OXYGEN DISSOCIATION ACROSS A BORON-DOPED CARBON NANOTUBE:

FUEL CELL CATALYSIS

By

Matthew Creed Powell

This paper is submitted in partial fulfillment of the requirements of the Honors Program with the Department of Chemistry and Biochemistry.

Examining Committee Approved By:

__________________________ _____________________________

Dr. Hee-Seung Lee Dr. Hee-Seung Lee

__________________________ Faculty Supervisor

Dr. Gabriel Lugo

__________________________

Dr. Michael Messina

_____________________________

Department Chair

_____________________________

Honors Council Representative

_____________________________

Director of Honors Scholars Program

University of North Carolina Wilmington

Wilmington, North Carolina

May 2012

1

Acknowledgements

First and foremost, I would like to thank Dr. Hee-Seung Lee for presenting me

with this distinctive opportunity. Without his guidance and patience this would not have

been possible. Also I would like to thank my committee members, Dr. Gabriel Lugo and

Dr. Michael Messina, for their support. I owe gratitude to my honors liaison, Dr. Antje

Almeida, for coordinating and organizing this program. Finally, I would like to thank my

family and friends for their unrelenting moral support. Without any of these people, this

pressing research would not have been possible.

2

Table of Contents

Abstract……………………………………………………………………………………

3

I. Introduction……………………………………………………………………

4

II. Computational Method……………………………………………………….

12

A. Electronic Structure Calculation…………………………………………

12

B. Nudged Elastic Band Method…………………………………………….

13

C. Computational Details…………………………………………………….

15

III. Results and Discussion………………………………………………………...

16

3

A. Convergence Test………………………………………………………….

16

B. Band Structure And Density of State Calculation………………………

18

C. Oxygen Adsorption………………………………………………………..

21

D. Nudged Elastic Band Calculation………………………………………...

25

E. Atom Projected Density of State…………………………………………

36

IV. Conclusion……………………………………………………………………..

36

References……………………………………………………………………………..

38

4

ABSTRACT

In recent years, we have witnessed the catalytic effect of doped, single walled

carbon nanotubes (SWCNTs) on the reduction of oxygen in regards to the proton

exchange membrane fuel cells (PEMFC). This is achieved by providing a surface on

which diatomic oxygen can bind and subsequently dissociate. In this thesis, we explore

the catalytic ability of a boron-doped (5, 5) SWCNT (B3SWCNT)computationally. To

understand the cooperative effect of boron, one of the CNT hexagons (C6) is replaced by

C3B3 and an oxygen molecule is placed nearby. In achieving optimized product and

reactantstructures, a series of density functional theory (DFT) calculations were

performed. With geometrically optimized structures, four different product structures are

considered and possible minimum energy reaction paths are estimated via the nudged

elastic band (NEB) method. Of the reaction paths obtained, an average activation barrier

of 1.01 eV was calculated. The most favorable reaction path has the activation barrier of

.505 eV. This activation barrier is not only much lower than that of a pristine (5, 5)

SWCNT, but it is also lower than the previous result with one boron atom. This may

imply that higher boron density facilitates oxygen dissociation. Lowdin population

analysis shows that the oxygen molecule appears to be in a reduced state, resembling an

5

O2- configuration while in the reactant(chemisorbed) state. Molecular oxygen acquires

this electron density from the boron atoms in the (5, 5) B3SWCNT. This finding is

consistent with the notion that reduced form of oxygen is much more reactive than

molecular oxygen.

I. Introduction

The proton exchange membrane fuel cell (PEMFC) is an understudied energy

source that holds the potential to augment the planet’s energy and environmental crises.

If the subject of the PEMFC is pursued, large scale implementation could radically

reduce environmental and health hazards, along with greatly reducing earth’s dependence

on conventional energy systems. Advanced application could potentially revolutionize a

wide range of energy systems, ranging anywhere from personal electronics to

automobiles. Unfortunately, current application of the PEMFC lacks efficacy due to an

array of component inadequacies. This, with possible economic factors, has led to

diminished research and application of the PEMFC since its dawning in the 1960’s.

In the most basic form, the PEMFC works by oxidizing hydrogen and reducing

oxygen to produce water. The operational mechanism of PEMFC is described

schematically in Fig. 1. Hydrogen oxidation [Eq. (1)] takes place on an anode and oxygen

is reduced on the cathode [Eq. (2)]. These two equations represent general fuel cell redox

reactions. Protons are transferred via membrane from anode to cathode, producing H2O,

and resulting in a 2 to 4 electron transfer depending on intermediates and oxidizing

6

species.1 The most widely used membrane for a PEMFC is Nafion (Dupont). Nafion is

desirable mostly because of its high proton conductivity.2

H2 → 2H+ + 2e-(1)

(½)O2 + 2H+ + 2e- →H2O (2)

Figure 1.This is a schematic of a typical PEMFC. Note that a precursor to the reaction is dissociation of H2 and O2.3

Each of the redox reactions are facilitated with the aid of a metal catalyst such as

platinum (Pt). Originally designed for the Apollo Lunar Missions, platinum loaded

carbon is recognized as the predominant fuel cell redox catalyst. Figure 2 below displays

7

the implementation. Unfortunately, platinum catalyst efficiencies are rather low, ranging

from 20% to 30%.

The low efficacy is a product of many factors; one problem being platinum’s

strong affinity for carbon monoxide (CO). This is known as CO contamination. CO

contamination is a result of substantial d-π back bonding that takes place between Pt’s d-

orbital and CO’s π orbital. The permanent occupation of a Pt coordination site by CO

greatly reduces the likelihood of reactant species experiencing redox catalysis by

platinum. Consequently, the PEMFC experiences time dependent drift, which is, a steady

decrease in efficiency throughout its lifespan. Also, not all of the platinum is exposed to

the reactants because it is clumped in a disorganized manner on the carbon support.4

These factors, combined with the high cost of rare metals, render platinum loaded carbon

impractical for wide scale usage. Fuel cell redox catalysis is the focus of this research,

more specifically, the oxygen reduction reaction catalysis.

Figure 2.Platinum catalyst dispersed across a carbon support. The disorganized fashion in which the platinum catalyst is applied contributes to some of the PEMFC’s shortcomings.4

8

Recently we have seen that carbon nanotubes (CNTs) show great potential for

being a feasible catalyst support system.5-15They appear to be more mechanically and

chemically stable than a conventional carbon support system, possess high electric

conductivity, lack cracks, and have larger surface areas. Also, the activity of the CNT

allows for doping. Doping allows for other reactive elements to be covalently bonded to

the CNT surface which greatly alters the chemistry of the system. These factors make

CNTs an appealing alternative for carbon black support in PEMFCs.

The carbon nanotube is essentially an infinite hexagonal carbon network that is

rolled cylindrically. They are synthesized by various techniques; direct-current arc

discharge, laser ablation, thermal and plasma enhanced chemical vapor deposition (CVD)

and recently developed self-assembly of single crystals of SWCNTs, are among the most

popular methods.16,17

A carbon nanotube can be rolled differently to create varied chirality. The

manner in which graphene sheets are formed determines their types of activity. Figure

3displays different conformations of CNT’s and figures 3 and 4 display rolling

strategies.CNTs possess variable conducting properties (ranging from metallic to

moderate band-gap semi-conductors). This unique property comes from the manner in

which the graphene sheet is rolled. Typically, nanotubes are specified by tube diameter,

d, and chiral angle, θ. Chiral vector, Ch is the line that connects two crystallographically

equivalent positions, O and C, on a graphene sheet. Ch is determined by translation

indices n and m and their effect on basis vectors a1 and a2.

9

Ch=na1 + ma2 (3)

The zigzag CNT is characterized by having a chiral angle, θ, is measured

between the chiral vector Ch with respect to the zigzag direction (n,0), where θ=0 and

contains unit vectors a1 and a2. Armchair nanotubes have chiral angle, θ=30°, and has

translation indices (n,n). The other forms of nanotubes are defined as a pair of different

indices (n,m). Slight changes of these parameters can lead to varied chemical properties.

Thezigzag CNTs are semiconducting and the armchair CNTs are metallic.18,19The helical

CNTs have demonstrated ferromagnetic properties and display high magnetization at

room temperature.20Figure 5 shows the two main classes of carbon nanotubes: single-

walled and multi-walled carbon nanotubes (SWCNT and MWCNT).

Figure 3.The chiral vector O⃑Cor Ch=na1+ma2 is defined on the hexagonal lattice of carbon atoms (a graphene sheet) by unit vectors a1 and a2 and the chiral angle θ with respect to the zigzag axis, i.e. (n,0).19

10

Figure 4.This figure displays different ways to roll a graphene sheet to produce variable chirality.19

a) b)c) d)

Figure 5.The above figure displays different CNT conformations. From left: SWCNTs a) armchair, b) zigzag, c) helical, and d) MWCNT.21

11

Figure 6.Purified CNT’s, synthesized by chemical vapor deposition (CVD).22

Platinum-doped CNTs have been utilized successfully in lab settings to produce

higher efficiencies, but the fact that they rely on expensive metals renders them a less

feasible catalyst.6 Also, the platinum-doped CNTs are subject to CO contamination

which can become a serious setback in the lifespan of a PEMFC. With this, exploration

into the usage of nonmetal catalyst is essential. Nitrogen and boron are electronically

similar to carbon and can replace carbon in the CNT, leaving the CNT structure intact but

altering the chemistry significantly.

In the nitrogen doped system, nitrogen changes the chemical bonding

environment and is capable of increasing the binding energy of diatomic oxygen.10

Oxygen can bind to either nitrogen or carbon but quantum mechanical calculations

suggest that the carbon atoms adjacent to the nitrogen respond to the nitrogen’s

12

electronegativity with a relatively high positive charge density. With this, it is

understood that redox cycling reduces carbon which invites adsorption of diatomic

oxygen to return to a formal oxidation state.15

In this thesis, we investigate the possibility of using boron-doped (5, 5) single-

walled carbon nanotubes (B3SWCNTs) as a catalyst. More specifically, we studied the

effect of boron-doping on the oxygen reduction reaction (ORR) computationally via

density functional theory (DFT). Structure design and doping sites play a critical role in

the overall efficacy; subsequently the aim of this research is to manipulate the boron-

doped SWCNT to improve catalytic effect on the ORR and eliminating the use of

precious metal catalyst.

The mechanism for oxygen dissociation across a doped CNT can be classified by

three major steps. These steps include physisorbtion, chemisorbtion, and dissociative

adsorption. The first phase is a physisorbtion. In the physisorbed state, the oxygen-

oxygen bond is largely intact but interaction between diatomic oxygen and the nanotube

is apparent. Next is the chemisorbed state. As diatomic oxygen moves closer to the

nanotube, the oxygen-oxygen bond weakens. Finally, dissociative adsorption occurs

after overcoming the reaction barrier and molecular oxygen dissociates into single

oxygen atoms.10,11,23

To understand the detailed ORR mechanism on B3SWCNTs, we performed

nudged elastic band (NEB) calculations and the minimum energy paths toward the

possible ORR products were investigated. The barriers for the ORR on B3SWCNTs are

compared with those on pristine CNTs and the CNTs with low-level boron doping.

13

II.Computational Method

Actively pursuing a high efficiency B3SWCNT requires a fundamental

understanding of the system’s catalytic activity as the electrode reaction takes place. To

achieve this, computational and theoretical investigation is necessary. Computational and

theoretical data have been achieved for a single boron atom doped to a SWCNT but never

with a boron cluster (B3) integrated into the SWCNT.15With this, promise of increased

catalytic activity is anticipated.

A. Electronic Structure Calculations

All electronic structure calculations were done within the framework of density

functional theory (DFT). In DFT, energy is a unique functional of electron density, which

is defined as

n ( r⃑ )=∑i=1

occ

|φi( r⃑)|2 (3)

whereφ i are electron orbitals that are derived from the Kohn-Sham equation. The

abbreviation, occ, represents all occupied electron orbitals. The Kohn-Sham equation is

provided below,

(−12∇2+V KS ( r⃑ ))φ i ( r⃑ )=εi φi ( r⃑ ) (4)

where VKS(r) is the Kohn-Sham potential that produces the same electron density for

Kohn-Sham system as the real system. If electron density is known from KS equation,

total energy can be calculated. The energy functional in the Kohn-Sham (KS) DFT

scheme is given by

14

E [n(r⃑ )]=T s [n( r⃑)]+∬d r⃑ d r⃑ n ( r⃑ )n( r⃑ ')r⃑− r⃑ ' + Exc [ n ]+∫ d r⃑V ext ( r⃑ ) n(r⃑ ) (5)

where , n( r⃑) is the electron density, E [n(r⃑ )]is the total energy of the system, T s [n(r⃑ )]is

the kinetic energy of all electrons in the system, V ext ( r⃑ ) is the external potential due to

nuclei, r⃑ is the position vector of the electrons, and E xc [n ] is an exchange-correlation

functional that is designed to account for electron correlation effects and remaining

quantum effects. The ∬d r⃑ d r⃑ n ( r⃑ )n (r⃑ ')r⃑−r⃑ ' term represents electron-electron interactions

and the ∫ d r⃑ V ext ( r⃑ ) n(r⃑ ) accounts for electron-nuclei interactions. Both of these

interactions are Coulombic in nature.25,26

B. Nudged Elastic Band Calculations

Nudged Elastic Band (NEB) calculations were performed to predict minimum

energy reaction paths for ORR between products and reactants. The minimum energy

path, MEP, resides on a potential energy surface (PES). Figure 7 is an image of a PES.

The reactants and products are located in local minimums and are separated by an energy

barrier of some degree. To begin NEB calculations, product and reactant structures are

required and they were obtained from standard geometry optimization calculations. Once

the reactant and product structures are determined, intermediate structures (called

images) are estimated based on the structures of reactants and products. The structure of

each image is then optimized so that it falls on the MEP as is depicted in Figure 7.

15

Figure 7.Initial and product locations rest in local minimums on the potential energy surface (PES). NEB images are geometrically optimized by the perpendicular force, and pushed up to the MEP.24

The following force is important to the geometry optimization in NEB.

�∇V ( x ( s) )=τ (s) ⟨τ (s)|∇V ( x (s ) ) ⟩+τ (s)⊥ ⟨ τ (s)⊥|∇V ( x (s ) )⟩ (6)

Force is given by the gradient of the potential, ∇V . The reaction coordinates, s, are

designated in such a way thats=0 representsthe reactant and s=1represents the product.

The actual coordinates are defined by x (s ) for a given s value and τ (s) indicates the

direction of the minimum energy path (MEP). The force parallel to the MEP constitutes

the τ (s) ⟨ τ (s)|∇V ( x (s ) ) ⟩ portion of the equation and the perpendicular force is given by

τ (s)⊥ ⟨ τ (s)⊥|∇V ( x ( s ) ) ⟩. To ensure that each image falls on the true MEP (not global

minimum such as reactants or products locale) geometry optimization of each image is

16

carried out in the direction perpendicular to the MEP. With this, calculating only the

perpendicular force is required. When the perpendicular component of the force equation

equals 0, convergence has been reached.

�∇V ( x ( s ) )−τ (s ) ⟨ τ (s )|∇V ( x ( s )) ⟩=0 (7)

To prevent images from clumping on the MEP it is necessary to apply an artificial

spring force between subsequent images. The following equation demonstrates this

fundamental process.

F̂ i=−∇V ( x (s ) )+τ ( s ) ⟨ τ (s )|∇V ( x (s ) ) ⟩+τ ( s) ⟨ F̂is|τ (s ) ⟩ (8)

In this instance, F̂ i is the force on image i. Recognizably, the term

−∇V ( x (s ) )+τ ( s ) ⟨τ (s )|∇V ( x (s ) ) ⟩ is the perpendicular force contribution and τ ( s ) ⟨ F̂is|τ (s ) ⟩

is the spring force along the MEP.25,26

C. Computational Details

All calculations were performed with the QuantumEspresso package27. We chose

Perdew-Wang91exchange-correlation (XC) functional and Vanderbilt ultra-soft

pseudopotential.28,29This combination of XC functional and pseudopotential has been

used in many studies of metal doped CNT systems. The energy cut-off and cell size were

optimized to ensure the convergence (see Sec. III.A). We used periodic boundary

condition with an orthorhombic super-cell accommodating 6 unit cells of (5, 5) SWCNT

(total 120 carbon atoms), where three carbon atoms are replaced by boron atoms. The

convergence threshold for geometry optimizations (including NEB) was 4.0x10-

4hartree/bohr.

17

III. Results and Discussion

A. Convergence Test

All of the calculations were performed on a six unit cell (5,5)-SWCNT. A

pristine (5-5)-SWCNT unit cell has 20 carbon atoms. The CNT system under

investigation has 120 atoms, three of which are boron atoms spaced one carbon away

from each other, forming a boron cluster. Figure 8 shows the optimized structure of boron

doped CNT studied in this work (B3SWCNT) with an optimized energy of -1352.111 Ry

(Rydbergs). Periodic boundary conditions were applied to simulate an infinitely long

system despite using a limited cell size in the present study.

Figure 8.Geometrically optimized, (5, 5) BSWCNT with integrated boron cluster (E=-1352.111 Ry) .The blue areas are boron atoms and the green portion represents carbon atoms.

18

To begin, it was necessary to determine optimal calculation parameters through a

series of convergence tests. The total energy dependence on the energy cutoff was

necessary to determine the number of basis functions required to expand each orbital.

The following equation defines this process.

φ i=∑i=1

❑

C iΨ i(r⃑ ) (9)

The term φ i, are electrons orbitals as seen in Equation 1. Expansion coefficients

are given by C i , and Ψ i are basis functions. An energy cutoff of 25 Ry was determined

by this method as is shown in Figure 9. This value stands as a compromise between

accuracy and computational cost.

Figure 9.Total energy dependence with respect to energy cut-off (Ry)

19

An orthorhombic supercell large enough to avoid any serious interaction with the

periodic image was necessary. The dimensions a=b=20 Å were used and the c axis was

determined by a convergence test. To determine optimum cell size along the c-axis, a

convergence test was achieved by varying cell size and performing geometric

optimization calculations on each variation. Figure 10 shows the total energy as a

function of cell size along the c-axis. From the graph, it was possible to deduce the

optimal cell size of 14.887 Å with the total system energy of -1352.111 Ry.

Figure 10.Total energy variation with respect to the cell-size (length of c-axis).

B. Band Structure and Density Of State Calculations

Armchair CNTs exhibit metallic properties which may play a role in their

catalytic activity in regards to possessing the ability to pass electrons. With this, it is

20

necessary to use (5, 5)-CNTs to retain electrical conductivity after boron-doping. Band

structure calculations were performed to investigate and compare the electronic

properties of boron-doped systems. Figure 11 shows the band structure of a pristine (5,

5)-SWCNT and a singly doped SWCNT 15, whereas Figure 12 shows the band structure

of the B3SWCNT studied in the present thesis. The Fermi level is set to 0 in band

structure plots. For the pristine CNT, there is the characteristic band crossing at the Fermi

level, representing π(occupied) and π¿(unoccupied) bands from the non-bonded

p-orbitals of carbon. The lack of a band gap is evidence of the metallic character of

pristine (5, 5)-CNT.

As shown in Figure 11, the boron doping with a single boron atom appears to

have minor effect to the overall metallic nature. When one boron atom is doped to the

SWCNT, the characteristic π-π* band crossing is still largely intact, only to be pushed up

a little due to the introduction of new boron-related bands below Fermi level. On the

other hand, the addition of the boron cluster appears to have more serious impact on the

electronic properties of CNT. This data is shown in Figure 12 along with a density of

state plot (DOS).The system is still metallic since there is no band gap at the Fermi level.

Therefore, despite the band structure shift at the Fermi level, B3SWCNT can still conduct

electricity. However, the π-π* band crossing is largely missing in the band structure of

boron cluster doped CNT. This is probably due to the broken mirror symmetry in the

system. The DOS plot is used to represent the low population of electrons around the

Fermi level.

21

Figure11.Band structure calculation of pristine (5, 5) SWCNT (left) and boron-doped (5,5) SWCNT. Note the band crossing at the Fermi level. These figures exhibit metallic systems.15

Figure 12.Band structure (left) and DOS (right) plots. The presence of band crossing at the Fermi level shows that the addition of 3 boron atoms does not alter the metallic nature of the (5,5) SWCNT.

22

C. Oxygen Adsorption

Necessary to the finding the minimum energy paths were optimized structures of

products and reactants. Extensive search for the possible chemisorbed, physisorbed, and

dissociative adsorption structures was performed for the ORR on the (5, 5)-B3SWCNT.

The geometry optimizations of each structure lead to their lowest energy configuration.

Some of the optimized images are displayed below.

The physisorbed configuration can be described as a weak Van Der Waals

attraction that takes place between the B3SWCNT and the molecular oxygen adsorbate.

In this stage the covalent bond between molecular oxygen is virtually undisturbed.

Evidence of this is in Figure 13. In structure a, the oxygen-oxygen (O-O) bond length is

1.237 Å, which suggests that this bond is unaltered. This compares closely to a literature

value of 1.21 Å for diatomic oxygen.30As expected from the physisorbed nature of O2 -

B3SWCNT interaction, the oxygen-boron (O-B) distance for the structure a is very large

(3.393Å).

a. E = -1416.0551 Ry b.E = -1416.0551Ry c. E = -1416.0355Ry

Figure13. This figure lists some possible physisorbed states for an oxygen across a (5, 5) B3SWCNT. The green atoms represent carbon, blue atoms are boron, and the red atoms are oxygen. Their ground state energies are included.

23

In the chemisorbed configuration, the oxygen-boron bond distance has decreased

to the point of exhibiting covalent behavior. Also, the O-O bond distance is increased

which indicates the beginning of the dissociation of molecular oxygen. Figure 14 depicts

three of the many chemisorbed images generated for this study. The O-O bond length is

1.462 Å for the structure d and 1.317 Å for structure f. This proves that the O-O bond

has weakened and is beginning to dissociate. Note that structure d has both oxygen atoms

bonded to boron, whereas only one oxygen atom is bonded to boron in structure f. The

boron-oxygen bond distance has also decreased dramatically from the physisorbed state,

to the point of exhibiting covalent behavior. They have decreased from ~3-3.5Å to ~1.5-

1.7 Å. To estimate the strength of O2 – B3SWNCT interaction, the binding energy of O2

was calculated using the equation below.

Eb=E (O2−B3 SWCNT )−E (O2 )−E (B3 SWCNT ) (13)

In this equation, Eb represents the binding energy of O2 and E(O2-B3SWCNT) is

the total energy of the optimized B3SWCNT with O2 adsorbed to the surface. E(O2) and

E(B3SWCNT) are the energies of diatomic oxygen and B3SWCNT, respectively. The

binding energy for a chemisorbed state, using structure f as the final optimized

B3SWCNT-O2, was determined to be 0.18 eV, which is rather small. However, this is

significantly larger than the binding energy of oxygen toward the SWCNT with single

boron doping.15The partial (or projected) density of state (PDOS) calculated reveals that

the spin state of chemisorbed oxygen in structure f is still triplet. It is well known that

molecular oxygen (3O2) does not bind to pristine SWCNT at all and the interaction of

triplet oxygen is physisorption at best. Therefore, it is important to observe that boron

24

doping promotes oxygen binding, which is the necessary first step toward the oxygen

dissociation.

d. E = -1416.0815 Ry e. E = -1416.0616 Ry f. E = -1416.0645Ry

Figure 14.Possible chemisorbed states for the (5, 5) B3SWCNT.

The binding energy of chemisorbed oxygen in structure d is even higher, 0.41 eV,

with both oxygen atoms bonded to boron. It is interesting to note that the spin state of

oxygen is no longer triplet, but it is singlet. It is well documented that triplet-singlet

transition is highly desirable for molecular oxygen to dissociate. Therefore, it is expected

that structure d is one of the possible intermediate structures toward complete

dissociation of oxygen.

Figure 15 and 16 show some potential dissociative adsorption states. The O-O

bond is completely broken and the two oxygen atoms are each bound to a carbon and

adjacent boron. These products were designed intentionally by placing individual oxygen

atoms on the nanotube before any geometric optimization calculation took place.

Geometry optimizations ensued and of the products, Figure 16 displays the most stable

with a total energy of -1416.4057 Ry. For this product, the O-O bond distance is 2.724

Å, the O-B distance is 1.434 Å, and the O-C (oxygen-carbon) bond distance is 1.383Å.

25

These O-O bond distances ensure the oxygen bond is broken. Also, the O-B and O-C

bond express the covalent bonding of oxygen to the B3SWCNT surface. In all of the

products, oxygen adsorption breaks a carbon-boron (C-B) bond and inflicts variable

forms of distortion on the entire system.

g. E = -1416.2510 Ry h. E = -1416.2492 Ry i. E = -1416.3250 Ry

Figure 15.Eligible dissociative adsorption states for the (5, 5) B3SWCNT-O2 (products).

j. E = -1416.4057 Ry

Figure 16.Most favorable product (most stable, lowest energy, dissociative conformation) for the (5, 5) B3SWCNT-O2.

26

D. Nudged Elastic Band Method.

The mechanism of the oxygen reduction was thoroughly studied using Nudged

Elastic Band Method (NEB). It is accepted that oxygen reduction on a platinum catalyst

fuel-cell electrode occurs via two parallel reaction pathways.1 Equation 14 displays the

more efficient and more prevalent, four electron transfer.

4 e−¿+4 H+¿+O2→2 H 2O ¿ ¿ (14)

The less frequent and less efficient pathway is the two electron transfer [Eq. 15]. As you

can see in Figure 15 below, hydrogen peroxide is a byproduct instead of water.

2 e−¿+2H +¿+O2 →H 2O2 ¿¿ (15)

Faradaic efficiency gauges the efficiency of electron transfer in an

electrochemical system. The four electron transfer is preferred over the two electron

pathway due to having a higher Faradaic efficiency and a more favorable byproduct

(water).1 The above reactions [Eqs. 14-15] represent the entire fuel-cell redox reaction but

the reaction mechanism actually occurs by a series of elementary steps. One of these

steps, critical to the present study, is the dissociation of surface bound molecular oxygen

across the (5, 5) B3SWCNT [Eq. 16].

O2→ O+O (16)

Detailed understanding of the mechanism was pursued using NEB calculations.

NEB calculations are used to determine the minimum energy path (MEP) between

product and reactant. With this data, it is possible to determine details including

activation energy (Ea), transition state, and stable intermediate structures and their relative

energies. Each NEB calculation involved 12 images. Images 1 and 12 were

geometrically optimized reactant and product, respectively, and the calculation generated

27

10 intermediate structures. The amount of intermediate images used for this research was

determined as a compromise between the desire for maximal mechanistic information

and minimal computational cost. In addition to typical NEB, we utilized the climbing

image (CI-NEB) setting to improve the activation energy accuracy. This is accomplished

by pushing likely transition states to the top of the energy barrier by applying a spring

force to each image.

To begin, a selection of reactant-product pairs had to be made out of the

previously geometrically optimized structures discussed in Sec III.C. The favored

combinations of product and reactant structures were chosen based on stability and the

necessity of the product being lower in energy than the reactant. Also, to balance the

desire for as much mechanistic information as possible with computational cost, the

reactant was chosen by being chemisorbed with one oxygen to the (5, 5) B3SWCNT.

This reactant image is preferred because it is more general and could potentially lead to a

wide array of products. For these reasons, structure f, in Figure 14 is the reactant of

choice for each of the four products considered in this work.

The dissociative adsorptions states in figures 15 and 16 (g, h, i, and j) were

selected to be the products based on their stability. Figure 17 is a general outline of the

four NEB product/reactant pairs included in this work. Path I, II, III, and IV correspond

to g, h, i, and j from figures 15 and 16, respectively. Figure 18 shows the schematic

representation of the core of structure f with key atoms labeled. This will help to put

MEP explanations into perspective.

28

Figure 17.This figure displays the reaction paths analyzed by NEB calculation along with the overall change in energy (ΔE). The reactant corresponds to structure f in Figure 12, and each of the products is shown as structures g, h, i, and j in figures 14 and 15.

Figure 18.A schematic of the boron cluster and oxygen molecule in the structure f

29

The first path under investigation was Path I. To begin, diatomic oxygen rotates

counterclockwise until the Oj-Oi bond is parallel to the B1-C1 bond. The Oj-Oi bond

breaks and Oj bonds to C1. Subsequently, Oi bonds to C3 and Oj bonds to B2. First the B2-

C1 bond breaks, then the B1-C3 bond breaks. Figure 19 displays the NEB results with Ea=

2.1 eV and a transition state (TS) at image 7 that had an energy of -1415.910 Ry. When

reviewing the transition state it apparent that the O-O bond is broken with an atomic

distance of 1.84 Å. After the transition state, the reaction declines steadily to completion

without any stable intermediate structure.

30

(a)Ea= 2.1 eV

(b)

Figure 19.(a) Energy profile for the MEP for Path I. The activation energy for Path I is Ea = 2.1 eV, (b) Transition state structure for Path I (image seven on the MEP). Oxygen bond is broken expressing an O-O bond distance of 1.84 Å.

31

Path II was the only paththat rendered evidence of a stable intermediate state

after the first of two transition states. In Path II, the Oj-Oi bond rotates slightly

counterclockwise, orienting Oj closer to B3. The Oj-Oi bond elongates and breaks. Oj

bonds to B3, this temporary bond facilitates Oj’s jump to C2. Meanwhile, Oi bonds with

C3 and the C3-B1 bond breaks. Finally, Oj bonds also with B2 and the C2-B2 bond breaks.

The first TS had an energy of -1416.008 Ry and is shown in Figure 20, (b)(image 4 on

the MEP). Figure 20, (c) and (d), are the stable intermediate and the second TS,

respectively. The O-O bond length of first TS structure is 1.41 Å which shows that it is

largely intact but experiencing a bond lengthening. The stable intermediate, Fig. 20(c)

(image 8), has and energy of -1416.097 Ry and the O-O bond length is2.79 Å (broken).

Also The second TS (image 9), Fig. 20(d), has an energy of -1416.100 Ry, and

requires .086 eV from the stable intermediate to complete the reaction. Figure 20(a)

displays this overall MEP with an Ea = 0.88 eV.

32

(a) Ea= 0.88 eV

(b)(c) (d)

Figure 20.(a) Energy profile for the MEP for Path II. The structures of first transition state (a), a stable intermediate (b), and the second transition state (c), are also shown.

33

(a)Ea= 0.62 eV

(b)

Figure 21.(a) Energy profile for Path III with the activation barrier of 0.62 eV(b)The image of the transition state.

34

Figure 21 displays the results from Path III. To start, Oj-Oi leans toward B3 and

the Oj-Oi bond breaks. Oj moves to bond to C2, in turn breaking the C2-B3 bond.

Simultaneously, Oi bonds with C3 and subsequently breaks the C3-B1 bond. The MEP is

shown in Fig. 21(a) with a transition state at image 6 (Fig. 20(b)). The transition state has

energy of -1416.018 Ry and the oxygen molecule has dissociated. The O-O bond length

is 1.98 Å, which solidifies the claim to oxygen dissociation. Each of the oxygen atoms

have bonded to an adjacent boron atom at the TS. The B-O bond lengths are 1.46 Å and

1.44 Å for B1-O1 and B2-O2 respectively. The activation energy was Ea= 0.62 eV.

The final path chosen for NEB calculations was Path IV. This reaction begins

with diatomic oxygen uniformly shifting down toward the center of the ring that contains

the boron cluster. Next, Oj bonds with B3. At this point the diatomic oxygen bond

breaks. Oi bonds with C1 and the C1-B1 bond. Then, Oj bonds to C2, similar to Oi, and

breaks the C2-B3 bond. Path IV is favored for having the most stable product

conformation. After NEB calculations ensued it was found that Path IV had the lowest

activation energy of the four paths, with a value of Ea = 0.50eV. Similar to the other

reaction pathways (except Path II), Path IV, had one transition state, at the sixth image

into the calculation. Figure 22 displays the MEP and the transition state structure. The

transition state has an overall energy of -1416.027 Ry. In the transition state, the O-O

bond distance is 1.77 Å, which shows that the O-O bond has been broken, and that they

have bonded to adjacent boron atoms (B-Oi=1.45 Å, B-Oj=1.49 Å), similar to Path III.

After a subtle rise in energy to the transition state, the reaction follows a relatively abrupt

decline in energy to the product formation.

35

(a) Ea= 0.50eV

(b)

Figure 22.(a) The energy profile of the MEP for Path IV, most favorable reaction path with lowest activation energy (0.50 eV) and one transition state. (b) Structure of TS.

36

Table 1.A summary of the results to the NEB calculation.

Path Activation Energy (eV)Number of Stable Intermediates Number of TS

I 2.10 0 1II 0.88 1 2III 0.62 0 1IV 0.50 0 1

Table 1 summarizes the results of the NEB calculations. Path I had the highest

activation energy of 2.1 eV and Path IV with the lowest with Ea = .50 eV. Each of the

paths, excluding Path II, displayed a steady rise to the transition state (TS) and

subsequently, a steady decline to the product.

When taking activation energy and total system energy into consideration Path

IV appears optimal out of the four. There is one transition state and no stable

intermediates which suggest the pathway’s simplicity. The present results with boron

cluster doped CNT (B3SWCNT) shows substantial improvement over the previous results

with only one boron (B1SWCNT).15 The lowest activation barrier for oxygen dissociation

on B1SWCNT was found to be 0.81 eV.15 Other reaction paths considered previously for

B1SWCNT had activation barrier over 1.2 eV. The lower activation energies we observed

with B3SWCNT in the present study is most likely due to the fact that B-C bond is

weaker than C-C bond. In Path IV, both oxygen atoms are attached to B-C bonds and the

B-C bonds are partially broken, leading to significant distortion of overall CNT structure.

On the other hand, with B1SWCNT, at least one of the two oxygen atoms is always

attached to C-C bond. The reaction paths with B1SWCNT are also more complicated than

37

those studied in this work with B3SWCNT, typically having more than one transition

state.

E. Atom Projected Density of State

Atom projected density of state (PDOS) calculations lead to interesting

differences in the electronic structure of molecular oxygen adsorbed to the pristine (5, 5)

SWCNT and the (5, 5)-B3SWCNT. An isolated ground state oxygen molecule is in the

triplet electronic state.15However, triplet-state oxygen does not bind to a pristine

SWCNT. To achieve molecular oxygen adsorption to a pristine (5, 5) SWCNT the

molecule must undergo a triplet-singlet electronic transition. However, the molecular

oxygen adsorbed on boron has doublet character, with the total magnetization of 1μB. In

addition, oxygen becomes electron rich, with the total number of valence electrons equal

to 12.3. This indicates that the electronic structure of adsorbed O2 moves toward that of

O2-, which is known to be highly reactive. On the other hand, the average number of

valence electrons of boron is 2.84, which shows that electrons are transferred from boron

to oxygen. Although, the boron directly attached to oxygen is slightly more negative, the

difference is negligible. This implies that the effect of boron is cooperative. This is also

seen from the fact that the activation barrier is reduced from 0.8 eV to 0.5 eV when more

boron atoms are found around the adsorbed oxygen molecule.

IV. Conclusion

Oxygen dissociation on boron doped carbon nanotube (B3SWCNT) is studied

with the density functional theory (DFT) and nudged elastic band (NEB) calculations.

From a series of NEB calculations, the most likely reaction path is determined to be path

38

IV, where two oxygen atoms are adsorbed on two crystallographically identical boron

atoms, followed by the insertion of each oxygen atom into B-C bond. The activation

barrier for this path is 0.5 eV, which is a substantially smaller than the previous results

with (5, 5)-SWCNT doped with only a single boron atom. Atom projected density of state

(PDOS) calculation shows that oxygen molecule is negatively charged, whereas boron

atoms are positively charge, implying electron transfer from boron to oxygen. In fact, the

adsorbed molecular oxygen has 2O2- character, which is highly reactive. However, all

three boron atoms are equally charged, indicating cooperative effect of boron. This

should have contributed to the lower activation barrier found in the present B3SWSCNT

system.

The activation barrier of 0.5 eV (~11 kcal/mol) is still relatively large, but our

calculations are done for gas phase systems. It is expected that the presence of solvent

reduces the activation barrier significantly. Therefore, as a future work, it would be

interesting to see the role of solvent in oxygen dissociation on the surface of doped

carbon nanotube.

39

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