Formation, growth and oxidation of soot: A numerical study

Transcription

1 Formation, growth and oxidation of soot: A numerical study Abhijeet Raj Clare College A dissertation submitted for the degree of Doctor of Philosophy at the University of Cambridge January 2010

2 Preface The work presented in this dissertation was undertaken at the Department of Chemical Engineering and Biotechnology, University of Cambridge, between October 2006 and November It is the original work of the author unless specifically acknowledged in the text. Chapter 3 of this thesis includes work from the dissertation submitted by the author in June 2007 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 thesis contains approximately 42,000 words, 76 figures and 10 tables. The following articles and preprints have been published based on the work presented here: 1. A. Raj, M. Celnik, R. Shirley, M. Sander, R. Patterson, R. West and M. Kraft, A statistical approach to develop a detailed soot growth model using PAH characteristics, Combust. Flame, 156(4), , doi: /j.combustflame A. Raj, P. L. W. Man, T. S. Totton, M. Sander, R. A. Shirley and M. Kraft, New polycyclic aromatic hydrocarbon (PAH) surface processes to improve the model prediction of the composition of combustion-generated PAHs and soot, Carbon, 48, , doi: /j.carbon A. Raj, M. Sander, V. Janardhanan, and M. Kraft, A study on the coagulation of polycyclic aromatic hydrocarbon clusters to determine their collision efficiency, Combust. Flame, 157, , doi: /j.combustflame M. Sander, A. Raj, O. Inderwildi, M. Kraft, S. Kureti, and H. Bockhorn, The simultaneous reduction of nitric oxide and soot in emissions from diesel engines, Carbon, 47, , doi: /j.carbon

3 5. A. Raj, M. Sander, and M. Kraft, A mechanistic study on the simultaneous reduction of soot and nitric oxide from diesel engine exhaust, c4e Preprint Series, Tech. Report 83, Cambridge, Abhijeet Raj Friday 22 nd January, 2010 (first submitted Friday 22 nd January, 2010) Acknowledgements I would like to thank my supervisor, Prof. Markus Kraft for his guidance during the course of my PhD. I also thank Dr Robert Patterson and Dr Matthew Celnik for their constant support and advice in my first year at Cambridge. I am grateful to the Cambridge Commonwealth Trusts (CCT), Clare College and the Board of Graduate Studies for their financial support. I acknowledge the support of EPSRC under EP/C547241/1 and EP/E01724X/1. 3

4 Summary This thesis presents a new model to study the growth of polycyclic aromatic hydrocarbons (PAHs) in a combustion environment. The purpose of the development of this model is to improve the fundamental understanding of the inception and growth of soot, and to remove some of the assumptions underlying previous soot models. The model tracks the planar structure of PAH molecules, which are present in soot particles, enabling the exact distribution of reactive sites on a PAH along with the number of C and H atoms to be found. For the first time, the structural information of the PAHs is presented in terms of correlations and statistics for the reactive sites to facilitate the development of a soot growth sub-model. A detailed reaction mechanism is required to study the growth of PAHs. With the mechanism present in the literature, the model under-predicts the composition (C/H ratio) of PAHs. Therefore, new reactions are proposed to dehydrogenate the computed PAHs, and improve the model prediction. The new reactions are investigated using density functional theory and transition state theory to determine their rate constants, and are included in the reaction mechanism. Along with chemical growth in a flame, PAHs can also coagulate with each other to incept soot particles. A successful coagulation of PAHs depends strongly on the size and the mass of the colliding PAHs. A soot inception sub-model is developed in the form of a mathematical expression, which provides the probability of coagulation after the collision of PAHs. This sub-model substantiates the claim that pyrene may not be the soot incepting species as widely believed. High-temperature combustion produces NO x molecules along with soot. An after-treatment device is required to trap these pollutants. In such a device, the quantities of soot and NO x can be decreased due to their reaction, forming N 2, CO and N 2 O, and thus the filter can be regenerated if the required temperature is provided. However, the exact pathway for these reactions is unclear. Therefore, a detailed reaction mechanism is developed, which describes the interaction between PAHs (soot) and nitric oxide (NO). This mechanism is used in a PAH model to simulate their simultaneous reduction. The results are compared to the experimental observations, both qualitatively and quantitatively. Such a comparison is shown for the first time. 4

5 Contents 1 Background Soot from combustion Experimental techniques Gas-phase chemical species Soot particles and their precursors Theoretical understanding of soot formation PAH formation PAH growth Soot inception Soot growth and oxidation PAH and soot modelling PAH models Soot models Simultaneous Soot-NO x reduction Structure of the thesis Methodology Stochastic modelling Kinetic Monte Carlo algorithm Error Estimation Chemical modelling Quantum chemistry Transition state theory Steady-state analysis Model development for PAH growth Problem description The ARS-PP Model PAH Reactions Cyclodehydrogenation process PAH processes

6 3.4 KMC-ARS Model State Space Data Structure Jump Processes KMC Algorithm Site-Counting Model Experimental validation Results and Discussion Statistical Analysis Site-Counting Model Validation Conclusion New PAH Processes Problem description Reaction pathways Calculation details PAH Process PAH Process KMC-ARS Model Results and discussion Reaction rates KMC simulation Sensitivity analysis Conclusion Soot inception model Problem description KMC-ARS model Flame simulation PAH primary particle (PAH-PP) model Results and discussion PAH mass spectra Conclusion Soot oxidation by nitric oxide in after-treatment devices Problem description Calculation details Results and discussion PAH nitric oxide interaction Reaction rates KMC simulations

7 6.4 Conclusion Conclusion Conclusions of the thesis Suggestions for future work A PAH reactions 180 7

8 Chapter 1 Background This chapter provides background information about some of the products of combustion soot particles, polycyclic aromatic hydrocarbons (PAHs), and NO x molecules. No experiments were conducted for this thesis. However, experimental results from the literature were used for model validations. Therefore, a short description of the experimental techniques are provided. The models for soot particles and PAHs are introduced, and their features are highlighted. 1.1 Soot from combustion Combustion is the basis for over 90% of the technologies being used and developed to meet today s energy requirements [1]. Energy required by industries and households in the form of electricity and heat, and for transport purposes mainly comes from non-renewable fuels such as coal, oil and gas. Over the last two decades, the demand for these energy sources has increased drastically [2]. The rate at which the fuel is being consumed has raised two major concerns the depletion of non-renewable energy sources, and the increased level of pollutants in the atmosphere. The former problem will affect the generations to come, while the problem of pollution can have direct and immediate effects on the present living beings. To solve the former problem, alternative energy sources such as biofuels, nuclear power and waste matter, and renewable sources such as wind and solar energy are being considered [3, 4]. The main causes of the latter problem are the 8

9 products of the combustion such as CO, CO 2, NO x, SO x and soot (particulate matter) [5]. Since the main focus of this thesis is on soot and to some extent on NO x, the rest of this thesis will concentrate on these topics. Nitric oxide, NO, which is present in the highest concentration among all the NO x molecules emitted from combustion devices such as gas turbines and engines [5], is involved in the depleting the ozone layer [6]. It also causes photochemical smog and acid rain [7]. Soot is a carbonaceous material produced as a result of incomplete combustion in fuel-rich high-temperature environments. It is mainly added to the atmosphere from coal power plants, chemical factories and motor vehicles [8]. Upon inhalation, soot is known to cause adverse health problems. It can aggravate underlying pulmonary and cardiac problems leading to premature death or increased morbidity [9]. Soot particles less than 5 nm in diameter cannot be filtered by the respiratory tract and can enter the lungs, causing cancer and asthma [10]. Apart from the health threats, these particles are responsible for heat loss in combustion devices through radiation. They are also involved in darkening of ice on polar caps leading to their faster melting [11]. In contrast, carbon black [12] is used in industries as pigments in inks, coatings and plastics, and as reinforcement in rubber and plastic products. Soot particles provide luminosity to flames and fires, and radiate heat from these adiabatic systems to the surrounding thus providing warmth near them. Even though the presence of soot is long known, the complex formation pathway for it is still under investigation [13, 14]. Along with soot particles, polycyclic aromatic hydrocarbons (PAHs) are also produced in combustion devices. These molecules are generally very small (< 3 nm), transparent to visible light, difficult to detect and highly carcinogenic (especially the heavy ones) [15 18]. PAHs can affect eyes, skin, liver and kidney if kept in contact for a long time [19]. Therefore, it is crucial to reduce the formation or at least reduce the emission of soot and PAHs to avoid possible threats to health and environment. An important step towards the control of pollution by the government is pollution regulation [20]. For particulate matter, the restrictions have been mainly imposed on size and amount. This makes it essential to have a quantitative knowledge about the pollutants and the factors affecting their production. The concentrations of small soot particles and heavy PAHs are particularly important, as they 9

10 are thought to be more harmful than large soot particles [18, 21]. Their detection in experiments is possible, but very difficult [22, 23]. To reduce the emission of soot particles into the atmosphere, they are captured using particulate filters [24]. The design of the filters requires an estimate of the size of the particles to be captured along with their amount. In order to obtain the quantitative information about soot, conducting experiments in all the desired combustion conditions is not practical due to large uncertainties, long time and high cost involved [17, 25]. Therefore, a robust model for soot and PAHs is required to effectively predict their concentrations and size distributions, which in turn requires an insight into their formation and growth pathways [26]. Based on the experimental observations, a number of theories for the formation of soot and PAHs are proposed in the literature that can help in developing a model [27]. 1.2 Experimental techniques The combustion of fuels is an extremely fast process involving several chemical and physical reactions. In a flame, it takes place on a millisecond time-scale and micrometre length-scale. This makes the detection of hundreds of chemical species being formed and destroyed in this process extremely challenging. These chemical species can also form nanometre-sized soot particles in a fuel-rich combustion environment. However, their formation pathway is still under study. In order to develop a mechanistic understanding of the complex processes occurring in a combustion environment, experimental measurements are vital. Some of the experimental techniques used for the quantitative and the qualitative analysis of the molecules and the particles produced during combustion are discussed below Gas-phase chemical species The combustion of fuel molecules leads to the formation of various gas-phase species such as H, H 2, C 2 H 2, OH, O 2, CH 3 and aromatic compounds. These species are particularly important for the formation and growth of soot particles [28, 29]. The commonly used scientific methods to detect and measure the concentration of gas-phase species are molecular beam mass spectrometry (MBMS) 10

11 [30] and gas chromatography (GC) [31, 32]. In MBMS, a sample of gas volume containing the chemical species from a flame are withdrawn, and a molecular beam is formed using a nozzle-skimmer system. The molecules are ionised using a laser source and resolved using a time-of-fight mass spectrometer (explained later). In GC, a sample of gas volume is stored in a gas chamber. Using a syringe, a small amount of gas from the chamber is injected into a GC column, and diluted using a carrier gas. The column is fitted with a number of capillary tubes having the tube walls coated with absorbents. The interaction of the molecules with the tube walls, which depends upon their chemical and physical properties, changes their injection rates into the detector present outside the column. The species mole fractions are determined by analysing the gas samples collected by the detector at different time intervals Soot particles and their precursors Several methods are used in the literature to detect and analyse soot particles and their precursors in flames such as scanning electron microscopy (SEM) [33], atomic force microscopy (AFM) [34], transmission electron microscopy (TEM) [35], small angle X-ray scattering (SAXS) [36], small angle neutron scattering (SANS) [37], light absorbtion (extinction) experiments [38] and mass spectrometry [39]. These methods are briefly described below. The experimental techniques and observations which are relevant to this study are discussed in detail. Soot particles: morphology SEM and TEM are the popular techniques used to determine the particle structure [33, 35]. In SEM, particle surface is scanned using an electron beam. The projected beam on soot can get scattered, remove secondary electrons through inelastic scattering or cause emissions of electromagnetic radiation. These along with the electrons absorbed by the sample are monitored, and used to determine soot topology. AFM is capable of scanning the surface of soot particles deposited on an atomically flat substrate to obtain their 3D topological map with angstrom resolution in height and nanometer resolution in the plane parallel to the surface 11

12 [34]. In order to investigate the arrangement of molecules inside a soot particle (i.e. its internal structure) along with its outer structure, transmission electron microscopy (TEM) is used. In this method, soot particles present in a flame are irradiated (heated) using a laser pulse, and collected with a thermophoretic probe on a grid [35, 40]. The images of the collected particles are produced using an electron beam. There are three main TEM techniques to analyse the soot particle structure bright field transmission electron microscopy (BFTEM), dark field transmission electron microscopy (DFTEM) and high resolution transmission electron microscopy (HRTEM). The BFTEM images are formed by the direct incident or the transmitted electron beams. These images mainly reveal information about the particle opacity, size and shape such as the aggregate structure of soot. In order to obtain information about the internal structure of soot, DFTEM images are required. These images are formed by the diffracted beams from the atomic layers present in soot. As a result, they carry information about the crystallinity of soot i.e. the internal arrangement of soot precursors in soot (described later). The increase in crystallinity increases the diffraction of incident beams, which in turn increases the brightness of DFTEM images. High resolution transmission electron microscopy (HRTEM) also known as phase contrast microscopy is a combination of bright and dark field TEM. In this case, the diffracted beam is combined with the transmitted beam to reconstruct soot structure. These images show that a soot particle is composed of primary particles linked together to form an aggregate [41, 42]. The primary particles are near-spherical in shape, and are crystalline near the outer edge. This crystallinity arises due to stacking of planar polycyclic aromatic hydrocarbons (PAHs) indicating that PAHs are soot precursors. The stacked PAHs form parallel atomic layers and align themselves along the periphery of primary particles [35, 43 47]. However, their nuclei are believed to be amorphous in nature [41]. HRTEM images of partially oxidised soot particles were observed in [41], which show hollow centres, indicating the presence of amorphous and thus more reactive carbon sheets in the centre of the primaries. This amorphous nature arises from the random orientation of PAHs [41]. The crystallinity of soot due to the presence of parallel atomic layers near the periphery of primary particles is also evident from the X-ray diffraction studies [45]. The diffraction pattern from the X-ray spectroscopy experiments confirms 12

13 the presence of crystallites in soot particles. Braun et al. [48] observed soot particles from diesel engines in various conditions and concluded that the amount of crystallites (stacked graphene sheets or planar PAHs) always exceeds the amount of randomly oriented PAHs in diesel soot. A study on the morphology of soot particles from different fuels was conducted by Vander Wal and Tomasek [49]. It was concluded that the degree of crystallinity depends on the fuel being pyrolysed to produce soot. The degree of crystallinity was highest in soot from the pyrolysis of acetylene as compared to soot from benzene and ethanol. The PAHs or graphene sheets present in soot from acetylene and benzene were planar. However, the PAHs present in soot from ethanol were observed to have curvature. In [43], the spherical substructures in the centre of primary particles were designated as inner core and fine particles. Several layers of PAHs having bending structures were observed around the fine particles, indicating the involvement of non-planar PAHs having embedded 5-member rings [26] in soot nucleation. In their work as well, the outer layer of soot was observed to have graphitic crystallites, which may undergo polycyclic growth due to molecules, ions or radicals with two to four carbon atoms [43]. In brief, the above experimental findings on soot morphology suggest that the surface growth of a soot particle might be taking place through the growth of PAHs comprising it. Soot particles and precursors: characterisation and quantitative analysis One of the widely used instruments to quantify the size distribution of soot particles in the range of nm is differential mobility analyser (DMA) [17, 50 52]. In this method, the sampled soot particles are diluted and cooled to avoid any further physical or chemical processes to take place. Thereafter, the particles are charged, and separated using an electrostatic classifier based on their electrical mobility. Their size distribution is determined by counting these particles using a condensation particle counter [50]. AFM is also used to determine the size distribution of soot particles by collecting them on a mica surface [17]. To measure soot volume fraction, Eisner and Rosner [53] have developed an intrusive method called thermocouple particle densitometry (TPD). In this method, a thermocouple is inserted in a flame and the temperature histories are noted at a 13

14 particular height above the burner (HAB), which are correlated to soot volume fraction [53, 54]. The absorption and scattering measurements can evaluate the number density, mean particle sizes and volume fraction of soot particles and their precursors (PAHs and their stacks) [55]. For example, ultraviolet-visible (UV-Vis) absorption spectroscopy is used to determine the concentration of soot particles and their precursors [56]. This method requires the absorption of monochromatic light. Soot particles can be detected by a visible light, whereas soot precursors require UV rays for detection [56]. The variation in the absorption of light by the particles with the wavelength of light determines their concentration. Laser induced incandescence (LII) and laser induced fluorescence (LIF) are used for soot particles and PAHs, respectively [55]. In LII, soot particles are irradiated with a laser pulse [57]. The enhanced thermal radiation (incandescence) is measured to determine their concentration. The particle size is related to the time required for it to cool down to the surrounding temperature. The particles can also be imaged using this method to determine their structure and mean particle size. In LIF, a laser source is used to excite an electron in a PAH molecule, which gets de-excited after some time and emits light in different directions [55, 58]. The intensity of the emitted light can be used to determine its concentration. LIF is also used to measure the concentration of gas-phase species listed in section and flame temperature [59]. The simultaneous LIF LII measurements are conducted to determine the region in a flame where the inception of soot takes place by monitoring the fluorescence from PAHs and incandescence from soot particles [55]. Incident beam scattering experiments using X-ray (SAXS) or neutron beam (SANS) can also be conducted to obtain information about soot particle size distribution, mean particle diameter, number density, volume fraction, pore sizes and surface to volume ratio [36, 37, 60]. Resonance enhanced multi-photo (two-photon) ionisation (REMPI) followed by time-of-flight mass spectrometry (TOF-MS) is a popular technique to measure the composition and characteristics of PAHs and their stacks [61 63]. The majority of the experimental data taken from the literature for model validation in this work were obtained by using this technique. Figure 1.1 shows the experimental setup for the photo ionisation TOF-MS. The PAH molecules are drawn from a low-pressure (low-sooting) flame using a nozzle inside a flow reactor main- 14

15 Figure 1.1: A figure showing different parts of a reflectron time-of-flight mass spectrometer (TOFMS). This figure has been reproduced from [64]. tained at a low pressure, and are diluted using an inert gas [65]. A narrow jet of molecules collected in the flow reactor is formed by using a nozzle followed by a skimmer-like diaphragm. These molecules are then ionised using a photoionisation source such as low-intensity ArF laser pulse. At this stage, two types of ionisation can take place single photon and two-photon (REMPI). For the single PAH molecules (not present in any stack), two photons are required, one to put the electron in an excited state, and the second one to remove it [66]. For the PAHs present in a stack such as PAH dimers, a single photon is required for their ionisation [65]. Thereafter, the ions are accelerated using an electric field. After leaving the electric field, the ions enter a flight tube with some velocities, which do not vary in the tube. The velocity gained by an ion depends on its mass and charge, which in turn determines the time required for it to reach the end of the flight tube. In most cases, a reflectron is used, as shown in figure 1.1, to deflect the ions using an electric field to reduce the length of the flight tube. The ions are collected by an ion detector such as a multichannel plate detector [67]. In this detector, the ions are allowed to hit the wall of one of the channels under the influence of an electric field to generate multiple electrons. These electrons are detected by additional means such as an anode present at the other end of the channels, which measure 15

16 the total current. An electrical signal depending upon the time of flight of the ions in the flight tube is generated, which is recorded using a time to digital converter (TDC). The mass of an ion, which depends on its time of flight is calculated using TDC. In order to obtain mass spectra, the above mentioned procedure is repeated several times. The ions with the same time-of-flight are binned together, and the particle counts are plotted for different masses (or time-of-flights). Based on the mass of an ion (PAH), its composition in terms of the number of C and H atoms is determined. For the analysis of PAHs comprising a soot particle, experimental techniques such as laser microprobe mass spectroscopy (LMMS) [39] and size exclusion chromatography (SEC) [68] are used. In LMMS, soot particles are sampled from a flame using a thermophoretic probe, and collected on a TEM grid. The partially vaporised samples are ionised by a laser beam, and analysed using a time-of-flight mass spectrometer. In SEC, a soot sample is dissolved in a solvent, and the soluble PAHs are separated using a high pressure liquid chromatograph. These PAHs are analysed using mass spectroscopy or scattering techniques to determine their composition. To determine the functional groups and bonding present in soot or PAHs, fourier-transformed infrared (FTIR) [69] and surface-enhanced Raman scattering (SERS) [70] are used. In FTIR, soot samples are analysed using a fourier transform IR spectrometer. The IR spectrum reveal the information about the bonding, and the aliphatic and aromatic groups present in the sample. In SERS, the same information is obtained by observing the Raman spectrum. 1.3 Theoretical understanding of soot formation From experimental observations, some information about the chemical and physical processes taking place in a combustion environment is obtained. For example, the aggregate structure of soot indicates coagulation to be an important phenomenon, the presence of C 2 H 2 in abundance hints at its role in soot growth, and the presence of PAH stacks in soot indicates their involvement in the inception of soot. Not only experimental findings, but also some theoretical calculations on the combustion processes have helped in drawing intelligent conclusions about the 16

17 possible pathways for the chemical processes and the formation of soot particles from the gas-phase species. Some of the important findings that have contributed to our understanding on soot formation are stated below PAH formation In [71], it was proposed that the smallest 6-member aromatic hydrocarbon, benzene is formed in a flame by aliphatic molecules and radicals that are generated by the pyrolysis of fuel molecules [72]. The main contributing species are C 2, C 3 and C 4 molecules or radicals, and the pathways for the formation of benzene from them are discussed in [27, 73]. The structures of some of the chemical species referred to in this section are shown in figure 1.2. In [74], the formation of benzene Figure 1.2: Structures of the chemical species. (a) Cyclopentadienyl (CPDyl), c- C 5 H 5. (b) Cyclopentadiene (CPD), c-c 5 H 6. (c) Naphthalene, C 10 H 8. (d) Biphenyl, C 12 H 10 (a biaryl). (e) Pyrene, C 16 H 10. (f) Vinyl, C 2 H 3. (g) Propargyl, C 3 H 3. (h) Vinylacetylene, C 4 H 4. (i) Cyclohexane, C 6 H 12. A radical is represented by a dot on the structure. through various pathways was studied theoretically. It was concluded that the self-combination of propargyl radicals (C 3 H 3 ) is the major route. The formation of PAHs is not restricted by the presence of aliphatic chains. In an experimental study on the thermal decomposition of phenol [75], the resonantly stabilised cyclopentadienic compounds were found to be present in abundance, which led to the formation of PAHs. In [76], the reaction pathways for the formation of PAHs such as benzene and naphthalene from CPDyl radicals (c-c 5 H 5 ) were theoreti- 17

18 cally studied using quantum chemistry. The rates for these reactions provided in [77] were used in [74] to model the formation of PAHs in a low-sooting flame. It was found that the self-addition reaction of CPDyl radicals was fast enough to significantly contribute to the formation of PAHs with 2-3 rings [74, 78] in at least the low sooting flames. The detailed mechanisms for the formation of PAHs from CPD and CPDyl can be found in [79, 80]. Experimental studies on the flames of cyclic hydrocarbons such as cyclohexane [81], and aromatic and alkyl substituted aromatic hydrocarbons [82, 83] suggest some other pathways for PAH formation. For example, in a cyclohexane flame, benzene can be formed by the dehydrogenation of fuel molecules [81]. In aromatic flames such as a naphthalene flame, the larger PAHs can form directly through the PAH addition reactions and the cyclodehydrogenation process [82]. These studies indicate that the pathway for the formation of small PAHs in a flame depends upon the fuel structure PAH growth Once a PAH molecule forms, it can grow by: (a) the hydrogen-abstraction carbon-addition (HACA) mechanism [72, 84] involving the addition of acetylene (C 2 H 2 ) at aromatic radical sites; (b) the addition of methyl (CH 3 ), vinyl (C 2 H 3 ), propargyl (C 3 H 3 ), polyynls (C 2n H 2 ) and CPDyl radicals on PAH radicals as summarised in [85 89]; and (c) PAH addition reactions, involving addition of a PAH/PAH radical over another to form biaryls [82]. In all the suggested pathways, the reactions proceed via the abstraction of an H atom from the PAHs by an H atom present in the gas-phase. The migration of H atoms on the PAH edge shifting the radical positions plays an important role in the progress of the reactions [86]. Out of all the mechanisms listed above for PAH growth, the HACA mechanism is one of the most widely used mechanisms to study the growth of soot particles [29, 90, 91], though it may not be the only mechanism. In [74], it was concluded through a theoretical study that the use of HACA mechanism for PAH formation without any other mechanism can under-predict the concentration of PAHs in low-sooting flames. In [92], the effect of the fuel molecules on the pathway to soot was studied, which showed that irrespective of the mechanisms leading to the formation of small PAHs, all the pathways quickly relax to 18

19 the HACA mechanism due to the low concentrations of other reactants present in the gas-phase in the post-oxidation zone of a flame [86]. Therefore, the growth of large PAHs (with more than 2-3 rings) can be assumed to mainly take place through the HACA mechanism Soot inception In the last few decades, a large number of experimental and theoretical investigations [17, 64, 86, 93] have been conducted to understand the formation of soot particles from gaseous species. However, the transition from PAHs to soot still remains the least well-understood step in soot formation. There are two pathway for the inception of soot present in the literature chemical growth and physical coagulation. In [94], the growth of PAHs through polymerisation (addition of PAHs over each other) has been suggested to nucleate soot [74]. This suggestion is based on their experimental observations in a low sooting flame, which show that the amount of C atoms present in aromatics and soot remains constant after the oxidation zone. This indicates that soot particles grow only via the addition of PAHs over each other, and carbonisation (increase in C/H ratio) through dehydrogenation processes takes place in the latter stage of their growth. This pathway for soot nucleation can predict very well the soot mass, but will severely under-predict the particle diameter [86]. The presence of PAH stacks and clusters in the experimental HRTEM images of soot particles, as discussed above, suggests that a physical process, that is, the coagulation of PAHs may be responsible for soot inception. This widely accepted hypothesis has provoked a large number of theoretical studies on the stability and relative orientation of PAHs present in dimers and higher order stacks in flame environments [93, ]. In soot models, pyrene dimerisation is considered to be the soot nucleation step [101, 102]. The validity of this assumption has been tested in a number of studies [99, 103], and is still debated [104]. In one of the earlier studies on PAH coagulation [96], the equilibrium constant for this process, A + B AB was determined by assuming that all steps are reversible and that equilibrium is attained at each step. Using the calculated equilibrium constants, the concentration of PAH dimers was evaluated, and it was concluded that the 19

20 PAH dimerisation may not be responsible for soot nucleation, as the number density for newly incepted soot particles in flames were severely under-predicted. In [84], the authors argued that the assumption of equilibrium after PAH coagulation may not hold in a flame environment, and the dimerisation process may proceed irreversibly. The PAH coagulation flux needs to be computed kinetically instead of using the equilibrium assumption. In [105], the concentration profiles of PAHs present in aliphatic flames were observed experimentally. This study concluded that it is possible to predict the number density of incepted soot particles by taking into account the coagulation of PAHs. This result did not agree with the findings of Miller et al. [96] due to the very low concentration of PAHs assumed in their study to calculate the number density. To determine the contribution of PAHs and C 2 H 2 in soot nucleation and growth, another study was conducted by Mckinnon and Howard [98]. In their study, it was found that, to predict the soot volume fraction observed in a sooting benzene flame, a PAH collision efficiency of 0.1 to 0.5 was required (collision efficiency is the probability of coagulation after collision, and is a factor multiplied to the gas kinetic rate for PAH collision in a given pressure regime to obtain an estimate of the PAH coagulation rate [106]). A similar range was proposed by Miller in a kinetic study on PAH agglomeration [97]. Recently, the value of coagulation efficiency for small nanoparticles has been determined experimentally by D Alessio et al. [52]. For particles below 2 nm, this value has been proposed to be less than To model the soot nucleation and/or PAH coagulation process, different collision efficiencies have been used in the literature: 1 in [84], 0.3 in [107], and between 10 5 and 1 in [108]. In [108], a soot model was presented to take into account simultaneous formation and growth of particulates and PAH molecules using a sectional method. The authors concluded in this study that the PAH coagulation processes in their reaction mechanism did not play a vital role due to low values of coagulation efficiencies assumed for the PAHs larger than pyrene. It was shown that a significant variation in the predicted particulate volume fraction can be obtained with the change in collision efficiency, and thus, is an important factor for the theoretical study of soot nucleation. 20

21 1.3.4 Soot growth and oxidation After the inception of particles, soot mainly grows via four processes (I) chemical growth by C 2 H 2, (II) chemical growth by PAHs (through biaryl formation), (III) condensation of PAHs (coagulation of a PAH molecule with soot), and (IV) coagulation of soot particles. The first three processes increase the total soot mass, and the last one is involved in increasing soot diameter. The chain-like structure of soot as observed in TEM images arises due to process IV. From the simulation results for a sooting aliphatic flame [74], it was concluded that around 60% of the number of C atoms present in PAHs and soot comes from the addition of C 2 H 2 (process I). In [109], a benzene flame was simulated, and it was observed that out of the total mass gained by all the soot particles, around 90% came from C 2 H 2 addition (process I), and the rest from the addition of PAHs (process II). Therefore, irrespective of the fuel for a flame, C 2 H 2 always contributes significantly to the soot mass [86]. The reduction in soot mass can occur in a flame due to the oxidation reactions by O, O 2, OH and H 2 O 2. However, because of the comparatively higher concentrations of OH and O 2, only these reactants are able to effectively oxidise soot particles [110]. As a soot particle grows, its reactivity towards the reactants such as H and C 2 H 2 decreases [27, 29]. This may be happening due to the decrease in the availability of reactive sites (defined later) on soot particles because of steric hinderance [29]. However, it is difficult to determine the amount of unavailable sites on soot, as the exact reason behind it is still unclear. It is thought to occur due to the internal arrangement of PAHs in soot. The reactive sites on PAHs present in the core of a soot particle may not be readily accessible to the chemical species such as C 2 H 2 responsible for soot growth. Also, the reactive sites on PAHs may get hindered due to the presence of nearby PAHs. Another reason may be the growth of a PAH molecule comprising soot around itself thus hindering some of the reactive sites. 21

22 1.4 PAH and soot modelling Based on the theoretical understanding of the processes leading to soot and PAH formation, a number of soot and PAH growth models are present in the literature. The studies on the growth of soot and PAHs are essentially the same because the growth of soot takes place through chemical reactions on the edges of the PAHs comprising it. The soot and the PAH models have undergone major developments in the last two decades [27, 29, 102, ]. Various changes have been introduced in the model assumptions on PAH structures, and on the morphology and inception of soot particles. Some of the commonly encountered PAH and soot models present in the literature, and relevant to this thesis are discussed below PAH models In order to understand this section, the knowledge about certain characteristics of the PAHs that distinguish one PAH from the other is required. A PAH can be described by the number of C atoms, number of H atoms and the distribution of reactive sites on its edge. A reactive site is a structure present on the outer edge of PAHs formed by two consecutive surface carbon atoms (those carbon atoms having bonded H atoms). The sites are differentiated by the number of carbon atoms required for their formation. Simple PAH geometry requires that a site has exactly two edge carbon atoms, and zero to four bulk carbon atoms (those carbon atoms not having a bonded H atom). In this way four elementary sites are defined free-edge (FE), zig-zag (ZZ), armchair (AC) and bay (BY), as shown in figure 1.3. The zig-zag, armchair and bay sites can be easily differentiated from each other based on the number of bulk carbon atoms required in their formation. Additionally, a 5-member ring (R5) can occupy a zig-zag site [114], therefore these have also been included in the models. A detailed reaction mechanism containing reactions on the different types of reactive site is present in the literature to study the growth of PAHs [114], and its development is still in progress. The mechanism is being appended with the newly proposed reactions [ ]. For some of the already known reactions, the reaction rates in the mechanism are being updated [114, 118, 119]. The re- 22

23 Figure 1.3: An example PAH showing the principal surface site types. action kinetics and the energetics of the elementary reaction are mostly studied using computational quantum chemistry and transition state theory, which will be discussed later. Using the detailed reaction mechanism and a stochastic algorithm, a PAH model is simulated to track the evolving structure of a PAH as it grows in a flame-like environment. The salient features of some of the PAH models present in the literature are mentioned below. Planar kmc model In [114], a PAH growth model developed over several years [114, 120, 121] is presented to study the unidirectional growth of PAHs (growth is restricted to the horizontal sites only). In this model, a substrate PAH molecule is required over which the addition of C atoms from the gas phase molecules can take place. A kinetic Monte Carlo (kmc) algorithm, explained later, is used to simulate the growth of PAHs. For the simulation, it is assumed that the mole fractions of the chemical species such as H, H 2 and C 2 H 2, and the temperature are constant. The structure of the substrate PAH is updated after each reaction on it. In the mechanism, the short-lived intermediate chemical species are assumed to be in steady-state. This assumption makes the simulations computationally less expensive. Further details on this assumption will be provided later. The outcome of the model is very interesting as it can give an estimate of the growth rate of PAHs or soot [120]. 23

24 KMC-MD model In [122], a PAH growth model to study the unrestricted growth of PAHs in three dimensions was developed based on two important tools the kmc algorithm and molecular dynamics (MD). The kmc algorithm is used to determine the reaction that can take place on a PAH molecule based on the rates of the possible PAH reactions. After the addition/removal of atoms or molecules on/from the PAH depending upon the chosen reaction, a molecular dynamics simulation is carried out to relax the PAH structure through bond rotations so that thermal equilibrium can be attained by the PAH. Both the kmc and the MD steps are coupled and take place alternatively. As an input, the model requires the species and the temperature profiles, and the reaction rate constants. In [ ], this model was used to simulate the growth of PAHs in several premixed laminar and counter-flow diffusion flames. Many PAH characteristics such as their composition in terms of the number of C and H atoms, their aspect ratio, the density and the porosity of non-planar PAHs can be predicted by this model [124, 125] Soot models As discussed above, the formation of soot involves four steps: inception, surface growth, condensation of PAHs and coagulation of soot particles [29]. For these steps, different model assumptions have been made and changed from time to time to improve model predictions, after more information about soot has been made available or more robust numerical techniques have been introduced for solving soot models [27, 29, 113, ]. Some of the advanced soot models and their assumptions are briefly discussed here. ABF model The ABF model is a spherical particle model developed by Appel et al. [29]. This model is based on the chemical mechanism of Wang et al. [27] to determine the flame structure, which was slightly modified to improve the model predictions. The involvement of the gas-phase molecules in the formation and growth of soot particles necessitates the coupling of gas phase chemistry of the flame with the 24

25 soot particle dynamics. Being in line with the above argument, the ABF model is comprised of two submodels: one accounts for the gas phase chemistry thus providing the chemical species profiles, and the other accounts for particle inception, growth and aging thus giving an estimate of the soot particle ensemble. The inception of soot is assumed to take place through pyrene dimerisation. The chemical growth of soot takes place via the HACA mechanism, but is restricted to the armchair sites only. The model is solved using the method of moments [72]. To model particle ageing (decrease in soot reactivity with time), a correlation known as the alpha correlation has been developed in [29]. This correlation evaluates the fraction of the sites on soot which is available for surface growth depending upon the flame temperature and particle size. The parameters involved in this correlation were obtained by comparing the simulated soot volume fraction to their experimental values for six laminar premixed flames. For nascent soot, this fraction is close to one, but its value decreases with the maturity of soot particles. Two different correlations for the decrease in soot reactivity with the time spent by it in a flame are proposed in [101, 129], depending upon the age of the particle and flame temperature. A decent estimate of the concentrations of the gas-phase species are obtained with the ABF chemical mechanism [29, 130]. However, the soot observables such as soot volume fraction and mean particle diameter are under-predicted for some of the flames studied in [29, 129, 131]. Particle structure and composition models The assumption of the spherical nature of soot particles is removed in the surfacevolume model developed by Patterson et al. [132]. A stochastic algorithm is used to simulate this model [113]. The surface area and the volume of soot particles are made independent of each other. This is done by tracking the surface area and the number of carbon atoms in the particles after each physical or chemical process on them. The particle volume is calculated by assuming a constant soot density of 1.8 g/cm 3 (density of carbon black). This model has been taken forward by West and Celnik [133], and is called particle structure and composition model (PSCM). In the PSCM, detailed information about a soot particle such as number of primary particles (spherical nanostructures forming the chain-like aggregate structure of a 25

26 soot particle), the sizes of individual primaries, the surface area of the particle, and the composition in terms of the number of C and H atoms present in it [118] are tracked [133]. The model assumptions on soot inception and surface growth were same as the assumptions in the ABF model. Some other literature based surface-volume soot models are the volume-surfacehydrogen (VSH) model developed by Blanquart et al. [134, 135] and sectional aerosol dynamics model developed by Thomson et al. [136, 137]. As the name suggests, the VSH model has three independent variables volume, surface area and the number of hydrogenated carbon sites on soot surface. In this model, soot is assumed to nucleate through the coagulation of PAH dimers [134, 138]. The PAH dimers are formed from the gas-phase species ranging from naphthalene (C 10 H 8 ) to cyclopenta[cd]pyrene C 18 H 10. Similar to the ABF model, soot is assumed to grow through the HACA mechanism. Soot surface site density required to evaluate the surface growth rate of soot particles is calculated from the number of H atoms and surface area. Therefore, the alpha correlation of the ABF model is not required. This model is solved using the method of moments [134]. The VSH model predicts the soot observables such as soot volume fraction, number density, primary particle diameter and C/H ratio reasonably well as compared to the univariate models [134]. The sectional model uses sectional method to solve the model [136]. In this model, soot aggregate number density along with the number of primary particles are tracked. Each aggregate is assumed to be composed on equal sized spherical primaries. In [137], a good agreement between the simulated soot observables such as average primary particle diameter, primary particle number density, average number of primaries per aggregate, soot volume fraction and particle size distribution functions, and the experimental observations is shown. The model assumptions on soot inception and surface growth were same as the assumptions in the ABF model. Aromatic site counting primary particle (ARS-PP) model The above specified models assumed that the surface growth of soot takes place through the addition of C 2 H 2 on armchair sites only, as described by the HACA mechanism. However, it is known that other types of site can also be present 26

27 on the PAH molecules comprising soot as shown in figure 1.3, and the growth on those sites can also contribute significantly to the mass of a soot particle [114]. Therefore, a new model called the aromatic site counting primary particle (ARS- PP) model has been developed [126]. This model assumes that a PAH molecule can be fully described by the number of C atoms, H atoms and the reactive sites present on its edge. The structural information of the PAHs present in soot particles is not stored, but rather the structure is estimated by using correlations and statistics, which will be described later in Chapter 3. The growth of soot through the chemical reactions on different types of site is considered, which leads to an improved prediction of soot mass [118, 126]. This model removes the assumption of the restricted growth of soot and the correlation proposed in [29] for soot ageing. However, the inception of soot like the above specified models takes place through pyrene dimerisation. Polycyclic aromatic hydrocarbon primary particle (PAH-PP) model As mentioned in section 1.3.3, the capability of pyrene to form dimers or higher order stacks is still questioned. Therefore, in order to remove the assumption of soot inception through pyrene dimerisation, a model called the PAH-PP model is developed. In this model, the PAH molecules are allowed to grow, and after becoming sufficiently large, they are able to coagulate together to form dimers or higher order stacks [139]. The coagulation of the colliding PAHs is controlled by their collision efficiency. The PAH molecules are allowed to grow even when they are present in a stack. All the PAH stacks with two or more PAHs in them are considered as soot particles. Small PAH clusters are assumed to be spherical. The coagulation of PAH stacks gives rise to an aggregate structure of soot. This model based entirely on the coagulation of PAHs and PAH clusters, is the most advanced one with least assumptions on soot inception and growth. Further development of this model is required to take into account, the ageing of soot. The ARS-PP model and the PAH-PP model have been developed based on the work presented in Chapters 3 and 5 of this thesis. 27

28 1.5 Simultaneous Soot-NO x reduction Like soot particles, NO x molecules present in the exhaust from diesel engines and other combustion devices, are known to be hazardous to human health and environment. Continuous exposure to nitric oxide, NO, which is present in highest concentration among all the NO x molecules [5] can lead to tissue toxicity and renal diseases [140, 141]. The impact of these molecules and soot on the environment has already been discussed. Therefore, it is absolutely necessary to work towards the reduction or, if possible, complete removal of these pollutants from the engine exhaust gases. Recently, a wide variety of work, both experimental as well as theoretical, has been conducted in order to reduce the formation of soot and NO x [ ]. For NO x molecules, most of the suggested methods involve post-combustion gas treatment to trap them or convert them into N 2 and O 2 /H 2 O, and are briefly listed below. Zeolite and activated carbon [146] have been suggested for absorbing NO x molecules at low temperatures (< 500 K). At high temperatures, NO can be desorbed from zeolite, or can be converted to N 2 and CO on activated carbon with or without the use of catalysts [142]. One of the most popular techniques to reduce NO x is Selective Catalytic Reduction (SCR) [24, 147, 148]. This method requires a catalyst (for example, V 2 O 5 ) and a reducing agent (for example, urea or NH 3 ) for the conversion of NO x to N 2 and H 2 O. NH 3 reacts with OH on the surface of catalysts to form an NH 2 radical, which, on reaction with NO, forms N 2 and H 2 O. The NH 2 radical forms at high temperatures, and therefore this method has a very narrow temperature range of applicability. Furthermore, along with the high cost involved, it is very difficult to store NH 3 and occasionally, loss of it occurs to the environment. To avoid this loss, an NH 3 trap is required. Urea is easy to store, but its conversion to NH 3 is a slow process. A low-cost method, which does not require catalysts, is also suggested in the literature: Selective Non-Catalytic Reduction (SNCR) [24, 147]. In this method, NH 3 is allowed to interact with the exhaust gas as soon as the gas leaves the engine, when the temperature is very high. However, a low conversion of NO x to N 2 and H 2 O by NH 3 is obtained possibly due to low mixing [149]. Nakanishi et al. [149] have suggested the use of methylamine (CH 3 NH 2 ) as the reducing agent for SNCR. CH 3 NH 2 generates 28

29 NH 2 radicals at a very low temperature (around 300 C). However, this method becomes less efficient in the presence of particulate matter (PM). The three-way catalytic converters effectively convert CO to CO 2, hydrocarbons to CO 2 and H 2 O, and NO x to N 2 and O 2 in gasoline engines [24]. However, these converters do not perform well for NO x in the presence of O 2, especially when the concentration O 2 is > 2%. In a diesel exhaust, about 10% O 2 is present, which significantly decreases their ability to reduce NO x. Exhaust gas recirculation (EGR) in engines can reduce the formation of NO x by decreasing the combustion temperature. However, this method also has a limited usage, as it increases the formation of soot while reducing NO x [150]. The above mentioned techniques focussed on NO x reduction. For capturing the particulate matter, or soot, a diesel particulate filter (DPF) in the exhaust pipeline is used, which has an efficiency of over 99% [151]. However, such filters require periodic regeneration to avoid pressure build-up in the exhaust pipe when their pores are clogged. The most economical way to regenerate them would be to oxidise soot using NO x and O 2, as they are already present in the engine exhaust. However, the temperature of these gases are relatively low ( 300 C) as compared to the temperature inside engines. This makes the non-catalytic oxidation of soot difficult to achieve. To enhance its oxidation rate, several methods have been suggested. For example, using oxidation catalysts in the DPFs to burn unburnt fuel and hydrocarbons present in the engine exhaust, and thus raising the soot temperature, can accelerate its oxidation process [152]. Also, Pt and BaO based catalysts, which are very efficient NO carriers (through the formation of nitrates on their surface), can capture NO and release it later, when required, to oxidise soot [153]. Generally, layers of catalysts are placed on the DPFs to enhance the oxidation rate of trapped soot. The catalysts help in the soot oxidation by fixing elemental O atoms on the soot surface from O 2 present in the gas-phase (for example, Fe 2 O 3 [154]). However, it is a challenging issue to efficiently utilise the catalysts due to loose mixing of soot and catalysts [155]. To improve this mixing, catalyst precursors (for example, Ce based fuel additives) are sometimes injected in the engine, and catalysts get trapped on the soot surface [151, 156]. Several studies are present in the literature on catalytic oxidation of soot by NO x and O 2 [154, 157, 158]. However, the role of the catalyst is not very well understood. To 29

30 investigate this, experimental studies were conducted in [153, 154]. It was found that the catalysts are mainly involved in elemental O addition on soot. They are not directly involved in CO/CO 2 removal from soot, NO x addition on soot, or in the formation of N 2 /N 2 O on the soot surface. Therefore, oxidation of soot by NO x takes place non-catalytically. From the studies reported above, it is clear that NO x and O 2 are potential candidates to oxidise soot. The kinetics of soot oxidation by O 2 has been studied in detail in [ ]. However, the interaction between soot and NO x molecules leading to the formation of N 2 and N 2 O is very complex, and is not very well understood [144]. It is observed in experiments that soot NO x reactions stop after some time, but the reason is not clear. It is believed that this happens due to the formation of stable surface functional groups such as pyrrolic, pyridinic and pyridonic fragments, as there is evidence for the presence of such groups on soot [143, 163]. Several theoretical studies have been conducted in the past, but, a detailed mechanism showing the formation of such groups is not present in the literature. In order to accurately predict the burn-out of soot in DPFs, it is necessary to improve the mechanistic understanding on the interaction between NO x and soot to produce CO and N 2. For mechanism development, several experiments on soot oxidation by NO and NO 2 have been carried out to characterise the species being formed in the reaction, and the possible routes for their formation have been suggested [ ]. In [168], it is mentioned that the oxidation of soot by NO 2 is faster than NO. However, NO 2 is only involved in the addition of an O atom to the soot surface leading to the formation of NO in the gas-phase [169, 170]. Further oxidation of soot can take place by NO. Therefore the study of soot oxidation by NO is important. In order to verify the proposed mechanism, and to ensure that the intermediate species proposed in the mechanism are stable, quantum chemistry calculations, as shown in [ ], are required. In this direction, recently, an article was published on the theoretical study of the simultaneous reduction of soot and NO molecules [174]. Two reaction pathways along with the rates of the elementary reactions were presented. This study was restricted to zigzag sites on soot particles, and a need for the mechanism extension to other types of site was highlighted. Chapter 6 focusses on different reactive sites that can be present on soot, and the interaction of NO molecules with them. 30

31 1.6 Structure of the thesis The rest of the thesis is structured as follows. Chapter 2 provides the details of the numerical methods and software used for this thesis. Chapter 3 describes the development of a PAH model, which has been used throughout this thesis to study the growth and oxidation of PAHs using detailed reaction mechanisms. Chapter 4 introduces new PAH processes in the reaction mechanism. Experimental validations of the PAH model have been shown in Chapters 3 and 4. In Chapter 4, a sensitivity analysis has also been carried out to assess the effect of the uncertainties in the theoretically calculated reaction rate constants of the elementary reactions present in the PAH growth mechanism on the simulation results. Chapter 5 utilises the PAH model along with a PAH population balance solver to study the coagulation of PAHs and their clusters. Based on this study, a soot inception sub-model is developed. Chapter 6 describes the reaction pathways through which soot and NO x molecules can be simultaneously reduced in an after-treatment device. Finally, Chapter 7 contains conclusions of the work presented and suggests some ways in which the novel elements developed herein might be taken forward. 31

32 Chapter 2 Methodology A theoretical examination of the growth and oxidation of PAH molecules and soot particles demands the development of a PAH model. A numerical technique and a detailed reaction mechanism is required to solve the model. In this work, a stochastic algorithm has been used to solve the model. For the development of a reaction mechanism (or to append the mechanism with the new reactions), quantum chemistry calculations have been carried out. The model for PAH growth also involves certain assumptions to reduce the chemical mechanism. This chapter deals with the existing numerical techniques and the model assumptions that were used to generate the results presented in subsequent chapters. 2.1 Stochastic modelling This section focusses on the stochastic method used to solve the model, and estimate the numerical errors associated with the stochastic algorithm. A general form of the algorithm and mathematical expressions have been provided, which will be made problem-specific in the next chapter Kinetic Monte Carlo algorithm The kinetic Monte Carlo (kmc) algorithm is a stochastic algorithm which can be used to predict the time evolution of a system having various processes occurring in it. The main inputs are the process or event rates and a state space. A state space 32

33 is a theoretical space that represents all possible states of a system. For example, a ball moving in space can be represented by a six-dimensional state space: E = (x, y, z, v x, v y, v z ), where x, y and z are the coordinates of the object in the three-dimensional space, and v x, v y and v z are the velocity components in those dimensions. Before starting the simulation, the state space needs to be initialised with the input conditions. The steps involved in this algorithm are listed below [175]: 1. Set t Initialise the state space. 3. Calculate the rates of all the possible processes, R i, where i = 1, 2... I and I is the total number of processes. 4. Generate an exponentially distributed waiting time τ using a parameter λ = I i=1 R i (sum of all the process rates). 5. Update t t + τ 6. If t t stop, then END. 7. Choose a process based on the probability calculated using its rate, and update the state space according to the chosen event. 8. Go to step Error Estimation The random variation in the values of a variable with simulation run is an inherent property of a stochastic algorithm. To estimate the statistical fluctuation in the simulated result of a variable, L trial runs are generated. The empirical mean of the realisations of the random variable Y : [y 1 (t), y 2 (t),..., y L (t)] is calculated, and is represented by ȳ(t): ȳ(t) = 1 L L y l (t) (2.1) l=1 33

34 The empirical variance, η is then calculated using equation 2.2: η(t) = 1 L L yl 2 (t) [ȳ(t)] 2 (2.2) l=1 The half-width of the error bound about the average value is calculated using the central limit theorem (equation 2.3) with a = 3.29 for a confidence level of 99.9%. ɛ(t) = a η(t) L (2.3) The confidence interval for a variable, y(t) is then represented by: I = [ȳ(t) ɛ(t), ȳ(t) + ɛ(t)] (2.4) The standard error of the mean ȳ, S E is given by: S E (t) = η(t) L (2.5) 2.2 Chemical modelling To propose a reaction mechanism involving chemical reactions on the combustiongenerated gas-phase species, the energetics and the kinetics of the reactions are required. Experiments can be conducted to obtain them, but the rates suggested from the experiments have a very limited temperature-range of applicability, and sometimes, involve a large uncertainty [142]. A decent estimate of the reaction rates can be obtained by theoretically evaluating the energetics of a reaction through quantum chemistry calculations and then the kinetics using transition state theory. In this thesis, these two theoretical methods have been used as tools with the sole purpose of proposing new PAH reactions to extend the chemical mechanism, thereby improving the model predictions. The GAUSSIAN 03 [176] suite of programs was used to perform all the quantum chemistry calculations. Sections and provide a brief introduction to quantum chemistry, transition state theory and some terminologies to be used in the forthcoming chap- 34

35 ters Quantum chemistry Quantum chemistry calculation is generally conducted to predict the stable structure of a molecule, and evaluate certain thermochemical quantities such as potential energy, entropy and heat capacity. It involves solving the Schrödinger equation (ĤΨ = EΨ, where Ĥ is the Hamiltonian operator, Ψ is the wavefunction and the eigenvalue E is the energy). Ĥ is the sum of the kinetic energies of the electrons and the nuclei, and the interaction (potential) energies quantifying electronelectron, electron-nucleus and nucleus-nucleus interactions. A wavefunction is a function of the spatial positions of the electrons and the nuclei in a molecule, and describes its wave nature. Physically, the square of a wavefunction provides the probability density of finding an electron in a certain location. So far, the Schrödinger equation can be solved analytically for one electron systems only, and approximate solution methods have been proposed for many body problems (multiple nuclei and electrons). A major challenge in many body problems is to account for the effect of electron-electron interaction on the total energy E. Some of the common approaches to obtain an approximate solution of the Schrödinger equation are listed below. The description provided here is taken from [ ]. Ab initio methods The ab initio methods attempt to solve the Schrödinger equation with a model for the electronic wavefunctions, some fundamental constants and the atomic numbers of the constituent atoms. The most common among all such methods is the Hartree Fock (HF) method. In this method, to account for the electron-electron repulsion in an n electron system, each electron is assumed to be moving in an average electronic field or potential due to the other n 1 electrons. The distance between a nucleus and an electron is given importance, not the relative positions of the electrons. A self-consistent field (SCF) theory is used, in which the Schrödinger equation is solved iteratively. Firstly, the wavefunctions are approximated with trial orbitals, and used to calculate the spherically averaged potential. 35

36 With this potential, the Schrödinger equation is solved for all the electrons, and the wavefunctions are refined. This iteration continues until the change in the wavefunctions becomes negligible. The wavefunctions are then self-consistent. With this approximation, the HF theory ignores the relative positions of the electrons, which can significantly change the wavefunction. This is called the correlation error in the HF method. There can be two types of Hartree Fock calculations restricted and unrestricted. In a restricted calculation, the two electrons present in an orbital with α and β spins (or ±1/2) are forced to have the same spatial wavefunction. In an unrestricted calculation, all the electrons are allowed to have different spatial wavefunctions. The assumption involved in a restricted calculation generally holds for closed-shell states of atoms (electrons in pairs). For open-shell systems (with unpaired electrons), an unrestricted calculation gives more accurate energy than a restricted calculation. A disadvantage of an unrestricted open-shell calculation is that the wavefunction is no longer an eigenfunction of the total spin Ŝ 2 = 2 s(s + 1), where is the reduced Planck s constant, and s equals half the number of unpaired electrons. This may introduce some error in the computed energy, geometry and calculated spin density of the molecules [179]. This error is called spin contamination. The expectation value of the spin operator Ŝ2, S 2 gives a measure of the amount of spin contamination introduced. If there is no spin contamination, S 2 should be equal to s(s + 1). In practice, a molecular wavefunction obtained from quantum calculations is considered to be reasonable if the difference between S 2 and s(s + 1) is less than 10% [179]. In ab initio methods, a wavefunction is described by a linear combination of basis functions. The basis functions are used to describe the shape of the orbitals in an atom, and a set of such functions is called a basis set. The basis functions can be of two types: Slater-type orbitals (STOs) and Gaussian-type orbitals (GTOs). Generally, GTOs are used in the calculations as they are computationally less expensive. A sufficiently large number of basis functions is required to obtain a reliable result. Certain notations are used for basis sets, which indicates the number and type of basis functions being used to describe an orbital. For example, a double zeta (DZ) basis set means that two basis functions are used for each orbital. A split-valence basis set provides one basis set to the inner-shell atomic orbitals 36

37 and two to the valence orbitals (because they take part in the bond formation, and therefore, a larger accuracy is desired). When bonds are formed, atomic orbitals get distorted (polarised) due to the presence of other atoms. To take the polarisation effect into account, basis functions representing higher energy orbitals are also included in the basis set (for example, p orbitals for hydrogen). In this thesis, the G(d,p) basis set has been used in Chapters 4 and 6. The G denotes that Gaussian-type orbitals are used. For each inner-shell orbital, a liner combination of 6 GTOs has been used. The three numbers 311 (read as 3-1-1) suggests that for a valence orbital, three independent functions are used one with three GTOs, and the other two with single GTOs. The first + sign indicates that a set of diffuse functions has been used for heavy atoms. The diffuse functions allow for the cases where the electron density is more spread out over the molecule. The second + indicates that a set of diffuse functions has been used for light atoms (hydrogen and helium) as well. The (d,p) accounts for the polarisation effect explained before. A set of d orbitals is added to the elements present in the second and third rows of the periodic table (which includes the elements C, N and O, which are important for this work), and p orbitals are added to H atoms. This basis set is considered to be sufficiently large for the theoretical studies on organic molecules [181]. Apart from Hartree-Fock theory, some other popular ab-initio techniques are Møller Plesset (MP) many-body perturbation theory [182] and coupled cluster (CC) theory [183]. Both the theories provide alternative approaches to find the correlation energy. The coupled cluster theory is considered to be one of the most accurate theories in quantum chemistry, but is prohibitively slow for large molecules. Semi-empirical methods The ab-initio methods are computationally very expensive. In order to reduce the computation time, some semi-empirical methods have been suggested, which make many approximations (for example, on integrals) and use some adjustable empirical parameters. The parameters are obtained by fitting the computed results to the experimental data or ab-initio calculations. The electron correlation effect 37

38 is also included in the fitted parameters. Care should be taken while using this method as the results can be significantly incorrect if the molecule being computed is not similar enough to the molecules in the database used to parameterise the method. Some examples of semi-empirical methods are Modified Intermediate Neglect of Differential Overlap (MINDO) [184], Parameterised Model number 3 (PM3) [185] and Austin Model 1 (AM1) [186]. Density functional theory (DFT) Density functional theory is known to be computationally less expensive than the ab initio methods with a reasonable accuracy in the computed results. It is based on the Hohenberg-Kohn theorem, which states that the ground state wavefunction can be uniquely determined from the ground state electron density. Mathematically, the energy E is a functional (a function of another function) of the electron density ρ, which depends upon the spatial positions of the electrons r. E can be expressed as: E[ρ(r)] = T [ρ(r)] + U[ρ(r)] + V [ρ(r)] (2.6) where, T is the kinetic energy, U is the electron-electron interaction energy, and V is the potential energy due to the nuclei (nucleus-nucleus and nucleus-electron interactions). If all these energy terms are exactly known, the total energy can be minimised (δe/δρ = 0), and the ground state electron density can be obtained. However, the effects of electron-electron interaction on potential and kinetic energies are not known exactly, and therefore, some approximations are required. T is expressed as the sum of Kohn-Sham kinetic energy T S [ρ(r)] of a system with non-interacting electrons of density ρ and an unknown residual T R. T S can be obtained from the single particle Kohn-Sham orbitals φ i (r) of the i th electron in a non-interacting system. The potential energy due to electron-electron interaction is expressed as a sum of the classical electrostatic interaction energy U H (Hartree or Coulomb energy) and an unknown residual U R. The sum of these two residuals T R and U R is known as the exchange-correlation energy E XC. E XC is negative, which indicates that electron-electron interaction reduces the total energy. It mainly arises due to the tendency of the electrons with like as well as 38

39 opposite-spins to avoid each other. The total energy can now be expressed as: E[ρ(r)] = T S [ρ(r)] + U H [ρ(r)] + V [ρ(r)] + E XC [ρ(r)] (2.7) The only unknown term in equation 2.7 is E XC. An approximated expression for this functional is constructed. The most common approximated functionals are local functionals based on local-density approximation (LDA), generalised functionals based on generalised-gradient approximation (GGA) and hybrid functionals based on Hartree Fock energy, GGA and LDA. In LDA, the distribution of electrons is assumed to be homogeneous, and therefore, functional evaluated at a spatial position depends only on the electron density at that position (more precisely, in a differential volume element, the electron density is assumed to be constant). With this assumption, E XA can be evaluated numerically. The total energy can then be minimised to get ρ(r). In GGA, this assumption of homogeneity is removed by calculating E XC using electron density along with its gradients at each point. One of the popular GGA-type functional is BLYP having exchange functional of Becke [187] and correlation functional of Lee, Yang and Parr [188]. A hybrid functional is constructed by a linear combination of the Hartree-Fock exchange functional and any number of exchange and correlation density functionals. An example of a hybrid functional is B3LYP [189], which involves the correlation functional of Lee Yang and Parr (LYP) and exchange functional of Becke along with three parameters determined through a fitting procedure (like semi-empirical methods). The choice of a functional depends upon the investigated system. The B3LYP hybrid functional is one of the most successful functionals for organic molecules [179]. Kohn-Sham equations In order to implement DFT to many body problems, the Kohn-Sham approach is generally used. As shown previously, T S depends on the orbital functional (a linear combination of the basis functions, which depends upon the basis set being used), and a direct minimisation of energy cannot be done to obtain electron density. Therefore, the energy is minimised indirectly using Kohn-Sham equations. 39

40 This scheme starts with the differentiation of equation 2.7: 0 = δe δρ = δt S δρ + δu H δρ + δv δρ + δe XC δρ = δt S δρ + v H(r) + v(r) + v XC (r). (2.8) The potential terms v H, v and v XC are either known exactly (v H and v) or through approximations (v XC ). If a system with non-interacting particles is considered in which the particles move under a potential v S (r), the minimisation condition would be: 0 = δe δρ = δt S δρ + δv S δρ = δt S δρ + v S(r). (2.9) The electron density obtained by solving equation 2.9 would be ρ S, which would be same as the solution for equation 2.8 (ρ = ρ S ), if v s = v H + v + v XC. With the potential v S, the Schrödinger equation, given by equation 2.10 for a noninteracting system can be solved to obtain the Kohn-Sham orbitals φ i (same as the orbitals required to evaluate the kinetic energy). ] [ 2 2 2m + v S(r) φ i (r) = ε i φ i (r). (2.10) In this equation, m and ε i are the molecular mass and the energy in a noninteracting system, respectively. These orbitals φ i can be used to reproduce the electron density ρ(r) using equation 2.11: ρ(r) ρ S (r) = N φ i (r) 2. (2.11) i In equations , the variables are calculated in the following order (cyclic): ρ v s φ i ρ S ρ. This shows that the problem needs to be solved iteratively. Therefore, an initial guess is required for ρ(r), which is used to evaluate v S. Solving equation 2.10 provides the φ i, which can generate a revised value for ρ(r) using equation This procedure is repeated until convergence is achieved and a self-consistent solution for ρ is found, which can be used to calculate the total energy of the molecular system. Density functional theory is able to predict the molecular energy with an accuracy within about 5 kcal/mol in a reasonable computation time [116]. This theory 40

41 has been used in this work to predict the energies of the stable molecules and the transition states involved in an elementary reaction along with some other properties such as moment of inertia and vibrational frequencies required to evaluate a reaction rate, as shown in section Transition state theory Transition state theory (TST) has been used to evaluate the rate constants of the elementary reactions taking place on a PAH molecule. A brief discussion on the main features of TST [190] is provided here. According to TST, in a reaction between the two molecules, A + BC AB + C, an activated complex, called a transition state, forms after their collision. The energies of the reactants, the transition state and the products calculated with DFT can be used to make a potential energy diagram, as shown in Figure 2.1. Such diagrams give a clear indication of the exothermicity or the endothermicity of a reaction. The energy difference between the transition state and the reactants is Figure 2.1: A potential energy diagram showing the conversion of reactants to products going through a transition state. called the activation energy (E a ). According to classical mechanics, a success- 41

42 ful reaction requires crossing this activation energy barrier. However, according to quantum mechanics, there is a finite possibility of the reactants to form the products without having the energy to cross the barrier [177]. This phenomena is called quantum mechanical tunnelling. This increases the rate of a reaction calculated using classical transition state theory, especially when a reaction involves very light species such as H atoms. E a and temperature are the two main factors controlling the rate of a reaction. A reaction rate constant is calculated using the partition functions. The partition functions are quantities that determine the statistical mechanical properties of a system in thermodynamic equilibrium. The rate constants are represented in terms of the the partition functions of the reactants and the transition state, as shown in equation 2.12, k = κ (T ) k BT h Q NR i=1 Q e Ea k B T (2.12) i where, κ is the tunnelling correction factor, T is the temperature, k B is Boltzmann s constant, h is Planck s constant, Q is the total partition function of the transition state, Q i is the total partition function of the reactant i, and N R is the total number of reactants. The total partition function is evaluated as the product of the translational partition functions (per unit volume), Q t, rotational partition functions, Q r, vibrational partition functions, Q v and electronic partition functions Q e. Q e is approximated as the electronic (spin) multiplicity of the molecular structure, which is equivalent to the degeneracy of the ground state. The expressions for the other partition functions are given below: ( ) 3/2 2πmkB T Q t = (2.13) h 2 ( ) 8π 7/3 3/2 k B T Q r = (I a I b I c ) 1/2 (2.14) Q v = h 2 η j=1 e hν j/2k B T 1 e hν j/k B T. (2.15) In the above expressions, m is the molecular mass, I a, I b and I c are the moments of inertia along the principal axes, ν j is a non-negative vibrational frequency, and η 42

43 is the total number of non-negative vibrational frequencies. For a linear molecule (with I a = I c = 0), Q r = 8π 2 I b k B T/h 2. The derivations of the expressions for partition functions can be obtained from [191]. The unknown parameters such as moments of inertia, mass, electronic multiplicity and activation energy required to obtain the reaction rate constants are obtained from quantum chemistry calculations. As mentioned before, transition state theory does not consider the quantum tunnelling effect. This may lead to an under-estimation of the rate constants for the elementary reactions. To assess the role of quantum tunnelling, there are four efficient methods to evaluate the tunnelling correction factor (or, transmission constant): Wigner correction, Eckwart correction, Zero-curvature tunnelling (ZCT) correction, small curvature tunnelling (SCT) correction. The first two onedimensional methods are mainly used for the rates calculated using TST. The curvature tunnelling methods are generally used for the rates calculated using variational transition state theory (VTST). ZCT and SCT predict the correction factor very efficiently, especially at low temperatures (T < 500 K). However, at higher temperatures (T > 500 K), the correction factors determined by all the methods begin to converge to similar values [192, 193]. In this work, the Wigner method was employed to obtain the tunnelling correction factors for all the elementary reactions. This correction factor, κ(t ) is expressed as: ( ) hν 2, (2.16) κ(t ) = k B T where, ν is the imaginary frequency of the transition state. The rate constants are then calculated at various temperatures in the range of K using equation The Wigner correction factor is then multiplied to the calculated rate constants. A linear least-square fitting algorithm is used to fit the modified Arrhenius expression, as shown in equation 2.17 to the data points of the rate constants in order to obtain the rate coefficients A, n and E. T 0 is taken to be 1 K. ( ) n ( ) T E k(t ) = A exp, (2.17) RT T 0 43

44 2.2.3 Steady-state analysis In the literature, several PAH growth pathways are provided. Most of the pathways involve the abstraction of an H atom, followed by the addition of a chemical species (in case of a growth reaction), or abstraction of one or more C and H atoms. Generally, more than one intermediate species are involved in a reaction pathway. For example, in an armchair growth process, as shown in Figure 2.2, seven elementary reactions (both forward and backward) and two intermediate species are involved. While modelling the growth of PAHs, if all the elementary Figure 2.2: A reaction pathway for the growth of a ring on an armchair site a typical example of HACA growth mechanism. reactions are accommodated in the PAH growth mechanism and the structures of all the intermediate species are tracked, the simulations would become computationally very expensive and prohibitive for detailed analysis of PAH growth [120]. Therefore, in order to reduce the mechanism and obtain a single rate expression for a PAH growth process, all the short-lived intermediate species are assumed to be in steady state, and some of the frequently encountered reactions such as acetylene addition, ring formation and ring breakage reactions are assumed to be irreversible [114, 126]. This assumption was first taken by Frenklach in [120] to study PAH growth. The reason that was given in [120] is quoted here: Many steps of the assumed reaction mechanism proceed through formation of relatively unstable intermediate species, whose decomposition rates are orders of magnitude faster than the gas-surface collision rates. Inclusion of such short-lived intermediates would substantially increase the computational time, to the extent that stochastic simulations 44

45 may become impractical. As common to this situation, the small reaction time scales were removed by assuming the short-lived intermediates to be in the steady state. To validate this assumption, the knowledge of the forward as well as the backward rates for all the elementary reactions present in the PAH growth mechanism is required. This information for most of the reactions is not available in the literature, and therefore, DFT calculations are required to be performed on those reactions. DFT calculations on large PAHs require a significant amount of computational time and generally face convergence issues. Therefore, this validation was not carried out in this thesis, and is highlighted as a future work. As an example, the outcome of the above specified assumptions on the armchair growth process is shown below. The rate of the formation of species (see figure 2.2) are as follows: d[c] dt d[d] dt = k 5 [D] (2.18) = k 4 [C 2 H 2 ][B] k 5 [D] (2.19) d[b] dt = k 1 [H][A] + k 2 [OH][A] k 1 [H 2 ][B] k 2 [H 2 O][B] k 3 [H][B] k 4 [C 2 H 2 ][B] (2.20) d[a] dt = k 1 [H][A] k 2 [OH][A]+k 1 [H 2 ][B]+k 2 [H 2 O][B]+K 3 [H][B] (2.21) In the above equations, A, B, C and D are the chemical species shown in Figure 2.2. The square brackets represent the concentration of the enclosed species. The rate of formation of an armchair ring is given by R = d[d]/dt i.e. equation The steady-state assumption makes d[c]/dt = d[b]/dt = 0. With these constraints, the rearrangement of equations gives a single rate expression for the armchair growth process, as represented by equation ( ) k 1 [H] + k 2 [OH] R = k 4 [C 2 H 2 ][A] (2.22) k 1 [H 2 ] + k 2 [H 2 O] + k 3 [H] + k 4 [C 2 H 2 ] Similar rate expressions can be obtained for all the PAH processes listed in Chapters 3 and 4. 45

46 Chapter 3 Model development for PAH growth This chapter provides the details of a PAH growth model, called the kinetic Monte Carlo aromatic site (kmc-ars) model, which describes the structure and growth of planar PAH molecules. This model is used in the development of a detailed soot model which describes the evolution of an ensemble of soot particles based on their PAH structure. Since storing the structural information about all the PAHs present in a soot particle is computationally unfeasible, a simpler model called the site-counting model is developed. This model replaces the structural information of the PAH molecules by their functional groups augmented with statistical closure expressions. This closure is obtained from the kmc-ars model. Additionally the effect of steric hinderance in large PAH structures is investigated. A large part of this chapter is published in Raj et al. [111]. By the end of this chapter, the reader should be able to find answers to the following questions: If there already exists two different PAH growth models in the literature, why was a third one developed? Can such models be validated? How can the gap between the PAH models and the soot models be reduced? 3.1 Problem description The soot models such as the ABF model present in the literature are known to under-predict the soot observables [129, 131, 136]. In [129], it is shown through a sensitivity analysis that increasing the surface growth rate of soot helps in re- 46

47 ducing the difference between the predicted and the experimentally observed soot mass and diameter. Clearly, the soot growth sub-model needs to be refined, which requires detailed knowledge about the surface active sites present on the particles. Since the chemical growth of soot takes place through reactions between the comprising PAHs and the gas-phase species, the information about their reactive sites can be obtained from the study of the growth of PAHs [84]. There exists two PAH growth models in the literature (described in section 1.4) a planar kmc model to study the unidirectional growth of planar PAHs [114], and the kmc-md model to study the three dimensional growth of PAHs using a kinetic Monte Carlo (kmc) algorithm and molecular dynamics (MD) calculations [115]. The restriction on the growth direction in the planar kmc model may under-predict the PAH (or soot) growth rate. The simulation of the kmc-md model is computationally very expensive [194], and can take almost a day for a single PAH molecule. The inclusion of such detailed model into a soot model is therefore not feasible with current computing resources. The aim of this chapter is to develop a new PAH growth model, called the kinetic Monte Carlo aromatic site (kmc-ars) model, which lies somewhere in between the planar kmc model and the kmc-md model in terms of model assumptions. This model studies the two-dimensional growth of PAHs. MD calculations are not required, and therefore it is computationally very cheap. A statistical method has been presented which allows the structure of the resultant PAHs to be described by simple, rapidly computed, expressions. This makes it possible to incorporate this advanced model into a soot model to account for surface growth of soot particles for the first time through an approximate model called the site-counting model [195]. 3.2 The ARS-PP Model In [195] a detailed soot particle population balance model was developed (see section for details), in which soot particles were described by their reactive sites. In this model, it is assumed that a PAH molecule can be fully described by three major characteristics: the number of carbon (C) atoms, number of hydrogen (H) atoms, and the number of reactive sites. In Chapter 1, five elementary sites 47

48 were defined (Figure 1.3): free-edges, zig-zags, armchairs, bays and 5-member rings. PAH geometry also requires that, for a closed loop, each site must have two neighbouring sites. This is an important consideration as, in general, surface processes at one site will affect at least two other sites. In this chapter, a number of site terminologies are used, which are defined here: Elementary sites: The sites in Figure 1.3 are called elementary sites. Combined sites: These sites are formed by more than one consecutive elementary site. Parent site: The site on which a chosen reaction takes place. This site gets replaced in the reaction. Neighbour sites: In a reaction on a parent site, the two sites present on the either side of the parent site are called neighbour sites. After a reaction, neighbour sites change their types in a defined way PAH Reactions In the literature, a large number of reactions by which a PAH molecule can grow are available [114, 123, ]. Celnik et al. [195] have collected an extensive set of PAH reactions along with their rate constants at a pressure of kpa, which are required to develop the PAH growth mechanism. The present work involves PAH growth simulations at two different pressures: 2.67 kpa and kpa. For the simulation at kpa, the set of reactions provided in [195] was used. A literature survey was undertaken to obtain the rate constants for the PAH reactions at a pressure of 2.67 kpa, and a list of elementary reactions along with their Arrhenius rate constants and references are provided in Table 3.1. More than one set of rate constants for some of the reactions at the same pressure were available in the literature, which varied significantly from one another, and are listed in the same table. For reactions 7, 9 and 10, rate constants were available for aromatic species with different number of rings, like benzene, naphthalene, phenanthrene 48

49 and pyrene. For such reactions, the rate constants evaluated for aromatic species with highest number of rings were used in this work. In Table 3.1, different symbols have been used to represent the sites present on the edge of a PAH molecule, and are explained below: C s A radical site C s R5 5-member ring C s,fe R6 6-member ring occupying a FE site C s,fe R5 R5 next to FE C s,zz R5 R5 next to ZZ C s,ac R5 R5 next to AC C s,ac R6 6-member ring next to AC C s,i PAH with i number of rings C s (er5) Embedded R5 ring on PAH edge It can be noticed that a number of reactions involve adjacent elementary sites (combined sites). Table 3.1: PAH Surface Reactions. The rate constants are of the form: AT n exp( E/RT), and at a pressure of 2.67 kpa. No. Reaction A a n E a Ref. Hydrogen abstraction from, and addition to free-edges, zig-zags and armchairs 1 C s H + H C s + H [109, 200, 201] -24a C s + H 2 C s + H [202] -24b C s + H 2 C s + H [120] -24c C s + H 2 C s + H [203] 2a C s + H C s [112] 2b C s + H C s [109, 200, 204] 3 C s H + OH C s + H 2 O [112] -3 C s + H 2 O C s H + OH [112] Hydrogen abstraction from, and addition to, 5-member rings 4 C s R5 + H C s R5 + H [109, 200, 205] -25a C s R5 + H 2 C s R5 + H [206, 207] -25b C s R5 + H 2 C s R5 + H [207, 208] -25c C s R5 + H 2 C s R5 + H [205] 5 C s R5 + H C s R LP limit [199] b HP limit [199] b 6 C s R5 + H C s R5H [109, 200, 206] c -22 C s R5H C s R5 + H [112] d Free-edge ring growth 7a C s + C 2 H 2 C s C 2 H [28] 49

50 No. Reaction A n E a Ref. 7b C s + C 2 H 2 C s C 2 H [28] 8a C s C 2 H 2 C s C 2 H + H [109, 200] 8b C s C 2 H 2 C s C 2 H + H [28] 9a C s + C 2 H 2 C s C 2 H + H [28] 9b C s + C 2 H 2 C s C 2 H + H [28] 9c C s + C 2 H 2 C s C 2 H + H [28] 9d C s + C 2 H 2 C s C 2 H + H [28] 10a C s C 2 H + C 2 H 2 C s (C 2 H)C 2 H [28] 10b C s C 2 H + C 2 H 2 C s (C 2 H)C 2 H [28] 11a C s (C 2 H)C 2 H 2 C s R [195] 11b C s (C 2 H)C 2 H 2 C s R [112] e Free-edge ring desorption 12 C s,fe R6 C s (C 2 H)C 2 H [209], 1500 K. f [209], 2000 K [209], 2500 K. 13 C s,fe (C 2 H)C 2 H 2 C s C 2 H + C 2 H [28] g 14 C s C 2 H + H C s C 2 H same as reaction 2 [209] 15 C s C 2 H + H C s C 2 H [28] 16 C s C 2 H 2 C s + C 2 H [28] g 5-member ring addition to zig-zags 17 C s + C 2 H 2 C s R5 + H [112] 5-member ring desorption 18 C s R5 C s C 2 H [121] Armchair ring growth 19 C s + C 2 H 2 C s C 2 H 2 One step armchair ring growth (ABF model) [28] 20a C s + C 2 H 2 C s R6 + H [109, 200] 20b C s + C 2 H 2 C s R6 + H [210, 211] 20c C s + C 2 H 2 C s R6 + H [28] 5-member ring migration 21 C s,zz R5H C s R5 + H [114], 1500 K. 5- to 6-member ring conversion at free-edges ([114]) 22 C s,fe (R5H ) + C 2 H 2 C s (R5H )C 2 H [114], 2000 K [114], 2300 K. same as reaction 23 [114, 120] 23 C s,fe (R5H ) + C 2 H 2 C s (R5H )C 2 H + H same as reaction 16 [114, 120] 24 C s,fe (R5H )C 2 H C s R6 same as reaction 11 [114] 50

51 No. Reaction A n E a Ref. 6- to 5-member ring conversion at armchairs 25 C s,ac R6 C s R5 + C 2 H 2 same as reaction 12 [114] 5- to 6-member ring conversion at armchairs 26 C s,ac R5H C s R6 + H [114], 1500 K [114], 2000 K [114], 2300 K. Free-edge oxidation 27a C s R6 + O 2 C s C 2 H + HCO + CO [29] 27b C s R6 + O 2 C s C 2 H + HCO + CO [27] 27c C s R6 + O 2 C s C 2 H + HCO + CO [212] 28 C s R6 + OH C s C 2 H + CH 2 CO [27] 29 C s C 2 H + O C s + HCCO [27] Armchair oxidation 30a C s,fe + O 2 C s + 2CO [29] 30b C s,fe + O 2 C s + 2CO [27] 30c C s,fe + O 2 C s + 2CO [212] 31 C s,fe + OH C s + CHO + CH [27] Benzene addition 32a C s + C 6 H 6 C s C 6 H 5 + H [109, 200] 32b C s + C 6 H 6 C s C 6 H 5 + H [197], 300 K [197], 500 K [197], 700 K [197], 1000 K [197], 1500 K [197], 2000 K [197], 2500 K. 5-member bay closure ([196]) 33 C s, i C s, i+1 + H [196] 6-member bay closure ([213]) 34 C s, i + H C s, i + H HCTH407 h -34 C s, i + H 2 C s, i + H HCTH407 h 35 C s, i C s, i+1 H HCTH407 h 36 C s, i+1 H C s, i+1 + H HCTH407 h 37 C s, i C s, i+1 + H HCTH407 h Embedded 5-member ring migration to zig-zags ([196]) 38 C s (er5) C s (R5) [196] 39 C s (R5) + H C s (R5) [196] 51

52 No. Reaction A n E a Ref. a The units are kcal, mol, cm and sec. b Analogous to C 2 H 3 + H C 2 H 4 [114]. The rate constant for this reaction was calculated using the high-pressure and the low-pressure limit rate constants, and was expressed in Troe falloff form [198] as suggested in [199]. The parameters required to express the rate constant in Troe form were obtained from [199]. c Analogous to C 2 H 4 + H C 2 H 5. [114] d Analogous to C 2 H 5 C 2 H 4 + H. [114] e Analogous to n-c 6 H 5 A1. f Assumed to be same as decyclisation of a phenyl radical. g Calculated using equilibrium constant. h Level of theory used for DFT calculations in the present work. 3.3 Cyclodehydrogenation process New rates for the reactions involved in the cyclodehydrogenation process leading to the formation of a 6-member ring on PAHs (6-member bay closure) have been evaluated using density functional theory (DFT) with the HCTH/407 functional [214] by Raphael A. Shirley. For this purpose, a theoretical study on the conversion of Benzo[ghi]perylene to Dibenzo[c,g]phenanthrene was conducted. A free-radical mechanism (Table 3.2, process S15) has been taken from the literature [213] for the cyclodehydrogenation process. In order to verify the performance of the HCTH/407 functional, two tests were performed. Firstly, the experimentally observed C-H bond dissociation energies (BDEs) of 113.9, and kcal/mol [215] were calculated with the HCTH/407 functional as kcal/mol at T = 0 K. The more accurate (and substantially slower) MP2/6-31G(d,p) level of theory predicts a BDE of kcal/mol for instance [215]. The second validation involves comparing the energy required to dehydrogenate benzene by removing its two ortho substituents to form 1,2-Dihydrobenzene with spin multiplicity, singlet (C 6 H 6 C 6 H 4 + H 2 ). The high-cost high-accuracy methods of MP2/6-311G(d,p), QCISD/6-311G(d,p), CCSD(T)/6-311G(d,p) and BLYP/6-311G(d,p) predict the energy required as 86.1, 91.2, 86.8 and 82.8 kcal/mol, respectively [216], whereas our calculations with 52

53 Figure 3.1: A potential energy diagram showing energies of the chemical species (CS) and transition states (TS) for the cyclodehydrogenation of Benzo[ghi]perylene to Dibenzo[c,g]phenanthrene. Solid line represents the route proposed in [213]. Dashed line represents a route suggested in this work. HCTH/407 predict a value of 90.8 kcal/mol. A recent experimental report gives the required energy as 86.6 ± 3.0 kcal/mol at T = 298 K [196]. The level of prediction of experimental observations by the HCTH/407 functional provides adequate ground for its use for similar theoretical calculations on PAHs present in our molecular system. Figure 3.1 shows the relative energies of all the chemical species and transition states involved in the mechanism at 0 K. The dashed lines in Figure 3.1 show a new possible reaction path. The calculated rate constants for the reactions involved in the mechanism are listed in Table 3.1 (reactions 34 37) PAH processes Table 3.2 shows a list of PAH processes involving 5-member and 6-member ring addition and removal, and oxidation of reactive sites. This list is based on the 53

54 Route I [217] Route II [114] Figure 3.2: Different routes for free-edge growth. reactions provided in [195] amended with the reaction for bay closure studied in this work and some other reactions from the literature [114, 196, 197, 217]. The reaction mechanisms are provided in Table 3.2. For each process listed in this table, the intermediate species are assumed to be in steady-state. The PAH processes are represented as jump processes (see Table 3.2). The rate expressions for the jump processes obtained after the steady-state analysis are presented in the same table. In the rate expressions, the term [C S ] represents the concentration of parent site S. Appel et al. [29] argued that the hydrogen atom on armchair and bay radical sites can easily jump from one side to another [218]. This process will double the rate of PAH growth processes involving these sites, like armchair growth reaction and bay closure reactions. In the light of above argument, PAH growth simulations were carried out by doubling the rates of armchair growth and bay closure reactions. In the literature, two different routes for the free-edge growth reaction are available, as shown in Figure 3.2: Route I involves an intermediate species with a free-radical after the addition of C 2 H 2 in step 2 as suggested in [120]; Route II involves direct addition of C 2 H 2 with the removal of an H atom. It is for the first time that both the routes are included in a PAH growth mechanism. There can be two different ways to include the two routes in the PAH growth mechanism: (a) Considering free-edge growth via the two routes as two different growth processes. In this case, the two resulting jump processes will be identical, but will have different rates. (b) Combining the two routes to form a single reaction mechanism (as shown in Table 3.2 for process S1). In this work, the second method 54

55 was used to incorporate the two routes in the PAH growth processes as they were very similar to each other. Table 3.2: Monte-Carlo Jump Processes Process [Ref.] Parent site S1 Free-edge ring growth [120, 217] Free-edge Jump Process: Rate: ( (k 7b + k 9b ) k 1[H]+k 3[OH] k 1b [H 2]+k 2a[H]+k 3[H 2O]+(k 7b +k 9b )[C 2H 2] ) [C 2 H 2 ][C fe ] S2 Armchair ring growth [29, 195] Armchair Jump Process: Rate: k 20a ( k 1[H]+k 3[OH] k 1b [H 2]+k 2a[H]+k 3[H 2O]+k 20a[C 2H 2] ) [C 2 H 2 ][C ac ] S3 Free-edge ring desorption [120, 195] 6-member ring Jump Process: Rate: k 12 ( ) k 1[H]+k 3[OH] k 1b [H 2]+k 2a[H]+k 3[H 2O]+k 12 [C fe R6] 55

56 Process [Ref.] Parent site S4 6- to 5-member ring 6-member ring next to armchair conversion at armchair [114, 195] Jump Process: Rate: k 25 ( ) k 1[H]+k 3[OH] k 1b [H 2]+k 2a[H]+k 3[H 2O]+k 25 [C ac C fe R6] S5 5-member ring addition [121, 195] Zig-zag Jump Process: Rate: k 17 ( k 1[H]+k 3[OH] k 1b [H 2]+k 2a[H]+k 3[H 2O]+k 17[C 2H 2] ) [C 2 H 2 ][C zz ] S6 5-member ring desorption [121, 195] 5-member ring Jump Process: Rate: k 18 ( ) k 4[H] k 4c[H 2]+k 5[H]+k 18 [C zz R5] S7 5- to 6-member ring 5-member ring next to free-edge conversion at free edge [114] Jump Process: Rate: ( ) (k 7b + k 9b ) k6[h] k 6+f f[c 2 H 2 ][C fe R5], 56

57 Process [Ref.] ( where f = k 1[H]+k 3[OH] k 1b [H 2]+k 2a[H]+k 3[H 2O]+(k 7b +k 9b )[C 2H 2] Parent site ) S8 5- to 6-member ring 5-member ring next to armchair conversion at armchair [114, 195] Jump Process: Rate: k 26 ( ) k6[h] k 6+k 26 [C ac R5] S9 Free-edge oxidation by O 2 [27, 195] 6-member ring Jump Process: Rate: k 27c ( k 1[H]+k 3[OH] k 1b [H 2]+k 2a[H]+k 3[H 2O]+k 27c[O 2] ) [O 2 ][C fe R6] S10 Free-edge oxidation by OH [27, 195] 6-member ring Jump Process: Rate: k 28 [OH][C fe R6] S11 Armchair oxidation by O 2 [27, 195] Free-edge Jump Process: Rate: k 30c ( k 1[H]+k 3[OH] k 1b [H 2]+k 2a[H]+k 3[H 2O]+k 30c[O 2] ) [O 2 ][C fe ] 57

58 Process [Ref.] Parent site S12 Armchair oxidation by OH [27, 195] Free-edge Jump Process: Rate: k 31 [OH][C fe ] S13 Benzene addition [197] All site types Jump Process: Rate: k 32a ( k 1[H]+k 3[OH] k 1b [H 2]+k 2a[H]+k 3[H 2O]+k 32a[C 6H 6] ) [C 6 H 6 ][C s ] S14 5-member ring migration [114] 5-member ring next to zig-zag Jump Process: Rate: k 21 ( ) k6[h] k 6+k 21 [C zz R5] S15 6-member bay closure [85] 6-member bay Jump Process: Rate: k 36 ( ) k 34[H]+k 3[OH] k 34[H 2]+k 2a[H]+k 3[H 2O]+k 36 [C bay ] 58

59 Process [Ref.] Parent site S16 5-member bay closure [196] 5-member bay Jump Process: Rate: k 33 ( ) k 1[H]+k 3[OH] k 1b [H 2]+k 2a[H]+k 3[H 2O]+k 33 [C bay ] S17 Embedded 5-member ring Embedded 5-member ring next migration to zig-zags [196] to two adjacent free-edges Jump Process: Rate: k 38 ( ) k 1[H]+k 3[OH] k 1b [H 2]+k 2a[H]+k 3[H 2O]+k 34 [C fe,fe er5] 3.4 KMC-ARS Model A kmc algorithm has been developed to simulate the growth of single PAH molecules. KMC allows the structure of the growing PAH molecule to be tracked explicitly, hence no assumptions are required about the shape of the structure. The model is formulated mathematically in terms of the state-space and the jump processes (and their rates). In order to create an efficient numerical algorithm a higher level data structure is also defined, on which the jump processes are more easily described State Space Tracking the structure of a PAH requires knowledge about the position of the C atoms and the bonds between them. As a PAH has a similar structure to graphite, 59

60 it is clear that the bulk C atoms must bond with three others (not differentiating between single and double bonds), while surface C atoms form chemical bonds with two other C atoms and possibly a H atom. In other words, sp 2 hybridisation for all the C atoms is assumed. Thus, the simplest state space required to track the structure of a PAH molecule includes the following information: the positions of the C atoms, and the information about the bonds associated with the C atoms. The latter information is stored in terms of the positions of the other C atoms to which a C atom is bonded. For 2D representation of PAHs with planar or nearplanar geometry [219], the state space E can be represented as: E = (i, j, i 1, j 1, i 2, j 2, i 3, j 3 ) Z 8 (3.1) where (i, j) are the coordinates of a C atom, and (i n, j n ) n=1, 2, 3 are the coordinates of the surrounding C atoms bonded to the C atom at (i, j). For a surface C atom, (i 3, j 3 ) is not defined, and is set to a predefined value, thus providing a method to differentiate a surface C atom from a bulk C atom. This state space includes all the possible states/structures adoptable by a PAH molecule. It would also be possible to generalise this state space further to 3D, by including additional coordinates and defining them in the set of real numbers. While this state space is sufficient to fully define a PAH structure, definition of the Monte-Carlo jump processes on it is very difficult. Therefore, in order to simplify the problem, a higher order data structure is defined using the above state space, and the jumps are defined using this data structure, which are described in the next section Data Structure In this study, to track the PAH structure, a 2D grid is generated and the starting PAH molecule is placed on it such that each C atom is assigned a grid point. Figure 3.3 shows an example grid with a pyrene molecule. This 2D grid does not store the actual C-C bond lengths, however, this is acceptable as the bonds are implicitly represented in the rate expressions by the surface sites. Therefore, if the PAH molecule represented on a 2D grid is not present in any stack, it may 60

61 Figure 3.3: An example grid showing a pyrene molecule. develop a non-planar geometry. Two vectors are defined using the above state space to describe this problem: a carbon atom vector c, and a site vector s. The vector c stores the following information: the two site types of which the C atom is a part, S 1 and S 2, the site indices (each site of a particular type is differentiated from others based on its index), S in1 and S in2, the carbon atom type (bulk or surface), C type, and its spatial coordinates, i and j. Thus, c can be represented as: c = (S 1, S 2, S in1, S in2, C type, i, j) Z 7 A site vector s was employed to store the following information: site type, S type, site index (explained above), S in, and the coordinates of the two surface C atoms, (i 1, j 1 ) and (i 2, j 2 ). Therefore, s can be represented as: s = (S type, S in, i 1, j 1, i 2, j 2 ) Z 6 The PAH structure is then fully described by the data structure e: e = (c, s) (3.2) Jump Processes The jump processes listed in Table 3.2 are defined on sites of a particular type (parent sites). The information stored in vector s is used to define the rate (R i ) of 61

62 jump process i using the equation: R i = k i f i C N site (e) (3.3) where k i is the Arrhenius rate constant of the form AT n e E/RT (listed in Table 3.1), f i is the fraction of radical sites of the parent type, found using the steady-state assumption, C is the concentration of the gas-phase species involved in the reaction and N site (e) is the number of parent sites on the structure, and is obtained from the data structure e. The expressions for the rate constants of intermediate reactions and the fraction of radical sites of the parent type can be obtained from Tables 3.1 and 3.2. On simulation of a jump the vectors c and s must be updated to reflect the changes to the PAH structure. Processes may add or remove C atoms, which must be reflected in the c vector, and the parent site will usually be destroyed. Additionally, the neighbour sites must also be updated in the s vector KMC Algorithm The kmc algorithm used to track the growing structure is described below. This algorithm updates the PAH structure by removing the used sites and carbon atoms and adding the newly formed ones after each reaction. 1. Set t Initialise 2D starting structure by providing all the required information (Figure 3.3): e e 0, where e 0 E. 3. Calculate the jump rates: R i = k i f i C N site, i = 1, 2... I where I is the number of processes in Table Generate an exponentially distributed waiting time τ = ln U r /λ, where λ = I i=1 R i and U r is a uniform random number between 0 and Update t t + τ 62

63 6. If t t stop, then END. 7. Choose the c th reaction, if c 1 i=1 R i < U rλ c i=1 R i, where U r is a uniform random number between 0 and Uniformly select a site of correct type (Table 3.2) and determine the positions of the two surface C atoms. 9. If ring addition reaction, determine the positions of the C atoms to be added and go to step If ring desorption reaction, go to step If the site is hindered by surrounding C atoms then go to step Update e E according to reaction (Table 3.2). 13. Update neighbour sites: (a) 6-member ring: For an addition reaction, change the neighbour site type by moving it ahead in the one of the following lists (depending on whether 0 or 1 five-member ring is involved): {F E ZZ AC BY } or {R5F E R5ZZ R5AC R5BY }. For a desorption reaction, move back in one of the above lists. (b) 5-member ring: For addition reaction, change the neighbour site type 14. Go to step 3. in the following way: For site S {F E, ZZ, AC, BY }, S R5S and R5S R5SR5. For desorption reaction, R5S S, and R5SR5 R5S. 3.5 Site-Counting Model The site-counting model presented by Celnik et al. [195] determines the soot particle composition and PAH sites information, assuming soot surface to be formed by stacking together of planar PAHs. It preserves the information about reactive 63

64 sites, but neglects the spatial structure of PAHs to make this model computationally very cheap. This model abridges the gap between the PAH growth models and the simple soot particle models [129, 130, 132]. The motivation of this model was to produce as much information about the PAH structure of soot as possible, while keeping the computational expense low enough to simulate particle populations, rather than just single particles [195]. The state space required for this model is nine dimensional, and is given by [195] E = (C, H, N F E, N ZZ, N AC, N BY, N R5, S a, N P AH ) where N x is the number of site type x, C and H are the number of carbon and hydrogen atoms respectively, S a is the surface area of the particle and N P AH is the number of PAHs which make up the particle. It is worth mentioning that the size of the PAHs in a soot particle can be different from each other. Based on this state space, particle processes like, inception, jump processes representing surface growth, and coagulation, on each particle of type x E can be defined by ordinary differential equations (ODEs) of the following form: dx dt = F (x, N AC R6, N R5F E, N R5AC, N R5ZZ, N R6, P S,m ) (3.4) where N y is the number of combined-site type y in the particle (see Figure 3.10 for combined sites on an example PAH), P S,m is the probability of a site type S {ED, ZZ, AC, BY } to act as a neighbour site in a process with index m {1,..., number of processes in Table 3.2}. The terms N y and P S,m in the function F are required to completely close the ODEs. It is clear that these terms require structural information about PAHs, and cannot be exactly determined if the PAH structure is not tracked. Therefore, a statistical method is developed using the kmc-ars model for the equation closure, in which N y and P S,m are expressed as functions of x, and are briefly explained below: N y : The combined sites (N y ) are involved in a number of reaction steps (S3, S4, S7 S10, S14 and S17) in Table 3.2. In the site-counting model, since the relative positions of the sites are not tracked, the counts of combined sites, required to calculate the reaction rates, cannot be determined. Therefore, the site-counting 64

65 Figure 3.4: An example of jump process S2. The site counts for both the molecules are provided. The affected sites are shown in bold face. model needs an approximation to the structure to be calculated. This structural information is obtained using the kmc-ars model to find correlations for the combined sites (N y ) in terms of elementary sites involved in their formation. A method to obtain the correlations for the major combined sites is detailed in section P S,m : As mentioned before, a reaction on a parent site affects more than one site at a time. Figure 3.4 shows how an armchair growth reaction on phenanthrene to form pyrene affects two free-edges (neighbour sites) along with an armchair site (parent site). In this example, the types of the neighbour sites were changed from free-edges to zig-zags. Thus, unless the structure of PAHs is tracked, it is not possible to exactly know the neighbour sites to be updated after a reaction. The kmc-ars model provides the information about the neighbour sites in different reactions in terms of weights to the counts of elementary sites. These weights are used to calculate P S,m. A detailed explanation of the method used to obtain the site-weights and neighbour probabilities is provided in section A major advantage of site-counting model is that it is computationally very fast compared to the kmc-ars model. A real-time kmc simulation for a PAH molecule takes about 1.5 seconds of computation time with the site-counting model and about 30 minutes with the kmc-ars model in the same gas-phase environment. 3.6 Experimental validation In this work, PAH growth simulations were carried out in several laminar premixed flames of C 2 H 2, C 2 H 4 and C 6 H 6 to develop correlations revealing struc- 65

66 Table 3.3: Flame initial conditions Flame Pressure Composition (mole %) Cold gas velocity [C] Fuel (kpa) Fuel O [O] 2 Ar (cm/sec) Ref C 2 H [59] C 6 H [66] C 2 H [220] C 2 H [220] C 2 H [220] C 2 H [220] C 2 H see text C 2 H [50] C 2 H [50] C 2 H [50] C 2 H [50] tural information of PAHs in different flame environments. Their variation with flame properties like type of fuel, cold gas velocity, C/O ratio and pressure was also studied. The operating conditions for these flames are provided in Table 3.3. In the literature, no experimental study on a C 2 H 4 O 2 flame without any diluent at a pressure of 2.67 kpa was available. Therefore, a hypothetical C 2 H 4 O 2 flame (flame 7) was created for simulation, which uses the operating conditions of flame 4. All the flames were simulated using the ABF chemical mechanism [29] along with CHEMKIN package [221] and PREMIX [222] to obtain the chemical species profiles. PREMIX is a computer program to calculate the temperature and species profiles in a laminar premixed flame, which has been modified to account for the consumption of gaseous species due to their reactions with soot particles (see [72, 223] for details). The rate constants for the oxidation of PAHs by O 2 in the ABF chemical mechanism were updated with the new rates evaluated in Ref. [118]. Figure 3.5 shows the computed profiles of major chemical species for the flames 1, 2 and 4. In the literature, experimentally observed species profiles were available for flame 1 only and its comparison with the computed profiles is shown in Figure 3.5(a). The growth of PAH molecules in all the flame environments was studied using the computed species profiles. 66

67 (a) C 2 H 4 flame. Filled markers: computed species profiles. Hollow markers: experimentally observed profiles. (b) C 6 H 6 flame (simulated profiles only). (c) C 2 H 2 flame (simulated profiles only). Figure 3.5: Major chemical species profiles for the flames 1, 2 and 4, respectively (Table 3.3). 67

68 PAHs present in a low pressure C 6 H 6 flame (flame 2) and C 2 H 2 flames (flames 3 6) have been observed experimentally in [66, 220] using Resonance Enhanced Multi-Photon Ionisation (REMPI) and time of flight mass spectrometry (TOF- MS). The observed ensemble of PAHs at a particular HAB is represented on a C-H diagram, where each data point denotes a PAH with a fixed number of C and H atoms. In this work, the kmc-ars model was validated by comparing the PAH ensembles obtained computationally with the experimentally observed ensembles represented on C-H diagrams for the two flames. For the simulations using the kmc-ars model, a seed molecule (or starting structure) is required. To study its effect on simulation results, computed C-H diagrams for flame 2 were obtained with two different seed molecules: pyrene and benzene (not shown here). No significant variation in the C-H diagrams with the seed molecule was obtained. In this work, pyrene was chosen as the seed molecule, as it is considered to be important for soot nucleation [29]. Figure 3.6 shows C-H diagrams for flame 2 at three different HABs. The dotted lines in the figures represent the positions of peri-condensed PAHs (such as benzene, pyrene, coronene and circumcoronene) on C-H diagrams [66]. Peri-condensed PAHs approximately follow the following relationship: N H = (6N C ) 0.5, where N H and N C are the numbers of C and H atoms in the PAH [123]. The line for peri-condensed PAHs has been provided as a guideline to observe the development of PAH ensembles with HAB. The data points above this line represent H rich PAHs and below H poor PAHs with respect to the most peri-condensed six-member ring structures [66]. The C-H diagrams show that the observed PAH ensembles at the three HABs were very well predicted by the kmc-ars model. In this flame environment, benzene addition on PAHs was found to dominate over other reactions for the lower HABs (less than 7 mm), and the reactions involving acetylene dominated at higher HABs. This result is in agreement with the prediction of [123]. Figure 3.7 shows a C-H diagram for flame 4 containing the simulated along with the experimentally observed ensemble of PAHs with upto 70 carbon atoms. It is evident from the C-H diagrams of the two flames that the concentration of data points near the pericondensed line in case of flame 4 is higher than that of flame 2 indicating the presence of H-poorer PAHs in flame 4 as compared to PAHs in flame 2 with same C atom count. It was interesting to note that in both the flame environments, free- 68

69 (a) HAB = 10 mm. (b) HAB = 7 mm. (c) HAB = 5 mm. Figure 3.6: C-H diagrams for the C 6 H 6 flame at different HABs. 69

70 Figure 3.7: C-H diagram for the C 2 H 2 flame at HAB = 7 mm. edge growth through route 2 (Figure 3.2) dominated at lower flame temperatures (< 1000 K), and route 1 dominated at higher temperatures (or higher HABs). In the environment of flame 4, benzene addition on PAHs did not play a significant role due to its low concentration. Figures 3.8(a) and 3.8(b) show computed PAHs from the two flames having the same number of C atoms. It is well known that the PAHs having 5-member rings bordered by not more than two 6-member rings are planar in geometry (the term planar refers to the planar arrangement of C atoms) [26]. PAHs with upto 70 C atoms from flame 5 mostly have 5-member rings on zig-zags, thus bordered by two six-member rings only, and a very few embedded 5-member rings. Hence, the simulation predicts almost planar PAHs for the C 2 H 2 flame, as was observed in [220]. The embedded five-member rings occur due to the closure of 5-member bays with the present reaction mechanism. Bay sites on PAHs were observed to occur most commonly due to benzene addition reaction at lower HABs and due to free-edge growth reaction at higher HABs, and hence, bay closure reaction was more important in the environment of flame 2. Embedded 5-member rings formed due to closure of 5-member bays were common in computed PAHs from flame 2. 70

71 (a) C 6 H 6 flame. (b) C 2 H 2 flame. Figure 3.8: Example computed PAHs for the flames 2 and 4, respectively. Therefore, the simulation predicts PAHs with some geometrical distortions for this flame. These results are in concordance with the predictions of Griesheimer et al. [82] for an aromatic flame. In [82], a naphthalene flame was observed experimentally, and was concluded that the PAHs dominating the gas phase were formed by the addition of one PAH/PAH radical over another (biaryl formation). The biaryls thus formed are considered to be highly reactive, and can form 5 or 6-member rings by cyclodehydrogenation, if they have bay sites. It is clear that the addition of PAHs/PAH radicals can play an important role in the PAH growth mechanism for the flames of aromatic hydrocarbons and cyclic compounds such as cyclohexane flame [81], where the concentration of PAHs is higher as compared to aliphatic flames. The C-H diagrams presented in this chapter contain data points corresponding to PAHs with even number of C and H atoms. PAHs with odd number of C atoms can arise due to: presence of aliphatics with odd number of C atoms like C 1 and C 3 hydrocarbons, presence of 5-member rings on free-edges (for example, indene) or on armchairs (for example fluorene), and presence of 6-member rings on zigzags (for example, phenalene). Reactions leading to PAHs with odd number of C atoms were not included in the reaction mechanism, and therefore, such PAHs were not obtained. The H content of PAHs with the same number of C atoms not only varies with the type of the fuel generating them, but also with HAB. The C-H diagrams for 71

72 Figure 3.9: Number fraction of elementary sites for different C atom counts and HABs. flame 2 in Figure 3.6 show that PAHs at lower HABs are H-richer than those at higher HABs. It was suggested by Weilmünster et al. [220] that for the same number of C atoms, H-rich PAHs involve more bays and armchairs and less 5- member rings than H-poor PAHs. To verify this, ensembles of PAHs with the same number of C atoms were generated for different HABs, and the variation in the concentration of elementary sites on the PAHs with HAB was studied. Figure 3.9 shows the concentration of elementary sites on PAHs, represented in terms of their number fractions for different HABs and C atom counts. For the computed PAHs with n number of C atoms, the empirical mean of the number fraction of a site S {R5, ED, ZZ, AC, BY }, x S,n was obtained using the following expression: x S,n = N S,n / i S N i,n, where N S,n is the average number of sites of type S present on the PAHs. It is clear from Figure 3.9 that for the PAHs with the same number of C atoms, the number fractions of armchairs and bay sites decrease and that of 5-member rings increases with HAB, thus making PAHs H-poorer with HAB. This result is in line with the predictions of Weilmünster et al. [220]. The comparison of the computed results with experimental findings presented here suggests that the model is capable of predicting the experimental observations 72

73 very well. However it is limited by the assumption of 2D growth of PAHs. 3.7 Results and Discussion The validation of the kmc-ars model against some key experimental findings in the previous section warrants its use to get the statistical closure expressions for the site-counting model, as indicated in section 3.5. In order to obtain this closure, a detailed statistical analysis of the results based on the study of growth of PAHs in the flame environments listed in Table 3.3 is presented Statistical Analysis This section details the methodology adopted to obtain the unclosed terms in the site-counting model: N y and P S,m (defined in section 3.5). Additionally, the effect of steric hinderance in larger PAH structures is investigated. For the results presented in this section, PAH growth simulations were carried out a large number of times in order to obtain average variations in the required random variables and confidence intervals over them (see section for details). Combined-Site Correlations The site-counting model requires some approximations to describe the combined sites because it does not store the PAH structural information. Figure 3.10 shows four types of combined sites on an example PAH structure. The kmc-ars model can be used to provide this information by developing correlations. The particle state space is multidimensional, therefore the number of combined sites will be functions of many variables, particularly the number of carbon atoms, and the number of all elementary sites. However, it was assumed to be sufficient to describe the combined site counts by just one particle property. The correlations for the combined sites are based on the variation in their counts with one of their constituent elementary sites. To obtain the correlations, the simulations described above were run 500 times and the combined site counts were stored along with the elementary site counts. Figure 3.11(a) shows the number of R6 rings as a 73

74 Figure 3.10: An example PAH molecule showing combined sites. function of free-edge count, and Figure 3.11(b) shows the number of R6 rings adjacent to armchairs as a function of armchair count for flame 8. A nearly linear relationship was observed in all cases. The correlations were obtained by using a least-squares algorithm to fit a linear function to the data, averaged over all simulations. The correlations for the combined site, R5ZZ involved in process S14 (Table 3.2) were not obtained as this reaction does not affect the site counts in the site-counting model [195]. Meaningful correlations for the combined site involving two FE s next to an embedded R5 (process S17, Table 3.2) could not be obtained as it occurred very infrequently on the computed PAHs. As an R6 ring consists of three consecutive free-edges, they cannot exist when there are just two free-edges, hence a correlation of the form N R6 = a(n F E 2) was obtained. The armchair count was chosen as the fitting variable for the AC R6 site count as the armchair count was always found to be lower than the free-edge count, hence the combined site count should be more sensitive to the number of armchairs. For the combined sites involving R5, the R5 count was chosen for the same reason. The correlations for the combined sites required by the site-counting model (N y ) were evaluated for all the flames listed in Table 3.3 to study their variation with flame properties like fuel, cold gas velocity, pressure and C/O ratio. Detailed statistics are provided only for atmospheric pressure flames It is because such correlations have been used in [212] in the site counting model to predict the soot observables like soot volume fraction, number density and particle size distribution functions for flames Given below are the correlations for 74

75 (a) R6 ring count as a function of free-edge count. (b) AC R6 site count (R6 ring next to an armchair) as a function of armchair count. Figure 3.11: Correlations for combined sites. Solid lines show linear approximations, dashed lines show confidence intervals. 75

76 these flames: N R6 = N AC R6 = N R5F E = N R5AC = (N F E 2) if N F E > 2 (flame 8) (N F E 2) if N F E > 2 (flame 9) (N F E 2) if N F E > 2 (flame 10) (N F E 2) if N F E > 2 (flame 11) 0 if N F E N AC if N F E > 2, N AC > 0 (flame 8) 0.36 N AC if N F E > 2, N AC > 0 (flame 9) 0.35 N AC if N F E > 2, N AC > 0 (flame 10) 0.35 N AC if N F E > 2, N AC > 0 (flame 11) 0 if N F E 2, N AC N R5 if N F E > 0, N R5 > 0 (flame 8) 1.25 N R5 if N F E > 0, N R5 > 0 (flame 9) 1.2 N R5 if N F E > 0, N R5 > 0 (flame 10) 1.22 N R5 if N F E > 0, N R5 > 0 (flame 11) 0 if N F E 0, N R N R5 if N AC > 0, N R5 > 0 (flame 8) N R5 if N AC > 0, N R5 > 0 (flame 9) N R5 if N AC > 0, N R5 > 0 (flame 10) N R5 if N AC > 0, N R5 > 0 (flame 11) 0 if N AC 0, N R5 0 (3.5) (3.6) (3.7) (3.8) It can be noticed that these correlations do not vary much for flames 8 11, and can be concluded that the change in cold gas velocity does not affect the correlations. In a similar fashion, correlations for flames 3 6 were evaluated. These low pressure flames differed in C/O ratio and/or cold gas velocity. For these flames as well, correlations were found to be varying negligibly indicating no effect of C/O ratio on the correlations. Average values of the correlation coefficients for 76

77 these flames along with the other flames simulated in this work are provided in Table 3.4. It can be seen in Table 3.4 that the correlations for the flames having different fuels but same pressure (flames 2 7) differ from each other. Similarly, comparing the correlations for flame 1 and flames 8 11 in the same Table shows that the correlations are dependent on flame operating pressure as well. Since the correlations reflect the resulting PAH structure in a flame environment, the changes in correlations with the type of fuel and pressure of the flames may be due to the change in the dominant PAH growth processes (discussed in section 3.6 for C 6 H 6 and C 2 H 2 flames), which can significantly change the PAH structures [224]. The domination of a PAH growth process in a flame environment depends on its rate, which in turn depends on species concentration and rate constants of the PAH reactions (equation 3.3). Chemical species profiles vary significantly with the type of fuel in the flame (see Figure 3.5), and the reaction rate constants depend on pressure [27]. Therefore, the dominant PAH processes in flames with varying pressure and/or fuels may be different, leading to a change in PAH structures and thus the correlations. The correlations and the PAH statistics discussed further in this chapter have been provided for all the flames listed in Table 3.3. This is to make the simulation of these flames along with the flames observed under similar conditions possible using the site-counting model to predict substantial details of soot particles like soot volume fraction, number density, particle size distribution functions, C/H ratio and average PAH sizes [195, 212]. Neighbour Statistics When a surface reaction occurs it is necessary to update the neighbour site types, however, information about the neighbour sites is not available in the site-counting model. As outlined in section 3.5, P S,m is required to obtain this information. Only the jump processes involving six-member rings, and oxidation of reactive sites in Table 3.2 are considered here, as those involving only 5-member rings do not change neighbour sites, and processes S7 and S8 were observed to occur so infrequently that meaningful statistics could not be obtained. It was initially assumed that neighbour sites of type S {ED, ZZ, AC, BY } are selected for process m with the probability P S,m (t) = N S (t)/n tot (t), where N S (t) is the number 77

78 Table 3.4: Correlation coefficients for the simulated flames. Correlation coefficients Flame R6 a AC R6 b R5F E c R5AC d unavail F E e unavail AC f a b c d e 1 e 1 f 1 f a N R6 = a (N F E 2) b N AC R6 = b N AC c N R5F E = c N R5 d N R5AC = d N R5 e N unavail F E = tanh(e 1 log(e 2 N F E + 1)) f N unavail AC = tanh(f 1 log(f 2 N AC + 1)) of sites of type S at time t, N tot (t) is the total number of sites (ignoring 5-member rings), and m {1,..., number of processes in Table 3.5} is the process index. However, it was found that when using these probabilities the site-counting model did not agree with the kmc-ars model, which suggests that some sites are more likely than others to be neighbours for certain processes. Therefore, site count weights were introduced for each process such that the weighted counts are given by: N S,m (t) = W S,m N S (t), hence the probability of a site of type S being selected at time t for process m becomes: P S,m (t) = N S,m (t) N tot,m(t) (3.9) where N tot,m(t) is the sum of the weighted site counts and depends on the process m. It is assumed that the site weights do not depend strongly on PAH size, therefore they are considered to be constant for each process. This assumption is supported by the kmc-ars simulations conducted for this study. In order to calculate the site-weights, several kmc-ars simulations were performed. For each simulation there are K events, and K m denotes the number of times event m occurred. On selection of the t th jump process, where 78

79 t {1, 2,..., K}, the following information was stored: the time point t, the jump process index, m t, the types of both neighbour sites, T 1 (t) and T 2 (t) and the counts of all site types: N ED (t), N ZZ (t), N AC (t), N BY (t). L S,m shall denote the number of times a site of type S acted as a neighbour for process m. In the limit of large K m, the probability of a site acting as a neighbour is assumed to approach P S,m = L S,m /K m, therefore, by summing over each jump process and solving the following equation, the site-weights can be obtained: K m t=1 W S,m N S (t) W F E,m N F E (t) + W ZZ,m N ZZ (t) + W AC,m N AC (t) + W BY,m N BY (t) = L S,m (3.10) where S {ED, ZZ, AC, BY } and m {1,..., 9} (processes listed in Table 3.5). As there are four possible site types which may act as neighbours; freeedges (FE), zig-zags (ZZ), armchairs (AC) and bays (BY), equation 3.10 gives a system of four linear equations for each process m, which can be solved using a standard numerical technique such as a Newton method. Equation 3.10 was solved for the four elementary sites, with the additional constraints of W S,m 0 and S W S,m = 1. Table 3.5 shows the site-weights for the principal reactions for flames These weights are used to calculate P S,m site-counting model using equation 3.9. = f (W S,m ) in the It is clear from Table 3.5 that assuming equal weights for all the sites would lead to an unrealistic PAH molecule using the site-counting model. For the reactions involving R6 desorption and conversion of a 6-member ring to a 5-member ring, the free-edge site-weight (W F E (3 6)) is zero, as it is not possible to desorb a six-member ring having more than three consecutive free-edges together with the current reaction mechanism. Thus, a free-edge cannot exist as the neighbour site of a R6 ring. Similarly, for armchair oxidation reactions (reactions S11 and S12 in Table 3.2), a free-edge cannot exist as a neighbour site. Therefore, the freeedge site-weight (W F E (7, 8)) is zero. For a 6-member bay closure reaction, a bay cannot be present as a neighbour, as it is geometrically prohibited. Therefore, for this reaction, W BY is zero. A study on the variation in neighbour site-weights with flame properties was also conducted. It can be seen in Table 3.5 that these weights 79

80 Table 3.5: Neighbour site-weights for the principal reactions for flames 8 11 No. Process Reaction Flame W F E W ZZ W AC W BY 1 S1 FE growth C C C C S2 AC growth C C C C S3 R6 desorption C C C C S4 R6 to R5 at AC C C C C S9 FE oxidation by O 2 C C C C S10 FE oxidation by OH C C C C S11 AC oxidation by O 2 C C C C S12 AC oxidation by OH C C C C S15 Bay closure C C C C

81 Figure 3.12: Neighbour site-weights of elementary sites for different reactions for the C 2 H 2 flames (flames 3 6). The reactions corresponding to the reaction numbers (on x-axis) are listed in Table 3.5. For each reaction, the four consecutive parallel stacks represent flames 3 to 6 from left to right. for flames 8 11 do not vary significantly indicating no effect of cold gas velocity on them. Variation in the neighbour site-weights with C/O ratio, operating pressure and type of fuel of the flames has been shown graphically in Figures 3.12, 3.13 and 3.14 respectively. It can be easily concluded from these figures that the site-weights do not vary significantly with C/O ratio (variation within 8%), but varies with the type of fuel and pressure, as was observed in the case of combined sites correlations. 81

82 Figure 3.13: Variation in neighbour site-weights of elementary sites for different reactions with pressure for the C 2 H 4 flame. The reactions corresponding to the reaction numbers (on x-axis) are listed in Table 3.5. For each reaction, first stack represents average neighbour siteweights for flames 8 11, and second stack represents flame 1. 82

83 Figure 3.14: Variation in neighbour site-weights of elementary sites for different reactions with the type of fuel. The reactions corresponding to the reaction numbers (on x-axis) are listed in Table 3.5. For each reaction, the three consecutive parallel stacks represent three different flames at the same pressure (2.67 kpa): first stack C 6 H 6 flame (flame 2), second stack C 2 H 4 flame (flame 7), third stack C 2 H 2 flame (flames 3 6). 83

84 Figure 3.15: A computed PAH molecule from flame 8 at HAB = 5 mm. Filled circles and stars denote unavailable free-edges and armchairs respectively. Hollow symbols denote available sites. Unavailable Sites As PAH molecules grow, their structure can become complex and it is possible for some sites to be unavailable for reaction because they are hindered by nearby aromatic rings. This has been referred to as steric hinderance. Figure 3.15 shows how free-edges and armchairs can become unavailable on a computed PAH molecule from flame 8. This generally occurs when the structure grows around on itself. This effect should also be observed if PAH molecules are stacked close together, and is probably one of the major contributing factors of the alpha correlation for inactive sites in the ABF model [29]. Such contorted structures, as observed in Figure 3.15 would most likely give rise to a 3D structure as the nearby hydrogen atoms interact, however, if the molecule was constrained in a stack this may be less energetically favourable, as the bending of a PAH may not be allowed due to the presence of nearby PAHs. It is more likely in this case that the hydrogen are abstracted and a C-C bond is formed through bay closure reactions later on in the flame. The kmc-ars model allows unavailable sites to be counted explicitly. Figures 3.16(a) and 3.16(b) show the fraction of unavailable free-edges and armchairs respectively as functions of the free-edge and armchair counts. The fraction of unavailable sites firstly increases with the site counts before reaching an asymptotic limit at larger site counts. A function of the form Y = tanh(a log(bx + 1)) was found to describe this asymptotic behaviour well. The curves in Figure

85 (a) Fraction of unavailable free-edges. (b) Fraction of unavailable armchairs. Figure 3.16: Unavailable sites. Solid lines show a tanh fit. Dashed lines show confidence intervals. were fitted by trial and error, and the equations for flames 8 11 are given below: N unavail F E = N unavail AC = tanh(0.573 log(0.024 N F E + 1) flame 8 tanh(0.752 log(0.018 N F E + 1) flame 9 (3.11) tanh(0.852 log(0.016 N F E + 1) flame 10 tanh(0.984 log(0.014 N F E + 1) flame 11 tanh(0.599 log(0.044 N AC + 1) flame 8 tanh(0.777 log(0.037 N AC + 1) flame 9 (3.12) tanh(0.867 log(0.031 N AC + 1) flame 10 tanh(0.934 log(0.024 N AC + 1) flame 11 The above equations predict very similar variation of unavailable free-edges with free-edges count for flames The equations for unavailable armchairs show a similar trend. Therefore, the correlation coefficient for only flame 8 is presented in Table 3.4. A similar trend was observed for flames 4 7. Therefore correlation coefficients for only flame 4 is provided in the same Table along with the 85

86 (a) C atom count as a function of time (b) Site count as a function of time Figure 3.17: Comparison of the results from the kmc-ars model and the sitecounting model for flame 8. Dashed lines show the results from the site-counting model and solid lines show the result from the kmc- ARS model. coefficients for other flames listed in Table 3.3. The equations of the above form are remarkably similar to the alpha correlation [29], used in the ABF soot model to determine empirically the number of active sites on soot particles. The alpha correlation is used to model particle aging, which is the observed phenomenon that soot particle become less reactive with age. The correlations presented here have a similar role, as they effectively decrease the number of active sites present on the PAHs with the simulation time Site-Counting Model Validation The statistics and correlations described above were implemented in the sitecounting model, and identical simulations were performed using the site-counting model and the kmc-ars model for flames Figures shows the comparison of the PAH characteristics: carbon atom count and number of elementary sites on the PAHs in flames These figures show that the site-counting model and the kmc-ars model 86

87 (a) C atom count as a function of time (b) Site count as a function of time Figure 3.18: Comparison of the results from the kmc-ars model and the sitecounting model for flame 9. Dashed lines show the results from the site-counting model and solid lines show the result from the kmc- ARS model. (a) C atom count as a function of time (b) Site count as a function of time Figure 3.19: Comparison of the results from the kmc-ars model and the sitecounting model for flame 10. Dashed lines show the results from the site-counting model and solid lines show the result from the kmc- ARS model. 87

88 (a) C atom count as a function of time (b) Site count as a function of time Figure 3.20: Comparison of the results from the kmc-ars model and the sitecounting model for flame 11. Dashed lines show the results from the site-counting model and solid lines show the result from the kmc- ARS model. predict similar carbon atom counts, and the number of free-edges, zig-zags and armchairs at all observed flow times. The close agreement of the number of elementary sites is important because the site counts are used to calculate the process rates. Also, this signifies that the site-counting model predicts PAHs very similar to those computed by the kmc-ars model. A comparison between the two models has also been shown in our previous work [195] in a flame-like environment. The extent of agreement of the computed PAH characteristics by the two models is very encouraging. It shows that the detailed PAH growth model can be confidently accommodated into a soot particle population balance using the site-counting model. Figure 3.21 shows the variation in the number of PAH sites with the number of C atoms. It can be concluded from this figure that the correlations for unavailable sites are not very significant for small PAH molecules. 88

89 Figure 3.21: Comparison of the results: Dashed lines show the results from the site-counting model and solid lines from the kmc-ars model. Filled symbols show the results from site-counting model without correlations for unavailable sites. 89

90 3.8 Conclusion A new detailed PAH growth model (kmc-ars model) has been developed. This model considers growth of a PAH molecule in all directions, irrespective of the orientation of reactive sites. A large set of PAH processes along with the reactions involved in the PAH growth has been presented. DFT simulations to evaluate the rates of the reactions involved in the cyclodehydrogenation process to form a 6- member ring on PAHs have been carried out. A new route for this reaction is also suggested. A kinetic Monte Carlo algorithm and a data structure has been developed to track the structure of a PAH molecule, as it grows in a flame-like environment. This model allows the exact estimation of the distribution of sites on a PAH molecule. The validation of the kmc-ars model has also been carried out by comparing the number of C and H atoms of the experimentally observed PAHs having up to 70 C atoms with the computed ones, and a good agreement has been obtained. The site-counting model proposed by Celnik et al. [195] allows this detailed PAH growth model to be coupled into soot particle population balances by neglecting PAH structure. This model is computationally very fast. Since the sitecounting model neglects the PAH structure, the structural information about the PAH molecule is provided by the kmc-ars model. Correlations have been developed for different flame environments which describe the number of combined sites, which are required to calculate the rates of some reactions. Site type weights have been found which allow neighbour sites to be selected appropriately without prior knowledge of the structure. A method to calculate the site weights using results obtained from the kmc-ars model has been described. It has also been shown that as a PAH molecule grows, reactive sites can become unavailable due to steric hindrance. The fraction of unavailable sites increases rapidly with the size of the PAHs initially, but shows an asymptotic behaviour afterwards. Correlations for the fraction of unavailable sites have also been developed. All the PAH statistics detailed in this chapter have been shown to be independent of cold gas velocity and C/O ratio of the flames, but depend on the type of fuel and pressure. The statistics have been obtained for the commonly observed premixed laminar flames, which can be used in the site-counting model 90

91 along with soot particle population balance to predict soot observables like soot volume fraction, number density, particle size distribution functions, C/H ratio and average PAH sizes [195, 212]. The results of the kmc-ars model have been compared to the site-counting model. The agreement between the carbon atom counts and the principal site counts is reasonable, which suggests that the detailed PAH growth model can be implemented in the soot particle population balances through the site-counting model without much loss of information. 91

92 Chapter 4 New PAH Processes This chapter introduces new PAH processes, which can cause dehydrogenation and rounding of PAH molecules. The current PAH growth mechanism is extended by including the new processes, and the kmc-ars model is used to study PAH growth with the extended mechanism. The effect of the inclusion of new PAH processes in the chemical mechanism on the predicted composition of large PAH molecules is shown. A sensitivity analysis is carried out to study the effect of the change in reaction rates on the computed results. A large part of this chapter is published in Raj et al. [225]. By the end of this chapter, the reader should be able to find answers to the following questions: Why are the new PAH reactions required if a satisfactory agreement was obtained between the computed and the observed PAH ensembles in the previous chapter? Are the computed results from the kmc-ars model sensitive to the rate constants of PAH reactions? 4.1 Problem description In Chapter 3, it is shown through the kmc simulations that the present reaction mechanism predicts, reasonably well, the ensembles of the PAHs observed in the flame environments of C 2 H 2 and C 6 H 6 [66, 220]. However, the comparison was only shown for PAHs with less than 70 carbon atoms. PAHs having more than 70 carbon atoms are also observed in flames at higher heights above 92

93 the burner (HABs) [220]. Those PAHs present at higher HABs mostly contain peri-condensed rings (H-poor PAHs). Weilmünster et al. [220] provides the composition of such PAHs in terms of C/H ratios. In the literature, no comparison between the observed and the computed ensembles of large PAHs has been shown. If the mechanism provided in the previous chapter is used to compute the C/H ratios for PAHs with more than 70 carbon atoms, an under-prediction is obtained (shown later in this chapter) due to formation of H-rich PAHs in the simulations. In [118], it is shown by using the ARS-PP model that the current reaction mechanism under-predicts the composition (C/H ratio) of soot particles as well. Through an experimental study on PAHs present in an aliphatic flame, it was suggested in [220] that, at higher HABs, the PAH growth rate decreases due to decrease in the concentration of chemical species like C 2 H 2. At such locations, processes involving PAH rearrangement and ring desorption mainly take place. These processes cause dehydrogenation and rounding of PAHs, and therefore are required to be included in the PAH growth mechanism. Keeping the above arguments in mind, in this chapter, the detailed PAH growth mechanism has been extended by including two new PAH rearrangement and ring desorption processes. Two highly competitive routes for each process have been suggested. A theoretical study has been conducted using density functional theory (DFT) and transition state theory (TST) to determine the rates for the elementary reactions involved in the suggested processes. The kmc-ars model has been used along with the extended PAH growth mechanism to study the effect of the inclusion of the new processes on the composition of computed PAHs in a C 2 H 2 flame. A majority of the rate constants used in the chemical mechanism are taken from the literature, which were derived theoretically using quantum chemistry calculations such as DFT [27, 28, 112]. As mentioned in Chapter 2, there may be some errors associated with the calculated values, which may affect the simulation results. Therefore, a sensitivity analysis has been carried out by varying the rate constants of all the elementary reaction involved in the PAH growth mechanism to study its effect on the results computed using the kmc-ars model. 93

94 4.2 Reaction pathways This section details the elementary reaction steps involved in the new PAH processes proposed in this work. Both the processes require the presence of a 6- member ring adjacent to a bay site (a combined functional site) to take place. To reduce the computational expense for quantum calculations, the smallest model molecule fulfilling the above requirement, benzo[c]phenanthrene was chosen as the parent molecular structure. Before discussing the new pathways, information about the level of theory used for the quantum chemistry calculations is provided in the next section Calculation details The molecular structures of the stable chemical species and transition states involved in the proposed PAH processes were optimised using the B3LYP hybrid functional and the G(d,p) basis set. For the stable species, the structures were optimised with different spin multiplicities to determine the multiplicity with the minimum energy and reasonable geometry. Vibrational frequencies were also calculated, and it was ensured that the stable species do not have any imaginary frequencies and the transition states have only one imaginary frequency. The vibrational mode of the imaginary frequency of all the transition states was animated to confirm that the motion correctly connects the corresponding reactants and products. Before employing B3LYP/ G(d,p) for the theoretical calculations in this work, a number of experimental validations were carried out by comparing the experimental data available for carbon-hydrogen systems with the calculated values. The bond dissociation energy of the C-H bond in benzene was determined using B3LYP/ G(d,p), and was found to be kcal/mol. This value agrees reasonably well with the experimental C-H bond dissociation energies of 113.9, and kcal/mol provided in Gribov et al. [215] and refs. therein, and a recent value of ± 0.5 kcal/mol given in [226]. The PAH processes proposed in this work require an abstraction of an H atom present on the PAH for initiation. Therefore, the B3LYP functional was used to study the H-abstraction 94

95 process on different hydrocarbons, for which experimentally determined reaction energies and barrier heights were available. For methane H-abstraction reaction (CH 4 + H CH 3 + H 2 ), B3LYP/ G(d,p) predicts the reaction energy and barrier height to be 0.94 and 9.54 kcal/mol, respectively, which compare reasonably well with the experimental values of 0.6 and 11.9 kcal/mol [213, 227, 228]. The gold-standard coupled-cluster singles, doubles and perturbative triples, CCSD(T)/AUG-cc-pVQZ predicts the barrier height for this reaction as 14.9 kcal/mol [229]. A similar calculation was done for benzene H-abstraction reaction (C 6 H 6 + H C 6 H 5 + H 2 ). The reaction energy and the barrier height calculated with B3LYP/ G(d,p) were 7.28 and 12.2 kcal/mol, respectively. In [201], these energies were determined by performing single point energy calculations using RCCSD(T)/6-31G(d,p) on the geometries optimised using MP2/6-31G(d), and were found to be 11.8 and 22.3 kcal/mol, respectively. An experimental investigation on this reaction reports its reaction energy as 8.95 kcal/mol [227]. It is clear from the above comparisons and similar comparisons in the literature [201, 213, 230, 231] that the B3LYP functional under-predicts the reaction barrier heights. This under-prediction can lead to an overestimation of the reaction rate constants. According to the findings of [116] and refs. therein, the error in the calculated reaction barrier introduced by density functional theory (DFT) can be as high as 5 kcal/mol. Figure 4.1 shows the effect of uncertainty in reaction barrier height (activation energy) on the rate constant, assuming it to be in the modified Arrhenius form (k(t ) = A T n exp ( E RT ) ). It is clear from this figure that, for T > 1000 K, the change in the rate constant remains within an order of magnitude, even when E = 5 kcal/mol. However, at lower temperatures ( 300 K), an under-prediction in the barrier height by 5 kcal/mol can over-predict the rate constant by more than three orders of magnitude. Therefore, a large error in the reaction barrier is not permissible at low temperatures. A further inaccuracy in the quantum calculations can arise due to spin contamination in open shell systems. In [231, 232], it is shown by observing S 2 for a number of stable species and transition states that DFT introduces a negligible amount of spin contamination. The values of S 2 for all the chemical species and transition states involved in the proposed processes are shown later. 95

96 Figure 4.1: Effect of change in activation energy on the reaction rate constant. E represents the error in evaluated reaction barrier height (activation energy), E. k and k are the rate constants with activation energies E and E+ E, respectively PAH Process 1 Figure 4.2 shows the potential energy diagram for the conversion of benzo[c]phenanthrene to pyrene. The reaction is initiated by the abstraction of an H atom present in the bay region of CS1. The abstraction process reduces the steric congestion in CS2. This was evident from the optimised geometries of CS1 and CS2. The 3D geometry of CS1 caused by the repulsion between the nearby H atoms in the bay region was lost, and CS2 gained a planar geometry, as observed in [196]. The structural stabilisation of CS2 leads to a lower reaction energy of 1.09 kcal/mol for this H-abstraction process, as compared to benzene H-abstraction reaction, which involves a reaction energy of 7.28 kcal/mol (see section 4.2.1). The next step involves the breakage of a 6-member ring near the bay region (decyclisation reaction). This reaction requires a potential energy barrier of kcal/mol to 96

97 Figure 4.2: Potential energy diagram showing energies of the chemical species (CS) and transition states (TS) involved in the conversion of benzo[c]phenanthrene to pyrene at 0 K. After the formation of CS6, two probable routes are shown here by solid and broken lines. Similarly, after the formation of CS4, two probable routes are shown by dotted and broken lines. be overcome. A similar ring-breakage mechanism has been proposed in [114] for the PAH processes involving conversion of a 6-member ring to a 5-member ring, and 6-member ring desorption. After the decyclisation of a 6-member ring, three possibilities can arise: (a) desorption of one of the aliphatic chains, (b) recombination of the aliphatic chains to form a 6-member ring, and (c) formation of cyclopentadienylidenecarbene type structure (with only one radical) by the two aliphatic chains. The possibilities (a) and (c) form the basis for the two PAH processes proposed in this work. In process 1, the desorption of a C 2 H 2 molecule can take place via two routes one involving the mediation of a H atom, and the other involving direct desorption of C 2 H 2. The H-mediated desorption of C 2 H 2 97

98 has been suggested in [114] by simultaneous addition and removal of an H atom and a C 2 H 2 molecule, respectively, as shown below: (4.1) For this route, a negative reaction barrier was found. A further analysis of this pathway led to the conclusion that a stable molecule, CS4 gets formed by the addition of an H atom on CS3. The reaction CS3 +H CS4 involves a barrier of 4.6 kcal/mol. The desorption of a C 2 H 2 molecule can then take place from CS4 to form CS5. Figure 4.3 shows the structures of the chemical species and the transition states involved in this route. After the formation of CS5, the principal (a) CS3 (b) TS3 (c) CS4 (d) TS4 (e) CS5 Figure 4.3: Structures of the chemical species and transition states involved in the conversion of CS3 CS5. reactions, that take place are H addition, H shift between the C atoms forming a bay site, bond formation between nearby C atoms, and removal of an H atom 98

99 (from CS7 or CS10) to regain aromaticity, as shown in Figure 4.2. The direct removal of C 2 H 2 from CS3 can form CS3, which requires an energy barrier of 42.1 kcal/mol to be overcome. Once CS3 is formed, it can lead to the formation of a pyrene radical by following the same routes as CS5, as shown in Figure PAH Process 2 Figure 4.4 shows the potential energies of the chemical species and the transition states involved in the conversion of benzo[c]phenanthrene to cyclopenta[cd]pyrene relative to the starting species: CS1 and two H atoms. This process involves dehydrogenation of a PAH molecule through ring rearrangement. Similar to process 1, Figure 4.4: Potential energy diagram showing energies of the chemical species (CS) and transition states (TS) involved in the conversion of benzo[c]phenanthrene to cyclopenta[cd]pyrene at 0 K. Two probable routes are shown here by solid and broken lines. it initiates with the abstraction of an H atom and decyclisation of a 6-member ring. This decyclisation is followed by the formation of cyclopentadienylidenecarbene type structure (CS3 CS11). For this reaction, a potential energy of only 4.3 kcal/mol is required, which is comparable to the energy barrier of 4.6 kcal/mol 99

100 Table 4.1: S 2 for the species involved in pathways 1 and 2 obtained using B3LYP/ G(d,p) level of theory. For singlet, doublet and triplet states, S 2 should be 0, 0.75 and 2, respectively. The number in the bracket shows the spin multiplicity. Chemical S 2 Chemical S 2 Transition S 2 Transition species species states states S 2 CS1 (1) 0 CS2 (2) TS1 (2) TS2 (2) CS3 (2) CS4 (3) TS3 (3) TS4 (3) CS5 (1) 0 CS6 (2) TS5 (2) TS6 (2) CS7 (2) CS8 (1) 0 TS7 (2) TS8 (2) CS9 (2) CS10 (2) TS9 (2) TS10 (2) CS3 (2) CS4 (3) TS3 (2) TS4 (3) CS5 (3) CS6 (2) TS5 (3) TS6 (3) CS7 (3) CS8 (3) TS7 (3) TS8 (3) CS11 (2) CS12 (2) TS9 (3) TS11 (2) CS13 (2) CS14 (1) 0 TS12 (2) TS13 (2) CS15 (2) TS14 (2) TS15 (2) TS16 (2) required for the reaction CS3 CS4. This implies that both the pathways proposed in this work are highly competitive. After the formation of CS11, reactions involving C-C bond formation, H-shift and H-removal to regain aromaticity primarily take place. In [196], a different pathway for process 2 has been proposed, in which the reaction proceeds without the opening of a 6-member ring. This is detailed in section 4.4. Most of the species involved in both the pathways have radical sites on them, and therefore, unrestricted DFT calculations were performed on such open-shell systems. To evaluate the amount of spin contamination introduced by DFT, S 2 values were found for all the chemical species and the transition states, and are shown in Table 4.1. It is clear from this table that the amount of spin contamination introduced by DFT is negligible for our molecular system, as the difference between S 2 and s(s + 1) is less than 10%. 100

101 4.3 KMC-ARS Model The kmc-ars model was developed in Chapter 3 to study the growth of single PAH molecules using a detailed chemical mechanism with 17 PAH processes in it. The mechanism is extended by including 3 more processes as shown in Table 4.2. Table 4.2: New PAH reactions along with the jump processes and the process rates obtained after steady-state analysis. The reaction steps S1 S17 are provided in Chapter 3. Steps [Ref.] Parent site S18 6-member ring desorption at bay 6-member ring (Process 1) next to bay Jump Process: Rate: k 2a ( ) k 1a[H]+k 24[OH] k 1[H 2]+k 25[H]+k 24[H 2O]+k 2a [C bay R6] S19 6-member ring rearrangement at bay 6-member ring (Process 2) next to bay Jump Process: Rate: k 2a ( ) k 1a[H]+k 24[OH] k 1[H 2]+k 25[H]+k 24[H 2O]+k 2a [C bay R6] S20 6-member ring rearrangement at bay [196] 6-member ring (Process 3) next to bay Jump Process: Rate: k 26 ( ) k 1a[H]+k 24[OH] k 1[H 2]+k 25[H]+k 24[H 2O]+k 26 [C bay R6] 101

102 In [196, 216], process 2 was studied with a different pathway. Their pathway has also been included in the PAH mechanism, and is listed as process 3 in Table 4.2. The rates of the elementary reactions involved in the pathway of process 3 were evaluated in [196]. The rate expressions for the new processes obtained after a steady state analysis are given in Table Results and discussion Reaction rates The rate constants of the elementary reactions involved in the new proposed processes are listed in Table 4.3. It is worth mentioning that the Wigner correction factor varied between 2.5 and 1 in the temperature range of K for all the reactions, and it remained close to 1 for T > 1000 K. The rate constants for some of the elementary reactions, which are present in the rate expressions of the jump processes (in Table 4.2), but not studied in this work, were taken from the literature. These are also provided in Table 4.3. One of the principal steps in processes 1 and 2 is the decyclisation of a six member ring. In [209], the rate constant for the decyclisation of phenyl radical was evaluated using MIND0/3 (a semi-empirical method) [184]. Two of the PAH processes proposed in [114] (6-member ring desorption and conversion of 6-member ring to 5-member ring) involved decyclisation of a 6-member ring. A rate constant for this reaction is given in their work, but, its origin is not clear. Figure 4.5 provides the comparison between the rate constants for the decyclisation reaction from the literature and the rate constant evaluated in this work. A good agreement between all the rate constants was obtained, especially at high temperatures. This provides further support to the level of theory used in this work. 102

103 Figure 4.5: Comparison of the rate constants for decyclisation of a six-member ring. Hollow circles: rate constant for the decyclisation of phenyl ring evaluated by Dewar et al. [209]. Dashed line: rate constant for 6-member ring breakage reaction used by Frenklach et al. [114]. Solid line: rate constant for the decyclisation of 6-member ring adjacent to a bay site evaluated in this work. Table 4.3: Elementary reaction rate constants in the form: AT n exp( E/RT). The units are kcal, K, mol, cm and sec. p.w. represents the rate constants calculated in the present work using B3LYP/ G(d,p). No. Reaction A n E Ref. Process 1 1a CS1 + H CS2 + H p.w. 1b CS1 + H CS2 + H [196] -1 CS2 + H 2 CS1 + H p.w. 2a CS2 CS p.w. 2b CS2 CS [209] 2c CS2 CS [114] 3 CS3 + H CS p.w. 103

104 No. Reaction A n E Ref. 4 CS4 CS5 + C 2 H p.w. 5 CS5 + H CS p.w. 6 CS6 CS p.w. 7 CS6 CS p.w. 8 CS7 CS8 + H p.w. 9 CS9 CS p.w. 10 CS10 CS8 + H p.w. 11 CS3 CS3 + C 2 H p.w. 12 CS3 + H CS p.w. 13 CS4 CS p.w. 14 CS7 CS p.w. 15 CS8 CS6 + H p.w. 16 CS4 CS p.w. 17 CS5 CS6 + H p.w. Process 2 18 CS3 CS p.w. 19 CS11 CS p.w. 20 CS12 CS p.w. 21 CS13 CS14 + H p.w. 22 CS11 CS p.w. 23 CS15 CS14 + H p.w. Other reactions 24 CS1 + OH CS2 + H 2 O [112] -24 CS2 + H 2 O CS1 + OH [126] 25 CS2 + H CS [112] 26 CS2 CS16 (P rocess 3) [196] KMC simulation For the PAHs in the size range of 6 to 70 C atoms, the comparison between the computed and the observed ensembles of PAHs is already shown in Chapter 3. For the experimentally observed PAHs with more than 70 C atoms, the information about their composition in terms of C/H ratio is provided in [220] for a C 2 H 2 flame (C/O = 1, cold gas velocity = 42 cm/sec, pressure = atm). The simulated concentration profiles of the chemical species present in this flame 104

105 (a) (b) Figure 4.6: C/H ratio vs C atom count for large PAHs. (a) C/H ratio diagram with the PAH growth processes listed in Chapter 3 (old model); (b) C/H ratio diagram after appending the old process list with the PAH processes proposed in this chapter (new model). The solid black lines in both the sub-figures represent the PAHs with peri-condensed rings. The dashed lines are the smooth fitted curves through the simulated data obtained using the locally weighted least squared error method. are provided in the previous chapter. Those species profiles were used to generate, computationally, a PAH ensemble consisting of PAHs with the number of C atoms in between 70 and 320 in the C 2 H 2 flame using the kmc-ars model at HAB = 25 mm. Figure 4.6 presents a comparison between the simulated and the observed PAH ensembles, with and without the inclusion of the proposed PAH processes in the chemical mechanism. The simulation results obtained using the mechanism without the new PAH processes in it would be referred to as the results from the old model, and those obtained after including the new processes in the mechanism, as the results from the new model. The black solid lines in the sub-figures represent the positions of peri-condensed PAHs on C-H diagrams [66]. The grey broken lines in this figure are the smooth fitted curves through the simulated data obtained using the locally weighted least squared error method. Figure 4.7 represents the smooth fitted curves through the computed C/H ratios 105

106 Figure 4.7: Improvement in the model prediction of C/H ratio of large PAHs. The black circles represents the average C/H ratio of experimentally observed PAHs. The black solid line and the black broken line represent the average C/H ratios of computed PAHs with and without including the new PAH processes in the mechanism, respectively (also shown in Figure 4.6). The corresponding grey lines represent the systematic errors in the computed C/H ratios. 106

107 (a) C 24 H 12 (C/H = 2) (b) C 24 H 10 (C/H = 2.4) (c) C 24 H 10 (C/H = 2.4) Figure 4.8: Example PAHs with the same number of C atoms. (a) represents a peri-condensed PAH. (b) and (c) represent PAHs with C/H ratio greater than the peri-condensed structure with the same number of C atoms. with and without the new PAH processes in the mechanism (shown by the black solid line and the broken line, respectively) and the experimentally observed C/H ratios of the PAHs (shown by black filled circles). The systematic errors in the simulated C/H ratios (difference between the observed and the computed C/H ratios) are also shown by corresponding grey lines. It is clear from this figure that the introduction of new PAH processes has improved the predicted C/H ratio for the large PAHs. It can be seen in Figure 4.6 that some of the simulated PAHs have C/H ratio greater than those in peri-condensed structures (all the data points above the solid black line). This is due to the presence of 5-member rings surrounded by two to four 6-member rings on the PAHs. Some example PAHs of such kind are shown in Figure 4.8. This figure shows a peri-condensed PAH (C 24 H 12 ), and two isomers of C 24 H 10. The C/H ratios of the C 24 H 10 isomers are greater than the peri-condensed structure with the same number of C atoms. Such PAHs with C/H ratio greater than the peri-condensed structures can also exist if they have alkynyl side chains, which are poor in H atom content such as C 2 H chain. However, the reaction mechanism used in this work does not allow the formation of aliphatic side chains such as CH 3 and C 2 H on PAHs. For PAHs larger than 200 C atoms, the C/H ratios of the computed PAHs are significantly under-predicted. There can be three probable reasons behind it (a) the assumption of planar or near-planar growth of PAH molecules: If an 107

108 Figure 4.9: Armchair growth reaction on an embedded 5-member ring surrounded by four 6-member rings. embedded 5-member ring surrounded by four 6-member rings is present on a PAH, the armchair growth reaction on it (Figure 4.9), which can further dehydrogenate the PAHs, is not allowed in the simulation. This is because, the resulting PAH molecule would acquire a 3D geometry, and molecular dynamics would be required to determine the resulting structure, which can significantly increase the computational time. In [115], the variation in simulated C/H ratio of PAHs with PAH mass and residence time in a flame was obtained by studying the 3- dimensional growth of PAHs using kinetic Monte Carlo (kmc) and molecular dynamics (MD) methodologies (the kmc-md model). With no assumptions on the PAH structure and with a similar chemical mechanism used in Chapter 3, C/H ratio of 5 is predicted for PAHs with around 320 C atoms. This value is the same as the average predicted C/H ratio for such PAHs with the old mechanism, as shown in Figure 4.6a. Therefore, the structural assumption in our simplified and computationally inexpensive PAH growth model may not explain the under-predicted C/H ratio. (b) the uncertainties in the rate constants: The use of incorrect process rate constants can completely change the growth pathways of PAHs, leading to the formation of H-rich PAHs. However, the uncertainties in the theoretically calculated rate constants are not known, and therefore, its effect on the computed PAH composition is difficult to determine. A further analysis on this possibility is provided later. (c) the requirement of more rearrangement processes to dehydrogenate the large PAHs: The introduction of new PAH processes in the chemical mechanism similar to the ones proposed in this work can cause further dehydrogenation of larger PAHs. It is worth mentioning that PAHs with more than 200 C atoms are not present in high concentrations in the premixed laminar aliphatic flames [104]. 108

109 Figure 4.10: Reaction counts for some of the principal PAH processes listed in Chapter 3 and Table 4.2 (S1: Free-edge growth; S2: Armchair growth; S3: R6 desorption; S5: R5 addition; S6: R5 desorption; S18 S20: see Table 4.2). The bars in black colour represent the reaction counts, when the PAH reaction rates are not perturbed. The bars in grey colour represent the reaction counts, when the rate constants of the reactions involved in S18 and S19 are reduced by a factor of 10. As mentioned previously, for process 2, a pathway different from the one proposed in this work, is suggested in [115, 216] (see process 3 in Table 4.2). It was possible to determine the number of times, processes 2 and 3 took place on the PAH molecules in the simulation. Figure 4.10 shows a comparison of the number of process events that occurred on the PAHs in the environment of C 2 H 2 flame in 500 simulation runs. It is clear from this figure that the pathway proposed in this work for the conversion of benzo[c]phenanthrene to cyclopenta[cd]pyrene is highly competitive with the one proposed in [115, 216]. All the three processes (S17 S19) take place at higher temperatures (T > 1200 K) in the simulations. As shown in Figure 4.1, an under-predicted barrier height by DFT calculations can lead to an over-estimation of the rate constants by an order of magnitude (at higher temperatures). Therefore, firstly a preliminary order of magnitude analysis was conducted on the two proposed processes (S18 and S19) by reducing their rate constants evaluated in this work by a factor of 10, and then analysing its effect 109

110 on the kmc simulation results. It can be seen in Figure 4.10 that this reduction in rate constant significantly reduced the number of times, those processes took place on PAH molecules. In this test, the effect of rate-reduction on the counts of processes S18 and S19 is more pronounced due to the presence of a competing process, S20, occurring on the same reactive site type, which is required by S18 and S19 to take place. The higher process rate of S20 (as compared to the reduced rates of S18 and S19) diminishes the probability of S18 and S19 to take place on a PAH, when all the three processes are competing for the same reactive site. It is clear from the above analysis that the occurrence of a PAH process gets affected significantly with the variation in the rate constants of elementary reactions, obtained through DFT calculations. However, as indicated in section 4.2.1, at present DFT is the only available theoretical methodology which can provide some information about the reaction rates on PAHs in a reasonable computation time. This indicates the need for a detailed analysis of the uncertainty in the DFT results. Therefore, a sensitivity analysis was carried out to study the effect of perturbations in the reaction rate constants on the computed C/H ratio, assuming that the reaction rates vary within an order of magnitude. This assumption of a uniform uncertainty makes the analysis shown in the next section, a worst case analysis as the systematic error is expected to be biased in one direction (though the exact nature of the systematic error is unknown). It is worth mentioning that it is for the first time that an analysis on the uncertainty in DFT results has been carried out, and its impact on the simulation results has been demonstrated Sensitivity analysis For all the elementary reactions present in the new model, the rate constants k i s were varied within an order of magnitude by multiplying perturbing factors f i s ranging between 0.1 and 10 to get the perturbed rate constants k i s: k i = f i k i, 1 i n where n is the number of elementary reactions in the PAH growth mechanism. The perturbing factors f i s were generated using logarithmically distributed ran- 110

111 dom numbers between 0.1 and 10, as explained ahead. Firstly, uniformly distributed random numbers R i s between -1 and 1 were generated. Thereafter, the perturbing factors were calculated as: f i = 10 R i The purpose of generating logarithmically distributed random numbers was to achieve their uniform distribution on a log-scale in the range The perturbed rate constants were then used to evaluate the process rates in the simulation. 200 sets of perturbing factors were generated. For each set of factors, an ensemble of 200 PAH molecules was computed. The grey shaded area in Figure 4.11 shows the range in which the average C/H ratios of the computed PAHs would lie, if the rates of the reactions present in the mechanism appended with the proposed processes (new model) are varied within an order of magnitude. All the experimental data points are present well within the shaded area. It is clear that the predicted C/H ratios can be significantly affected by varying the PAH reaction rates. A similar sensitivity analysis was carried out with the old model (without the new PAH processes). In order to compare the results computed from the old and the new model, the mean values of the C/H ratios were evaluated, as shown by black and grey thin solid lines, respectively, in Figure 4.11 (see the figure inset). Note that, to evaluate the mean, all the data points (C/H ratios) obtained for different sets of perturbing factors were used in both the cases. The standard errors on the calculated means are shown by corresponding broken lines. Clearly, the mean of the C/H ratios of the PAHs computed with the new model is closer to the experimental data than the one computed with the old model. For all the sets of perturbing factors, the C/H ratios predicted by the new model were greater than the old model due to the presence of dehydrogenation reactions proposed in this work. Additionally, it is worth mentioning that the computed data points were non-uniformly distributed over the grey region (Figure 4.11) even though the mean C/H ratio was present almost in the middle of this region. With the old model 82% of the total data points, and with the new model 72% of the total data points were found to lie below the experimental data. This implies that a vast majority of the computed PAHs were rich in H atoms. Though the new pro- 111

112 Figure 4.11: Sensitivity analysis. The grey shaded area represents the range in which the average simulated C/H ratios would lie, if all the reaction rates present in the mechanism appended with the proposed processes (new model) are varied within an order of magnitude. The black circles represent the experimental data points. Solid thin black line: mean over all the simulated C/H ratios obtained using the new model (mean over the shaded area). Dashed black lines: mean ± standard error. Solid thin grey line: mean over all the simulated C/H ratios obtained with the above mentioned variation in the rates of the reactions present in the old model (without the proposed processes). Dashed grey lines: mean ± standard error. 112

113 posed PAH processes improve the predicted composition, future work is required in order to provide further improvements in the model predictions. 4.5 Conclusion This chapter presents two new PAH surface processes, which can lead to PAH dehydrogenation through ring decyclisation, followed by desorption of an alkyl chain, or rearrangement of the alkyl chains to form a 5-member ring. A new sequence of reactions for the H-mediated desorption of C 2 H 2 has been suggested. Two probable routes for each process have been provided one based on the migration of a hydrogen atom in the bay region, and the other involving bond formation between nearby C atoms in a bay region. The B3LYP functional with the G(d,p) basis set has been used for the quantum mechanical calculations on the chemical species and the transition states involved in the pathways. The rate constants for all the elementary reactions were calculated using transition state theory (TST), and were corrected to account for quantum tunnelling using the Wigner correction method. Both the processes are highly competitive with each other. A kinetic Monte Carlo simulation of the previously proposed PAH growth model (the kmc-ars model) in a C 2 H 2 flame environment was carried out by including three new processes (two new processes proposed in this work and one taken from the literature) in the PAH growth mechanism. The proposed processes improve the model prediction of the C/H ratio for large PAHs, especially, the PAHs with 70 to 200 C atoms. For most of the reactions present in the mechanism, the rate constants have been obtained form quantum calculations. The rate constants evaluated using DFT and TST can get over-predicted by a factor of about 10 in a high-temperature environment. To assess the effect of inaccuracy in reaction rate constants on kmc simulation results, a detailed sensitivity analysis has been conducted by varying the rate constants of all the reactions present in the PAH growth mechanism within an order of magnitude (by multiplying perturbing factors varying between 0.1 and 10 to the rates). A significant variation in the C/H ratios of the computed PAHs was observed with the change in reaction rate constants. Therefore, a high accuracy in the rate constants is required. 113

114 Chapter 5 Soot inception model This chapter presents a theoretical study on the physical interaction between polycyclic aromatic hydrocarbons (PAHs) and their clusters of different sizes in laminar premixed flames. Two models are employed for this study: the kmc-ars model to study PAH growth with the extended mechanism presented in Chapter 4, and a new multivariate PAH population balance model, called the PAH primary particle (PAH-PP) model to study PAH coagulation. PAH mass spectra are generated using the PAH-PP model, and compared to the experimentally observed spectra for a laminar premixed ethylene flame. Through this comparison, a correlation for the collision efficiency of PAHs is proposed. A large proportion of this chapter is published in Raj et al. [139]. By the end of this chapter, the reader should be able to find answers to the following questions: How large should a PAH be before it starts coagulating with other PAHs in a flame environment? Does the collision efficiency play an important role in proposing a soot model based entirely on the coagulation of PAHs? 5.1 Problem description One of the least well-understood areas in soot formation is the inception of soot through the formation of PAH clusters. As mentioned in Chapter 1, in the majority of soot models, the dimerisation of pyrene is assumed to nucleate a soot particle. In [129], it is shown through a sensitivity analysis that the size of the PAH as- 114

115 sumed to incept soot can significantly affect the predicted size distribution of soot particles with less than 5 nm in diameter. In fact, assuming a PAH larger than pyrene to incept soot improves the predicted size distribution of small particles. Given that the small particles are more harmful for human health, it is absolutely necessary for a model to be able to accurately predict their number density and size with a high accuracy. In [129], Singh et al. have also studied the effect of the value of collision efficiency (probability of coagulation after collision) of PAHs on soot particle size distributions. Reducing the value of collision efficiency reduces the size of soot particles present in a simulated ensemble. A very low value for the collision efficiency even converts the bimodal distribution of particle size distribution functions (PSDFs) to unimodal (i.e. removes the distinction between newly incepted soot particles and mature particles formed through coagulation). In brief, a correct size of soot-incepting PAH and a good estimate of collision efficiency are required in order to accurately predict the size distributions of soot particles of all sizes, and especially small ones. This chapter lays the foundation for a soot model based entirely on the formation, growth and coagulation of PAHs and their clusters of different sizes using kinetic Monte Carlo methods. Such a soot model will be presented, and used to conduct a theoretical study on the interaction between PAHs. The PAH ensembles required for this study will be generated computationally at different heights above the burner (HABs) in laminar premixed ethylene flames using the kmc- ARS model and an extended PAH growth mechanism. The PAH mass spectra will be generated computationally to determine the relative abundance of PAH clusters in the ensemble, and compared to the experimentally observed mass spectra for several laminar premixed flames to propose a correlation for collision efficiency. 5.2 KMC-ARS model The computational study of soot inception or PAH coagulation requires the simultaneous simulation of a large number of PAHs, in which, along with their surface growth, the PAHs are also allowed to coagulate together to form clusters. With the kmc-ars model, it becomes computationally very expensive to simultaneously simulate the surface growth and the coagulation of numerous PAHs. This is be- 115

116 cause, a large amount of structural information is required to be stored for all the PAHs in each simulation run. Therefore, in this work, for the first time, the kmc- ARS model has been combined to a PAH population balance model, which can be used to study the coagulation of PAHs computed using the kmc-ars model at different residence times. This approach is based on the separation of the two processes, surface growth and coagulation. Two assumptions are made: (a) the rates of the surface growth processes on a PAH are independent of the number of PAHs present in a stack. For example, the rate of armchair growth reaction in a stack, as shown in Figure 5.1, is assumed to be same as the rate of this reaction on an independent PAH (Phenanthrene + C 2 H 2 Pyrene + H 2 ). (b) all the reactive sites present on a PAH are equally accessible irrespective of its position or orientation in a PAH stack or cluster. Note that a PAH stack refers to a set of PAHs aligned parallel to each other, and a cluster represents a set of randomly oriented PAHs. If a PAH is present in the core of a soot particle, the reactive sites on it may not be readily accessible to the chemical species such as C 2 H 2 and H responsible for soot growth if these species are not able to diffuse to the core of a soot particle (or if the reactive sites on PAHs are hindered due to the presence of nearby PAHs). In other words, the concentrations of these chemical species inside a soot particle may not be same as their gas-phase concentrations. Therefore, this assumption on the accessibility of sites may lead to an over-prediction of the soot mass due to over-estimation of soot (PAH) surface growth. However, such information about the accessibility of a site on a PAH in a soot particle is not available. Therefore, PAH growth was simulated by uniformly selecting a site present on a PAH. It is worth mentioning that since a soot particle is of nanometer length-scale, the presence of chemical species inside a soot particle may not be limited by their mass transfer from gas-phase to within the particle. In that case, soot mass will not be affected by this model assumption. With the above assumptions, PAH ensembles were generated in different flame environments, using the algorithm described in Chapter 3. The following section provides the information about the laminar premixed ethylene flames, which were selected for this work. 116

117 Figure 5.1: Armchair growth reaction on a PAH present in a stack. The model assumes that the rate of a reaction on a PAH is independent of the number of PAHs present in a stack. Table 5.1: Flame initial conditions [64]. Flame Pressure Composition (mole %) Cold gas velocity Mass flux 10 Fuel (mbar) Fuel O 2 (cm/s) (g/s.cm 2 ) 1 80 C 2 H C 2 H C 2 H C 2 H C 2 H Flame simulation Table 5.1 lists the laminar premixed flames simulated in this work to study the growth of PAHs and the formation of their clusters such as dimers and trimers. The reason behind choosing these flames was the availability of the experimentally observed mass spectra of PAH monomers and dimers. The concentrations of the chemical species present in these flames and important for the study of PAH growth such as C 2 H 2, H, H 2, O 2 and OH, and the flame temperature profiles were not measured. This information was obtained by simulating the flames using the ABF chemical mechanism [29] along with the CHEMKIN package [221] and PREMIX [222]. New rates for the oxidation of PAHs proposed in [118] were used in the mechanism. The ABF chemical mechanism has been validated pre- 117

118 viously by comparing the experimental species profiles with the computed ones for a number of laminar premixed aliphatic flames [29, 111]. Figure 5.2 shows the computed species and temperature profiles for the flames 1 5. With increasing pressure, an increase in the maximum flame temperature was observed. The rate of O 2 consumption was also found to increase substantially with increasing pressure (see O 2 profiles in Figure 5.2). However, the profiles of other chemical species shown in this figure did not change significantly with pressure. With these simulated profiles, the PAH growth simulation was carried out using the kmc- ARS model. Pyrene was taken as the starting structure or the seed molecule for all the simulations. For each flame environment, growth of 1000 PAH molecules were simulated. The information about the composition of all the PAHs (number of C and H atoms) at different residence times (or heights above the burner, HABs) in flames were stored. This information will be referred to as PAH trajectories in flames from now onwards. Figure 5.3 shows the PAH number distribution in the ensemble of PAHs at different heights above the burner for flames 1 5. No change in the PAH number distribution was obtained with further increase in the number of PAHs from 1000 in the simulated ensemble. This shows the ensemble size used to study the PAH growth was sufficiently large. With increasing pressure, an increase in the number of large PAH molecules was observed. At HAB = 0 mm, only pyrene was present, as it was chosen as the seed molecule. Note that non-zero concentrations of all the chemical species were present at HAB = 0 due to upstream diffusion (though the concentrations of species other than fuel molecules are very low). At lower HABs ( 10 mm), PAHs with less than 150 C atoms were present in abundance. However, at higher HABs, the PAH ensembles were mostly dominated by the PAHs having C atom count in the range of To study the coagulation of these computed PAHs, a stochastic population balance model was required, and is detailed in the next section. 5.4 PAH primary particle (PAH-PP) model A multivariate PAH population balance model, named as the PAH-PP model, is developed to study the coagulation of PAHs. A kinetic Monte Carlo algorithm is employed to solve the model. It is assumed that the PAH growth processes are 118

119 (a) Flame 1 (b) Flame 2 (c) Flame 3 (d) Flame 4 (e) Flame 5 Figure 5.2: Computed profiles of the major chemical species present in flames 1 5 at height above the burner (HAB) = 30 mm. These profiles were used to study the growth of PAHs in the flame environments. 119

120 (a) Flame 1 (b) Flame 2 (c) Flame 3 (d) Flame 4 (e) Flame 5 Figure 5.3: Variation in the number of PAHs with C atom count (mass distribution) in an ensemble containing 1000 PAH molecules at different HABs for flames

121 independent of the particle structure as a consequence of the assumptions made in the kmc-ars model. The outcome of this coagulation model depends on the concentrations of the colliding PAHs, their probability of a successful collision (collision efficiency) and the frequency of PAH collision. For the two colliding PAHs a and b, the rate of coagulation R Ca,b is given by the following expression: R Ca,b = C E E F β a,b C a C b (5.1) where, C E is the collision efficiency, E F (= 2.2) is the van der Waals enhancement factor [105], β a,b is the coagulation kernel [106] (a measure of the frequency of PAH collisions in m 3 /s), and C a and C b are the concentrations of colliding PAHs a and b, respectively, in m 3. For this work, the expression for β a,b in a free molecular regime was used, which is given as [72]: β a,b = πk B T 2µ a,b (D col,a + D col,b ) 2 where, k B is the Boltzmann constant, T is the flame temperature, µ a,b is the reduced mass of the colliding PAHs, and D col,a and D col,b are the collision diameters of the colliding PAHs, as defined later. The collision diameter of a PAH monomer, D P AH can be evaluated using the following expression for peri-condensed PAHs in Å [72]: D P AH = d A 2 nc 3 where d A denotes the size of a single aromatic ring and equals Å, and n C is the number of C atoms in the PAH. For the PAH clusters with n PAH number of PAHs, the collision diameter, D col is evaluated in the following way: D col = max(d max PAH, D sphere ) (5.2) where D max PAH is the collision diameter of the biggest PAH in the cluster, and D sphere is the collision diameter of a spherical particle with the mass of PAH cluster and the density of 1.8 g/cm 3 (same as soot density). For small PAH clusters, D max PAH is larger than D sphere, and vice-versa for large clusters. 121

122 At time t, an exponentially distributed waiting time for the coagulation process to take place, τ with parameter λ is calculated, where λ is the sum of the rates of all possible coagulation events in an ensemble having n(t) number of PAH clusters [72, 106]: λ = 1 n(t) n(t) 2 i=1 j=1 R Ci,j The time for the next process is calculated as t = t + τ. Two PAH clusters are chosen from the ensemble for coagulation based on a probability calculated using their coagulation rate. In order to reduce the computational time required for the above steps, an stochastic algorithm for coagulation, described in [128, 233], was employed. After each coagulation event, the information about all the PAHs present in the ensemble was updated based on the database of PAH trajectories. The whole procedure was repeated for the desired simulation time. In order to follow the above procedure, the model requires a multi-dimensional data structure to store various information about each PAH cluster present in the ensemble such as number of PAHs in the cluster, their mass and diameter, and a unique identifier for each PAH molecule. The simulation results were obtained by averaging the results over 50 runs. For each run stochastic particles were used. This modelled sample size was found to be sufficiently large, as no change in the computed results were obtained with further increase in it. The computer program to solve the PAH-PP model was written by Markus Sander. The further details about this model will be provided in a forthcoming publication by him. 5.5 Results and discussion A PAH mass spectra is required to obtain information about the abundance of different PAHs present in a flame. Recently, experimental studies have been conducted on a number of laminar premixed flames to obtain the PAH mass spectra using photoionisation mass spectroscopy (explained in section 1.2.2) [64, 104, 234]. Through this study, for the first time, it was possible to obtain the mass spectra for the potential soot precursors, PAH stacks, which may help in under- 122

123 standing the soot formation mechanism. Such spectra of PAH clusters in the laminar premixed flames listed in Table 5.1 were computationally generated using the PAH-PP model. The following sections present the comparison between the experimentally observed and the computed PAH mass spectra PAH mass spectra In order to calculate the coagulation rate, a value of collision efficiency (C E ) is required (see equation 5.1). In the first instance, the suggested values of C E for PAHs in the literature, for example, in [98] and in [108], were used to simulate the coagulation of PAHs in the environment of flame 2. Figure 5.4 shows the computed PAH mass spectra for flame 2 when C E = 0.3, an average value of the range ( ) suggested in [98]. In the computed spectra, monomers and dimers are represented by black and grey lines, respectively. No such colour difference in the experimental data was available. However, information about certain noticeable features of the spectra was provided in the literature to distinguish monomers from dimers, and are listed later. In the experimental spectra, the concentrations of the PAHs were represented in terms of the intensity of ion signals for different PAH masses [104]. It is mentioned in [104] that these intensities are related to the number density of PAHs in flames, but no information or correlation is provided for their conversion into PAH number density. For the computed spectra, PAH number density was used to represent the concentrations of PAHs. Due to the absence of information about the PAH concentrations from experiments (specifically, for PAH dimers), only qualitative comparison between the two spectra was possible. For the qualitative comparison between the computed and the observed mass spectra, three features were selected: Position of the maxima of PAH dimers in the two mass spectra: In the experiments, the intensity of PAH dimers increased with PAH mass, and after reaching a maximum, their intensity decreased with further increase in mass. For all the flames studied in this work, the PAH mass corresponding to the maximum intensity of PAH dimers in the experimental spectra was found in the range of 900 u 1100 u. This value was compared to the PAH mass corresponding to the maximum number density of PAH dimers in the 123

124 computed spectra. Position in the spectra after which no significant amount of monomers were present: With increasing PAH mass, the concentrations of larger PAH monomers were found to decrease. After the PAH mass of 1200 u, a negligible amount of monomers was present in the experimental spectra. The computed monomer spectra are also expected to exhibit a similar behaviour. Spread of the dimer mass spectra on the either side of the maxima: In the experiments, PAH dimers with mass less than 600 u were not observed indicating that small PAHs are not able to form stable dimers in flame environments. Furthermore, a negligible amount of dimers existed after the PAH mass of around 1800 u when the flame operating pressure was above 120 mbar. Therefore, the majority of PAH dimers is expected to exist in the mass range of 600 u 1800 u in the computed spectra. It can seen in the computed spectra presented later in this chapter that these features varied significantly with the change in collision efficiency, and therefore, were suitable for comparing computed and the experimental spectra. For the case shown in Figure 5.4, due to a very high value of collision efficiency, negligible amount of PAHs remained as monomers and dimers in the computed ensemble at HAB = 30 mm. Moreover, the computed dimer spectra were found to be widely distributed over a vast PAH mass range of 500 u 4000 u (not shown here), as compared to the experimentally observed spectra (600 u 1800 u). Thereafter, C E was varied between as a function of the diameters of colliding PAHs [108]. As observed in [108], the suggested variation in C E led to very few PAH collisions, resulting in a significantly low number density for PAH dimers. These findings clearly indicate that the suggested values for C E cannot reproduce through simulations, the position of the maxima and the concentration of PAH dimers in the computed spectra. Therefore, in this work, a fitting procedure was adopted to obtain an expression for the collision efficiency, and is detailed in the next section. It should be noted that all the comparisons between experimental mass spectra and computed spectra shown in this chapter are limited to PAH monomers and dimers, as the experimental spectra for higher order PAH stacks 124

125 (a) Experimental mass spectra (b) Computed mass spectra Figure 5.4: PAH mass spectra at an operating pressure of 120 mbar (flame 2) at HAB = 30 mm with a constant collision efficiency of 0.3. In the computed spectra, PAH monomers are represented by black lines, and dimers by grey lines. Negligible amount of PAH monomers and dimers were present in the PAH ensemble at HAB = 30 mm for such a high value of collision efficiency, as they were consumed in the formation of larger PAH clusters. were not available for these flames. However, no limitation on the maximum number of PAHs that can be present in a cluster was imposed in the simulations. Collision efficiency In order to study the variation in collision efficiency, the knowledge about the flame and PAH parameters, which can significantly affect the probability of coagulation after collision, was required. In the literature, a number of theoretical studies have been conducted on PAH dimerisation. These studies were helpful in determining the parameters on which the collision efficiency may depend. For example, in [95] it is mentioned that during the PAH growth process, at some point, the van der Waals attractive potentials can become sufficiently large to hold the PAHs together in the flame environments. Therefore, the size (mass) of the PAHs is an important factor in determining its stability. The soot model developed in [108] considered the successful PAH collisions to depend on the diameters of the colliding PAHs. In [234], the PAH mass spectra in different flame environments 125

126 were observed, and it was concluded that the flame temperature may play a significant role in successful PAH collisions. A recent study by Herdman et al. [93] on PAH clusters shows that their binding energies correlate very well with the reduced mass of the colliding PAHs. The above findings suggest that the collision efficiency may depend on the flame temperature, PAH diameter and/or the PAH mass. In this study, these three parameters were individually tested to determine the ones that highly affect the collision efficiency and provide the desired variation in it, as described below. Firstly, the collision efficiency was varied with the flame temperature. At low temperatures (low HABs), only small PAHs were present in the flames in high concentrations. Therefore, collision efficiency close to zero was required to prevent their coagulation in order to avoid the depletion of such PAHs from the ensemble (in other words, to avoid the situation encountered in Figure 5.4). At high temperatures, PAHs of very different sizes were present, and therefore, assuming the same collision efficiency for all such PAHs led to the spreading of dimer spectra over a vast mass range, which is not observed experimentally. Further discussion on the variation of collision efficiency with temperature is provided later. Thereafter, the variation in collision efficiency with the average diameter of the colliding PAHs was studied. This variation led to the formation of PAH dimers having a large size difference in the constituent PAHs (for example, a benzenecoronene dimer) due to very high concentrations of small PAHs. The mass spectra produced through simulation for this case predicted the maxima of the PAH dimers at lower PAH masses, and was not consistent with the experimental results. This result suggests that the dimers of PAHs with large size difference (specifically if one of the constituent PAHs is smaller than pyrene) may not be stable in flame environments. This is also hinted at in the study by Miller et al. [96], where very low values of equilibrium constant were obtained for the formation of PAH dimers with a large size difference in the constituent PAHs. A similar conclusion was reached in a recent theoretical study on the stability of hetero-molecular PAH dimers in high temperature environments through their binding energy calculations [93]. To reduce the formation of such PAH stacks in the simulation, collision efficiency was varied with the reduced mass of the colliding PAHs, so 126

127 Figure 5.5: Two PAH (cuboid) stacks (a and b) with the same mass but different collision diameters and number of constituent PAHs. that a large difference in the masses of the colliding PAHs would produce a low reduced mass, and thus a low value of collision efficiency would be used for the rate calculation. This parameter did not differentiate between the PAH clusters with the same mass, but with different collision diameters and number of PAHs in the cluster, as shown in Figure 5.5. The variation in collision efficiency with reduced mass led to formation of distinguishable humps for PAH monomers and dimers in the computed mass spectra. However, the spectra for dimers were more widely distributed over higher PAH masses than observed experimentally. From the above observations, two main conclusions were drawn: (a) collision efficiency depends both on the mass as well as on the collision diameter of the colliding PAH clusters, so that the clusters as shown in Figure 5.5 can be differentiated; (b) a successful coagulation depends mainly on the mass M min and diameter D min of the smaller of the two colliding clusters. With these two variables for the collision efficiency, equation 5.3, was adopted, which could restrict the value of C E in between 0 and 1 in a desired way (for a satisfactory prediction of experimental mass spectra). C E = 1 ( ( 1 + exp A D3 min M min + ( M min ) )) 6 (5.3) B C Note that the correlation for C E present in the literature clearly points out that it should exhibit exponential variation [52, 235]. Equation 5.3 was inspired by the suggested correlation in the literature. In this equation, the units of diameter and mass are Å and g/mol, respectively. The fitting parameters, A, B and C in 127

128 the expression for collision efficiency were obtained by comparing the computed spectra for flame 2 with the experimental spectra. Their values were varied several times manually until a satisfactory agreement between the computed and the experimental spectra was obtained. For each set of parameters considered, the three features of the mass spectra, listed in section were compared. The parameter values of A = 2 g/(mol.å 3 ), B = 980 g/mol, and C = 10 (dimensionless) were able to satisfactorily reproduce the experimental spectra and the noticeable features for flame 2, as shown in Figure 5.6. For example, in the experiment, the maximum intensity for PAH dimers was observed at a PAH mass of around 1000 u, and in the computed spectra, maximum number density was obtained at around 1100 u (though no significant variation in the number density of PAH dimers was obtained between 1000 u and 1100 u). Also, the dimer spectra were observed to originate at around 600 u in experiments [104], and after 500 u in the simulations. The spread of the dimer spectra on the either side of the maxima was very similar in both computed and the observed spectra. No further improvement in the computed spectra could be obtained by changing the fitting parameters. It should be noted that these parameters do not carry any physical meaning, and were only used for fitting purpose. Figure 5.7 shows the range of values for the collision efficiency required for a satisfactory agreement between the computed and the observed spectra for this flame. This figure shows that the collision between two PAH clusters would always lead to coagulation if the smaller PAH cluster has mass and collision diameter, greater than 1200 u and 20 Å, respectively, as C E = 1 for all such clusters. Figure 5.8 presents a contour plot of collision efficiency. The positions of some of the commonly observed PAHs are marked in this figure. In the simulation, considerable amount of coagulation took place when the mass and collision diameter of the smaller of the two colliding PAHs were greater than 360 u and 10 Å, respectively. An example PAH monomer (C 30 H 14 ) satisfying such criteria (mass = 374 u, diameter = 10.8 Å) is shown in the figure. In [236], it is shown through theoretical calculations that coronene (mass = 300 u, diameter = 9.7 Å) may not form stable clusters at high temperatures, and therefore, may not incept soot. The approximate size for PAHs capable of forming clusters proposed above is higher than that for coronene, and therefore, is reasonable. To further substantiate this claim, theoretical calculation are required in the future 128

129 using PAH potentials to determine the smallest PAH that can form stable clusters in high temperature ( 1900 K) environments. The work on it is ongoing in our research group. The inability of PAHs smaller than the above mentioned size to form dimers can be explained in terms of the potential well depth of their interaction potential curve or their binding energy [93, 235]. In [235], through a coarse grain method and molecular dynamics on PAHs, interaction potentials between different PAH pairs were studied, and it was shown that the potential well depth or the binding energy differs with PAH pairs. In order to form a PAH dimer or higher order clusters, the internal energy of the PAH pair should be sufficiently lower than the potential well depth. In their study, an expression for the collision efficiency of PAHs as a function of temperature and potential well depth is provided. From the expression, it is clear that at a given temperature only those PAH pairs have sufficiently high collision efficiency to form PAH clusters, which have a very high potential well depth (binding energy). In [93], the binding energies for different PAH pairs were evaluated, and it was shown that the binding energy increases with increase in the reduced mass of the colliding PAHs. In other words, increasing the size of the smaller of the two colliding PAHs increases the well depth. It was concluded that only the PAH pairs with reduced mass greater than 90 have sufficient binding energies to form dimers at high temperatures. In Figure 5.8, similar results are highlighted through the dashed line. This dashed line represents the line for peri-condensed PAHs such as pyrene, coronene and circumcoronene. For two colliding PAH monomers, increasing the mass and the diameter of smaller of the two colliding PAHs increases the collision efficiency (see the dashed line). The area above this line in the figure is only accessible to PAH clusters with more than one constituent PAHs (for example, a C 38 H 16 dimer). The correlation for C E with the set of parameters obtained for flame 2 was also used to compute the spectra for the flames at different pressures (Table 5.1), and their comparison with the observed spectra is shown in Figures Figure 5.13 shows the constituent PAHs of an example computed PAH dimer with a mass of 1090 u present in flame 2. Figure 5.14 shows the variation in the number fraction of the PAH clusters with the number of PAHs present in the cluster. For a PAH cluster with i number of PAHs, the number fraction, x C,i was calculated using the following expression: 129

130 (a) Experimental mass spectra (b) Computed mass spectra Figure 5.6: PAH mass spectra at an operating pressure of 120 mbar (flame 2) at HAB = 30 mm. In the computed spectra, PAH monomers are represented by black lines, and dimers by grey lines. The position of the maxima of PAH dimers and the spread of the spectra for dimers on the either side of the maxima were well predicted. Figure 5.7: PAH collision efficiency C E as function of the mass M min and the collision diameter D min of the smaller of the two colliding PAH clusters. C E = 1 if the smaller PAH cluster has mass and collision diameter, greater than 1200 u and 20 Å, respectively. 130

131 Figure 5.8: A contour plot for the PAH collision efficiency CE. PAH coagulation starts taking place when the mass and collision diameter of the smaller of the two colliding PAH clusters become greater than 360 u and 10 A, respectively (for example, C30 H14 ), when CE The dashed line in the figure represents the line for peri-condensed PAHs. The area above this line in the figure is only accessible to PAH clusters with more than one constituent PAHs (for example, a C38 H16 dimer). Note that CE presented here is mainly applicable in high temperature combustion environments similar to those studied in this work, as, at present, the correlation does not depend on flame parameters such as temperature. 131

132 (a) Experimental mass spectra (b) Computed mass spectra Figure 5.9: PAH mass spectra at an operating pressure of 80 mbar (flame 1) at HAB = 30 mm. In the computed spectra, PAH monomers are represented by black lines, and dimers by grey lines. At low pressure, the spectra for PAH dimers were widely spread over the PAH mass. (a) Experimental mass spectra (b) Computed mass spectra Figure 5.10: PAH mass spectra at an operating pressure of 150 mbar (flame 3) at HAB = 30 mm. In the computed spectra, PAH monomers are represented by black lines, and dimers by grey lines. At high pressures ( 150), the computed spectra for PAH dimers were observed to shrink (narrow distribution over the PAH mass). 132

133 (a) Experimental mass spectra (b) Computed mass spectra Figure 5.11: PAH mass spectra at an operating pressure of 180 mbar (flame 4) at HAB = 30 mm. In the computed spectra, PAH monomers are represented by black lines, and dimers by grey lines. At high pressures ( 150), the computed spectra for PAH dimers were observed to shrink (narrow distribution over the PAH mass). (a) Experimental mass spectra (b) Computed mass spectra Figure 5.12: PAH mass spectra at an operating pressure of 220 mbar (flame 5) at HAB = 30 mm. In the computed spectra, PAH monomers are represented by black lines, and dimers by grey lines. At high pressures ( 150), the computed spectra for PAH dimers were observed to shrink (narrow distribution over the PAH mass). 133

134 Figure 5.13: Example computed PAHs (C 40 H 16 and C 48 H 18 ) present in a PAH dimer in flame 2 at HAB = 30 mm. The collision diameters of the two PAHs are 12.5 Å and 13.7 Å, and their masses are 496 u and 584 u, respectively. The collision efficiency for this PAH pair is x C,i = N C,i / i=1 N C,i, where N C,i represents the number of clusters in the ensemble with i PAHs. It can be observed in the figure that an increase in pressure increases the number of PAH clusters with large number of PAHs ( 40) in them. This is due to the increase in the number of collisions taking place between the PAHs, and the presence of larger PAHs at higher pressures. With the use of proposed correlation for C E, the computed spectra were able to predict certain trends followed by the experimental spectra. For the low pressure flame (flame 1), the computed spectra for PAH dimers were found to be very widely distributed over the PAH mass (Figure 5.9). In the experimental spectra as well, their distribution was very wide, and no clear distinction between the monomer and the dimer spectra was visible. This indicates that higher order PAH clusters did not form in high concentrations in this flame. This is also evident from Figure 5.14, where for the 80 mbar flame, clusters with more than about 40 PAHs were not obtained in the simulations. On increasing the pressure to 150 mbar (flame 3), a significant decrease in the number density of PAH dimers for PAH mass greater than 1500 u was observed in the computed as well the experimental spectra (Figure 5.10). The reason behind this was an increase in the number of PAH collisions with increasing pressure, which led to the quicker conversion of PAH dimers to higher order stacks. It can be seen in Figure 5.14 that at this 134

135 Figure 5.14: Number fraction of the clusters with different numbers of PAHs comprising them, computed at different pressures (flames 1 5). A bimodality in the distribution of cluster number fraction is observed at higher pressures. 135

136 pressure, PAH clusters with up to about 350 PAHs in them were obtained. A further increase in pressure (Figure 5.11 and 5.12) shows an overall decrease in the number density of the computed PAH dimers for all PAH masses, especially at 220 mbar, where the maximum number density of PAH dimers was less than m 3 (lowest among all the flames). This happened due to the reason mentioned above. In flame 5, clusters with around 1000 PAHs in them were obtained in simulations. Such large clusters were not obtained at lower pressures. Furthermore, with increasing pressure, the number density of PAH monomers with mass more than 1000 u were also found to decrease due to the reason explained above. Therefore, the spread of the mass spectra for PAH monomers and dimers was found to reduce with increasing pressure (due to the absence of PAH monomers and dimers with higher masses), as can be seen in Figures For all the flames studied, the maxima in the number density of computed PAH dimers were always obtained in the mass range of 1000 u to 1200 u, which is very close the experimental mass range of 900 u to 1150 u. For high pressure flames, the computed spectra for monomers and dimers were found to be broader than the observed spectra. There can be two possible reasons behind it. Firstly, the assumption of equal accessibility of all the reactive sites on the PAHs in the kmc-ars model leads to the formation of some large PAHs (with mass greater than 1000 u), which may not be present in flames. These large PAHs in the ensemble, though very low in concentration, can give rise to dimers of higher masses, leading to the broadening of the mass spectra of monomers and dimers. This shortcoming in the model, as mentioned in section 5.2, is currently unavoidable. Secondly, the gas-phase chemical mechanism at 120 mbar pressure was used for all the flames, due to the absence of mechanisms at other pressures in the range of mbar. This can also be responsible for the discrepancies between the observed and the computed spectra. It is very interesting to note that, in Figure 5.14, the increase in pressure changes the unimodal distribution of cluster number fraction to bimodal, which is a typical characteristic of particle size distribution functions (PSDFs). For bimodal PSDFs, the first mode represents nascent or newly incepted soot particles, and the second mode represents the particles formed through coagulation [129]. At 220 mbar, a minimum value for the first mode is observed for clusters with 136

137 around 10 PAHs in it. Taking the analogy from PSDFs, the PAH clusters with 10 PAHs may be regarded as nascent soot, and all the higher order PAH clusters, as mature soot particles. It is important to mention that the proposed correlation does not account for the change in C E with flame parameters such as temperature and pressure. C E can be a strong function of flame parameters, as a dimer which is not stable in flame environments (for example, when temperature 1800 K) may be stable at room temperature [99, 103, 234, 235]. Such a variation could not be captured with the available experimental data on PAH clusters, as the maximum flame temperatures varied within 50 K and the pressure varied within 0.14 bar for all the flames (see Figure 5.2 and Table 5.1). Therefore, the correlation in its present form is suitable for high temperature environments similar to those studied in this work. Further investigation, both experimental and theoretical, is required for a multi-dimensional treatment of collision efficiency, which can account for all the affecting parameters. 5.6 Conclusion This chapter presents a study on the coagulation of PAH clusters in laminar premixed ethylene flame environments. A new multivariate PAH population balance model, named as the PAH-PP model was developed to simulate the coagulation of PAHs generated computationally using the kmc-ars model. The two PAH processes - surface growth and coagulation were separated in order to reduce the computational time to simulate soot (PAH cluster) formation in flames. With the use of the PAH-PP model, the mass spectra of PAHs were generated computationally, and compared to the experimentally observed spectra. The comparison between the observed and the computed mass spectra was conduced by examining three noticeable features (a) position of the maxima of PAH dimers in the mass spectra, (b) position in the spectra after which no significant amount of monomers were present, and (c) spread of the dimer mass spectra on the either side of the maxima. It was concluded that the collision efficiency of PAHs is an important parameter, which significantly affects the position of the maxima for PAH dimers and higher order stacks, and their spread in the computed spectra. To determine 137

138 the factors on which the collision efficiency may depend, its variation with flame temperature, collision diameter, and mass of the colliding PAHs was studied. The collision efficiency was found to depend strongly on the mass and collision diameter of the smaller of the two colliding PAH clusters. By comparing the computed mass spectra with the experimental spectra for a C 2 H 4 -O 2 flame, a correlation for this efficiency (a new inception sub-model), C E was proposed. The same correlation was then used to generate the spectra for a number of laminar premixed C 2 H 4 -O 2 flames at different pressures. The position of the maxima of PAH dimers was very well predicted with the proposed correlation for all the flames. For two colliding PAHs, a very low value of collision efficiency was required to properly predict the position of the maxima of PAH dimers in the spectra, if one of them had mass less than 360 u and diameter less than 10 Å. This indicates that the collisions involving PAHs smaller than pyrene, or collisions between very large PAHs and small ones may not be successful in a high-temperature environment. The unsuccessful collision between small PAHs is also evident from the experimental spectra, as no PAH dimers were observed below the PAH dimer mass of about 600 u. The simulated number fraction of PAH clusters were also obtained for all the flames studied in this chapter. It was shown to develop bimodality with increasing flame operating pressure, which is a typical behaviour exhibited by soot particle size distribution. The two modes can help in distinguishing nascent soot particles (small PAH clusters) from the mature ones (formed mainly from the coagulation of large PAH clusters). The number fraction of PAH clusters with large number of constituent PAHs was found to increase with increasing pressure. 138

139 Chapter 6 Soot oxidation by nitric oxide in after-treatment devices This chapter introduces new reaction pathways showing the non-catalytic interaction between soot and nitric oxide (NO) for their simultaneous reduction. The reaction mechanism presented in [174] is extended by including new reactions to improve the model predictions. The energetics and the kinetics of the new reactions are studied using density functional theory and transition state theory, respectively. The kmc-ars model is used to simulate the interaction between NO and soot to form CO, N 2 and N 2 O. The simulation results are compared to the experimental findings. The computed PAH structures are analysed to determine the functional groups responsible for the decrease in soot reactivity towards NO with increasing reaction time. A large part of this chapter is published in Raj et al. [237] and Sander et al. [174]. By the end of this chapter, the reader should have answers to the following questions: How can NO molecules oxidise soot collected on particulate filters? At what temperature can this reaction take place? If a model is developed for soot-no interaction, how effectively can it predict the experimental observations? 139

140 6.1 Problem description The problems associated with soot and NO x present in the exhaust from diesel engines have already been discussed in section 1.5. One of the several methods suggested in the literature to remove these pollutants from the engine exhaust is continuously regenerating traps (CRTs) [24]. In such traps, NO and NO 2 are used to oxidise soot particles collected on the filter. The soot-no interaction is particularly interesting because this reaction takes place non-catalytically, and NO is present in highest concentration in the engine exhaust among all the NO x molecules. The rate at which soot can be oxidised by NO depends greatly on temperature. Also, soot-no reactions stop after some time in experiments. However, the exact reason behind it is not known. In order to address these issues, a model can be developed to simulate soot-no interaction, which can provide information about the reactivity of soot at different temperatures and the reasons behind the reduction in its reactivity towards NO with reaction time. For developing such a model, a detailed mechanism is required containing reactions between NO x and soot to produce CO, N 2 and N 2 O. The purpose of this chapter is to present a detailed reaction mechanism depicting the interaction between NO and soot surface. The proposed reaction pathways have been studied using density functional theory. The kmc-ars model has been used to study the oxidation of PAHs (soot precursors) employing the detailed reaction mechanism. The reactions which dominate during the NO oxidation process have been determined using this model. The resulting structures from the oxidation simulations have been analysed to determine possible reasons for the experimental observations which suggest that the reactions between soot and NO stop after a certain period of time. 6.2 Calculation details Similar to Chapter 4, the molecular structures of the stable chemical species and transition states involved in the reactions were optimised using the B3LYP hybrid functional and the G(d,p) basis set. Before using B3LYP/ G(d,p) level of theory for the theoretical calcula- 140

141 tions, the results obtained from the DFT calculations were validated by comparing them with experimental or theoretical data available for carbon-nitrogen-oxygen systems. Firstly, the reaction energy for the reaction N + NO N 2 + O was evaluated using B3LYP/ G(d,p), and was found to be 308 kj/mol. This value compares very well with the literature value of kj/mol [227]. The reaction energy involved in the removal of a CO molecule was determined using the reaction C 6 H 5 O C 5 H 5 + CO. A value of 127 kj/mol was found, which agrees reasonably well with the value of kj/mol present in the literature [227]. It is clear from these comparisons that DFT predicts, reasonably well, the reaction energies for the molecular system under investigation. 6.3 Results and discussion PAH nitric oxide interaction It is known that the chemisorption of NO on soot leads to the formation of CO, N 2 and N 2 O [165]. In order to understand the mechanism for their formation, knowledge of the composition and the reactive sites of soot particles is required. Since a soot particle is composed of PAHs, the knowledge about the reaction pathways for the interaction between soot and NO can be obtained through the study of the reactivity of NO molecules towards the sites present on PAHs. In a recently published paper by Markus Sander [174], two reaction pathways describing the chemisorption of NO on PAHs composed of zigzag sites, and the formation CO and N 2 were presented (see Figure 6.1). In brief, both the pathways involve the addition of NO molecules, leading to the removal of N 2 in subsequent steps. The remaining O atoms on the soot surface can then oxidise soot to form CO. The reaction pathways were studied using DFT and the rates for the elementary reactions were evaluated using transition state theory. The kmc-ars model was used to simulate the simultaneous reduction of PAHs and NO at zigzag sites. As observed in experiments, it was found in the simulations that the NO PAH reaction stops after some time. Figure 6.2 shows an example simulated PAH structure, which could not react further with the reaction mechanism proposed in [174]. 141

142 (a) (b) Figure 6.1: Two reaction pathways showing soot-no interaction. These pathways on zigzag sites have been taken from [174]. There can be two possible reasons for the reactions to stop: a) absence of reactive sites for the chemisorption of NO, or b) absence of reactions in the mechanism for the newly generated reactive sites and atoms such as embedded and surface N atoms (as shown inside circles in Figure 6.2), which may react further. Assuming that the reaction mechanism is incomplete, we have explored new pathways for the formation of N 2, N 2 O and CO on different types of reactive site and N atoms. As a consequence of DFT calculations on large PAHs being very computationally expensive, the smallest possible PAH model molecules fulfilling the requirements of the mechanism for each pathway have been chosen. Pathway 1 Figure 6.3 shows the energy diagram for pathway 1. This pathway requires the presence of an armchair site in between two zigzag sites. The main purpose of choosing this site combination was to study the formation of an N 2 ring on an armchair site, and to check for the possibility of the removal of such N 2 rings from PAHs. To meet this requirement, pentaphene with four active (radical) carbon atoms (CS1) was chosen as the model molecule, as shown in Figure 6.3. In this pathway, firstly, two NO molecules are chemisorbed on the zigzag sites. No transition state could be obtained for this reaction. This reaction was highly exothermic with a reaction energy of 861 kj/mol. In [174], the reaction energy for the adsorption of two NO molecules on naphthacene was reported to be 964 kj/mol. This difference in the reaction energy indicates that the stability of NO molecules on 142

143 Figure 6.2: An example simulated PAH structure, which cannot react further with the reaction mechanism proposed in [174]. This figure has been reproduced from [174]. Some sites on this structure are shown in circles, which may react further if reactions for those sites are included in the mechanism. AC: Armchair site, BY: Bay site (defined in figure 1.3). 143

144 Figure 6.3: Pathway 1: Potential energy diagram showing the formation of an N 2 molecule on a PAH, when two NO molecules are chemisorbed on two zigzag sites, and the two N atoms interact on an armchair site. For PAH reactions to take place through this pathway, an armchair site in between two zigzag sites is required (fulfilled by CS1). The aim behind studying this pathway was to check the possibility of the removal of a N 2 molecule adsorbed on an armchair site, as molecules adsorbed on armchair sites are very stable (discussed later). 144

145 Figure 6.4: N 2 ring breakage on an armchair site of a PAH molecule. Figure 6.5: CO removal from a PAH molecule. PAHs depends strongly on the orientation of the reactive zigzag sites. After NO chemisorption, one of the two N-O bonds on the PAH breaks. The two nearby N atoms present on the armchair site form a bond, creating the most stable species in this pathway, CS4 with a six member N 2 ring on it. Thereafter, one of the C-N bonds can break, forming an N 2 chain. This reaction is endothermic involving a reaction energy of 268 kj/mol. For this reaction, a transition state could not be found for such a large PAH structure (CS4). Therefore, this reaction was studied on a smaller PAH, phenanthrene, as shown in Figure 6.4 in order to obtain the rate for this reaction. After the opening of the N 2 ring (CS5), N 2 molecule can get desorbed from the PAH. This desorption was found to be exothermic with a reaction energy of 80 kj/mol. The remaining two O atoms can oxidise the PAH molecule through the formation of CO molecules. The removal of CO molecules from PAHs has already been studied in [ ], and hence the detailed mechanistic study of this reaction was not carried out in this work. Only one pathway for CO removal was studied in this work, as shown in Figure 6.5, due to reasons mentioned later in this chapter. The potential energy barrier involved in this reaction was 443 kj/mol, which matches reasonably well with the calculated values of 416 kj/mol in [160]. The difference in these values is likely due to the use of different model molecules and different levels of theory for the quantum calculations. 145

146 Figure 6.6: Pathway 2: Potential energy diagram showing the formation of an N 2 molecule on a PAH, when two NO molecules are chemisorbed on two armchair sites. The chemical species with one of the N-O bonds broken on an armchair site was not found to be stable. Therefore, N-N ring formation (CS8 CS9) took place with the simultaneous breakage of both the N-O bonds (unlike pathway 1). For PAH reactions to take place through this pathway, a zigzag site in between two armchair sites is required (fulfilled by CS7). Pathway 2 In Pathway 2, the chemisorption of NO molecules on armchair sites of a PAH molecule, and the possibility of further reactions was studied. Figure 6.6 shows the potential energy diagram along with the chemical species involved in this pathway. Dibenzo[a,l]tetracene with 4 active carbon atoms (CS7) was chosen as the model molecule. The addition of NO molecules on CS7 was exothermic giving an energy change of 890 kj/mol, which is higher than the reaction energy involved in the chemisorption of NO molecules on zigzag sites in pathway 1. To ensure that the energy released in the addition of NO on armchair sites is indeed higher than that on zigzag sites, this energy was calculated on small PAHs (shown in Figure 6.7) to minimise the effect of the relative orientations of reactive sites (as stated in section 6.3.1). The reaction energy for the addition of NO on the zigzag 146

147 (a) (b) Figure 6.7: Addition of NO on active zigzag and armchair sites of small PAHs. (a) NO addition on Naphthalene radical. (b) NO addition on Phenanthrene radical. site of Naphthalene was found to be 79 kj/mol. This energy was 198 kj/mol for the addition of NO on the armchair site of Phenanthrene indicating that the NO molecule forms a very stable structure on armchair sites [171]. Unlike pathway 1, this mechanism does not proceed with the breakage of one of the N-O bonds on the PAH, as the resulting molecule is not stable (geometry optimisation of the molecule with one of the N-O bonds of CS8 broken resulted in the formation of CS8 again). In this case, both the N-O bonds break simultaneously to form an N- N ring on the PAH (CS9). This reaction CS8 CS9 is exothermic with a reaction energy of 8 kj/mol. Thereafter, the N 2 molecule gets desorbed from the PAH. The resulting O atoms can oxidise the PAH through the formation of CO molecules. Pathway 3 In pathway 3, the interaction between two NO molecules chemisorbed on a zigzag site and an armchair site was studied. Figure 6.8 shows the energy diagram for this pathway. Benzo[a]tetracene with four active carbon atoms (CS11) were chosen as the model molecule. Only the NO molecule present on the zigzag site undergoes N-O bond breakage, which reduces the distance between two N atoms on the PAH to facilitate N-N ring formation (CS13 CS14). It is interesting to note that the potential energy barriers, E required to be overcome for the N 2 ring formation in the pathways 1 3 follow the order: E CS3 CS4 (56 kj/mol) < E CS13 CS14 (60 kj/mol) < E CS8 CS9 (205 kj/mol). This shows that the presence of NO on armchair sites increases the energy required for the formation of an N 2 ring on PAHs. Thereafter, similar to pathway 1, an N 2 chain forms on the PAH, 147

148 Figure 6.8: Pathway 3: Potential energy diagram showing the formation of an N 2 molecule on a PAH, when two NO molecules chemisorbed on a zigzag and an armchair site interact with each other. For PAH reactions to take place through this pathway, two consecutive zigzag sites are required next to an armchair site (fulfilled by CS11). The energy barrier required for the N-N ring formation in this pathway ((CS13 CS14)) is higher than the barrier for the same reaction in pathway 1 (CS3 CS4). This shows that a higher energy is required to break an N-O bond when it is present on an armchair site as compared to a zigzag site. 148

149 Figure 6.9: Desorption of N 2 chain from a PAH. which subsequently gets desorbed. The transition state involved in the desorption of N 2 from PAH (CS15 CS16) could not be found. Therefore, this reaction was studied on a smaller PAH molecule, as shown in Figure 6.9 to determine the rate for this reaction. Pathway 4 Figure 6.10 shows the potential energy diagram along with the chemical species involved in pathway 4. As mentioned before, a large number of surface N atoms were present on the simulated PAH structure (Figure 6.2), and therefore, PAH reactions were required in the mechanism for their removal. The purpose of mechanism 4 is twofold: a) to present the reactions that can take place on surface N atoms, and b) to propose a route for the formation of N 2 O. For this mechanism, a surface N atom was required on a zigzag site. Therefore, anthracene with an N atom and two radical C atoms on it (CS17) was chosen as the model molecule. Firstly, NO chemisorption on CS17 takes place, forming a 5-member N 2 O ring on the zigzag site. This type of chemisorption of NO on surface N atom is also shown in [173]. For any further reaction to take place, the energy barrier (226 kj/mol) has to be overcome. At this stage, there can be two possible ways to break the N 2 O ring, as represented by chemical species CS19 and CS21. The chain-like N 2 O structure (CS19) or the branched chain-like structure (CS21) can get desorbed from the PAH, thus releasing N 2 O in the gas-phase. The chemical species CS21 can also donate its O atom to a nearby active site on the PAH by overcoming a potential energy barrier of 142 kj/mol. The molecule CS22 formed after this O- transfer is very stable, and this highly exothermic reaction has a reaction energy of 514 kj/mol. The N 2 chain present on CS22 can get desorbed to form species CS23, which in turn can get oxidised by the O atom to release CO. 149

150 Figure 6.10: Pathway 4: Potential energy diagram showing the formation of an N 2 and an N 2 O from a surface N atom present on a PAH. 150

151 Figure 6.11: Pathway 5: Potential energy diagram showing the formation of N 2 O from embedded N atoms involved in the formation of 5-member rings on PAHs. Pathway 5 Pathway 5, as shown in Figure 6.11, is very similar to pathway 4, except that this pathway requires the presence of an embedded N atom forming a five membered ring on an armchair site of a PAH molecule. Tetraphene with an embedded N atom and two radical C atoms on it (CS24) was chosen as the model molecule. The embedded N atom on PAH is very stable and a high energy barrier of 221 kj/mol has to be overcome to add an NO molecule to it. This results in the formation of a 6-member N 2 O ring (CS25). The breakage of this N 2 O ring to form a branched N 2 O chain (CS26) requires an energy barrier of 284 kj/mol to be overcome. This branched N 2 O chain can then get desorbed from the PAH. The high activation energies required in this pathway makes it difficult to occur at low temperatures, as will be shown later. 151

152 Figure 6.12: Pathway 6: Potential energy diagram showing the chemisorption of NO molecules on a bay site of a PAH molecule, and the transfer of O atom to a nearby C atom. Pathway 6 It was found from the kmc simulations in [174] that CO removal from soot surface creates a number of bay sites. These sites may be occupied by NO molecules. Pathway 6, as shown in Figure 6.12, involves the addition of NO at bay sites. To study this pathway, indeno[1,2,3,4-pqra]tetraphene with two radical C atoms (CS28) was chosen as the model molecule. It can be seen in Figure 6.12 that the first step of NO chemisorption requires a very high energy barrier of 222 kj/mol to be overcome indicating that the reaction would mainly take place at high temperatures. After the addition of NO on PAH, the O atom can get transferred to a nearby carbon radical, thus creating an embedded N atom in a 6-member ring. This O- transfer reaction is highly exothermic with a reaction energy of 238 kj/mol. The transferred O atom can cause the removal of a CO molecule. Pathway 7 It has been shown in pathway 6 that embedded N atoms in a six member ring can get formed through the chemisorption of NO molecules at bay sites. Another reaction that can lead to the formation of embedded N atoms is shown in Figure

153 Figure 6.13: Formation of an embedded N atom from a surface N atom in the bay region of a PAH molecule. In [172], the vertical addition of NO on a PAH was studied leading to the desorption of N 2 O. However, after the addition of NO on PAH, several possibilities can arise. These possibilities or routes have been studied in pathway 7, as shown in Figure Specifically, the reactions leading to the removal of embedded N atoms through the formation of N 2 or N 2 O were explored. Benzo[c]phenanthrene with an embedded N atom in the bay region and two radical C atoms (CS31) was used as the model molecule. In this case, chemisorption of NO leads to the formation of two types of chemical species depending upon the orientation of the NO molecule. The vertical addition of NO on PAH forms CS35, and parallel addition of NO to the reactive site forms CS32. Out of these two chemical species, CS32 is more stable due to the higher reaction energy involved in its formation, as can be seen in Figure After the formation of CS32, similar to pathway 1, the N-O bond can break to form CS33. This breakage leads to the formation of an N 2 chain on PAH (CS34), with one N embedded in the PAH molecule. Such an embedded N 2 chain is stable, as its removal requires an energy barrier of 170 kj/mol to be overcome. The vertical addition of NO on CS31 leads to the formation of CS35 (as denoted by broken lines). After CS35 is formed, there are two possible routes: O-transfer to a nearby C atom (CS33), or removal of N 2 O (CS36). The chemical species CS33 is more likely to form over CS36 at low temperatures due to a low energy barrier of 35 kj/mol. After the formation of CS33, the N 2 molecule can get desorbed. 153

154 Figure 6.14: Pathway 7: Potential energy diagram showing the reactivity of embedded N atoms involved in the formation of 6-member rings on PAHs towards NO molecules. The low energy barriers involved in this pathway (except for N 2 O removal) indicate that embedded N atoms can be removed in the form of N 2 at low temperatures Reaction rates The rate constants of the elementary reactions involved in the new proposed pathways are listed in Table 6.1. Table 6.1: Elementary reaction rate constants in the form: AT n exp( E/RT). The units are kcal, K, mol, cm and sec. p.w. represents the rate constants calculated in the present work using B3LYP/ G(d,p). No. Reaction A n E Ref. Pathway 1 1 CS1 + 2NO CS2 Infinitely fast [174] 2 CS2 CS [174] 3 CS3 CS p.w. -3 CS4 CS p.w. 4 CS4 CS p.w. -4 CS5 CS p.w. 5 CS5 CS6 + N p.w. -5 CS6 + N 2 CS p.w. 154

155 No. Reaction A n E Ref. Pathway 2 6 CS7 + 2NO CS8 Infinitely fast [174] 7 CS8 CS p.w. -7 CS9 CS p.w. 8 CS9 CS10 + N p.w. -8 CS10 + N 2 CS p.w. Pathway 3 9 CS11 + 2NO CS12 Infinitely fast [174] 10 CS12 CS [174] 11 CS13 CS p.w. -11 CS14 CS p.w. 12 CS14 CS p.w. -12 CS15 CS p.w. 13 CS15 CS16 + N p.w. -13 CS16 + N 2 CS p.w. Pathway 4 14 CS17 + NO CS18 Infinitely fast [174] 15 CS18 CS p.w. -15 CS19 CS p.w. 16 CS19 CS20 + N 2 O p.w. -16 CS20 + N 2 O CS p.w. 17 CS18 CS p.w. -17 CS21 CS p.w. 18 CS21 CS p.w. -18 CS20 CS p.w. 19 CS21 CS p.w. -19 CS22 CS p.w. 20 CS22 CS23 + N p.w. -20 CS23 + N 2 CS p.w. Pathway 5 21 CS24 + NO CS p.w. -21 CS25 CS24 + NO p.w. 22 CS25 CS p.w. -22 CS26 CS p.w. 23 CS26 CS27 + N 2 O p.w. -23 CS27 + N 2 O CS p.w. Pathway 6 24 CS28 + NO CS p.w. 155

156 No. Reaction A n E Ref. -24 CS29 CS28 + NO p.w. 25 CS29 CS p.w. -25 CS30 CS p.w. Pathway 7 26 CS31 + NO CS32 Infinitely fast [174] 27 CS32 CS [174] 28 CS33 CS p.w. -28 CS34 CS p.w. 29 CS31 + NO CS35 Infinitely fast [174] 30 CS35 CS p.w. -30 CS33 CS p.w. 31 CS35 CS36 + N 2 O p.w. -31 CS36 + N 2 O CS p.w. CO removal reaction 32 C 6 H 5 O C 5 H 5 + CO [159] 33 C 18 H 8 O 2 C 18 H 8 O + CO [238] 34 C 14 H 7 O C 13 H 7 + CO p.w. It is worth mentioning that the Wigner correction factor varied between 1.5 and 1 in the temperature range of K for all the reactions, and it remained close to 1 for T > 1000 K. The rate constants for some of the elementary reactions not studied in this work were taken from the literature (these are also provided in Table 6.1). One of the principal steps in all the pathways is the removal of CO molecules from PAHs. In [159], the rate constant for the reaction C 6 H 5 O C 5 H 5 + CO (also shown in Figure 6.15a) was determined through a shock tube experiment on phenyl oxidation in the temperature range of K. The rate constants measured in this work are readily used in soot growth models [27, 239]. Recently, Sendt et al. [238, 240] studied the oxidation of PAHs by O 2 in detail using B3LYP/6-31G(d) level of theory, and theoretically evaluated the rate constant for the removal of CO from a model PAH molecule, as shown in Figure 6.15b. The rate constant proposed in [240] is much lower than the one proposed in [159]. Due to this discrepancy in the literature, the rate for CO removal was evaluated in this work. Figure 6.16 provides the comparison between the rate constants for this reaction from the literature and the rate constant evalu- 156

157 (a) (b) Figure 6.15: (a) CO removal reaction studied experimentally in [159]. (b) CO removal reaction studied using DFT in [240]. ated in this work. It can be seen in this figure that the rate proposed in this work agrees more closely with the rate of Sendt et al. [240]. This is due to similar levels of theory used to determine the rate constants (B3LYP/6-31G(d) in [240] and B3LYP/ G(d,p) in this work) KMC simulations As mentioned in section 6.3.1, the kmc-ars model was successfully applied in [174] to simulate the simultaneous reduction of PAH and NO. The reaction mechanism used in the previous work has been extended here by including the PAH reactions present in pathways 1 7. As mentioned in [174], the PAH reactions were assumed to be irreversible, as some of the backward reactions required the concentrations of gas-phase species such as CO, N 2, and N 2 O, which were unavailable. A detailed kinetic modelling of soot NO reduction is required by using a chemical mechanism and a chemistry solver such as CHEMKIN [221] in order to determine the concentrations of the gas-phase species (for example, CO, N 2 and N 2 O) formed during the reactions. Such a detailed analysis is beyond the scope of this work, as the main aim of this study is to improve the mechanistic and fundamental understanding of the interaction between NO and soot. With the detailed PAH NO mechanism, the PAH model was used to study the formation of CO, N 2 and N 2 O. Figure 6.17 shows the substrate molecules used in this work. In [174], only structure 1 was used as the substrate molecule. An example PAH in Figure 1.3 and the statistical study in Chapter 3 show that the PAHs comprising a soot particle can have different types of reactive sites on them. As shown in Figure 6.17, structure 1 mainly involves zigzag sites, struc- 157

158 Figure 6.16: Comparison of the rate constants for CO removal from PAHs present in the literature with the one evaluated in this work. 158

159 (a) Structure 1 (b) Structure 2 (c) Structure 3 Figure 6.17: Substrate PAH structures with different numbers of reactive sites (armchairs (AC) and zigzags (ZZ) and bays (BY)) to study soot NO interaction. Number of sites of type x = N x. (a) N ZZ = 40, N AC = N BY = 0. (b) N ZZ = 24, N AC = 16, N BY = 0. (c) N ZZ = N AC = 12, N BY =

160 ture 2 consists of zigzag and armchairs sites and structure 3 consists of zigzag, armchair and bay sites on its edge. The simulation results were obtained for all the three substrate structures. The simulations were carried out in two different NO environments: Environment 1 [146] NO concentration was kept constant at 1500 ppm, and the temperature was varied between 300 o C and 900 o C linearly at the rate of 5 o C/min. Therefore, the total reaction time was 120 min; Environment 2 [165] NO concentration was taken to be 500 ppm, and the temperature was held constant (isothermal conditions). The simulations were carried out at 4 different temperatures: 650 o C, 750 o C, 850 o C and 950 o C in order to study the effect of temperature on the PAH oxidation rate, and the formation of the major product species CO and N 2. All the simulation results presented in this chapter were evaluated using all the three substrate molecules. For each substrate, 300 simulation runs were carried out. If not mentioned, the presented results were obtained by taking an average over the simulation results obtained for all the substrate molecules. In all the cases studied here, simulation was found to stop after some time. An attempt has been made to identify the molecular functional groups present on the final PAH structures that prevent the further oxidation of PAHs. CO desorption rate As shown in the previous section, three different rate constant are available for the desorption of CO from the PAHs. In [146], temperature programmed reaction between carbon black and NO in the absence of O 2 was carried out at a heating rate of 5 o C/min (NO environment 1 in section 6.3.3). It was observed that CO removal took place from the soot surface only after the temperature increased above 873 K (600 o C). This information was used to choose a rate constant among the three, as described below. The kmc simulations were carried out in the NO environment 1 on the three substrate molecules using the three proposed rate constants. Figure 6.18 shows the variation in the fraction of NO converted to N 2, N 2 O and CO with temperature, and with different rate constants for CO removal. This fraction X m was calculated as: X m = 2 N m /N NO, where N m is the average number of molecule m released from PAHs, N NO is the average number of NO molecules chemisorbed on PAHs, and m is N 2 or N 2 O. For CO molecules, 160

161 Figure 6.18: Fraction of NO chemisorbed on PAHs converted to CO, N 2 and N 2 O. The species profiles with superscript (1) were obtained with the rate constant for CO removal proposed by Frank et al. [159], those with superscript (2) were obtained with the rate constant proposed by Sendt et al. [160], and those with superscript (3) were obtained with the rate constant proposed in this work. 161

162 Figure 6.19: Comparison of the temperature at which the desorption of CO molecules from soot starts taking place in experiments in NO environment 1 [146] with the temperatures obtained through kmc simulations with different rates for CO removal. Frank et al.: Temperature for CO removal obtained with the rate constant of Frank et al. [159]. Sendt et al.: Temperature obtained with the rate constant of Sendt et al. [160]. Present work: Temperature obtained with the rate constant proposed in this work. X CO = N CO /N NO (as only one NO is involved in producing a CO molecule). It can be seen in Figure 6.18 that with the CO desorption rate given in [159], CO formation starts taking place at a temperature below 600 K, while with the other rate constants, CO removal does not take place before 800 K. Figure 6.19 shows the temperatures at which the formation of CO starts taking place with the three different rate constants, and their comparison with the experimentally observed value. With the rate constant proposed in [160], CO removal from PAHs started at around 840 K. This value agrees reasonably well with experiments, but the amount of CO removed was very low (Figure 6.18). In [146], in 120 minutes of 162

163 reaction time, NO concentration in the gas-phase decreased by about 500 ppm, and about 400 ppm of CO were produced. This gives an approximate amount of the NO molecules converted to CO as 80%. However, with this rate, only about 15% of the NO molecules chemisorbed on PAHs were converted to CO in 120 minutes. The rate constant evaluated in this work is slightly higher than the rate of [160]. With this rate, CO desorption started taking place at around 820 K, which is reasonably close to the experimental value. The slight difference can be due to the model assumption of irreversibility of the PAH reactions. Also, at the end of 120 minutes of simulation time, around 45% of the adsorbed NO got converted to CO, which is closer to the experimentally observed fraction than the previous case. The rate constant for the chemisorption of NO molecule at some of the reactive sites on PAHs were assumed to be infinitely fast (see Table 6.1), as transition state could not be found in those cases [174]. Due to this, substrate molecules get covered with NO molecules in around 0.1 sec. Since the rates for the reactions involving N atoms are very fast, the removal of N 2 and N 2 O from PAHs starts taking place at low temperature. This may not happen in practical conditions, and therefore the temperature at which the formation of N 2 starts cannot be compared to the experiments. At the end of 120 minutes, the fraction of NO converted to N 2 was around 65% in experiments, and around 40% in simulations. Section lists some of the possible reasons behind the under-prediction in the conversions of NO to N 2 and CO found in the simulations. As observed in experiments [152, 165], the formation of N 2 and N 2 O takes place simultaneously. Out of the three routes suggested in this work for the formation of N 2 O on soot surface (in pathways 4, 5 and 7), only those suggested in pathways 4 and 7 led to N 2 O formation at low temperatures. It is evident from the simulation results shown above that the rate constant for CO desorption reaction proposed in this work predicts the experimental results better than the rate constants present in the literature. Therefore, the simulation results shown in the rest of this chapter were evaluated with the new rate constant. 163

164 Reactive sites It is shown experimentally in [241] that the reactivity of soot towards NO depends strongly on their internal structure. In their study, four carbonaceous materials carbon black, activated carbon, fullerene black and graphite were oxidised using NO. Qualitatively, similar trends were shown by all the materials. However, an appreciable variation in the amount of NO converted on soot surface was observed. There may be various reasons behind it such as the difference in the structural arrangement of PAHs in soot, difference in the reactive sites present on the PAHs and the difference in the amount of impurities present in the particles. Since, in this work, single PAH molecules were used to study soot NO interaction, the effect of internal structural variation cannot be studied. However, the effect of the change in reactive sites on PAHs can be studied with the PAH model. The kmc simulations were carried out in NO environment 1 on the three structures shown in Figure 6.17 individually. Figure 6.20 shows the change in the fraction of NO converted to N 2 and CO with the change in reactive sites on PAHs. The highest conversion was found with structure 1 and the lowest with structure 3. Clearly, the stability of NO on armchair sites and the lower reactivity of NO towards bay sites makes structure 3 least desirable for NO conversion. The zigzag sites show maximum reactivity towards NO molecules. Figure 6.21 shows the quantitative comparison of the conversion of NO molecule chemisorbed on different PAH substrates to CO and N 2 with the experimental findings in NO environment 1 (as mentioned in section 6.3.3). It can be seen in this figure that the conversion of NO to CO and N 2 in the simulations on structure 1 were closer to the experimental observations than the other cases. The change in the fraction of NO converted to CO and N 2 with the change in site types on PAHs can be one of the reasons for their under-prediction in the previous section, if the soot samples used in experiments in [146] were rich in zigzag sites. For all types of reactive site, formation of N 2 took place before the formation of CO, which is in agreement with the experimental observations [146]. The presence of N and O atoms on soot particles from before the start of the experiments (as impurities) may also explain the model under-prediction. Another reason for this under-prediction may be the use of incomplete mechanism for the simulations. For example, no reac- 164

165 Figure 6.20: Effect of the presence of different types of reactive sites on a PAH molecule. The presence of armchair and bay sites on a PAH molecule causes a decrease in the formation of CO. This is due to the formation of a very stable functional group when NO gets chemisorbed on armchair sites, and low reactivity of NO towards bay sites at low temperatures. 165

166 Figure 6.21: Comparison of the experimentally observed conversion of NO to CO and N 2 with the simulation results obtained for different substrate PAH molecules. The first stack represents the experimental results observed in [146]. The stacks 2 4 represent the simulation results obtained on the substrate structures 1 3, respectively. The fifth stack represents the simulation results averaged over the three substrate structures. The error bars show the confidence interval of 99.9% on the computed mean values. 166

167 tions are present in the mechanism for the formation of CO 2, which is observed in experiments. This highlights the possibility of the further extension of this mechanism. Temperature effects In [165], the effect of temperature on the formation of CO and N 2 was studied experimentally in NO environment 2 (isothermal conditions). It was observed that with increasing temperature, the number of O atoms remaining on soot surface decreased, and the number of N atoms increased for a given reaction time. In this work, the number fractions of N and O atoms present on the PAH were tracked in the kmc simulations at four different temperatures (650 o C, 750 o C, 850 o C and 950 o C), and are shown in Figure The number fraction for surface atoms X SA were evaluated as X SA = N SA /N NO, where N SA is the average number of surface atoms, N NO is the average number of NO molecules adsorbed on the PAHs. It can be seen in this figure that the simulation results are qualitatively in agreement with the experimental results. In this case, quantitative comparison cannot be carried out due to the absence of information about the adsorbed NO molecules on the soot surface in experiments. At all the temperatures studied, the number fraction of N atoms remaining on the PAH varied within a small range of 0.5 to 0.6, i.e. around 50-60% of N atoms from NO remained on the PAH. This agrees reasonably well with the measurements of Reichert et al. [154], where 40-63% of N atoms were found to remain on the soot surface in soot NO experiments. In Figure 6.22, a significant change in the number fraction of O atoms, and a noticeable change in the number fraction of N atoms on the PAH were obtained with increase in the temperature from 650 o C to 950 o C. This indicates that some of the reactions in the chemical mechanism become active only at high temperatures. This is also evident from Figure 6.23, in which the computed PAH structures at two different temperatures after a simulation time of 120 mins are shown. At 650 o C, the PAH structure is covered with O atoms, as CO desorption does not take place very often at this temperature. After some reaction time, the soot NO reaction stops due to the formation of functional groups which are very stable such as embedded N and NO, and the absence of sites available near the reactive atoms such as surface 167

168 Figure 6.22: Number fraction of N and O atoms present on PAH surface at different times and temperatures (the number fractions were calculated as the ratio of the number of surface atoms to the number of NO molecules added). The increase in temperature causes number fraction of O atoms to decrease due to increase in CO removal from PAHs, and number fraction of N atoms to increase due to increase in the formation of stable C-N complexes such as NO at bay sites. 168

169 (a) (b) Figure 6.23: Example computed PAH structures obtained at time, t = 7200 sec in isothermal conditions, when the concentration of NO was 500 ppm. (a) Temperature = 650 o C, (b) Temperature = 950 o C. Structure 2 (Figure 6.17) was chosen as the substrate PAH structure for simulation at both the temperatures. The functional groups which were responsible for the reduced reactivity of PAHs at two different temperatures are shown inside grey circles. 169

170 N atoms for NO addition. At this temperature, there were five main functional groups, as shown inside grey circles and numbered in Figure 6.23a, that prevented further addition of NO on PAH 1) six-member NO ring; 2) embedded N atom in a 5-member ring; 3) surface N atom; 4) surface O atom; 5) bay site. With increase in temperature, the computed PAH structure changed significantly. Figure 6.23b shows the functional groups present on PAHs at 950 o C inside grey circles, which were responsible for the reduced reactivity of soot 1) six-member NO ring; 2) embedded N atom in a 5-member ring; 3) embedded NO in bay sites; 4) surface O atom; 5) embedded N atom in a 6-member ring; 6) surface N atom; 7) bay site. At all the temperatures, some of the surface N atoms were found to be nonreactive due to the absence of nearby reactive sites to aid the further addition of NO molecules. At 950 o C, the amount of surface O atoms were much less than their amount at 650 o C due to the increase in PAH oxidation rate through CO removal. This is evident from Figure With increase in temperature, the initial rate of carbon oxidation increases. At 650 o and 750 o, the rate of oxidation is very slow. However, at higher temperatures, most of the O atoms present on the PAH are removed through the formation of CO in less than 2000 s. The oxidation rate decreases with time as the number of removable O atoms decreases. For example, the O atoms present in the embedded NO on a bay site or in a 6-member NO ring are difficult to remove even at high temperatures (when none of the reactions proposed in pathways 2 and 3 on 6-member NO rings can take place due to the absence of nearby NO rings with desired orientations for further reactions). The O atoms in 5-member NO rings are able to oxidise PAHs, as the N-O bond can break easily. The computed structures in Figure 6.23 show that the PAH becomes inactive earlier at low temperatures than at high temperatures. This is because some of the reactions present in the chemical mechanism do not take place at low temperatures, even if the reactive sites required for them to take place are available. Figure 6.25 presents the average counts of some of the principal reactions taking place on PAHs at different temperatures. The PAH reactions corresponding to the numbers present on the X-axis in this figure are explained in the caption. The average count of N 2 molecules formed by surface N atoms on PAHs (reaction 1) do not change significantly with temperature. However, N 2 formation from embedded N atoms increases with increasing temperature (reaction 2). Similar behaviour 170

171 Figure 6.24: Oxidation rate of carbon atoms present in PAHs at different temperatures, calculated as the change in C atom count per unit change in time ( C ). A significant increase in the oxidation rate was observed t when the temperature increased from 650 o to 950 o. 171

172 Figure 6.25: Average counts of some of the principal reactions that took place on PAHs. Reaction 1 total N 2 removal from surface N atoms (mechanisms 1 3 and those proposed in [174]); Reaction 2 N 2 removal from embedded N atoms (mechanism 7); Reaction 3 N 2 O removal via mechanism 4; Reaction 4 N 2 O removal via mechanism 5; Reaction 5 N 2 O removal via mechanism 7; Reaction 6 embedded NO formation via mechanism 6; Reaction 7 O transfer on PAH via mechanism 7; Reaction 8 total CO removal. The formation of N 2 and CO dominates at all the temperatures. 172