Single Chirality Single-Walled Carbon Nanotubes:
Isolation and Application
by
Rishabh M Jain
LC-)
B.S.E., B.Sc., University of Pennsylvania (2009)
M.Sc. Optics and Photonics, Imperial College London (2010)
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Submitted to the Department of Materials Science and Engineering
in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
May2015
2o I
C
C Massachusetts Institute of Technology. All rights reserved
Signature of Author..............
Signature redacted ......................
Department of Materials Science and Engineering
May 22,2015
............
C e rtifie d by .................................................................................................................
Michael S. Strano
Department of Chemical Engineering
.- ThPsV Supervisor
Certified by...............................
Signature redacted
Yang Shao-Horn
Departments of MeC
nicalnd %tv$j9science and Engineering
Signature. . redacted
........ ......... .. .............................
.
A ccep te d by .......................................................
Chair, Depart
nald R. Sadoway
Committee o Graduate Students
1
U)
2
Single Chirality Single-Walled Carbon Nanotubes:
Isolation and Application
By
Rishabh M Jain
Submitted to the Department of Materials Science and Engineering on May 22, 2015 in Partial
Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Materials Science and
Engineering
ABSTRACT
Single Walled Carbon Nanotubes are of great interest as a semiconducting material with diameters
around 1nm and length in the 100s of nm to mm range. The large aspect ratio, near-infrared
wavelength bandgap and a high conductivity enable a large number of optical and optoelectronic
applications inaccessible by other materials. However, carbon nanotubes as produced are
heterogeneous in electronic properties that are dependent on their chirality. Small changes in
geometry of the tube dramatically change the bandgap of the tube, and whether it is metallic or
semiconducting.
This thesis establishes the first reproducible method by which to separate a single electronic type of
carbon nanotube, i.e. a single chirality. The mechanism by which this separation occurs is explored
experimentally and via quantitative modelling. The thesis ends with a demonstration of the first
near infrared single chirality carbon nanotube solar cell.
Thesis Supervisor: Michael S. Strano
Title: Carbon P. Dubbs Professor of Chemical Engineering
3
Acknowledgements
The completion of this thesis was an incredible journey that would not have been possible without the
help, support and inspiration of several people. The influence of all of my family, friends and colleagues
has been important, and certainly contributed to my ability to complete this work.
The most instrumental person in the completion of this thesis was my advisor, Professor Michael Strano.
I have been influenced deeply by his vision and passion for creating new, interesting and useful things
that to others seem impossible. His keen insight to experimentally deconstruct a problem has led me to
be the best scientist and innovator I can be. I will always be thankful for the inspiration and
opportunities I have had while in his lab over the five years of my PhD.
I would like to express deep gratitude to my committee members, Professor Silvija Gradecak and
Professor Yang Shao-Horn. They provided me with useful advice and insight at critical stages of my Ph.D.
and helped ensure that I was building a successful thesis. In addition to my committee members, I would
like to thank every faculty member who has taught or mentored me in any way, and the staff at the
materials science academic office. Specifically, I'd like to thank Angleita Mireles who is nothing but
helpful at every step of the way. I would also like to express my thanks to the NSF GRFP and NDSEG
fellowship programs for their financial support throughout the five years of my graduate career.
This thesis would certainly not have been possible without the help, support, experimental and
analytical contributions, laughs and frustrations of my lab mates. I am thankful to the entire Strano
group at MIT. However, I must give specific thanks to Kevin Tvrdy, Rebecca Han, Micha Ben-Naim and,
Steven Shimizu who were collaborators, co-authors and great friends that had a direct impact on my
professional and personal development.
Finally, I would like to express my deepest gratitude to my friends and family who have been and always
will be a constant source of support and inspiration. I must give a special thanks to my family, my
parents, Mahendra and Vanita for making me the best version of me and their constant love and pride
in anything I do. My sister, Riddhi, is an awesome friend and constant source of positive energy. Of
course, my wife, Isha, has been a constant source of support and encouragement in the good times and
bad as I finished this thesis. I only hope I can provide as much love and support as I have received to
each and every one of you!
4
Table of Contents
1.
Overview ...............................................................................................................................................
8
2.
Introduction ........................................................................................................................................
10
2.1
Carbon Nanotubes......................................................................................................................10
2.1.1
Structure .............................................................................................................................
10
2.1.2
Electronic Structure and Optical Properties .....................................................................
12
2.2
Single Chirality Single W alled Carbon Nanotubes...................................................................
2.2.1
Purifying Single Chirality SW NT.......................................................................................
14
2.2.2
Gel Based Separation of SW NT .........................................................................................
16
Outline of Thesis .........................................................................................................................
2.3
3.
4.
13
Gel Based Separation of Carbon Nanotubes: A Kinetic M odel........................................................
18
20
3.1
Introduction ................................................................................................................................
20
3.2
Experim ental M ethods ................................................................................................................
21
3.2.1
Preparation of Aqueous SW NT Suspension ...................................................................
21
3.2.2
Prim ary Pass Single Chirality SW NT Separation ...............................................................
23
3.3
Experim ental Results...................................................................................................................
25
3.4
Kinetically Driven Com petitive Binding M odel .......................................................................
29
3.4.1
Binding M odel Form ulation ............................................................................................
29
3.4.2
M odeling SW NT Solution and Sephacryl Gel ...................................................................
34
3.4.3
M odel Validation.................................................................................................................
36
3.5
Single Chirality SW NT Separation Scale Up..............................................................................
3.6
Conclusion...................................................................................................................................40
38
A Quantitative Theory of Adsorptive Separation for the Electronic Sorting of Single-Walled Carbon
Nanotubes...................................................................................................................................................42
5
4.1
Introduction ................................................................................................................................
42
4.2
Experim ental M ethods................................................................................................................
44
4.2.1
Preparation of Aqueous SW NT Suspension .....................................................................
44
4.2.2
Prim ary Pass Single-Chirality Sem iconducting SW NT Separation ...................................
44
4.2.3
Absorbance Spectroscopy and SW NT Distribution Analysis........................................... 45
4.2.4
Binding Rate Constant Determ ination .............................................................................
4.3
Theoretical Developm ent .................................................................................................
46
4.3.2
Param eter Specification ...................................................................................................
52
Results and Discussion ................................................................................................................
58
4.4.1
Effect of Surfactant Concentration on SWNT Adsorption to Sephacryl .........................
58
4.4.2
Varying Ultrasonication Duration ...................................................................................
66
4.4.3
Varying Ultracentrifugation Duration. ............................................................................
69
4.5
Conclusion...................................................................................................................................71
Com petitive Binding in M ixed Surfactant System s for SW NT Separation .......................................
72
5.1
Introduction ................................................................................................................................
72
5.2
Experim ental M ethods................................................................................................................
73
5.2.1
Preparation of Aqueous SW NT Suspension .....................................................................
73
5.2.2
Single-Chirality Sem iconducting SW NT Separation Process. ..........................................
73
5.2.3
Absorbance Spectroscopy...............................................................................................
74
5.3
Results and Discussion ................................................................................................................
74
5.3.1
Single Surfactant System s ...............................................................................................
74
5.3.2
M ixed Surfactant System s...............................................................................................
76
5.4
6.
46
4.3.1
4.4
5.
M odel Form ulation .....................................................................................................................
45
Conclusion...............................................................................................................................83
Single Chirality SW NT Solar Cell..........................................................................................................
6.1
Introduction ................................................................................................................................
84
84
6
6.2
Experimental M ethods................................................................................................................84
6.2.1
SW NT Solution and Single Chirality Isolation...................................................................
85
6.2.2
Procedure for Film Preparation ......................................................................................
87
6.2.3
Photovoltaic Device Construction ....................................................................................
90
6.2.4
Optical Transfer M atrix Solution Calculation...................................................................
91
6.2.5
Electrical Characterization Techniques...........................................................................
93
6.3
Results and Discussion ................................................................................................................
6.4
Conclusion...................................................................................................................................96
93
7.
Conclusions.........................................................................................................................................97
8.
Future Work ......................................................................................................................................
100
9.
List of Publications ............................................................................................................................
105
10.
References ........................................................................................................................................
107
7
1.
Overview
This thesis describes the isolation and application of single chirality single-walled carbon nanotubes.
The first part of this thesis describes both experimental and theoretical investigations into the
isolation of single chirality carbon nanotubes. The latter part of the thesis shows the first application
of a bulk of these materials in an optoelectronic device, specifically a solar cell.
Carbon nanotubes have recently garnered a great deal of attention due to their remarkable
properties as a semiconducting material with applications in biological detection, electronic
components, and optoelectronic devices. However, as grown carbon nanotubes are a mixture of
metals and semiconductors. In chapter 3 of this thesis I describe a process I developed by which
specific semiconducting species of carbon nanotubes can efficiently be separated from a mixture of
nanotubes. In order to carry out the separation we pass a surfactant suspended solution of the
nanotubes through a dextran based gel and find the binding to the gel to be a kinetic process that is
chirality dependent.
The process described in chapter 3 has at this point been used by several groups in some form.
However, it was unclear why the separation process occurs at a molecular level. Several groups used
qualitative arguments to explain why the separation occurs. In chapter 4, I provide the quantitative
theory that describes why there is a chirality dependent rate constant for the separation process.
Specifically, I find that the surfactant coverage on the nanotubes creates different effective charge
densities around the nanotubes, and therefore a chirality dependent interaction potential between
the nanotube and the gel. I performed both experimental and theoretical investigations to prove
that the surfactant coverage on the tube is the governing aspect of the separation. At this juncture it
is well agreed upon that the surfactant coverage on the tube governs the separation, and this insight
has been used to further the ability to efficiently separate nanotube chiralities.
The strong understanding of the single surfactant system leads to a thorough study of mixed
surfactant system in chapter 5 between sodium dodecyl sulfate and a bile salt surfactant. I study
three specific bile salt surfactants, sodium cholate, sodium deoxyxholate and sodium taurocholate,
chosen specifically because they are commonly used in SWNT studies. I show that there is a
competitive binding between the surfactants on the SWNT surface that is chirality dependent and
has a strong impact on the separation process.
8
In chapter 6 of this thesis I use the one specific chirality, the (6,5) nanotube to develop the first all
nanotube near infrared photovoltaic. I show that in order to create a solar cell, it is essential that the
nanotube layer be of a single chirality, and in a demonstration device achieve 1% EQE at the
nanotube absorption peak in the near infrared part of the spectrum. Further, I show that with the
introduction of just 20% impurity (6,4) nanotubes, that the efficiency reduces 40 fold, to an
insignificant value. This demonstration highlights the opportunities available for creating new
devices and architectures with single chirality carbon nanotubes, and I will highlight some recent
examples of other applications where single chirality nanotubes have significantly enhanced device
properties.
In summary, this thesis clearly outlines new methods and insights for obtaining single chirality
carbon nanotubes and demonstrates the potential of this new class of material in optoelectronic
applications.
9
2.
Introduction
Single Chirality Single Walled Carbon Nanotubes are a relatively new class of materials that were
first accessible in 2006.1 This early process in separating carbon nanotubes of a single chirality led a
tremendous growth of interest in the use of this material for opto-electronic and electronic
applications,2 including transistors,3 light emitting devices 4 and solar cells. 58- The biggest advantage
these materials hold over traditional silicon and other competing nanomaterials is the high electron
mobility 4 and the very small diameter (~1nm) that enables drastic miniaturization of devices.
2.1
Carbon Nanotubes
Carbon nanotubes as a class of material were made popular in 1991 by Sumio lijima's discovery of
multi-walled carbon nanotubes in an arc discharge experiment.9 The paper published in Nature has
been cited over 25,000 times, is amongst the top 50 most cited papers of all time. This one statistic
alone provides evidence of the deep interest in this material. Over the years, thousands of scientists
and engineers have found various interesting application for nanotubes."
1
Even industry has
started using nanotubes for reinforcement of metals, with products from baseball bats and tennis
racquets to cars using nanotubes in the alloy.' 3
2.1.1
Structure
A carbon nanotube is quite simply a sheet of graphene that is rolled up to form a tube. The
nanotube is identified by the way in which the graphene sheet is rolled, and how many concentric
tubes there are within one nanotube structure.
4
A nanotube that has several concentric tubes is
called a multi-walled carbon nanotube. Multi-walled nanotubes were the type of nanotube that was
discovered by S. lijima and has gained the highest industrial relevance." Figure 1 shows a cutthrough rendering of a multi-walled nanotube which is exactly how the structure appears.
10
Figure 1: A cut-through schematic of a multi-walled carbon nanotube showing the concentric tubes of graphene that
create the structure. (image by Eric Wieser via Wikimedia commons)
In this thesis, we are only concerned with single-walled carbon nanotubes (SWNTs), meaning
nanotube structures that have only one tube of rolled up graphene. When studying these materials,
we are heavily concerned with the way in which that graphene sheet is rolled, and we designate that
property as the chirality of the tube. In order to assign the chirality of the nanotube, we choose two
vectors, al and a2 as shown in Figure 2.
T
> (n,o) zigzag
(nm,) armchair
Figure 2: A schematic showing the two vectors that designate the chirality of a nanotube. The vectors designate the point
on the graphene sheet where the carbon atoms are joined when 'rolled' to form a nanotube.
11
The number of steps taken in each direction to reach the point of overlap when rolling the graphene
sheet is commonly notated with the variable 'n' and 'm', this makes up the chirality of the nanotube
as (n,m). As is noted in the figure, there are special designations for certain classes of chiralities. The
zigzag chiralities are those that are rolled along only the al vector, and the armchair chiralities are
rolled along the equidistant vector of both al and a2, i.e. (n,m) with n=m.
2.1.2
Electronic Structure and Optical Properties
Carbon nanotubes have several fascinating properties, but for the purposes of this thesis we are
focused on the optical and electronic properties of SWNTs, both of which are derived from the
electronic structure.'
4
Carbon nanotubes have a unique electronic dependence; the chirality of the
SWNT is what determines the electronic properties. The electronic properties are derived from the
electronic structure of graphene. The chirality then introduces a secondary periodicity on the carbon
atoms over the graphene periodicity. This secondary structure of the tube has a significant impact
on the electronic structure, and creates nanotubes that are either metallic or semiconducting. There
is a simple way to determine whether the tube will be metallic or semiconducting, simply take the
difference of the chiral indices and if it is divisible by 3, it is metallic, otherwise it is semiconducting:
i.e. if (n-m) mod 3 = 0 the SWNT is metallic. We will not go into the derivation of the band structure
in this thesis as it is not central to the understanding of this work. The details for deriving the
electronic structure can be found in R. Saito's book.14
Among the semiconducting tubes, the band gap of the tube depends on the chirality of the
nanotube. In general, the diameter of the tube is inversely proportional to its band gap. The simple
way to interpret this is drawing an analogy to a particle in a box calculation of energies, as the size
reduces, the confinement increases and this creates an increase in the band gap. The bandgap of all
SWNTs is direct as shown in Figure 3A, and as such, carbon nanotubes fluoresce when they are
either electrically or optically pumped. Further, the density of states of a nanotube is highly
discretized due to the 1-dimensionality of the nanotubes, Figure 3B shows a representative density
of states diagram of a SWNT. As we can see in the figure, there are multiple possible transitions,
labelled as Exy where x and y are the conduction and valence band edges as measured from the
Fermi energy level. Due to momentum conservation considerations, Exy transitions are allowed only
when x = y. The discrete nature of the density of states implies that there are very distinct
absorbance peaks for a SWNT. In fact, each SWNT chirality has distinct transition energies. This
12
enables us to study a mixture of nanotubes by scanning an excitation source across wavelengths and
measuring the emission at each excitation wavelength. This produces an excitation emission map as
shown in Figure 3C. Each peak seen in the figure is attributed to a single chirality of SWNT.
A
B
E
k
E I
E12
k
2'
V1,00
PPM"MMM'-'
00
7M_'
400
EY6011191
Figure 3: Figure showing the basic electronic structure and optical properties of SWNTs. (A) is the band diagram of a
semiconducting SWNT showing that the gap is direct. (B) is a representative semiconducting density of states showing the
different transitions available, E12 is a disallowed transition whereas E 22 is allowed. (C) is an excitation emission diagram for
a mixture of nanotubes showing that each tube has distinct energy transitions. Image from Ref 2
2.2
Single Chirality Single Walled Carbon Nanotubes
The previous section set up an overview of the properties of single walled carbon nanotubes in
general. What is clear to infer from that discussion is that it is difficult to use an arbitrary mixture of
nanotubes in optoelectronic applications due to the diversity of electronic structures that they
create with very small differences in the chiral structure. For example a (6,6) nanotube is metallic,
while a (6,5) tube is semiconducting with a bandgap close to 1eV, however, the difference in
diameter is less than 1 Angstrom. It hence becomes critical to be able to produce SWNT of a single
chirality. Unfortunately, current commercial techniques used to produce SWNT can at best produce
a 60% by weight mixture of a single chirality.15 Typical commercial production methods produce
mixtures of SWNTs in a 1:2 ratio of metallic to semiconducting SWNT, as is expected based on the
rolling vector dependence discussed in the previous section.
16
13
While there have been several attempts to directly grow single chirality SWNT, these efforts have
not produced SWNT in either the quantities or purities that would be needed for practical
applications.
Hence, the field has taken the approach of purifying the SWNT after it has been
produced. In the next section we will discuss in detail some of the approaches taken till date.
2.2.1
Purifying Single Chirality SWNT
The first successful attempt at separating SWNT by chirality was shown by Ming Zheng in which he
used a (GT) 20 DNA sequence to wrap and suspend the carbon nanotubes in an aqueous
suspension.
He then used anion exchange chromatography and collected several fractions of the
nanotubes as they eluted from the column. Remarkably, there was a fraction that contained a
majority fraction of the (6,5) SWNT. His group published a follow up study to this work in 2009 using
a similar method, where they discovered DNA sequences that could bind to specific chiralities and
hence were able to separate 12 different semiconducting SWNT with at least 70% purity.19 The
absorbance spectra of these separated SWNT are shown in Figure 4.
HI-Pco
(8.7)
400
60
aan
100
,200
Figure 4 Absorbance spectra of 12 single chirality SWNT separated via DNA-wrapping based ion exchange
chromatography. The top spectrum is the spectrum of the starting material suspended in an aqueous solution showing the
diversity of SWNTs in the starting material."9
14
The method created by Ming Zheng was inspirational to the field. However, it is a difficult
experiment to perform, has low yields and is very expensive. In 2006, an alternative strategy was
invented by Mike Arnold to enable the separation of SWNT via density gradient ultracentrifugation. 1
This process takes advantage of small differences in density of surfactant wrapped carbon
nanotubes dependent on the chirality. This process was significantly more accessible to the rest of
the field than the chromatography method, and there were a large number of follow up studies.
21 The process was refined to the extent that several different chiralities
were separated via a small
modification to the process as shown in Figure
5.20
6,4
C)
Unsorted HiPco
1,000 1,200 1,400
Wavelength (nm)
Figure 5 Separation of single walled carbon nanotubes via a modified density gradient centrifugation procedure. The
absorbance spectra of different fractions of the sample are shown on the right and demonstrate the ability to produce
highly enriched SWNT samples.
The process also enabled the separation of very high purity (6,5) carbon nanotubes, 3 and is the basis
of a line of purified SWNT that can be purchased from Nanointegris.16 This process is certainly the
most popular way to separate nanotubes even today. However, it is clear, even from the image
above, that the process is very low yield, and hence still too expensive for several commercial
applications. The current use for this method is purely scientific.
15
The most recent method that has been developed to separate SWNT by chirality is a two phase
separation method that was also developed by the group of Ming Zheng.2 This method was first
published in 2013 by CY Khiprin et. al. 22 The method is remarkably simple to implement and enables
reasonable levels of purity of 7 different SWNT chiralities. Briefly, they use PEG and Dextran to
create a 2 phase solution that separates surfactant covered SWNT to into the two phases based on
their hydrophobicity, as shown in Figure 6.
PEG
Dextrn+
W4
Dspersant
Layer
Atom phe
Figure 6 Schematic showing the procedure for the 2 phase separation process developed by cY Khiprin et. al. The
22
surfactant coated SWNT separate based on their differences in hydrophobicity.
The process itself is very scalable and cheap to implement. Unfortunately, this process depends on
small differences in hydrophobicity based on surfactant coverage and requires several iterative
steps in order to obtain high purities of a single chirality. 3 This means that the yields are once again
very low. Nevertheless, there is certainly the possibility that this method evolve to improve yields
and enable commercial scale production of single chirality SWNT.
2.2.2
Gel Based Separation of SWNT
While each of the methods described in the previous section show some promise and certainly are
shaping the field, they all suffer from yield issues. In the summer of 2011, the Kataura group in
Japan developed a remarkably simple way to separate SWNT by chirality that was both high yield
and high purity. 24 As of toa
today modifications developed to this method seem to produce the highest
yields and volumes of single chirality SWNT the field has observed to date.2 s 2 7 In fact as will be
described later in this thesis, our group was able to produce several liters of single chirality SWNT via
a modification to this process. 27
16
The process itself uses a dextran based gel, Sephacryl 200, packed into a series of columns through
which SWNT suspended in 2wt% Sodium Dodecyl Sulfate (SDS) is passed. This process is iterated
several times in serial until nothing binds to the gel. As the SWNT pass through the gel, each column
binds certain chiralities of the gel, and these SWNT can be eluted with 5wt% SDS. This process is
shown in Figure 7.
SWCNT/
dspersion
Adsorpion sites
Interaction order
Gel
A
COL I
trongest
Semi-SWCNTs
coi
Col. 2
2
rnL1
[~
~ ~1~~~~Weakest
Wam
Metaille
SWCNTs
CoL 3
_I
4Mi
Figure 7 Schematic showing the gel based process for separating SWNT developed by Kataura and co-workers. The
diagram depicts the selective nature of the process, where the strongest binding SWNT bind in the top column, while
metals do not bind at all. The image from left to right shows the evolution of the gel over time as more SWNT solution is
24
poured into the top column.
This process is the foundation for the work in this thesis. When this procedure was first published,
there were few groups that were able to replicate the results that were shown. In this thesis we
actually take this process several steps further, improving the yield, purity and reproducibility of the
process.
17
2.3
Outline of Thesis
This thesis focuses on the purification of single walled carbon nanotubes by chirality, and developing
the first application of this material in an optoelectronic device. The following questions on single
chirality SWNT are addressed via this thesis:
"
What process can be used to separate SWNT by chirality in a high yield, and high purity?
*
What is the mechanism of this process both at the process and molecular scale?
"
How can we modify this process in order to obtain different levels of purity and yield?
*
What optoelectronic device can be built at the macroscopic scale using single chirality SWNT
that is otherwise impossible to implement?
These questions are addressed in approximately the order in which they are conveyed above. The
thesis starts in chapter 3 by creating a method to separate single walled carbon nanotubes using the
dextran based gel, Sephacryl 200. A highly reproducible method is developed that enables the
separation of 4 different chiralities of SWNT at very high purity levels. We then investigate the
process in detail and learn that it is a first order kinetic process. We are able to extract the rate
constants of 7 chiralities of SWNT by fitting a first order kinetic model to the process. 27
After establishing a process level model for the separation of the SWNT, in chapter 4 we dive deeper
into the reason why we observe different rate constants for different chiralities of SWNT. We
carefully vary several parameters of the separation process and observe that there is a strong SDS
dependence on the rate constant of the binding. What we hypothesize based on this observation
that the phase around the SWNT has a charge that is dependent on both the chirality of the SWNT
as well as the bulk SDS concentration in solution. The reason the SDS displays a charge is that a
fraction of the SDS has the Sodium counter ion dissociate from the molecule when in solution. This
dissociation is directly dependent on the morphology of the SDS on the SWNT, and is well
understood to be the reason why SDS wrapped SWNT are colloidally stable. We develop a full model
that accounts for these effects and find that the charge per unit length on the tube that enables the
separation process agrees with experimental results from zeta potential measurements. We are
thus able to identify the molecular level mechanism responsible for the SWNT separation process.2 s
18
We take the findings of the quantitative model one step further and find that important process
variables for the separation such as sonication time and centrifugation time and speed can be
explained with our model.
25
We also explore the impact that using mixed surfactants has on the
separation, and specifically discuss the competitive binding between different surfactants on the
nanotube surface. We find that the competitive binding is chirality specific for each surfactant
mixture as should be expected given our work with SDS. We study the use of a few common bile salt
surfactants, sodium cholate, sodium deoxycholate and sodium taurocholate. We are able to show
the chirality dependent competitive binding between SDS and sodium cholate, probably the most
important surfactant mixture for SWNT separation used today.20-22, 28
This strong understanding of SWNT separation has enabled us to collect large volumes of single
chirality SWNT, and we use this material to enable the first all-SWNT active layer solar cell in chapter
6. The development of this solar cell proved that it is necessary to use only single chirality SWNT
when making macroscopic optoelectronics. We observe a 40x reduction in performance when we
add only 20% impurity to the SWNT of a second semiconducting species. We also demonstrate in
this work that we are able to harness energy from the near infrared part of the solar spectrum and
paved the way for several follow on studies by other groups in the field.
19
3.
Gel Based Separation of Carbon Nanotubes: A Kinetic Model
Adapted with permission from Tvrdy, K., Jain, R. M., et al. ACS Nano 2013, 7, 1779-1789. Copyright
2013 American Chemical Society.
3.1
Introduction
As discussed in the previous chapter, single-walled carbon nanotubes (SWNTs) have promising
applications that include biological sensing11, 2 9 and opto-electronics. 2 '
30-32
However, because SWNT
demonstrate electronic properties (metallic vs. semiconducting of various bandgap) based on slight
variations in their chiral wrapping vector (n,m),3 3 their inclusion in laboratory-scale devices has
largely been limited to applications where electronic heterogeneity is tolerable. In order to better
understand the chirality dependent properties of SWNT, and further utilize those properties in
practical devices, it is necessary to separate preparative scale quantities of SWNTs according to
specific SWNT chirality.
The separation of SWNT by chirality has been an important research focus since the discovery of
tubular carbon nanomaterials.
Bottom-up approaches toward separation attempt to control
ensemble scale growth through the use of specialized catalytic nanoparticles and SWNT growth
conditions. 3 4 , 3
(6,5) chirality.15
For example, SWeNT's SG65i growth process results in a 40% enrichment of the
On the other hand, top down approaches toward separation discussed in the
previous chapter have seen some success, the include electrophoretic18, 19,3-41 selective chemical
reactivity, 42 44 density gradient ultracentrifugation (DGU),1,
methods.
2
3, 20, 21, 28, 45
and gel-based retention
4'46
Initial work by Kappes and coworkers demonstrated the ability of an amide-functionalized hydrogel
(Sephacryl
S200) to separate metallic and semiconducting SWNT suspended in sodium dodecyl
sulfate (SDS). 47 Further progress was made by Kataura and coworkers as described in chapter 2.2.2,
who used multiple iterations of a single-surfactant process to yield 13 unique semiconducting SWNT
types, ranging in purity from 46-94% 4 Here, we further develop the understanding of hydrogel
based single chirality SWNT separation by modeling the interactions of individual chiralities of
semiconducting SWNT with amide functionalized hydrogels. The mechanism for separation using
either DGU or gel retention methods remains speculative due to the complicated nature of
experimentally determining molecular dynamics at the nanoscale.
For example, models suggest
20
that the chirality dependent buoyant density that allows for chiral selectivity via DGU may be caused
by chiral specific packing of surfactant molecules on the surface of semiconducting SWNT. 48 Zeigler
and co-workers
described the mechanistic interaction of SWNT with agarose gel as a
chromatography governed by the morphology of SDS on the surface of a SWNT. 49 Further, Kataura
and co-workers have described the adsorption of SDS suspended SWNT with either agarose or
Sephacryl as a batch adsorption process, specifically determining energetic changes in the
adsorption of semiconducting vs. metallic SWNT to each separation medium.50
In this chapter, we demonstrate that the separation of single chirality SWNTs is a kinetically driven
forward adsorption process, using the same gel medium utilized by Kataura and co-workers in their
initial work. 24 Through modeling experimental results as such, we estimate chirality dependent rate
constants for the interaction of semiconducting SWNTs with separation gel media. The agreement
between our experimentally-observed and model-predicted separations, and the assignment of
chirality specific rate constants describing the binding of semiconducting SWNT to Sephacryl gel,
provides a basis for the future understanding and modification of the laboratory and industrial scale
separation of semiconducting SWNT using functionalized hydrogels. The understanding developed
here of single chirality SWNT separation has implications for process scalability, which we achieve
here at 15 times larger volume than what has been previously demonstrated experimentally.
3.2
Experimental Methods
3.2.1
Preparation of Aqueous SWNT Suspension
Raw HiPco SWNT (Unidym, Lot: R0513) was first processed using the organic aqueous phase
separation suggested by the manufacturer for the creation of solid SWNT samples. Specifically,
deionized water was added to solid SWNT cake at 20mL/g, vigorously stirred, and transferred to a
separation funnel. A small aliquot of hexane was then added, and the mixture was stirred and
allowed to phase separate. Iterations of hexane addition, stirring, and separation were repeated
until no black SWNT flakes appeared in the aqueous phase, which was yellow in color and contained
non-SWNT materials remaining from the HiPco synthesis process. The aqueous phase was removed
from the funnel via phase separated gravity extraction. The organic phase, which contained the
purified SWNT, was transferred to a storage container and placed in a drying oven at ~120*C until
21
completely dry, typically 24-48h. Finally, the resultant SWNT powder was homogenized via grinding
with a mortar and pestle.
A SWNT suspension at 1mg/mL in sodium dodecyl sulfate (SDS, Sigma) was generated by weighing
out 100mg SWNT into a 250mL beaker and adding 100mL of an aqueous solution of 70mM SDS.
This solution was subjected to mild bath sonication (Branson 2510) for 5min to break apart
macroscopic SWNT pieces. The beaker containing the homogenized SWNT solution was placed into
a temperature controlled bath held at ~4-5 0C, and subjected to tip sonication at 20W for 20 hours
(Branson Digital Sonifier 250, Cole Parmer 04710-40 YA" Tip, tip placed ~10mm from bottom of
beaker).
In order to ensure that the SWNT solution in 2%wt SDS is equivalent for every run of the separation
method, we use Raman spectroscopy to ensure that the nanotubes are of similar sonication state
from run to run. Importantly, we note a very low D/G ratio for a long sonication process, here found
to be around 2%,
Figure 8A. Further, we found that the relative radial breathing mode peak heights changes
continuously over the course of the 20 hours of sonication and is hence a good indicator of the
sonication state for a given experiment.
Figure 8B shows the radial breathing mode section of the spectrum, with the y axis normalized to
the G-peak height, so as to normalize by the total SWNT concentration being measured. The Raman
spectrum is collected immediately after the 20 hour, 20 Watt tip sonication step of the sample, and
immediately prior to the separation procedure (i.e. after centrifugation), and the expected spectrum
is shown in
Figure 8. We find that other than the concentration of SWNT, the peak features and relative
intensities do not change before and after centrifugation. We do note that it is important to perform
each step of the process without lengthy rest periods, likely due to the bundling of the SWNT
playing a role if too much time is allowed to elapse between steps. Further, absorbance data for the
SWNT solutions is also shown in
Figure 8C, however, the large baseline (even after centrifugation) and poor features do not provide
for an easy way to discern differences in the sonication state, as the RBM does, it only allows us to
develop an approximate calibration of concentration for our initial SWNT sample.
22
Immediately following tip sonication the sample is subjected to ultracentrifugation at 187,000 x g for
4 hours (32,000 rpm, Beckman Coulter Optima L100 XP, SW 32 Ti Rotor, Beckman 344058 40mL
Tubes). The top 90% of the supernatant was then removed from each ultracentrifuge tube and used
immediately as the initial sample for the primary pass single chirality semiconducting SWNT
separation procedure described below.
A*
20 COLS SaMpB.
Fonowing
I
1.0
0.07
1
sdanf un
--
.w=
U
20 COU
-
Fonoeng
U*1~V mw*ipgb
C. 20 Cols Sample Folowing Ultracrnvifugpbon
Raae
SpeCSenu
--
0.06
G-peak -
0.8
0.05
OGao: 0,0238
0.6
90.04
OA
0-2
J03
=002
0.0
(02
0
0.01
500
1000
1500
2000
10
Wavenumber (crn')
150
200
250
300
Wavenumber (cm-)
350
400
600
800
M
1000
o (nr)
1200
Figure 8 (A) Raman spectrum of the initial SWNT sample taken immediately prior to the separation of the SWNT solution
showing low D/G ratio. (B) Radial Breathing Mode region of the Raman spectrum. (C) Absorbance measurement of a 100x
diluted SWNT solution in 2% SDS.
3.2.2
Primary Pass Single Chirality SWNT Separation
The separation procedure is realized through modifications of the methodology previously
published by Kataura and coworkers.
24
10mL of the prepared SWNT suspension is passed through a
1.4mL stationary bed of 70mM SDS equilibrated Sephacryl S200 gel, which is held in place by the
porous frit of a Pierce Biosciences 10mL column (Product #29924), Figure 9, Step 1. Flow rate of
SWNT through the gel medium was held at 1 ml/min, controlled by sealing the top of each column
with a needle pierced rubber stopper and using a syringe pump to control column over-pressure. By
using this technique, total per column residence time was held constant, a step that was not taken
in previous descriptions of stacked, cascade style column-to-column flow. 2 4 We believe that
controlling this aspect of the separation aids in the overall repeatability of the procedure as well as
contributes to the purity of the separated single chirality SWNT, as discussed later.
After passing the entirety of the SWNT solution, the Sephacryl gel is then washed with 4mL of 70mM
SDS solution under atmospheric conditions (i.e. flow rate is not controlled), which removes residual
23
SWNT solution from the gel, but retains physically adsorbed materials, Figure 9, Step 2. Following
the rinsing step, the column is eluted with 4mL of neat 175mM SDS solution under atmospheric
conditions, which removes previously adsorbed material from the Sephacryl gel and allows for its
collection as a separated SWNT sample, Figure 9, Step 3.
Repeated iterations of this process were performed, whereby the flow through from Step 1 is then
utilized as the starting material for Step 1 in the proceeding iteration. Material eluted by 175mM
SDS is labeled as "Column 1" for the first procedural iteration, and subsequent iterations are labeled
in numerical order. A diagram for the complete process is shown in Figure 1.
becomes starting material for followina column
"u
step 1
stop 2
stop 3
adsorption
rinse
desorption
gel adsorbs
SSWNT
remain
sephcacryl gel
frit W
unadsorbed
assed
I
residual
. SWNT
rnsed away
8
remain
residual
pasdreleased
released
rWT
WN
collection
container
I flow through from previous column
Figure 9 Illustration of the three step process utilized to perform a single adsorption column of single chirality
semiconducting SWNT separation. Step 1: passing of a SWNT mixture through a Sephacryl gel bed resulting in selective
adsorption of SWNT to gel. Step 2: rinsing of residual, non-adsorbed SWNT from the gel using SWNT free 70mM SDS
solution. Step 3: desorption of bound SWNT from gel through passing of SWNT free 175mM SDS solution through
gel/SWNT matrix. Note that this process is explicitly different from previously published Sephacryl gel based SWNT
separations as we do not form a cascade of columns, but rather pool together material following Step 1 from each column,
and use it as the staring material for the subsequent column.
As SWNTs are passed through a stationary Sephacryl gel bed, those with the largest affinity for the
gel are selectively removed from the bulk solution during early separation iterations (early columns),
while those with relatively less affinity are selectively removed at later iterations. This process has
been utilized to yield few-chirality samples by Kataura and coworkers, whereas multiple separation
stages (running the separated material from a primary stage through a secondary set of columns)
24
IMMM
was necessary to achieve single chirality separation.2 4 A full list of separable species through multistage gel separation, along with their separation order, has been published.24
Experimental Results
3.3
We carried out a typical separation as described in the experimental section such that bulk SWNT
solution was iteratively flowed through repeated columns of fresh Sephacryl until no significant
adsorption of SWNT onto or desorption of SWNT from a Sephacryl bed column was noted. The
resultant per-column absorption spectra of the solution eluted during the 175mM desorption step
over the course of a 20 column separation are illustrated in Figure 10. Note that while slight
variance does exist when experimental conditions are repeated, the separation represented in
Figure 10 represents a typical separation carried out under described conditions, and will be the
basis for the predicted model later developed in this work.
1.25
1.001
0.75
0.5
025
Column Number
1
5
10
15
20
C204
Cot 15
col 10
Col 5
2D0
400
i66 1000 120
wavelength (nm)
;60
1400
Iaf
(7,3)
(6,4)
(8,3)
strongest
affinyCol
(6,5)
(7,5)
(7,6)
(8,6)
weakest
fty
Figure 10 Absorption spectra of semiconducting SWNT desorbed from Sephacryl over the entirety of a 20 column
separation run with 10mL of SWNT solution through 1.4mL of Sephacryl-200 at a 1mL/min adsorption, the conditions are
detailed in the experimental section. A photograph of a 20 column separation is also shown, displaying coloration of the
nanotube solutions from yellow, to purple, to blue, to green. Note that the coloration becomes weak at the end as the
concentration of SWNT reduces at the end of the separation.
Figure 10 illustrates the general trend of increasing diameter with column number, similar to that
observed by Kataura.2 4 It is also interesting to note that by the
2 0 th
column the absolute absorbance
value reduces, indicating the amount of SWNT being absorbed to the column is generally reducing
with increasing columns number.
25
In order to analyze the chirality concentrations of the SWNT present in a given elution of a column
we fit Lorentzians to the Ell peaks in the elutions. We intentionally forego the fitting of the other
parts of the spectrum, including the E 22 peaks, as this is an unnecessary complication given that all
observable species have salient Ell peaks. Further, there are no metallic peaks observed, and hence
fitting in the visible region has no relevance in ensuring the lack of metals either. The background in
the Ell region for the majority of the samples we analyze is linear, and hence a linear subtraction is
taken before fitting the spectra. The actual Ell peak values are manually fed in to match the data
taken. The fits to the various spectra for a typical separation show very high fidelity with respect to
the residuals. However, as the intensity of the peaks reduces and we separate larger diameter
SWNT, the residuals increase slightly due to an increase in baseline in comparison to the peaks.
Representative fits from the separation are shown in Figure 11. However, the exact nature of the
baseline is not the focus of the study, and has been the subject of other's work. Further, we
acknowledge that this method of purity analysis does not account for the exact profile of a pure
SWNT sample, and we expect under-predicts the purity of the samples reported in this study that
are likely close to completely pure.
Column 5
O.S
I.
I
-
10. -
--
0.610
'I
j
(6M)
0.4'I
-
r' waft
(-6
0.2.
SmO
900
10
1100
Vtv~e ngth
1200
I
I
0
02o..Oh
-a
s
I.
I
0.6
I
02
0,0
1200
00
W
O1M00
110O
120D
-
0.60(7
I
anP.W
(7.31
-(A
4
0.
1300
n)
0
I
Column 17
Column 10
01
I
wn
]
I
01
I
-02
Figure 11 Representative absorbance fits and residuals of the fit using Voigt line shapes from the 20 Column separation
that is studied in this article. The residuals and fits show excellent fits for initial columns with high SWNT concentration,
however as the SWNT concentration decreases the residuals increase slightly due to an incomplete background
subtraction.
Within the 20 column separation, we were able to spectroscopically identify the separation of seven
unique semiconducting SWNT species. The best-fit peak summation for eluted samples that contain
both single and multiple SWNT chiralities are shown in Figure 12 A, along with fit residuals.
26
6.4
-
A
Column
1.0
Column 7 1.0
1
08
0.8.
0.6
Wa e
06
7:'
7
(7n6g
--( .6
J
0.0.
0.0'
.
- .
0.24
0.05
su1.28
01100 12001300
Wavelength (nm)
00.2080 400
B
0.30
0.25.
ut
. P
(6,
0.2;
96 %o
0,4&
0.)
900 1000 11001200130
Wavelength (nm)
.
.ui
80.20.
-
.
0.21
.0
. .
Punty- 9f'%. 1.6
(65)
1.2
73
M0.2
-0.2
1?0.15
0.
00.10.
0.005.4LE.
0.00.
1.t rg
Purity._____
h56%
_0.
Puty 64%
0.8
0.8.
0.4,04
0.2.
0.0........................0.0
400
800
1200
400
800
1200
Wavelength (nm)
Wavelength (nm)
Figure 12 (A) Absorption spectra (solid biack line) and best fit lorentizan profiles (dashed lines) of extracted
semiconducting nanotube solutions from both a single chirality column (Column 1) as well as a mixed chirality column
(Column 7).Both of these samples are taken from the 20 column separation shown in Figure 10. (B) Absorption spectra of
specific single columns highlighting the ability of this process to generate chirally pure and highly enriched semiconducting
SWNT samples. Note that purities reported were calculated using the peak fitting algorithm described in this work.
Given the
previously calculated chirality dependent length
density of carbon atoms
in
semiconducting SWNT,3 3 the previously reported per-carbon-atom optical cross section for (6,5)
semiconducting SWNTs 5' of a = 1.7
x 10-17
cm 2 (and assuming this value is constant across all
chiralities), and using the average separated length of semiconducting SWNT obtained from this
procedure8 <g>=300nm, it is possible to assign a chirality dependent absolute number of extracted
SWNT per column. Although it remains purely an estimate of the per column number of separated
SWNT, this parameter is necessary when formulating a SWNT separation model that accounts for a
1:1 binding ratio between semiconducting SWNT and Sephacryl binding sites, as we do later is this
work.
In contrast to other reports, here we demonstrate the generation of chirally pure and highly
enriched SWNT samples utilizing only a single pass of the starting SWNT material through a series of
27
Sephacryl gel columns. Specifically, we report the (6,5) chirality as 96% pure, which is more pure
than previously reported separations using either DGU or gel-separation. Further, we report the
(7,3), (7,5) and (7,6) highly enriched samples as 87%, 56% and 64% pure, respectively, each
significantly more pure than what was realized previously during a first-pass separation. 4
The
absorbance spectrum of each of these single chirality and highly enriched samples is shown in Figure
12B.
To further investigate the effects of SWNT/Sephacryl interaction on the separation quality, we
designed an alternative scheme whereby instead of 1OmL of SWNT solution flowing through a
stationary 1.4mL Sephacryl bed, 1OmL of SWNT solution and 1.4mL of Sephacryl were vigorously
mixed together inside a round bottom flask for 10min, the same amount of time required to
complete a single flowed-through column.
However, during the stirring, care was taken to not
allow the solution to bubble, as this leads to difficulty in recovering all of the material. Following
mixing with SWNT solution, Sephacryl was then physically isolated by pouring the SWNT/Sephacryl
mixture into an empty fritted column and applying an overpressure to pass the SWNT solution
through the column in ~15sec, whereas the Sephacryl and selectively adsorbed SWNT were retained
by the frit. The Sephacryl was then processed in an identical manner as the flow through scheme
following SWNT adsorption (Figure 9, steps 2-3).
Processing the same starting material side by side in both a flowed through and stirred manner
provided insight into the nature of Sephacryl gel based SWNT separation, and direction toward the
construction of a model to describe it. Interestingly, a side by side comparison of the per column
absorbance features of the separation carried out in these two fundamentally unique procedures
yielded nearly identical results. Specifically, separation order, quantity of chirality specific SWNT
separated, and number of columns required to separate the same amount of material were
qualitatively the same through 10 iterative columns of SWNT separation, Figure 13. We have also
plotted chirality per column plots for these experiments, and it can easily be seen that the two
experiments give very similar progressions in the separation of SWNT. In terms of designing a gel
based SWNT separation model, this finding suggests that regardless of the physical nature of the
SWNT/Sephacryl interaction (flowed or stirred) the resultant separation behaves as though the two
are well-mixed. The following section describes in detail the formulation of a SWNT separation
model that predicts the experimental observations made here.
28
s
Flowed through Co
Flowed throuah Columns
Stirred Columns
Stirred Columns
5
e
L15
Ci)
200
400
600
800
1000
1200
200
400
600
Wavelength (nm)
(6,5)
1.80E+014
1.80E+014
1 .50E+014
1000
CCL
1200
(6
5)
1 .50E+014
Z1.20E+014
Z1.20E+014
9.OOE+013
0
800
Wavelength (nm)
9.OOE+013
(7,5)
36
(7,6)
(7,5)
E+013
(7 3)
E64)E
z 3.00E+013
8(34S
0.00E+000
3.00E+013 (6,4)
80.00E+000
0
2
4
6
Column Number
8
10
0
2
4
6
8
10
Column Number
Figure 13 Side by side comparison of the stirred and flowed methods of separation showing the equivalence
processes and hence the validity of the well mixed container assumption in the model.
3.4
Kinetically Driven Competitive Binding Model
3.4.1
Binding Model Formulation
of
the two
Given the observed equivalence between a separation carried out such that 1) SWNT flow through a
stationary bed of Sephacryl gel held by a porous frit, and 2) SWNT and Sephacryl gel were physically
mixed and later separated using a porous frit; we developed a model that describes the gel assisted
separation of SWNT based on the principles of a series of well-mixed semi-batch reactors, such that
each subsequent adsorption "reactor" models a single column of SWNT separation. This model is
grounded within the assumption that within each column there exists a number of generic Sephacryl
binding sites,
OT,
each of which may bind to any chirality of semiconducting SWNT.
Further,
semiconducting SWNT interact with empty Sephacryl binding sites at a given time, 0(t), in a chiral
specific manner, such that SWNT of like chirality have like binding affinities for unoccupied Sephacryl
sites, Figure 14. Here we suggest that a Sephacryl binding site for a semiconducting SWNT is enabled
2 3
by secondary amide groups displayed along the polymer backbone, as proposed by others.s ,s
29
lone e-,pirs
C -NH
%HACRYL BEAD
medium affinity
Figure 14 Cartoon depiction of the kinetically driven competitive binding model we develop to describe the single chirality
separation of semiconducting SWNTs. Carbon nanotubes chiralities with the strongest affinity for secondary amide groups
present on the surface of Sephacryl hydropolymer beads bind first to those sites, allowing for their selective extraction as a
chirally pure aliquot.
The binding of semiconducting SWNT to an unoccupied Sephacryl site is generally described by the
interaction of each SWNT chirality, Nn,m, with an empty Sephacryl binding site, 8, such that following
a binding event, a bound SWNTn,m/Sephacryl pair, Pn,m, is created.
N,, +n~m
0
kf
"'T" 'P
k,
Equation 1
Where kfn,m and krn,m are the forward and reverse rate constants, respectively, of the chirality
dependent interaction between a SWNT and an unoccupied binding site. Here, the subscripts (n,m)
designate the wrapping vectors n and m which are commonly used to assign SWNTs by chirality. 33
The chirality dependent equilibrium constant, Kn,m, can then be written in terms of the forward and
reverse rate constants.
Kn,m
kf
n,m
n,m
Equation 2
30
Within each Sephacryl column, there exists a finite amount of Sephacryl, and thus a finite number of
binding sites. To maintain a balance of available binding sites, it is necessary to hold the total
number of unoccupied sites, 0, along with the sum of total number of bound SWNTn,m/Sephacryl
pairs, Pnm, constant and equivalent to the total number of available binding sites per column,
mW
0(t)+jP
OT-
=1'
n,m
Equation 3
Where here, the time dependence of both 0(t) and Pn,m(t) is explicitly written, as binding events are
dynamic over the course of SWNT/Sephacryl interaction. We can then write the time dependent
change in number of free SWNT, Nn,m, within a well mixed reaction volume V as:
dt
N
k
V
Nn
k(
'
d( N
(0)
""
VK
( P,
Equation 4
The adsorption is assumed to be isochoric. Substituting site balance terms into Equation 4 for 0 and
Pn,m yields:
dtN
(Nn)
k'm(
(t))K OT
A~
k"N(vL
-
(Nni (to) -Nn,.
k"
n)
dt Vn,m
(to)- N,
nK1,m1
Equation 5
In order to verify that the system is driven by kinetics and is not in equilibrium, experimental
attempts were made to demonstrate the reversibility of Equation 1, but were not fruitful.
Specifically, following the Sephacryl rinsing step (Figure 9, step 2), which was carried out at 70mM
SDS concentration, we made attempts to release the adsorbed SWNT from the Sephacryl by passing
copious amounts of 70mM SDS solution through the Sephacryl and monitoring the absorbance of
the passed solution, which showed no traces of desorbed SWNT.
If this reaction remained at
equilibrium at 70mM SDS, the addition of neat surfactant solution would shift the equilibrium to the
reactants side, and result in the desorption of bound SWNT.
We conclude, then, that SWNT
adsorbed to Sephacryl at 70mM SDS concentration do so irreversibly, and thus construct this model
not as an equilibrium reaction, but rather as a series of forward binding rate constants. The removal
of a desorption reaction at 70mM SDS is realized through the elimination of the last term in Eqn. 5.
31
Finally, we describe the second order kinetics in terms of reactant and product concentrations,
where we write the rate constant kf in units of C 0 's', where CO is the concentration of binding sites
on the Sephacryl. We can explicitly write the volume of the Sephacryl and that of the SWNT
separately, where the concentration of binding sites on the Sephacryl is a constant:
d
"(Cnnk
(C
("'
Z(tC
dt
Seph
(t)-Cn,(
n,m
Equation 6
where Cnm is the chirality dependent concentration of SWNT, and
Vseph
is the volume of the
Sephacryl. Note that the only time dependent term of Equation 6 is the chirality dependent
concentration of unbound SWNT, and thus this equation represents the most simplified expression
for describing the dynamic binding of SWNTs to Sephacryl.
Equation 6 consists of a series of
interdependent differential equations, each of which represents the time dependent change of a
specific chirality of SWNT in the presence of a finite number of Sephacryl binding sites. Because of
this, it is necessary to solve this series of nonlinear differential equations numerically.
To calculate the chirality dependent per-column retention of semiconducting SWNT as per the
outlined model in the main body of the text, we utilized MatLab (version 7.14.0.739, R2012a), a
computational interface that includes functionality for solving differential equations. Specifically,
we manually fed a home written script values corresponding to number of SWNT separated as a
function of both chirality and column (determined using fitting algorithm/procedure described in
main text). We then summed over all separated columns to determine the chirality dependent total
amount of SWNT starting material, Nn,m.
NN )
simnulated starting solution
all I
alcolumns
(A'ns"'" )experimentally
extracted
Equation 7
This vector contained the basis for the chirality dependent material that was allowed to interact
with generic Sephacryl binding sites.
In order to solve the interdependent series of differential equations listed in the main body of the
text, we used the ordinary differential equation solver "odel5s" from the Matlab library.
Specifically, we programmed the solver to iteratively solve for the following two equations:
32
k
d(N,1)=
t}t0r
"N
dO7 = -OY (k/,,,,,
)
Equation 8
Equation 9
where Nn,m is the chirality dependent number of unbound SWNT-a vector whose length is one
greater (to include phantom species) than the number of SWNT chiralities under investigation, V is
the reactor volume-a scalar, k is the reaction rate constant between an unoccupied binding site
and an unbound semiconducting SWNT-a vector equivalent in length to Nn,m, and 0 is the number
of unbound sephacryl binding sites-a scalar.
Here, Equation 8 accounts for the time dependent removal of Nn,m from the system, which is
dependent on Nn,m itself, along with the number for free binding sites, both of which are time
dependent. To account for the time dependent removal of binding sites from the reactor, Equation
9 is introduced. The differential equation solver then solves these two equations iteratively in time
with solver-determined time steps to calculate the total change in Nn,m and binding sites over the
course of reaction time t. This total change represents the total chirality dependent number of
bound SWNT per column-a vector equivalent in length to Nn,mTo calculate the total number of chirality dependent SWNT bound to the fresh (unoccupied) number
of Sephacryl binding sites present in column 2, the chirality dependent number of unbound SWNT
that were not bound in column 1 is used as the starting material.
(Nn,n) starting solution,
Column 2
(Nn,m
)simulated starting solution
n
ni/COlumn I
Equation 10
This material is then used to calculate the chirality dependent number of bound SWNT for column 2
using Equation 8 & Equation 9, and again, Equation 10 is used to calculate the starting solution for
column 3. This procedure is iterated upon until the desired number of columns has been simulated.
To achieve a best fit between experimental and simulated datasets, we utilized the solver
"Isqcurvefit" within the Matlab library. Fitting parameters included the chirality dependent rate
constant for each observed semiconducting SWNT along with that of the "phantom species."
33
3.4.2
Modeling SWNT Solution and Sephacryl Gel
To compare simulated data with experimentally conducted separations, as we do here for the
separation shown in Figure 10, initial values for
Nn,m
were calculated by summing the amount of
each chirality experimentally extracted over the entirety of the 20 column separation. The result of
this summation was a mixture of seven semiconducting SWNT species of varying quantity. After 20
passes through fresh gel, the eluted SWNT solution still contained trace quantities of the (7,6)
chirality, suggesting that this chirality was not entirely depleted from the bulk solution; therefore
the total amount collected in elutions is less than the total amount of (7,6) SWNT initially present in
solution.
To compensate for this discrepancy, 1.5 times the separated amount of (7,6) was
substituted for N 7 ,6 in the simulated bulk SWNT solution.
Note that this estimate is only an approximation of the original solution, which also contains
metallic SWNT as well as other semiconducting species.
However it is well documented that
metallic SWNTs do not interact with hydrogels commonly used for SWNT separation,24,
S4
and thus
can be excluded here. Further, while SDS suspensions of HiPco SWNT are known to contain greater
than seven semiconducting chiralities,55 here such were either not separated by this procedure, or
were separated in such small quantities that identification via absorbance spectroscopy was not
straightforward. Regardless, the limitation of this analysis to seven semiconducting species provides
ample experimental data from which the quality of the model can be judged. The total number of
SWNT for each modeled chirality before it interacts with the first column of Sephacryl
(Nn,m (Col=1,
t=0)) is listed in Table 1.
Further, it was observed that upon elution of the columns, especially the initial columns, the gel
retained a dark coloration even after the elution (Figure 15C). Hence, there is material retained on
the column that does not elute with the 175mM SDS solution. In order to investigate the nature of
this material, a column that was eluted with 175mM SDS, was then eluted with Sodium Cholate.
Upon elution with 46mM Sodium Cholate (SC), the column was still colored, however some of the
material was released and the absorbance spectrum (Figure 15B) of this material shows evidence of
it being composed of some amount of SWNT that was not eluted, but largely of carbon impurities
such as fullerenes, and small nanotube fragments and bundles, that typically comprise the
background of SWNT solutions.s6
34
A
B
-0- Sum of Separated SWNT
- Carbon Impurities
--
0.8
x
80.6
Z21 Vol, X I
0
C)
-0.4
175mM SDS Elution
-46mM
SC Elution
I
predominantly
SWNT
predominantly
rbon impuriies
0.
0
:*01
CO
V.
5
10
15
Column Number
- - -
- - - -
-
3
800
1200
Wavelength (nm)
400
C
Figure 15 (A) Analysis of the total number of desorbed SWNT measured per column over the course of 20 columns. The
local maximum at column 6, followed by the further reduction of extracted SWNT per column, suggests the presence of
carbon impurities that occupies Sephacryl binding sites but is not experimentally observed. A qualitative estimation for
the gel occupancy of carbon impurities is denoted by the grey shaded region in columns 1-5. (B) Absorbance spectrum of
the retained carbon impurities, showing the presence of mostly fullerene fragments, broken nanotubes and bundles, and a
small quantity of SWNT that is not eluted with 175 mM SDS (C) Photograph of the first 5 columns after the Swt% SDS
desorption step, showing the presence of carbon impurities that do not get removed from the column, and hence occupies
available binding sites on the Sephacryl gel. Note the decreasing level of coloration as column number increases, indicating
a reduction in the quantity of carbon impurities.
Examination of the experimentally extracted SWNT species over 20 columns is illustrated in Figure
15A, which shows the total amount of SWNT separated per column over the entire separation.
According to a selective adsorption mechanism, the most strongly adsorbing SWNT chirality should
out-compete the remaining species in early columns, and only after the SWNT with the largest
affinity for Sephacryl binding sites are removed can subsequent species be adsorbed.
This
mechanism then asserts that there should be an inverse relationship between total amount of
SWNT collected and column number. However, experimentally we note minimal site occupancy by
semiconducting SWNT at early columns, as illustrated in Figure 15A, due to the carbon impurities
not being eluted at 175mM SDS.
35
The addition of carbon impurities that are not eluted allows for the trend of equal or less adsorbed
material per column with increasing column iterations. In terms of modeling the aforementioned 20
column separation, the amount of carbon impurities present in the starting SWNT mixture
impurities
(Ncarbon
(Col=1, t=O)) was allowed to vary in order to obtain the best possible agreement between
experimental and modeled results.
Choosing a value for 0, which translates to the total number of binding sites per the 1.4mL of
Sephacryl gel utilized per column, is not straightforward. The geometry, density, or average spacing
between adjacent amide groups within this material is not known. In order to simplify this model,
we approximated this complex material as a collection of equivalent binding sites that, besides their
chirality specific affinities for SWNT, are otherwise identical. In terms of the simulation separation,
we iteratively varied 0 to obtain the best possible agreement between experimental and modeled
Not surprisingly, strong agreement was achieved when 0 was chosen such that it
results.
approximately matched the total amount of material eluted per column, effectively simulating the
SWNT overloading conditions that have previously been reported as necessary to effectively
separate SWNT with amide based gel.
3.4.3
Model Validation.
To simulate the SWNT separation achieved by processing the first SWNT/Sephacryl column, the
model uses Equation 6 to calculate the number of chirality specific binding events that occur
between
Nn,m
or
Ncarbon impurities
and 6 within volume V over the course of time t. Specifically, we
chose to model the experimentally utilized conditions of time t=600sec and volume V=0.01L
(approximately equivalent to the SWNT volume, as the Sephacryl volume is small) to allow for a
direct comparison between the model experiment.
SWNT/Sephacryl column, quantities of
Nn,m
and
Following the simulation of the first
Ncarbon impurities
were reduced by the specific amount
of each that was adsorbed to the first column, and then taken as the starting solution for the
simulation of the second column. The second column was then simulated in an identical manner to
the first, starting with 0 free binding sites. Repetitions of this simulation were then used to model a
separation over the experimentally relevant number of iterative columns. The basis for the
experimental comparisons is summarized in a single plot which uses the aforementioned fitting
procedure to extract the chirality dependent number of separated SWNT per column, as illustrated
in Figure 16 for the 20 column separation experiment.
36
Experimentally
(6,5)
Observed
2
'r
z
-1
Simulated
Parbon (6,5)
impunte
t,
,3 (7,5)
,3
( ,)
7,)75)
6
(8,3
1
(8,
5
10
(7,6)
)
15
(8,6)
20
1
5
Column Number
10
15
20
Column Number
Figure 16 Chirality specific column-by-column analysis of gel-based semiconducting SWNT separation. A direct comparison
between the experimentally desorbed material over 20 columns (left), and that predicted by the model outlined here
(right), qualitatively demonstrates the accuracy of a kinetically based competitive binding model to describe gel-based
semiconducting SWNT separation. Specific parameters used to generate the simulation shown in the (right) figure are
listed in Table 1 as well as the text.
Using experimentally extracted values for Nn,m, Ncarbonimpurities, V=0.01L, per-column interaction time
t=600sec, and eT=2.2x10 , we were able to perform a best fit analysis around each chirality specific
SWNT/Sephacryl binding rate constant. The resultant model-predicted column-dependent SWNT
separation is shown in Fig 6B. Best fit values for kn,m and kcarbon impurities along with starting quantities
for each Nnm and Ncarbonimpurities are listed in Table 1. In the following paragraphs, we further discuss
the ability of this model to describe SWNT gel based separation, and its implications on
modifications of SWNT separation procedures.
Carbon
(7,3)
(6,4)
(8,3)
(6,5)
(7,5)
(8,6)
(7,6)
7.9x101
5.9x10
2.8x10
4.OxlO
6.8x10
7.8x10"
3.2x10 1
Impurities
Nnm(Col=1, t=O)
6.3x10"
9.2x10
5.7x10"
kn,m, (Co
1.6x10'
411'
.x0
s1 )
9.4x102 I1.T6x107
.6x1I
Table 1 Experimentally determined values for initial number of chirality specific semiconducting SWNT present in starting
suspension (Nnm), along with best fit values for initial number of carbon impurities, and binding rate constants describing
the chirality specific interaction of SWNT with Sephacryl.
A direct comparison between experimentally extracted values and modeled values of SWNT
adsorbed per column show strong agreement, as exhibited in Figure 16. The quality of this fit
combined with the relative simplicity of this model indicates that the underlying chemical process
that governs this separation can be described as a kinetically driven selective adsorption of
semiconducting SWNT to Sephacryl binding sites.
We do not observe concentration driven
desorption of SWNT from Sephacryl when excess solvent solution is passed through the gel in
the rinsing step to remove unbound SWNT (Figure 9, step 2), hence showing no dependence of the
process on a retention time as would be the case for certain types of chromatography.
37
Reasoning as to why the binding of semiconducting SWNT to Sephacryl at 70mM appears
irreversible, while at 175mM release of SWNT results in the chiral selectivity of the separation
process, remains unclear.
Note that, while Sephacryl itself is a spherically shaped cross-linked
57
hydrogel with amide and dextran functionality, this model simplifies this matrix as a series of
equivalent SWNT binding sites. In reality, the binding of SWNT to Sephacryl most likely involves the
interaction of a series of potentially non-equivalent amide binding sites with a single semiconducting
nanotube, the sum of which constitutes the total change in free energy associated with the binding
event. It is also assumed that the concentration of binding sites, CO, is fixed, and here was found to
be 1.6x10 18 sites/liter, where the volume of the Sephacryl is taken based on approximately 80% by
volume of get and 20% by volume of solvent (here 70mM SDS). Further, it has been shown that the
change in free energy associated with SWNT/Sephacryl binding for a mixture of semiconducting
50
SWNT becomes more negative, and thus is more favorable, at SDS concentrations below 70mM.
49
The findings demonstrated elsewhere and here further demonstrate the complex relationship
between
a
semiconducting
carbon
nanotube
and
an
immobile
hydrogel
with
multiple
functionalities, as mediated by the presence of surfactant molecules. Future studies focused on this
interaction, and specifically its reversibility as a function of SDS concentration (desorption not
modeled here), need to be conducted in order to better understand and more fully control the gel
based SWNT separation process.
3.5
Single Chirality SWNT Separation Scale Up
Here, we have laid the foundations for the classification of Sephacryl gel mediated SWNT separation
as a kinetically driven selective adsorption process. Hence, this system behaves more similarly to an
adsorption chromatography, where the eluent is different from the first solvent. As such, one does
not expect this methodology to suffer from the scaling issues associated with retention time
dependent chromatography based separations. To test this, we first utilized our model to simulate
the expected outcome of a separation carried out under both native (described earlier) and 15 times
scaled up conditions. Specifically, scaled conditions were simulated such that amount of starting
material of semiconducting SWNT, carbon impurities, and Sephacryl binding sites; along with reactor
volume and total interaction time, were all 15 times that of the native conditions, and all other
38
reaction assumptions and modeling procedures remained constant. The predicted separation for a
15 times scale up, which showed nearly identical per-column chirality contents as the native
separation, is shown in Figure 17A.
A5xScaleUp
B
1.25
1.00
C
0.7500
0.500)
0.25
8
Col20
Col 15
Col 10
-
Col 5
400
660 800 1000
Wavelength (nm)
1200
Col 1
1400D
Figure 17 Demonstrations of the advantages of SWNT separation via a scalable process. (A) Absorbance spectra of the
SWNT separated as a 15x scale up. (B and C) Large volumes of single chirality semiconducting (6,5), B, and semiconducting
mixed chirality (7,5), (7,6) and (8,3), C, can be generated using fewer procedural iterations. (D) By intentionally choosing to
not fully scale the 175mM SDS volume used during the desorption step, it is possible to desorb SWNT into smaller liquid
volumes, resulting in the separation of more concentrated solutions-Col 4 shows an optical density of 4.8 with a 1cm
path length. Note that to capture images B and C it was necessary to place the vessels in front of an open window on a
sunny day due to the path length and optical density of the samples.
To take advantage of the predicted scalability of this process, we carried out a 20 column separation
at 15 times scale, and found that indeed, the resultant per-column extracted semiconducting SWNT
was qualitatively similar to that obtained from a native scale separation. The successful scaling of
this separation process allowed for two distinct advantages regarding SWNT separation that are not
possible at native scaling.
First, scaling of the SWNT separation process allows for the collection of large volumes of single
chirality semiconducting SWNT material through fewer procedural iterations. Through scaling, it
was possible for us to accumulate liters of both single chirality and selective chirality semiconducting
samples over a relatively short period of time. Here, we show liter quantities of both single chirality
(6,5) and mixed chirality (7,5), (7,6), and (8,3) in Figure 17B and C, respectively. The ability to quickly
generate large quantities of separated single chirality SWNT has advantages on the laboratory scale,
where construction of macroscopic films or other SWNT solids from pure materials necessarily
requires quantities of SWNT that would be significantly more laborious to produce using separation
39
based on density gradient centrifugation. Also, generation of large quantities of material bolsters
the feasibility of single chirality semiconducting SWNT as an industrial scale material, making further
investigations into the unique properties of single chirality SWNT and how those properties can be
utilized to make next generation electronic and optical devices more attainable.
Second, scaling of the SWNT separation process allows for the generation of high density single
chirality semiconducting SWNT solutions.
In order to concentrate the SWNT desorbed from the
Sephacryl during processing of a scaled separation, we intentionally decreased the volume of
175mM SDS used during that step. By reducing the 175mM SDS volume four times, we found that it
was possible to selectively desorb SWNT into a smaller volume, resulting in a more concentrated
solution, Figure 17D. It is important to note, however, that a small portion of the desorbed SWNT
are not collected by the smaller 175mM SDS volume, most likely due to the incomplete desorption
caused by reduced total interaction time between adsorbed SWNT and the desorption solution.
Despite this small loss, however, a four times reduction in 175mM SDS volume allowed for us to
attain 20mL single chirality (6,5) samples with optical densities of approximately 4.8 using a 1cm
path length-Fig. 17D, Column 4. The straightforward generation of high density single chirality
semiconducting SWNT samples is advantageous when using these materials as biosensors, as sensor
signal scales proportionally with total sensor concentration.
3.6
Conclusion
This study has demonstrated the ability to predictably reproduce and scale a gel-based separation of
SWNT that allows one to obtain pure single chirality samples in very large quantities in a single pass
separation process. We were able to make this advancement by achieving thorough understanding
of the SWNT separation mechanism as a competitive kinetic adsorption. By creating a model, we
could accurately reproduce the dynamic binding and elution of each chirality, allowing us to
estimate chiral specific rate constants.
This simple, descriptive model for SWNT separation
describes the process level physics of this system, and the rate constants were determined based on
the outcome of this separation. However, the fundamental question of what leads to the difference
in rate constants among various chiralities of SWNT and why SDS wrapped SWNT allows for single
24
chirality separation remain speculative. ,
49
Further studies are necessary to understand this
40
complex system, and with such an understanding, we expect the costs associated with single
chirality SWNT separation to reduce dramatically. With recent work by Park et. al. we are already
8
seeing commercial potential for SWNTs as transistors.5
Once large-scale, inexpensive production
of single chirality SWNT is a reality, such advancement stands to substantially influence both the
fields of optoelectronics and biological sensing.
41
4.
A Quantitative Theory of Adsorptive Separation for the Electronic
Sorting of Single-Walled Carbon Nanotubes
Adapted with permission from Join, R. M.,Tvrdy, K., et al. ACS Nano 2014, 8, 3367-3379. Copyright
2014 American Chemical Society.
4.1
Introduction
Developments in the separation of preparative quantities of semiconducting SWNT based on their
chiral wrapping vector (n,m)1
3, 19-21, 33, 40, 46, 47,
have furthered investigations into the effects of
60
58
chiral inhomogeneity on photovoltaic ~ and biosensor performance.
As discussed in detail in
previous chapters, the use of a commercially available amide-functionalized dextran hydropolymer
(Sephacryl S200)47 as a separation medium and the further discovery of single-surfactant (sodium
24
we have
dodecyl sulfate, SDS) interaction conditions which yield single-chirality separation,
quantitatively described gel-based SWNT separation as a second-order forward reaction with
chirality dependent kinetic rate constants.
27
However, the mechanism by which varying SDS
concentration affects the selective adsorption/desorption of SWNT to Sephacryl, which ultimately
enables separation of single-chirality SWNT, was unknown.
The fundamental SWNT-SDS-Sephacryl
interactions24,27,47 need to be better understood in order to further advance single-chirality SWNT
separation. Kataura and co-workers provided qualitative demonstrations that temperature affects
the chiralities that can be separated via a change in the SDS state.
26
They also proposed a qualitative
model of how SDS morphology affects the relative affinity of metal vs. semiconducting carbon
nanotubes when separated using a gel.6 ' Additionally, Hennrich and co-workers offered an
experimental description of the effects of pH and 1-dodecanol on gel-based SWNT separation.
Finally, work by Schapter and colleagues observed experimentally that SDS changes the resultant
separation.
63
3
While these experimental demonstrations reveal the importance of SDS and SDS
concentration, a specific description of the role that the surfactant plays for single chirality
semiconducting carbon nanotube separation is as yet unclear. In this chapter, we develop the first
quantitative theory of this adsorptive separation, which describes the elution order, adsorption
kinetics, and surfactant and ionic strength dependences observed experimentally. By relating
phenotypical variables of SWNT separation under a single model, we demonstrate and provide
novel insight into the molecular scale interactions that control separation.
parameter,
We introduce a new
n,m, defined as the chirality- and surfactant concentration-dependent effective charge
42
density associated with SDS wrapped SWNT, which ultimately determines the efficiency, diameter
range, and purity of single-chirality SWNT separation. This charge density is physically due to the
incomplete cationic association of Na' with the SWNT association dodecylsulfate anion, a
phenomenon demonstrated previously in SDS micelles.64
This work is distinguished from previous contributions that have been informative but largely
qualitative.26
49,
s0,
61-3,
s
We were the first to provide a quantitative analysis of the separation
process, reporting the binding rate constants for semiconducting SWNT with Sephacryl gel at 70mM
SDS concentration,
27
and showing that the elution profiles and selectivity were well described by a
second-order irreversible adsorption mechanism. However, the molecular-scale origin of these
forward rate constants and their dependence on SWNT chirality remained unaddressed.
expand upon our previous forward binding rate model
separation
procedure,
as
validated
66
Here, we
to provide a molecular-scale picture of the
experimentally
through
perturbation
of
surfactant
concentration. Furthermore, some of the experimental steps proposed to achieve SWNT separation,
such as the need to expose bulk-synthesized SWNT materials to harsh ultrasonication for 20 hours,
lack clear explanation. Understanding the role of these procedures and how they ultimately affect
the resultant separation is important to further optimize this process.
Some insight into the relationship between surfactant and SWNT optical and physical properties has
already been achieved.47'67-2 Further, it has been previously demonstrated that surfactant enabled
colloidal suspensions of individualized SWNT retain a per-SWNT charge which can be used to predict
relative material stability.73 The choice of optimal surfactant for SWNT separation has also been the
subject of investigation, and of the many types screened, SDS was shown to be paramount in its
66
ability to separate metallic from semiconducting SWNT.
In this chapter, we first briefly describe the standard experimental procedure used to achieve monosurfactant single-chirality SWNT separation.24,
2
We then outline the molecular-scale model
developed here which empirically describes the surfactant mediated binding of SWNT to Sephacryl
gel. Finally, we report observations made when perturbing the standard experimental procedure
with regards to both the SWNT suspension and the surfactant medium, and relate these
observations to the model developed herein.
Understanding this separation process in a
comprehensive way enables the engineered design of more efficient and specifically tailored SWNT
separation procedures for broader application of SWNTs in semiconductor, biosensor and other
applications.
43
4.2
Experimental Methods
The experimental techniques used in this work closely resemble the methods we developed for the
work discussed in the previous chapter. We elaborate on the specifics again here for clarity.
4.2.1
Preparation of Aqueous SWNT Suspension
In order to prepare the SWNT solutions used in this work, we follow the gel-based separation
procedure previously described,2 7 modified from the method published by Kataura and coworkers.2 4 Raw HiPco SWNT (Unidym, Lot: R1831) was first processed using the organic-aqueous
phase separation suggested by the manufacturer for the creation of solid SWNT material, which we
homogenize and grind with a mortar-and-pestle to create the fine powder used as our starting
SWNT material. The SWNT powder is weighed (100mg) and dispersed in 100ml of aqueous sodium
dodecyl sulfate (SDS, Sigma 98%) solution at the SDS concentration of interest (17-105mM). This
solution is homogenized via bath sonication (Branson 2510) for 5 minutes and placed into a
temperature-controlled bath held at 5 C and sonicated using a Branson Y" tip sonicator (Branson
Digital Sonifier 250, Cole Parmer 04710-40 Y" tip placed ~10mm from bottom of beaker and total
per-tip use regulated to <100h) at 20W for a duration ranging from 2-20 hours, as specified.
Following ultrasonication, the sample contains individually suspended SWNT, SWNT bundles, and
other amorphous carbon material.27'5s The presence of bundles is minimized via ultracentrifugation
at 187,000 x g (32,000 rpm, Beckman Coulter Optima L100 XP, SW 32 Ti Rotor, Beckman 344058
40ml Tubes) for 15min to 4 hours, as specified. The top 90% of the supernatant is used immediately
as the initial sample for the primary pass single-chirality semiconducting SWNT separation
procedure described below.
4.2.2
Primary Pass Single-Chirality Semiconducting SWNT Separation
The procedure used to perform the separation of SWNT very closely follows the separation
developed in our previous work.
However, in this study we vary one of the following aspects of the
initial SWNT solution: sonication time, centrifugation time, or SDS concentration. In each case 10ml
of the solution is passed through 1.4ml of Sephacryl S200 gel (equilibrated to the same SDS
concentration as the SWNT solution) at a rate of
1ml/min, regulated by syringe-pump-controlled
44
overpressure. Unabsorbed solution is collected as the 'flow through,' which is used as the starting
solution for the following iterative column. After washing the Sephacryl with 4ml of SDS solution
equivalent in concentration to the initial SWNT solution, adsorbed nanotubes are eluted and
collected by passing 175mM SDS through the gel. Fresh Sephacryl is loaded into a new column, and
this process is iterated to yield the specified number of 'separation columns' referred to here.
4.2.3
27
Absorbance Spectroscopy and SWNT Distribution Analysis
Absorbance spectroscopy (Shimadzu UV-3101PC) is used to analyze the chirality distribution of the
separated SWNT samples produced by the gel separation method. The lowest-energy Ell
absorbance peaks are fit using Lorentzian lineshapes after performing a manual background
subtraction to minimize any broad absorbance features that do not correlate with SWNT absorption,
Figure 18. The fitted peak heights are used to determine the quantity of each SWNT chirality in the
5
sample using the per-carbon-atom absorbance cross section of the (6,5) chirality, ' as absorbance
cross section values for other SWNT have not been determined experimentally to date.
4.2.4
Binding Rate Constant Determination
The separation and quantification procedures described above are iterated to yield various chirality
distributions for each iterative column under specified separation conditions. We have previously
shown that this separation procedure behaves as a well-mixed batch reactor which can be described
using second-order forward adsorption kinetics. 2 7 Specifically, a fixed number of Sephacryl binding
sites are assigned to each separation column, which interacts with the separable semiconducting
SWNT present in the starting solution in a manner dictated by second-order kinetics. A unique
binding rate constant k, is determined for each SWNT chirality, which is responsible for the overall
separation order and relative yield of semiconducting SWNT per gel column.
27,5
s Here, this model is
used to determine the binding rate constant for each separable chirality under specified run
27
.
conditions in an identical manner to what was done previously for standard separation conditions
45
. ..........
1.4
1.2
Column 1
17mM SOS Adsorption
1.0 - 175mM SDS Desorption
raw
background'
corrected
1.2
-
-
* Column 1
- 70mM SDS Adsorption
175mM SDS Desorption
-
raw
backgroundcorrected
1.0
0.8
0.8
w 0.6
Ca
e0.6
80.4
-00.4
0.2
0.2
800
900
0. 3
1000 1100 1200
Wavelength (nm)
0.0
8 00
1300
-
1000
1100
1200
1300
Wavelength (nm)
1.4
Column 1
17mM SDS Adsorption
175mM SDS Desorption
raw + bkrd. sub.
sum offits
0.6
900
Column I
70mM SDS Adsorption
175mM SDS Desorption.
--raw + bkrd. sub.
-sum
of ft
1.2
4
1.0
0.8
cc 0.4
C
e
0.6
*Co
0.4
0.2-
0.2
A flu-
800
900
1000 1100 1200
Wavelength (nm)
1300
-C
800
U
900
I
1000 1100 1200
Wavelength (nm)
1300
Figure 18 Examples of best-fit analysis used to analyze Ell region (800-1350nm) of absorbance spectra and quantify
relative amounts of each SWNT chirality present in a given elutant. Examples of non-linear background subtraction using
polynomial expression Y = a2+bx+c for column with many (left) and fewer (right) SWNT present are shown in the top two
panels, while the individual contributions of each SWNT species, as modeled by a Lorentzian lineshape, toward the total
spectrum are shown in the bottom two panels for a column with many (left) and fewer (right) SWNT species present.
Determining absolute number of SWNT from fitted Lorentzian lineshape height was determined using previously described
27
methodology.
4.3
Model Formulation
4.3.1
Theoretical Development
To model the interaction involving the SDS mediated adsorption and desorption of SWNT to and
from a Sephacryl binding site, it is important to consider the physical properties of all three
materials involved in these events, depicted geometrically in Figure 19A.
46
B
A
70mM SDS-SWNT Energy Profile
500
40 o
High Affinity
Low Affinity
300
High Affinity
200
E 10 0
21
d
U
-
- 50 S
--
(7,3) (6,4) -
(8,3) (8,4) -
(9,4)
(10,2)
(6,5) -
(7,6) -
(9,5)
-(9,1)
sI-9
-100 S
-(7.5)
0
Cri
-(9,2)
-(8,6)
1
0
-
Low Affinity
-(8,7)
-(12,1)
2
3
Distance (nm)
SS
Figure 19 (A) Graphical representation of SDS wrapped SWNT and the parameters that are important to its interaction
with the gel, displayed here as a sphere. (B) The chirality dependent energy profile as a function of SWNT-Sephacryl
surface separation distance in the presence of 70mM SDS.
The binding of a semiconducting SWNT to a Sephacryl site can be generally described in terms of the
total system energy V(d) as a function of the distance between the Sephacryl and SWNT surfaces, d.
Here, we estimate this energy as the sum of three unique distance dependent contributions: van der
Walls attractive (on
surface)
der wools),
electrostatic repulsive (Veectrostatic), and hard-surface repulsive (Vhard
forces.
V (d) = Vvan der Waals (d)-Velecrostatic (d) -VHard
Sphere
(d)
Equation 11
The attractive energy between SWNT and a Sephacryl binding site is modeled to first-order by the
van der Waals interaction between an anisotropic planar surface and a SWNT of radius rswNT, as
described previously by Rajter et. al.74 and utilized to describe the interactions of type-purified
SWNT with both quartz and polymer substrates,7 5
2(d-do)
van der Waals
(d)
-
F~
(HN(
24dW
HN
(3~ rHr
1
i2
1+
eq(d-do)
6 (d
H
1
Equation 12
47
where
HN
and
HF
are the Hamaker coefficients in the near and far limit of SWNT-plane separation,
respectively, and 0 and do are blending terms accounting for the transition between short and long
range interactions.
Electrostatically, we assign a repulsive force which arises from the common anionic charge shared
by the amide binding site on Sephacryl 200 and the SWNT.73 The radially-dependent interaction
between a plane of uniform charge density
(OSEPH)
and length
and a plane of uniform charge density wrapped
e, both surrounded by a liquid with dielectric
into a cylinder (aswNT) of radius
rswNT
permittivity e and debye length
has been solved by Oshima et. al. :76
VElectrostatic
2V5
(d)
- g 0
)
rKrS
SWNT K0
EcOK K ( KrSWNT
0
QEPH
K
Kd +
SEPH
j--c
)
-2Kd
2eEEK
+
tSWNT
KO (KrT)
c2 K K( KrW)
rsWNT +
rS
2
d
Equation 13
where -0 is the vacuum permittivity and K, is the modified Bessel function of the n'h kind.
The assumption of an interaction with the amide group is not central to the theory developed here,
as the system is equilibrated in SDS, thus it may be the case that ionized SDS molecules on the gel
provide the repulsive force. This would be similar to the commonly implemented SDS-PAGE
technique, where SDS is used in order to stabilize proteins against aggregation through the
introduction of a charged surfactant. This does not, however, explain the preferential selectivity of
SWNT onto Sephacryl, as opposed to other gels. Previously, amide groups have been shown to have
an adsorption affinity for semiconducting SWNT.s 3 To further verify the specific functionality of
Sephacryl allowing for SWNT separation, we added each of the two Sephacryl hydrogel precursor
molecules: Dextran and Methyl Bisacrylamide (MBA), to a 35mM SDS suspension of (6,5) SWNT. We
noted that for an addition of up to 100mM Dextran, there is no significant change in the absorption
spectrum, however upon addition of 100mM MBA, there was a ~10nm redshift in the spectrum
(Figure 20). This was true both in the presence (Figure 20 A and B), and absence (Figure 20 C and D)
of the Dextran, showing a direct interaction of the SWNT with the MBA, and supporting our
supposition that the amide functionality of Sephacryl is responsible for SWNT adsorption.
48
A.
B.
1.2
1.2
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
02
0.0
0.0
MBA induced redshift
--
*
-
---
-
400
600
1000
1200
Wavelength (nm)
C.
,-, -.-,
800
95(
960
.
S
970
980
990
1000
1010
.
ik
1020
Wavelength (nm)
D.
, -
1.2
a
DEX
100mM DEX
100mM DEX +1OnM MBA
100mM DEX + 1mMMBA
2% SDS (6,5) SWNT (baseline)
-
.
mM DEX
-OmM
1.2
MBA induced tedshift
1.0
1.0
0.8
0.8
0.6
0.6
_e
4OA
.0
0.4
-ImM MBA
0.2
0.2
0.0
0.0
S MBA .TM
-----
400
600
800
1000
Wavelength (nm)
1200
950
960
970
10*m MBA
2% SDS (6,S) SWNT (b*Weine)
980
990 1000
Wavelength (nm)
1010
1020
Figure 20 (A and B) Absorbance spectra of separated (6,5) SWNT suspended in 35mM SDS followed by the addition of
various concentrations of Dextran (legend in panel B) and then MBA showing that with the addition of up to 100mM
Dextran there is no optical change, however, at 100mM MBA there is a 10nm redshift (seen in B). (C and D) Absorbance
spectra of separated (6,5) SWNT suspended in 35mM SDS followed by the addition of various concentrations of MBA alone
showing that the 10nm redshift (seen in D) is a result of the interaction of SWNT with the MBA, not influenced by the
Dextran.
Finally, the hard-surface repulsion between a Sephacryl binding site and a semiconducting SWNT
can be described by:77,78
VHar Sphere (d
A
Ad
Equation 14
where A is the hard-surface coefficient.
49
Given these contributions to Equation 11, it is possible to consider the total system energy as a
function of SWNT-Sephacryl separation distance d for a variety of relevant semiconducting SWNT
chiralities. As an example, the (6,5) chirality has a radius
rswNT=
0.379nm; using parameters gSWNT=
le~/nm , aSEPH= 0.1 e/nm2, E= 80, K= 0.87nm (equivalent to 70mM SDS),
2
e = 10nm
(estimated SWNT
length per Sephacryl binding site, further discussion below), HN= 481meV, HF= 538meV, P= 0.15, ro=
0.4nm and A = 2.4 x 10 13meV nm 12, the contribution of VvanderWaals,
Veiectrostatic,
and
VHardSphere
to the
total V(d) is depicted in Figure 21. Further details regarding the choice of specific parameters and
1000 1
800 -
.
1
,
the equations governing such are provided in the following section.
Contributions to Total Energy Profile
600
rVfile
400
V
200
EV
-200
Va
C
w -400
-600
-800
-1000
der Wa's
r5&,N0.379nm
4
YSWNT
1
.Oe-nm
[SDS]=70mM
0
1
2
3
Separation Distance (nm)
Figure 21 Contributions to the total separation distance dependent energy profile (Equation 11) from electrostatic forces
(Equation 12), van der Waals forces (Equation 13), and hard sphere forces (Equation 14). Specific conditions presented are
for a (6,5) SWNT (rswNT = 0.379nm) with surface charge density oswNr= le~/nm 2 surrounded by [SDS] = 70mM. Note that
the local energy maximum occurring at d z 0.5nm corresponds to the balance between electrostatic repulsive and van der
Waals attractive forces, and is the effective energy barrier, dependent on GSWNT, that determines the rate of adsorption of
SWNT onto a sephacryl binding site.
As noted in Figure 19B, the total energy profiles are dominated by hard-surface repulsion at small
distances (d < 2A), by van der Waals attraction at intermediate distances (2A < d < 4A) and by
electrostatic repulsion at long distances (4A, < d < 3nm); thermal energy dominates at distances
greater than ~3nm. Note that hard-surface repulsion balances van der Waals attraction to produce
a Lennard-Jones like potential well, the bottom of which represents the surface-surface separation
distance between a bound SWNT-Sephacryl pair,
db0),d.
Here, we do not account for an SDS layer
between the nanotube and the Sephacryl in the bound state because the morphology of SDS is
known to be dynamic, 6 7 and a rigid-layer-like picture is likely inaccurate. We also note that the exact
energy of the bound state predicted by Equation 11 is an approximation, where a more complete
50
picture of bound state energetics would necessarily include additional solvent effects such as water
excluded by the bound SWNT, as well as the amide-SWNT interaction energy. However, there is no
evidence for a semiconducting SWNT chiral dependence in these energies, and we find here that the
electrostatic repulsion term is the most salient for determining chiral selectivity. Nevertheless, there
is an opportunity to perform a more detailed ab-initio calculation to fully understand this system
that is outside the scope of this work.
To model the rate at which semiconducting SWNT bind to Sephacryl sites, we consider the total
distance dependent interaction profile for a given SWNT chirality (such as presented in Figure 18B)
that governs the energetics of a binding event traversing from d = -, over the energetic barrier
within the electrostatic repulsion-dominated region, and arriving at d =
db,,nd.
Defining such a
binding event as a collision, the rate constant associated with a particle traversing the energy profile
V(d) from d=- to d=dUnd developed by Fuchs78'7 is given by:
41TD
k
_e B"
dd
Equation 15
where
kB
is the Boltzmann constant, T is absolute temperature, and D is the diffusion coefficient,
80
determined using an adapted Einstein-Smoluchowski relation for a cylinder (SWNT) in turbulent
flow around a sphere (Sephacryl bead):"'
In
D=
kBT
L
2rLWW
+0.58
(2+S
0.4 g
+0.06R
Equation 16
Here, rq is the dynamic viscosity of water, L is the length of the SWNT, and Sc and Re are the
dimensionless Schmidt and Reynolds numbers, respectively.
Using the energy profile for the (6,5) chirality depicted in Figure 18B, Equation 15 and Equation 16,
and values of L=300nm, T=298K, r7=1.OxlOPa-sec, Sc=1.1x1Os, and Re=2.5x10s, a reaction rate
1
constant of 1.3 x 109 M sec' is calculated (see the following section for detailed calculation of Sc
and Re). Interestingly, this binding rate constant is within an order of magnitude when compared
51
with the k6,5 published previously, obtained with an irreversible site-limited batch reactor model to
describe Sephacryl-based separation of single-chirality (6,5) SWNT from a multi-chirality solution in
70mM SDS.
USWNT,
27
To reconcile these two models, we consider the charge associated with the SWNT,
which is a consequence of the incomplete association of Na+ counter ions with the SDS
micelle surrounding the SWNT.6
By altering the associated charge from
USWNT=
le/n M2 to
USWNT
0.94e/nm 2 , and keeping all other parameters identical, one obtains an energy profile for the (6,5)
SWNT associated with the experimentally determined second-order binding rate constant. This
profile is integrated over distance using Equation 16 to yield a reaction rate constant of k,(6,s) = 6.4 x
10~ M_
sec , a value that is nearly equivalent to that reported earlier for (6,5) SWNT binding to
Sephacryl in 70mM SDS. 2 7 Similarly, other chiralities charge densities were adjusted to accurately fit
the rate constants at 70mM SDS adsorption, giving the energy profiles depicted in Figure 18B. It is
important to note that throughout this work, we assume an average SWNT length of L=300nm for all
chiralities.
Average length for the (6,5) chirality separated by this same methodology was
8
determined experimentally using AFM, the relatively short length of which is likely due to
prolonged ultrasonication.2 The sorting of SWNT by length remains an active and important area of
research, and while the effects of SWNT length on surfactant mediated gel separation are of
potential importance to this methodology, such are beyond the scope of this work.
This study investigates the effects of SDS concentration on the process of SWNT adsorbing to
Sephacryl binding sites. Specifically, the model developed here is used as a guide to understand the
experimental observations presented in the following sections. While a complete understanding of
the molecular dynamics governing these processes remains speculative, general agreement
between our developed model and experimental results is demonstrated based on work by others
6 773
as well as previous Zeta
regarding the morphology and charge state of SDS wrapped SWNT,
potential measurements of SDS wrapped SWNT..
We use the theory developed above to
quantitatively predict the experimental adsorption kinetics of the separation process. Our findings
both contribute to the basic understanding of the SDS-SWNT structure and inform ways to further
improve and manipulate gel based SWNT separation.
4.3.2
Parameter Specification
Below is a specific description of each parameter used here to model the distance dependent
interaction of semiconducting SWNT with Sephacryl.
52
*
rSWNT
-
units: nm - range:
0.346nm (6,4 chirality) to 0.516 (8,7 chirality) - the radius of the
Single Walled Carbon Nanotube (SWNT) which is adsorbing to the sephacryl surface. These
values are calculated by considering the geometrical effects of wrapping a two dimensional
graphene lattice into a cylinder using the chiral vectors commonly associated with SWNT.
*
GSWNT~ units: e/nm
2
- range:
0.185e /nm
2
(7,3 chirality in 17mM SDS) to 1.393e~/nm
2
(6,5
chirality in 105mM SDS) - the surface charge density on the SWNT that causes an electrostatic
interaction between the SWNT and the sephacryl surface. Surface charge density is used here
because it is the quantity used directly by Oshima et. a/. to quantify the electrostatic interaction
between a single SWNT and a charged surface.
In this work, values of
0
SWNT
are varied and
utilized as the single best-fit parameter used to match experimental and modeled data.
"
k-units: units: e-/nm - range: 0.410e~/nm (7,3 chirality in 17mM SDS) to 3.316e~/nm (6,5
chirality in 105mM SDS) - the linear charge density on the SWNT that causes an electrostatic
interaction between the SWTN and the sephacryl surface. In addition to surface charge density,
we believe it to also be informative to consider the linear charge density (e-/nm)
for each
SWNT, which allows a more apples-to-apples comparison between SWNT of different chirality.
Linear charge density (k) is related to surface charge density by Equation 8 in the main text.
*
GSEPH -
units: e/n M 2
-
value: 0.len/nM 2 - the surface charge density on the sephacryl that causes
an electrostatic interaction between the SWNT and the sephacryl surface.
Surface charge
density is used here because it is the quantity used directly by Oshima et. al. to quantify the
electrostatic interaction between a single SWNT and a charged surface.
*
E- units: unitless - value: 80 - the dielectric permittivity of water, which effects the electrostatic
interaction between charged SWNT and charged sephacryl.
*
K-
813
units: nm- - range: 0.428nm 1 (17mM SDS) to 1.049nm' (105mM SDS) - the inverse Debye
length associated with the charges dissolved in the aqueous medium surrounding and
separating the SWNT and the sephacryl, which effects the electrostatic interaction between
charged SWNT and charged sephacryl. The inverse debye length was calculated using DebyeHuckel Theory:14
53
2q 2 N c
ECO BT1 024
Equation 17
where for the systems under investigation here, there exists only one ionic species present in
solution (Sodium Dodecyl Sulfate, SDS), which for every molecule dissolved in solution
contributes 2 ions, each with charge q 2 =1, and is present in molar concentration c. Also,
NA
is
Avagadro's number, E and Eo are the dielectric permittivity of water and the vacuum permittivity
(5.52x10~5 e2 meV nm'), respectively, kB is the Boltzmann constant (8.617x10- meV K), T is the
absolute temperature (298 K), and
1024 is unit
conversion factor of L/nm3.
f, - units: nm - value: 10nm - the linear distance of SWNIT with which a single sephacryl binding
site interacts. It is important to note that the exact nature of this distance is unknown, and
difficult to quantity experimentally given the imprecise nature of functional group density and
molecular structure associated with cross-linked hydrogels, i.e. sephacryl.
estimate, we choose a value of
As a reasonable
= 10nm, and for the sake of simplicity, presumed this
parameter to be independent of semiconducting SWNT chirality and SDS
concentration.
While quantitative values of
e
surfactant
are not known, and a chirality- and SDS
concentration-independent value of 10nm is likely an oversimplification. Although important, a
quantitative understanding of SWNT/sephacryl interaction length would justify an independent
study, and likely require both experimental and computational efforts, and is beyond the scope
of this investigation.
To further comment on the effect of
on the parameter of merit (k, chirality dependent linear
charge density as a function of SDS concentration), we calculated k while varying interaction
length from inm <
< 100nm, for the four SDS concentrations investigated here, and the
relevant SWNT chiralities for each SDS concentration, respectively, Figure 22. As shown, for a
given SDS concentration, the relative order of linear charge density vs. SWNT chirality
assignment is preserved across the interaction length parameter within
1nm <
< 100nm,
however, within this range, corresponding calculations of linear charge density can change over
approximately an order of magnitude.
While an order of magnitude of fluctuation of the
parameter of merit is significant, the specific choice of e = 10nm for the model presented here
appears to be a good initial approximation for two reasons: first, on the length scale of
54
polymeric/large molecule interactions, the scale of 10nm is intuitively relevant; and second,
because utilizing an interaction length of 10nm in the model presented here results in SWNT
linear charge density values within a factor of two to those predicted by zeta potential
measurements, a comparison which provides independent verification of our model. While
10nm does appear as a good first estimate of the interaction length parameter, the importance
of the SDS concentration dependence on SWNT/sephacryl interactions shown in this work
justifies a more detailed investigation of all parameters relevant to this model, including
SWNT/binding site interaction length C.
3
17mM SDS
+
(8,3)
+
(6,4) ---
(8.4)
--
(6,5)
(7.6)
v
(9.1)
(7,5)
(7,3)
-+
q
2
*
--
+
5
35mM SDS
(9,4)
+
---
(10,2)
.-
--
(9,5)
-
(9,2)
(8,6)
(8,7)
(12,1)
v
(7,3) --(8,3)
(6,4) +(8,4)
(6,5)
+-(7,6)
(9.1)
+ (9,2)
+
(8,6)
(7,5)
(9,4)
(10,2)
4
(9,5)
(8,7)
(12,1)
3
1
21
0L
0
9-
70mM SDS
87-
-0-
-6-
k
t
1O5mM
*
(7,5)
a+ 8,4),
(6.4) -+(6,5)
(8.3)
+
(7,3)
i7,6).
--
10
SDS
(6,4)
9
(6,5)
8
E
60
5
4
0D
ft7
0 2
2-
1
0
0
0
20
40
60
80
100
0
20
40
60
80
100
SWNT Length/Sephacryl Binding Site (nm) SWNT Length/Sephacryl Binding Site (rm)
Figure 22 The effect of SWNT/sephacryl interaction length (P) on the linear SWNT charge density (k, chirality dependent
linear charge density as a function of SDS concentration), within the range 1nm < P < 100nm. The specific choice of P =
10nm for the model presented here appears to be a good initial approximation because it is both intuitively relevant and
calculated estimates of k agree independently with those predicted by zeta potential measurements.
HN - units: meV - value: 481meV
- the non-angle dependent Hamaker coefficient at near
SWNT/sephacryl separation distances.
Value taken from experimental study reported by
.
Rajtner et. aL
55
*
HF
units: meV - value: 538meV- the non-angle dependent Hamaker coefficient at far
-
SWNT/sephacryl separation distances. Value taken from Rajtner et. al.. 85
*
1
- units: unitless - value: 0.15
SWNT/sephacryl
- a parameter that determines the distance over which
interaction transitions from
being well-described
Hamaker term (HN) and the far-distance Hamaker term
(HF).
by the near-distance
Value taken from Rajtner et. al.,
where the specific relationship that describes the distance dependent transition between near
and far Hamaker terms is reported in Equation 90 of that work.s
*
ro- units: nm - value: 0.4nm - a parameter that determines the specific distance at which the
SWNT/sephacryl
interaction
transitions from
being well-described
Hamaker term (HN) and the far-distance Hamaker term
(HF).
by the
near-distance
Value taken from Rajtner et. OL.,
where the specific relationship that describes the distance dependent transition between near
and far Hamaker terms is reported in Equation 90 of that work.
*
A - units: meV nm 12 - value: 2.405 x 108 meV nm 1 2
5
- the hard sphere coefficient which
describes the distance dependent energy of bringing two atomic radii within close proximity.
Value obtained from a previous computational study involving the interaction of two carbon
nanotubes of identical diameter. 6
Details of the calculation of Sc and Re used in Equation 16 in the model.
The Schmidt number (S) is calculated using the standard formula8'-
s
7
SpDAB
Equation 18
where rl is the dynamic viscosity of the surrounding fluid (water, rl = 1.002 x 10- Pa sec), p is the
density of the surrounding fluid (water, p = 1 x 1015 kg nm
2
m-), and
DAB
is the molecular diffusion
coefficient, which for SWNT in water, has been previously described using an adapted Einstein'
Smoluchowski relation for a cylinder:8
DAB =kBT
f
Equation 19
56
and
3,L7
_
f =
L
in
+0.32
_2rMNT _
Equation 20
Combining Equation 18 through Equation 20 yields the simplified term for the Schmidt coefficient
used here:
3;1
-
Sc =
pkBT
In
3L
L .
]
.32
Equation 21
where L is the length of the SWNT (L = 300nm), kg is Boltzmann's constant (kB = 1.38 x
104
Pa nm 3 K-
1), T is absolute temperature (T = 298 K), and rswNT is the radius of the SWNT cylinder (ranging from
0.346nm for 6,4 chirality to 0.516 for 8,7 chirality). Note that the Schmidt number is a unitless
coefficient.
To determine the Reynolds number (Re) associated with the interaction of SWNT with Sephacryl
beads, we approximate our flowed column system as a stirred vessel, which we previously
demonstrated to be a good approximation .2 The Reynolds number for a stirred vessel is calculated
using the standard formula:
PN2
R
-
pND
dle
)7
Equation 22
where
r
is the dynamic viscosity of the surrounding fluid (water, rq = 1.002 x
the density of the surrounding fluid (water, p = 1 x
1015 kg
10-
kg m 1 sec 1 ), p is
nm 2 m-1), and N and D are the rotational
frequency and diameter of the paddle used to stir the system, respectively (N = 25 sec 1, D = 10 cm =
108 nm). Note that the Reynolds number is a dimensionless coefficient.
57
4.4
Results and Discussion
The model formulated above provides a basis for the development of a molecular level mechanism
describing gel-based SWNT separation, as guided by the experimental observations presented in the
remainder of this work. Specifically, we quantitatively outline the effects of perturbing SWNT
solution starting material (by varying duration of both ultrasonication and ultracentrifugation) and
SDS surfactant concentration on the resulting single-chirality semiconducting SWNT separation.
Empirical results of each perturbation are compared with model predictions, providing mechanistic
insights into the separation process.
4.4.1
Effect of Surfactant Concentration on SWNT Adsorption to Sephacryl
The effect of SDS concentration on surfactant morphology around SWNT has been the subject of
various studies. For example, the morphology of the SDS layer on a semiconducting SWNT is known
to be affected strongly by both SDS concentration and solution ionic strength.67' 69 Further, it has
been shown that the morphology of SDS on metallic SWNT is relatively static vs. SDS concentration,
and is expected to have a saturated (maximum limit of SDS associated with SWNT surface) structure,
even at low concentrations.
67
Even more significant is the prediction that different semiconducting
SWNT chiralities have different concentrations at which the surfactant structure saturates.
Further, the
SDS
concentration dependent surfactant
morphology, which
67
is unique for
semiconducting versus metallic SWNT, and for different chiralities within the semiconducting SWNT
family, is believed to be the underlying phenomenon responsible for SWNT separation using density
gradient ultracentrifugation, where the buoyant density of SWNT is highly dependent on surfactant
packing.' 48 '69
Similarly, we find here that the surfactant concentrations, and presumably the surfactant structure,
play a central role in the selectivity of a gel to bind various chiralities of SWNT. To demonstrate this
effect, we prepared SWNT suspensions in the presence of 17, 35, 70 and 105mM SDS, each of which
was ultrasonicated for 20 hours at 20W and ultracentrifuged at 187kxg for 4 hours. Each sample
was then used as the starting material for an 8 column gel-based separation. In each case, the
Sephacryl gel and subsequent rinse steps were equilibrated to the same SDS concentration as the
SWNT solution. For each column of each SDS concentration, 175mM SDS was used to elute the
58
bound SWNT from the gel. The absorbance spectra of eluted samples from this process are shown
in Figure 23A, while quantitative analyses of these spectra presented using background subtracted
Lorentzian lineshape fitting is shown in Figure 23B&C.
A
SDS Dependent Separation Order
17mM SDS
3.0
35mM SDS
70mM SDS
105mM SDS
2.5
2.0
0
Col 1
_o12
1.5
Col 4
1.0
0
0.5
Col 6
0.0
,o17
:;ol8
400
800
1200
400
800
1200
400
B
800
3.5
800
1200
Wavelength (nm)
Chirality Dependent Binding
2.0
Adsorption [SDS)
--- 17 mM
+ 35 mM
- 70 mM
105 mM
3.0
2.5
z
400
C
SDS Dependent Total Binding
1-
1200
Wavelength (nm)
Wavelength (nm)
Wavelength (nm)
Adsorption [SDS]
17 mM
35 mM
70 mMM
=10 5 mM
1.5
2.0
1.0
1.5
t:
1.0
0.5
0.5
C
0
1
2
V. . y. .
3
4
..
5
6
Column Number
7
8
9
VI
I
kI
I
"
-
- .
.
0.0
() 'I
I ell W.* qaintNChi
Nk I-
Chirality
Figure 23 (A) Offset absorbance spectra of the eluted SWNT from various starting SDS concentrations, showing that as the
SDS concentration is increased the distribution and number of SWNT that bind are reduced. (B) Total SWNT per column for
each SDS concentration showing generally that at lower SDS concentrations there is a lower SWNT adsorption. (C) Bar
graph showing the total number of separated SWNT per chirality for each SDS concentration. Note that the number of
SWNT separated is highly dependent on SDS concentration, as predicted.
In this analysis, we note that when separated from solutions of lower SDS concentration, the
number of SWNT (Figure 23B), distribution of chiralities that are adsorbed within each column, and
the total number of separable chiralities, all increase (Figure 23C). For example, in the 17 and 35mM
SDS separations, we observe the additional presence of larger diameter SWNT, such as the (8,7) and
59
(12,1) chiralities. However, these species are not separated from solutions of higher SDS
concentration-at 105mM SDS only the (6,4) and (6,5) chiralities are separated. Hence, there is a
large discrepancy in what SWNT chiralities are separable based on the SDS concentration of the
SWNT suspension. This finding implies the presence of a chirality dependent strength of SWNTSephacryl affinity, to the extent that there exists a maximum SDS concentration for the separability
of each SWNT chirality on the timescale of this experiment.
Experiment vs. Model: 17mM SDS Adsorption, 175mM SDS Desorption
- (6,4)
7,3)
5x1OS
*-(6,)
3x10"
-2x10"
1x1io
I--
(W,")
(7,S)
-/
83
U
310"
3
5x1l-
/
-(84
.
.-.2X10
-(,'
-
-92
0
2X1O'3
/---(9,4)
-
5X"-(8,6)
x10"
W2xO"
-------- *
5X10*4
'1
)
.
X10"
1
2
34
78
Columin Number
1
2
3
4
0
k
6
7
Coufim Nuber
8
1
2
j.-(21)l
4 5 678
Couwmn Numiber
Figure 24 Panels showcasing the fit of experimentally determined separation over eight columns (solid squares) with the
irreversible forward binding kinetic separation model (lines) for each chirality. Lines obtained using model outlined
previously.2 All SWNT were desorbed from sephacryl column using 175mM SDS, however, four different SDS
concentrations were utilized to adsorb SWNT to the gel: 17mM, 35mM, 70mM, and 105mM. For clarity, only the 17mM
case is shown here.
In order to analyze the differences in adsorption at different SDS concentrations we use the theory
developed in this work to propose a molecular level picture of the system in each case. As described
above, this analysis begins by fitting the absorption spectra of a multi column separation to quantify
the presence of each chirality within each column of separation, as described previously27 and
shown for this work in Figure 24. Such quantities are then subject to a second-order forward
reaction binding model
27
to yield binding rate constants, kn,,m(SDS), between a Sephacryl gel binding
site and each experimentally extracted chirality, which we explicitly write here as being SDS
concentration dependent. The chirality and SDS concentration dependent binding rate constants for
60
the four SDS concentrations under investigation are listed in Table 1, where we note that rate
constants calculated at 70mM SDS are nearly identical to our previous study conducted under these
conditions where surfactant concentration was not explored.27
knm
(7,3)
knm
(M' sec ) I
2.8 x 10-6 -
70mM SDS
35mM SDS
18mM SDS
,nm)
0.41
10
0.41
(e/nm)
0.86
(Me' sec')
j_1.8 x 10-
knm
(o' sec'
1.7 x 10
105mM SDS
knm
(enm) (M 0 ' sec) k (e)/nm)
1.47
---- 6-, ----9--------
(6,4)
(6,5)
(9,1)
2.7 x 106
1.1 X 101.4 x 10 6
4.5 x 101.1 x 106
(8,4) L3.8 x10-7
(75)
(8,3)
(7,6)
(9,2)
(8,6)
(9,4)
1.9 x 10
3.7 x 10-7
1.1x_10 7
2.7 x 10-7
(10211.2_x_10_
0.510.48
0.60
0.51
0.620.68
0.62
0.73
0.65
__0.73
2.9 x 10-
1.74
1.6 x 10
2.85
6.4 x 109
2.23
2.4 x 10-
3.32
1.19
1.09
1.5 x 10-11
2.82
2.35
11.6 x 1011
x 10
1.18
1.23
x 10- 7
1.22
x10 7
x 10- 7
1.27
1.24
6.7 x 101.8 x 10 7
1.5 x 10
1.7
1.2
1.2
1.0
1.2
9.
x 107
1.7 x_1-7
.6
9.8 x 10:-
(8,7)
1.8 x 10-_
4.9 x 10-8
0.69
9.6 x 10-8
3.2 x 10-9
0.81
1.16
J
0-
(9,5)
(12,1)
0.79
1.00
2.7 x 10-
2
x1-
2.83
2.95
6.6 x 10
1
1.26
-
1.27
--
-
,---
1.29
1.63
Table 2 List of all binding rate constants, knm, determined here using the model outlined in the previous chapter along
with per unit-length charge (e/nm) associated with all SWNT chiralities identified here, using the model outlined in the
Model section above and Equation 23, under four different sDS surfactant concentrations. Note that values for knm and
(e/nm) not listed here at 70mM and 105mM are absent because corresponding SWNT chiralities were not separated at
the timescale under investigation here.
As an example, we show the best fits of this analysis (lines) in direct comparison with experimental
elution quantities (solid squares) for the separation performed in 17mM SDS, Figure 25A; those for
the other three surfactant concentrations were similarly fit. From the calculated chirality and SDS
concentration dependent adsorption rate constants, we apply the model developed earlier in this
work, whereby the SWNT surface charge density is the primary variable governing the height of the
barrier that the system must cross to undergo a binding event. The energy barrier dictates the rate
at which each SWNT chirality adsorbs to the gel, and therefore, the chirality composition of each
column. Because this barrier height is physically correlated with the electrostatic repulsion between
the like-charged amide binding site and surfactant-surrounded SWNT, a relatively larger SWNT
charge density corresponds to a relatively higher activation barrier for the binding event.
61
B
A
Elution Order at 17mM SDS
(7,3)
Parity Plot
(6,5)
3
A
(7,5)
3
*0
0
z
4A
(9 4)
(8.6)
3
= 17mM
0 =35mM
A = 70mM
~
S=
C 1012
(7,3)
(8,4)
(8,6)
(9 5)
OAAiZsI'
3
A
A
12345678
12345678
Column Number
z
C
A
*
A
10101
10
12345678
A
A
1
(6 4) (6,3)
(7,6) (9,2)
(9,4) (10,2)
(8,7) (12.1)
13
10
102
14
Number of Nanotubes Eluted (Experiment)
D
Theoretical Energy Profile at 17mM SDS
105M
AA)
(8,7)
0
SDS Dependent Charge Density
4.0
200
3.5
Upper charge limit for detectable adsorption
E3.0
1001-
2.5
E,
0
Ca)
K(6,4)
Il
W.
(7,3) -(8,3)
(8,4)
(6.5) -(7,6)
-(9,1)--(9,2)
(7.5) (8.6)
-500
-1000
-1500
0
1
2.0
~1.5
2
-(9,4)
1
(10,2)
(9,5)
(8,7)
(12,1)
0 1.0
-e(7,3) -+-(8,3)
(8,4)
-.- (6,5)-(7,6)
(9,1) -.- (9,2)
- -(7,5) - -(8,6)
M 0.5
S-a- (6,4) -.--
0 0.0
3
Distance (nm)
20
40
60
- -(9,4)
-(10,2)l
-+-(9,5)
-+--(8,7)
+-(12,1)
80
-
0,
[SDS]
5
(10.2)
0
z
0
1
1 0
0
E
13
< 10
(9.2)
(7,6)
3
C,,
A
100
#
1014
0
100
[SDSJ Adsorption Step
Figure 25 (A) Panels showcasing the fit of a kinetic model to the elution of each chirality for the 17mM SDS solution elution
profile, solid squares are experimental data and lines are theoretical fits. (B) Parity plot comparing the number of tubes
adsorbed based on our theory vs. the measured eluted SWNT (C) Energy profiles of each chirality of SWNT for the 17mM
adsorption as modeled to fit the elution data. (D) Charge density for each SWNT as a function of the SDS concentration in
which it is equilibrated.
In order to relate experimentally derived binding rate constants with molecular scale dynamics, we
matched the modeled binding rate constant (from Equation 21) with that predicted by our secondorder selective binding analysis using a best-fit analysis, assigning SWNT surface charge density as
the only free parameter. To relate the fitted SWNT surface charge density, asWNT (e nm 2), to a more
geometrically clear chirality independent parameter, we define here SWNT effective linear charge
density, n,,m (eInm), outlined by the following relationship:
62
Equation 23
This analysis demonstrates that by assuming a chirality and SDS concentration dependent charge on
each semiconducting SWNT, which are in turn derived from the incomplete cationic association of
Na' with the SWNT associated SDS anion, it is possible to describe the single-chirality gel based
SWNT separation in terms of molecular-scale interactions. A summary parity plot comparing the
number of tubes adsorbed based on our theory versus the measured eluted SWNT shows excellent
agreement (Fig 3B). The chirality dependent system energy as a function of SWNT-Sephacryl
separation distance for all fifteen chiralities separated from a SWNT solution in 17mM SDS is shown
in Fig. 3C, while the chirality and SDS concentration dependent SWNT charge density for all four SDS
concentrations investigated is shown graphically in Figure 25D and listed numerically in Table 2.
In order to compare the results listed in Table 2 with previous experimental findings, we translated
the charge densities listed here at 35mM SDS to equivalent Zeta potentials, using Debye-Huckel
theory for a cylinder8 8 and assuming that the Zeta potential is equivalent to the surface potential.
Using this method, Zeta potentials of between 30 and 60 mV are predicted from our SWNT surface
charges, which range from
0.86-1.63e^/nm in 35mM SDS. These potentials fall within the range of
previously published experimental Zeta potential measurements by others of 35mM SDS wrapped
SWNT (mean of 80mV), 73 where chiral inhomogeneity could be responsible for the breadth of the
Zeta potential measurement ( 20mV). The excellent agreement between our calculated charge
density value and experimentally validated values provides further evidence for the validity of
charge densities calculated using this theory and the assignment of such charges as the underlying
factor affording single chirality SWNT separation.
As can be seen in Figure 25D, the surface charge density of each SWNT chirality is predicted to
increase in a chirality dependent manner with increasing SDS surfactant concentration. Also, we
note the presence of a chirality dependent charge density at which the energy barrier height
associated with a binding event becomes sufficiently large as to prevent the binding of that species
on the timescale utilized here. This charge density, which we define as resulting in an effective
binding rate constant of 10-13 M- sec' or lower, occurs at approximately 3.5 e~/nm or greater, and
varies slightly depending on chirality. We postulate that at surfactant concentrations above this
point, SDS undergoes a morphological transition and the surfactant wrapping around a given SWNT
63
becomes effectively saturated, preventing the SWNT surface from interacting with the Sephacryl
binding site on the timescale of this experiment and therefore limiting the number of separable
chiralities (particularly those of large diameter) at SDS concentrations
70mM.
We use the above analysis to understand the influence of the change in SWNT charge state in the
context of gel-based single-chirality semiconducting SWNT separation. We hypothesize that at low
SDS concentrations, where a large quantity and distribution of SWNT adsorb to the Sephacryl gel,
there exist only minor differences in the SDS morphology around those SWNT species, leading to
similar chirality dependent surface charge densities, similar binding affinities, and low per-column
selectivity. Specifically, at relatively low SDS concentration we expect that the SDS is less densely
packed around the nanotube, which spatially allows the system to accommodate more Na' counterions. The increased cation concentration effectively negates the charge imbalance associated with
the SWNT-surfactant complex and reduces the relative difference in electrostatic repulsive forces
between different SWNT chiralities. The resultant low chiral selectivity can be seen in Figure 23A,
17mM SDS.
As the SDS concentration is increased from 17mM to 105mM, we expect that the chirality
dependency in counter-ion association becomes more pronounced. There are two important
aspects to this predicted change: (1) that the charge increases for all semiconducting SWNT
chiralities, and (2) that this increase is chirality dependent. We hypothesize that each SWNT chirality
displays different SDS packing morphologies dependent on surrounding SDS concentration, and
predict that chiralities not separated at larger SDS concentration are limited by SDS morphology
saturation at that concentration. The resultant separation is highly chirally selective, but unable to
separate large diameter SWNT (Figure 23A, 105mM).
To further understand the mechanism of the change in SDS morphology via concentration, we
increased the counter ion concentration by performing two simultaneous separations, one in which
the SWNT were eluted with 105mM SDS and the other with 105mM NaCl. In this experiment, all
other conditions were held constant as described in the methods section. The elution profiles of
these were very similar (Figure 26), showing that the ionic strength of the solution has a direct effect
on the morphology of the SDS, independent of SDS concentration. It is important to note that prior
to elution, the system still has SDS present in the gel, which is what allows the morphology change
despite not adding the higher concentration SDS. This observation provides further evidence for the
molecular picture of a morphology induced electrostatic change leading to the chiral separation. The
64
influence of NaCl on SDS wrapped nanotubes has been observed optically in previous studies, where
SDS morphology was assumed to be the driver of the observed change.6 7 Work by Hennrich and coworkers also shows that the charge of the system around the SWNT greatly affects the SDS
morphology, such that the introduction of just 5 M 1-dodecanol to the SWNT prevents it from
binding to the Sephacryl gel completely.62 The experiment presented in this work supports work by
other demonstrating the dynamic nature of SDS morphology on SWNT, which is significant to our
understanding of the Sephacryl gel-based separation.
A.
B.
Cal 3
o3
Co81al4
-
ol 5
1
Col7
Cl7
01
200
400
600
800 1000 1200
Wavelength (nm)
200
400
800
1000 1200
Wavelength (nm)
600
Figure 26 Absorbance spectra (each offset by 0.5 units for clarity) showcasing the equivalence of eluting the adsorbed
SWNT with either SDS or Nacl of equivalent Na concentration and volume. In both cases all other parameters were held
constant: 4h of 187kxg centrifugation, 1.4mL sephacryl per column equilibrated at 35mM SDS, solution flowed sequentially
through columns at 1mL/min using syringe pump controlled overpressure.
This mechanism can also be used to explain why metallic SWNT do not adsorb to the gel, an
observation made in the foundational studies using gels to separate SWNT . The SDS morphology
saturation has been shown to occur in metallic SWNT at low surfactant concentrations.6 So in the
model developed here, it implies that the activation barrier for metallic SWNT binding with
Sephacryl gel is too high for the SWNT to have an affinity for the gel. Further investigations, likely
using chirality dependent SWNT simulations at the molecular scale, are necessary to verify our
theory of chirality and concentration dependent morphology of the SWNT-surfactant complex. The
prediction of such a phenomenon using ab initio calculations would allow for more precise modeling
of SWNT separation, and inform the mechanism behind both gel-based and density gradient
nanotube separation techniques.
65
4.4.2
Varying Ultrasonication Duration
As specified in the experimental section, the bulk SWNT solution from which single-chirality material
is separated is prepared by weighing out (100mg) solid SWNT starting material and suspending it in
an aqueous SDS surfactant solution via Y2" tip ultrasonication at 20W. While the standard procedure
for this preparation calls for 20h of ultrasonication, important insight into the separation mechanism
is gained through systematically varying ultrasonication duration, and keeping all other separation
conditions constant (2h ultracentrifugation at 187k x g, 70mM SDS). The absorbance profiles of
ultracentrifuged samples sonicated for 1-18 hours are shown in Figure 27A.
With increasing
sonication time, the Ell peaks in the nIR region of the spectrum become more distinct while the
background absorbance decreases, , indicating that the ratio of individually dispersed SWNT to
other carbon materials (including SWNT bundles) increases with prolonged ultrasonication."9
In addition, we use Raman spectroscopy to track the evolution of peaks located in the radial
breathing mode (RBM) region (150-350cm') with increasing sonication time; each spectrum is
normalized to the height of the G peak (~1590cm'), Figure 27B. The noted Raman RBM peaks, each
of which corresponds to a unique SWNT chirality, change in height over the course of the 18h
sonication procedure, and can be used to track and assess the relative sonication state of a colloidal
SWNT suspension, Figure 27C. The origin for the evolution of the SWNT RBM spectrum during
ultrasonication is assigned to SWNT debundling, or an overall increase in the number of individual
SWNT in the dispersion, as demonstrated previously by Heller et. al. when using SWNT under
varying bundling conditions.89 Continued evolution of relative RBM peak heights over the course of
an 18h sonication further exemplifies the necessity of relatively long sonication periods to more
completely debundle SWNT.
Following ultrasonication (1h-18h) and subsequent ultracentrifugation, each SWNT starting material
was subject to the aforementioned separation procedure. The per-column elutions of the two
extreme cases, 3h and 18h, are shown in Figure 27D, while intermediate times are presented in
Figure 28. As the sonication time is increased, the separation changes from several chiralities in each
column with fewer numbers of a given chirality to highly pure single chiralities with each chirality's
total number increasing.
66
This observation is consistent with the assumption that increasing duration of the ultrasonication
step prior to SWNT separation results in the individualization of more SWNT from their as-received
bundled state. At small sonication time (Figure 27D, 3hr sonication) only a small fraction of each
chirality has been debundled, and relatively-less amorphous carbon fragments have been
generated,
which translates to a separation whereby an overabundance of binding sites in the first
several columns are occupied by non-specific-chirality SWNT, and little SWNT content is separated
from later columns. In contrast, at large sonication time (Figure 27D, 18hr sonication) a larger
fraction of each chirality has been debundled, and significantly more amorphous carbon fragments
have been generated, resulting in domination of the first several columns by amorphous carbon
fragments (which have been shown to have binding constants to Sephacryl gel much greater than
semiconducting SWNT27 which
do not
show spectroscopic signatures, and highly pure
semiconducting SWNT content in later columns.
B
A
C
RBM Raman Spectra
Absorbance Pre-Separation
I0.15 -f5m
lhr
3hr
0
0.4
C
0
n
-450 min
-50 min
V-
A0.5
C0010
(0
Shr
7.5hr
0.3
mjin
0 0.05
12hr
*
RBM Peak Height Evolution
--
0.20
I":
~CS!I
~
6)
-C
lco
0 0,12
a)
16hr
400 600
800 1000 1200
0
Wavenumber (cm- 1
3hr Sonication
E
18hr Sonication
4
8
20
-r=lI
(65)
-r=3x (8.5)
11000
5
bundle
500
-
OL
--
0
9
k=1.32x10 M
0
OL9
OL10
600
800 1000 1200
Wavelength (nm)
2
Wavelength (nm)
S
individual
SWNT'O
OL4
200 4
16
Effect of Bundling on Energy
6
C
12
Effective Sonication Time (hr)
)
Wavelength (nm)
5
0.04
G000
0
150 175 200 225 250 275 300 325 M
l9hr
0.1
E -8,3
0.08
14.5hr
0.2
-86
-9.4.-
0.18
-500
k
0
=
1
1.75 x
1
1
MI s
10
2
:3
Distance (nm)
Figure 27 (A) Offset absorbance spectra of the SWNT immediately before separation for various sonication times. (B) The
radial breathing mode (RBM) section of the Raman spectra for 3 specific effective sonication times here shown as 15min,
450min and 850min. (C) The peak heights of the RBM peaks of various SWNT chiralities, normalized to the G-peak height,
as a function of sonication time, showing a clear evolution of relative heights with time. (D) Offset absorbance spectra of
the separations carried out on SWNT that were sonicated for 3 and 18 hours, showing differences in separation based on
sonication time. (F) Energy profiles for a bundle of (6,5) SWNT compared to that of an individual (6,5) SWNT.
67
7 58 ufttSOfliCMIOfl
-
6
18
ufthasonication
S5
COLI
cou
4
COL4
co"
S 3
Co'"
COLS
A
$2
COLT
e 1
A
0
6
COLS
COLO
__________________r"
riahulica
-
168 uI~asonIcaU~n
n
M
",....
.
n.
COLI
A
4
eCuL
COLS
aoL4
COLS
cc"I
0
20 0
400
600 800 1000
Wavelength (nm)
3
1200
400
500 800 1000
Wavelength (nm)
1200
COI
COW
rOLS
10
3
400
600 800 1000
Wavelength (nm)
1200
Figure 28 Absorbance spectra (each offset by 0.5 units for clarity) showcasing the effects of starting material
ultrasonication time on resultant ten column separation. Ultrasonication, which was performed in a temperature
controlled bath and delivered 20W of power into a 1OOmL solution of 1mg/mL SWNT, was varied while all other
parameters remained constant: 2h of 187kxg centrifugation, 1.4mL Sephacryl per column, solution flowed sequentially
through columns at 1mL/min using syringe pump controlled overpressure.
This description of bundle-driven selective-separation presumes that only single-chirality SWNT bind
to Sephacryl gel, an assertion suggested by others
24
'2 7
without offering a mechanistic picture. To
understand the origins of this phenomenon quantitatively, we apply the theory developed in this
work to calculate the system energy as a function of SWNT-Sephacryl separation distance for a
SWNT bundle of seven like-chirality SWNT, Figure 27E. Assuming that a bundle of seven SWNT can
be effectively modeled as a single SWNT with thrice the diameter and identical surface charge
density, SWNT bundling results in a predicted interaction potential with a significantly larger barrier
height, which effectively prevents the binding of a relatively small seven-SWNT bundle to a
Sephacryl gel binding site. This explains and demonstrates the importance of the ultrasonication
step, where atypically long sonication times (~20 hours) are necessary to improve the selectivity and
yield of the separation process.
It is important to note that along with bundle dynamics, prolonged sonication is also known to result
in nanotube cutting,8 which has been shown to both reduce and narrow the length-distribution of
solution phase SWNT. 90 Experimentally, it remains unclear how to deconvolute SWNT cutting from
68
0
SWNT bundle reduction in terms of solution phase Sephacryl gel interactions, as the generation of
solution phase SWNT requires ultrasonication, which necessarily both cuts and debundles SWNT.
While all observations and analysis here are consistent with a change in bundling state, and not a
change in length distribution, as the predominant mechanism for ultrasonication effect on
semiconducting SWNT separation, methodological progress in SWNT length sorting is necessary to
more fully understand its effect on this process, and could serve as a valuable extension to the
model and work presented here.
4.4.3
Varying Ultracentrifugation Duration.
Following ultrasonication, SWNT suspensions are typically subjected to ultracentrifugation and
retention of only the top fraction, with the ultimate intent of increasing the ratio of individually
suspended SWNT in the solution. To investigate the effects of this practice on the outcome of a
single-chirality SWNT separation, we sonicated three SWNT solutions for 20 hours each at 20W, and
ultracentrifuged the samples at 187kxg for 15 minutes, 2 hours and 4 hours, respectively. The
absorbance spectra of these samples show a reducing baseline with increasing centrifugation time,
Figure 29A, as is consistent with the expectation that ultracentrifugation can effectively separate
individually dispersed SWNT from the rest of the carbonaceous materials, which are known to have
a relatively featureless, sloping baseline.s6 It is important to note that in addition to removing SWNT
bundles and carbonacious impuritis from the solution, prolonged ultracentrifugation also effectively
reduces the total SWNT content-or overall SWNT concentration--of the solution that is used to
perform the gel separaiton. Although previous findings suggest that separation dynamics should be
affected primarially by the concentration of individualized SWNT, and not by total SWNT
concentration, we explored this variation through a control experiment whereby 10 columns of
separation were performed. SWNT concentration alone was varied and all other parameters such as
SDS concentration, total SWNT content, and total per-column SWNT/Sephacryl interaction time,
were held constant. This control demonstrated that at initial SWNT concentrations of 0.25, 0.50,
and 1.00mg/mL, the resultant separated SWNT did not vary significantly over 10 columns, as shown
in Figure 30.
Using these three suspensions shown in Figure 29A as starting materials, we performed a standard
separation of 10 columns for each sample. Remarkably, there is not significant variation in either the
per-column chirality distribution or total SWNT amount, Figure 29B.
However, we note that
69
increased centrifugation (lower initial baseline absorbance) yields eluted suspensions that also show
an overall lower baseline in the absorbance spectrum, i.e. there is less carbon impurity as
centrifugation time is increased. This is evident in both the absorbance spectra of a selected
common column (Column 5 is shown in Figure 29C) as well as through visual inspection of the 10
column elutions, with sample color becoming more distinct as the carbon impurity content reduces,
Figure 29D. Although increased carbonaceous material does not appear to significantly affect the
resultant SWNT separation, its effect on performance of devices constructed from purified SWNT
remains unclear, and is the subject of an ongoing investigation.
B
A
Elution Order of (6,5) SWNT
Starting Material
C
-e
0
-- 15min
- -2hr
-- 4hr
CD
.
,
0.6
-
2.0
-15mi
2hr
4hr
1.5
n-
z
0.4
31.0
0.2
0.0
4(
0.5
10
E 0.0
-3
I.
600
1000
800
z
1200
O
2
4
6
8
10
Column Number
Wavelength (nm)
C
D
Comparison of Baseline
-- 15min
1.0
LO
>-21hr
0)
E
).8.0
eVa
0
0
).2
(1)
1.0
200
400
600
800
1000 1200
Wavelength (nm)
Figure 29 (A) Absorbance spectra of the SWNT immediately before separation for various sonication times (B) The peak
height per column of the (6,5) SWNT for the different centrifugation times, showing very small differences in quantity and
almost no difference in separation trend. (C) Absorbance spectra of Column 3 for the 3 different centrifugation times,
showing large baseline differences. (D) Photographs of the elutions from the 3 different centrifugation times, showing that
a lower baseline leads to color differentiation as chirality distribution
70
7
SWNT
[SDS]= 70mM
6
SWNT: 0.25mg/mL
ISDSJ = 70mM
SWNT: 0.50mg/mL
Volume: 20mL
Volume: 40mL
5
. ......
04
1t
SehacM
SWfNT
Sephacryl
Volume = 1.4mL
Flow Rate: 40mL/10min
SephacMA
SWNT
Volume = 1.4mL
[SDSJ = 70mM
SWNT: 1.00mng/ML Flow Rate: 10ml/110min
Volume: I10mL
Volume = 1.4mL
Flow Rate: 20mL/10min
COL2
/,
C0OL2
A COL3
"-
C0L3
COL1
CL4
-COL4
_e0
COLO
Al
200
400
600
800
Wavelength (n
1000
1200
-
200
CLOL8
400
600
800
1000
Wavelength (nm)
1200
200
400
600
800 1000
Wavelength (nm)
1200
Figure 30 Absorbance spectra (each offset by 0.5 units for clarity) showcasing the effects of concentration on resultant ten
column separation. All non-concentration factors were held constant, such as SDS concentration, total SWNT amount
introduced to each column, Sephacryl volume per-column, and total per-column SWNT/Sephacryl interaction time.
Despite different SWNT concentrations, the resultant separated SWNT did not vary significantly over 10 columns.
4.5
Conclusion
In this section of the thesis, we have demonstrated the use of a quantitative theory for the
prediction of single-chirality SWNT gel based separation. This description ultimately relates
experimentally observed binding rate constants with a chirality and SDS concentration-dependent
surface charge density associated with semiconducting SWNT.
Building a molecular-scale
mechanistic model for the gel-based SWNT separation process affords a more complete
understanding of the various factors that influence this process, and provides insight into the
dynamic and important role that surfactant morphology plays. This work develops foundational
theoretical principles toward the eventual realization of industrial scale, high yield, high purity,
single-chirality semiconducting SWNT separation.
71
5.
Competitive Binding in Mixed
Surfactant Systems
for SWNT
Separation
5.1
Introduction
The separation of single walled carbon nanotubes (SWCNTs) by chirality continues to gain immense
interest in recent years with significant advances that enable both high purity and high yield
separation of carbon nanotubes.1 , 3, 8, 17,
18, 21-27, 40, 63, 65,
91 These efforts from both our group and
others have clearly demonstrated the ability to separate single chirality SWCNTs at scales that are
,
now enabling the next generation of nanotube-based optical sensors 60 , 92 and optoelectronics.,6 8
, ,s 3
93, 94
Mechanisms to understand these separations have also been proposed in order to help guide higher
purity and yield separation processes.
12 25, 27, 49, 61, 63, 95
''''''
In all cases, it is well agreed upon that the role
of surfactants in these processes is instrumental. In this study, we explore experimentally for the
first time the impact of using different surfactants and surfactant mixtures in the gel based
separation. We show that the addition of bile salt surfactants modifies the chiralities of SWNT that
separate, showing a chirality dependent binding of these surfactants on SWNT.
In previous chapters we have developed a quantitative model that shows the SDS charge state is the
most likely reason for chirality-based separation.2s Furthermore, our group2s and others63 have
shown that in the range of 0.5 to 5 wt% SDS in aqueous solution, nanotubes exhibit different
surfactant coverage levels which affects their binding affinity to the gel. Other studies related to
altering the SDS phase around the tube have used temperature, 26 pH, 61' 96 and salt 25 ,67 to manipulate
the SDS phase around the tube, and most of these studies agree with our previous findings.25 These
studies have shown that it is likely that the adsorption occurs directly between the SWNT surface
25 97
and the Sephacryl, where the surfactant mediates the chiral selectivity but not the binding itself. ,
An early high throughput study
66
of various surfactants guided researchers to heavily rely on SDS,
we expect this is due to the flexible morphology of the surfactant on the tube. However, other
13,20,21,482,
methods, such as density gradient centrifugation,'22,4 and the two phase separation method,
23 have found success via the use of surfactant mixtures.
A recent study on the mechanism of the 2
phase separation shows the use of surfactant mixtures most heavily affects the coverage on the
72
surface of the nanotube by each surfactant. 98 The use of a bile salt surfactant creates a more tightly
bound structure on the surface of the tube which leaves a lower fraction of the surface of the tube
exposed. 99 In the two phase method this phenomenon is exhibited quite clearly; an increase in the
SC concentration makes the nanotubes more hydrophilic as less of the tube surface is exposed. 22,23,
98
In this study we use these same surfactant coverage guiding principles to establish methods of using
mixed surfactants in the separation of carbon nanotubes via the gel based method. We first
establish the protocol used to enable various monosurfactant separations. We then study the
concentration-dependent effect of mixing various bile salt surfactants with SDS. We studied the four
most commonly used surfactants for these systems, SDS, Sodium Cholate, Sodium Deoxycholate,
and Sodium Taurocholate. This study will help outline a path to not only understand the gel based
separation processes further, but also help understand how surfactant mixtures compete for SWNT
coverage and their chiral dependence.
5.2
Experimental Methods
5.2.1
Preparation of Aqueous SWNT Suspension.
To prepare the solutions for this study, we follow the procedure we have previously established in
our other work.2 s, 2 7 As in our previous study, we use raw HiPco SWNT (Unidym, Lot: R1831), which
we first convert to a powder. We then disperse 100mg of the raw nanotube powder in 100ml of
aqueous surfactant solution, where the surfactant is one of four surfactants we are studying in this
work. We sonicate the solution for 20 hours, followed by 4 hours of ultracentrifugation at 187,000 x
g, as done previously. The top 90% of the solution is then used as the sample for this study. At this
juncture is when we add the second surfactant for the mixed surfactant study, in the appropriate
quantity to create the final mixture. We then gently mix the solution and let the mixture stand for
about 10 minutes to equilibrate the solution.
5.2.2
Single-Chirality Semiconducting SWNT Separation Process.
The procedure used to perform the actual separation follows the process that we have used
previously. For the full details see the previous chapters.25 ' 27 Briefly, we pass 10 ml of the nanotube
73
solution through 1.4 ml of Sephacryl 200 gel at a rate of
1ml/min. As before the solution that does
not adsorb to the gel is collected and used iteratively as the solution for the next column.
Importantly, the rinse step in this work is done using a surfactant solution with concentrations
equivalent to that in the nanotube solution. Elution is still performed using 175 mM SDS in every
experiment in order to maintain comparable results unless otherwise specified.
5.2.3
Absorbance Spectroscopy
As in all of our previous work,2 s,
27
absorbance spectroscopy is used to analyze the chirality
distribution of the separated SWNT samples produced by the gel separation method. We fit the Ell
peaks with a Lorentzian lineshape after a linear background subtraction in order to capture the
chirality distribution. The fitted peak heights are then used to estimate both the absolute and
relative quantities of the SWCNTs. The majority of the analysis in this work depends on this analysis.
5.3
Results and Discussion
This study focuses on the effect of using various surfactants and mixtures of these surfactants on the
gel based separation mechanism. We will first analyze the single surfactant systems, and then the
mixed surfactant systems. We implicitly use our previously developed quantitative model,2s and the
methods developed in those works to understand the experiments that we perform with both the
single and mixed surfactant systems.
5.3.1
Single Surfactant Systems
The first study that we perform is with single surfactant systems of three of the four surfactants of
interest. We study various concentrations of each of the surfactants of interest, SDS, SC, and SDOC.
We choose these surfactants because of their common usage in separation protocols.i'
21
,22,
66,99 The
bile salt surfactants are all related to each other, SC, SDOC, and STC, are all very similar to each
other with a single point mutation in the chemical structure. 99 However, these minor differences
cause major differences in the surfactant coverage on the SWNT. Unfortunately, STC is commercially
only sold in small quantities, such that creating a 100 ml SWNT sample that is comparable to our
74
other samples is difficult. Further, our mixed surfactant experiments show that it is highly unlikely
that any SWNT would adsorb when using this surfactant alone.
We run the separation process with each of these surfactants and analyze the eluted content. In
order to analyze the separation process, we run eight columns of the separation and take
absorbance spectra of the eluted sample. Figure 31 shows spectra for an adsorption with each
surfactant at 0.5% by weight solution of the respective surfactant.
,
2.5
0.5% SC
0.5% SDOC
0.5% SDS
3.0
1.00
.
a)
_
1.5
5
0.75 -
a
1.0
2.0
o0)
5
0. 0
1.5
CCU
o
20.5
1.0
0.50
0.01
400
800
Wavelength (nm)
1200
0.0
400
800
Wavelength (nm)
1200
0.0
400
800
1200
Wavelength (nm)
Figure 31: From left to right, the desorption spectra of several columns of SWNT suspended in 0.5 wt% of SDS, SDOC, and
SC. The spectra indicate that SDS is the only surfactant that allows SWNT to adsorb to the gel. Interestingly SC seems to
allow some amorphous carbon to bind and desorb from the gel, as indicated via the sloping baseline. However no SWNT
bind in just SC or SDOC surfactant suspensions.
The SWNT suspensions with a surfactant other than SDS do not show any SWNT adsorption or
desorption. This result agrees with previous observations that SDS is unique in its ability to enable
the separation of SWNT based on chirality.2
'63,66
We agree with the hypothesis that SDS has this
ability due to its flexible morphology and equilibrium coverage ratios that are chirality and
concentration dependent. The partial coverage of SDS of the SWNT enables part of the SWNT
surface to stay exposed, and therefore adsorb to the gel, 25' 67,96 or in the two phase method, a
22 23 98
dynamic and controllable hydrophobicity. , ,
Our previous work shows both experimentally and via a quantitative model, that SDS has a chirality
and concentration dependent morphology and coverage on the SWNT surface.2 s We learnt that at
low SDS concentrations, the surfactant has a low coverage on the tube, and a lower effective charge
per unit length. Further, we learnt that larger diameter semiconducting tubes show greater SDS
coverage than smaller diameter tubes at the same bulk SDS concentration. This understanding
75
enables us to now interrogate the SWNT-surfactant system with other surfactants as well as mixed
surfactants.
Despite a lack of adsorption when suspended in SC or SDOC alone, several groups have shown that
mixing surfactants can be used to fine tune the separation, especially when using the density
gradient1
3, 20
or 2-phase methods.23, 98 A systematic study of mixed surfactants in the gel based
system is presented here for the first time.
5.3.2
Mixed Surfactant Systems
We perform the surfactant mixture study via the creation of mixtures of SDS with one of the bile salt
surfactants at experimentally relevant concentrations of 0 to 2% by weight of each. The first
concentration mixtures that we attempt is to add a small fraction, 0.3wt%, of the bile salt surfactant
to an otherwise standard separation process at 2 wt% SDS concentration. We carry out the
separation process for 20 columns in order to ensure that we reach the point at which we no longer
see any SWNT adsorbed to the gel. Figure 32 shows the spectra and images of the desorbed SWNT
from the 20 columns on descending order, where the SWNT was eluted using 5wt% SDS.
As is shown in the spectra in Figure 32, the addition of a bile salt surfactant to SDS significantly alters
the separation of the SWNT. The SDS-only separation looks similar to what has been shown in
previous work, both by our group and others. The addition of either STC or SC does not prevent the
separation, but changes it. The addition of SDOC however does completely prevent the separation.
This implies that we can say with certainty that the bile salt surfactants outcompete the SDS binding
on the SWNT to varying levels. It especially showcases that SDOC binds the SWNT the most tightly,
as has been shown by our groups and others.
We notice two important trends in the STC and SC additions. The SC addition enables and promotes
the separation of larger diameter SWNT, in a way similar to reducing the SDS concentration. Based
on our previous work, we expect that if larger diameter SWNT can be adsorbed to the gel, then it
implies that the SDS is not tightly packed on the SWNT. We expect that the SC additive is binding
tightly on the SWNT, however it does not completely outcompete the SDS. The ability to separate
some SWNT, and especially larger diameter SWNT implies that the SC allows the SDS to partially
cover all chiralities of SWNT, including the large diameters.
76
S2%SDS
2% SDS +.3%
SC
4
U
3
0
2
CU
1
0'
5
2% SDS+ 0.3% STC
4
2% SDS + 0.3% SDOC
1-7
-5
o3
C
CU
03
C
0
400
600
800
1000
Wavelength (nm)
1200'
400
600
800
1000
1200
Wavelength (nm)
Figure 32: Absorbance spectra of 20 columns of eluted SWNT that were adsorbed to the gel in surfactant solutions noted
in the header of each plot area. Under each absorbance spectrum is a photograph of the first 10 columns of eluted SWNT,
showing clearly visible differences in the quantities and purities of the SWNT solutions. Interestingly, the 3 bile salt
surfactants show dramatically different separations despite small chemical moiety differences. Note that the addition of
even a small amount of SDOC prevents any SWNT adsorption.
The total number of separable SWNT in both cases (SDS alone and SDS + 0.3% SC) is similar. In fact,
as was the case with a lower SDS concentration, the mixed surfactant enables more SWNT to get
bound (7.3 x
1014
SWNT) over the 20 columns than just SDS at 2% (6.3 x
1014
SWNT). Figure 33
shows the quantities of each SWNT eluted for every column when STC, SDOC and SC are added to
the SDS SWNT mixture. The absorption spectra for these separations are shown in Figure 34.
Further, Figure 31 and Figure 33 showcase that the chiralities of SWNT are also similar between a
77
0.5% SDS and the 0.3% SC addition to the 2% SDS solution. This implies that the addition of a small
quantity of SC reduces the overall surface coverage of the SDS surfactant on the SWNT. While a
molecular picture cannot be precisely drawn from this observation, we expect that the SC additive
influences the morphology of the SDS to assume a loose packing that enables more SWNT and larger
diameter SWNT to adsorb to the gel.
2% SDS
1. x10'
1 4x10*
(7.3)
1 2(10
(.5)
1 Ox 10
(6,4)
+
2% SDS + 0.3% SC
3.5x10"
a- 06.) -- (9,1)
3-Ox iO'
8.7)- 0(21)
-
2 5x10"
3
2Ox104
8 Ox10
1 5x10'
6 Ox10
z
1 ox104
4 Ox1O'
'3
Ox 10
70
z
00
8x 10
DS+
'3
0 .3% S C'
% DS + .3%
SDOC
801'
7X 10'
6x10'
680x10"
5x10
C-
S410'
0
4 0x10"
0
3x10
2x10
20x10" Z
1x10'
0
5
10
Column Number
15
20
0
5
10
0.0
15
20
Column Number
Figure 33: Calculated quantities of SWNT per column per chirality of 20 columns of eluted SWNT for each surfactant
mixture. The amount of nanotubes changes dramatically for each surfactant mixture, and hence each graph has a different
y-axis. We specifically not that the SC addition enables several large diameter chiralities to be eluted within the first 5
columns. Further, it is obvious that the (6,5) tube is most efficiently eluted in the SDS only elution. Finally, the addition of
0.3% STC shows in column 1 an elution of only the (7,3) tube.
78
2% SDS
2% SIDS + 0.3% STC
2% SIDS + 0.3% SC
2% SIDS + 0.3% SDOC
4
0
(D
Ca)
-2
0
1
U
CA
4
0 3
2
-2
0
0
200
400
600
800
1000
1200 200
400
600
800
1000
1200
Wavelength (nm)
Wavelength (nm)
Figure 34: Absorbance spectra of 20 columns of eluted SWNT that were adsorbed to the gel in surfactant solutions noted
in the header of each plot area. Interestingly, the 3 bile salt surfactants show dramatically different separations despite
small chemical moiety differences. Note that the addition of even a small amount of SDOC prevents any SWNT adsorption.
The STC addition in contrast to the SC addition has a chiral selectivity that enables the separation of
SWNT specifically with absorbance peaks close to 1250 and 950 nm. We further analyzed the
spectra to determine specifically which SWNT are adsorbed and eluted with this surfactant mixture
as seen in figure 3. We find that the (7,3), (6,5), (9,1), (8,3), (8,4), and (9,2) SWNT are preferentially
adsorbed over the 20 columns of separation performed as shown in Figure 35. All of these chiralities
have diameters between 0.7 and 0.8 nm. In fact, column 1 has over 80% pure (7,3). Further, the
4
total number of SWNT that are adsorbed to the gel over the 20 columns is much smaller (1.6 x 101
SWNT) than the SDS or SDS + SC experiments. The selectivity is very different than what has been
seen previously by our group and others.2 4 '
25,
,
3
These observations imply that the STC binds
certain chiralities tighter than others at the same bulk STC concentration. We expect what we
observe in our experiments is that the SDS can outcompete the less tightly bound STC chiralities,
and this enables their adsorption and desorption to and from the gel. This seems to suggest that
these small diameter SWNT have a lower binding affinity to the STC than other chiralities. This
79
chirality dependent binding of STC was previously shown in work from our group in the context of
reactions with aryl diazonium salts.99
2.5E+14 -t
SDS
SDS+SC
-
2E+14
1.2E+14
9E+13
-
1.5E+14
6E+ 13
1E+14
E
-
0
2
3E+ 13
-
5E+13
I-I-I
0
I
I
I
m
0
e3N\10-NN 4;3 NN
<N,
2.5E+13
k 3s AN N'N
O;e' 0-
-
15E+129
SDS+STC
2E+13
zl.5E+13
Z0 1E+13
5E+12
11.
Ql'
NN b ri bN NN
,', iA 0'
SDS+SDOC
12E+12
I-2 9E+11
I11=
lI I I II I I P I Ii0.I
0
2 6E+11
I
II
I
\o
II
3E+11
I
OZ
I1
Figure 35: Chiralities eluted over all 20 columns worth of the separation for each of the surfactant mixtures. The bars make
it very obvious which SWNT chiralities are preferentially absorbed to the gel. As is expected, the (6,5) tube is most strongly
absorbed and eluted in the SDS only case. Note also that the SDOC absolute levels of SWNT are within the noise limit of
detection by our spectrometer, we do not believe there are any measurable quantities of SWNT eluted with the addition
of SDOC.
In order to study in further detail the effects of mixing the surfactants, we carry out experiments
where we sonicate 2 wt% SDS with the SWNT. We then add an incrementally increasing fraction of
Sodium Cholate in adsorption, however we still elute the sample with 5% SDS as discussed in the
methods section. We perform the separation for 8 columns and the absorption spectra are shown in
Figure 36(A).
80
At
2% SDS + O.5%SC
2% SDS + 0.3%SC
2% SDS +0.7%SC
i-t
__2
(D
400
600
800
1000
1200
Wavelenoth (nm)
B.
400
800
600
1000
1200
Wavekength (nm)
400
600
800
1000
1200
Wavelength (nm)
C.
1.0
2% SDS + 0.3%SC-
--
(
.3) --
-+(9,2)-
(6,4) --
(6,S)---(9,1)
(8,G) -9-(9,4)-- (10.2)
0.8
.~0.4
0
z
0.3
1
0.5
0
Wt% of Sodium Chofate added
2
Figure 36: (A) From left to right and top to bottom, the eluted SWNT absorbance spectra of several columns (column 1 on
top, column 8 at the bottom) of SWNT suspended in 2wt% SDS with the incremental addition of Sodium Cholate. (B) From
top to bottom, pictures of the eluted samples with incremental addition of sodium cholate, showing an obvious reduction
in SWNT as SC fraction is increased. (C) Normalized change in the quantity of SWNT eluted in column 2 (a representative
column) of the separation as the SC fraction is increased. Note that the x-axis is not a linear scale so that it is easier to see.
Interestingly the change in number of SWNT eluted is chirality dependent as the SC concentration is increased. Also, at the
point at which 2%SC is added, there is no detectable SWNT in the solutions.
As we expect, as we increase SC percentage in the bulk solution we reduce the amount of SWNT
that bind to the gel as the Sodium Cholate outcompetes the SDS for tight coverage around the tube,
eventually leaving no exposed surface to bind with the gel. As others have noted in density gradient
or 2-phase separation methods, changing the ratio of SC to SDS changes the amount of the surface
of the SWNT that is exposed. Using this understanding is instrumental to being able to tailor either
the gel based separation or other methods, especially the density gradient and 2 phase methods
which uses precisely these two surfactants and in these ratio ranges. The field still does not have a
good way to visualize the precise structure of the surfactant on the tube when in solution. However,
we can say with certainty that the SC binds tightly with the SWNT and that as the concentration of
SC increases to 2%, it outcompetes the SDS coverage on the SWNT.
81
What is interesting to note is that the binding competition between SC and SDS is once again
chirality dependent. We fit the peaks for each of the spectra and observe the changes in the amount
of each chirality of nanotubes eluted as the sodium cholate concentration increases. Figure 4(C)
shows the change in quantities of each chirality for the second column we elute as the SC
concentration is increased. This plot makes it obvious that the fractional change is more dramatic
for some chiralities than others. The change seems to be the least for larger diameter tubes, and the
most for smaller diameter tubes. This ordering is similar to the saturation ordering of SDS on a
SWNT (larger diameter SWNT saturate the earliest). This is consistent with our previously defined
model of SDS packing on the tube,25 as at 2% SDS, we expect that the smaller diameter tubes are
less saturated and hence have the ability to accommodate more SC and cause a dramatic difference
to the fractional binding and elution of those tubes. Of specific interest is the (6,5) chirality, which
sees a very large change from 0.3 to 0.5% SC, indicating that the loose structure of SDS at 2% is
easily out competed at even lower concentrations of SC. What is surprising however is that the (7,3)
tube seems to change very slowly with increasing SC concentration, even though we know the SDS
packing is not saturated on the (7,3) tube. This implies that even the SC surfactant does not have a
strong affinity for this tube. It is important to remember that for each chirality we have to consider
the competitive binding individually. Each surfactant will have a binding affinity that is chirality
dependent and hence competitive binding on the tube surface must be considered for each chirality
separately. We conduct a similar experiment for SDOC and STC where we added 0.3% and 0.7% by
weight of each of these surfactants and measure the absorbance spectra in each case, as is shown in
Figure 37. We note once again that SDOC binds very tightly at even low concentrations and do not
observe any eluted SWNT. Further, we note that for STC, as was the case for the SC, the biggest
change from 0.3% to 0.7% is the absolute concentrations for each of the eluted chiralities. Given the
low concentrations of SWNT eluted with STC, we were unable to reliably quantify the per chirality
difference in binding over the noise levels in the spectra. Never the less, our experiments give the
first quantitative insight into the relative competitiveness of SDS and SC in a chirality dependent
fashion, and this system is currently the most important for SWNT separation in both the density
gradient and 2 phase separation methods.
82
Sc
1.8
1.6
14
0 12
C
0.3%STC
0.7%SDOC
0.7%STC
A
..
.
..
.........
.
A
1.0
0.8
0.3%SDOC
C',
0.2
0.0
0.7%sC'
1.8
1.6
0.4
1 '4
A
1.2
1.0
0.8
0.6
C')
0.4
C
0.2
0.0
400
600
800
1000
Wavelength (nm)
1200
400
600 800 1000
Wavelength (nm)
1200
400
600
800
1000
1200
Wavelength (nm)
Figure 37: Absorbance spectra of the SWNT eluted when a 2% by weight of SDS suspended SWNT has been modified via
the addition of SC, SDOC and STC respectively (left to right) in concentrations of 0.3% and 0.7% by weight (top to bottom).
As is the typical case, absorbance spectra are read as the top spectrum coming from column 1 and the bottom spectrum
from Column 8. Note that only in the SC addition case do we observe large quantities of SWNT eluted in both cases, SDOC
does not elute any SWNT, and STC at 0.7% elutes a very small quantity of SWNT.
5.4
Conclusion
All of our observations point to the same conclusion that mixed surfactant systems can be used and
controlled to carefully regulate and modify the separation of SWNT using any of the popular
processes in literature today. Importantly, we show that SC and SDS compete within concentration
ranges of 0-2% each and have a strong chiral dependence. We also show that with STC, there are
ways to specifically modify the separation and obtain only specific chiralities, which are likely the
chiralities which STC binds least strongly too. We expect that our findings will enable further
understanding of SWNT surfactant systems and their importance in the emerging field of chirality
separation of SWNT.
83
6.
Single Chirality SWNT Solar Cell
Adapted with permission from Jain, R. M., Howden, R., et al. Advanced Materials 201Z 24, 44364439. Copyright 2012 John Wiley and Sons.
6.1
Introduction
The incorporation of single-walled carbon nanotubes (SWNTs) into next generation solar cells as
near infrared absorbers has demonstrated the potential to efficiently harness energy in the 1000nm
to 1400nm range5 ,7 ,3 2',11 . However, SWNT-enabled photovoltaics (PVs) to date have required the
use of polymers, which served as either SWNT-wrapping (isolating) agents5'
7, 32, 100
or as direct
components of the photoactive layer10 1 103. While such layers are expected to increase device
performance at the laboratory scale, the use of polymers in PV devices is oftentimes restrictive due
to low photostability and the necessity of highly controlled environments for assembly and
characterization0 4 . In contrast, carbon nanotubes have the strong advantage of being extremely
2
.
stable in air while at the same time absorbing in the near infrared region of the solar spectrum
Here, for the first time, we demonstrate a polymer-free carbon based photovoltaic which relies on
exciton dissociation at the SWNT/C 60 interface. Through the construction of a carbon based solar cell
completely free of polymeric active or transport layers, we show both the feasibility of this novel
device as well as inform the mechanisms for inefficiencies in SWNT and carbon based solar cells.
6.2
Experimental Methods
To study the case of an all carbon nanotube phase, we designed and constructed a device whereby
electrons and holes are conducted through C 60 and SWNT layers, respectively, and excitons are
dissociated at the interface between the two, Figure 38. Further, device assembly using only highly
purified single chirality (6,5) SWNTs'
20, 24
allows for the distinction between intrinsic losses and
those caused by impurities in SWNT chirality that have dominated many systems reported in the
literature.
84
A
B
silver - 100nm
C60 - 70nm
(6,5) SWNT film - 1 00nm
patterned In:SnO2 (ITO)
glass supporting substrate
incident glass/ITO
(6,5) SWNT film - 100nm
C6 - 70nm
silver
(6,5) SWNT
C60
silver
light
ITO
->-4.5-
--
1eV
-5.1 eV
-6.0
-6.2 eV
Figure 38 Schematic and energy diagram of polymer-free carbon nanotube photovoltaic device. Layered threedimensional device architecture (A) which allows for the fabrication and analysis of multiple devices from a single SWNT
film, and cross-sectional diagram (B) emphasizing the directional transport of charge carriers. Energy diagram (C) of
device, illustrating a type-Il heterojunction.
6.2.1
SWNT Solution and Single Chirality Isolation
HipCO SWNT from Unidym Corp. (100mg) were weighed into a 250ml glass beaker to which was
added 100ml of 2wt% Sodium Dodecyl Sulfate (SDS) purchased from Sigma Aldrich. The beaker was
then placed into a chilled water bath which is maintained at 100 C via the use of a chiller. The water
level in the bath is kept at a height higher than the nanotube solution and the total volume of the
bath is approximately 1litre. A Y2" probe tip sonicator made by Cole Palmer is placed in the center of
the beaker at a height of 1cm above the bottom of the beaker and the solution is sonicated at 20W
for 20 hrs. The sonicated SWNT solution is then centrifuged in a Beckman Coulter ultracentrifuge at
154,000rcf for 4 hours. The top 90% of the solution is used for the separation.
The SWNT solution prepared in step 1 is now passed through columns containing Sephcryl-HR 200 in
order the isolate the (6,5) chirality. In order to do so, 3 plastic columns purchased from Thermo
Scientific are arranged vertically on a ring stand, and 1.4ml of Sephacryl 200-HR is placed into each
column. Each column is then separately washed and equilibrated with 10ml of 2wt% SDS solution,
allowing excess SDS to drain through. With the columns arranged vertically, 10ml of the SWNT
solution is pipetted into the top column and then allowed to drain through the 3 column stack. Once
excess SWNT solution has drained through, the columns are each washed with 5ml of 2wt% SDS
solution, to remove unbound SWNT. The SWNT adsorbed to each of the columns are then
separately eluted using 4ml of 5wt% SDS solution. The first two columns will typically contain (6,4)
and (7,3) impurities, with the third column containing highly purified (6,5) SWNT, Figure 39.
1.00
500
1000
500
1000
0.5
a
-
0.75
0.25
0.00
0.75
0.50
E
0.25
-
C14
0.00
<0.75
<
0.50
0.25
0.00
Wavelength (nm)
Figure 39 Absorbance of the SWNT eluted from each of the columns using the column separation method.
It is commonly accepted that the ends of a carbon nanotube act as exciton quenching sites, and as
we have deposited a random network of SWNTs, we expect the length of the nanotube to play a
role in the efficiency of the device. We took AFM data of the SWNT solution deposited on Silicon to
ensure the SWNT were long enough to allow reasonable transport through the film. We found the
average SWNT length to be 285nm
65nm, Figure 40.
0im
1
4
3
2
3.1 nm
2.8
2.6
2.4
2.2
2.0
1.8
1.6
1.4
3
1.2
1.0
4
0.8
0.6
0.4
14
12
10
.28
6
I
4
2
00
00014lr
o00
000"4T
D00
Length (nm)
Figure 40 AFM image of SWNT deposited on a Silicon substrate showing single nanotubes along with the
distribution of over 70 individual tubes to calculate average tube length used in the devices.
6.2.2
length
Procedure for Film Preparation
The films made for this communication were deposited using a vacuum filtration method as
originally introduced by L.Hu et al.' 05 In this study, we use Anodisc 25 Alumina membranes with a
0.2pm pure size that are 25mm in diameter. The membranes are allowed to rest on a glass frit and
with the vacuum on are first washed with 20ml of deionized water. Then SWNT solution obtained
from the purification process is diluted from approximately a 4wt% in SDS solution to a lwt% in SDS
solution, this allows for a lower SDS concentration as well as a lower SWNT concentration, which
87
facilitates uniform SWNT deposition across the film. 40ml of the diluted SWNT solution is then
slowly added to the vacuum filtration setup and upon filtration of the entire volume the vacuum line
is left open for a few minutes to let residual fluid escape the film. The film is then washed with 50ml
of deionized water to wash away the surfactant from the solution, Figure 41. Once again, after the
water has filtered through the vacuum line is kept open to allow residual liquid to filter out. The film
is then allowed to dry in air for an hour and is then dried in an oven at 800 C for 4 hours.
0
120 -~HiPCO
90
1
2
3
SDS
Na
Si
Na
60
30I-Fei,
0
65 film
0:
60
p
0
1
2
3
Voltage (V)
Figure 41 Energy Dispersive X-Ray (EDX) data showing that the (6,5) films do not contain Na+ down to 0.1% levels, while
control HiPcO in 2wt% SDS dropcast films do show signal for Na+.
In order to dissolve the membrane, the film is allowed to rest on a petri dish filled with 3M NaOH
solution for 15 minutes. The NaOH solution is then completely replaced with deionized water by
flushing the NaOH solution out with a large quantity of deionized water. The SWNT film is then
carefully deposited onto the substrate of interest by allowing the film to settle on the substrate
from the water bath. The film is then left to dry in air for 1hr and then annealed in an oven at 2000C
for 4 hours to get rid of any residual water and other volatile impurities.
In order to ensure all of the surfactant is washed away during the deposition of the film, we
performed energy dispersive x-ray spectroscopy (EDX) at 3kV for a 10minute acquisition time and do
not see a peak from Na+ down to 0.1% levels, while controls of a dropcast SWNT film suspended in
2% SDS do show the Na+ signal, Figure 41.
To further qualify the quality of the SWNTs used in the device, we performed Raman measurements
using a 633nm laser with a Horiba Jobin-Yvon Raman spectroscopy system. The measurements were
88
taken in both the solution and film form and the defect peak at 1350 cm-1 is very small in
comparison to the G-peak at 1590 cm-1, Figure 42.
0
2000
4000
0
2000
Wavenumber
(cm')
4000
i33000
C 22000
L1100
I
0-
4500
-
6000
CO
-
1500
04
Figure 42 Raman data of the SWNT in both solution and film form showing extremely low D to G peak ratios, suggesting
very low levels of defects in the nanotubes that would act as exciton quenching sites.
Resultant films showed coloration from the SWNTs, but were sufficiently transparent to allow for
transmission based optical characterization, Figure 43D. In the (6,5) SWNT film, spectroscopic peaks
associated with both absorbance (Figure 43E) and 2D emission (Figure 43F) are red-shifted and
broadened as compared to those of the (6,5) SWNT solution-absorption and emission from 977nm
to 1030nm and 982nm to 1063nm, respectively. We assign this shifting and broadening to the
increased dielectric screening present in SWNTs surrounded by other nanotubes, as opposed to
surfactant and solvent molecules. 0 6 The photoluminescence from the film further demonstrates the
high purity of the SWNT matrix with respect to the (6,5) chirality. Specifically, only the (6,5) chirality
emission peak is present-Figure 43C and F. Given that exciton energy transfer (EET), has been
shown to be highly efficient in both large107 and small'08 bundles of SC-SWNTs, we exclude, for the
first time, the potential of inhomogeneity in SWNT chirality from the list of possible inefficiencies in
a SWNT based photovoltaic device.
89
A
SWNT Solution B
B
C
____,.
0
-750
1.5
-700
1.0650
~0.
s.w
0.
i550
.
----- 00100
-0
-w
-QO
-11
0.0 -_
0 a0wvenen%
D
SWNT Film
E
o
(n
Emission nm)1 2 00
F__
04.
2
0.3,
0
02
Q0.1
M
W
0.0 -
600
0.5
'R550
500
k 00
2nm)
Emission
'Naveength (n
Figure 43 Characterization of liquid and film single chirality (6,5) SWNT samples. Photographs (A, D), absorbance traces (B,
D), and 2D emission spectrographs (C, F) of both SWNTs suspended in 2% SDS solution (A, B, C) and formed into a 100nm
thick film (D, E, F). The strong absorption and emission peaks are indicative of a single-chirality SWNT sample.
6.2.3
Photovoltaic Device Construction
Devices were constructed by depositing 100nm thick, highly pure surfactant free (6,5) SWNT films
atop an ITO/glass support in a planar heterojunction geometry. This film served as the p-type layer,
while a thermally evaporated 70nm thick layer of C 60 served as the n-type material. The back
electrode was formed by thermal deposition of silver, completing the photovoltaic device Figure
38A.
Electrons and holes are collected at the C 60/silver and SWNT/ITO interfaces, respectively, Figure 38B.
The active layer thicknesses were rationally chosen to maximize device performance based on total
light absorbed and transfer matrix calculations of the optical field discussed in the next section.
Energetically, the choice of (6,5) SWNTs and C60 forms a type 11 heterojunction device 0 9, Figure 38C.
Here, we explicitly choose to forego the use of an electron or hole blocking layer-one or both of
which have become common in the fabrication of organic planar heterojunction devices104 -with
the goal of gaining insight into the performance and limitations of an all carbon active and transport
layer. We plan to explore the implementation of these layers in future studies, with the ultimate
goal of maximizing photovoltaic efficiency.
90
The C60 (Sigma Aldrich, 99.9%), and the top Ag cathode (Sigma) were thermally evaporated using
shadow masking at a base pressure of 1
x
10-6 Torr at rates of 1.0 A/s for the organic materials and
2 A/s for Ag. The C60 was purified via thermal gradient sublimation before use. Ag was used as
received. Pre-patterned ITO substrates (Thin Film Devices, 20 O/sq) were cleaned by subsequent
sonication in Dl water with detergent, DI water, acetone, and isopropyl alcohol, followed by 30
seconds of 02 plasma cleaning.
The device structure was confirmed via cross-sectional SEM. The cross section was created by
mechanically cleaving the device such that all 4 layers were visible. A JOEL 6700 SEM was used, set
at 1kV with a working distance of 2.9mm and using the secondary electron imaging (SEI) detector.
The image, Figure S6, clearly shows the 4 layers that are used in the device. However, we note that
the SWNT layer seems to have slightly collapsed and sheared such that the interface is no longer
sharp. SWNT have a strong binding force with adjacent SWNT and this is a possible explanation for
the bundled shearing that appears to have occurred during cleaving.
Figure 44 cross-sectional scanning electron microscope (SEM) image showing the four distinct layers in the planar
heterojunction device. Arrows drawn from SWNTs intended as guide to the eye for SWNTs hanging from the cleaved
interface. Note that because of the cleaving method utilized and the inter-woven nature of the SWNT layer, assignment of
SWNT layer thickness via cross-sectional SEM is not accurate due to hanging SWNTs draped over its cross section.
Accurate SWNT film thickness was determined via surface profilometry of isolated SWNT films, as described in the main
text.
6.2.4
Optical Transfer Matrix Solution Calculation.
Electric field intensity calculations were carried out using an optical transfer matrix solution adapted
from Petterson et. al.110 and made available by Burkhard et. al."' In order to carry out the
calculations, we measured the refractive index values of the various layers using a J. A. Woollam
spectroscopic ellipsometer from 200nm to 1000nm and found they corresponded well with the
91
values made available by Burkhard et. al.m' However, the values for the SWNT film refractive index
were checked against literature values for highly conductive SWNT thin filmsm and we found the
refractive index to correspond closely to the values seen previously. However, as the instrument
was only able to measure out to 1000nm, we linearly interpolated our experimental measurements
to 1040nm, and find that the difference in field calculation is minimal and hence believe this to be a
strong assumption, Figure 45.
1000nmi
}
1.2
0.8-
C
C
10nm1
Al
\
V
0.6
X
SWNT
ITO
V
0.8
I
_
0
10
D
10
50
O
20
5
30
35
5
300
3;0
N0.2
0
0.20-
0
10
0
400
Position in Device (nm)
Figure 45 Transfer Matrix solutions for the optical field through the device stack modeled at 960, 1000 and 1040nm
showing the local maximum remains at the interface, and is similar for a normalized calculation.
We modeled the electric field strength across the thickness of the device at X=1040nm for varying
thicknesses of both the SWNT and C60 layers, Figure 46. A 70nm C60 thickness shows a maximum
within the SWNT layer near the SWNT/C60 interface, allowing for maximum probability of exciton
generation at spatially-close distances to the interface and hence maximizing dissociation. Other
C60 thicknesses maximize the field further away from the interface. Further, while reducing SWNT
thickness seems to increase the field strength while maintaining a maximum at the interface, we
chose to use 100nm based on reduced surface roughness and lower probably of shorting of devices.
Devices made with 70nm SWNT films shorted in our experiments.
92
Varying SWNT Thickness at 70nm C60
Varying C60 Thickness at 100nm SWNT
-
I
-
10040
100-0
-100-11
-
7- -70
-100-70
130-70
0
0.::
CC
-so
0
so
100
Position
ISO
_200
:20
300
350
in Device (nm)
1 0
Position in
:0
:50
200
%so
Device (nm)
Figure 46 Optical transfer matrix solutions for (left) varying SWNT film thicknesses and (right) varying C6 0 film thicknesses.
The legend shows the values in nm of the SWNT-C60 thicknesses. Dotted lines act as guides to the eye for the boundaries of
each layer. Note for varying SWNT thickness, the boundary line is matched to the legend color.
6.2.5
Electrical Characterization Techniques
Current-voltage measurements were recorded by a Keithley 6487 picoammeter in nitrogen
atmosphere. Devices were tested using 100 mW/cm2 illumination provided by a 150 W xenon arclamp (Newport 96000) filtered to AM 1.5G.
The EQE spectrum was collected using a home built setup. The light sources that were used were a
Xenon arc lamp for the visible to the beginning of the near IR and a Quartz tungsten halogen lamp
for the majority of the near infrared, both supplied by Newport. The light source was sent through a
monochromator and the source is chopped. The monochromatic light is then swept through the
wavelength range of interest and read out through a lock-in amplifier in order ensure that low levels
of signal can be read. The EQE spectrum was found to overlap exactly for the part of the spectrum
read by both detection mechanisms from 900 to 1100nm. The testing facility is kept under a
nitrogen atmosphere in a glove box in order to keep out any contamination similar to that
performed by P.R. Brown et. a 1.113
6.3
Results and Discussion
Performances of seven identically fabricated devices were measured under 100mW/cm 2 AM1.5
illumination to find of V 0c=0.32 0.025V, J 5c=0.76 0.045mA/cm 2. Hence, we calculate FF=0.32 0.029,
and q=0.79 0.15% for our devices. The best device performed at Voc=0.33V, J,,=0.81mA/cm
2
93
FF=0.37, and n=0.10%, Figure 47A. The measured overall efficiency of 0.10% is comparable to
114-116
polymer based photovoltaics where SWNT were added to increase active layer conductivity'
. To
ensure that the SWNTs were contributing to the observed photocurrent, an external quantum
efficiency (EQE) spectrum was acquired using calibrated monochromatic excitation from 300 to
1100nm, Figure 47B. We note that a large part of the photocurrent is contributed by the C 60 layer,
as evidenced by the EQE peaks in the 300-600nm region, a phenomenon which could partially be
due to the creation of a Schottky barrier at the C 60/Ag interface". Importantly, a peak is present in
the near infrared which directly corresponds with the absorbance of the (6,5) SWNT film, Figure
47B, inset. This is the first demonstration of photocurrent response from a SWNT film made of a
single SWNT chirality.
A
-0.8
-
"E-0.6
E
-0.4
-0.2
B 5
Pure (6.5) SWNT
2
1OOmW/cm
Dark
LU0.4
0.3
Voc = 0.33V
FF = 0.37
j = 0.10%
950
1050
Wavelength (nm)
1
0.2
0.1
0.3
0
0
.
.
0.0
0.5
3
Isc = 0.81 mA
0.0
-860
400
600
16o6
Pure (6,5) SWNT
4
Voltage (V)
C
Wavelength (nm)
D
- - -
- -
E
-0. 4
,0
FF = 0.25
q 0.0025%
0.000
0.010
Voltage (V)
ll
80:20 (6,5):(6,4) SWNT
Isc 0.58m
-0. 2 Voc
0.017V
0.
Pure (6,5) SWNT
-
680:20 (6.5):(6.4) SWNT
100mW/cm 2
Dark
-0.
0.020
C1E1
Figure 47 Photovoltaic characterization of polymer-free carbon nanotube solar cell. IV (A) and EQE (B) of pure (6,5) SWNTC-60 device. Inset in (B) emphasizes region corresponding to Eli transition in (6,5) SWNTs. IV characterization of 80:20
(6,5):(6,4) SC-SWNT by weight (C), and schematic representation of the recombination centers introduced when a
semiconducting nanotube film is constructed with multiple chiralities, (D). IV curves shown both under AM1.5 illumination
(red) and in the dark (blue).
94
In order to comment on the importance of monodispersity in SWNT chirality, we constructed
control devices from a film made with 80:20 (6,5):(6,4) semiconducting SWNT by weight. These
devices showed extremely poor performance in Vc, Is,, and fill factor, Figure 47C. Power conversion
efficiency was reduced in this device by over 30 times relative to the device constructed with a pure
(6:5) film. This discrepancy can be explained by the lack of a well-defined uniform bandgap within
the SWNT film and at the SWNT/C60 interface. Because of the presence of (6,4) SWNTs, electron and
hole traps are formed within the carbon nanotube film, serving as centers for exciton
recombination, Figure 47D.
It is important to note that this demonstration of the negative effects of a multi-chirality SWNT
active layer on photovoltaic device performance is relevant because of the SWNT/SWNT junctions
present within a polymer-free device. In their pioneering work, Arnold et. al. demonstrated the first
.
SWNT based photovoltaic using a matrix comprised of polymer, C6 0, and unpurified HiPCo SWNT 5
According to Arnold, in order to fully exploit the potential of SWNTs in photodetectors, the SWNT
must be isolated from each other and paired with semiconductor layers that have the appropriate
energetics for efficiently dissociating SWNT excitons5 . Our finding explains why to this point devices
constructed with a SWNT active layer necessitated polymeric wrappings, as they lacked the single
chirality SWNT material necessary to prevent carrier trapping.
This report of a polymer free carbon nanotube based solar cell represents an important step
forward in the evolution of carbon based photovoltaics. However, in terms of device efficiency,
polymer free SWNT layers are still outperformed by previous reports using SWNT/polymer matrices.
For example, the observed EQE peak efficiency at the nanotube Ell transition, 0.5%, is lower than
other studies which employ SWNTs as the absorbing layer'
3.
We expect improvement of
photocurrent obtained from a completely polymer free SWNT-C 60 device with future optimization. In
fact recent work from our group shows that a vertically aligned single chirality nanotube film can
produce EQE values in the near IR close to 70%.11'
A possible reason for sub-optimal device performance is the use of a SWNT layer that is significantly
thicker than the estimated bulk exciton diffusion length. Many studies have reported the exciton
diffusion length within single nanotubes as hundreds of nm119, 120. However, fewer studies have
investigated the exciton diffusion length through collections of contacting nanotubes. Bindl et. al. 7
reported an approximate diffusion length of 2nm within a nanotube film, however, this value was
determined with the presence of a polymeric wrapping around the nanotubes. Through a reduction
95
of polymeric wrapping, Bindl et. al. report an increase in diffusion length, therefore, we predict
further increase in diffusion length in the limit of a polymer free SWNT film.
However, exciton
diffusion lengths have never been directly measured in single-chirality films of this purity, making it
difficult to approximate the exact value. Elucidation of exciton diffusion lengths in pure SWNT films
will be the subject of future work.
We expect exciton diffusion through the film to largely be governed by exciton hopping mechanisms
and EET. To date, evidence for band-like continuum behavior, akin to observations in quantum dot
superlattices12 ', has not been realized in SWNT films. However, there is recent evidence to suggest
the possibility of excitonic tunneling in nanotube bundles 122 . The exact mechanisms, rate, and
diffusion lengths of excitons in these films will be the subject for future studies.
6.4
Conclusion
An all carbon photovoltaic device has been demonstrated where a film of highly purified (6,5)
carbon nanotubes acts as the active photoabsorption layer. There is evidence to suggest that tight
control over the electronic structure of the SWNTs has enabled a V, higher than previously
demonstrated in other SWNT active layer devices. While the device efficiency is low, it is interesting
to note that it is comparable to many polymer-SWNT bulk heterojunction devices. Only a 20%
impurity by weight of a second chirality of semiconducting SWNT (6,4) results in a more than 30
times decrease in power conversion efficiency. This work provides a foundation for future work
aimed at increasing the efficiency of polymer-free all-carbon photovoltaics via several mechanisms,
including active layer thickness modulation, bulk heterojunction geometries and SWNT alignment.
96
7.
Conclusions
This thesis has advanced the field of single chirality single walled carbon nanotubes, with several key
findings that have been published and cited by several other groups.
The first part of this thesis was aimed at establishing a highly reproducible and scalable method for
separating single chirality SWNT. We established such a process and found that in a single iteration
of the process that we are able to separate out at least 4 different chiralities with high levels of
purity. Specifically, we found that the (7,3) and (6,5) SWNTs are separated at very high purities. We
also discovered at a process level that the separation can be modelled using simple second order
kinetics, dependent only on the number of available sites on the Sephacryl, and the quantity and
rate constants of the SWNTs. Using this model we were able to extract the rate constants of each of
the separated species of SWNT in our system. We find that the rate constants span 6 orders of
magnitude across the chiralities separated using 2% by weight of SDS. This large differentiation in
the rate constants is what enables the separation of various chiralities. The understanding of this
process has enabled us to scale the process up to large volumes, and in this thesis we present a case
of separating 150ml of suspended SWNT in SDS. Other than the equipment and material availability,
this simple demonstration shows that it is possible to scale the separation to arbitrarily large
volumes.
We then went on to interrogate the process further, to understand the underlying cause for the
differences in rate constants based on chirality. We formulate a theory that shows that surfactant
coating on the nanotube surface is the primary driver for the difference in rate constants. SDS forms
a coating on the SWNT and partially dissociates the Na' ion to create a charge on the surface that
acts as a repulsive force against the Sephacryl gel. This charge dissociation is highly dependent on
the coverage of the SDS on the specific (n,m) SWNT. We theorize that lower surface coverage on the
SWNT leads to lower counter-ion dissociation. Hence, the higher the SDS coverage density, the
higher the charge, and the higher the repulsive force against the Sephacryl. We find that this
repulsive force, when compounded with a simple Van der Waals attraction via DLVO theory enables
us to explain the chiral differences in the rate constants. Amazingly, the per length charges needed
to fit the theory to the observed rate constants fall within experimentally relevant ranges as
measured by zeta potential measurements. This implies that the simple electrostatic repulsion
97
model that we develop is both sufficient, and experimentally verifiable to explain the separation
process.
Using the theory that we developed, the first significant observation that we can explain is the
change in chiralities that are adsorbed and eluted as the bulk SDS concentration is changed. As the
SDS concentration is reduced, the surface coverage on a given SWNT reduces, and all of the
chiralities have a greater affinity for the hydrogel. The inverse holds true as well, as we increase the
SDS coverage, the repulsion also increases. As this effect is chirality dependent, at a 3% SDS
concentration, only the (7,3) and (6,5) SWNT show adsorption and elution from the gel. In addition
to having a strong understanding of the impact of SDS concentration, the same theory was used to
explain the need for the centrifugation and sonication times used for the separation process.
Specifically, the theory predicts the need for individual SWNT in the separation process as bundles
effectively increase the SDS coverage and therefor the charge density around the nanotubes. In
order to obtain a high fraction of individual SWNT, it is necessary to sonicate the sample for a long
period of time as well as to centrifuge it a high speeds for long durations.
Upon developing a strong understanding of the separation process of a single surfactant system for
SWNT separation, we interrogated what the effects of using a mixed surfactant system would be.
This thesis provides the first experimental and quantitative analysis of using mixed surfactant
systems to modify and control the hydrogel based separation of single-chirality, single-walled
carbon nanotubes (SWNT). We chose to use bile salt surfactants, sodium cholate, sodium
deoxycholate, and sodium taurocholate. These surfactants were chosen as they are commonly used
to create SWNT suspensions. More importantly, sodium cholate is used in the separation of SWNT
via the density gradient' and 2 phase2 2 methods as described in this thesis. We find that the addition
of up to 2% by weight of sodium cholate or sodium taurocholate enables dramatic changes in the
chiralities that can be eluted and the order in which they elute. Importantly, we not only
demonstrate the isolation of various highly enriched fractions, but also prove that this competitive
binding of surfactants on the nanotube is chirality dependent. This novel understanding will allow
for both novel fundamental surfactant interaction insight, and improved separation procedures in
general, including the hydrogel based method, density gradient ultracentrifugation and the 2 phase
method.
The final chapter of this thesis used the developments of the first part of the thesis that enable the
separation if single chirality SWNT. We use the process to separate large volumes and high purity
98
(6,5) SWNT, which we then used in the first demonstration of a single chirality optoelectronic
device. We fabricated a simple planar heterojunction solar cell, and found that a simple architecture
of electrodes, SWNT and C6 0, was sufficient to get exciton dissociation and create a 0.1% efficient
solar cell. The remarkable finding in the fabrication of the device was that the introduction of just
20wt% (6,4) SWNT reduced the efficiency 40x. We believe this is because of exciton trapping due to
the inhomogeneous band gap. While the efficiency of this system is low, we learned that it is
possible to create a photoactive layer out of nanotubes as long as the electronic properties are
homogenous. Since the development of this device, there have been several other SWNT
6
photovoltaics developed by other groups.6'm-1s Notably a study by the Arnold group verifies our
finding that a single chirality SWNT solar cell can considerably increase the EQE of the cell. We hence
successfully established a strong basis on which future optoelectronic devices can be built.
99
8.
Future Work
Our work has established a basis for two fundamental areas of exploration within single chirality
SWNT exploration. The separation techniques in this work have significantly advanced the field,
however, it is certainly not the final iteration of such a process. An obvious constraint of the current
process is the ability to only separate out highly pure SWNT of two chiralities. There is a lot of work
that has to be done to manipulate the process in order to produce high purity SWNT of several other
chiralities. There is already some progress on this front with the groups of Kataura
and Kappes 96
making advances on the process in recent years. Similarly, the two phase method from the Ming
Zheng group at NIST has shown the ability to isolate several highly enriched fractions of single
chirality SWNT. 23,126
There are several key questions remaining to be answered about the separation process. This thesis
has provided the first quantitative and mechanistic theory to understand the selectivity in the SWNT
separation process. In our model, we fit the effective charge density to prove that the surfactant
charge is in fact a well-supported theory for why we see separation. However, there is still no
understanding of why there is a chirality dependent coverage of surfactant on the SWNT surface.
Current MD simulations still assume that the nanotube is essentially just a metallic rod of low
dimensions (see Figure 48), and hence the majority of the work published in the MD field has been
71
on metallic tubes exclusively. , 127-129
Figure 48: Representative image produced by MD simulations of SDS on SWNT surface, in this case the simulation was
performed on the (6,6) chirality SWNT.7 The simulation is conducted assuming a graphene sheet rolled into the
appropriate diameter, and hence cannot capture semiconducting SWNT behavior.
100
A second major consideration for the gel based method is what enables Sephacryl to discriminate
based on chirality while agarose can only discriminate metallic vs. semiconducting tubes. 50 We find
evidence that it is likely due to the amide group within the gel. However, the specific reason for the
binding is as yet unclear. Understanding the binding with the gel is not only important from a
fundamental perspective, but will also enable the field to create other gels that could potentially be
more discriminating, cheaper and easier to reuse. From this perspective, the two phase method is
easier to understand as it is a simple hydrophobicity argument that enables the separation.
The great benefit of both the gel based and 2 phase methods that are currently being used is that
there the process is naturally scalable to large volumes without the need for much parallel
processing. In fact, the work from this thesis served as the initial basis from which a now commercial
method was produced. The technology was successfully transferred to Nano-C, Inc. in Westwood,
MA and they are able to sell semiconducting nanotubes to customers.
I expect that in the next
few years, the process for purifying single chirality SWNT will reach a level of yield and reliability
that makes the process easy to implement by any group or corporation. I certainly hope that these
efforts will carry forward and that there will be a clearly repeatable way to separate single chirality
SWNT of various chiralities in the next few years.
The ability to separate large quantities of single chirality SWNT will have several important
implications. From a fundamental science standpoint it will enable us to ask basic questions about
nanotubes that have a chirality dependence. The field has already started asking very important
questions about exciton transport between different nanotubes.""3 2 These studies have only been
possible due to the ability to create highly enriched semiconducting nanotube films.
(C)
Figure 49 Schematic of the system studied by the Martin Zanni group of all semiconducting sWNT films.132 The purified
films enabled analysis of (a) intra bundle transport, (b) inter-bundle energy transfer through space, and (c) inter-bundle
energy transfer via diffusion to the crossing point.
101
The next area where further work will be needed is in the development of various applications that
are enabled by the ability to work with large volumes of single chirality SWNT. We showed that for
solar cells, and likely other optoelectronic applications, that it is critical to use single chirality SWNT.
The device fabricated in this work however, is not optimized and has a low efficiency of just 0.1%.
We expect that by optimizing the device architecture, we can improve this by 2 orders of
magnitude, and make SWNT solar cells a competitive material for solar applications. In fact, as noted
in the chapter on solar cell development in this thesis, work from our group has already shown the
ability to obtain EQE values of close to 70% in single chirality SWNT films, as shown in Figure 50."'
Also, the field has moved forward significantly till date, with the Ren group at KU showing a 3%
efficient nanotube based solar cell.1 24 However, the majority of the contribution to the photocurrent
in this system came from the fullerene derivative in the cell. The Arnold group has shown
experimentally that single chirality solar cells have the ability to operate at EQE of 34%.6 In addition
to further work in the solar application, there will likely be more activity in the development of near
infrared light emitting devices. A recent study by a group out of China has demonstrated the ability
to produce a flexible near infrared light emitting device enabled by chirality enrichment.
1000
(1) = 100 nm
400 nm
800 nm
EQE
08
04
0)
03
02
2200
01
02 04 04 08
02
04 06 0
02 04 06 00
Density (fraction of max)
Figure 50 Figure showing the EQE of various SWNT solar cell devices when the SWNT are vertically aligned. The figures
show that with increasing density of the SWNT and increasing average length, it is possible to create solar cells with peak
EQE at close to 70%. 118
The nanotube field has seen a rather consistent interest in building a computer out of carbon
nanotubes where the SWNT act as the transistor material rather than silicon. However, recent years
have shown tremendous progress in realizing
down below the 20nm mark.
ICs13 3
with nanotube transistor channel lengths going
Even though these recent studies are significant developments to
realizing nanotube based computing, the challenge of heterogeneous electronic properties still
102
impairs the efforts that are being put into this work. The ability to work with homogenous
electronic-type, single chirality SWNT will have a major impact on transistor development as there
will no longer be a need to 'burn away' metallic tubes and each transistor will behave the same.
In addition to optoelectronic and electronic applications, single chirality SWNT can enable much
higher sensitivity for applications in biological detection. One such application is the ability to make
ratiometric sensors such that one chirality is wrapped with a corona phase that selectively detects
for a biomolecule of interest, while the other chirality is used as a control within the same
environment. This enables the simultaneous measurement of a control sample within a single
measurement. There is also the opportunity to multiplex measurements, such that each chirality is
selective to a single biomolecule of interest. In this way, simultaneous measurements can be made
of several biomolecules within the same sample or environment. The first proof of this principle will
soon be published by our group.13S
16000
6.5 PVA
4000.
-
-
t=Omn
+-NOt=Sm
+ NOt = 10 min
9 12000
10000
7.6 ss(GT)ls
8000.
z
S4000,
0:2000.
0
950
1000
1050 1100 1150 1200 1250
Wavelength (nm)
Figure 51 Fluorescence spectra showing the (7,6) SWNT quenching upon addition of NO to the system, while the (6,5)
SWNT which has been wrapped with a different polymer has a lower sensitivity to the NO addition. 3 s
Other groups have shown that chirality sorted SWNT have greatly enhanced ability to imagine in
vivo as well as enable efficient laser induced heating for applications such as photothermal
therapy.136 However, these applications in biological detection are just the initial use cases for single
chirality SWNT. It is expected that the use of single chirality SWNT for any imaging platform
previously developed will not only increase the reproducibility of the platform, but also the increase
the precision of measurements. These beneficial effects come as a direct consequence of having
103
homogenous bandgap material within any system. The beneficial effects are already being seen by
projects in our group, the results of which are forthcoming in publications.
With the numerous expected and already observed significant benefits to the use of single chirality
SWNT, there will likely be increased activity in the field. I expect that the application for which
nanotubes are used today will improve significantly in yield, reproducibility and sensitivity, as we
move toward having bulk quantities of homogenous electronic-type carbon nanotubes. Further,
there are several novel applications that have not even been considered in this thesis that could be
enabled by virtue of highly pure nanotube materials.
104
9.
List of Publications
Rishabh M Jain, Kevin Tvrdy, Rebecca Han, Zachary Ulissi, Michael S Strano 'Quantitative Theory
of Adsorptive Separation for the Electronic Sorting of Single-Walled Carbon Nanotubes', ACS
Nano, 2014, 8, 3367
-
Rishabh M Jain, Kevin Tvrdy, Rebecca Han, Andrew J Hilmer, Thomas P McNicholas, Michael S
Strano 'A Kinetic Model for the Deterministic Prediction of Gel-Based Single-Chirality SingleWalled Carbon Nanotube Separation', ACS Nano, 2013, 7, 1779
-
Rishabh M Jain, Rachel Howden, Kevin Tvrdy, Steven Shimizu, Andrew J Hilmer, Thomas P
McNicholas, Karen K Gleason, Michael S Strano 'Polymer-Free Near-Infrared Photovoltaics with
Single Chirality (6,5) Semiconducting Carbon Nanotube Active Layers', Advanced Materials,
2012, 24, 4436
-
Darin 0 Bellisario, Rishabh M Jain, Zackary Ulissi, Michael S Strano 'Deterministic Modelling of
Carbon Nanotube Near-Infrared Solar Cells', Energy &Env. Science, 2014, 7, 3769
-
Olga A Dyatlova, Christopher Koehler, Peter Vogel, Ermin Malic, Rishabh M Jain, Kevin C Tvrdy,
Michael S Strano, Andreas Knorr, Ulrike Woggon 'Relaxation dynamics of carbon nanotubes of
enriched chiralities', Phys. Rev. B, 2014, 90, 155402
-
Thomas P McNicholas, Victor Cantu, Andrew J Hilmer, Kevin Tvrdy, Rishabh Jain, Rebecca Han,
Darin Bellisario, Jiyoung Ahn, Paul W Barone, Bin Mu, Michael S Strano 'Magnetoadsorptive
Particles Enabling the Centrifugation-Free, Preparative-Scale Separation, and Sorting of SingleWalled Carbon Nanotubes', Particle, 2014, 31, 1097
-
Antonio C Brand5o-Silva, Rogerio MA Lima, Cristiano Fantini, Alcenrsio Jesus-Silva, Marcio ARC
Alencar, Jandir M Hickmann, Rishabh M Jain, Michael S Strano, Eduardo JS Fonseca 'Near
infrared nonlinear refractive index dispersion of metallic and semiconducting single-wall carbon
nanotube colloids', Carbon, 2014, 77, 939
-
Qing Hua Wang, Darin 0 Bellisario, Lee W Drahushuk, Rishabh M Jain, Sebastian Kruss, Markita
P Landry, Sayalee G Mahajan, Steven FE Shimizu, Zachary W Ulissi, Michael S Strano 'Low
Dimensional Carbon Materials for Applications in Mass and Energy Transport,' Chem.
Mater., 2014, 26, 172
-
Kyungsuk Yum, Jin-Ho Ahn, Thomas P McNicholas, Paul W Barone, Bin Mu, Jong-Ho Kim,
Rishabh M Jain, Michael S Strano 'A Boronic Acid Library for the Selective, Reversible Near-
105
Infrared Flourescence Quenching of Surfactant suspended Single-Walled Carbon Nanotubes in
Response to Glucose', ACS Nano, 2012, 5, 819
106
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