Stochastic modelling of the growth of carbonaceous materials
This thesis investigates the processes and morphologies involving key molecules that constitute carbonaceous materials, namely polycyclic aromatic hydrocarbons (PAHs), by applying a detailed particle model solved with a stochastic numerical method. In particular, a Kinetic Monte Carlo (KMC) algorithm is used to study the time-dependent transformations of PAHs in a reactive chemical environment, and thus the model is referred to as a KMC model. Numerical techniques to improve the stochastic simulation of PAHs are proposed. Regarding the PAH transformations, special emphasis is given to processes that integrate or remove curvature, as the morphology of PAHs has direct consequences on the carbonaceous materials they subsequently form. A new methodology to calculate the process rates in KMC models of PAH growth is developed. The methodology uses a combination of the steady-state and the partial-equilibrium approximation. Comparisons of the results obtained with the new methodology show good agreement with those provided by simulations using a detailed chemical mechanism under conditions relevant to flames (temperatures between 1000 and 2500 K, equivalence ratios between 0.5 and 10). The new methodology is used to calculate the rate of different stochastic processes in KMC simulations of PAH growth of premixed ethylene-oxygen flames. The results of the KMC model with the new methodology are consistent with the concentrations of species calculated using a detailed chemical mechanism for the growth of small PAHs. An algorithm to efficiently simulate the migration of partially-embedded five-member rings in PAHs is proposed. The algorithm defers the update of the computational carbonaceous structure whilst successive migration processes are sampled and is thus called the deferred update algorithm. The exactness and computational performance of the deferred update algorithm are investigated. A comparison of the algorithm with one in which the structure of the molecule is updated after each process is included. The deferred update algorithm is exact in the sense that it produces the correct sites in the migration of partially-embedded five-member rings. The computational time saved by the deferred update algorithm is proportional to the number of deferred steps and is, on average, observed to be two orders of magnitude faster than the reference algorithm. A KMC model that includes processes to integrate curvature due to the formation of five- and seven-member rings is used to simulate PAHs growing in lightly sooting ethylene and acetylene counterflow diffusion flames. New processes to form seven-member rings and to embed five-member rings via hydrogen-abstraction-acetylene-addition and bay closure reactions are included for the first time. The mass spectra of PAHs that are predicted by the model are compared against experimental data, and the distribution of embedded five-member rings and seven-member rings is studied as a function of spatial location, molecule size and frequency of events sampled in the simulation. The number of events and proportion of PAHs containing embedded five-member rings and seven-member rings is analysed at the end of the simulation domain. The formation of seven-member rings and the embedding of five-member rings is shown to be a competitive process. Both types of rings are observed more frequently at longer residence times. The growth of carbonaceous materials is studied using a KMC model that captures the growth and oxidation of six-member and partially-embedded five-member rings. Circumcoronene molecules are grown at 1500 K and 1 atm in the presence of varying mole fractions of atomic and molecular oxygen and constant mole fractions of hydrogen and acetylene. Four regions of carbon growth associated with different carbonaceous products a􀀀re identified. Graphene is formed in the presence of high mole fractions of atomic oxygen (10−4 < XO ≤ 10−2). Fullerenes are formed in the presence of low mole fractions of atomic oxygen and high mole fractions of molecular oxygen (XO ≤ 10−4) and (10−2 < XO2 ≤ 10−1). Low mole fractions of both atomic and molecular oxygen (XO ≤ 10−4 and XO2 ≤ 10−2) result in structures that become curved as simulation time progresses. The highest mole fractions of atomic oxygen (XO > 10−2) produce small structures. The production and consumption of partially-embedded five-member rings are suggested to explain the formation of the observed structures. The oxidation of partially-embedded five-member rings produces sites that grow into graphenic structures. Formation and subsequent embedding of partially-embedded five-member rings result in curved structures that resemble fullerenes. These findings suggest that different carbonaceous materials can be synthesised by varying the concentration and type of oxidising species.
Kinetic Monte Carlo, Graphene, Fullerenes, Detailed particle model, Carbonaceous nanoparticles, Soot
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