0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014

-172

-167

-162

-157

-152

-147

-142

Marvin A. Malone Jr.1, Hernan L. Martinez1

1Department of Chemistry, California State University, Dominguez Hills, Carson, CAKenneth R. Rodriguez2, James V. Coe2, and Shaun M. Williams2

2Department of Chemistry, Ohio State University, Columbus, OH

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)

We gratefully acknowledge support from the National Institutes of Health through Grants Numbers:

NIH MBRS RISE R25 GM62252

NIH NIGMS/MBRS SCORE S06 GM08156

Introduction

Motivation

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.

Enthalpy vs. Length: (9,0) zigzag

Methods and Materials

Results:Enthalpy vs. Length: (5,5) armchair

PM3 vs. G3

We calculate the thermochemistry of each SWNTs using normal mode analysis with Gaussian 03 on a Linux Beowulf Cluster.

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).

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.

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.

Bulk Enthalpy versus 1/D2

Acknowledgements

Enthalpy vs. Length: (10,10) armchair

Predicting Bulk Properties by Extrapolating the Energetics of Buckytubes (SWNTs)

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.

0.0 0.1 0.2 0.3 0.4 0.5

nc-1

-250

-230

-210

-190

-170

-150

-130

610 8

4

G3PM3

PM3G3

50

406020

G2

98K

AB

E/n

c (k

cal/m

ol)

mH(g) + nC(g) HmCn(g)

*The plot of the Gibbs Free Energy versus Length for each single-walled carbon nanotube exhibit the same characteristics as the plot of the Enthalpy versus Length. All tubes (open, half-capped and double-capped) converge to the same bulk value for each nanotube {(5,5) (9,0) and (10,10)}.

Conclusions

0.00 0.01 0.02 0.03 0.04 0.05

-170

-169

-168

-167

-166

-165

-164

-163

-162

-161

-160

-159

-158

1/D2

Bu

lk

H29

8KA

BE/n

c (k

cal/

mo

l)

0.00 0.01 0.02 0.03 0.04-180

-170

-160

-150

-140

-130

-120

H29

8KA

BE/n

c (k

cal/

mo

l)

nc-1

-164.22

Hgraphite = -171.23

Hgraphite = -171.23

-164.31

H29

8KA

BE/n

c (k

cal/

mo

l)

nc-1

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007

-172

-170

-168

-166

-164

-162

-160

-158

-156

-154

-152

H29

8KA

BE/n

c (k

cal/

mo

l)Hgraphite = -171.23

-167.28

nc-1

A single-walled carbon nanotube can be described as a graphene sheet rolled into a cylindrical shape so that the structure is one-dimensional 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.

y = 210.03x – 168.69R2 = 0.985

• Semi-Empirical PM3 is capable of producing analogous absolute energetics (i.e. Atomic Binding Enthalpy at 298 K) at bulk to the G3 theory.

• At finite sizes capping each carbon nanotube has a significant effect on the stability of the nanotube, however at bulk the open, half-capped and double-capped nanotubes converge to the same value.

• For the most part, the stability at bulk becomes greater as the diameter of the single-walled carbon nanotube increases.

• 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.

(6,0)

(5,5)(9,0)

graphene

(6,7)(7,7)

(8,8)

(8,9)(10,10)