study of the mechanism of irreversible …
TRANSCRIPT
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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
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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
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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
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bringing the research field closer to the many potential applications of single-chirality
SWNT.
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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
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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
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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
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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
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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.
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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.
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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.
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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
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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.
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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
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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
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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.
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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.
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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
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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
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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
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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
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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.
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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.
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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.
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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.
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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
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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.
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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.
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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.
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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
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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.
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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
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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.
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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
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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.
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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.
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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.
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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.
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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.
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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.
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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
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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
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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.
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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
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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
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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)
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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
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( ) ( )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.
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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.
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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.
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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.
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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.
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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
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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
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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.
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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.
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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.
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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.
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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.
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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%)
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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.
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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
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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
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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).
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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).
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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
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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
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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
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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
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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)
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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.
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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.
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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.
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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.
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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
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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.
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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.
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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.
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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.
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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
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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
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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
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(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.
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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
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distinguish between irreversible adsorption sites and irreversible adsorption SWNT,
preliminary evidence supports the former.
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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.
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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.
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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.
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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
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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.
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