Predicting Bulk Properties by Extrapolating the Energetics of Buckytubes (SWN
Marvin A. Malone Jr.1, Hernan L. Martinez1
1Department
of Chemistry, California State University, Dominguez Hills, Carson, CA
Kenneth R. Rodriguez2, James V. Coe2, and Shaun M. Williams2
2Department
Motivation
Nanotubes have numerous practical applications in such fields as:
Material science, Chemistry, Biology, Medicine and
Engineering.
Understanding the physical properties of single-walled carbon
nanotubes (SWNTs) allows one the ability to determine which
structures will be more stable at bulk (infinte length)
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60
40 20
50
10 8
 All of the data is subsequently used to compute the energetic
values of interest to us (this calculation is done using a Mathcad
template designed for this purpose). A data fit analysis then
follows to obtain the bulk properties as an extrapolation when the
size of the SWNT goes to infinity.
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Hgraphite = -171.23
(6,0)
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(5,5)
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(9,0)
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(6,7)
(7,7)
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(8,8)
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y = 210.03x – 168.69
R2 = 0.985
(8,9)
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graphene
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4
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0.000
0.002
0.004
0.006
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0.008
0.010
0.012
0.014
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0.01
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0.03
0.04
0.05
1/D2
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PM3
G3
Enthalpy vs. Length: (10,10) armchair
Conclusions
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• Semi-Empirical PM3 is capable of producing analogous absolute
energetics (i.e. Atomic Binding Enthalpy at 298 K) at bulk to the G3
theory.
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PM3
G3
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0.1
0.2
0.3
0.4
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0.5
nc-1
Results:
Enthalpy vs. Length: (5,5) armchair
H298KABE/nc (kcal/mol)
 We obtain the heat of formation, the corrections for the H, G,
and ZPE, as well as the ZPE of each molecule and atom from the
Gaussian output.
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Methods and Materials
 We are using the semi-empirical PM3 method to do frequency
calculations on each SWNT (using the flags: # int=pm3 opt
freq=numer to ensure calculation culmination).
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 We calculate the thermochemistry of each SWNTs using normal
mode analysis with Gaussian 03 on a Linux Beowulf Cluster.
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Bulk H298KABE/nc (kcal/mol)
mH(g) + nC(g) HmCn(g)
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H298KABE/nc (kcal/mol)
Ab-intio G3 is one of the best theoretical methods available for use
when calculating absolute energetics. Unfortunately, G3 is a very
stringent method which takes a long time to calculate the
thermochemistry of small molecules. Use of such a method with the
size of molecules that we use in this project would be
computationally demanding. Fortunately, Rodriguez et. al, have
performed a comparison of G3 and PM3. Their figure shows that
although at finite sizes G3 is better than PM3, PM3 is comparable to
G3 at infinity.
Objective
The goal of our project is to determine the atomic binding enthalpy
of formation and the atomic binding free energy at 298K. We do
this on a per carbon basis for each nanotube at finite size and then
extrapolate those thermochemical quantities to infinite length to
determine the bulk energetic values for each nanotube.
Bulk Enthalpy versus 1/D2
Enthalpy vs. Length: (9,0) zigzag
H298KABE/nc (kcal/mol)
A single-walled carbon nanotube can be described as a graphene
sheet rolled into a cylindrical shape so that the structure is onedimensional with axial symmetry. Since their discovery in 1990 by
S. Iijima, scientist have been very interested in exploring this unique
form of carbon. In doing so researchers have discovered that
single-walled carbon nanotubes have interesting physical, chemical
and mechanical properties. The three types of single-walled carbon
nanotubes are: armchair, zigzag and chiral. Each type is based on
n and m character indexes. For the armchair, n equals m, for all
positive integers. For the zigzag, n equals a positive integer and m
must be equal to 0. For the chiral, n and m can be any combination
of positive integers as long as they don’t satisfy the rules for the
armchair or zigzag.
PM3 vs. G3
G298KABE/nc (kcal/mol)
Introduction
of Chemistry, Ohio State University, Columbus, OH
• At finite sizes capping each carbon nanotube has a significant effect
on the stability of the nanotube, however at bulk the open, halfcapped and double-capped nanotubes converge to the same value.
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• We are still in the process of studying the parameterization of bulk
energetics based on n and m, but with an R2 value of 0.985 the
results seem very promising.
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• For the most part, the stability at bulk becomes greater as the
diameter of the single-walled carbon nanotube increases.
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0.000
Hgraphite = -171.23
0.001
0.002
0.003
0.004
0.005
0.006
0.007
Acknowledgements
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We gratefully acknowledge support from the National Institutes of
Health through Grants Numbers:
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*The plot of the Gibbs Free Energy versus Length for each single-170
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0.00
Hgraphite = -171.23
0.01
0.02
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0.03
0.04
walled carbon nanotube exhibit the same characteristics as the plot of
the Enthalpy versus Length. All tubes (open, half-capped and doublecapped) converge to the same bulk value for each nanotube {(5,5)
(9,0) and (10,10)}.
NIH MBRS RISE R25 GM62252
NIH NIGMS/MBRS SCORE S06 GM08156