the diluted bead mixture are deposited onto a glass microscope,

with a glass cover slide on top, and a 10x magnification for collecting images.

44

CHAPTER III

SDS-SWNT ADSORPTION MORPHOLOGY AND PACKING

3.1 Adsorbed SWNT-SDS

Though this thesis mainly focuses on irreversible SWNT adsorption to Sephacryl, an

earlier project studied the SWNT saturation of the hydrogel surface and the number of

adsorption sites per gel volume. Prompted by the observation of another student that the

maximum number of adsorbed SWNT per gel volume could be predicted within an order

of magnitude by assuming SWNT pack closely together on the gel surface, this section

attempts to build on the initial calculation by including SDS in the model. Such a study

could provide further insight into the nature of SWNT adsorption on Sephacryl S-200, in

addition to a better understanding of SWNT-gel interactions in general.

Though the main research focus was changed towards irreversible adsorption before

a conclusive model could be developed here, some results proved useful when studying

irreversible adsorption. Most notably, the maximum number of adsorbed SWNT per gel

volume was determined, in addition to identifying a trend between this maximum number

of SWNT and the SDS concentration used during adsorption. Section 3.2 briefly describes

the initial hypotheses developed to approach the problem, section 3.3 gives an overview of

the experimental setup, section 3.4 compares the predicted trends against the experimental

data, while section 3.5 addresses the possibility of equilibrium between the solution and

adsorbed states.

45

3.2 Hypothesized SDS-SWNT Adsorption Morphology and Packing

In solution, SDS forms micelles around SWNT, the morphology of which is known

to depend on the surrounding SDS concentration.88 Figure 3.1 shows several predicted

SDS-SWNT micelle morphologies, illustrating how the morphology changes with SDS

concentration. Given this concentration dependent behavior in solution, this thesis

proposes that SDS on gel-adsorbed SWNT exhibit similar behavior, with lower SDS

concentrations leading to smaller micelles on adsorbed SWNT, and higher concentrations

leading to larger micelles, where the micelle size affects how many SWNT can adsorb to

the gel surface.

Though the original model over-estimated the maximum number of adsorbed

SWNT, it provides a good starting point to improve on. Working with the simple

assumption that SWNT pack onto the gel surface in an orderly manner, and that SDS

micelles determine how closely SWNT can pack, then the maximum number of SWNT

Figure 3.1. Predicted SDS morphologies on SWNT at A) low SDS concentrations; B) mid concentrations; and C) high concentrations, demonstrating the change in micelle size with increasing SDS concentration, where the SDS concentration is defined according to the number of adsorbed SDS molecules per nanotube length. Figure modified from reference 88.

46

that can adsorb to a volume of hydrogel depends on four variables: 1) the SWNT packing

arrangement; 2) the SWNT length; 3) the SDS micelle morphology; 4) and the gel surface

area. With these factors in mind, a ‘close-packing’ model was proposed to explain the

relationship between the number of adsorbed SWNT and the SDS concentration, as

portrayed in Figure 3.2, and described in section 3.2.2.

Considering that the close-packing model may overestimate how closely SWNT can

pack, a second packing arrangement is also proposed to test for a lower limit of packing

density, called the ‘circular-packing model,’ as depicted in Figure 3.3.

Figure 3.2. ‘Close-packing’ adsorption scheme, where SWNT arrange in a close, orderly manner, separated by SDS: A) low SDS concentration, with a smaller effective SWNT diameter; B) high SDS concentration, with larger SDS micelle and effective SWNT diameter.

47

This circular-packing describes the adsorbed SWNT as occupying a circular area

defined by the SWNT length, where the SWNT radius and SDS micelle size are ignored

due to being an order of magnitude smaller. Consequently, this model has no dependence

on micelles or SDS concentration. Section 3.2.3 explains the details of this model in more

detail, but before doing, section 3.2.1 describes the process of approximating the gel

surface area.

3.2.1 Gel Surface Area

For each of the two models mentioned in the previous section, both require

knowledge of the gel surface area to estimate the maximum number of adsorbed SWNT.

To determine this, optical microscope images were used to measure the average gel bead

radii, as described in section 2.5.2. Figure 3.4 shows such an image below.

Figure 3.3. The ‘circular-packing’ model, where SWNT adsorb onto the gel surface with a packing density approximated by the circular arrangement here.

48

By determining the average surface area per bead, and estimating the total number

of beads per gel volume, the total gel surface area per gel volume can be estimated, as done

using Equations 3.1-3.4.

2bead beadA 4 r= π (3.1)

3bead bead

4V r3

= π (3.2)

bead3

gel bead bead

N 3V V 4 r

ε ε= =

π (3.3)

gel beadbead

gel gel bead

A N 3AV V r

ε= = (3.4)

Where Abead is the bead surface area, rbead is the mean bead radii (20 μm), Vbead is the bead

volume, bead

gel

NV

is the number of beads per gel volume, ε is the unitless bead packing

efficiency (random close packing, 0.641), and gel

gel

AV

is the total gel surface area per gel

Figure 3.4. Optical microscope image of Sephacryl S-200 diluted by a factor of 10 at 10x magnification and in 2.0 wt % SDS. The scale bar represents 100 μm.

100 μm

49

volume. Regardless of the packing model used, the maximum number of adsorbed SWNT

per gel volume can be predicted using Equation 3.5.

gelSWNT

gel gel SWNT bead SWNT

AN 1 3 1V V A r A

ε= = (3.5)

Where SWNT

gel

NV

is the maximum number of adsorbed SWNT per gel volume, and ASWNT is

the occupied area per SWNT. The next two sections outline the exact details of each model,

including how the gel surface area per volume is used.

3.2.2 Close-Packing Model

In this model, the size of SDS micelles on the adsorbed SWNT is assumed to depend

on the SDS concentration used during adsorption, with larger micelles at higher SDS

concentrations, and vice versa. With larger micelles, the SWNT occupy more surface area

on the gel, decreasing the maximum number of SWNT on the gel. To describe the surface

area occupied per SWNT, the nanotubes are treated as occupying a rectangular area

determined by the nanotube length, diameter, and micelle thickness, as outlined by

Equation 3.6.

( ) ( )SWNT SWNT SWNT g SDS SDSA 2L r d xL 1 x W = + + + − (3.6)

Where LSWNT is the SWNT length (300 nm),68 rSWNT is the SWNT radius, approximated as

0.5 nm for the predominant SWNT chiralities used here, and dg is the graphitic distance,

or van der Waals radii of the SWNT (0.17 nm). The remaining terms in Equation 3.6

describe the contributions from SDS, where LSDS is the SDS “length” (1.9 nm), and WSDS

is the “width” of the SDS molecule (0.57 nm). The final term, x, is used to adjust the

50

orientation of SDS on the SWNT surface, where x = 1 corresponds to SDS oriented

perpendicular to the SWNT, as in Figure 3.2B, whereas x = 0 corresponds to SDS oriented

parallel to the SWNT, as in Figure 3.2.A. In context of this, the maximum number of

adsorbed SWNT per gel volume is given by Equation 3.7.

( ) ( )SWNT

gel bead SWNT SWNT g SDS SDS

N 3 1V r 2L r d xL 1 x W

ε=

+ + + − (3.7)

3.2.3 Circular-Packing Model

As stated before, the circular-packing model assumes that each SWNT occupies a

circular area, the diameter of which is defined by the SWNT length, as was shown in Figure

3.3. Equation 3.8 provides the method to calculate the area per SWNT, as according to

this model.

2SWNT SWNTA L

4π

= (3.8)

From this, the maximum number of SWNT per gel volume is calculated via Equation 3.9.

2SWNT

2gel bead SWNT

N 12 1V r L

ε=

π (3.9)

Where ε is squared to account for the inefficient packing of SWNT onto the gel surface.

With the mathematical details of each model described in sections 3.2.2-3.2.3, section 3.3

provides the experimental details of determining the maximum number of SWNT per gel

volume.

51

3.3 SWNT Saturation Experimental Details

To determine the maximum number of SWNT per gel volume, an iterative process

was used, as based on a standard column separation. Though SWNT adsorb to the gel on

the order of minutes, and SWNT solutions take approximately 10 minutes to flow through

a column, it is possible that any SWNT solution will flow through too quickly to saturate

the gel. If not saturated, any measurement would underestimate the maximum number of

adsorbed SWNT. Thus, the need for an iterative process. Figure 3.5 outlines the overall

procedure.

Figure 3.5. An iterative gel saturation process, where a SWNT solution is repeatedly flowed through a gel until the number of SWNT remaining in the solution remains constant, as determined by absorbance spectroscopy between each flowthrough.

52

To elaborate, the process follows three series of steps:

1) Flow a SWNT solution of known content through a column containing a known

volume of gel.

2) Gather the flowthrough, and rinse the gel of any residual SWNT solution into a

separate vial, using an SDS solution of the same concentration used in the

SWNT solution.

3) Take the absorbance spectrum of the flowthrough, and compare to the

absorbance of the solution from Step 1. If the two differ, repeat the process in

the same column, using the flowthrough as the SWNT solution for Step 1.

Columns were prepared with 0.25 mL of Sephacryl, as described in section 2.4.1.1,

and the entire procedure was performed at 5 different SDS concentrations: 0.5, 1.0, 2.0,

2.5, and 3.0 wt %. Additionally, the experiment was repeated twice under identical

conditions.

To simplify the absorbance spectra analysis, pre-separated SWNT solutions were

used, as obtained by a standard column separation described in section 2.4.1. The pre-

separated SWNT solutions were diluted from 5.0 wt % SDS to the appropriate

concentrations mentioned above for saturation, each to the same final volume of 24.0 mL.

After each flowthrough, gels were washed with 1.0 mL of the appropriate SDS solution.

53

To illustrate the process of saturation, Figure 3.6 shows the measured SWNT

concentration of each flowthrough plotted versus the corresponding number of times the

solution has been through the column, where the first data point corresponds to the original

solution.

As seen, the plot levels off with additional flowthroughs, indicating that the gel has

reached saturation. Experiments at other SDS concentrations showed similar behavior, but

levelled off at different SWNT concentrations. With this, Equation 3.10 can be used to

calculate the number of adsorbed SWNT per gel volume.

SWNT 0 f

gel gel

N SWNT SWNTV V

−= (3.10)

Where SWNT0 is the number of SWNT in the original solution before contact with the gel,

and SWNTf is the number of SWNT in the final flowthrough. With this experimental

procedure, section 3.4 compares the analyzed results.

0

5E+13

1E+14

1.5E+14

2E+14

2.5E+14

3E+14

0 1 2 3 4

[SW

NT]

(#/L

)

Flowthrough Number

Figure 3.6. SWNT concentration of flowthrough solutions plotted versus the respective number of times through the column, as gathered according to Step 3 of the procedure described above. Experiment performed at 2.0 wt % SDS. Error bars represent standard deviation for n = 2 duplicates.

54

3.4 Comparison of Predicted and Experimental Results

With the experimental details outlined in the previous section, and the models

described in sections 3.2.2-3.2.3, this section address the agreements and disagreements

between the experimental and predicted results. Table 3.1 lists the adsorbed SWNT per

gel volume for the close-packing and circular-packing models, in addition to experimental

results.

Modeled Values Experimental Values

SDS wt % N/A 0.5 1.0 2.0 2.5 3.0 Experimental SWNT per gel

volume N/A 1.5E+16 1.8E+16 1.5E+16 9.6+15 5.4E+15

Experimental Standard Deviation N/A 1.7E+14 1.3E+15 1.8E+15 4.6E+14 6.7E+14

Min Close-Packing 6.2E+16 N/A

Max Close-Packing 2.4E+17 Circular-Packing 8.7E+14

As Table 3.1 demonstrates, the close-packing model greatly overestimates the

number of adsorbed SWNT per gel volume, even with the inclusion of SDS to the effective

SWNT diameter, whereas the circular-packing model greatly underestimates the number.

Examining the experimental data in closer detail in graphical form reveals an interesting

nonlinear trend, illustrated in Figure 3.7.

Table 3.1. Experimental and predicted maximum number of adsorbed SWNT per gel volume. All adsorbed SWNT values number per gel volume in liters.

55

Rather than a continuous decrease in the number of adsorbed SWNT with increase

in SDS concentration, the trend seems to reverse at low SDS concentrations, with a

maximum somewhere between 1.0 and 2.0 wt %. More data points would be needed to

verify such a trend in full.

Though the results here do not establish anything conclusively, it does indicate the

experimental SWNT packing density on the surface of the SWNT lies somewhere between

the between the close- and circular-packing models. As stated in the beginning of this

chapter, the research focus changed from this project to the irreversible adsorption project.

Some useful information was obtained though. Specifically, the number of adsorbed

SWNT required to saturate the hydrogel was used in the following chapter on irreversible

adsorption, and the nonlinear trend between the number of adsorbed SWNT and the SDS

concentration suggests a more complex type of interaction at the gel surface, providing a

Figure 3.7. Experimental number of adsorbed SWNT per gel volume at five different SDS concentrations, showing a nonlinear trend between the number of SWNT and SDS concentration. Error bars indicate standard deviation for n = 2 replicates.

0

2E+15

4E+15

6E+15

8E+15

1E+16

1.2E+16

1.4E+16

1.6E+16

1.8E+16

2E+16

0.5 1 1.5 2 2.5 3

SWN

T pe

r Gel

Vol

ume

(#/L

)

SDS Concentration (wt%)

56

starting point for future modelling attempts. Regardless, little more time will be spent on

this topic, with the exception of one more matter discussed in the next section, while future

work on this project will be discussed in chapter V.

3.5 Gel Saturation versus Equilibrium

One might argue that SWNT adsorption to the gel is limited by an equilibrium

between adsorbed SWNT and SWNT in solution, as illustrated by Equation 3.11, rather

than being limited by the amount of available gel surface area.

[ ][ ]

Ads

Sol

SWNTK

SWNT= (3.11)

Where [SWNTAds] is the concentration of adsorbed SWNT, [SWNTSol] is the concentration

of SWNT in solution, and K is an SDS-dependent equilibrium constant. To determine

whether equilibrium or saturation limit the number of adsorbed SWNT, a simple

experiment can be performed: perform the procedure outlined in Figure 3.5 until no more

SWNT adsorb, and then let the gel mix with a neat SDS solution of the same concentration

used for adsorption. If an equilibrium exists, then SWNT should be observed in the SDS

solution after mixing for some length of time. If no SWNT are observed, then adsorption

is limited by saturation of the gel. Figure 3.8 shows the results from such an experiment,

demonstrating the lack of equilibrium after 1.7 hours. Additional measurements were done

at 24 hours and 36.8 hours, showing similar results with no evidence of equilibrium.

57

Figure 3.8. The absorbance spectra of the original SWNT solution before adsorption, the final flowthrough after adsorption, and the equilibration solution after 1.7 hours, showing no measurable number of SWNT.

0

0.02

0.04

0.06

0.08

0.1

0.12

350 450 550 650 750 850 950 1050 1150 1250 1350

Abs

orba

nce

Wavelength (nm)

Original Solution Flowthrough 1.7 hr Equilibration

58

CHAPTER IV

KINETICS AND MECHANISM OF IRREVERSIBLE ADSORPTION

4.1 Dynamics of Adsorbed SWNT on Sephacryl

While the adsorption process of single-walled carbon nanotubes onto Sephacryl

hydrogel has been studied to some degree, relatively little effort has been devoted to

understanding the nature and dynamics of the adsorbed SWNT-Sephacryl system, an

intermediate and important step in the separation process of selective-adsorption and

desorption. Understanding this aspect of gel-SWNT interaction could lead to

improvements in SWNT separation, in addition to an improved general understanding of

interactions between SWNT with other species. This chapter focuses on the study of the

adsorbed SWNT-Sephacryl system; in particular, the mechanism of irreversible

adsorption, the role SDS plays in this process, and the kinetics-based models and

experiments used to explain this phenomenon. Beginning with an initial hypothesis, the

chapter works towards a final model in an iterative manner, as directed by experimental

results.

4.2 Proposed Mechanism: SDS Rearrangement

Given the relatively little attention paid to the phenomenon of irreversible

adsorption in the literature, developing an initial model to explain the phenomena brings

some difficulty. Specifically, what sort of interactions occur between SWNT, SDS, and

Sephacryl in the adsorbed state, and how might these interactions contribute to irreversible

adsorption? Does SDS maintain a micelle-like shell around adsorbed SWNT, and could

such a system undergo rearrangement, do SWNT defects affect adsorption, and how might

59

irregularities in the gel surface change interactions with SWNT, if such irregularities exist?

Figure 4.1 illustrates these possible factors, suggesting possible situations involved in

irreversible adsorption.

In context of the potential situations portrayed in Figure 4.1, one fact illuminates

the matter: while adsorbed to the gel, the proportion of irreversibly adsorbed SWNT

increases over time, i.e., SWNT are less likely to desorb if left on the gel for ~60 minutes

or longer before elution than if eluted within a few minutes of adsorption. Given this, some

change must occur after adsorption to cause irreversible adsorption, which suggests using

kinetics experiments to study the process.

Figure 4.1. Various possible situations involved with SWNT adsorption: A) Rearrangement of SDS-SWNT on the gel surface; B) SWNT adsorbing to a gel irregularity (right) differently than SWNT on a regular gel surface (left); C) SWNT with defect (right) adsorbing differently than a non-defective SWNT (left).

60

As an initial hypothesis, this thesis proposes a mechanism involving the

rearrangement of the SDS micelle surrounding each SWNT, as first shown in Figure 4.1.A.

In this hypothesis, the SDS micelle acts as a steric energy barrier between the SWNT and

gel, initially preventing close contact between the two. Given sufficient energy, the SDS

micelle can rearrange, allowing the SWNT to move closer to the gel, in a lower energy

state. Figure 4.2 shows what a hypothetical energy diagram might look like for such a

mechanism, where an adsorbed SWNT starts in an initial adsorbed state, passes through a

transition state involving SDS rearrangement, and ends in a significantly lower state close

to the gel surface. In this final state, the large activation energy to desorb leaves the SWNT

irreversibly adsorbed under standard conditions.

Reaction 4.1 provides the corresponding chemical reaction for such a process,

where SWNTSol, a SWNT in solution, weakly adsorbs to the gel as SWNTw, followed by

irreversible adsorption as SWNTI.

Sol W ISWNT SWNT SWNT→ → (4.1)

Free

Ene

rgy

SWNT-Sephacryl Distance

DB

C

A

Figure 4.2. Hypothetical energy diagram showing the system energy versus separation distance between SWNT and gel surface, with an initial adsorbed state (A) and barrier to desorption (B), final low energy, irreversibly adsorbed state (C), and intermediate transition state (D).

61

This reaction illustrates two facts: the proposed irreversible adsorption mechanism follows

1st order kinetics, and all SWNT can become irreversibly adsorbed, given enough time.

Equation 4.2 provides the rate equation for 1st order kinetics, while Equations 4.3-4.4 gives

two forms of the integrated rate equation, showing how the concentration of weakly

adsorbed SWNT changes over time.

[ ][ ]W

Wd SWNT

k SWNTdt

− = (4.2)

W t

W 0

[SWNT ]ln kt[SWNT ]

= −

(4.3)

[ ] [ ] ktW Wt 0SWNT SWNT e−= (4.4)

Where [SWNTw] is the concentration of weakly adsorbed SWNT on the gel, k is the rate

constant, t is time, and [SWNTw]t and [SWNTw]0 are the concentrations of weakly adsorbed

SWNT at times t and time zero, respectively. After acquiring experimental [SWNTw] data,

ln[SWNTw] can be plotted versus time to verify whether the reaction follows first order

kinetics, while also determining the rate constant from the slope of such a plot.

In addition to these kinetics predictions, higher SDS concentrations are known to

result in greater numbers of SDS on carbon nanotube surfaces.88 According to the

assumptions of this mechanism of SDS rearrangement, a greater number of SDS on SWNT

would lead towards a greater steric hindrance, a larger activation energy, and consequently

a smaller rate constant. In summary, the proposed mechanism provides three distinct

predictions: the reaction follows 1st order kinetics, all SWNT can become irreversibly

adsorbed if given sufficient time before elution, and higher SDS concentrations used during

adsorption should result in smaller irreversible adsorption rate constants. Several

assumptions are made in this model, specifically: 1) the SWNT length distribution is

62

assumed to be narrow enough that all SWNT of the same chirality adsorb to the gel with

the same affinity; 2) SWNT in solution do not bundle to any considerable amount before

adsorption; 3) SWNT do not overlap or interact with each other when adsorbed on the gel;

4) and the temperature in the lab is assumed to be a constant 20 °C. With these assumptions

and predictions in mind, the next section addresses the relevant experimental details,

followed by the experimental results in the section after that.

4.3 Experimental Design

Given the hypothesis from the previous section, this section describes the

experimental design. The experiments focus primarily on determining the number of total

SWNT initially adsorbed to the gel, the number of SWNT that can be eluted or that are

weakly adsorbed, and the number of SWNT remaining irreversibly adsorbed after elution.

In overview, the kinetics experiments are performed as follows:

1) Acquire purified SWNT solution of known concentration and volume, using a

standard SWNT separation, as described in section 2.4.1.

2) Mix SWNT solution and gel to adsorb SWNT, saving the remaining SWNT

solution of unadsorbed SWNT for analysis.

3) Let SWNT remain adsorbed to gel for a specific time, and then elute.

4) Repeat experiment with identical samples, allowing the SWNT to remain adsorbed

for different times before elution.

Section 4.3.1 describes the procedure for Step 1, while section 4.3.2 describes the

procedure for Steps 2-4, and section 4.3.3 explains the data interpretation, where Steps 1-

4 are referenced throughout. To study the role of SDS in the mechanism, the procedure

63

was repeated with different SDS concentrations, and unless specified otherwise, all kinetics

experiments were done in triplicate.

4.3.1 SWNT Pre-Separation

Using unseparated SWNT would complicate analysis by the presence of many

chiralities and impurities. Consequently, SWNT solutions were separated beforehand via

standard column separations. Standard conditions were used, as outlined in section 2.4.1,

using SWeNT SG65i (6,5)-enriched SWNT, with 3.0 mL of 5.0 wt % for elutions rather

than the usual 4.0 mL. For use in kinetics, the SWNT solutions must be diluted to lower

SDS concentrations for adsorption to occur, and smaller initial volumes lead to smaller

final volumes and greater final concentrations.

Preparatory-separations were done eight times in parallel. The separated samples

were spectrally analyzed to determine the (6,5) purity, and the purest six samples were

mixed together to form one solution of sufficient total SWNT content to saturate the total

volume of gel in the kinetics experiments, the importance of which is discussed in section

4.3.2. The solution was divided into three equal aliquots, and each was diluted to equal

volumes and SWNT concentrations, but to different SDS concentrations. While the purest

(6,5) samples were used, significant proportions of (6,4) SWNT were also included to

compensate for the difficulty of obtaining large quantities of pure (6,5), and to ensure that

gels were saturated. In analysis, only the (6,5) chirality was included, as according to the

assumptions of the hypothesized used here, SWNT-SWNT interactions are non-existent or

negligible. Additionally, different chiralities will most likely adsorb irreversibly at

different rates. The analysis could be repeated with the (6,4) chirality, but was not done so

64

here. As indicated earlier, this process produced sufficient SWNT to only run kinetics

experiments at three different SDS concentrations. Consequently, the process was repeated

to obtain SWNT for the additional three SDS concentrations.

4.3.2 Kinetics Setup

For measuring the kinetics of irreversible SWNT adsorption, the experimental

design emphasizes consistency between samples, especially concerning control over the

time between SWNT adsorption and elution. A standard column separation was

considered, but this presented inconsistent flowthrough, rinsing, and elution times, adding

a significant amount of variation between samples. As such, a mixed separation was used

instead for greater consistency over such variables, as described in section 2.4.2. To ensure

consistent conditions and to account for all adsorption sites on the hydrogel, all gels were

saturated via mixing with an excess number of SWNT. For each SDS concentration to be

investigated, seven identical tubes were prepared with 0.25 mL of Sephacryl equilibrated

to the needed SDS concentration, and for each set of kinetics experiments, three different

SDS concentrations were investigated in parallel. As stated earlier, all kinetics experiments

were done in triplicate, giving 21 samples for each SDS concentration.

For Step 2 of the procedure outlined in section 4.3, 4.0 mL of SWNT solutions of

the appropriate SDS concentration were added to each tube, mixed for 15 minutes, and

centrifuged at 2000 rpm for 30 seconds. The SWNT solution was removed and set aside

for analysis, leaving the gel with adsorbed SWNT behind in the tube. A total of 7.0 mL of

SDS solution were added to each tube to rinse the gel, using SDS of the same concentration

used for equilibration. This was mixed for 5 minutes, centrifuged at 2000 rpm for 30

65

seconds, and the supernatant was removed. For Step 3, the gel was kept in the closed tube

to prevent drying while time passed before elution. After allowing the gel to sit for a

specified time after the end of adsorption, 1.0 mL of 5.0 wt % SDS was added, mixed for

5 minutes, centrifuged at 2000 rpm for 30 seconds, and the supernatant was removed for

analysis. The process was repeated for all centrifugation tubes, as mentioned in Step 4,

varying the time between adsorption and elution from 40 minutes to 3 days.

4.3.3 Data Interpretation

In context of the mechanism outlined in section 4.2, this section emphasizes how

experimental data is related to the SWNT described in the mechanism: specifically, the

total number of adsorbed SWNT, the number of weakly adsorbed SWNT, and the number

of irreversibly adsorbed SWNT. The total number of adsorbed SWNT can be determined

from Equations 4.5.

T 0 FSWNT SWNT SWNT= − (4.5)

Where SWNTT is the total number of SWNT adsorbed to the gel, SWNT0 is the number of

SWNT in the original solution from Step 1, and SWNTF is the number of SWNT in the

solution after adsorption from Step 2. Similarly, the number of weakly adsorbed SWNT

is calculated using Equation 4.6.

W eSWNT SWNT= (4.6)

Where SWNTw is the number of weakly adsorbed SWNT, and SWNTe is the number of

SWNT eluted by 5.0 wt % SDS in Step 3. Lastly, the number of irreversibly adsorbed

SWNT goes as follows in Equation 4.7.

I T eSWNT SWNT SWNT= − (4.7)

66

Where SWNTI is the number of irreversibly adsorbed SWNT. Referencing Equations 4.2-

4.4, the amounts of weakly adsorbed SWNT do not need to be converted to units of

concentration since any volume components cancel, but if wanted, concentrations can be

calculated by Equation 4.8.

[ ] WW

gel

SWNTSWNTV

= (4.8)

Where Vgel is the volume of gel containing the adsorbed SWNT. Given these relationships,

the next section provides experimental results and comparison to predicted trends.

4.4 Comparison of Experimental Results and Predicted Trends

With the experimental designs and data interpretation outlined previously, this

section compares the experimental and predicted trends, using Equations 4.2-4.4 of the

proposed SDS rearrangement mechanism. The experimental relationship between weakly

adsorbed SWNT and time is discussed first in section 4.4.1, and as becomes apparent, the

experimental data does not support the initial hypothesis. As such, section 4.4.2 begins

with a new hypothetical mechanism, followed by a comparison of the predicted and

experimental trends. Section 4.4.3 examines the corresponding rate constants, while

section 4.4.4 addresses the possibility of multiple processes for irreversible adsorption.

Lastly, section 4.4.5 discusses a second, possible interpretation of the irreversible

adsorption data.

67

4.4.1 Initial Hypothesis: Weakly Adsorbed SWNT vs Time

Figure 4.3A shows the concentration of weakly adsorbed (6,5) SWNT on the gel

versus time, compared with predicted data from Equation 4.4, and Figure 4.3B shows the

corresponding ( )W tln [SWNT ] versus time plots with best fit and R2 value for adsorption

done at 2.25 wt % SDS. Obviously, the plots in Figure 4.3 show poor agreement between

predicted and experimental trends, with a R2 value of 0.80 for the best fit in 4.3.B.

Furthermore, the data in 4.3.A suggests that the number of weakly adsorbed SWNT levels

off at a nonzero value, whereas the hypothesis predicted that weakly adsorbed SWNT

would approach zero over time. Table 4.1 lists the R2 values for all six SDS concentrations,

further showing poor agreement to the hypothesized trend, with R2 values falling into the

0.72-0.86 range, and average value of 0.81.

SDS wt % 1.25 1.50 1.75 2.00 2.25 2.50 R2 0.80 0.72 0.80 0.85 0.80 0.86

Table 4.1. The R2 values of the 1st order irreversible adsorption kinetics analysis, with six different SDS concentrations used for adsorption, as determined from plots of ln[SWNT] versus time.

68

While the initial SDS rearrangement hypothesis does not explain the observed

behavior, the data suggests a new aspect to consider: only a limited number of SWNT may

become irreversibly adsorbed, indicating the possibility of a limited number of specific

adsorption sites for irreversible adsorption.

y = -1.5E-04x + 3.6E+01R² = 8.0E-01

35

35.5

36

36.5

0 500 1000 1500 2000 2500 3000 3500 4000 4500

ln[S

WN

T]

Time (min)

Time vs ln[SWNT] for (6,5) SWNT in 2.25 wt% SDSB

0

1E+15

2E+15

3E+15

4E+15

5E+15

6E+15

0 500 1000 1500 2000 2500 3000 3500 4000 4500

[SW

NT]

(#/L

)

Time (min)

Time vs Predicted and Experimental Weakly Adsorbed (6,5) [SWNT] in 2.25 wt% SDS: Initial Hypothesis

Predicted [SWNT] Exp [SWNT]

A

Figure 4.3. Plot of the concentration of weakly adsorbed (6,5) SWNT versus time in 2.25 wt % SDS (A), and the corresponding plot of versus time (B), including best fit and R2 values. Error bars represent standard deviations.

69

4.4.2 Revised Hypothesis: Irreversible Adsorption Sites

In this revised hypothesis, two types of adsorption sites are assumed to exist, called

types A and B, where type A sites lead to weak adsorption with no change over time, while

type B sites correspond to an initial weak adsorption leading to irreversible adsorption over

time. For type B sites, the conversion from weak to irreversible adsorption is still assumed

to follow 1st first order kinetics, as originally described in Equations 4.2-4.4 for the first

hypothesized mechanism. Figure 4.4 describes the overall reaction scheme for this

hypothesis, where SWNT can adsorb to one of two different sites.

Given this new overall process, the conversion from weak to irreversible adsorption

follows 1st order kinetics, described in Reaction 4.9 and Equation 4.10.

B,W B,ISWNT SWNT→ (4.9)

Figure 4.4. Overall reaction scheme for adsorption sites types A (SA) and B (SB), where SWNT- - -SA and SWNT- - -SB represent weak adsorption, and SWNT-SB represents irreversible adsorption, and k is the rate constant of irreversible adsorption.

70

W,BW,B

d SWNTk SWNT

dt − = (4.10)

Where SWNTB,W are SWNT weakly adsorbed to type B sites, and SWNTB,I are SWNT

irreversibly adsorbed to type B sites. Given that type A sites do not undergo irreversible

adsorption, the overall behavior of weakly adsorbed SWNT follows Equations 4.11-4.12.

[ ] [ ] ktW A B,Wt 0

SWNT SWNT SWNT e− = + (4.11)

[ ] [ ]W At

B,W 0

SWNT SWNTln kt

SWNT

− = −

(4.12)

Where [SWNTW]t is the total concentration of weakly adsorbed SWNT at time t, [SWNTA]

is the concentration of SWNT adsorbed to type A sites, and [SWNTB,W]0 is the

concentration of SWNT weakly adsorbed to type B sites at time zero. Using experimental

data in the lefthand side of Equation 4.12 and plotting the result versus time allows one to

measure agreement between the data and the hypothetical trend.

In terms of potential agreement between experimental and predicted data, this

mechanism explains the time dependence of irreversible adsorption, while also explaining

why only a portion of the SWNT can become irreversibly adsorbed over time. Before

comparing experimental and predicted data, the procedure for assigning values for

[SWNTA] and [SWNTB,W]0 must be explained. Considering that eventually the only

weakly adsorbed SWNT will be the SWNT adsorbed to type A sites, as according to

Equations 4.11-4.12 the value of [SWNTA] can be assigned by Equation 4.13.

[ ] [ ]A W tSWNT SWNT=∞

= (4.13)

Where [ ]W tSWNT=∞

is the concentration of elutable SWNT as time approaches infinity.

Since the longest time used was only 3 days and the conversion from weak to irreversible

71

adsorption does not appear to have levelled off completely in Figure 4.3, Equation 4.13 can

be modified to include an adjustment factor, A, to account for that.

[ ] [ ]A W t 3 daysSWNT A SWNT=

= (4.14)

Where [ ]W t 3daysSWNT=

is the number of weakly adsorbed SWNT at 3 days. To optimize

agreement between experiment and predicted trends, A can be adjusted, with most values

falling into the 0.92-0.99 range, and a few values in the 0.7-0.9 range. Exact values used

are listed in Table 4.2. Similarly, values for B,W 0SWNT are defined by Equation 4.15.

[ ] [ ]B,W W A00SWNT SWNT SWNT = − (4.15)

Where [ ]W 0SWNT is optimally the number of weakly adsorbed SWNT at time zero

immediately after adsorption, which can be approximated from [ ]W 40minSWNT , the number

of weakly adsorbed SWNT at 40 minutes, the earliest measurement. Alternatively, one

could move the B,W 0SWNT variable to the right-hand-side of Equation 4.12, allowing a

best-fit algorithm to determine the best value for agreement between experiment and

prediction, though the two methods produce identical results.

Similar to Figure 4.3, Figure 4.5 compares the predicted data from the new

hypothesis to the same experimental data used earlier, focusing on (6,5) SWNT adsorbed

in 2.25 wt % SDS.

72

0

2E+15

4E+15

6E+15

0 500 1000 1500 2000 2500 3000 3500 4000 4500

[SW

NT]

(#/L

)

Time (min)

Time vs Predicted and Experimental Weakly Adsorbed (6,5) [SWNT] in 2.25 wt% SDS: Revised Hypothesis

Predicted [SWNT] Exp [SWNT]

A

y = -8.1E-04x - 1.5E-01R² = 9.4E-01

-5

-4

-3

-2

-1

0

1

0 500 1000 1500 2000 2500 3000 3500 4000 4500Inte

grat

ed 1

st O

rder

Rat

e Eq

uatio

n

Time (min)

Time vs Revised Integrated 1st Order Rate Equation for (6,5) in 2.25 wt% SDSB

Figure 4.5. Comparison of predicted data versus experimental data, using the revised hypothesis: plot of weakly adsorbed (6,5) SWNT versus time in 2.25 wt %

SDS (A), and plot of vs time (B) with best fit and R2

value. Error bars represent standard deviations.

73

Judging by the R2 value of 0.94, the experimental data matches the hypothesized

trends with much better agreement, providing support for the revised hypothesis. Table

4.2 lists the values for R2, A, [ ]ASWNT , and B,W 0SWNT for each of the six SDS

concentrations, corroborating the agreement between hypothesis and experiment, with R2

values of 0.91-0.98, and an average of 0.95. Sections 4.4.3-4.4.4 continue investigation of

other aspects of the mechanism.

4.4.3 Rate Constants and SDS Concentration

According to the original hypothesis, the conversion from weak to irreversible

adsorption involved the rearrangement of SDS, allowing for a stronger interaction between

SWNT and gel, where greater amounts of SDS on SWNT at higher SDS concentrations

would lead to greater activation energies and smaller rate constants. Though the original

hypothesis failed to account for the relationship between weakly adsorbed SWNT versus

time, the concept of SDS rearrangement may still apply to the revised hypothesis. As stated

earlier, kinetics experiments were done at six different SDS concentrations, and Figure 4.6

shows the (6,5) SWNT irreversible adsorption rate constants plotted versus the

SDS wt % 1.25 1.50 1.75 2.00 2.25 2.50 R2 0.92 0.94 0.91 0.98 0.94 0.98 A 0.85 0.79 0.94 0.95 0.98 0.92

[ ]ASWNT (1015 #/L)

4.0 2.5 3.8 2.8 2.4 1.5

B,W 0SWNT (1015 #/L)

3.1 4.0 3.0 2.9 2.8 2.0

Table 4.2. List of all R2, A, [ ]ASWNT , and B,W 0SWNT values for the revised

analysis of the weakly adsorbed SWNT at six different SDS concentrations.

74

corresponding SDS concentrations, obtained from the plots of [ ] [ ]W At

B,W 0

SWNT SWNTln

SWNT

−

versus time.

As seen in Figure 4.6, the trend of rate constant versus SDS concentration does not

follow the predicted trend, but rather goes in reverse, with higher SDS concentrations

leading to greater rate constants, though the large standard deviations for some

measurements makes any detailed analysis questionable. With such information, the

simple model of SDS rearrangement does not hold, and in retrospect, numerous factors

could contribute to irreversible adsorption rate constants. As a simple example, higher

SDS concentrations could lead to a higher ionic strength in solution, effectively shielding

electrostatic interactions. If electrostatic interactions contribute to the activation energy of

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6

Rate

Con

stant

(1/m

in)

SDS Concentration (wt%)

(6,5) Irreversible Adsorption Rate Constants vs SDS Concentration

Figure 4.6. Irreversible adsorption rate constants versus respective SDS

concentration, as obtained using plots versus. Error

bars indicated standard deviation. The dashed line exists as a guide to highlight any trend or lack thereof.

75

irreversible adsorption, such as repulsion between SDS molecules during rearrangement,

shielding would decrease the activation energy and increase the rate constant. To study

this matter, simple salts such as NaCl could be included in solution during adsorption to

change the ionic strength of solution without altering the SDS concentration. Regardless,

further study is needed to understand this aspect of irreversible adsorption.

4.4.4 Multiple Pathways and Overall Mechanism

Returning to the number of weakly and irreversibly adsorbed SWNT at time zero,

one could conclude from Equations 4.11-4.12 and Figure 4.5 that no SWNT are irreversibly

adsorbed immediately after initial adsorption, but comparing the total concentration of

adsorbed (6,5) SWNT to the concentration of weakly adsorbed (6,5) SWNT at times of

~40 minutes (the earliest time measurement) shows a large disagreement between the two

values, as demonstrated in Figure 4.7, where the kinetics data from Figure 4.5.A is

compared to adsorbed SWNT concentration, and corroborated by all other experiments at

other SDS concentrations. For reference, the total adsorbed (6,5) [SWNT] was calculated

from the difference between the original SWNT solution and the flowthrough.

Considering the slow rate of the mechanism established thus far, this disagreement

indicates that a significant number of SWNT adsorb irreversibly before any sizable number

of SWNT could irreversibly adsorb via the mechanism described in section 4.4.2,

suggesting an additional mechanism for irreversible adsorption. To give a preliminary

explanation for this, a third type of adsorption site (type C) may exist, where type C

corresponds to one of two possibilities: initial weak adsorption followed by very fast

irreversible adsorption, similar to type B, or an initial irreversible adsorption with no

76

intermediate weak adsorption, analogous to type A adsorption, but for irreversible rather

than weak adsorption.

Such a mechanism requires further study to validate, such as making kinetics

measurements at shorter times than currently used to measure irreversible adsorption in the

first moments of the overall process. While insufficient data is currently available to

support any specific model, the data in Figure 4.7 supports the concept that an additional

irreversible adsorption mechanism must be present. Additionally, a few hypotheses can be

proposed as to what such a mechanism would look like. As mentioned in the previous

paragraph, such a mechanism could follow one of two reactions: either a one-step process,

or a two-step process, respectively illustrated in Reactions 4.16-17.

Sol C,W C,ISWNT SWNT SWNT→ → (4.16)

Sol C,ISWNT SWNT→ (4.17)

Figure 4.7. Kinetics data from Figure 4.5 compared to the total (6,5) [SWNT] adsorbed to the gel, showing a large disagreement before any significant amount of irreversible SWNT should have occurred.

0

2E+15

4E+15

6E+15

8E+15

1E+16

1.2E+16

1.4E+16

0 500 1000 1500 2000 2500 3000 3500 4000 4500

[SW

NT]

(#/L

)

Time (min)

Kinetics Data Compared to Total (6,5) [SWNT] Adsorbed to Gel

Predicted [SWNT] Exp [SWNT] Total [SWNT] Adsorbed

77

Where Reaction 4.16 is analogous to Reaction 4.1 but with faster kinetics, while Reaction

4.17 leads to irreversible adsorption with no intermediate weak adsorption. To accompany

these reactions, Figure 4.8 shows what the corresponding energy diagrams would be for

these two processes, similar to Figure 4.2 for the initial hypothesis of this chapter.

Further experimentation could establish which, if either, of these mechanisms

describes type C irreversible adsorption. If type C adsorption follows the two-step process

and assuming the kinetics are of a measurable rate, then additional kinetics measurements

at times less than 40 minutes would show a fast but continuous decrease between the total

One-Step Mechanism

Free

Ene

rgy

SWNT-Sephacryl Distance

Irreversible Adsorption

Weak Adsorption

Free

Ene

rgy

SWNT-Sephacryl Distance

Irreversible Adsorption

Figure 4.8. Hypothesized energy diagrams for Reactions 4.16 (two-step) and 4.17 (one-step), showing potential mechanisms that type C sites might follow towards irreversible adsorption, emphasizing the differences between the two processes.

Two-Step Mechanism

78

(6,5) adsorbed and the amount of weakly adsorbed (6,5) at 40 minutes in Figure 4.7. In

contrast, if the one-step mechanism is followed, then kinetics measurements at times less

than 40 minutes would follow the already established type B rate equation given in

Equations 4.10-12, with a discontinuity between the weakly adsorbed (6,5) SWNT at time

zero and the total adsorbed (6,5). Such additional measurements could be made at times

as early as ~22 minutes with no change in experimentation, other than handling a smaller

number of samples simultaneously, but that is a matter of future work. To illustrate what

the overall adsorption process might look like, Figure 4.9 shows the overall reaction

scheme, assuming type C irreversible adsorption follows a one-step process.

Figure 4.9. Overall hypothetical reaction scheme for weak and irreversible adsorption, assuming type C sites (SC) follow a one-step process, where SWNT-SC represents SWNT irreversibly adsorbed to SC.

79

4.4.5 Irreversible Sites versus Irreversible SWNT

In the revised hypothesis discussed so far, the mechanism was assumed to require

the involvement of multiple types of adsorption sites, types A, B, and C. While this

provided good agreement between hypothesis and experiment, it could also be explained

by the presence of multiple types of SWNT, types A, B, and C, analogous to the respective

adsorption sites. Such a mechanism would lead to mathematically equivalent kinetics as

those given in Equations 4.10-4.12, meaning no distinction could be made between the two

hypotheses by such a comparison.

Fortunately, the two can be distinguished another way: if the process depends on

specific irreversible adsorption sites, these sites could be permanently occupied by SWNT

adsorbed to the gel for a sufficient length of time, leaving no such sites for future

irreversible adsorption if the gel is reused. On the other hand, if irreversible adsorption

depends on specific SWNT, reusing the gel with a fresh solution of SWNT would lead to

further irreversible adsorption.

Dedicated experiments were used to study this matter, though they were poorly

performed and yielded no usable information. Despite this, some information to support

irreversible adsorption sites can be gathered from previous experiments. Since the SWNT

solutions used here were first purified via a column separation, and if specific SWNT are

required for irreversible adsorption, then a sizable portion would have been removed by

this first separation, especially any SWNT required for type C adsorption. This would

leave no specific SWNT for irreversible adsorption to occur during the kinetics

experiments. While this is not entirely conclusive and further experiments are needed to

80

distinguish between irreversible adsorption sites and irreversible adsorption SWNT,

preliminary evidence supports the former.

81

CHAPTER V

CONCLUDING THOUGHTS AND FUTURE WORK

5.1 Summary

As Chapter I discussed, SWNT require chirality separation for many applications,

and hydrogel separations offer one method to do so in a cost-effective manner. With such

separations in mind, this thesis focused on two overarching questions: how do SWNT pack

onto the Sephacryl surface during adsorption, and what is the mechanism of irreversible

SWNT adsorption?

Regarding irreversible adsorption, research successfully determined part of the

overall mechanism, with a clear direction for additional investigation. More specifically,

the work indicated that at least three general types of adsorption sites exist on the gel, where

two lead to irreversible adsorption. Of these two, one slowly leads to irreversible

adsorption over time according to 1st order kinetics (B), whereas the other leads to

irreversible adsorption much more quickly through a currently undiscovered mechanism

(C).

While the first research question remains active, research did yield some

information of practical use, as well as suggesting future modelling approaches. The

number of adsorption sites per gel volume was determined at different SDS concentrations,

providing guidelines for later experiments requiring gel saturation, in addition to

demonstrating a nonlinear trend between the number of sites and SDS concentration,

suggesting a more complicated phenomenon than originally assumed.

The following sections discuss the importance and implications of this work, the

shortcomings and unanswered questions, and future work, respectively.

82

5.2 Importance and Implications

Focusing on the matter from a mechanistic viewpoint, the work in this thesis serves

to further understanding of SWNT hydrogel separations, as well as improving the general

understanding of interactions between SWNT and other species. In particular, the number

of adsorption sites per gel volume plays a central role in the adsorption kinetics, where

SWNT compete for the limited number of sites. Additionally, understanding how the

number of sites depends on the SDS concentration would give insight into the types of

interactions between SWNT, SDS, and hydrogels, such as how important are electrostatic

interactions versus dispersion forces? While this work did not answer such questions, it

provides a starting point for further work to do so, providing an upper and lower limit to

the adsorption packing density, while also demonstrating the need to consider SDS micelle

behavior in more depth.

With irreversible adsorption, further knowledge of this process offers both

economic and scientific benefits. From an economic standpoint, significant amounts of

SWNT are lost to irreversible adsorption during separation, reducing the effectiveness and

cost-efficiency of the method. Understanding irreversible adsorption and how to reduce it

would benefit progress towards SWNT applications, promising more cost-effective

solutions. In the context of general knowledge, understanding how the adsorbed SWNT

system evolves could give insight into how other systems involving SWNT might evolve

over time: will intentionally made structures involving SWNT rearrange in a similar

manner, thus hindering some applications, and could such processes be used to produce

dynamic SWNT materials? Better understanding of the mechanism irreversible SWNT

adsorption could contribute to such questions.

83

5.3 Shortcomings and Unanswered Questions

Several shortcomings exist for the work presented here, most notably the

disagreement between modelling and experiment in regard to the content of Chapter III.

Namely, modelling did not predict the nonlinear trend between the two variables, nor did

it correctly predict the degree to which the number of adsorption sites depends on SDS

concentration. Lastly, experiments were only done in duplicate, bringing into question the

validity of the experimental results.

While the work on irreversible adsorption yielded significantly more promising

results, with good agreement between hypothesis and experiment, some shortcomings also

exist here. Most notably, agreement obtained between the predicted and experimental

trends depended on inclusion of an adjustment variable, A, in Equation 4.14, where the

disagreement between the model and experimental data could be significant if such a

variable was not included. Though the matter could be remedied with further experiments,

as discussed in section 5.4, it currently presents a shortcoming in the work. Additionally,

another issue includes the insufficient work to conclusively support that specific adsorption

sites are responsible for irreversible adsorption, rather than specific SWNT.

In regard to unanswered questions, the research did not explain the trend between

irreversible adsorption rate constants and SDS concentration, nor did any results indicate

what might be the nature of the hypothesized irreversible adsorption sites. Likewise,

whether or not irreversible adsorption via type C sites involves a weakly adsorbed

intermediate was not answered either. The next section discusses how some of these

questions might be answered.

84

5.4 Future Work

Given the shortcomings and unanswered questions, there is much room for future

work in this area. Beginning with the matter of the number of adsorption sites and the

dependence on SDS concentration, the problem could be approached with a more

comprehensive model that takes electrostatic interactions into account. In such a model,

SWNT could be modelled with a SDS-dependent surface charge, as modelled elsewhere,69

where adsorbed SWNT repel unadsorbed SWNT, decreasing the energetic favorability of

further SWNT adsorption at higher SDS concentrations, though explanation of the

relationship between SDS and adsorption sites may not be explained by such a model,

where the number of sites increases with increasing SDS concentration. A more

comprehensive model may need to examine the thermodynamics of micelles in more detail.

In terms of irreversible adsorption, additional experiments could be done to clarify

some matters. For example, longer kinetics experiments could be done with more samples,

allowing SWNT to remain adsorbed for times longer than three days to ensure complete

conversion of type B adsorbed SWNT from weakly to irreversibly adsorbed, removing the

need to use an adjustment variable in Equation 4.14. Similarly, the issue of irreversible

sites versus irreversible SWNT could be better clarified by performing the experiment

described in section 4.4.5, where a gel would be saturated, left long enough to ensure

conversion of all possible weakly adsorbed SWNT to irreversibly adsorbed SWNT, and

followed by elution. With this, the gel could be reused with a new SWNT solution to test

whether adsorption sites or SWNT are responsible for irreversible adsorption.

Moving beyond experimental shortcomings, further work could be devoted to

studying how SDS is involved in irreversible adsorption. For example, the relationship

85

between irreversible adsorption rate constants and SDS concentration could be modelled

from an electrostatic perspective that considers the possibility of Coulombic screening by

charged particles. Besides kinetics constants, other aspects of the process could also be

studied, such as the activation energy of irreversible adsorption. By comparing the

activation energy to values such as ΔG of SDS micelle formation around SWNT, such

investigation could provide some insight into whether SDS rearrangement is involved in

irreversible adsorption. Additionally, other surfactants could be studied. Specifically, if

some surfactants are known to adsorb more strongly to the SWNT surface, experiments

could be designed to study whether such surfactants would slow the rate of irreversible

adsorption, further providing insight into the matter.

5.5 Closing Thoughts

The research in this thesis provides a foundation towards a better understanding of

one aspect of SWNT hydrogel separations, namely, irreversible SWNT adsorption, in

addition to the potential for a better understanding of SWNT behavior in general. Many

facets of SWNT behavior in such systems remain unexplored, and improved insight into

such matters will play a great role in future applications and related discoveries.

86

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