22-1 1. I

Richard H. West

Description

• cours magistral - matière potentielle : practical cells
• cours magistral
• cours magistral - matière potentielle : problems

22-1 Homework solutions 1. I2 + 2e 2I- Na+ + e Na } the half cell with the more -ve E will be the anode E(I2) > E (Na) 2. Au + + e Au I2 + 2e 2I- The way to do these is to write out both as reductions and then from info given see which is the anode --it will have the most negative E } anode E(Au) > E (I) 3.

• -3 lecture
• cathode cell compartment
• standard cell
• solution by reduction to cu
• ni2
• -4 equation review
• reaction
• cell

Sujets

• Cours magistral
• Problem
• Équation
• Réduction
• Review
• Solution
• Réaction
• Standard
• Cathode

Informations

• Publié par: lukam
• Nombre de lectures: 36
• Langue: English
• Poids de l'ouvrage: 5 Mo

Extrait

Modelling the Chloride Process
for Titanium Dioxide Synthesis
Richard Henry West
Clare College
A dissertation submitted for the degree of
Doctor of Philosophy at the
2008Preface
This dissertation is the result of my own work and includes nothing which
is the outcome of work done in collaboration, except where specifically
indicated in the text. The work presented was undertaken at the Depart-
ments of Chemical Engineering at the University of Cambridge, UK, and
the Massachusetts Institute of Technology, USA, between September 2004
and May 2008. Chapters 3, 4 & 5 of this dissertation include work from
the dissertation I submitted in July 2005 for a Certificate of Postgraduate
Study. No other part of this thesis has been submitted for a degree to this
or any other university. This dissertation contains approximately 44,033
words and 42 figures.
Some of the work in this dissertation has been published:
1. R. H. West, G. J. O. Beran, W. H. Green, and M. Kraft. First-principles
thermochemistry for the production of TiO from TiCl . J. Phys.2 4
Chem. A, 111(18):3560–3565, 2007. doi:10.1021/jp0661950
2. R. H. West, M. S. Celnik, O. R. Inderwildi, M. Kraft, G. J. O. Beran,
and W. H. Green. Toward a Comprehensive Model of the Synthesis
of TiO Particles from TiCl . Ind. Eng. Chem. Res., 46(19):6147–6156,2 4
2007. doi:10.1021/ie0706414
3. R. H. West, R. A. Shirley, M. Kraft, C. F. Goldsmith, and W. H. Green.
A Detailed Kinetic Model for Combustion Synthesis of Titania from
TiCl . Technical Report 55, c4e-Preprint Series, Cambridge. Also sub-4
mitted to Combust. Flame, 2008.
Richard Henry West
May 19, 2008 (approved corrections November 19, 2008)
iAbstract
Modelling the Chloride Process
for Titanium Dioxide Synthesis
Richard Henry West
This dissertation is about the gas-phase oxidation of titanium tetrachlo-
ride, used industrially to produce titanium dioxide particles:
TiCl + O ! TiO + 2Cl .4 2 2 2
Thermochemical data for intermediate Ti O Cl species are calculatedx y z
using quantum chemistry (mostly density functional theory) and statisti-
cal thermodynamics. By comparing results from three different density
functionals, isodesmic and isogyric reactions are shown to be very im-
portant for determining standard enthalpies of formation of these species.
The energy of TiOCl , important both in the chemical mechanism and in2
determining standard enthalpies of other species, is determined more ac-
curately using coupled cluster CCSD(T) calculations.
Predictions of chemical equilibrium composition help to identify likely
intermediate species and give clues to the critical nucleus size, above
which a molecule can safely be treated as a particle.
For the first time, a detailed kinetic model for this system is constructed
from spin-permitted elementary reactions; it rapidly converts TiCl to4
oxygen-containing dimer species (Ti O Cl ). Flux and sensitivity analy-y z2
ses guide the development of an improved kinetic model, which is com-
pared with experimental data from a rapid compression machine and a
plug flow reactor.
The gas-phase kinetic model is coupled to a particle population-
balance model (PBM), solved stochastically, using an existing operator-
splitting method; the coupling is improved by an adaptive splitting-
step size. The PBM is extended to track sizes of primary particles
within each agglomerate particle; rules are provided for inception, surface
growth, coagulation, and sintering. This information is used to estimate
particle shapes and the coupled model is used to simulate laboratory and
industrial reactors.
It is impractical to extend the kinetic model beyond Ti O Cl manually,2 y z
so steps are taken towards automating the process. A reaction mechanism
generator developed for hydrocarbons, RMG, is modified to model tita-
nium oxychlorides. An algorithm is presented for predicting molecular
geometries, enabling the automation of quantum chemistry calculations.Acknowledgements
I would like to thank my supervisor Dr Markus Kraft for his
supervision and guidance, and Prof. William H. Green for his.
Their helpful and friendly post-docs and students are too nu-
merous to name individually; in particular, however, Gregory
Beran, Matthew Celnik, Raphael Shirley and Franklin Gold-
smith helped directly with the work described in these pages.
Roger Place and John Edwards provided helpful encour-
agement from an industrial perspective. Tioxide Europe Lim-
ited and the EPSRC provided funding, and Clare College gen-
erously gave additional financial assistance in the form of a
West Bursary.
I would also like to thank all of my friends for their motiva-
tion and advice, Kathy and Rosalynne for their support and pa-
tience, but most of all my parents for their unconditional love
and encouragement.
Richard West, May 2008, Cambridge
iiiContents
List of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
List of tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
1 Introduction 1
1.1 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Structure of thesis document . . . . . . . . . . . . . . . . . . . 2
2 Background 3
2.1 What is titanium dioxide? . . . . . . . . . . . . . . . . . . . . 3
2.2 How is dioxide made? . . . . . . . . . . . . . . . . . 4
2.3 Why improve it? . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.4 Why model it? . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 Related Work 10
3.1 Experimental work . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 Population balance models . . . . . . . . . . . . . . . . . . . 13
3.3 Gas-phase chemistry . . . . . . . . . . . . . . . . . . . . . . . 17
3.4 Surface . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.5 Sintering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.6 Modelling approaches . . . . . . . . . . . . . . . . . . . . . . 25
4 Thermochemistry 26
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.2 Quantum Chemistry . . . . . . . . . . . . . . . . . . . . . . . 27
4.3 Enthalpies of formation: isodesmic and isogyric reactions . . 49
4.4 Finding temperature variations: statistical thermodynamics 63
ivCONTENTS
4.5 Polynomial fitting . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.6 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . 77
5 Chemical Equilibrium 78
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.2 Theory: finding chemical equilibrium . . . . . . . . . . . . . 79
5.3 Method: . . . . . . . . . . . . . 82
5.4 Results: Equilibrium composition . . . . . . . . . . . . . . . . 85
5.5 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . 88
6 Gas-Phase Kinetic Model 89
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.2 Background theory . . . . . . . . . . . . . . . . . . . . . . . . 90
6.3 Devising the first kinetic model . . . . . . . . . . . . . . . . . 95
6.4 Characterising the first kinetic model . . . . . . . . . . . . . . 99
6.5 Improving the kinetic model . . . . . . . . . . . . . . . . . . . 106
6.6 Simulating the gas phase . . . . . . . . . . . . . . . . . . . . . 112
6.7 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . 119
7 Population Balance Model 120
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7.2 Sweep: a particle population-balance solver . . . . . . . . . . 121
7.3 MOPS: a coupled and chemistry solver . 126
7.4 Improving the population balance codes . . . . . . . . . . . . 128
7.5 Process sub-models . . . . . . . . . . . . . . . . . . . . . . . . 137
7.6 Simulating plug-flow reactors . . . . . . . . . . . . . . . . . . 140
7.7 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . 145
8 Automatic Reaction Mechanism Generation 147
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
8.2 Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
8.3 Introducing RMG . . . . . . . . . . . . . . . . . . . . . . . . . 149
8.4 Modifications to RMG . . . . . . . . . . . . . . . . . . . . . . 151
8.5 Results 1: RMG in action . . . . . . . . . . . . . . . . . . . . . 154
vCONTENTS
8.6 Improving thermochemistry: beyond group additivity . . . 155
8.7 Estimating molecular geometries . . . . . . . . . . . . . . . . 156
8.8 Results 2: Molecular . . . . . . . . . . . . . . . . . 158
8.9 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . 159
9 Conclusions 161
9.1 Follow-up work . . . . . . . . . . . . . . . . . . . . . . . . . . 161
9.2 Final summary . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Bibliography 165
List of Citation Uses . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
Nomenclature 186
viList of Figures
2.1 White paper, containing TiO pigment. . . . . . . . . . . . . . 32
2.2 Transmission Electron Micrograph of TiO pigment parti-2
cles after milling . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Light scattering mechanisms (based on DuPont Titanium
Technologies, 2002). . . . . . . . . . . . . . . . . . . . . . . . . 6
3.1 Typical apparatus for furnace-heated flow-tube reactor . . . 11
3.2 The two lowest energy isomers of Ti O as calcu