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How to cite this thesis Surname, Initial(s). (2012) Title of the thesis or dissertation. PhD. (Chemistry)/ M.Sc. (Physics)/ M.A. (Philosophy)/M.Com. (Finance) etc. [Unpublished]: University of Johannesburg. Retrieved from: https://ujcontent.uj.ac.za/vital/access/manager/Index?site_name=Research%20Output (Accessed: Date).

A DENSITY FUNCTIONAL THEORY STUDY ON THE MODIFICATIONS OF GRAPHENE NANOSHEETS WITH SELECTED METALS

By EPHRAIM MURIITHI KIARII Student number: 216088393

Thesis in fulfilment of the requirement for the degree

MASTERS OF SCIENCE In CHEMISTRY

In the

FACULTY OF SCIENCE of the UNIVERSITY OF JOHANNESBURG

Supervisor

:

PROF. PENNY P. GOVENDER

Co-supervisors

:

DR. KRISHNA K. GOVENDER

:

PROF. PATRICK G. NDUNGU March, 2018

DEDICATION:

I dedicate this work to my parents, Mr. & Mrs Kiarie, for dedicating their resources to help me in my studies. To my loving wife Eudias and girls Claire & Doris it was not easy being away from home and to my loving sisters Charity and Rachael. To my sis, Winfred may your soul rest in peace!!!.

iii

PUBLICATIONS AND PRESENTATIONS:

The work presented in this thesis has been presented at national and international conferences. Furthermore, results emanating from this study have been published or submitted to peer-reviewed journals for publication. Peer-reviewed Publications 1. E. M. Kiarii, K. K. Govender, P. G. Ndungu and P. P. Govender. The generation of charge carriers in semi conductors-A theoretical study. Journal of Chemical Physics Letters (2017) DOI: 10.1016/j.cplett.2017.04.051 2. E. M. Kiarii, K. K. Govender, P. G. Ndungu and P. P. Govender. Simulation from the first principal theory on the effect of supporting silica on graphene and the new composite material. Journal of Chemical Physics Letters (2017) DOI: 10.1016/j.cplett.2017.05.034 3. E. M. Kiarii, K. K. Govender, P. G. Ndungu and P. P. Govender. A DFT study on the effect of supporting titania on silica graphene epoxy graphene and carbon

nanotubes

-

interfacial

properties

and

optical

response.

Journal of Computational Condensed Matter (2017) DOI: http://dx.doi.org/10.1016/j.cocom.2017.08.003 4. E. M. Kiarii, K. K. Govender, P. G. Ndungu and P. P. Govender. A DFT Study on the transportation of charge carriers in graphene systems. Journal of Nature Physics (2017) Manuscript No.: NPHYS-2017-05-01431 (Under review)

iv

Conference and symposium presentations 1. E.M. Kiarii, P. G. Ndungu, K.K. Govender & P.P. Govender (2017). Simulation from the first-principles calculation on the effect of supporting silica on graphene and the new composite material (Oral presentation and Poster presentation).

SACI inorganic and Carman physical chemistry

Symposium, Arabella hotel and Spa Hermanus, Western cape South Africa. 25TH - 29TH June 2017. 2. E.M. Kiarii, P. G. Ndungu, K.K. Govender & P.P. Govender (2017). Supporting titania on silica, graphene, epoxy graphene and carbon nanotubes: A first-principles study (Oral presentation). 9th World Congress on Materials Science and Engineering & Engineering, at Rome, Italy 12 th 14th June 2017. 3. E.M. Kiarii, P. G. Ndungu, K.K. Govender & P.P. Govender (2016). Simulation from the first principles on the effect of supporting titania on silica, graphene, epoxy graphene and carbon nanotubes and the layers: interfacial properties and optical response.

(Poster presentation). CHPC 2016

National Meeting, East London, South Africa 5th - 9th December 2016. 4. E.M. Kiarii, P. G. Ndungu, K.K. Govender & P.P. Govender (2016). First principles simulations on the effect of supporting titania on silica, graphene, epoxy graphene and carbon nanotubes (Oral presentation). The 6th University of Johannesburg cross faculty postgraduate symposium South Africa, 14th October 2016.

v

ACKNOWLEDGEMENTS

Sincere thanks to following institutions

for their assistance: The financial

contributions of the Faculty of Science: University of Johannesburg-South Africa, Centre of Nanomaterials and Science Research: Department of Applied Chemistry, National Research Foundation (TTK14052167682), NRF Freestanding Funding and Global Excellence and Stature (GES) funding from the University of Johannesburg . Centre for High-Performance Computing (CHPC), 15 Lower Hope Road, Rosebank, Cape Town for allowing me to use their facility. The following for their individual contribution to the overall success of this worthy course: PROF. PENNY P. GOVENDER - Department of Applied Chemistry, University of Johannesburg, Johannesburg, South Africa. PROF. PATRICK G. NDUNGU-

Department of Applied Chemistry, University of Johannesburg, Johannesburg, South Africa.

DR. KRISHNA K. GOVENDER-

Centre for High-Performance Computing, 15 Lower Hope Road, Rosebank, Cape Town.

UJ Computational Chemistry Members (Mr. Martin Magu, Mr. Samuel Oppong, Mr. William Anku, Mr. Ephraim Marondedze, Mr. Francis Opoku, Mr. Peter Chijioke, Mr. Wahab Olaide, and Ms. Renu Kumari) of the Computational Chemistry group and Analytical Chemistry Research Group (Mr. Eric Ngigi, Ms. Veronica Wanjeri and Mr. Tarekegn Dolla). Your support and assistance in the form of suggestions and laboratory materials are highly appreciated. Thank you also for moral support and ensuring that the study and lab environment was always conducive to learning and

vi

research. Last but not least administrators in the Department of Applied Chemistry you were of great help, namely, Ms. Leah, and Mr. Sifiso, and others. Thank you.

vii

ABSTRACT

The modifications of graphene nanosheets with a metal oxide is a state of the art subject that has received large amounts of interest over the past decade. In the current work density functional theory studies are conducted to better understand and provide more insight into the experimentally determined results of these systems. Our calculations were done using the DFT + U approach to mimic the experimental results and avoid the known underestimation achieved by standard DFT. The generalized gradient approximation of Perdew-BurkeErnzerhof functional as implemented in Cambridge Serial Total Energy Package within the Material Studio 2016 software package was used to treat the exchange-correlation effects. The electron-ion interaction was described using the ultrasoft pseudopotentials. A systematic study of electronic and optical properties of titanium dioxide under visible light was simulated using first principles calculations.

The findings

support the application of TiO2 in photo energy generation after graphene modifications.

A theoretical band gap of 3.15 eV complimented

the

experimentally obtained band gap of 3.2 eV. Finally, our results revealed that upon protonation there was charge generation and this has the potential for application in photo energy generation. Studies of graphene as a support and transport material in photocatalysis, which is used to store generated charge carriers, are also reported.

A model of

graphene was generated and the morphological, electronic, phonon properties electrostatic potentials, as well as ballistic transport properties of the materials,

viii

were theoretically investigated. In this study, silica polymorphs on graphene and epoxy graphene were also studied (since silica is used as support material with many photocatalytic materials) to determine the interfacial and optical properties of the composite material.

The powder diffraction patterns and Raman spectra for the silica

polymorph structural models, as well as graphene and epoxy graphene monoxide, was generated using first principle methods.

The electronic and

optical properties and work function analysis of the polymorphs with graphene or epoxy graphene monoxide as starting molecules, together with the layered systems are compared.

In this study, the optical properties of the layers

generated are found as sensitive to the visible light region in both epoxygraphene monoxide and graphene composites. Finally, a first principles study of titania was conducted as used in photocatalysis to generate charge carriers. Models of titania, silica, graphene, epoxy graphene monoxide, single wall carbon nanotubes and their respective layers were studied in order to investigate their morphological, electronic, optical properties and electrostatic potentials. A physisorbed study was carried out on the layers generated in relation to their electronic and optical properties. To understand the electron movement during photocatalysis, a projected density of state study was conducted in order to assess the orbital contribution in the charge transfer.

ix

TABLE OF CONTENTS

Section

Page

DECLARATION: ................................................................ Error! Bookmark not defined. DEDICATION: ..................................................................................................................... ii PUBLICATIONS AND PRESENTATIONS: .................................................................. iv ACKNOWLEDGEMENTS: ............................................................................................... vi ABSTRACT ...................................................................................................................... viii TABLE OF CONTENTS .................................................................................................... x LIST OF TABLES ............................................................................................................xvi LIST OF FIGURES AND SCHEMES .........................................................................xviii LIST OF ABBREVIATIONS ........................................................................................ xxiv

CHAPTER 1 : INTRODUCTION ...................................................................................... 1 1.1 Background ................................................................................................................... 1 1.2 Problem Statement ...................................................................................................... 3 1.3 Aim .................................................................................................................................. 3 1.4 Objectives ...................................................................................................................... 3 1.5 Outline of the Thesis .................................................................................................... 4 1.6 References .................................................................................................................... 6

CHAPTER 2 : LITERATURE REVIEW......................................................................... 8 2.1

Introduction............................................................................................................... 8 2.1.1 Nanoscience-The Inside Story .................................................................... 8

x

2.1.2 Carbon Nanostructures ................................................................................ 9 2.1.2.1 Carbon Nanotubes (CNTs) ....................................................11 2.1.2.2 Graphene Nanostructures......................................................12 2.1.2.3 Defects in Graphene Nanostructures ...................................14 2.1.2.3.1 Vacancies and Adsorbed Atoms....................14 2.1.2.3.2 Bending of Graphene Nanotubes ..................15 2.1.2.3.3 Edges of Graphene Nanostructures ..............15 2.1.2.4 Graphene Oxide (GO) ............................................................16 2.1.3 Generation of Charge Carriers in Semiconductors (TiO2) ....................18 2.1.3.1 Different Phase Structures of TiO2 .......................................21 2.1.4 Titanium Dioxide on Carbon-based Materials. .......................................24 2.1.5 Transport of Charge Carriers by CNT’s (Graphene systems) ..............24 2.1.6 Time-of-Flight Method (TOF).....................................................................25 2.1.6.1 Sandwich Time-of-Flight Method (S-TOF) ..........................26 2.1.6.2 Coplanar Time-of-Flight Method (C-TOF) ...........................27 2.1.7 Silica on CNTs and Graphene ..................................................................29 2.1.8 Titanium Dioxide on SiO2/CNT Composite versus CNT .......................31 2.2 COMPUTATIONAL APPROACH.............................................................................32 2.2.1 Introduction...................................................................................................32 2.2.2 Semi-empirical and Ab initio Methods......................................................33 2.2.3 Density Functional Theory .........................................................................36 2.2.4 Model Chemistries ......................................................................................39 2.2.5 Computing of First Order Rate Constants ...............................................41 2.2.6 Molecular Orbital Theory and Charge Transfer ......................................42

xi

2.2.7 Computing Spectral Data ...........................................................................43 2.2.7.1

Infrared and Raman spectroscopy ....................................45

2.2.7.2

Quantum

Chemical Calculation

of IR and

Raman

Spectra...................................................................................45 2.3 References ..................................................................................................................47

CHAPTER 3 : COMPUTATIONAL DETAILS ..............................................................63 3.1

Introduction.............................................................................................................63 3.1.1 Biovia Materials Studio (2016) ..................................................................63 3.1.2 Cambridge Sequential Total Energy Package (CASTEP) ....................64

3.2 References ..................................................................................................................66

CHAPTER 4 : THE

GENERATION

OF

CHARGE

CARRIERS

IN

SEMICONDUCTORS - A THEORETICAL STUDY ....................................................71 4.1. Introduction ................................................................................................................71 4.2. Model Structures and Method ...................................................................................75 4.2.1 TiO2 Bulk and Surface Models ..................................................................75 4.2.2 Surface Model of TiO2 ................................................................................76 4.2.3 Protonated Model of TiO2 ...........................................................................76 4.2.4 Simulation Parameters ..............................................................................77

4.3 Results and Discussion .............................................................................................77 4.3.1 Powder Diffraction and Raman Analysis ................................................77 4.3.2 Atomic Population Net charge...................................................................79 4.3.3 Electronic Properties...................................................................................83 xii

4.3.3.1 Band Structure .........................................................................83 4.3.3.2 Total Density of State (TDOS) and Partial Density of State (PDOS) .....................................................................................84 4.3.3.3 Spin Density of State .............................................................86 4.3.3.4 Electron Density Difference and Electron Localisation Function....................................................................................87 4.3.3.5 Phonons in TiO2 .......................................................................89 4.3.4 Electrostatic Potential .................................................................................90 4.3.5 Optical Properties ........................................................................................91 4.4 References ..................................................................................................................93

CHAPTER 5:

A DFT STUDY ON THE TRANSPORTATION OF CHARGE

CARRIERS IN GRAPHENE SYSTEMS .................................................................... 100 5.1 Introduction .............................................................................................................. 100 5.2 Computational Details .............................................................................................. 104 5.2.1 Model Building........................................................................................... 104 5.2.2 Simulation Parameters ........................................................................... 104 5.3 Results and Discussion .......................................................................................... 105 5.3.1 Morphological Analysis............................................................................ 105 5.3.2 Electrons in Graphene ............................................................................. 106 5.3.3 Band Structure .......................................................................................... 108 5.3.4 Total Density of State and Partial Density of State ............................. 108 5.3.5 Electron Localization Function .............................................................. 109 5.3.6 Phonons in Graphene.............................................................................. 109 5.3.7 Electron-Phonon Coupling ...................................................................... 111 xiii

5.3.8 Electrostatic Potential .............................................................................. 113 5.4 References ............................................................................................................... 115

CHAPTER 6: SIMULATION FROM THE FIRST PRINCIPALS THEORY ON THE EFFECT OF DOPING SILICA ON GRAPHENE AND THE NEW COMPOSITE MATERIAL...................................................................................................................... 120 6.1 Introduction .............................................................................................................. 120 6.2 Computational Details .............................................................................................. 125 6.2.1 Model B ui ldi ng ........................................................................................ 126 6.2.2 Simulation Parameters ............................................................................ 126 6.3 Results and Discussion .......................................................................................... 127 6.3.1 Morphological Analysis............................................................................ 127 6.3.3 Electronic Properties ............................................................................... 129 6.3.4 Electronic Properties of Bulk .................................................................. 130 6.3.5 Electronic Properties of Surface and Layers of Silica Polymorphs .. 131 6.3.6 Optical Properties ..................................................................................... 134 6.3.7 Electrostatic Potential Calculations ....................................................... 136 6.4 References. .............................................................................................................. 138

CHAPTER 7: A DFT STUDY ON THE EFFECT OF SUPPORTING TITANIA ON SILICA GRAPHENE EPOXY GRAPHENE AND CARBON NANOTUBES ........ 144 7.1 Introduction .............................................................................................................. 144 7.2 Computational Details ............................................................................................. 147 7.2.1 Model Building .......................................................................................... 147 xiv

7.2.1.1 Bulk and Surfaces ................................................................................. 147 7.2.1.2 Single Layer and Two Layers ............................................................. 149 7.2.1.3 TiO2 Interacts with Silica/G and Ep-GO Nano Composites ........... 150 7.2.1.4 G and Ep-GO is sandwiched between TiO2 and Silicon Dioxide .. 150 7.2.1.5 TiO2 interacts with Single Wall Carbon Nanotube (SWCNT)......... 150 7.2.2 Calculations Details ............................................................................................. 151 7.3 Results and Discussion .......................................................................................... 151 7.3.1 Morphological Analysis ........................................................................... 151 7.3.2 Electronic Properties ............................................................................... 153 7.3.3 Optical Properties ..................................................................................... 157 7.3.4 Mechanism of Electron Transfer in Layer............................................. 160 7.4 References ............................................................................................................... 162

CHAPTER 8: CONCLUSION AND PERSPECTIVE .............................................. 166 Appendices ..................................................................................................................... 171 A1. Electrostatic potentials used in Table 6.4 and Table 6.5 for the work function of the surface and layers of the nanosheet in the ground state graphene being on top and bottom respectively ........................................... 171 A2. Band structures used in Table 7.1 for the bandgaps of the surface and layers of the nanosheet in the ground state graphene, Epoxy graphene and SWNT being on top and bottom respectively ................................................ 174

xv

LIST OF TABLES

Table

Description

Page

Table 2.1

Four main polymorphs of TiO2 ............................................................21

Table 3.1

The

hardware

parameters

for

the

cluster

used

in

the

calculation ……………………………………………………………. 65 Table 4.1

Structural

parameters

of

body-centered

tetragonal

TiO2

(Anatase)………………………………………………………………75 Table 4.2

Calculated versus experimental powder diffraction and Raman peaks of TiO2 (Anatase)…………………………………………….. 79

Table 4.3

Atomic population net charge………..……………………………. 80

Table 4.4

Effect of changing proton position on the net atomic charge…….82

Table 5.1

Phonon frequencies at critical point in cm-1 out of plane єa and in plane є# branches, respectively…………………………………. 103

Table 5.2

Graphene (G) structure

lattice

parameter

and

atomisti c

positions …………………………………………………………... 104 Table 6.1

Graphene (G) a nd E p o xy Graphene monoxide (Ep-GO) m o d e l lattice parameters………………………………………………...... 125

Table 6.2

Calculated electronic properties of SiO2 polycrystal structures.. 131

Table 6.3

Calculated electronic properties of SiO2 Graphene and epoxy graphene layers. ................................................................................ 131

xvi

Table 6. 4

The work function on the surface and layers of the nanosheet in the ground state (graphene in bottom position)................................... 137

Table 6. 5

The work function on the surface and layers of the Nanosheet in the ground state (graphene on top position) ........................................ 137

Table 7.1

Lattice parameters unit cells used to build the bulk models ....... 148

Table 7.2

Energy

gaps

of

individual

elements

surface

and

layers

generated ............................................................................................ 156 Table 7.3

Work function of the various variable samples ............................. 160

xvii

LIST OF FIGURES AND SCHEMES

Figure

Description

Page

Figure 2.1

Electron density as characterized by the states for materials in different dimensions ............................................................................10

Figure 2.2

Carbon structures; (a) Graphite, (b) Single graphene sheet, (c) closed end carbon nanotube, (d) multiwall nanotube as well as (e) fullerene C 60 Where grey dots represent carbon atoms and the white hydrogen. .....................................................................................11

Figure 2.3:

Triangular lattice structure of graphene. ...........................................13

Figure 2.4

Calculated atomic structure of a-GMO, ep-GMO, GDO, mix-GMO and z-GMO, along the xy, yz, xz planes view ...............................18

Figure 2.5:

An illustration of the electronic property of a semiconductor .........19

Figure 2.6:

TiO2 in different crystal structure arrangement: (a) anatase (b) rutile (c) brookite ..........................................................................................22

Figure 2.7 :

Various Silica polymorphs: (a) cristobalite high (b) cristobalite low (c) quartz (d) quartz beta (e) stishovite .............................................29

Figure 2.8: Figure 2.9:

Illustration of Gaussian functions and their product .......................35 Diagram illustrating the electromagnetic spectrum ………………….44

xviii

Figure 4.1.

Effective charge generation and separation in TiO2 . ......................73

Figure 4.2.

Structural model of (a) titanium dioxide and a representation of the (b) surface (101) with their respective charge distribution. Red dots represent oxygen and grey dots represent titanium........................76

Figure 4.3.

Experimental

versus

calculated

powder

diffraction

zTiO 2

(Anatase) ................................................................................................78 Figure 4.4.

Calculated Raman spectrum of TiO2 (Anatase)...............................78

Figure 4.5.

Atomic population net charge categorised by atoms ......................81

Figure 4.6.

Structural

model of protonated Titania oxygen showing the

variation of proton by position; (a) un-protonated, (b), (c), (d), and (e) positions O1 , O2 , O3 & O4 respectively .......................................82 Figure 4.7.

Band structures for (a) bulk, (b) surface (101) and (c) protonated surface (101) TiO2.................................................................................84

Figure 4.8.

TDOS of the bulk of titanium dioxide. ................................................85

Figure 4.9.

PDOS of the bulk of titanium dioxide.................................................85

Figure 4.10.

Split non-magnetic atomic configurations of (a) Ti 3d, (b) O 2p and (c) TiO2. ..................................................................................................86

Figure 4.11.

(a) Electron density, (b) electron density difference and (c) electron localization function for the bulk TiO2 versus (d) electron localization function and (e) electron density difference. ....................................88

Figure 4.12.

Calculated phonon dispersion of anatase along the high symmetry directions and density of phonon state..............................................90

xix

Figure 4.13.

Electric potentials on (a) TiO2 surface, (b) one proton added, (c) two protons added and (d) three protons added to TiO2 surface. The red and green dashed lines are the vacuum and Fermi level, respectively. ...........................................................................................91

Figure 4.14.

Calculated optical properties of TiO2 .................................................92

Figure 5.1:

The lattice structure of graphene..................................................... 101

Figure 5.2.

Two dimensional

phonons of monolayer pnictides at different

loadings ............................................................................................. 103 Figure 5.3.

Schematic structure of generated graphene ................................. 104

Figure 5.4

Calculated (a) versus experimental (b) powder diffraction patterns for graphene, respectively. ............................................................... 105

Figure 5.5.

Calculated (a) versus experimental (b) Raman spectrum of a single layer of pristine graphene respectively........................................... 106

Figure 5.6

Calculated band structure of pristine graphene in the Brillouin zone. .................................................................................................... 107

Figure 5.7

Calculated Total density of state (a) and Partial Density of state (b) of graphene ......................................................................................... 107

Figure 5.8.

Electron localisation function for a calculated single layer of graphene ............................................................................................. 109

Figure 5.9

Phonon dispersion relations of bulk graphene (a) Calculated and (b) Experimental………………………………………………….....110

xx

Figure 5.10

The

average potential

profile along

Z-axis

from top and

bottom. ................................................................................................. 114 Figure 6.1

Use of silica on graphene or epoxy graphene as a support. ...... 120

Figure 6.2

Graphene with no bandgap (a) and bandgap opening (b) through substrate induced band opening ..................................................... 122

Figure 6.3

Various silica polymorphs: (a) cristobalite high (b) cristobalite low (c) quartz (d) quartz beta (e) stishovite .......................................... 123

Figure 6.4

Structural models generated; (a) G-quartz beta, (b) G - quartz, (c) G - stishovite, (d) G- cristobalite high, ( e ) G- cristobalite low, (f) G O - stishovite, (g) Ep-GO-quartz beta, (h) Ep- G O - quartz, (i) EpGO - cristobalite high and (j) Ep-GO - cristobalite low. .............. 126

Figure 6.5

Calculated

powder diffraction

spectra for graphene, epoxy

graphene monoxide, cristobalite low, stishovite, quartz beta and cristobalite high, respectively ........................................................... 128 Figure 6.6

Calculated

Raman

spectra

for graphene, epoxy graphene

monoxide, stishovite, quartz, quartz beta, cristobalite high and cristobalite low respectively.............................................................. 129 Figure 6.7

Band structures for (a) graphene, (b) epoxy graphene monoxide and partial density of state (PDOS) for (c) graphene and (d) epoxy graphene monoxide........................................................................... 130

Figure 6.8

PDOS of the epoxy graphene monoxide orbital contributions - (a) cristobalite high layer, (b) carbon, (c) oxygen, (d) silicon ............ 133

xxi

Figure 6.9

PDOS of the orbital contributions for (a) graphene - quartz beta layer, (b) carbon, (c) oxygen and (d) silicon .................................. 134

Figure 6.10.

Optical properties for graphene, epoxy graphene monoxide and silica polymorph structures ............................................................... 135

Figure 6.11.

Optical properties analysis for layers of (a) SiO2 graphene and (b) epoxy graphene ................................................................................. 136

Figure 7.1.

Charge

generation

and

band

gap

reduction

in

the

TiO2 composite. ................................................................................. 145 Figure 7.2

Charge transfer and separation in the G-TiO2 composite. .......... 146

Figure 7.3

Structural models of surfaces and layers built to explore electronic and optical properties of generated TiO2 composites. ................. 149

Figure 7.4

Calculated

powder diffraction patterns

of graphene,

Epoxy

graphene monoxide, TiO2-anatase, SiO2-cristobalite and single wall carbon nanotube (SWCNT).............................................................. 152 Figure 7.5

Calculated Raman spectra for SiO2-cristobalite, TiO2-anatase, and Epoxy graphene monoxide and graphene ..................................... 153

Figure 7.6

Band structure and density of state of starting molecules (a) anatase, (b) cristobalite low, (c) graphene and (d) epoxy-graphene monoxide ............................................................................................. 154

Figure 7.7

Orbital contributions in the layers by elements namely Ti, Si, C and O and their layers with graphene (G) and epoxy graphene (GO) respectively. ........................................................................................ 155

xxii

Figure 7.8

Optical properties of graphene (G), epoxy graphene (GO) and, single wall carbon nanotube (SWCNT) and their composites. ... 158

Figure 7.9

Comparative optical properties of TiO2 layers generated. .......... 159

xxiii

LIST OF ABBREVIATIONS

CVD

Chemical Vapour Deposition

DFT

Density Functional Theory

DFT-B

Density Functional Tight-Binding

CNTs

Carbon Nanotubes

TiO2

Titanium Dioxide (Titania)

SiO2

Silicon Dioxide (silica)

IR

Infra-Red

OLEDS

Organic Light Emitting Diodes

LEDS

Light Emitting Diodes

0D

Zero Dimensional

1D

One Dimensional

2D

Two Dimensional

3D

Three Dimensional

z-GMO

Zigzag Graphene Monoxide

a-GMO

Armchair Graphene Monoxide

ep-GMO

Epoxy Graphene Monoxide

mix-GMO

Mixed Graphene Monoxide

GO

Graphene oxide

Ep-GO

Epoxy Graphene

GDO

Graphene Dioxide

VB

Valence Band

CB

Conduction Band

HOMO

Highest Occupied Molecular Orbital

xxiv

LUMO

Lowest Unoccupied Molecular Orbital

STOs

Slater-Type Orbitals

GTO

Gaussian-Type Orbitals

CNDO

Complete Neglect of Differential Overlap

TZ

Triple-Zeta

EG

Energy Gap (Bandgap)

XRD

X-Ray Diffraction

xxv

CHAPTER 1: INTRODUCTION 1.1 Background Carbon is a naturally occurring element and the sixth most abundant. Much has been known about it for a long time [1]. It occurs in allotropes namely diamond, amorphous, graphite, among others [2]. Examples of carbon compounds include amorphous carbon and black soot obtained from burning wood or hydrocarbons used as fuel or in ink industries, paints and rubber products. Graphite, the softest among the sp3 hybridized carbon allotropes [3], is used in steel manufacturing to coat the foundry moulds of the metal industry. Furthermore, it is the alloy component used in the manufacturing of tennis racket frames. In the automobile industry, it is used in the production of brake linings, brakes, engine parts, clutch facings, and mechanical seals friction components. In addition, it is also used in the making of paints which are anti-corrosive. In high-technology industries, graphite has many uses, most conspicuously in the batteries made of lithium-ion for laptops, small tools electronic cars, and electrical devices [4]. In addition, is used in the production of alkaline battery, metal powders, industrial lubricants, also as polymer and rubber components containing graphite [5]. Lastly, graphite is used for the medical purpose as an absorbent in cases of oral intoxication or poisoning [6]. Although graphite does occur naturally synthetic graphite can be made commercially by treating petroleum coke [7]. Diamond, of natural origin, is one of the hardest substances known [8] and used as jewellery.

Most of the commercially available diamond is man-made, by 1

CHAPTER 1: Introduction

pressurising graphite at high temperature.

Diamond and graphite differ in their

crystal structures only.

Buckminsterfullerene’s [9] are spherical molecules with the formula C 60, also known as Buckyballs and are of much scientific interest owing to their recent discovery. A single fullerene has 60 or 70 carbon atoms joined together by covalent bonds to form a structure that resembles a soccer ball. They can incorporate other atoms within their structure, have magnetic and/or superconductive characteristics and are capable of withstanding high pressures. When open they form a flat hexagonal, chicken wire like (honeycomb) lattice which is one atom thick (graphene).

Graphene, a two dimensional structure, have tightly packed carbon atoms that are bonded together through covalent bonds arranged in a hexagonal chicken wire like lattice. It is the thinnest and lightest compound known to man, i.e. one atom thin. It forms the strongest compound discovered to date (graphene’s ultimate tensile strength is 130 billion Pascal compared to 400 million for A36 steel or 375.7 million for Aramid (Kevlar)) [10]. Graphene is the lightest at 0.77 milligrams per square sheet [6] and the best conductor of heat near room temperature. Having a thermal conductivity of ~ 0.44 × 103 ± 4.84

to 0.48 ×103 ± 5.30

W/mK [11]. These

properties, among the ones undiscovered about graphene, have made it the subject of this research.

When a semiconductor is placed on a graphene substrate its crystallinity changes compared to when they are placed on silicon [12]. Its charge transference through the polymer film is strongly boosted. This makes it possible to produce more efficient electronic appliances, such as organic solar cells and organic light emitting diodes

2


(OLEDS) and light emitting diodes (LEDs). Graphene can transport electrons at high speed due to its unique properties. This makes the material very attractive as a component in applications like flexible solar cells and advanced batteries [12]. However, to gain a better understanding, theoretical studies are required to elaborate on these properties.

1.2 Problem Statement The study of graphene nanosheets have been extensively conducted through various experimental work, but very little has been done to theoretically understand how charge carriers are generated and transported in these chemical systems.

1.3 Aim To use theoretical methods to investigate how modifications of graphene nanosheets with selected metals enhance its activities.

1.4 Objectives 1.

To investigate the generation of charge carriers in semiconductors (e.g. titania).

2.

To explore how the transportation of charge carriers in graphene systems occur.

3.

To simulate and investigate how the supporting of silica on carbon nanotubes (CNTs) and graphene systems improves the properties of the new composite material.

4.

To explore why photo-activity increases with TiO2 on SiO2/graphene/CNT composite over pristine graphene systems and CNTs.

3


1.5 Outline of the Thesis This thesis is made up of eight chapters. Chapter one is an introduction containing the background information, problem statement, aims and objectives of this study. Chapter two gives a literature review with two main sections.

Section one provides a description on nanoscience,

discusses carbon nanostructures and graphene with its oxides. It further details the generation of charge carriers in semiconductors, different phase structures of titania (TiO2), TiO2 - carbon based materials, transport of charge carriers and use of silica on graphene and carbon nanotubes. Finally, titanium dioxide on silica/graphene composites compared to graphene is explored. Section two provides detail on the computational approaches, focusing specifically on semi-empirical, ab-initio, density functional theory (DFT) and density functional tight–binding (DFTB) methods.

This section also looks at model chemistries,

computing first order rate constants, molecular orbital theory, charge transfer and computing spectral data. Finally, the section ends with the quantum chemical calculation of Raman spectra and IR. Chapter three describes the computational software: Biovia Material Studio 2016 and Cambridge Sequential Total Energy Package (CASTEP). The theoretical calculations and corresponding results are detailed in chapters’ four to seven. Chapter four, describes the results on the generation of charge carriers in semiconductors (i.e. titania). Chapter five: the transportation of charge carriers in graphene systems. Chapter six touches on the effect of supporting silica on CNT's and graphene systems is presented and on the improvement of the properties of the new composite material. Finally, chapter seven explores why photo-activity

4


increases with TiO2 on SiO2/graphene/CNT composite over pristine graphene systems and CNTs. A general conclusion and perspective for future studies is provided in chapter eight.

5


1.6 References 1.

C. S. Jeffery. Principles and Perspectives in Cosmochemistry. Aruna Goswami and B. Eswar Reddy eds. Astrophysics and Space Science Proceedings, Springer, Verlag Berlin Heidelberg (2010). pp. 379-417

2.

L. Nistor, V. Ralchenko, I. Vlasov, A. Khomich, R. Khmelnitskii, P. Potapov, J. Van Landuyt. Formation of Amorphous Carbon and Graphite in CVD Diamond upon Annealing: A HREM, EELS, Raman and Optical Study. Physica Status Solidi (A) 186 (2001) 207-214.

3.

H.O. Pierson, W. Andrew. Handbook of Carbon, Graphite, Diamonds and Fullerenes: Processing, Properties and Applications. Noyes Publications Park Ridge, New Jersey, USA (2012). pp. 11-58.

4.

M. Armand, J.-M. Tarascon. Building Better Batteries. Nature 451 (2008) 652657.

5.

W. Bollmann, J. Spreadborough. Action of Graphite as a Lubricant. Nature 186 (1960) 29-30.

6.

A. Shteynle. Clinical Efficiency of Absorbing Wound Dressing Consisting of Nanostructured

Graphite in Comparison with Other Modern Dressings.

Strategic Technology (IFOST), 7th International Forum on IEEE (2012). pp. 15. 7.

A. Carbons. Asbury Carbons Product Information. Asbury Carbons: Asbury, NJ, (2004). https://asbury.com/materials/ Accessed on 10/03/16

8.

J. Walker. Optical Absorption and Luminescence in Diamond. Reports on Progress in Physics 42.10 (1979): 1605.

9.

H.W. Kroto, J.R. Heath, S.C. O'Brien, R.F. Curl, R.E. Smalley. C60: Buckminsterfullerene. Nature 318 (1985) 162-163. 6


10. L. Dhiman, D. Ashutosh. Multifaceted Graphene: Novelity in Electronics. International Journal of Advanced Research in Electrical Electronics and Instrumentation Engineering 3 (2014) 11807-11811. 11. A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, C.N. Lau. Extremely High Thermal Conductivity of Graphene: Experimental Study. Materials Science (2007) 1-16. 12. D. Barbero, S. Synchrotron, R. Lightsource, D. O. E. Office and S. U. Facility. Semiconductor Works Better when Hitched To Graphene. Functional Materials 25 (2015) 664–670.

7

Advanced

CHAPTER 2: LITERATURE REVIEW

2.1

Introduction

This chapter is made up of two sections.

Section one gives a description of

nanoscience, carbon nanostructures and graphene with its oxides. Details of the different phase structures of titania (TiO2), generation of charge carriers in semiconductors, TiO2 - carbon based materials, titanium dioxide on silica/graphene composites versus graphene is explored together with the transport of charge carriers and use of silica on graphene and carbon nanotubes. Section two describes the computational approaches: ab-initio, semiempirical, density functional theory (DFT) and density functional tight–binding (DFTB) methods, model chemistries, computing of first order rate constants, molecular orbital theory, charge transfer and computing spectral data, as well as quantum calculation of Raman spectra and IR are also given.

2.1.1 Nanoscience-The Inside Story Nanoscience is the study of atomic and molecular assemblies with dimensions ranging from 1 nm to 100 nm, while nanotechnology is concerned with the incorporation of such assemblies into devices [1]. A nanometre can be described by a length of eight carbon atoms. When considering a nanoscale system discrete atoms involved are totalled.

8

Chapter 2: Literature Review

In Nanoscience study many specialists to work together on a common research topic, specialists combines a multiplicity of subjects such as chemistry, biology, and physics. It advances information from these disciplines then looks at the scientific hitches from several viewpoints, such as focusing on constituents of living entities and reactions concerning molecules or dynamics of the molecular systems. To find a mutual and comprehensible scientific explanation is one of the biggest obstacles to scientists.

Nanoscience attempts in finding solutions for the overburdening

energy usage in the world, for example, exploiting the functions of different materials like solar cells.

Nanoscience is at the initial stage to a broader understanding and at the extremely early phase of emerging and designing devices, attempting to attain better resolution experimentally with imaging, improved selectivity, great accuracy and efficiency with computer aided models of representative systems of great magnitude.

The nanoscale phenomena in the systems is categorized as

nanostructures.

2.1.2 Carbon Nanostructures Carbon is a well-known natural element, crucial for life, in addition to biological functions. The unearthing of recent carbon nanomaterials in the 80's and 90's have extensively influenced the interest in nanoscience: Kroto et al. [2] presented a set of simple, empilical chemical and geodesic rules which relates to the stability of fullerenes in 1985. This was later followed by Iijima in 1991 [3] who reported the preparation of carbon cages. Reports also includes the observation of carbon anions by Ugarte in 1992 [4], chemical vapour deposition (CVD) synthesis of aligned 9


nanotube films by Ren et al. in 1998 [5], and nanotube single crystals (2002) by Schlitter et al. [6]. Of interest in this study is the graphene first mentioned by Mouras [7] describing a single sheet of graphite.

Carbon nanostructures offer a full collection of dimensions (Figure 2.1) namely 0D (zero dimensional) e.g. fullerenes, 1D (one dimensional) e.g. graphene nanotubes and nanoribbons, 2D (two dimensional) such as graphene as well as 3D (three dimensional) e.g. diamond and graphite (Figure 2.2).

Figure 2.1 Electron density as characterized by the states for materials in different dimensions [8]

Fullerenes (Figure 2.2 (e)) are spherical in shape and made of graphene hexagon molecules, however, some pentagons are added into the graphene make a sensible curvature

and maintain the spherical shape.

From the modern carbon

nanomaterials, graphene is mainly favoured for use, due to its auspicious structural, electrical, optical and mechanical characteristics [9, 10]. These include uses like nano-electronic constituents, nano-electromechanical products, energy storage and sensors [11].

10


Breakthrough progress is made to attain the frontier of a mono layered graphene [9, 12-14]. Graphene is described as the backbone base in the formation of carbon nanomaterials [14].

Figure 2.2 Carbon structures; (a) graphite, (b) single graphene sheet, (c) closed end carbon nanotube, (d) multiwall carbon nanotube (e) fullerene - C60 [15]. (grey dots represent carbon atoms and the white hydrogen)

2.1.2.1 Carbon Nanotubes (CNTs) Carbon nanotubes (Figure 2.2 (c)) are allotropes of carbon with a cylindrical nanostructure. They are made of a rectangular section of graphene sheet. The cutting direction of the graphene sheet defines the type of tube produced. Armchair, achiral and zigzag tubes, can be either metallic or semiconductive in nature. These properties enable CNTs to become applicable in mechanical devices, which require strong hexagonal networks. They have found application as the building blocks for hydrogen storage because of their unusual mechanical properties. As an example, a single-walled carbon nanotube has a Young’s modulus that is approximately five

11


times more than steel and a tensile strength that is approximately 375 times more than that of steel [16]. At present, nanotubes make the shrillest front-edge of carbon nanomaterials field, together with graphene. Macroscopic diamond and graphite, as well as amorphous carbon structures, have been extensively reported by Meyer et al. [12]. 2.1.2.2 Graphene Nanostructures. The Castro-Neto et al. [17] study provided considerable explanation on graphene’s electrical properties, while the many-body effects was covered by Kotov et al. [17]. Transport properties were done by Das Sarma et al. [18], MacDonald et al. [19] and Vozmedano et al. [20]. An outstanding review of various aspects of Graphene and quantum, was initiated in the proceedings of the Nobel Symposium 148 by Geim and Novoselov [21]. There has also been considerable interest in the past decades, on Graphene with respect to its potential in various applications, such as transparent electrodes, photodetectors and transistors [22]. However, graphene is referred to as a semiconductor since it has a zero band gap. Klein [23] reported that it is challenging to restrain electrons with an electrostatic gate. However, a decrease in the side dimensions of the graphene may resolve the zero-energy gap. Consequently, size quantization occurs and the band gap is induced. Finally, semimetallic finite-size graphene converts into a semiconductor. Graphene thus yields nanostructures, which is grouped into; quantum dots and nanoribbons. Graphene nanoribbons (GNR) can be cut having different width. This is achieved through electron-beam lithography and an etching mask [24, 25].

Graphene

quantum dots (GQDs) are small fragments of graphene. However, GQDs have dimensions of 20 nm in diameter and below. The theoretical and experimental study

12


of GQDs has closely followed the work on graphene. GQDs can be fabricated by cutting graphene sheets using a top-down approach. In parallel, organic chemists synthesized large graphene-like molecules with well-defined molecular structure using a bottom-up approach [26, 27]. More recently, GQDs have been chemically adapted and used for the first time in applications in the area of energy conversion [28], bioanalysis [29] and sensors [29].

Crystalline graphene has 2-dimensional properties with carbon atoms closely arranged in a hexagonal pattern, such that each atom has four bonds: three σ-bonds join three carbon atoms neighbouring with one π-bond oriented above or below the connected atoms. The atoms are 1.42 Å apart [30]. Graphene’s structure is described as a hexagonal lattice and is viewed as two interleaving triangular lattices (Figure 2.3).

Figure 2.3: Triangular lattice structure of graphene [30]

13


This perception was effectively used in the calculation of the band structure for a single layer of graphite by tight-binding approximation [30]. The stability of graphene is due to its closely packed carbon atoms and sp 2 hybridized orbital with a combination of orbitals s, p x and py constituting the σ-bond [30]. The final pz orbital overlap makes the π-bond. The π-bonds hybridize forming the π∗-bands and πband [30]. The bands are accountable for most of graphene's distinguished electrical properties, through the half-filled band that permits free-moving electrons [30].

2.1.2.3 Defects in Graphene Nanostructures 2.1.2.3.1 Vacancies and Adsorbed Atoms Carbon has flexible bonding aspects that yield possibilities of creating adsorbed atoms. Possible defects are transferred into graphene with different defects from the adsorbed atoms resulting in mixed carbon nanomaterials [31]. Doping, i.e. deposition of non-metallic and/or metallic atoms, in graphene structures is an example of such an application which is a method used to fine-tune the structural behaviour and chemical activity. These doped materials find use in nanoelectronics, batteries and catalysis [32].

Doping introduces defects (vacancies). Vacancies, which are holes, reduce the structural strength. A vacancy created during doping affects the binding strength. Together with the possible presence of vacancies, adsorbed atoms which are noncovalently joined to the lattice also affect binding strength.

Vacancies find

applications in the Junction formation with CNTs therefore accurate preparation can improve the extent to which the material resists deformation in response to an

14


applied force of composite materials. It is difficult to control defect formation since they originate from the preparation and growth processes. Although defects are not in all cases preferred, some research in this field has taken advantage on the defects and junctions [33].

2.1.2.3.2 Bending of Graphene Nanotubes Graphene can grow into a large sheet. Carbon nanotubes (CNTs) can be made from graphene sheets as they bend. Bending within elastic limits of a material retains the material’s structure. Bending had been studied and seen in isolated CNTs between electrodes made out of CNTs [34]. Nanotubes can be combined with spotted minerals commonly found in serpentinite rocks from the earth's mantle and made using specifically designed substrates e.g. quartz to form nanotube serpentines. Nanotube serpentine is a material taking advantage of the defects. Devices such as antennas, radiators and cooling or heating elements benefit from the bending of these materials. 2.1.2.3.3 Edges of Graphene Nanostructures Graphene sheet reduction through cutting, forms graphene nanostructures with either zigzag or armchair type edges. Edges are involved in chemical reactivity [35], electronic structure [36] and vibrations [37]. The chemical reactivity of carbon drives the selective functionalization of graphene to the edges. This is an interruption of the sp2 hybridization of graphene in the honeycomb lattice, which is in contrast to the comparative unreactive basal plane. The unsaturation of the pz orbital and the break of the π conjugation on an edge increase the energy of the electrons at the edge sites, leading to specific chemical reactivity and electronic properties [38]. This

15


is significant during catalyzed development of carbon nanotubes in particular metalcarbon junctions [39]. The electronic properties of graphene, often in connection with the growth of the nanotube, or the electronic edge states have been studied extensively [40]. Due to less harmonization, atoms making the edges are more subject to reconstruction than those in the bulk, such materials have low melting temperatures, which usually begin from the edges or in areas near a defect. The effect of different edge properties on graphene nanoribbons have been described for the functionality of nano-electronic materials as used in transistor [41, 42]. Large vacancies have been found to deform with reconstructions [43] while, small or few-atom vacancies in the edges cannot be contrasted, in such a case, reconstructions take place during the closure [44]. 2.1.2.4 Graphene Oxide (GO) Pristine graphene has a zero bandgap. Much research has been done on how to tune the band gap in graphene-based semiconductor materials [45]. The band gap tuning is achieved in pristine graphene via nanopatterning [46, 47], application of gate voltage [48-51], or chemical functionalization [52-54]. In addition, the largescale manufacture of pristine graphene sheets remains challenging. Using GO, the functionalization product of graphene sheets oxidation can be fashioned by exfoliation [55]. Therefore, GO (which can have different compositions with several oxidation levels) synthesis conditions and processes are of significant interest. The solubility of GO in ethanol, water and among other liquids can be utilized as a precursor for establishing large-scale graphene, as well as the functionalization of the infusible and insoluble pure graphene sheets.

16

GO, being flexible, can be


modified as a semiconductor, an insulator, or a semi-metal having the potential for wiring to bio- and organic molecules. Zhang et al. [56] proposed either of the two types of configuration as a model of graphene oxide which predicts the atomic structure of GO by comparing to highly accurate synchrotron-based

X-ray

absorption near edge measurement [57]. The oxidation of graphite yields two types of GO: monoxides and dioxides. The epoxy graphene monoxide pair arrangement has been used for a low energy structural model for stoichiometric graphene oxides in theoretical calculations [55, 58]. Recently,

Zhang et al. [56] proposed either

type configuration as the ground state of the stoichiometric graphene oxide. They observed that the zigzag graphene monoxide (z-GMO) and armchair graphene monoxide (a-GMO) have lower energy and are more stable than the epoxy graphene monoxide (ep-GMO) and mixed graphene monoxide (mix-GMO) reported earlier by Xiang et al. [55]. In addition, the molecular dynamics study showed that graphene dioxide (GDO), which is not yet synthesized is not stable at high temperature in contrast to the z-GMO, which is stable up to 2000 K [56]. The electronic properties of GO depend on chemical structure [59-61]. The epoxide functional group significantly induces the local distortion of graphene with a new bond formed by graphene and oxygen atoms.

This affects the bonding

characteristics of carbon changing from planar sp 2 to partial sp3 hybridization. Considering an arrangement of epoxy functional group in fully oxidized graphene sheet and the effect of epoxy arrangement on electronic properties on the graphene sheets using a molecular carbon and oxygen (C:O) ratio of 1:1, results obtained from experimental measurement of Mattson et al. [58] yielded possible perspectives (Figure 2.4).

17


= Oxygen =Carbon

ep-GMO

a-GMO

GDO

Mix-GMO

z-GMO

Figure 2.4 Calculated atomic structure of a-GMO, ep-GMO, GDO, mix-GMO and z-GMO, along the xy, yz, xz planes, respectively [62]

2.1.3 Generation of Charge Carriers in Semiconductors (TiO2) When an electric field is applied through a metal, electric charge is conducted by accelerating the negatively charged electrons to the cathode from the anode. The result is that charge transfer occurs. Metal atoms are held together by metallic bonds. These bonds are formed by the atoms valence electrons joining together and surrounding the positively charged ions created by the nuclei and the core electrons of the filled valence band. Unlike in metals, both holes and electrons are responsible for charge transfer in semiconductors.

Positively charged holes i.e.

vacancies in the filled valence band or positively charged particles, also carry charge. Carrier generation thus takes place when an electron moves from the valence band towards the conduction band. This results from its encounter with other electrons, holes, photons, or the vibrating crystal lattice itself.

18


The distinctive electronic property of a semiconductor is described by its conduction (CB) and valence band (VB). The VB of a semiconductor is constituted of highest occupied molecular orbital (HOMO), whereas CB is made up of the lowest unoccupied molecular orbital (LUMO) [63]. There is no electron state between the bottom of the CB and the top of the VB. The energy range between the CB and VB is called forbidden bandgap (energy gap), which is usually denoted as E G. The band structure, including the bandgap and the positions of VB and CB (Figure 2.5), is one of the important properties of a semiconductor as it defines the light absorption property, as well as the redox abilities of a semiconductor.

Density of state

Figure 2.5: An illustration of the electronic property of a semiconductor [63]

When a semiconductor absorbs photons with energy greater than or equal to its E G, electrons in the VB are promoted to the CB, and this leaves holes in the VB. The electron−hole pair generation process in a semiconductor like TiO2 can be expressed as eqn. 2.1. [63], 19


TiO2 + hν → e- (TiO2) + h+ (TiO2)

(eqn. 2.1)

These photogenerated electron and hole pairs undergo one of the following processes; (i) effectively migrates to the surface of the semiconductor, (ii) are retained in the defective sites in the mass and, or on the surface area of a semiconductor or (iii) recombines and releases energy as heat or photons. Processes (ii) and (iii) can generally be viewed as deactivation.

Only the

photogenerated charges that reach the surface of a semiconductor could be available.

The defect sites in the mass and on the surface may act as the

recombination centres, which will decrease the effectiveness of the reaction.

Efficient charge separation is important to consider because For example, preparation of semiconductor at high temperatures may lead to high crystallinity that reduces the formation of charge recombination defect sites. Nano wires [64, 65] may also aid in charge separation and therefore, aid in transportation.

In

comparison to a zero dimensional nanoparticle, one dimensional nanostructures have a better charge mobility thus improving the activity and minimizing the charge recombination.

TiO2 coupled with carbon-based materials, especially with graphene has attracted increasing attention. Graphene with defined electronic properties can be chemically bonded with TiO2 [42]. Graphene material exhibits high mobility of charge carriers and has good mechanical strength [66]. Therefore, these carbon-based materials enable charge transfer and inhibit the charge recombination process when

20


combined with TiO2 based photocatalysts. Ou et al. [67] synthesized a multiwalled carbon nanotube, TiO2, and Ni composite catalyst (MWCNT-TiO2: Ni) using a modified chemical vapour deposition method. In their findings, the MWCNT acted as a photosensitizer and increased the H2 evolution rate under visible light irradiation [67]. Graphene, as a cocatalyst on TiO2, is predicted to behave as an electron acceptor due to its lower potential of graphene when compared to the TiO2 composite [64]. The interface between two types of semiconductor material (junctions) including the contact of two materials with different electrical properties (heterojunction) , may be helpful for the charge separation. The enhanced activity may be due to the junction effect.

Further improvement of the photocatalytic properties of TiO 2/MWCNT

composites with silver nanoparticles through an improved plasmonic resonance effect has also recently been reported [65]. 2.1.3.1 Different Phase Structures of TiO2 TiO2 exists in four main polymorphs namely: anatase, rutile, brookite and TiO 2 (B). The structural parameters of these polymorphs are provided in Table 2.1.

Table 2.1. Four main polymorphs of TiO2 Unit Cell Parameters Crystal

Crystal

Space

a/nm

Form

structure

group

Anatase

Tetragonal

I41/amd

0.379

0.951

Rutile

Tetragonal

P42/mnm 0.459

0.296

Brookite

Orthorhombic

Pbca

0.918

0.545

0.515

TiO2(B)

Monoclinic

C2/m

1.216

0.374

0.651

21

b/nm

c/nm

β/deg

107.3


TiO2 consists of TiO6 octahedral compounds, which differ, in their distortion of the octahedron units, making four polymorphs, as shown in Figure 2.6.

(a)

(b)

(c) Oxygen Titanium

Figure 2.6: TiO2 in different crystal structure arrangement: (a) anatase (b) rutile and (c) brookite [15] For anatase, the octahedral arrangement is such that four edges are shared in the zigzag arrangement, while in rutile, the octahedral arrangement has two edges, which are connected in linear chains and in parallel [68]. Brookite has both corners and edges connected [69]. Rutile is mostly derived from layered titanates. Therefore, its structure is composed of corrugated sheets with both edges and corners shared [70]. The difference in lattice structures results in different mass densities and electronic band structures of TiO2. Rutile is most thermodynamically stable, while anatase and brookite are metastable. Rutile can normally be obtained after annealing the three polymorphs at elevated temperatures. Li and co-workers [71] investigated the typical transformation processes from anatase to rutile. The 22


phase

transformation

of TiO2 anatase

nanoparticles

originates

with

the

agglomerated anatase particles and then proceeds to a bulk phase conversion. The most extensive research on TiO2 is focused on using it as a material for solar energy conversions. These investigations are primarily on anatase and rutile.

Various

studies have been carried out using the TiO2 model semiconductor as a photocatalyst to produce H2 from biomass reforming, water splitting,

industrial

waste reforming, and to produce carbon-based solar fuels via CO2 photoreduction [63]. TiO2 only absorbs UV light up to 380 nm, which is an intrinsic limitation for the TiO2-based photocatalysts to achieve efficient light harvesting.

Anatase and rutile TiO2 structures are mostly used in the study of photocatalysts, where the difference in structure led to different electronic band structures, densities and energy gaps (bulk anatase has an energy gap of 3.20 eV, which corresponds to 384 nm, while rutile with E g 3.02 eV corresponding to 410 nm) giving anatase a slightly higher redox driving force and reduced absorbance in the visible region [63].

TiO2 photocatalytic reactions start from light absorption, usually restricted by the number and energy of the photons absorbed. Since it has a wide bandgap (E g ≈ 3.0 eV), it absorbs in the UV region, which is a major drawback. Much research has been devoted to extending absorption to the visible light region. Two most efficient strategies employed to do so include; (1) narrowing the bandgap of TiO2 by introducing other elements through bandgap engineering and (2) visible light active materials have been applied through surface sensitization, to act as light harvesters.

23


2.1.4 Titanium Dioxide on Carbon-based Materials Titanium dioxide has been coupled with carbon-based materials, especially with graphene.

Graphene has defined electronic properties and can be chemically

bonded with TiO2 [42]. Graphene material allows charge to flow easily and is of high strength [69, 70]. Therefore, these carbon-based materials enable charge transfer and inhibit the charge recombination process when combined with TiO 2 based photocatalysts.

2.1.5 Transport of Charge Carriers by CNT’s (Graphene systems) Graphene’s properties, such as ballistic transport, zero band gap, high mobility and ease of modulation of its electrical properties have made it peculiar. It has a zero density of state where the valence bands and conduction bands meet and a near Dirac point with a very low density of states [72]. Since graphene is one atom thick, its whole volume is exposed to the surroundings and its properties are very responsive to the surrounding atmosphere including temperature, substrate and adsorbate molecules. The charge transport in graphene-based organic semiconductors (OSs) is via hopping, as charge carriers must overcome large barriers between the molecules or localization sites [73]. In a region of crystalline order, the charge carrier mobility is relatively high due to short and organized (hopping) distances among molecules. The hopping site arrangement within a disordered material varies by both position and energy. Disorder includes structural disorder (defects) and the presence of chemical inhomogeneities and impurities. These abnormalities introduce trapping sites. These sites are due to the presence of water, chemical residues and grain boundaries in semi-crystalline materials [63]. Relatively low charge carrier mobility in disordered OSs is a consequence of weak intermolecular interactions and 24


resulting localization of charge carriers or confining by chemical impurities and other trap states formed by the structural disorder. Mobility is an important parameter that has been investigated to understand charge transport in OSs. The mobility of an organic material relies on its temperature, applied electric field, atmospheric conditions and molecular ordering. The time of flight (TOF) method is mainly used to experimentally determine mobility.

2.1.6 Time-of-Flight Method (TOF) TOF has been used extensively in most experimental studies of charge mobility in disordered organic materials [74]. The time of flight is founded on measurement of charge transit time (ttr) specifically, the time essential for photogenerated charge carriers at one electrode to move across the sample to the other electrode under an applied electric field. Electron-hole pairs are made by photo-excitation of the film through irradiation with a short pulse laser whose wavelength depends on the material. Depending on the polarity of the applied bias, photo-generated charge carriers will start moving to the other electrode. The drifting carriers build a current that can be calculated using (eqn.2.2), 𝑁𝑒𝑣⁄ 𝑑

(eqn. 2.2)

where N denotes the number of charge carriers in the material, e the elementary charge, d the film thickness and v is velocity. In this method, the hole and electron mobility can be studied separately. The TOF technique was suggested by W. E. Spear in 1957 [75, 76] as a method for carrier charge mobility in semiconductors.

The TOF method is used for determining the mobility of charge carriers by detection of their field-induced transport through a sample beginning at one electrode to the

25


arrival at the opposite electrode. This method avoids the intrinsic effects of the microscopic interface environment between the material and electrodes.

This

method also avoids high injection based currents in conventional transport measurements. There are two types of TOF methods:

1. Sandwich time-of-flight method (S-TOF), in which the material under investigation is sandwiched between two electrodes, and charge transport occurs in the direction perpendicular to the electrode surface. 2. Coplanar time-of-flight method (C-TOF), in which the material under investigation is deposited between two coplanar electrodes, and charge transport occurs in the direction parallel to the electrode surface. 2.1.6.1 Sandwich Time-of-Flight Method (S-TOF) In this method, the semiconducting material is sandwiched between the two electrodes, of which one is transparent for exciting photons. A strongly absorbed laser flash creates electron–hole pairs beneath the illuminated electrode.

The

applied voltage sweeps the appropriate type of carriers through the sample, while the other type of carrier is instantly collected at the illuminated electrode. The wavelength of the incident light corresponds to the maximum absorption of the material. The displacement current of the carriers moving across the sample is measured in the external circuit and allows for the determination of the ttr, which is identified by a sudden drop mobility is then calculated using (eqn 2.3): in the current that corresponds to the carriers reaching the collecting electrode [77, 78]. If two electrodes parallel to each other, are kept at a constant separation (d) and a

26


constant voltage (v) is applied between them, and the electric field (E) produced between them is uniform, defined as 𝐸 = 𝑉⁄𝑑, the mobility is then calculated 2

𝜇 = 𝑑 ⁄𝑉𝑡 𝑡𝑟

(eqn. 2.3)

since 𝑉𝑑 = 𝜇𝐸

𝑎𝑛𝑑

𝑉𝑑 = 𝑑⁄𝑡

(eqn. 2.4)

𝑡𝑟

2.1.6.2 Coplanar Time-of-Flight Method (C-TOF) In this method, the semiconducting material under investigation is deposited between two coplanar electrodes, and charge transport occurs in the direction parallel to the electrode surface. The material is excited with the incident light near the bias electrode and electron-hole pairs (excisions) are created. If a positive voltage is applied to the illuminated electrode, the electrons from dissociating excitations at the electrode/sample interface will rapidly move into the illuminated electrode leaving holes to drift across the sample to the counter electrode where they will discharge. Similarly, if a negative voltage is applied to the illuminated electrode, then the holes will be attracted to the negatively charged electrode, while electrons will drift in the opposite direction, enabling us to observe electron transport. The counter electrode is connected to the oscilloscope [74]. The important differences of C-TOF compared to the S-TOF method are listed below. 1. Charge transport in the S-TOF method is in the bulk of the material. However, in the C-TOF method, the charge flows across the thin film structure.

27


2. The channel length can be easily varied using a shadow mask or lithography technique.

In S-TOF method, the thickness of the sample must be over

several tens of microns and a lot of material is required for deposition. It is almost impossible to study the thin film materials especially the graphene like materials. C-TOF allows us to study structures that are similar or identical to field effect transistors (FETs). Electrical charge transport in semiconductors is typically studied by monitoring the current of the charge carriers that are either photogenerated or injected from metallic electrodes into the organic semiconductor (OS). However, the ohmic contacts for the OS are pre-requisites for the lossless transport, which is difficult to find especially for transport of both positive holes and negative electrons (ambipolar OSs), like graphene-related materials.

In order to avoid the role of metal/OS

interface, Pathipati [79] employed photo generation inside the OS layer, and the drift current of the charge carriers under the applied bias, known as displacement current measured in the external circuit. This method is called time-of-flight (TOF) photocurrent measurement technique. The rGO-based field effect transistor (FET) measurements reveal that the connectivity of graphitic domains has important implications on the conductivity, as well as on mobility of charge carriers. The mobility estimated for rGO on Si/SiO2 from both FET and TOF measurements are in good agreement [74]. The conductivity of rGO on fused silica and sapphire is two orders of magnitude higher than rGO on SiO2, due to the well-connected regions of graphitic domains [74].

28


2.1.7 Silica on CNTs and Graphene Silica (SiO2) is a chemical compound that is an oxide of silicon. Mostly it is obtained by mining and purification of quartz rock. SiO2 exists in various polymorphs; cristobalite high, cristobalite low, quartz, quartz beta and stishovite (Figure 2.7). Silica-derivative nanostructures are of special interest because of their hydrophilic nature, the ease of functionalization and wider potential applications [80]. In the past decade, uniform silica has been successfully deposited on a variety of colloidal metal particles [81], metal oxides and semiconductor quantum dots [82]. Several methods have been developed, such as plasma-enhanced chemical vapour deposition to coat silica on CNTs [83].

(a)

(b)

(d)

(e)

(c)

=O

= Si

Figure 2.7: Various Silica polymorphs: (a) cristobalite high (b) cristobalite low (c) quartz (d) quartz beta (e) stishovite

29


For pure nanocomposites [82, 84, 85], CNTs mainly improve wear resistance, selfsensing abilities and flame retardance by taking advantage of the excellent electric and thermal properties.

As a result of these important characteristics, a new

generation of multifunctional products may be developed [84]. Proper adhesion between matrices and fibres is a pre-condition of stress transfer thus the reinforcing fibres are improved to increase chemical and mechanical interactions [86], e.g. by oxidation [87] or whiskerization [88]. Carbon nanotubes improve the surface area and make interlocking possible, hardening at the fibre-matrix interface, and thus improving stress transferral. Baker and Downs [85] showed an increase of 4.75 times of the interfacial shear strength (IFSS) of the composites with carbon nanofiber-grafted carbon fibres. Large scale production of CNTs is done through chemical vapour deposition (CVD) techniques, proficient to meet the anticipated characteristics for combined applications, bulk production, specificity, high purity, acceptable quality and low cost. Chemical vapour deposition is the commonly used method to graft CNTs onto fibre surfaces [89,90].

Qian et al. [91] reported excellent wettability of carbon nanotubes by poly (methyl methacrylate) (PMMA). In their study, they found that the approach of creating hierarchical compounds with CNT-grafted fibres improves IFSS. This also gives a controlled way of having high loadings of oriented CNTs into the matrix wi thin the fibres. As a result, this improves critical engineering properties of conventional fibre reinforced combinations, like longitudinal compression, inter laminar shear strength and strength [91].

30


2.1.8 Titanium Dioxide on SiO2/CNT Composite versus CNT Titania has a relatively wide energy gap, and as a result, this has become a major impediment in its applications as a photocatalyst. This reduces its effective use within the visible light spectrum [92]. In order to overcome this disadvantage, various strategies have been employed to decrease the energy gap and hence , improve the production of charge carriers and the lifetime of charge carriers; reduce the recombination rate of the photogenerated electron and holes, and therefore, improve the overall photo-catalytic effectiveness of TiO2. In practice, the addition of non-metals or metals, either as surface deposits (layer) or chemically fused (a dopant), and the use of supports have been tested on TiO2 and cautiously manufactured as nanofibers, nanotubes, nanoparticles, mesoporous structures or as thin films [89].

To increase the general photocatalytic effectiveness of TiO2, support such as an ordered mesoporous material having mono-dimensional pores (31–64 Å) grade SBA-15 on carbon nanotubes has been reported [93]. SBA-15 is a grade of silica material having comparatively thick walls and bigger pores. This makes it hydrothermally steady with mesoporosity and microporosity. Its synthesis requires less time obtaining a tuneable morphological characteristic material. Many studies are reported in literature of the use of TiO2 supported on SBA-15 for photocatalytic applications [94, 95]. Among them, Yang et al.[89] considered several weight percentages of titania distributed on SBA-15. They applied a surfactant free sol-gel method and established that a 30 wt. percentage is the optimum photocatalyst for the degradation of methylene blue.

31


TiO2 nanoparticles, when used with multi-walled carbon nanotubes (MWCNTs) produces an improved photocatalytic activity [90]. Some fascinating results with earlier work [65, 90, 93] using titanium on multi-walled carbon nanotubes reported excellent physisorbed systems having improved photo activity. The reason for the improvement was thought to arise through longer-lived electron-hole charge carriers that finally yield large quantities of radicals. The CNTs give added sorption properties, and the composites greater visible light sorption properties [96, 97]. However, TiO2-carbon nanotubes have found application in making

hetero-

junctions in materials with improved photo-catalytic efficiency [90]. 2.2 COMPUTATIONAL APPROACH 2.2.1 Introduction The theoretical methods employed in this research includes both static and dynamic situations.

The calculations originate from first-principles equations.

However,

approximations are employed that limit the size of the system. These are easier or faster to solve and important to the underlying equations that are needed to attain any solution. In practice, ab initio methods do converge, to the exact solution of the true hydrogen atom.

All other molecules make use of approximations to the

fundamental equations.

Although they finally converge as the number of

approximations is reduced. It is difficult to eradicate all approximations, and residual error unavoidably still remains. Thus, the aim is to reduce the residual error, while keeping the calculations tractable.

32


2.2.2 Semi-empirical and Ab initio Methods In semi-empirical methods, many of the integrals are estimated by referring to spectroscopic data or physical properties, such as ionization energies, and then using a series of rules to set certain integrals to equal to zero.

In ab initio

approaches, effort is made to calculate the integrals that appear in the Fock model and overlap matrices.

Calculating all the integrals is a time-consuming task.

However, the task is simplified by conveying the atomic orbitals used in LCAOs (linear combination of atomic orbitals) as linear combinations of Gaussian orbitals. The Hartree Fock matrix elements consist of integrals in the form of eqn. 2.5, (𝐴𝐵 |𝐶𝐷) = ∫ 𝐴 (1)𝐵(1) (

𝑒2 4𝜋𝑒0 𝑟12

) 𝐶 (2)𝐷(2)𝑑𝑟1 𝑑𝑟2

(eqn. 2.5)

With A, B, C, and D being the atomic orbitals that are centred on different nuclei. When there are numerous orbitals used to form the molecular orbitals, the number of integrals increases to the fourth power of the number of atomic orbitals in the basis. For CNDO (complete neglect of differential overlap), all integrals are set to zero unless A and B are the same orbitals centred on the same nucleus and likewise for C and D. The persisting integrals are then attuned until the energy levels are compared with experimentally obtained results. Recent methods are less severe in decisions about which integrals are to be ignored but are all descendants of the early CNDO technique. These are commercially available in software packages, which are typically used for generating initial starting structures for the more intensive ab initio based simulations. They are also often used for large scale hybrid QM/MM MD simulations.

33


Several packages for ab initio calculations are available where they express the integrals in the linear combination of atomic orbitals (LCAOs) as Slater-type orbitals (STOs) (eqn 2.6) or linear combinations of Gaussian orbitals (eqn 2.7) 1

𝑆𝑇𝑂 𝑋𝑙𝑠

ℶ3 2

= ( 𝜋 ) exp(−ℶ𝑟)

(eqn. 2.6)

3

𝑋𝐺𝑇𝑂 𝑙𝑠

=

2𝛼 4 ( ) exp(−𝛼𝑟2 ) 𝜋

(eqn. 2.7)

Molecular orbitals (MO) are given by the linear combination of atomic orbitals (LCAOs) (eqn 2.8) 𝜓𝑖 = ∑𝑁 𝜇=1 𝐶 𝜇𝑖 ∅𝜇

(eqn. 2.8)

where ψ is molecular orbital and Φ atomic orbital basis set. This is an approximation if the summation is terminated and the types of basis functions used are Slater-type orbitals (STO), for a true H-atom. For Gaussian-type orbitals (GTO), the required orbitals in the closed form are computationally faster but less accurate and therefore, need more basis functions.

∅𝜇 = ∑𝑠 𝑑𝜇𝑠 𝑔𝑠

(eqn. 2.9)

where Φ is the atomic orbital basis set and g the primitive GTOs. In Gaussian-type orbitals (GTO) (eqn 2.9), the minimal basis set has one basis function for each orbital, e.g., 1 function for H (1s); 5 functions for Li to Ne (1s, 2s, 2px, 2py, 2pz). For good results, double-zeta basis set (DZ) with two basis functions in each orbital is required. The triple-zeta basis set (TZ) has three basis functions

34


for each orbital, but these are computationally expensive [98]. In the Pople-style basis sets: (3-21G) 1 function composed of 3 primitive Gaussians for inner shell orbitals plus 2 functions for the valence orbitals, one function composed of 2 primitives, one function a single primitive. The 6-31G basis set is comprised of 1 function composed of 6 primitive Gaussians for inner shell orbitals, 2 functions for the valence orbitals, one function composed of 3 primitives, and one function is a single primitive, 6-31G* has six d-functions for atoms other than hydrogen added, and 6-31G** has three p-functions for each hydrogen added. The advantage of GTOs over the Slater-type orbitals (STOs) is that the product of two Gaussian functions is itself a Gaussian function that lies between the centres of the two contributing functions (Figure 2.8).

Figure 2.8: Illustration of Gaussian functions and their product [98] In this way, the four-centre integrals in eqn. 2.10 become two-centre integrals of the form,

35


(𝐴𝐵 |𝐶𝐷) = ∫ 𝑋 (1) (

𝑒2 4𝜋𝜀 0 𝑟12

) 𝑌(2) 𝑑𝑟1 𝑑𝑟2

(eqn. 2.10)

where X is the Gaussian corresponding to the product AB and Y is the corresponding Gaussian form. Integrals of this form are much easier and faster to evaluate numerically than the original four centre integrals. Thus, more GTOs have to be used to simulate the atomic orbitals. However, adding more GTOs will result in an increase in computation time. Nonetheless, it is still faster than the Slater type orbitals offering an overall increase in the speed of computation and improved accuracy [1].

2.2.3 Density Functional Theory DFT is a technique that has gained considerable ground over the years. It has, among others, become the state of the art technique for the theoretical study of electronic structure and thus, is successfully and widely used in calculations by engineers and in science [76]. Its advantages are: moderate computational effort, reduced computer time, and in some cases (particularly d-metal complexes) better agreement with experimental values. Although several anticipated properties are obtained, some failures have been observed such as underestimation of band gaps which can be traced to the static correlation error and delocalization error as used in estimates.

The core focus of DFT is on electron density (ρ) instead of wave function (ψ) [76]. The ‘functional’ part comes from the fact that the energy of the molecule is a function of the electron density, [ρ] (eqn. 2.11): The electron density is itself a function of position, ρ(r), and in mathematics a function of a function is called a functional [16]. 𝐸 [𝜌] = 𝐸𝑘 + 𝐸𝑃;𝑒,𝑁 + 𝐸𝑃;𝑒,𝑒 + 𝐸𝑋𝐶 [𝜌]

(eqn. 2.11)

36


where 𝐸𝐾 is the total electron kinetic energy, 𝐸𝑃,𝑒,𝑁 the electron–nucleus potential energy, 𝐸𝑃,𝑒,𝑒 the electron-electron potential energy, and 𝐸𝑋𝐶 [𝜌] the exchange correlation energy, which takes into account all the effects due to spin. The orbitals used to construct the electron density (eqn. 2.12), 2 ρ(r) = ∑𝑁 𝑖 =1 |ψ 𝑖 ( 𝑟 )|

(eqn. 2.12)

are calculated from the Kohn–Sham equations [99], which are found by applying the variation principle to the electron energy, and like the Hartree–Fock equations [100] except for the term V XC, which is called the exchange–correlation potential (eqn. 2.13): 𝐸𝑙𝑒𝑐𝑡𝑟𝑜𝑛 −𝑛𝑢𝑐𝑙𝑢𝑒𝑠 𝑎𝑡𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛

𝐾𝑖𝑛𝑒𝑐𝑡𝑖𝑐 𝑒𝑛𝑒𝑟𝑔𝑦

⏞ ħ ∇2 − 2𝑚 𝑒 𝐼

⏞𝑁 𝑍 𝑒2 ∑ 𝑗 4𝜋𝜀0 𝑟𝑗𝐼

𝐸𝑙𝑒𝑐𝑡𝑟𝑜𝑛−𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛 𝑟𝑒𝑝𝑢𝑙𝑠𝑖𝑜𝑛

+

𝑗=1

⏞ 𝜌(𝑟2 )𝑒 2 ∫ 4𝜋𝜀0 𝑟𝐼2

{

𝐸𝑥𝑐ℎ𝑎𝑛𝑔𝑒 − 𝑐𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛

𝑑𝑟2 + ⏞ 𝑉𝑋𝐶 (𝑟1 )

𝜓𝑖 (𝑟1 ) = 𝜀𝑖 𝜓𝑖 (𝑟1 ) } (eqn. 2.13)

The exchange–correlation potential is the ‘functional derivative’ of the exchange correlation energy (eqn. 2.14). 𝑉𝑋𝐶 [𝜌] =

𝛿𝐸𝑋 𝐶 [𝜌]

(eqn. 2.14)

𝛿𝜌

The Kohn–Sham equations are solved iteratively and self-consistently. The electron density is initially a guess. For this step, it is common to use a superposition of atomic electron densities. Then the exchange–correlation potential is calculated by assuming an approximate form of the dependence of the exchange–correlation energy on the electron density and evaluating the functional derivative. For this

37


step, the simplest approximation is the local-density approximation giving in eqn. 2.15: 𝐸𝑋𝐶 [𝜌] = ∫ 𝜌(𝑟) 𝜀𝑋𝐶 [𝜌(𝑟)]𝑑𝑟

(eqn. 2.15)

where 𝐸𝑋𝐶 is the exchange–correlation energy per electron in a homogeneous gas of constant density. Next, the Kohn–Sham equations are solved to obtain an initial set of orbitals. This set of orbitals are used to obtain a better approximation to the electron density (from eqn 2.15) and the process is repeated until the density and the exchange–correlation energy are constant to within some tolerance [1]. The Hohenberg-Kohn theorem [101] on DFT states that there is a unique correlation among the electron wavefunction, the ground state electron density, and the effective potential. Moreover, every ground state exhibits the same intrinsic association with the electron density via the ground state wavefunction [102]. This theorem reduces the full many-electron issue to rely only on one variable (electron density), which determines the full many-electron wavefunction, as well as all the observables. The many-electron issue is still computationally expensive and difficult to deal with. Using the one-electron theory, the total energy of an interacting manyelectron system can be determined. The derivative of the Hamiltonian can also be used to solve forces directly based on the Hellman-Feynman theorem [103]. The Kohn-Sham method [99] completes the standard density functional theory method by simplifying the true interacting system with a non-interacting model system, which gives the same electron density as the interacting system. This task can effectively be accomplished with the help of the Hellman-Feynman theorem. In this theorem, the interactions, which are not accounted for in the non-interacting model system are fitted to an extra energy term

38


called the exchange-correlation energy. If the exchange-correlation energy is exact, the Kohn-Sham method is exact. The Kohn-Sham method converts the manyelectron problem to a set of separate and coupled single-electron problems. DFT requires a suitable basis set for the single-electron wavefunctions, as well as approximations for the exchange-correlation functional. Although the contribution from the exchange-correlation energy into the total energy is small, DFT plays a key role in investigating energy differences (e.g. adsorption energy). The commonly used basis set are the atomic orbitals, Gaussian functions or plane waves with the latter using Bloch's theorem [104] to describe the electron wavefunctions in the periodic potential of a lattice. The first one describes the atomic orbitals and the second one treats the wavefunctions with a set of Gaussian functions. Besides the basis sets, simplifications have also been used to decrease the computational load. Pseudopotentials treat only the relevant valence electron states by simplifying the inert core electrons with simple potential.

Solutions to the

pseudopotential method are pseudo wavefunctions, which vary from the real wavefunctions but offer similar information on the measurable observables.

2.2.4 Model Chemistries The model chemistries in this study involve DFT, B3LYP, M06 (meta-GGA) and LACVP*. DFT has been successively used in the study of atoms, molecules, clusters, surfaces and solids, and it has proven to be the method of choice for electronic structure theory in structural material science and surface chemistry. The main limitations of DFT are the type of functionals applied. Wrong choice(s) can lead to major drawback, hence the choice becomes crucial.

39


The DFT - B3LYP hybrid is quite inadequate in some parameter tests, such as van der Waals’ forces description, it is thus, appropriate for the main group elements in the periodic table other than transition elements [105]. Zhao and Truhlar developed a new variety of functionals called the M06-class which depend on the spin (densities, gradient, kinetic energy density) amongst others [105].

Zhao and

Truhlar’s development of the M06 family of local (M06-L) and hybrid (M06, M06-2X) meta-GGA

functionals

show

promising performance

for the

kinetic and

thermodynamic calculations without the need to refine the energies by post-HartreeFock methods. M06 gave good results for transition element energies as well as electronic wavefunctions when expanded via plane-wave correlation effects, exchange and basis sets, these can be included within either the generalized gradient (GGA) or local density (LDA) approximations for improved accuracy. Combining the use of plane wave basis sets and pseudopotentials enables extremely efficient geometry optimizations of molecules, solids, surfaces, and interfaces [105].

To account for the general underestimation and lattice constants overestimation by DFT, several approaches, such as the combination of PBE and GGA + U (where U is the Hubbard parameter), hybrid functionals, quasiparticle GW approximation (GWA) and other methods have been developed. DFT + U approach takes appropriate description for the localised and strongly correlated electron system due to the consideration of the electronic interactions of the d and f electrons as an intrinsic part of the electronic system. The approach gives precise information on

40


the electronic structure at the expense of computational cost. This method has been extensively used in other studies too [105].

The LACVP* basis set is a combination of the 6-31G basis set with the LANL2DZ effective core basis set, developed by Dunning, for first row elements [106], i.e. atoms from hydrogen to Argon are best described with the 6-31G basis set and the Alamos ECP plus double zeta basis set developed by Wadt and Hay [107] for the atoms Na to La and Hf to Bi [108]. The LACVP* basis set is the most successful basis set for the study of heavy transition metal chemistry and is most commonly used when these elements are involved.

2.2.5 Computing of First Order Rate Constants Calculating the rate constant of a first order reaction can be based on the vibrational transition state theory [109], in addition to multi-dimensional semi classical tunnelling corrections. The potential energy surface information is calculated from DFT. To calculate the rate of the carbon and hydrogen reaction, a combination of half exchange and Becke half [110] and Lee-Yang-Parr correlation functionals (BH&H-LYP)

are used to compute the potential energy surface using the 6-

311G(d,p) basis set. It has been found that the transition state geometries and BH&H-LYP generalized frequencies as functions of the reaction coordinate are in agreement with the QCISD calculations [111]. To advance the energetic results along the minimum energy path (MEP), the potential energy can be scaled along the MEP to match the more precise conventional barrier. This can be done at a series of sole point calculations within selected points along the MEP at an advanced level of the ab initio model [111]. Both methods produced rate constants in outstanding agreement with the experimental data. Direct ab initio dynamic 41


methods provide a practical and powerful dynamical simulation tool by merging the computational advantages of variational transition state theory and DFT. It is thus, possible to carry out detailed mechanistic and dynamic calculations of large and more complex chemical reactions from first-principles.

2.2.6 Molecular Orbital Theory and Charge Transfer The molecular orbital (MO) theory considers the molecular orbital of a whole molecule rather than the individual atoms that constitute it. In the bonding between two atoms, the pair of electrons occupy molecular orbitals that are a mathematical combination of the wave functions of the atomic orbitals of the two atoms involved [112]. The charge mobility of a covalently bonded material is defined as the ratio between the drift velocity of the charge carrier (𝑣) induced by the electric field and the amplitude of the applied electric field (𝐹) 𝑈 = 𝑣/𝐹. This is dictated by the diffusion coefficient (D) and is related to the diffusion coefficient via the Nernst–Einstein equation (eqn. 2.17).

𝑈 = 𝑒𝐷/𝐾𝐵 𝑇

(eqn. 2.17)

The carrier mobility strongly depends on the chemical structure and the preparation of the sample, the processing conditions and the measuring technique. The most common experimental methods used to characterize charge mobility is the time of flight [113], field effect transfer configuration [114], diode configurations [115] and pulse radiolysis [116].

42


Two models have been used theoretically: band and hopping, which describe charge transport and carrier mobility. In the band model, inorganic semiconductors are covalently bonded. The formation of bands, i.e. the conduction and valence is strongly distinct with a typical band gap of 1-3 eV. The advantage is taken in band model of well-constructed valence and conduction bands after scattering. In organic single crystals, weak van der Waals forces and the π-π interactions play a role in holding the constituent bonds together. The formation of a narrow band structure, presence of disorder and electron-phonon interaction restrict the validity of a band like charge transfer mechanism. Exceptions occur at high temperature and these lead to a band-hopping cross over. At high temperature the hopping model applies, as the phonon population becomes quite large in strong electron–phonon interactions. The existence of a narrow band and the strong electron-phonon interaction along with the structural disorder of the system causes the confinement of charge in a localized polaronic state. Thus, the mean-free path for the scattered charge carriers become comparable to the order of intermolecular spacing, which enforces the charge carriers to hop between adjacent localized states through a process called the thermal activated hopping mechanism [117]. This occurs mainly in organic molecules at room temperature where each step is described within the semi classical Marcus theory [118].

2.2.7 Computing Spectral Data When computing spectroscopic data the molecular phenomena that are being studied and described is based on the electronic spectrum as shown in Figure 2.9 [119].

43


Wavelength (nanometers) 0.01

1

100

1 nm Gamma

x-rays

104 1 micron

UV

infrared

106

108

1 mm

1010 1 meter

Radio waves

Rays Blue

Red

400 500

600 700

Visible Region

Figure 2.9: Diagram illustrating the electromagnetic spectrum

In the high energy region of gamma ray photons (>10 4 eV), nuclear processes are studied, e.g. in Mössbauer spectroscopy transition amid different states of a

57Fe

nucleus are investigated [120]. Radiation in the soft x-ray and hard areas (~104102 eV) brings atomic electronic transitions from core-levels into the non-bound or empty valence levels continuum [121]. Ultraviolet and visible photons (1-4 eV) induce electronic excitations from filled to empty valence levels [122]. It is this energy region where the photon energy is of the same order of magnitude as the energy of chemical bonds. Therefore, electronic spectroscopy straight probes chemical bonding. Underneath the energy of visible photons, it is no longer possible to induce electronic transitions consequently, infrared photons (0.01- 0.5 eV ~100 - 4000 cm1) which purely induce transitions between different vibrational levels of the molecule within a given electronic configuration at even lower energy (104 -105 eV; ~1-10 cm1) is applied. The

44


magnetic properties of the element are associated with electron spin. This is probed by electron paramagnetic resonance (EPR) or electron spin resonance (ESR) spectroscopy. For radio wave photons (106 – 107; ~0.001-0.01 cm1) one is only able to induce transitions between different states of magnetic nuclei and these are explored in NMR and electron nuclear double resonance (ENDOR) spectroscopy. 2.2.7.1 Infrared and Raman spectroscopy Raman spectroscopy and Infrared

are mutually

complementary

molecular

vibrational spectroscopies. Their central principles differ, but they are together used for the observation of the excitation of molecular vibrational energy states associated with the electronic ground-state potential energy surface [123].

In

Raman measurements, the excitation is a result of inelastic light scattering by a molecule. The shapes of different vibrations are characterized by different patterns of the joint nuclear displacements and are called normal modes. IR spectroscopy analyse vibrational excitations which come about upon the absorption of electromagnetic radiation. Based on the assumption that the PES is quadratic in atomic displacements, the vibrational states of an M-atom molecule are defined as a superposition of 3M-6 independent harmonic oscillators, which describe the collective harmonic vibrational motion of the nuclei about their equilibrium configuration. They transform under the irreducible representation to the molecular symmetry group and may, thus, be classified by their proportion [123]. 2.2.7.2 Quantum Chemical Calculation of IR and Raman Spectra Within the harmonic calculation, Raman and IR vibrational spectra are computed by using frequency calculations. Subsequently, harmonic vibrational frequencies are calculated by the value of the Hessian matrix at the ground state equilibrium

45


geometry, it is critical that frequencies are computed for the geometric structure optimized at the same level of theory [124]. Vibrational modes also indicate if a molecule is a minimum on the potential energy surface. This is when there are no imaginary (negative) frequencies.

Moreover, it can also show if you have a

transition state or saddle point when there is 1 negative frequency.

46


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62

CHAPTER 3: COMPUTATIONAL DETAILS

3.1

Introduction

This chapter briefly describes the quantum mechanical software and hardware used in this study.

3.1.1 Biovia Materials Studio (2016)

Materials Studio is a modelling and simulation software [1], which enable users in the areas of chemistry [2-4] and materials science [5-7] to predict and understand a material’s atomic and molecular structure via their computed behaviour and properties [1].

Calculations performed with the Biovia software gives efficient,

validated, and comprehensible quantum mechanical solutions founded on Density Functional Theory (DFT) [8-11] methods. The software is also capable of conducting simulations with hybrid quantum mechanics/molecular mechanics (QM/MM) [8, 9] and semi-empirical [10] methods for some systems as well.

Methods in quantum mechanics give accurate kinetic [11], thermodynamic [12-14], and structural [15] results, offering a useful adjunct to experimental results. These methods give insight into processes at the atomic level, making one understand why and how a process occurs. It is applied in various semiconductors [16], catalysis [17] and energy storage [18] materials. Materials Studio quantum and catalysis tools are known to accurately predict crystal and molecular geometry, chemical

63

Chapter 3: Computational Details

reaction pathways, optical properties, and spectral data such as UV/Vis, Raman, IR, and NMR amongst many others [1].

3.1.2 Cambridge Sequential Total Energy Package (CASTEP) This is an ab initio quantum mechanical program which uses DFT to simulate the properties of solids [19, 20], interfaces [21-24], and surfaces [25, 26] for a wide variety of materials, such as semiconductors [21], ceramics [27], and metals [28]. First principle calculations [29] enable researchers to find the nature and origin of the optical [30], structural and electronic [31] properties of a system without the need for any experimental input. CASTEP employs a total energy plane wave pseudopotential method [32] in the mathematical model of the material. The Materials Studio implementation of CASTEP substitutes core electrons with effective potentials acting on the valence electrons in the system [21]. Electronic wavefunctions are expanded via plane-wave basis sets, exchange and correlation effects, which can be included within either the local density (LDA) or generalized gradient (GGA) approximations [21, 29]. Combining the use of pseudopotentials and plane wave basis sets enables extremely efficient geometry optimizations of molecules,

solids, surfaces, and interfaces.

Thus,

the

Materials Studio

implementation of CASTEP can compute many electronic and optical properties using Density Functional Perturbation Theory (DFPT) called the linear response method. With this approach a wider range of properties can be computed than when using the so-called finite difference approaches, which requires repeated computations on a series of systems [21].

64


All computations were carried out on the LENGAU high performance computing cluster, located at the Centre for High Performance (CHPC) in Rosebank, Cape Town. The LENGAU high performance computing cluster is a penta scale system with DELL servers.

These servers are powered by Intel processors using FDR

InfiniBand. Table 3.1 The hardware parameters for the cluster used in the calculation [33] System Name

Lengau cluster

FAT Nodes

CPU

Intel Xeon (R) E5-2690 V3

Intel Xeon (R) E7-4850

CPU Clock

2.6 GHz

2.2 GHz

CPU Cores

24192

280

Number of Nodes

1008

5

Memory

126TB

5 TB

Rpeak

1006 Tflops

-

Rmax

782.9 Tflops

-

Interconnect

FRD InfiniBand Network

FRD InfiniBand Network

Shared storage

4PB Lustre storage

4PB Lustre storage

65


3.2 References [1]

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70

CHAPTER 4: THE GENERATION OF CHARGE CARRIERS IN SEMICONDUCTORS - A THEORETICAL STUDY

4.1. Introduction The need for energy has escalated with a high demand for renewable sources [1]. Solar energy is renewable and can be harnessed using semiconductors [2, 3]. This assists in less pollution and green energy production. Semiconductors depict two types of mobile carriers, these are; holes (h*) in the valence band (VB) and electrons (e-) in the conduction band (CB) [4]. There is a continuous transition of electrons between these two bands. Holes and electrons can be generated through thermal, impact ionisation, field emission and photo-generation. Thermal generation [5, 6] is always present whenever the temperature of the material is greater than 0 K. The temperature sets the intrinsic concentration of the mobile carriers in the material where it affects the reverse saturation currents in the junctions and sets the maximum operating temperature of devices. Thermistors temperature sensors are based on the thermal generation. Field emission [7, 8] occurs when the internal electric field is so high that it has torn out valence electrons.

Examples of its

application are in tunnel diodes according to the energy supplied. The recombination is always present and sets up an equilibrium in steady state. Recombination rate is controlled by the minority carrier lifetime [9]. The impact ionisation [10-12] sets the breakdown voltage in the devices and it is utilised in the operation of the Zener diode and the avalanche photodiode.

1Kiarii

Photogeneration [13-15] is the basis of the

et.al. Chemical Physics Letters (2017) DOI: 10.1016/j.cplett.2017.04.051 72

Chapter 4: The Generation of Charge Carriers in Semiconductors - A Theoretical Study photoconductors, photo diodes, phototransistors and photothyristor in addition to the solar cells. When a semiconductor absorbs photons with energy equal to or greater than its energy gap [16], the electrons in the VB are excited to the CB, while holes are retained in the VB. This hole-electron pair creation process in TiO2 is illustrated in eqn. 4.1 [17] :

TiO2 + hν → e- (TiO2) + h+ (TiO2)

(eqn. 4.1)

The band structure, including the bandgap and the positions of VB and CB, is one of the important properties of a semiconductor because it determines the light absorption property, as well as the redox capability of the semiconductor and its application. This results in direct and indirect bandgap semiconductors.

The photogenerated electron and hole pairs undergo one of the following processes; effectively moves toward the surface of the semiconductor, some are retained in the defective sites in the mass and/or on the surface area of the semiconductor while others may recombine and emit energy as heat or photons. When an electron falls from the conduction band into the valence band, a recombination process occurs and an electron hole pair disappears. The energy of recombination thus emerges as a photon of light. Inversely, when a valence electron is given an energy equal or greater than the energy gap, it is transferred to the conduction band and an electronhole pair is generated. Only the photogenerated charges that reach the surface of a semiconductor, as shown in Figure 4.1, would be available. The defect sites in the mass and the surface, as well as the edges, serve as the recombination centre, which decreases the effectiveness of the reaction.

72

Chapter 4: The Generation of Charge Carriers in Semiconductors - A Theoretical Study

Figure 4.1. Effective charge generation and separation in TiO2

TiO2 exists as four main polymorphs, these are anatase, rutile, brookite, and TiO 2 (B) [18]. In anatase, an octahedral arrangement appears as (221), this involves the sharing of four edges in a zigzag arrangement. In rutile, the octahedral arrangement is (001), two edges are involved, which connect in linear chains in a parallel fashion [19]. In brookite, both corners and edges are connected [20], while TiO2(B) is mostly derived from layered titanates. Therefore, its structure is composed of corrugated sheets having both edges and corners shared as TiO6 octahedral [21]. The difference in lattice structures generates a different mass density and electronic band structure of TiO2. Rutile is thermodynamically stable [22], while anatase, brookite, and TiO2 (B) are metastable [23]. Rutile can normally be obtained after annealing with the other three polymorphs at elevated temperatures [24]. Li and coworkers [25] investigated in detail the typical transformation processes from anatase

73

Chapter 4: The Generation of Charge Carriers in Semiconductors - A Theoretical Study to rutile. The phase transformation of TiO2 anatase nanoparticles starts from the agglomerated anatase particles, leading to a bulk phase transformation. The most extensively conducted research on TiO2 still lies in using it as a material for solar energy conversions, which is mainly investigated on anatase and rutile. Various kinds of research have been carried out using TiO2 as a model semiconductor photocatalyst to produce H2 gas from water splitting [26-28], biomass reforming [29, 30], industrial waste reforming [31], and to produce carbon-based solar fuels via CO2 photoreduction [17, 32]. TiO2 only absorbs UV light up to 380 nm, which is an intrinsic limitation for the TiO2-based photocatalysts to efficiently harvest light [33]. The difference in structure between anatase and rutile leads to different densities and electronic band structures.

Different band structures, for example, the bulk

materials of anatase (3.20 eV) corresponds to λ of 384 nm, while rutile (3.02 eV) corresponds to λ of 410 nm [17]. Thus, anatase has a slightly higher redox driving force than rutile and the light absorption rate by the former is slightly less than the latter. Anatase has a large surface area than rutile, this improves its light absorption abilities. TiO2 photocatalytic reactions start with light absorption and is initially restricted by the number and energy of the photons absorbed. Since it has a wide bandgap (E G ~ 3.0 eV), it absorbs in the UV region, making this a major drawback. Much research has been devoted to extending the absorption to the visible light region [34-37]. Two most efficient strategies employed include; (1) narrowing the band gap of TiO2 to allow it to absorb in the visible region of the light spectrum by introducing other elements through bandgap engineering.

In the second case,

visible light active materials have been applied through surface sensitization, on to the surface of TiO2 to act as light harvesters.

74

Chapter 4: The Generation of Charge Carriers in Semiconductors - A Theoretical Study 4.2. Model Structures and Method The study of anatase [38-40] produced results showing its potential in photocatalytic activity. Titania lattice parameters experimentally obtained [41] were found to be in line with those used in this study. We performed spin polarised Density Functional Theory (DFT) calculations on pure TiO2 and protonated TiO2. The average net charge for the systems was calculated using the Mulliken population analysis [42]. TiO2 was observed with a direct band gap of 3.15 eV between the conduction band minimum (CBM) and valence band maximum (VBM) at the Fermi level, which was comparable to the experimental value of 3.20 eV [43]. 4.2.1 TiO2 Bulk and Surface Models Table 4.1 gives the structural parameters used to build the bulk anatase model. Figure 4.2(a) illustrates the anatase model using ball and stick notation and the resultant model structure for surface (101) is provided in Figure 4.2 (b). Table 4.1 Structural parameters of body-centered tetragonal TiO2 (Anatase) Lattice parameters (Å) a

b

3.7842

3.7842

c 9.5146

Primitive cell Space group

Atom

141

Ti

0.0000

0.0000

0.0000

Ti

0.7500

0.2500

0.5000

O

0.2081

0.2081

0.0000

O

0.9581

0.4581

0.5000

O

0.7919

0.7919

0.0000

O

0.5419

0.0419

0.5000

75

Atomic-position


H

Ti 1

(a)

Ti 2

(b)

(a) (b) (c) (d) Figure 4.2. Structural model of (a) titanium dioxide and a representation of the (b)

surface (101) with their respective charge distribution. Red dots represent oxygen and grey dots represent titanium 4.2.2 Surface Model of TiO2 The crystallographic surface of anatase (101) was used in the surface properties calculations of TiO2. A periodic slab of (1x1) surface based on the (1x1) optimised surface of a (101) of titanium was built.

The size of the lattice w a s set at 11.16

x 7.44 x 23.91 Å, with the built vacuum region of 15 Å. 4.2.3 Protonated Model of TiO2 The surfaces of anatase (101) were used to model the protonated anatase. To one oxygen atom, a proton was attached then two more protons were added to different oxygens in the oxide maintaining a slab of (1x1) to (101) surface. At the different oxygen, a proton was added to ascertain the effect of varying the position of proton on the surface.

T h e built model maintained the lattice of 11.16 x 7.44 x 23.91 Å

with vacuum spacing of 15 Å supercell.

76

Chapter 4: The Generation of Charge Carriers in Semiconductors - A Theoretical Study 4.2.4 Simulation Parameters The geometry optimisation and electronic structure were calculated using DFT in the Cambridge Serial Total Energy Package (CASTEP) [44] code. Employing normconserving pseudopotentials as implemented in Material Studio 2016, and the generalised

gradient approximation

(GGA) functional

with Perdew Burke

Ernzerhof (PBE) for electron correlation effect was used. Since CASTEP does not calculate the value of U but uses it as an input parameter, U was set as 8.2. The k point 3 x 3 x 1 for DOS, cut off energy 400 eV, energy tolerance of 2.0 x 10-6 eV/atom, force tolerance 0.05 eV/Å, displacement tolerance 0.002 Å and a convergence threshold of 1.0 x 10-6 eV/atom was used. 4.3 Results and Discussion 4.3.1 Powder Diffraction and Raman Analysis The structural models were subjected to powder diffraction and Raman analysis, as shown in Figure 4.3 and 4.4, respectively using Material Studio 2016. A comparison with experimentally obtained XRD peaks [45-48] and Raman spectra [49] is presented in Table 4.2.

77


5000

Theoretical -Results

Experimental Results

100 4000 80

Intensity

3000 60

2000 40

1000

20

0

0 20

30

40

50

60

70

80

90

20

30

40

50

60

70

80

2-Theta

2-Theta

Figure 4.3. Experimental versus calculated powder diffraction TiO2 (Anatase) TiO2

20

Intensity

15

10

5

0 200

300

400

500

600

700

800

-1 Wavelength (cm ) Figure 4.4. Calculated Raman spectrum of TiO2 (Anatase)

78

90

Chapter 4: The Generation of Charge Carriers in Semiconductors - A Theoretical Study Table 4.2 Calculated versus experimental powder diffraction and Raman peaks of TiO2 (Anatase) Powder Diffraction Peaks (2-Theta) Calculated

25.35

37.9

48.15

54.08

54.2

62.9

69

70.5

75.5

82.9

Experimental

25.23

37.72

47.89

53.77

54.89

62.51

68.59

70.05

74.83

82.41

Calculated

174

295

337

481

504

672

Experimental

144

197

399

513

519

639

Raman Peaks

There were no major chemical shifts observed in the powder diffraction. The (101) peak was found to be at 25.271 deg, experimentally this was almost identical to the theoretically determined value of 25.23 deg, which is the main anatase peak. Moreover, the (004) peak was observed at 37.698 deg, which was consistent with the experimental value of 37.9 deg. The (200) peak, which appears at 47.980 deg., had shifted to 48.15 deg in theoretical calculations. The experimentally observed value of 54.992 deg at (211) corresponded with the theoretically determined value of 54.2 in this study.

A (204) peak was seen at 62.572 deg experimentally,

corresponding to 62.9 deg. theoretically. The shifts in XRD and Raman spectrum can be ascribed to the solvents used in the experimental synthesis or machine errors and the level of theory used in the calculations. However, the generated molecules were a representative of the desired anatase.

4.3.2 Atomic Population Net charge Table 4.3 shows atoms with their net charge for both protonated and unprotonated models and Table 4.4 shows the effect of changing proton position to the net atomic charge (Mulliken).

79

Chapter 4: The Generation of Charge Carriers in Semiconductors - A Theoretical Study Table 4.3. Atomic population net charge

Species Ion

Bond length

Un-protonated Net

Protonated Net charge

from (Ti1)

charge (eV)

(eV)

(Å)

H*0

H*1

H*2

H*3

H*

1

NA

NA

NA

NA

-0.08

H*

1

NA

NA

NA

0.23

0.24

H*

1

NA

NA

0.43

0.42

0.42

O

1

1.98824

-0.60

-0.74

-0.73

-0.71

O

2

1.98386

-0.53

-0.77

-0.75

-0.75

O

3

1.75664

-0.44

-0.64

-0.72

-0.72

O

4

2.15150

-0.60

-0.83

-0.82

-0.83

Ti

1

NA

0.71

1.24

1.18

1.22

Ti

2

2.91181

1.47

1.30

1.19

1.21

Ti1 Titanium ion 1, H* 0 un-protonated, H* 1 single proton, H* 2 two protons, H* 3 three protons added to different oxygen atoms attached to two Ti atoms in the supercell.

There was an increase in the net charge of the oxygen and titanium atoms onto which the protons were added (Table 4.3). A plot from the net charge of the unprotonated species in Figure 4.5 is a clear indication of charge generation.

80


2 H*0

H*1

H*2

H*3

Net Charge

1.5

1

0.5

0

O1

O2

O3

O4

Ti1

Ti 2

-0.5

-1

Atoms

Figure 4.5. Atomic population net charge categorised by atoms There was a significant increase in the net charge after protonation, though this only affected the oxygen – titanium (Ti 1) ion bonded. The second Ti ion was not bonded to the protonated oxygen and thus, was un-protonated. The (Ti 1) had the largest change of charge, possibly attributed to the oxygen charge being distributed to the titanium. The addition of extra protons did not increase the net charge but was evenly distributed without much deviation from the mean as illustrated by the 5 % error bars.

The effect of varying the proton position on the surface was studied using the model structures in Figure 4.6. The net charge was calculated and presented in Table 4.4 for each model.

81

Chapter 4: The Generation of Charge Carriers in Semiconductors - A Theoretical Study (a)

(b)

(c)

(d)

(e)

Figure 4.6. Structural model of protonated Titania oxygen showing the variation of proton by position; (a) un-protonated, (b), (c), (d), and (e) positions O1, O2, O3 & O4 respectively

Table 4.4. Effect of changing proton position on the net atomic charge Species

Ion

Bond

Un-

length

protonated

from

Net charge

(Ti1)

(eV)

(Å)

(U-P)

O1

O2

O3

O4

Protonated atoms Net charge (eV)

H*

1

NA

NA

0.08

0.36

0.36

0.43

O

1

1.97617

-0.76

-0.69

-0.75

-0.75

-0.74

O

2

1.98386

-0.73

-0.74

-0.69

-0.79

-0.77

O

3

1.75664

-0.63

-0.64

-0.59

-0.62

-0.64

O

4

2.15150

-0.59

-0.60

-0.57

-0.71

-0.83

Ti

1

NA

1.38

1.32

1.00

1.28

1.24

Ti

2

2.98295

1.32

1.25

1.23

1.24

1.30

Ti1 Titanium ion 1, U-P un-protonated, O1 proton on ion 1, O2 proton on ion 2, O3 proton on ion 3 O3 proton on ion 4 added to different oxygen atoms attached to two Ti atoms in the supercell.

The electrons are charge carriers in semiconductors where their movement is directed by the orbital in the valence and conduction bands. The oxygen atom has O 2p orbital in the valence band (Figure 4.10) and the Ti 3d orbital dominates the conduction band. The increase in charge in the oxygen shows more charge being concentrated in the valence band positive for charge generation. The distance

82

Chapter 4: The Generation of Charge Carriers in Semiconductors - A Theoretical Study from Ti to O4 was the longest in ion 4. Which had the highest increase in net charge.

This can be ascribed to the presence of the two Ti atoms in close

proximity.

4.3.3 Electronic Properties 4.3.3.1 Band Structure The experimental value of the energy gap of anatase has been reported as 3.2 eV [50, 51]. However, our calculated energy gap in this study was found to be 3.15 eV, see Figure 4.7a for the bulk material. This can be ascribed to the use of DFT + U employed to bring the calculated bandgap close to the experimental value and reduce the underestimation by the DFT method. The surface of (101) anatase generated a bandgap of 1.023 eV for surface before protonation (Figure 4.7b). The effect of protonation on the band structure of anatase was observed as the calculation results show a reduction in the bandgap of the protonated surface to 0.099 eV (Figure 4.7c). Protonation thus introduced a new orbital from the attached hydrogen and generated a new valence and conduction band, but this was insignificantly small in size to result in doping.

A total distortion of the even

distribution of the energy bands was observed from the cut surface after protonation with the majority moving to the conduction band and few bands were observed in the valence band of TiO2, an indication of charge movement. The overall band structures were calculated along high-symmetry directions in the Brillouin zone using electronic eigenvalues for both conduction and valence bands. The potentials and electronic charge densities were created throughout the simulation.

83


Figure 4.7. Band structures for (a) bulk, (b) surface (101) and (c) protonated surface (101) TiO2 4.3.3.2 Total Density of State (TDOS) and Partial Density of State (PDOS) Electronic eigenvalues on a fine Monkhorst-Pack grid were calculated non-self consistently for both conduction and valence bands, using potentials and electronic charge densities produced in simulation. In order to examine the nature of the states making the conduction and valence band edges, TDOS and PDOS was plotted

84

Chapter 4: The Generation of Charge Carriers in Semiconductors - A Theoretical Study showing the input of all atomic orbitals in TDOS and the distinct atomic shells in PDOS band edges (Figures 4.8 and 4.9).

Density of state (electrons/eV)

10

TDOS

8 6 4 2 0 -4

-2

0 2 Energy (eV)

4

6

8


Figure 4.8. TDOS of the bulk of titanium dioxide 10

s-orbital p-orbital d-orbital

Ti 3d 8

O 2p

6 4 2 0 -4

-2

0 2 Energy (eV)

Figure 4.9. PDOS of the bulk of titanium dioxide

85

4

6

8

Chapter 4: The Generation of Charge Carriers in Semiconductors - A Theoretical Study The 4s, 2p and 3d atomic shells were found to be responsible for the electron distribution in TiO2. The conduction band of TiO2 was dominated by Ti 3d orbital, while the valence band by O 2p. Thus, this suggests that the electrons would move from O 2p as illustrated in Figure 4.9. 4.3.3.3 Spin Density of State Using an external field, spin-polarized calculations were conducted on the

1.5 1.0

(a)



nonmagnetic atomic configurations of titania and oxygen (Ti and O) (Figure 4.10).

Ti 3d

0.5 0.0 -0.5 -1.0

4

(b)

O 2p

2 0 -2 -4

-1.5 0

5 Energy (eV)


-5

10

15

-4

-2

0

2

4

6

Energy (eV)

(c)

4

O 2p

Ti 3d

2 0 -2 -4 -6

-4

-2

0

2

4

6

8

Energy (eV)

Figure 4.10. Split non-magnetic atomic configurations of (a) Ti 3d, (b) O 2p and (c) TiO2 Titanium had the conduction band dominated by the 3d orbital and there was no much contribution in the valence band by titanium, however, in Figure (4.10b) 86

Chapter 4: The Generation of Charge Carriers in Semiconductors - A Theoretical Study oxygen had the highest occupation of the valence band. The O 2p was responsible for generated charge carriers concentration in the valence band as the attachment of a proton to an oxygen resulted in charge increase. In TiO2, there was an observed combination of the O and Ti properties, the material was comprising both minority and majority spins and the bandgap was clearly observed (Figure 4.10c).

Figure 4.10c showed no difference between minority and majority spins. This was due to its magnetic influence vanishing in the self-consistent (SCF) runs otherwise, an invented external magnetic influence would be included in the result. Therefore, the study was done using total energy as targets. Since the magnetic moment itself was not a variation quantity during the SCF cycle.

The spin contributions of individual elements confirm the PDOS electron movement observed earlier with Ti 3d orbital having the highest spin in the conduction band and small contributions from the O 2s, while the valence band has the highest spin resulting from O 2p with some contributions from Ti 3d orbital.

4.3.3.4 Electron Density Difference and Electron Localisation Function

To understand the photocatalytic performance of TiO2 the depiction of the electron density changes that occurred for the given electronic transition was considered using the information on the single-excited arrangements that was given to each transition. Electron localisation functions (ELF’s) measured the extent of spatial localisation of the reference electron. This provided a means for the representation of electron pair likelihood in multi-electronic systems (Figure 4.11).

87

ELF's

Chapter 4: The Generation of Charge Carriers in Semiconductors - A Theoretical Study usefulness stems from the manner in which it allows the analysis of electron localisation in a chemically intuitive way [52-55].

Figure 4.11. (a) Electron density, (b) electron density difference and (c) electron localization function for the bulk TiO2 versus (d) electron localization function and (e) electron density difference in the surface (101)

The electron depletion and accumulation gave insightful information about the repulsive and attractive nature of each interaction of the atoms involved. In these plots, the electron depletion and electron accumulation regions are depicted as red and blue isosurfaces, respectively. The electron density describes the concentration

88

Chapter 4: The Generation of Charge Carriers in Semiconductors - A Theoretical Study of electrons towards the core of the elements at maximum isosurface of 1.083 x 10-1 e-1 and electron absence at 1.678 x 10 -1 e-1. The single-excited arrangements

in Figure 4.11b were shown

with maximum

electrons

of

4.467 x10-1 e-1. The electron localisation function analysis shows that the evolution of the bonding structures is position dependent, which lies in the range of 0.000 to 1.000 e-1. A value of 0.500 e-1 corresponds to metal isosurface values and thus, an indication of metallic bonding and 1.000 e-1, which correspond to covalent bonding. For 0.000, it is undefined, meaning no interactions of the atoms occur in the unit cell. Ionic bonding is observed in the locations.

4.3.3.5 Phonons in TiO2

The vibrations of atoms in a solid can be treated in terms of elastic waves propagating through the solid.

The acoustic waves have a wide range of

frequencies and have a characteristic velocity in the solid. The atoms show discrete values of energy of the elastic wave, which is called photons and thus, quantized. This is analogous to the concept of phonons and the quantum of electromagnetic radiation calculations as shown in Figure 4.12, which was found to resemble those done by Fu and Zhao et al. [56]. Though some negative frequencies are observed throughout the whole Brillouin zones, the density of phonon state confirmed its dynamical stability. The majority of the phonons had positive frequencies, confirming the stability as shown from the density of phonon state (DOS).

89


Figure 4.12. Calculated phonon dispersion of anatase along the high symmetry directions and density of phonon state

4.3.4 Electrostatic Potential The amount of electric potential energy (work function) was calculated as being equal to a unitary positive charge (Figure 4.13) and was found to be equal to 4.403 eV, 2.481 eV, 2.406 eV, and 2.128 eV on a TiO2 surface, with one, two and three protons added to the TiO2 surfaces, respectively.

90

Chapter 4: The Generation of Charge Carriers in Semiconductors - A Theoretical Study 4

4

Electrical potential (eV)

(a) Electrical potential (eV)

0 Ф = 4.403 eV

-4 -8 -12 -16 -20 0.2

0.4

0.6 Z(Å)

0.8

(b) Ф = 2.481 eV

0 -4 -8 -12 -16 -20

1.0

0.2

0.4

0.6

0.8

1.0

0.8

1.0

Z(Å)

4

(c) Electrical potential (eV)

Electrical potential (eV)

4

Ф = 2.406 eV

0 -4 -8

-12 -16

(d) Ф = 2.128 eV

0 -4 -8 -12 -16

-20

-20

0.2

0.4

0.6

0.8

1.0

0.2

0.4

Z(Å)

0.6 Z(Å)

Figure 4.13. Electric potentials on (a) TiO2 surface, (b) one proton added, (c) two protons added and (d) three protons added to TiO2 surface. The red and green dashed lines are the vacuum and Fermi level, respectively

There was a decrease in the energy required to move an electron to infinity in the protonated surface as compared to the unprotonated. The decrease in energy implied that electrons would leave with ease once generated, this is an added advantage and can be exploited in photogeneration if the large band gap of TiO2 is addressed.

4.3.5 Optical Properties

Matrix elements for electronic inter-band transitions are calculated. The CASTEP analysis dialogue was used to generate grid and chart documents containing

91

Chapter 4: The Generation of Charge Carriers in Semiconductors - A Theoretical Study measurable optical properties. This was conducted for a wavelength range between (320-800 nm) to ascertain TiO2 application in photocatalysis as illustrated in Figure 4.14.

50000

(TiO2)

-1

Absorption (cm )

40000

30000

20000

10000

0 400

500

600

700

800

Wavelength (nm) Figure 4.14. Calculated optical properties of TiO2 There was maximum absorbance in the ultraviolet region of the light spectrum with no absorption in the range from (500 - 850) nm. This is a huge limitation for titania’s application in photo-generation or photocatalysis mechanisms.

92


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99

CHAPTER 5: A DFT STUDY ON THE TRANSPORTATION OF CHARGE CARRIERS IN GRAPHENE SYSTEMS

5.1 Introduction Graphene is an sp2 hybridized carbon allotrope [1]. Stacking several layers on top of each other converts graphene into graphite [2], in which different layers are bound together by weak Van der Waals’ forces. From the modern carbon nanomaterial, graphene is the most promising for applications, because of its promising properties, such as structural, electrical, mechanical, and optical characteristics [3-5]. A wide range of applications like nano electronic components, and nanoelectromechanical devices [6], take advantage of these properties. As an example, graphene has been used in hydrogen storage tank applications due to its advances in binding properties and mechanical devices of high strength with hexagonal network. Graphene’s structure is described as a hexagonal lattice and is viewed as two interleaving triangular lattices illustrated in Figure 5.1.

4

Kiarii et.al. Journal of Nature Physics (2017) Manuscript No.: NPHYS-2017-05-01431 (Under review)

101

CHAPTER 5: A DFT Study on The Transportation of Charge Carriers In Graphene Systems

Figure 5.1: The lattice structure of graphene

Using the tight-binding approximation, the triangular lattice structure of graphene was effectively studied by Cooper et al. in the band structure calculation of a layer of graphene [7]. Graphene stability is due to closely packed atoms of carbon and sp2 hybridized orbitals, a mixture of the s, px, and py orbitals, constituting the σ bond [7]. The π bond is made up of the final unhybridized pz orbital electrons, this π bond forms the π band and π* bands that are accountable for graphene’s distinguished electronic properties as there is free movement of electrons from the half-filled band [7].

Flexible bonding properties of carbon give various possibilities to enrich the properties of graphene with different defects and adsorbed atom, as well as the combinations of different type of carbon nanomaterials [8]. For example, deposition of metal atoms or incorporation of nitrogen or boron in the structure can be used to

101

CHAPTER 5: A DFT Study on The Transportation of Charge Carriers In Graphene Systems tune chemical activity and structural behaviour of graphene or metal atoms and have fundamental relevance in catalysis, batteries, and nanoelectronics [9]. Deposited atoms can be thought of as point defects, just like vacancies. Vacancies are holes, which make the structure weaker. The difference between defect and lattice atoms affect the binding strength together with the possible presence of vacancies. Moreover, ad-atoms can be found to be noncovalently bonded on top of the structures, outside the lattice, or covalently bonded inside the lattice. Comparing the mass and the number of valence electrons between the elements reveals their compatibility, Vacancies are needed in the formation of junctions between carbon nanotubes and therefore, correct preparation can improve the stiffness of composite materials. Although not preferred in all cases preferred, the existence of defects in samples is often unavoidable, because of the growth, the preparation, and the imaging methods.

Research in the field so far has given explanations about

electronic properties of defects and junctions [10]. Graphene edges are involved in chemical reactivity [11], electronic structure [12] and vibrations [13]. This edge chemistry is important for example in the catalysed growth of carbon nanotubes [14] to which carbon-metal interface is also related. The electronic properties of graphene, have been studied extensively [15] often in connection with the growth of the nanotube, or the electronic edge states [16]. Different theoretical calculations have also been conducted and compared against experimental results as illustrated in Table 5.1

102

CHAPTER 5: A DFT Study on The Transportation of Charge Carriers In Graphene Systems Table 5.1 Phonon frequencies at critical point in cm-1 out of plane єa and in plane є# branches, respectively T=A cm -1

M point, cm -1

єa

єa

є#

єa

K point, cm -1 єa

єa

єa

є#

15822 8681 13904 13234 12904 -

-

11944

-

4827

15873 -

-

12657

12654

-

5177

7

-

-

єa

-

єa

References

1

= [17], 2= [18],

3=

[19],

4 = [20],

5= [21], 6= [22]

5

5

5

1590

861

1389

-

-

-

1595

890

1442

1380

1339

1581

825

1425

1350

1569

884

1428

1597

893

1396

1285

-

-

-

636 1371

1246

994

535

[22]

1315

-

1300

1220

-

-

[20]

1368

1346

637 1362

1238

1002 535

[24]

1346

1338

640 1289

1221

1004 539

[24]

7= [23]

However, phonon frequencies are characterized by loading. This was observed by Jha et al. [25] in their study of two dimensional phonons of monolayer studies. Pnictides indicates a reduction in the frequency as the strain is increased at higher frequencies (Figure 5.2).

Figure 5.2. Two dimensional phonons of monolayer pnictides at different loadings [25]

103

CHAPTER 5: A DFT Study on The Transportation of Charge Carriers In Graphene Systems 5.2 Computational Details 5.2.1 Model Building The graphene (G) lattice was constructed with the lattice parameters provided in Table 5.2, with the graphene supercell represented in Figure 5.3 Table 5.2. Graphene (G) structure lattice parameter and atomistic positions [26] Structure

Graphene

Lattice parameters (Å) a b c C 2.4612 6.7090

Primitive cell Atomistic positions Space group 187

C 0.0000 0.0000 0.0000 C 0.3333 0.6666 0.0000

Figure 5.3. Schematic structure of generated graphene supercell

5.2.2 Simulation Parameters The geometry optimization, electronic structure, charge density and optical properties were calculated using Density Functional Theory (DFT) in the Cambridge Serial Total Energy Package (CASTEP) [27] program and employing norm-

104

CHAPTER 5: A DFT Study on The Transportation of Charge Carriers In Graphene Systems conserving pseudopotentials as implemented in the Material Studio 2016 software. Generalized gradient approximation (GGA) functionals of the Perdew Burke Ernzerhof (PBE) for exchange correlation effect was used. The k point was 6x6x1 for density of state,12x12x1 k point for the geometry optimization with a cutoff energy of 350 eV, energy tolerance 1.0x10-6 eV. Force tolerance was set at 0.03 eV, displacement tolerance 0.0001 Å and a convergence threshold of 1.0x10 -6 eV/atom. A vacuum slab was set at 15 Å to allow geometric relaxation and to avoid the layers collapsing on each other. 5.3 Results and Discussion 5.3.1 Morphological Analysis The morphology of the generated structures (Figure 5.3) was confirmed by the powder diffraction pattern (Figure 5.4a). This was found to be within experimentally determined patterns generated by Wang et al. [28] (Figure 5.4b). However, the experimental results show some chemical shifts in the NMR spectra of graphene

100

(002)

analysed.

(a)

(b)

Intensity

40

20

(101)

60

(100)

Intensity

80

0 20

25

30

35

40

45

50

2Ɵ – (degree)

2Ɵ – (degree)

Figure 5.4 Powder diffraction patterns for (a) calculated and (b) experimental [28] graphene, respectively

105

CHAPTER 5: A DFT Study on The Transportation of Charge Carriers In Graphene Systems The calculated

Raman spectrum (Figure 5.5a) of a single layer of graphene

(1780 cm-1) compared well to that found by Nechaev and Piscanec et al. (Figure 5.5b) [20, 21]. Further analysis of its electronic properties was conducted on the structures.

2000

(a)

(b)

Graphene

Activity

1500

1000

500

0

1740

1760

1780

1800

1820

1840

Wavelength (cm-1)

Figure 5.5. Raman spectrum of a single layer of pristine graphene (a) calculated and (b) experimental [29]

5.3.2 Electrons in Graphene To describe the electronic contributions of graphene in any system, the electronic structure of graphene was calculated. The Fermi level was set at zero as a dashed line. The band structures of graphene were also calculated for comparison with the projected density of state. For the bulk, the valence band maximum (VBM) and the conduction band minimum (CBM) were located at the Fermi level point in the Brillouin zone, with no band gap (E g) = 0 eV (Figure 5.6), which was identical to the experimental work by Nemanich et al. among others [31-33].

106


Figure 5.6 Calculated band structure of pristine graphene in the Brillouin zone

Moreover, graphene is made up of carbons with the p-orbital equally represented in both the VBM and CBM as can be observed from the Fermi level illustrated in the PDOS plot (Figure 5.7). (b)

1.4

Density of State (electrons/eV)

Density of State (electrons/eV)

T-DOS

(a)

2.5

2.0

1.5

1.0

0.5

s p

1.2 1.0 0.8 0.6 0.4 0.2 0.0

0.0 -6

-4

-2

0

2

4

6

8

10

-6

-4

-2

0

2

4

6

8

10

Energy (eV)

Energy(eV)

Figure 5.7 Calculated (a) total density of state and partial density of state of graphene

107

CHAPTER 5: A DFT Study on The Transportation of Charge Carriers In Graphene Systems The absence of band gap disqualifies it as a semiconductor and thus, graphene acts as a photosensitizer in the graphene composite, the electron-hole pair can be easily generated by visible-light irradiation on a semiconductor and then be effectively separated by the electron injection into the composite. Graphene thus acts as a direct photogenerated electron collector and transporter. This considerably reduces the electron-hole recombination, as well as increasing the catalytic reaction sites surface.

5.3.3 Band Structure Graphene’s energy gap was found to be zero (red line, Figure 5.6), which is in agreement with experimentally obtained results [31-33]. Graphene can clearly be revealed in a noticeable ambipolar electric field effect owing to its zero band gap (circled in Figure 5.6). This means that charge carriers can be continuously tuned between holes and electrons in the material and their mobility can be high even under ambient conditions.

5.3.4 Total Density of State and Partial Density of State The DOS was used to define the number of states for each interval of energy at each energy level of graphene that was available for occupation on average over space and time domains used by the system. Further information on the different contributions from various orbitals was computed, the s and p orbital states played the role of energy transfer in the graphene system as they were the only states available (Figure 5.7).

108


5.3.5 Electron Localization Function To gain more insight into the bonding nature of the ground-state graphene, the electron localization function (ELF) of the model was investigated. ELF is known to be an informative tool utilized to distinguish the different bonding interactions in solids. The probability of finding an electron in the lattice was calculated in a single layer of graphene (Figure 5.8). The space of reference electron was located, which showed a clear destination between the core 1.627 x 102 e-1 and valence electron 3.652 x 101 e-1. These were covalently bonded by forming one atom thick layer.

1.627x102 e-1 1.206x102 e-1 7.857x101 e-1 3.652x101 e-1 5.533 e-1

Figure 5.8. Electron localisation function for a calculated single layer of graphene

5.3.6 Phonons in Graphene A phonon is a quasiparticle, it is a combined excitation in an elastic arrangement of periodic atoms or molecules in matter.

It indicates an excited state of quantum

mechanical quantization of the modes of vibrations of elastic structures of the interacting particles. The study of phonons is significant because its calculations give a good understanding of the behaviour of graphene, in particular relating to conductivity.

Phonons are also significant in interpreting and calculating free

109

CHAPTER 5: A DFT Study on The Transportation of Charge Carriers In Graphene Systems carriers, mobility dependence of temperature in semiconductors, as well as electrical conductivity.

Graphene solid-state materials with crystalline structure

appear to have a unique set of discovered quasi-particles (phonons) (Figure 5.9a). However, our calculated results included the influence of the dynamical matrix, the phonon self-energy between the π bands, which was confirmed by the dashed lines are obtained by subtracting the dynamical matrix from the phonon self-energy between the π bands (Figure 5.9 b) [34]. For the single layer, the contribution of π bands was not taken into account thus, resulting in an increase in the frequency maximum at the respective critical points.

2000 1800

Frequency (nm)

1600 1400 1200 1000 800 600 400 200 0

T

H

K

G

(a)

(b)

Figure 5.9 Phonon dispersion relations of bulk graphene (a) calculated and (b) experimental [34]

The results obtained from ab initio calculations were found to be within the range of the experimental data in the single layer for the unstrained case. However, as Jha et al. [25] predicted the lack of loading was observed by the increment in phonons at the higher frequency and confirms our inconsistencies in theoretically determined

110

CHAPTER 5: A DFT Study on The Transportation of Charge Carriers In Graphene Systems critical points especially in the high frequency, which is a clear indication of the single layer state of the studied material. The increase can be attributed to the additions from the dynamical matrix and the phonon self-energy between the π bands. The phonon density of states has an influence on the graphene’s atom and the total phonon density of state. The nature of numerous branches in the phonon spectrum observed had contribution from the partial density of states on an atom from each phonon band. The absence of negative frequencies was an indication that the system is in its ground state and the phonons and electron coupling was present in phonon dispersions. This is responsible for electrical resistivity, phonon-mediated superconductivity and Jahn-Teller distortions among others.

5.3.7 Electron-Phonon Coupling Electronic transport plays a role in many of the prospective applications of graphene. Essential concept considered for charge carrier transport are the electron-phonon interaction.

When thermal energy is available, the ions vibrate around their

equilibrium positions. Those vibrations are usually well described by harmonic oscillators. They can be decomposed into a set of convenient quanta of vibrations called phonons. It does not concern an individual particle, but a collective movement of a very large number of atoms. In the Born-Oppenheimer approximation, electrons adapt instantaneously to the changes in the positions of the ions. They simply act as the restoring force of the harmonic oscillators, always bringing the ions back to their equilibrium positions.

Phonon excitations are described by wavefunctions

defining the displacements of each atom with respect to its equilibrium position. Those functions bear resemblance with the wave functions of the electrons. Their function is also a wave and is similarly characterised by quantum numbers.

111

CHAPTER 5: A DFT Study on The Transportation of Charge Carriers In Graphene Systems The momentum gives the periodicity of the propagating wave of displacements and is an in-plane quantity in graphene forming a phonon branch or mode. For a small momentum, it portrayed three kinds of modes: (i) longitudinal modes in which the ions move in the same direction as the momentum; (ii) transverse modes in which the atoms move in the plane of the graphene material, in the direction perpendicular to the momentum; (iii) out-of-plane modes in which the ions move in the out-of-plane direction. The scattering of electrons by phonons decreases the material’s efficiency in transporting electrons. In other cases, like conventional superconductivity, the electron-phonon interaction induces the pairing of electrons, which is the driving mechanism. The effect of electron-phonon coupling on the band gap of a semiconductor is calculated by considering the change in the vibrational free energy arising from the promotion of an electron from the valence to the conduction band or by calculating the change in the electronic bands due to the presence of vibrations. These two approaches can be shown to be equivalent, at least in the lowest order perturbation theory [35]. Using the second approach, the calculated zero temperature electronphonon correction to the electronic thermal (minimum) band gap 𝐸𝑔 is given by (eqn. 5.1.) < 𝐸𝑔 >=< Φ(q)│𝐸𝑔 (𝑞)│Φ(q) > ………………………………. (eqn. 5.1.) where │Φ│ is the ground state vibrational wave function within the harmonic approximation and is a Hartree product of simple harmonic oscillator eigenstates for each vibrational mode, which are simple Gaussian functions for the ground state. The expression in (eqn.5.1.) has been evaluated in literature by sampling 𝐸𝑔 using path integral methods [36, 37] or Monte Carlo methods [38, 39], or by using some variant of the expansion [40], 112

CHAPTER 5: A DFT Study on The Transportation of Charge Carriers In Graphene Systems 𝐸𝑔 (𝑞) = ∑𝑛,𝑘 𝑎𝑛𝑘 𝑞 2 𝑛𝑘

………………………………………… (eqn. 5.2.)

where (qnk) is the amplitude of the vibrational mode labelled by (n, k). Eqn. 5.1 was evaluated using the approximate expression (eqn. 5.2.), which is similar to the AllenHeine-Cardona theory, however the expression in eqn. 5.2. is more accurate because it includes the non-diagonal Debye-Waller term that is missing in the AllenHeine-Cardona theory [41]. We note that it excludes terms with higher powers of (qnk) and coupling between different points, whereas sampling methods include all of these terms and should, therefore, be more accurate. However, this expansion allows us to investigate the contribution from each vibrational mode independently. We also note that the use of DFT for calculating electron-phonon induced band gap corrections is appropriate, although DFT-GGA method is not accurate for the calculation of the absolute value of band gaps and in this study. The usual band gap underestimation of standard DFT approximations effects all frozen-phonon configurations in a very similar manner, and therefore, it is expected to cancel in the calculation of the band gap correction, as it is the difference between the static band gaps. This is supported by the numerical results of Giustino and coworkers [42].

5.3.8 Electrostatic Potential The calculated work function (Φ) was found to be 5.24 eV (Figure 5.10) and this was the minimum amount of energy required to remove an electron from the surface of graphene to infinity. This value describes the ease of removing an electron to infinity in a graphene system. The system with less than the calculated work function would find the electrons moving from graphene to the semiconductor easily. However, a situation where the semiconductor has a higher work function indicates that the

113

CHAPTER 5: A DFT Study on The Transportation of Charge Carriers In Graphene Systems electrons will move into the graphene system. This will result in electrons deposited on graphene hence, acting as a storage due to its large surface area. The high conductivity of graphene will lead to a faster means to distribute the electron when used as a medium increasing effective charge transfer, reducing the rate of recombination, and improving the photo activity. 10

5.24 eV

Electrostatic Potential (eV)

0

-10

-20

-30

-40

-50

-60 0.6

0.8

1.0

1.2

1.4

Z(A) Figure 5.10 The average potential profile along z-axis from top and bottom

114

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[12]

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[13]

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[19]

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[21]

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[22]

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119

CHAPTER 6: SIMULATION FROM THE FIRST PRINCIPALS THEORY ON THE EFFECT OF DOPING SILICA ON GRAPHENE AND THE NEW COMPOSITE MATERIAL

6.1 Introduction Solar energy utilization as a source of renewable green energy for semiconductors has been exploited in past decades. Its storage depends on the transportation model used. Recent research has focused on how to improve the transportation of generated carrier charges from semiconductors with decreased rates of recombination [1, 2].

This would improve the transfer and charge separation

process resulting in a reduced recombination rate [3]. The use of graphene has found such an application and is proving to be appropriate (Figure 6.1). Energy Visible light irradiation

Reduction

SiO2

Energy

Reduction

5.797eV

Oxidation oxidation M= Graphene or Ep GO

Oxidation

Figure 6.1 Use of silica on graphene or epoxy graphene as a support

2Kiarii

et.al. Chemical Physics Letters (2017) DOI: 10.1016/j.cplett.2017.05.034 122

CHAPTER 6: Simulation from The First Principal Theory on The Effect of Doping Silica on Graphene and The New Composite Material Graphene is an sp2 hybridized carbon allotrope and one atom thick [4].

The

thickness of graphene makes it very sensitive to slight changes in the environment [5]. The flexible bonding properties of carbon provide several different likelihoods to improve the properties of graphene with different defects and ad-atoms. Varying combinations of the different types of carbon nanomaterials are also made possible [6]. Graphene has ballistic transport, zero band gap, high mobility and ease of modulation of its electrical properties, thus making it of great research interest [7, 8]. It has a zero density of state (DOS) where the conduction and valence bands meet and also has a very low density of states near the Dirac point [9]. This enables easy flow of electrons between the valence and conduction bands. Since graphene is one atom thick, its whole volume is exposed to the surrounding and its properties are very responsive to the surrounding atmosphere including temperature, substrate and adsorbate molecules. The zero band gap property of graphene has been a drawback for its use as a semiconductor. However, the addition of silica may induce bandgap opening through substrate-induced band opening (Figure 6.2).

121

CHAPTER 6: Simulation from The First Principal Theory on The Effect of Doping Silica on Graphene and The New Composite Material

(a)

(b)

Figure 6.2 Graphene with (a) no bandgap and (b) bandgap opening through substrate induced band opening

Silica (SiO2) is mostly obtained by mining and purification of quartz in the earth's crust [10]. SiO2 exists in various polymorphs with stable forms, such as cristobalite high, cristobalite low, quartz, quartz beta and stishovite (Figure 6.3).

122


(a)

(b)

(d)

(e)

(c)

=O

= Si

Figure 6.3 Various silica polymorphs: (a) Cristobalite high (b) Cristobalite low (c) Quartz (d) Quartz beta (e) Stishovite

Silica-derivative nanostructures are of special interest because of their hydrophilic nature, the ease of functionalization and more widely potential application [11]. In the past decade, uniform silica has been successfully deposited on a variety of colloidal metal particles [12], metal oxides [13] and semiconductor quantum dots [14]. Several methods have been developed including plasma-enhanced chemical vapour deposition to coat silica on graphene [15, 16], electrodeless method [17], and laser physical vapour deposition [18] amongst many others.

For pure nanocomposites, graphene compounds mainly improve flame retardant wear, resistance and self-sensing abilities by exploiting the excellent thermal and

123

CHAPTER 6: Simulation from The First Principal Theory on The Effect of Doping Silica on Graphene and The New Composite Material electric properties [14, 19, 20]. As a result, a new generation of multifunctiona l products may be developed [19]. Proper adhesion between fibres and matrices is a pre-condition of stress transfer and the reinforcing fibres are modified to increase mechanical and chemical interactions [21], for example by oxidation [22] or whiskerization [23].

Carbon nanotubes increase the surface area and make

mechanical interlocking possible, creating a stiffening at the fibre-matrix interface thus improving stress transfer. Downs and Baker [20] first reported an increase of around 4.75 times (in the best case) of the interfacial shear strength (IFSS) of the composites with carbon nanofiber -grafted carbon fibres.

Large scale production of graphene compounds can be done through chemical vapour deposition (CVD) techniques.

CVD is proficient to meet the anticipated

characteristics for combined applications, bulk production, specificity, high purity, acceptable quality and low cost. Chemical vapour deposition is a common method used to graft CNTs into fibre surface [24, 25]. However, Qian et al. [26] indicated excellent wettability of carbon nanotubes by poly (methyl methacrylate) (PMMA). They found that the interfacial shear strength was improved by making the hierarchical compounds with CNT-grafting.

This contributed to longitudinal

compression, transverse stiffness, inter laminar shear strength and strength itself [26]. Nourbakhsh et al. [27] studied the interaction between carbon and oxygen atoms on C 18O2 configuration, which showed the appearance of a 0.2 eV bandgap when initially oxidized. Upon further increase in the oxygen density (27.8 %, configuration C 18O5) they reported an opening of a 1.4 eV direct bandgap. The bandgap value

124

CHAPTER 6: Simulation from The First Principal Theory on The Effect of Doping Silica on Graphene and The New Composite Material increased monotonically with the oxygen density. For an oxygen density as high as 50 %, the bandgap calculated was 3.6 eV. 6.2 Computational Details Graphene (G) and E p o xy Graphene (Ep G) models were generated using lattice parameters presented in (Table 6.1) and built into models of Cristobalite high, Quartz, Quartz beta, Stishovite, and Cristobalite low (Figure 6.3) obtained from crystallographic information files (CIF) [33]. The interface between graphene and SiO2 surfaces was simulated using a repeated slab model. To prevent the excess vertical coupling effect a vacuum separation was set at 15 Å.

In this study,

calculations for the bulk, as well as the surface of the material was done. The surface was obtained by cleavage of the bulk at (111) phase for each polycrystal and built into a single layer with graphene or epoxy graphene. T a b le 6 . 1 . Graphene (G) a n d E p o x y Graphene monoxide (Ep-GO) m o d e l lattice parameters Structure

Ep-GMO

Graphene

Lattice parameters (Å)

Primitive cell

a

b

c

Space group

5.68

2.64

15

Cmmm (65)

2.461

6.709

187

125

Atomistic positions C

0.3261

0.0000

0.5000

C

0.6739

0.0000

0.5000

C

0.8259

0.5000

0.5000

C

0.1741

0.5000

0.5000

O

0.5000

0.0000

0.5696

O

0.5000

0.0000

0.4304

O

0.0000

0.5000

0.5696

O

0.0000

0.5000

0.4304

C

0.0000

0.0000

0.0000

C

0.3333

0.6666

0.0000

CHAPTER 6: Simulation from The First Principal Theory on The Effect of Doping Silica on Graphene and The New Composite Material 6.2.1 Model Building Structural models generated in this study were built with each polymorph to explore the effect of silicon dioxide on graphene and epoxy graphene (Figure 6.4):

(a)

(f)

(b)

(g)

(c)

(d)

(h)

(i)

(e)

(j)

Figure 6.4 Structural models generated; (a) G-Quartz beta, (b) G - Quartz, (c) G Stishovite, (d) G- Cristobalite high, ( e ) G- Cristobalite low, (f) G O - Stishovite, (g) Ep-GO-Quartz beta, (h) Ep- G O - Quartz, (i) Ep-GO - Cristobalite high and (j) Ep-GO - Cristobalite low

6.2.2 Simulation Parameters First principles calculations were performed using Density Functional Theory (DFT) [28]. The geometry optimization, electronic structure and optical properties were calculated with the Cambridge Serial Total Energy Package (CASTEP) [29] program with norm-conserving pseudopotentials as applied in Material Studio 2016 [30]. The

126

CHAPTER 6: Simulation from The First Principal Theory on The Effect of Doping Silica on Graphene and The New Composite Material generalized gradient approximation (GGA) functionals [31] of the Perdew Burke Ernzerhof (PBE) [32] were used to treat the electron correlation effects.

Other

parameters such as the 12x12x1 k point mesh for DOS, 8x8x1 k point mesh for geometry optimization of relaxation with a cut off energy 600 eV, energy tolerance 2.0x10-5 eV, force tolerance 0.03 eV, displacement tolerance 0.0001 Å and a convergence threshold of 1.0x10 -6 eV/atom was also incorporated. Our calculated epoxy bandgap of 0.517 eV was based on the mono atomic layer formed with one atom interacting with an oxygen atom. 6.3 Results and Discussion 6.3.1 Morphological Analysis Powder diffraction patterns of pure polymorphs of silica were calculated (Figure 6.5). These results were used for phase identification of the structures in this study with copper as the radiation source. The polymorph structures were further calculated for the Raman spectra.

127


SiO2Cristobalite low SiO2 Stishovite SiO2 Quartz beta

600

SiO2 Quartz

Intensity

SiO2 Cristobalite high 400

200

0

15

20

25

30

35

40

45

50

55

60

2 - Theta

Figure 6.5 Calculated powder diffraction spectra for graphene, epoxy graphene monoxide, cristobalite low, stishovite, quartz beta and cristobalite high, respectively The corresponding Raman spectra (Figure 6.6) was based on inelastic scattering of monochromatic light. The plot results were compared with the experimental results published by Downs et al. [33] in the X-ray or neutron powder diffractometer patterns of crystalline materials in order to ascertain that the generated structures represented the actual molecules.

However, some peaks were in line with the

experimental results, while some inconsistencies were observed.

128


2500

700

Graphene

2000

Epoxy Graphene

600

400

Activity

Activity

500

1500

1000

300 200

500

100 0

0 1680 1700 1720 1740 1760 1780 1800 1820 1840 1860

600

800

1000

-1 Wavelength (cm )

30

1400

1600

1800

2000

2200

2400

Wavelength (cm-1)

Stishovite

1.6

25

Quartz beta

1.4 1.2

Activity

20

Activity

1200

15 10

1.0 0.8 0.6 0.4

5

0.2

0

0.0

400

500

600

700

800

900

400

-1 Wavelength (cm )

0.4

Cristobalite high

1000

1200

2.0

cristobalite_low 1.5

Activity

Activity

800

Wavelength (cm-1)

0.3

0.2

0.1

0.0 660

600

1.0

0.5

0.0

680

700

720

740

760

780

800

820

840

0

Wavelength (cm-1)

200

400

600

800

1000

1200

Wavelength (cm-1)

Figure 6.6 Calculated Raman spectra for graphene, epoxy graphene monoxide, stishovite, quartz, quartz beta, cristobalite high and cristobalite low respectively

6.3.3 Electronic Properties Pristine graphene was found to have a zero band gap (Figure 6.7), while epoxy graphene monoxide was found to be 0.517 eV. In reference to Nourbakhsh et al. a comparison of their results and ours indicated we were within the experimentally obtained range of 3.5 - 4.1 eV using UV spectroscopy [27, 34, 35]. Sevik et al. [36]

129

CHAPTER 6: Simulation from The First Principal Theory on The Effect of Doping Silica on Graphene and The New Composite Material and Yong et al. [37, 38] used DFT with LDA functional to calculate bandgaps of various silica polycrystals; Cristobalite high, Cristobalite low, Quartz, Quartz beta and Stishovite as later conferred. 14 10 8 6

Band energy (eV)

8 6 4 2 0 -2 -4 -6 -8

Density of state (eV)

G

K

(a)

G

M L

4 2 0 -2

-4 -6 -8 -10 -12

1.2

G Z

G

(b)

S R

2


Band energy (eV)

12 10

1 0.8 0.6 0.4 0.2

0

2.5

2 1.5 1 0.5 0

-6

-3

0

3

6

9

-6

-4

(c)

-2

0

2

4

6

8

(d)

Figure 6.7 Band structures for (a) graphene, (b) epoxy graphene monoxide and partial density of state (PDOS) for (c) graphene and (d) epoxy graphene monoxide

6.3.4 Electronic Properties of Bulk The calculated band structure, DOS and PDOS for the various silica polycrystals (Table 6.2) were compared with the previous theoretically determined structures using different functionals and found to be within the range for Cristobalite high with Stishovite being slightly less than what was obtained in reference [39] and [40] respectively. However, all the calculated bandgaps were low when compared to the experimentally determined values.

This can be attributed to the well-known

underestimation of band gap by the DFT method [41].

130

CHAPTER 6: Simulation from The First Principal Theory on The Effect of Doping Silica on Graphene and The New Composite Material Table 6.2 Calculated electronic properties of SiO2 polycrystal structures 1

Theo4

Cristobalite high

5.525

6.24

5.68

5.339

Cristobalite low

5.317

6.63

6.79

5.795

Quartz

6.073

5.84

5.59

6.050

Quartz beta

-

6.09

5.46

5.640

Stishovite

5.606

-

5.15

5.097

2= [42], 3=[40]

Theo

3

Theo

Theo1= [39],

Theo

2

Polycrystals

and Theo4 is observed in this work

6.3.5 Electronic Properties of Surface and Layers of Silica Polymorphs In order to understand the electronic properties of the layers made, a surface of (111) was cut in all the polycrystals and their band structure and DOS plots for the surface were calculated (Table 6.3). Band structure and DOS plots for a single layer of G and GO did not induce a bandgap in graphene. This indicates that no new valence bands were formed thus, confirming that the arrangement was purely physisorption. There was a decrease in the bandgap from the silica polymorphs surface (Table 6.3) as observed from the values provided.

Table 6.3 Calculated electronic properties of SiO2 Graphene and epoxy graphene layers. Surface

Graphene layer with

Epoxy graphene

0 eV

layer with 0.517 eV

Cristobalite high

0.340

0

0

Cristobalite low

0.064

0

0

Quartz

0.045

0

0.050

Quartz beta

0.077

0

0

Stishovite

0.069

0

0

131

CHAPTER 6: Simulation from The First Principal Theory on The Effect of Doping Silica on Graphene and The New Composite Material However, SiO2-GO band structure was found to have a 0.050 eV bandgap; a reduction from the initial 0.517 eV. This could be attributed to the presence of the highly electron rich epoxy oxygen coming into close proximity to the silica since the epoxide functional group significantly induces the local distortion of graphene by forming a new bond between graphene and oxygen. This inadvertently affects the bonding characteristics of carbon by changing from planar sp 2 to partial sp3 hybridization. In order to understand the mechanism of the electron transfer in the layers, a partial density of state was plotted for the graphene layer using quartz beta and epoxy graphene monoxide layer using Cristobalite high. In both cases, the valence band of the layers had a majority of the oxygen (O 2p) orbital contribution with the conduction bands made up of the carbon (C 2p). The epoxy graphene monoxide had a higher concentration of oxygen as observed with the high density of electrons in the valence band (Figure 6.8).

The graphene layer had all the oxygen

contributions from silica (Figure 6.9). The electron contribution in the epoxy system appeared skewed to the left of the Fermi level (valence band) with a low electron concentration at the conduction band while the pristine graphene was almost symmetrical in distribution.

132






(a)

O 2p

Si 2s

C 2p

(b) C 2p

C 2s

(c)

O 2p

O 2s

(d) Si 3p

2s3s SiSi

Si 2p

Energy (eV)

Figure 6.8 PDOS of the epoxy graphene monoxide orbital contributions – (a) Cristobalite high layer, (b) carbon, (c) oxygen, and (d) silicon

133






(a)

C 2p

O 2p

Si 2s 3s Si

C 2p

(b)

C 2s

(c)

O 2p

O 2s

Si 2p 3p Si

(d)

Si 2s Si 3s

Energy (eV)

Figure 6.9 PDOS of the orbital contributions for (a) graphene - quartz beta layer, (b) carbon, (c) oxygen and (d) silicon

6.3.6 Optical Properties Graphene and all silica polymorph structures had a high absorbance in the UV region (Figure 6.10 (a) and (b)) of the solar spectrum. However, Stishovite and epoxy graphene monoxide had a slight absorbance in the visible region

134

CHAPTER 6: Simulation from The First Principal Theory on The Effect of Doping Silica on Graphene and The New Composite Material (320 – 500 nm).

Figure 6.10. Optical properties for graphene, epoxy graphene monoxide and silica polymorph structures

There was a remarkable improvement of the absorption in the visible region after the formation of the nanocomposites (Figure 6.11 (a)). Stishovite layers had the highest absorbance in the visible region, while Cristobalite high had the lowest among the graphene layers. A similar observation in the epoxy graphene monoxide absorption maximum (Figure 6.11(b)) was observed with the least being the layer with quartz.

135


G-SiO2Quartz Beta layer G-SiO2Quartz layer

70

G-SiO2 Stishovite layer

80

GO-SiO2 Cristobalite high layer

G-SiO2 Cristobalite low layer

70

GO-SiO2 Quartz beta layer

Absorption (x103cm-1)

Absorption (x103 cm-1)

80

G-SiO2 Cristobalite high Layer

60 50 40 30 20 10 0

400

500

600

700

GO-SiO2 Stishovite layer

60

GO-SiO2 Cristobalite low layer

50 40 30 20 10 0

800

GO-SiO2 Quartz layer

400

Wavelength(nm)

500

600

700

800

Wavelength (nm)

Figure 6.11. Optical properties analysis for layers of (a) SiO2 graphene and (b) epoxy graphene

A great improvement in the absorbance was observed in the visible region as the layers led to a red shift in wavelength of the starting materials. This was observed in both graphene and epoxy graphene layers, the improvement can be ascribed to the presence of graphene as the system, which contains graphene only, had the highest absorbance when compared to the oxidized.

6.3.7 Electrostatic Potential Calculations To determine the ease of moving an electron between layers, the electrostatic potentials (work function) in the starting molecules and formed layers were calculated (Appendix A 1) and listed in (Table 6.4). There was a general decrease in potentials from the surface of polymorphs in comparison to the layer’s surface, an indication of less energy required to move an electron to infinity from the surface of the layers than from the individual polymorph surface.

136

CHAPTER 6: Simulation from The First Principal Theory on The Effect of Doping Silica on Graphene and The New Composite Material Table 6. 4 The work function on the surface and layers of the nanosheet in the ground state (graphene in bottom position) Polymorphs

Surface work

Graphene Layer

Epoxy Graphene

function

work function

layer work function

(eV)

(eV)

(eV)

Quartz

5.997

5.708

5.042

Quartz beta

6.669

7.144

6.287

Cristobalite high

5.923

5.713

5.627

Cristobalite low

6.542

5.427

5.330

However, the quartz beta had a work function of high value, this was ascribed to the arrangement of the atoms at the interface.

An observation that was further

confirmed from the calculation of the work functions with graphene on top of the individual polymorphs (Table 6.5).

Table 6. 5 The work function on the surface and layers of the Nanosheet in the ground state (graphene on top position) Polymorphs

Surface

Graphene Layer

Epoxy Graphene

Work function

work function

layer work

(eV)

(eV)

function (eV)

Quartz

5.997

5.045

4.360

Quartz beta

6.669

4.144

4.467

Cristobalite high

5.923

7.256

7.457

Cristobalite low

6.542

6.016

5.613

137

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143

CHAPTER 7: A DFT STUDY ON THE EFFECT OF SUPPORTING TITANIA ON SILICA GRAPHENE EPOXY GRAPHENE AND CARBON NANOTUBES

7.1 Introduction

Titanium dioxide (TiO2) is a photocatalyst with a relatively large band gap energy of 3.2 eV [1, 2]. This, among others, has been a major drawback since it cannot be efficiently used in natural visible light energy that filters through the earth’s surface [3]. To overcome this drawback, various strategies have been used to reduce the band gap, improve charge carrier generation [4] and lifetime of the charge carriers [5], as well as increasing the efficiency of its photocatalytic activity [6]. Various strategies could be applied to improve charge separation. For example, metals and non-metals have been used as dopants and surface deposits as supports. TiO2 has been doped in nanotubes, reduced to thin films, nanofibers or mesoporous materials (Figure 7.1). The preparation of semiconductors at high temperatures may lead to high crystallinity that reduces the formation of charge recombination defect sites.

Nano wire making [7, 8] may also aid in charge

separation and therefore, in transportation. In comparison to a zero dimensional nanoparticle, one-dimensional nanostructures have better charge mobility and activity and can, therefore, minimize the charge recombination.

3Kiarii

et.al.

Journal of Computational Condensed Matter (2017) DOI:

http://dx.doi.org/10.1016/j.cocom.2017.08.003 146

CHAPTER 7: A DFT Study on The Effect of Supporting Titania on Silica Graphene Epoxy Graphene and Carbon Nanotubes

Figure 7.1. Charge generation and band gap reduction in the TiO2 composite

TiO2 can be coupled with carbon-based materials, especially with graphene (Figure 7.2) and has attracted increasing attention.

Graphene with defined electronic

properties can be chemically bonded with TiO2 [9]. Graphene material exhibits a high mobility of charge carriers, as well as good mechanical strength [10]. Therefore, these carbon-based materials enable charge transfer and inhibit the charge recombination process when combined with TiO2 based photocatalysts.

Ou et al. [11] synthesized a multiwall carbon nanotube, TiO2, and Ni composite catalyst (MWNT-TiO2: Ni) by a modified chemical vapour deposition method. Their

145


findings revealed the role of MWNT as a photosensitizer to increase the H2 evolution rate under visible light irradiation [11].

Figure 7.2 Charge transfer and separation in the G-TiO2 composite

Graphene as a cocatalyst on TiO2 could act as an electron acceptor due to the lower potential of graphene/graphene

composite as compared to the TiO2-based

composite [7]. The junctions, including heterojunction, may be helpful for the charge separation. The activity enhancement may be due to the junction effect, as well as other factors. Further improvement of the photocatalytic properties of TiO2/MWCNT composites with silver nanoparticles via an enhanced plasmonic resonance effect was recently reported [8]. Since graphene is one atom thick, its whole volume is exposed to the surroundings and its properties are very responsive to the surrounding atmosphere including temperature, substrate and adsorbate molecules.

146


The defined electronic properties of graphene can enable it to be chemically bonded with TiO2 [12]. When titanium dioxide is coupled with graphene, the new material composite allows charge to flow easily, as well as have a high strength [10]. Therefore, these carbon-based materials enable charge transfer and inhibit the charge recombination process when combined with TiO2 based photocatalysts. To improve the overall photo-catalytic efficiency of TiO2, the use of a support, such as silica SBA-15 has been reported by Hintsho et al. [8]. Silica based materials have relatively large poles and thick walls making them hydro thermally stable with both microporosity and mesoporosity. Multi-walled carbon nanotubes enhance TiO2 photo activity with excellent physical-chemical contact as opposed to physical mixing. The improvement activity is due to the longer lived electron hole charge carriers. Carbon nanotubes (CNTs) provide additional sorption properties forming divalent metal ion composites of superior light sorption properties [13]. The CNTs form hetero-junctions [14, 15], which enhances the photocatalytic efficiency.

7.2 Computational D e t a ils 7.2.1 Model Building 7.2.1.1 Bulk and Surfaces The models built in this study of titanium dioxide (TiO2) on silica (SiO2), graphene (G), epoxy graphene monoxide (Ep-GO) and single-wall carbon nanotubes (SWCNT) were generated using CASTEP in Material Studio 2016. Using the lattice parameters unit cells (Table 7.1), the models were converted into supercells and cleaved into (111) surface for SiO2; (101) surface of TiO2; 5x2 graphene and 3x2 epoxy graphene monoxide (Figure 7.3).

147


Table 7.1: Lattice parameter unit cells used to build the bulk models Structure

Ep-GO

Lattice parameters (Å) a

b

5.68

2.64

Graphene

2.461

Titania

3.784

SiO2

c 15

6.709 3.784

9.514

Primitive cell Space group Cmmm(65)

hPn187 cFn141

3.929

cPn205

Ep-GO [16], TiO2 [18], Graphene [17], SiO2 [19]

148

Atomistic positions C C C C

0.3261 0.6739 0.8259 0.1741

0.0000 0.0000 0.5000 0.5000

0.5000 0.5000 0.5000 0.5000

O O O O C C

0.5000 0.5000 0.0000 0.0000 0.0000 0.3333

0.0000 0.0000 0.5000 0.5000 0.0000 0.6666

0.5696 0.4304 0.5696 0.4304 0.0000 0.0000

Ti

0.0000

0.0000

0.0000

Ti O

0.7500 0.2081

0.2500 0.2081

0.5000 0.0000

O

0.9581

0.4581

0.5000

O

0.7919

0.7919

0.0000

O

0.5419

0.0419

0.5000

Si

0.0000

0.0000

0.0000

Si

0.5000

0.0000

0.5000

Si

0.0000

0.5000

0.5000

Si

0.5000

0.5000

0.0000

O

0.3484

0.3484

0.3484

O

0.5454

0.3484

0.1516

O

0.3484

0.1516

0.8484

O

0.1516

0.8484

0.3484

O

0.6516

0.6516

0.6516

O

0.8484

0.1516

0.6516

O

0.1516

0.6516

0.8484

O

0.6516

0.8484

0.1516


TiO2 (101)

SiO2 (111)

SiO2 - G

TiO2 - G

SiO2 –G –TiO2

G - SiO2 - TiO2

Graphene

Epoxy-GO

SiO2 – Ep

Ep - SiO2 - TiO2

TiO2 – Ep

SiO2 - TiO2 – Ep

SWCNT SWCNT

SiO2 - TiO2

SWCNT TiO2 – SWCNT

G -TiO2 – SiO2

SiO2 – Ep –TiO2 TiO2 –SWCNT–SiO 2 SWCNT

Figure 7.3 Structural models of surfaces and layers built to explore electronic and optical properties of generated TiO2 composites 7.2.1.2 Single Layer and Two Layers The graphene and epoxy graphene generated models were two-dimensional structures as illustrated in Figure 7.3. Both surfaces were thus considered in the layer’s generation, however, for the carbon nanotube the open ends of the SWCNT was used to generate the layers, as the curved surface resembled the graphene flat surface. The layers generated demonstrated a case where (a) TiO2 interacts with SiO2, which represents the case that SiO2 is the major component of the composite (Figure 7.3 SiO2-TiO2).

149


(b) TiO2 interacts with G or Ep-GO, which represents the case that G or Ep-GO are the major components of the composite and therefore, TiO2 preferentially interacts with G or Ep-GO surfaces; (i) G-TiO2 model: TiO2 interacts with G, where G is parallel to TiO2 surface. (ii) Ep-GO -TiO2 model: TiO2 interacts with Ep-GO, where Ep-GO is parallel to TiO2 surface. 7.2.1.3 TiO2 Interacts with Silica/G and Ep-GO Nano Composites Silica intercalated in the middle of TiO2 and G interacted with both of them, see Figure 7.3 (TiO2-SiO2-G). This model was built in order to study the role of G in the TiO2 interaction with silica/G nano composites. Silica model was such that silica interacts with G having the O group of silica parallel to the G surface. While in Figure 7.3 the TiO2- SiO2- Ep-GO) model, silica interacts with Ep-GO. The O group of silica is near to the epoxy groups of Ep-GO. 7.2.1.4 G and Ep-GO is sandwiched between TiO2 and Silicon Dioxide

In this case, (Figure 7.3, TiO2-G-SiO2 or TiO2- Ep-GO-SiO2) G or Ep-GO intercalated in the middle of TiO2 and SiO2 and interacts with both of them. Models were built in order to study the role of G in the TiO2 interaction with G or Ep-GO nanocomposites as silica is on the opposite side not in contact with TiO2, in this model, Silica intercalates between G and TiO2 surfaces. Silica model: silica interacts with G or Ep-GO. Silica is modelled opposite and not in contact with TiO2 but parallel to the G or Ep-GO surface. 7.2.1.5 TiO2 interacts with Single Wall Carbon Nanotube (SWCNT)

The case that SWCNT is the major component of the composite and therefore, TiO2 preferentially interacts with (SWCNT) edges was represented in (Figure 7.3, 150


TiO2-SWCNT-SiO2); SWCNT is sandwiched between TiO2 and SiO2. In this case, SWCNT intercalated in the middle of TiO2 and SiO2 while interacting with both of them.

7.2.2 Calculations Details The first principles calculations were performed using CASTEP module of Material Studio 2016 [20].

Ultra soft pseudopotential was employed for all the DFT

calculations. The generalized gradient approximation (GGA) with Perdew-BurkeErnzerhof (PBE) exchange correlation functionals [21] was used to reduce the underestimation of DFT.

The plane wave cut-off energy was set at 400 eV.

Monkhorst-Park Scheme K-point grid [20] was set at 12x12x1.

The geometric

relaxation was obtained by Broyden-Flecher-Goldfarb-Shanno (BFGS) algorithm [20] until the forces were smaller than 0.03 eV/Å, the convergence threshold was set at 2.x10-6 eV/ atom. A vacuum slab was set at 15 Å to allow geometric relaxation and avoid the layers collapsing on each other.

7.3 Results and Discussion 7.3.1 Morphological Analysis Geometric relaxation was allowed to converge with a variation of ion positions in a fixed cell size. The powder diffraction patterns (Figure 7.4) and Raman spectra (Figure 7.5) for the structural models were calculated using Material Studio 2016. These were found to have comparable peaks to experimentally obtained peaks for the powder diffraction [22-25] patterns and Raman [25, 26] spectra. The results were used to verify that the models represented graphene, epoxy graphene, anatase and SiO2-Cristobalite. However, experimental results from Downs et al.

151


[20] showed shifts in the Raman spectra, a similar trend observed in the results presented in previous chapters. These shifts could be ascribed to either instrument errors or from solvents employed in the synthesis or the level of theory approximations employed in this study. However, the general trend observed was from both the theoretical and experimental data. 100

100

Epoxy Graphene

Graphene 80

Intensity

Intensity

80

60

40

60

40

20

20

0

0 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

2-Theta

2-Theta

100

100

TiO2

SiO2 80

Intensity

Intensity

80

60

40

20

60

40

20

0

0 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

20

22

24

26

28

2-Theta

30

32

34

36

38

40

42

44

2-Theta

100

SWCNT SWNT

Intensity

80

60

40

20

0 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44

2-Theta

Figure 7.4 Calculated powder diffraction patterns of graphene, epoxy graphene monoxide, TiO2-anatase, SiO2-cristobalite and single wall carbon nanotube (SWCNT)

152


SiO2

2.0

700

Epoxy Graphene

600 500

Activity

Activity

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400 300 200 100 0

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-100 600

100 200 300 400 500 600 700 800 900 10001100

800

1000

1200

1400

1600

1800

2000

2200

Wavelength (cm-1)

Wavelength cm-1 TiO2

12000

Graphene

20

10000 8000

12

Activity

Activity

16

8 4

6000 4000 2000

0

0 200

300

400

500

600

Wavelength (cm

700

-1

800

1700 1720 1740 1760 1780 1800 1820 1840 1860 1880

Wavelength (cm-1)

)

Figure 7.5 Calculated Raman spectra for SiO2-cristobalite, TiO2-anatase, and Epoxy graphene monoxide and graphene 7.3.2 Electronic Properties To investigate the electronic properties of the starting molecules and the layers made, the total density of state (DOS) and partial density of state (PDOS) were calculated and plotted (Figure 7.6). The band structure and density of state of the starting molecules (a) anatase, (b) cristobalite low, (c) graphene, (d) epoxygraphene monoxide and PDOS orbital contributions in the layers by elements namely Ti, Si, C, & O (Figure 7.7).

153


3.207 eV

5.795 eV

(a)

(b)

0.517 eV

(c)

(d)

Figure 7.6 Band structure and density of state of starting molecules (a) anatase, (b) cristobalite low, (c) graphene and (d) epoxy-graphene monoxide

For pure anatase, the valence band was mainly made up of O 2p state, while the conduction band was mainly composed of Ti 3d state as shown in Figure 7.7. The calculated bandgap for the bulk was 3.207 eV, which is comparable to the experimentally obtained band structure of 3.2 eV. The bandgap of graphene and epoxy graphene was found to be 0 eV and 0.517 eV, respectively (Figure 7.6).

154


Ti 3d

Ti

Cc

Density of state (electrons/ eV)

C 2s

C 2p

O 2p

o O

Si Si 3p

Si 3s

TiO Tio22-G-SiO -G-Sio22- layer

O 2p

C 2p Ti 3d

Si 3s

O 2p Tio2-GO-SiO TiO 2 -2 layer 2-GO-Sio

C 2p

Ti 3d

Si 3s

Figure 7.7 Orbital contributions in the layers by elements namely Ti, Si, C and O and their layers of graphene (G) and epoxy graphene (GO) respectively

155


It was observed in Figure 7.7 that the titanium element had the Ti 3d orbital contribution appearing in the conduction band. Silicon, Si 3s had an almost equal representation in both conduction and valence bands with Si 3p density inclined to the conduction band. However, carbon and oxygen 2p orbitals had the highest contributions in the conduction and valence bands, respectively. It is worth noting that the oxygen had a highest density of state (electrons/eV) in the valence band with contribution from both TiO2, SiO2 and Ep-GO.

The interaction of the

heterostructures, SiO2, graphene, carbon nanotube and graphene oxide with TiO2 photo catalyst material caused the O-2p and C-2p orbitals to shift closer to the Fermi level (Figure 7.7).

The bandgaps (Table 7.2) were generated from the band structures of the layers generated for optical analysis (Appendix A 2). Table 7.2 Energy gaps of individual elements surface and layers generated Element

Energy gap (eV)

TiO2 (101) surface

1.023

SiO2 (111) surface

0.064

Graphene

0.000

SWCNT

0.028

Epoxy graphene oxide

0.517

One Layer

Energy gap (eV) Two layers

Energy gap (eV)

SiO2-TiO2

0.018

G-TiO2-SiO2

0

TiO2-G

0.097

G- SiO2-TiO2

0

TiO2- GO

0.108

TiO2-G-SiO2

0

SWCNT-TiO2

0.035

GO-TiO2-SiO2

0.008

GO-SiO2-TiO2

0.086

TiO2-GO-SiO2

0.024

TiO2-SWCNT-SiO2

0.008

156


There was a reduction in the bandgap from the starting elements forming the layer. Nevertheless, TiO2 reduction in bandgap was an advantage as this goes ahead to reduce the large bandgap, which is a major limitation of TiO2 application in photocatalysis. The single layer of TiO2-G had a bandgap induction in graphene, while SWCNT-TiO2 had SWCNT bandgap increased. This can be ascribed to the TiO2 large bandgap influence in the slab cut at [101]. Therefore, when two layers were generated no energy gap in all graphene systems were observed and a large decrease in the SWCNT was noted. The reduction in the bandgap of the epoxy graphene monoxide composites resulted from the presence of the epoxide functional group.

The oxygen atom significantly induced the local distortion of

graphene with a new bond formed by graphene and oxygen atoms. This affects the bonding characteristics of carbon changing from planar sp 2 to partial sp3 hybridization. The reduction of the TiO2 band gap in the layers is an indication of possible application in photo-energy generation.

7.3.3 Optical Properties The significance of graphene systems in the optical improvement to the visible wavelength range was observed (Figure 7.8).

Graphene or epoxy graphene

monoxide composite sandwiched between titania and silica gave the highest absorbance (Figure 7.9).

The increase in absorption can be ascribed to the

resonance structure of graphene, which has been observed during fluorescence [27-29]. The lowest absorbance was observed for the titania-silica layer in which graphene is absent.

157


The interface between the hetero structures of silica, graphene, graphene oxide and carbon nanotube with the semiconductor-based photocatalyst (TiO2) showed enhanced absorbance in the visible light region. This would have a positive impact in photo generation and photo catalytic activity.

TiO2

G

SiO2

G-SiO2-TiO2 Layer

4

6x10

TiO2

TiO2-G-TiO2 Layer G- TiO2- SiO2 Layer

4

6x10

TiO2 - SiO2

GO-SiO2-TiO2

TiO2-GO

GO-SiO2-TiO2

GO -TiO2 -SiO2

TiO2-GO-TiO2

4

4

5x10 Absorption (cm-1)

5x10 Absorption (cm-1)

GO

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6x10

TiO2-2SWNT-SWCNT-SiO TiO SiO 2 Layer 2 Layer

4

5x10 -1)

600

Wavelength (nm)

Wavelength (nm)

Absorption (cm

500

4

4x10

4

3x10

4

2x10

4

1x10

0 400

500

600

700

800

Wavelength (nm)

Figure 7.8 Optical properties of graphene (G), epoxy graphene (GO), single wall carbon nanotube (SWCNT) and their composites

158


TiO 2 -SWCNT-SiO2Layer TiO 2 -G-SiO 2 Layer TiO 2 -GO -SiO 2 Layer TiO 2 - SiO 2 Layer

Absorption (cm-1)

70000 60000 50000 40000 30000 20000 10000 0 400

500

600

700

800

Wavelength (nm) Wavelength (nm)

Figure 7.9 Comparative optical properties of generatedTiO2 layers The graphene structure resonance easily fluoresces in the presence of light because of its resonance. This happens after absorption of electrons and promotion to a higher

energy

level

as

observed

by

Shang

et

al., Kim et

al. and

Thomas et al. [27-29]. Epoxy graphene also fluoresces, but not pure graphene. The presence of oxygen in its structure reduces the optical absorption in the visible wavelength. The presence of two substrates sandwiching the graphene or epoxy graphene enable both materials the ease of electron movement through the unpaired electrons in the π orbital in graphene. When both substrates appear on the same side, one became a screen to the other reducing interaction with graphene thus reducing absorption.

The conversion of sp 2 to sp3 hybridization in epoxy

graphene monoxide also affected the resonance structure electron movement in the epoxy layers.

159


7.3.4 Mechanism of Electron Transfer in Layer The effect of TiO2 on silica/graphene and epoxy graphene on different orientations on its work function, the electrostatic potential’s (ɸ) (Table 7.3) for these orientations were also calculated. Table 7.3 Work function of variable samples Materials

Work function (ɸ) (eV)

TiO2 (101) surface

4.043

SiO2 (111) surface

6.552

Graphene

5.577

Epoxy graphene oxide

5.878

One layer

Work function (ɸ) Two layers

Work function

(eV)

(ɸ) (eV)

SiO2-TiO2

5.707

GO-SiO2-TiO2

2.481

TiO2-G

3.986

G-TiO2-SiO2

5.274

TiO2- GO

3.845

G- SiO2-TiO2

3.692

SWNT-TiO2

6.046

TiO2-G-SiO2

5.904

SiO2- G

6.213

TiO2-GO-SiO2

6.138

TiO2-SWCNT-SiO2

5.523

The layers showed a significant decrease in work function for the TiO2-G, G-TiO2SiO2 and G-SiO2-TiO2 layers, which were smaller than that of freestanding graphene. GO-SiO2-TiO2 and TiO2-GO layers were smaller than that of freestanding epoxy graphene monoxide. However, TiO2 (101) surface had a higher work function than GO-SiO2-TiO2, TiO2-G, TiO2-GO and G-SiO2-TiO2 layers. This suggests that the electrons would easily move from the layers to TiO2 surface than be retained in the layers. More energy was required to move an electron from the SiO 2-TiO2, G-

160


TiO2-SiO2, TiO2-G-SiO2, TiO2-GO-SiO2 and TiO2-SWCNT-SiO2 layers and an indication of its ability to store the generated charge. SiO 2 (111) surface required the most energy to move the electron to infinity compared to all the systems, an indication of its inability to release the electron. We ascribe the work function decrease to the formation of an effective dipole layer oriented away from the substrate [30]. This dipole results from the transferred electron density around the surface, which has an oscillatory character and integrates to a positive charge toward vacuum and negative charge toward the substrate.

161


7.4 References [1]

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[2]

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[3]

Q. Zheng, B. Zhou, J. Bai, L. Li, Z. Jin, J. Zhang, J. Li, Y. Liu, W. Cai and X. Zhu. Self‐Organized TiO2 Nanotube Array Sensor for the Determination of Chemical Oxygen Demand. Advanced Materials 20 (2008) 1044-1049.

[4]

C. Hägglund, M. Zäch and B. Kasemo. Enhanced Charge Carrier Generation in Dye Sensitized Solar Cells by Nanoparticle Plasmons. Applied Physics Letters 92 (2008) 013113.

[5]

S. G. Kumar and L. G. Devi. Review on Modified TiO2 Photocatalysis Under UV/Visible Light: Selected Results and Related Mechanisms on Interfacial Charge Carrier Transfer Dynamics. The Journal of Physical Chemistry A 115 (2011) 13211-13241.

[6]

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of Nanostructured

TiO2 Films by Adsorption of Gold

Nanoparticles. The Journal of Physical Chemistry B 104 (2000) 1085110857. [7]

X. Liu, L. Pan, T. Lv, G. Zhu, Z. Sun and C. Sun. Microwave-Assisted Synthesis of CdS-Reduced Graphene Oxide Composites for Photocatalytic Reduction of Cr(vi). Chemical Communications 47 (2011) 11984-11986.

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[8]

N. Hintsho, L. Petrik, A. Nechaev, S. Titinchi and P. Ndungu. Photo-Catalytic Activity of Titanium Dioxide Carbon Nanotube Nano-Composites Modified With Silver and Palladium Nanoparticles. Applied Catalysis B: Environmental 156-157 (2014) 273-283.

[9]

K. Woan, G. Pyrgiotakis and W. Sigmund. Photocatalytic Carbon-Nanotube– TiO2 Composites. Advanced Materials 21 (2009) 2233-2239.

[10]

A. K. Geim and K. S. Novoselov. The Rise of Graphene. Nature Mater 6 (2007) 183-191.

[11]

Y. Ou, J. Lin, S. Fang and D. Liao. MWNT–TiO2: Ni Composite Catalyst: A New Class of Catalyst for Photocatalytic H2 Evolution from Water under Visible Light Illumination. Chemical Physics Letters 429 (2006) 199-203.

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Q. Huang, S. Tian, D. Zeng, X. Wang, W. Song, Y. Li, W. Xiao and C. Xie. Enhanced Photocatalytic Activity of Chemically Bonded TiO2/Graphene Composites Based on the Effective Interfacial Charge Transfer through the C–Ti bond. ACS Catalysis 3 (2013) 1477-1485.

[13]

G. P. Rao, C. Lu and F. Su. Sorption of Divalent Metal Ions from Aqueous Solution by Carbon Nanotubes: A Review. Separation and Purification Technology 58 (2007) 224-231.

[14]

Y. Jia, A. Cao, X. Bai, Z. Li, L. Zhang, N. Guo, J. Wei, K. Wang, H. Zhu and D. Wu. Achieving High Efficiency Silicon-Carbon Nanotube Heterojunction Solar Cells by Acid Doping. Nano Letters 11 (2011) 1901-1905.

[15]

Y. Jia, Z. Zhang, L. Xiao and R. Lv. Carbon Nanotube-Silicon Nanowire Heterojunction Solar Cells with Gas-Dependent Photovoltaic Performances and Their Application in Self-Powered NO2 Detecting. Nanoscale research letters 11 (2016) 299.

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[16]

S. D. Dabhi, S. D. Gupta and P. K. Jha. Structural, Electronic, Mechanical, and Dynamical Properties of Graphene Oxides: A First Principles Study. Journal of Applied Physics 115 (2014) 203517.

[17]

J. Tanaka. Ab Initio Quantum Chemical Calculation of the Pair Potentials of Superconductors. Physica C: Superconductivity and Its Applications 445 (2006) 150-153.

[18]

M. Horn, C. F. Schwerdtfeger and E. P. Meagher. Refinement of the Structure of Anatase at Several Temperatures. Zeitschrift für Kristallographie 136 (1972) 273-281.

[19]

Y. Kuwayama, K. Hirose, N. Sata and Y. Ohishi. The Pyrite-Type HighPressure Form of Silica. Science 309 (2005) 923-925.

[20]

Accelrys Software (2016) Materials Studio Simulation Environment. Release 2016, Accelrys Software Inc, San Diego, CA, (2016)

[21]

J. P. Perdew, K. Burke and M. Ernzerhof.

Generalized

Gradient

Approximation Made Simple. Physical Review Letters 77 (1996) 3865. [22]

M. N. Khan and J. Bashir. Small Angle Neutron Scattering and X-Ray Diffraction Studies of Nanocrystalline Titanium Dioxide. Journal of Modern Physics 02 (2011) 4.

[23]

N. O. Ramoraswi and P. G. Ndungu. Photo-Catalytic Properties of TiO2 Supported

on

MWCNTs,

SBA-15

and

Silica-Coated

MWCNTs

Nanocomposites. Nanoscale research letters 10 (2015) 1. [24]

T. Theivasanthi and M. Alagar. Titanium dioxide (TiO2) Nanoparticles XRD Analyses: An Insight. Cornell University Library (2013) arXiv preprint arXiv:1307.1091

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[25]

Downs, R.T., Liermann, H.P., and Yang, H. The analysis of Ti order/disorder in pseudobrookite by Raman spectroscopy: Implications for the geological exploration of Mars. Geological Association of Canada - Mineralogical Association of Canada Annual Meeting, St. Catherines (2004) 01-06.

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http://rruff.info/Anatase/R060277. Last Accessed on 20-12-2016

[27]

J. Shang, L. Ma, J. Li, W. Ai, T. Yu and G. G. Gurzadyan. The Origin of Fluorescence from Graphene Oxide. Scientific Reports 2 (2012) 792.

[28]

J. Kim, L. J. Cote, F. Kim and J. Huang. Visualizing Graphene Based Sheets by Fluorescence Quenching Microscopy. Journal of the American Chemical Society 132 (2009) 260-267.

[29]

H. R. Thomas, C. Vallés, R. J. Young, I. A. Kinloch, N. R. Wilson and J. P. Rourke. Identifying

the Fluorescence of Graphene Oxide. Journal of

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165

CHAPTER 8: CONCLUSION AND PERSPECTIVE From the outset, the main thrust of this study was to theoretically investigate how modifications of graphene nanosheets doped with selected metals enhance its activities. The following conclusions were made from the calculations: 1. The model of titanium dioxide was generated and confirmed by powder diffraction and Raman spectra. Generation of charge carriers was studied with a protonated model of TiO2. Calculation results revailed an increase in Mulliken net charge of the atoms making TiO2 upon protonation. However, the study also shows that the subsequent addition of protons did not increase the overall net charge instead the additional charge was evenly distributed. The electron distribution led to an increase in the charge concentration around the oxygen 2 p orbital and from the projected density of state (PDOS) the oxygen atom was constituted in the valence band, the generated charge was available for conduction. The change in position did not increase the net charge either but the charge was evenly distributed without much deviation from the mean as observed by the 5 % error bars. The phonon calculations confirmed their existence and that the system was in the ground state. Even though the electrostatic potential reduced upon protonation, the optical properties showed no absorbance in the visible solar region of the spectrum this limiting TiO2 application in photocatalysis. 2. Transportation of charge carriers in graphene was simulated using the model structure generated and confirmed by Raman and powder diffraction spectra.

166

Conclusion and Perspective

The electron bands in graphene were calculated and a zero bandgap observed. Projected electron density of states (PDOS) showed s and p orbitals at the conduction and valence bands. Electron localization function gave a clear picture of a single layer of graphene. However, the existence of phonon in graphene was confirmed and compared with theoretical and experimental results. The phonons were all positive, indicating a ground state for the model and a stable system. The electrons and phonons presence in graphene was confirmed by the electron phonon coupling plots.

The scattering of electrons by phonons

which decreases the material’s efficiency in transporting electrons in the bands and was not observed as there was a zero bandgap as anticipated the electron-phonon interaction induced the pairing of electrons. This formed the driving mechanism responsible for high conductivity in graphene systems , with both electrons and phonons freely transporting charge and its high sensitivity to neighbouring systems. The calculated work function (Φ) was found to be 3.863 eV. 3. Further investigations were simulated on the physisorbed properties of silica on CNT's and graphene systems. The various Raman and powder diffraction patterns were representative of the respective molecules. Calculated electronic properties of SiO2 polycrystal structures were within the range of the theoretically calculated results in previous studies. Silica interaction with graphene was physisorbed, which was confirmed by the absence of bandgap induction graphene layers.

167


Total PDOS of graphene and epoxy graphene layers plus elemental carbon, oxygen and silicon orbital contributions showed s and p orbitals within the fermi level. There was high electron density in the valence band of the epoxy graphene layer as compared to the pure graphene due to the presence of oxygen. Optical properties of graphene, epoxy graphene monoxide and silica showed predominant absorbance in the UV region of the solar spectrum. Nonetheless, this changed upon formation of layers, which lead to significant improvement in absorbance at the visible region. Stishovite layer had the highest absorbance in the visible region of the light spectrum, while cristobalite high had the lowest among the graphene layers. Similarly, the epoxy graphene monoxide absorption maximum was observed with the least absorbent being the layer with quartz. Decrease in potentials from the polymorphs surface was observed at the surfaces of generated layer’s, an indication of less energy required to move an electron to infinity from the surface of the layers than in individual polymorphs surface. The polymorphs structures significantly improve the optical properties and electrostatic potentials of the new composite material and would find applications in photocatalysis. 4. The study of the effect of supporting titania on silica graphene epoxy graphene and carbon nanotubes interfacial properties and optical response was conducted using the previous models and were found to have comparable peaks as obtained experimentally for powder diffraction and Raman spectroscopy. Orbital contributions in the layers by elements namely Ti, Si, C, and O and their layers with graphene and epoxy graphene indicated the presence of the various orbitals namely Ti-3d, Si-3p, O-2p, and C-2p. 168


Titanium 3d orbital contributed to the conduction band. Silicon 3s showed an almost equal representation in both conduction and valence bands with Si 3p density inclined to the conduction band. However, carbon and oxygen 2p orbitals had the highest contributions in conduction and valence bands, respectively. Oxygen had the highest density of state electrons/eV in the valence band with a contribution from TiO2, SiO2 and Ep-GO. The interaction of the heterostructures, silica, graphene, carbon nanotube and graphene oxide with TiO2 photo catalyst material caused the O-2p and C-2p orbitals to shift closer to the fermi level. The significance of graphene systems in respect to optical improvement in the visible wavelength range was observed. Graphene or epoxy graphene monoxide composite sandwiched between titania and silica produced the highest improvement. The lowest absorbance was in the titania-silica layer in which graphene is absent. The interface between the heterostructures of silica, graphene, graphene oxide and carbon nanotube with semiconductorbased photocatalyst (TiO2) showed enhanced absorbance in the visible light region. This would have a positive impact in photo generation and photo catalytic activity. The layers showed a significant decrease in work function for the TiO2-G, GTiO2-SiO2 and G-SiO2-TiO2 layers, which were smaller than that of freestanding graphene. GO-SiO2-TiO2 and TiO2-GO layers were smaller than that of free-standing epoxy graphene monoxide. However, TiO2 (101) surface had a higher work function than GO-SiO2-TiO2, TiO2-G, TiO2- GO and GSiO2-TiO2 layers. We attribute the work function decrease to the formation of an effective dipole layer oriented away from the substrate. This dipole results

169


from the transferred electron density around the surface, which has an oscillatory character and integrates to a positive charge in vacuum and negative charge in the substrate. A better understanding of the mechanisms for the photocatalytic reaction processes, including light harvesting, carrier migration and transport, with the elementary reactions at the atomic or molecular level is necessary for the improvement of the TiO2/graphene composites for solar energy conversion efficiency.

With a

comprehensive understanding of all of these processes, efficient TiO2-based photocatalytic systems may be developed. Combining time-resolved and spaceresolved spectroscopic techniques with computational studies, a more in-depth knowledge on charge separation in TiO2-based photocatalysts could be obtained. Due to the intrinsic limitations, TiO2 may not be a promising photocatalyst for solar fuels generation or photocatalytic splitting of water and CO 2 photoreduction. However, graphene is an ideal material for photosensitization as it possesses the desired properties and has great influence to absorbance in the visible region of the solar spectrum. Silica actually improves the optical properties of TiO2. It is thus not expected that a major breakthrough in solar energy production may occur on TiO2based photocatalysts but, as shown in this study, TiO2 can be an ideal model for semiconductor-based photocatalysts under modified conditions.

170

Appendices A1. Electrostatic potentials used in Table 6.4 and Table 6.5 for the work function of the surface and layers of the nanosheet in the ground state graphene being on top and bottom respectively

166

Appendices

172

Appendices

173

Appendices

A2. Band structures used in Table 7.1 for the bandgaps of the surface and layers of the nanosheet in the ground state graphene, Epoxy graphene and SWNT being on top and bottom respectively

TiO2 (101) surface

SiO2 (111) surface

174

Appendices

Graphene

Epoxy Graphene monoxide

175

Appendices

Single wall Nanotube

TiO2-GO layer

176

Appendices

TiO2-G layer

TiO2-SiO2 layer

177

Appendices

SWNT-TiO2 layer

GO-SiO2-TiO2 layer.

178

Appendices

TiO2-G-SiO2 layer

G -TiO2-SiO2 layer

179

Appendices

G - SiO2- TiO2 layer

TiO2-GO-SiO2 layer

180

Appendices

TiO2-GO-SiO2 layer

TiO2-SWNT-SiO2

181