A statistical approach to develop a detailed soot growth model using PAH characteristics Abhijeet Raj, Matthew Celnik, Raphael Shirley, Markus Sander, Robert Patterson, Richard West, Markus Kraft ∗ Department of Chemical Engineering, Cambridge University, New Museums Site, Pembroke Street, Cambridge CB2 3RA, UK article info abstract Article history: Received 4 July 2008 Received in revised form 27 October 2008 Accepted 15 January 2009 Available online 11 February 2009 Keywords: PAH Soot Aromatic site Kinetic Monte Carlo Simulation Modelling A detailed PAH growth model is developed, which is solved using a kinetic Monte Carlo algorithm. The model describes the structure and growth of planar PAH molecules, and is referred to as the kinetic Monte Carlo–aromatic site (KMC-ARS) model. A detailed PAH growth mechanism based on reactions at radical sites available in the literature, and additional reactions obtained from quantum chemistry calculations are used to model the PAH growth processes. New rates for the reactions involved in the cyclodehydrogenation process for the formation of 6-member rings on PAHs are calculated in this work based on density functional theory simulations. The KMC-ARS model is validated by comparing experimentally observed ensembles on PAHs with the computed ensembles for a C 2 H 2 and a C 6 H 6 flame at different heights above the burner. The motivation for this model is the development of a detailed soot particle population balance model which describes the evolution of an ensemble of soot particles based on their PAH structure. However, at present incorporating such a detailed model into a population balance is computationally unfeasible. Therefore, a simpler model referred to as the site-counting model has been developed, which 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, which is used to develop correlations and statistics in different flame environments which describe such PAH structural information. These correlations and statistics are implemented in the site-counting model, and results from the site-counting model and the KMC-ARS model are in good agreement. Additionally the effect of steric hindrance in large PAH structures is investigated and correlations for sites unavailable for reaction are presented. © 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved. 1. Introduction There is general consensus in the literature that soot parti- cles are formed from polycyclic aromatic hydrocarbons (PAHs), the growth of which is directly linked to the formation of soot parti- cles [1]. It was proposed in [2] that the smallest aromatic com- pound, benzene is formed in a flame by aliphatic molecules and radicals that are generated by the pyrolysis of fuel molecules [3]. Recent studies on the flames of cyclic hydrocarbons such as cyclo- hexane [4], and aromatic and alkyl substituted aromatic hydrocar- bons [5,6] show that the formation of benzene is not restricted to the presence of aliphatic molecules or radicals. For example, in a cyclohexane flame, benzene can form by the dehydrogenation of fuel molecules [4]. In the higher aromatic flames such as naph- thalene flame, the larger PAHs can form directly by the PAH addi- tion reactions and cyclodehydrogenation process [5]. A theoretical study on the addition of two five-member rings to form naphtha- lene, indene and benzene conducted by Wang et al. [7] suggests * Corresponding author. E-mail address: mk306@cam.ac.uk (M. Kraft). another mechanism for the PAH formation. These studies clearly show that the pathway for the formation of PAHs in a flame is strongly dependent on the structure of the fuel molecules. Once a PAH molecule forms, it can grow by: (a) the hydrogen-abstraction– carbon-addition (HACA) mechanism [3,8], involving addition of acetylene (C 2 H 2 ) at aromatic radical sites; and (b) PAH addition reaction, involving addition of a PAH/PAH radical over another to form biaryls [5]. To determine the geometry of PAHs present in soot particles, a number of morphological studies have been conducted in the past on soot generated from different sources, like flames and en- gines [9–11]. These studies reveal that soot particles mainly consist of planar PAH molecules. It is well known that a soot particle is composed of primary particles linked together to form a fractal ag- gregate [12,13]. High Resolution Transmission Electron Microscopy (HRTEM) images of soot particles show that the primary parti- cles are near-spherical in shape, and are crystalline near the outer edge. This crystallinity arises due to stacking of planar PAHs to form parallel atomic layers and their alignment along the periph- ery of primary particles [9–11,14]. However, the nuclei of primary particles are amorphous in nature. The presence of non-crystalline 0010-2180/$ – see front matter © 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2009.01.005