Modelling Interactions of Polycyclic Aromatic Hydrocarbons during Soot Formation

241 Pages·2012·7.73 MB·English

by  Timothy Stephen Totton

Modelling Interactions of
Polycyclic Aromatic Hydrocarbons
during Soot Formation
Timothy Stephen Totton
Churchill College
A dissertation submitted for the
degree of Doctor of Philosophy
November 17, 2011

Modelling Interactions of Polycyclic Aromatic
Hydrocarbons during Soot Formation
TimothyStephenTotton
This thesis investigates the intermolecular interactions between polycyclic
aromatic hydrocarbon (PAH) molecules in the context of soot particle inception
andgrowthbymeansofcomputationalchemistrymodellingtechniques.
The structure of clusters of PAH molecules is investigated using a popular
empirical atomistic potential, allowing comparison to experimental high
resolution transmission electron microscopy images of nascent soot. In addition,
the mass density of PAH clusters is computed and compared to existing values
usedinsootgrowthmodels.
High accuracy ab initio calculations are performed to assess the accuracy of
standard empirical potentials, demonstrating that such potentials are incapable
of accurately modelling PAH interactions throughout configuration space. In
response, a new anisotropic potential is developed from ab initio calculations,
termedthePAHAPpotential,andshowntopredicttheinteractionenergiesoffour
smallPAHdimersmoreaccuratelythanpreviouspotentials.
The PAHAP potential is further assessed against independent ab initio data
and experimental data in the form of second virial coefficients for benzene
vapour and the exfoliation energy of graphite. The new potential is shown to
outperform comparable transferable potentials and increased accuracy can be
achievedthroughtheuseofmorecomplexelectrostaticmodels.
Finally,thePAHAPpotentialisusedasareferencetodevelopasimplerpotential
suitableforuseinstandardmoleculardynamicscodes,andtheresultingpotential
isusedtostudytheclusteringofPAHmoleculesathightemperature.Equilibrium
constants for dimerisation are computed, based on a simple statistical mechanics
model, and molecular dynamics simulations are used to study cluster formation
at a range of temperatures. The results confirm recent experimental work which
suggests pyrene (C H ) dimerisation cannot account for soot particle inception
16 10
andthatlargerPAHmolecules,suchascircumcoronene(C H ),arerequired.
54 18
Acknowledgements
I thank Doctor Alston Misquitta, Doctor Dwaipayan Chakrabarti and Professor
Markus Kraft for their supervision throughout the period of study. I also thank
DoctorMarkMillerandProfessorDavidWalesfortheirhelpfuladviceonanum-
berofmatters.
Ithank DoctorMarkusSanderfor hishelpwithrunning theComputationalMod-
ellingGroup’ssootmodelsusedinChapter4,andIthankDoctorRafałPodeszwa
andProfessorKrzysztofSzalewiczforkindlyprovidingdatausedinChapter5.
Funding has been generously provided by the EPSRC, Shell Research Ltd. and
Churchill College, Cambridge. I specifically thank Doctor Roger Cracknell of
Shellforusefuldiscussionsduringthecourseofmywork.
IthankthemembersoftheComputationalModellingGroupfortheirsupportand
friendship, and in particular Doctor Sebastian Mosbach, Doctor Raphael Shirley
andDoctorNealMorganwhohavehelpedtoanswernoendofquestions.
Finally,Ithankmyparentsfortheircontinualloveandsupport.
iv
Preface
This dissertation is my own work and contains nothing which is the outcome of
workdoneincollaboration,exceptasspecifiedinthetextandAcknowledgements.
The work was performed at the University of Cambridge between October 2008
and September 2011. Chapters 2, 4 and 5 include work previously submitted for
a Certificate of Postgraduate Study in June 2009. No part of this thesis has been
submittedforadegreetothisoranyotheruniversity.
This dissertation contains approximately 60,000 words and 58 figures and tables.
Someoftheworkinthisdissertationhasbeenpublished:
1. T. S. Totton, D. Chakrabarti, A. J. Misquitta, M. Sander, D.
J. Wales, and M. Kraft (2010). Modelling the internal structure
of nascent soot particles, Combustion and Flame, 157, 909-914.
doi:10.1016/j.combustflame.2009.11.013
2. T. S. Totton, A. J. Misquitta, and M. Kraft (2010). A first principles de-
velopment of a general anisotropic potential for polycyclic aromatic hy-
drocarbons, Journal of Chemical Theory and Computation, 6, 683-695.
doi:10.1021/ct9004883
3. T. S. Totton, A. J. Misquitta, and M. Kraft (2011). Assessing the PAHAP
potential with application to the exfoliation energy of graphite, Journal of
PhysicalChemistryA,115,13684U˝13693.doi:10.1021/jp208088s
4. T. S. Totton, A. J. Misquitta, and M. Kraft (2011). A quantitative study
of the clustering of polycyclic aromatic hydrocarbons at high temperature,
PhysicalChemistryChemicalPhysics,inpress.doi:10.1039/C2CP23008A.
The work presented in this dissertation has also contributed, to a lesser degree, to
thefollowingpublications:
5. R. Shirley, Y. Liu, T. S. Totton, R. H. West, and M. Kraft (2009).
First-Principles Thermochemistry for the Combustion of a TiCl and
4
v
AlCl Mixture, The Journal of Physical Chemistry A, 113, 13790-13796.
3
doi:10.1021/jp905244w
6. A. Raj, P. L. W. Man, T. S. Totton, M. Sander, R. Shirley, and M. Kraft
(2010). New polycyclic aromatic hydrocarbon (PAH) surface processes to
improve the model prediction of the composition of combustion-generated
PAHsandsoot,Carbon,48,319-332.doi:10.1016/j.carbon.2009.09.030
7. T.S.Totton,R.Shirley,andM.Kraft(2011).First-principlesthermochem-
istry for the combustion of TiCl in a methane flame, Proceedings of the
4
CombustionInstitute,33,493-500.doi:10.1016/j.proci.2010.05.011
8. T. S. Totton„ A. J. Misquitta, and M. Kraft (2011). A transfer-
able electrostatic model for intermolecular interactions between poly-
cyclic aromatic hydrocarbons, Chemical Physics Letters, 510, 154-160.
doi:10.1016/j.cplett.2011.05.021
9. D.Chakrabarti,T.S.Totton,M.Kraft,andD.J.Wales(2011).Asurveyof
the potential energy surface for the (benzene) cluster, Physical Chemistry
13
ChemicalPhysics,inpress.doi:10.1039/C1CP22220A
TimothyStephenTotton
November17,2011
vi
“The works of the LORD are great, sought out of all them that
havepleasuretherein.”
Psalm111.2

Contents
Listoffigures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Listoftables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Novelelementsofthethesis . . . . . . . . . . . . . . . . . . . . 3
1.3 Structureofthethesis . . . . . . . . . . . . . . . . . . . . . . . . 4
2 BackgroundonSootFormation 7
2.1 Sootfromcombustion . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.1 Polycyclicaromatichydrocarbonsassootprecursors . . . 10
2.2 Sootparticleinceptionandgrowth . . . . . . . . . . . . . . . . . 13
2.3 Experimentalstudiesofsootinceptionandgrowth . . . . . . . . . 15
2.3.1 Experimentalevidenceofaliphaticfunctionalities . . . . . 18
2.4 Numericalstudiesofsootinceptionandgrowth . . . . . . . . . . 20
2.5 Thesisscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3 TheoryandComputationalMethods 25
3.1 Quantumchemistry . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1.1 Approximatesolutions . . . . . . . . . . . . . . . . . . . 27
3.1.2 Intermolecularinteractions . . . . . . . . . . . . . . . . . 35
3.2 Modelintermolecularpotentials . . . . . . . . . . . . . . . . . . 45
3.2.1 Anoteonnomenclature . . . . . . . . . . . . . . . . . . 45
3.2.2 Popularisotropicpotentialforms . . . . . . . . . . . . . . 46
ix
CONTENTS
3.2.3 Modellingexchange-repulsion . . . . . . . . . . . . . . . 47
3.2.4 Modellingdispersion . . . . . . . . . . . . . . . . . . . . 48
3.2.5 Modellingtheelectrostaticinteraction . . . . . . . . . . . 50
3.2.6 Parameterisingmodelintermolecularpotentials . . . . . . 51
3.2.7 Obtainingpoint-chargemodels . . . . . . . . . . . . . . . 53
3.3 EnergyLandscapesandBasin-Hopping . . . . . . . . . . . . . . 55
3.4 Statisticalmechanics . . . . . . . . . . . . . . . . . . . . . . . . 56
3.4.1 Approximations . . . . . . . . . . . . . . . . . . . . . . 57
3.4.2 Thermodynamicquantitiesfromthepartitionfunction . . 61
3.5 Moleculardynamics . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.5.1 Approximations . . . . . . . . . . . . . . . . . . . . . . 63
3.5.2 Integrationscheme . . . . . . . . . . . . . . . . . . . . . 64
3.5.3 Intramolecularpotentials . . . . . . . . . . . . . . . . . . 65
3.5.4 Temperaturecoupling . . . . . . . . . . . . . . . . . . . 66
3.6 Computersoftware . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.6.1 Quantumchemistrysoftware . . . . . . . . . . . . . . . . 69
3.6.2 Molecularmodellingsoftware . . . . . . . . . . . . . . . 69
3.7 Chaptersummary . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4 SootPropertiesfromMolecularModelling:ACaseStudy 73
4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.1.1 Massdensity:aparameterinsootmodels . . . . . . . . . 75
4.2 Computationalmethod . . . . . . . . . . . . . . . . . . . . . . . 77
4.3 Molecularclusters . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.3.1 Particledensity . . . . . . . . . . . . . . . . . . . . . . . 79
4.3.2 Varyingdensityinthesootmodel . . . . . . . . . . . . . 83
4.4 Chaptersummary . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5 ANewDescriptionofIntermolecularInteractions 87
5.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
x