The aim of this work is to present a new detailed multivariate population balance model to describe the aerosol synthesis of silica nanoparticles from tetraethoxysilane (TEOS). The new model includes a chemical representation of the silica particles to facilitate a detailed chemical description of particle processes. Silica nanoparticles are formed by the interaction of silicic acid monomers (Si(OH)4) in the gas-phase as reported in a previous study. A multidimensional population balance model is developed where each particle is described by its constituent primary particles and the connectivity between these primaries. Each primary, in turn, has internal variables that describe its chemical composition, i.e., the number of Si, free O and OH units. Different particle processes, such as inception, surface reaction, coagulation, sintering, and intra-particle reactions, are formulated from first-principles that alter the particle ensemble and are two-way coupled to the gas-phase. The free parameters in the model are estimated by fitting the model response to experimental values of collision and primary particle diameters using low discrepancy Sobol sequences followed by the simultaneous perturbation stochastic approximation algorithm. The simulation results are finally presented at different process conditions. A strong dependence of particle properties on process temperature and inlet concentration is observed. The desirable operating conditions for different industrial applications are also highlighted. This work illustrates the significance of adopting a multidimensional approach to understand, and hence control, complex nanoparticle synthesis processes.

This work proposes a kinetic model and an inception pathway for the flame synthesis of silica nanoparticles from tetraethoxysilane (TEOS). The kinetic model for the decomposition of TEOS is developed by generating reactions involving species that were reported in high concentrations at equilibrium. Flux and sensitivity analyses are then performed to identify the main reaction pathways. The parameters for these reactions are systematically fitted to experimental data using low discrepancy (LD) sequences and response surfaces. The main product of TEOS decomposition is deduced to be silicic acid (Si(OH)4). To increase computational efficiency, the kinetic model has been reduced by determining the level of importance (LOI) of each species and retaining only the important ones. This reduced kinetic model is then coupled to a detailed population balance model using an operator splitting technique. New particle inception and surface growth steps have been incorporated into the particle model in which particles form and grow by the interaction of Si(OH)4 monomers. Coagulation and sintering of particles are also included in the model and the material dependent sintering parameters have been determined by fitting the model to experimental values of collision and primary particle diameters using LD sequences. The particle size distributions and computer-generated TEM-style images have been generated and good agreement with experiments is observed. The gas-phase reactor composition and the temporal evolution of particle size at different temperatures are also presented.

We use a stochastic approach in order to investigate the production and evolution of aerosols in Titan's atmosphere. The simulation initiates from the benzene molecules observed in the thermosphere and follows their evolution to larger aromatic structures through reaction with gas-phase radical species. Aromatics are allowed to collide and provide the first primary particles, which further grow to aggregates through coagulation. We also consider for the first time the contribution of heterogenous processes at the surface of the particles, which are described by the deposition of the formed aromatic structures on the surface of the particles, and also through the chemical reaction with radical species. Our results demonstrate that the evolution of aerosols in terms of size, shape, and density is a result of competing processes between surface growth, coagulation, and sedimentation. Furthermore, our simulations clearly demonstrate the presence of a spherical growth region in the upper atmosphere followed by a transition to an aggregate growth region below. The transition altitude ranges between 500 and 600 km based on the parameters of the simulation.

The non-catalytic interaction between soot and nitric oxide (NO) resulting in their simultaneous elimination was studied on different types of reactive site present on soot. The reaction mechanism proposed previously was extended by including seven new reaction pathways for which the reaction energetics and kinetics were studied using density functional theory and transition state theory. This has led to the calculation of a new rate for the removal of carbon monoxide (CO) from soot. The new pathways have been added to our polycyclic aromatic hydrocarbon (PAH) growth model and used to simulate the NO–soot interaction to form CO, N2 and N2O. The simulation results show satisfactory agreement with experiment for the new CO removal rate. The NO–soot reaction was found to depend strongly on the soot site type and temperature. For a set of temperatures, computed PAH structures were analysed to determine the functional groups responsible for the decrease in the reactivity of soot with NO with increasing reaction time. In isothermal conditions, it was found that as temperature is increased, the number of oxygen atoms remaining on the soot surface decreases, while the number of nitrogen atoms increases for a given reaction time.

Chemie Ingenieur TechnikVolume 82, Issue 9 p. 1395-1395 PosterFree Access Ein detailliertes Rußpartikelmodell M. Sander, M. Sander University of Cambridge, Department of Chemical Engineering and Biotechnology, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this authorR. Patterson, R. Patterson University of Cambridge, Department of Chemical Engineering and Biotechnology, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this authorA. Raj, A. Raj University of Cambridge, Department of Chemical Engineering and Biotechnology, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this authorM. Kraft, M. Kraft mk306@cam.ac.uk University of Cambridge, Department of Chemical Engineering and Biotechnology, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this author M. Sander, M. Sander University of Cambridge, Department of Chemical Engineering and Biotechnology, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this authorR. Patterson, R. Patterson University of Cambridge, Department of Chemical Engineering and Biotechnology, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this authorA. Raj, A. Raj University of Cambridge, Department of Chemical Engineering and Biotechnology, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this authorM. Kraft, M. Kraft mk306@cam.ac.uk University of Cambridge, Department of Chemical Engineering and Biotechnology, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this author First published: 27 August 2010 https://doi.org/10.1002/cite.201050517AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume82, Issue9Special Issue: ProcessNet-Jahrestagung 2010 und 28. Jahrestagung der BiotechnologenSeptember, 2010Pages 1395-1395 RelatedInformation

In this paper we present studies of clusters assembled from polycyclic aromatic hydrocarbon (PAH) molecules similar in size to small soot particles. The clusters studied were comprised of coronene (C24H12) or pyrene (C16H10) molecules and represent the types of soot precursor molecule typically found in flame environments. A stochastic ‘basin-hopping’ global optimisation scheme was used to locate low-lying local minima on the potential energy surface of the molecular clusters. TEM-style projections of the resulting geometries show similarities with those observed experimentally in TEM images of soot particles. The mass densities of these clusters have also been calculated and are lower than bulk values of the pure crystalline PAH structures. They are also significantly lower than the standard value of 1.8g/cm3 used in our soot models. Consequently we have varied the mass density between 1.0g/cm3 and 1.8g/cm3 to examine the effects of varying soot density on our soot model and observed how the shape of the particle size distribution changes. Based on similarities between nascent soot particles and PAH clusters a more accurate soot density is likely to be significantly lower than 1.8g/cm3. As such, for modelling purposes, we recommend that the density of nascent soot should be taken to be the value obtained for our coronene cluster of 1.12g/cm3.

This paper 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: a detailed PAH growth model, referred to as the kinetic Monte Carlo—aromatic site (KMC-ARS) model [Raj et al., Combust. Flame 156 (2009) 896–913]; and a multivariate PAH population balance model, referred to as the PAH—primary particle (PAH-PP) model. Both the models are solved by kinetic Monte Carlo methods. PAH mass spectra are generated using the PAH-PP model, and compared to the experimentally observed spectra for a laminar premixed ethylene flame. The position of the maxima of PAH dimers in the spectra and their concentrations are found to depend strongly on the collision efficiency of PAH coagulation. The variation in the collision efficiency with various flame and PAH parameters is studied to determine the factors on which it may depend. A correlation for the collision efficiency is proposed by comparing the computed and the observed spectra for an ethylene flame. With this correlation, a good agreement between the computed and the observed spectra for a number of laminar premixed ethylene flames is found.

Chemie Ingenieur TechnikVolume 82, Issue 9 p. 1454-1454 VortragFree Access Neuer Pfad für die Synthese von Siliciumoxid-Nanopartikeln S. Shekar, S. Shekar University of Cambridge, Department of Chemical Engineering and Biotechnology, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this authorM. Sander, M. Sander University of Cambridge, Department of Chemical Engineering and Biotechnology, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this authorM. Kraft Prof., M. Kraft Prof. mk306@cam.ac.uk University of Cambridge, Department of Chemical Engineering and Biotechnology, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this author S. Shekar, S. Shekar University of Cambridge, Department of Chemical Engineering and Biotechnology, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this authorM. Sander, M. Sander University of Cambridge, Department of Chemical Engineering and Biotechnology, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this authorM. Kraft Prof., M. Kraft Prof. mk306@cam.ac.uk University of Cambridge, Department of Chemical Engineering and Biotechnology, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this author First published: 27 August 2010 https://doi.org/10.1002/cite.201050514AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume82, Issue9Special Issue: ProcessNet-Jahrestagung 2010 und 28. Jahrestagung der BiotechnologenSeptember, 2010Pages 1454-1454 RelatedInformation

In this work we present the new PAH-PP soot model and use a data collaboration approach to determine some of its parameters. The model describes the formation, growth and oxidation of soot in laminar premixed flames. Soot particles are modelled as aggregates containing primary particles, which are built from polycyclic aromatic hydrocarbons (PAHs), the main building blocks of a primary particle (PP). The connectivity of the primary particles is stored and used to determine the rounding of the soot particles due to surface growth and condensation processes. Two neighbouring primary particles are replaced by one if the coalescence level between the two primary particles reaches a threshold. The model contains, like most of the other models, free parameters that are unknown a priori. The experimental premixed flame data from Zhao et al. [B. Zhao, Z. Yang, Z. Li, M.V. Johnston, H. Wang, Proc. Combust. Inst. 30 (2) (2005) 1441–1448] have been used to estimate the smoothing factor of soot particles, the growth factor of PAHs within particles and the soot density using a low discrepancy series method with a subsequent response surface optimisation. The optimised particle size distributions show good agreement with the experimental ones. The importance of a standardised data mining system in order to optimise models is underlined.

This work proposes a new kinetic model and a novel inception pathway for the flame synthesis of silica nanoparticles from tetraethoxysilane (TEOS). The kinetic model for the decomposition of TEOS is developed by generating reactions involving species that were reported in high concentrations at equilibrium. Flux and sensitivity analyses are then performed to identify the main reaction pathways. The parameters for these reactions are systematically fitted to experimental data using low discrepancy (LD) sequences and response surfaces. The main product of TEOS decomposition is deduced to be silicic acid (Si(OH)4). To increase computational efficiency, the kinetic model has been reduced by determining the level of importance (LOI) of each species and retaining only the important ones. This reduced kinetic model is then coupled to a detailed population balance model using an operator splitting technique. New particle inception and surface growth steps have been incorporated into the particle model in which particles form and grow by the interaction of Si(OH)4 monomers. Coagulation and sintering of particles are also included in the model and the material dependent sintering parameters have been determined by fitting the model to experimental values of collision and primary particle diameters using LD sequences. The particle size distributions and computer generated TEM-style images have been generated and good agreement with experiments is observed. The gas phase reactor composition and the temporal evolution of particle size at different temperatures are also presented.

Chemie Ingenieur TechnikVolume 81, Issue 8 p. 1068-1068 VortragFree Access Detaillierte Modellierung der Rußbildung M. Celnik Dr., M. Celnik Dr. Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this authorT. Totton, T. Totton Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this authorA. Raj, A. Raj Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this authorM. Sander, M. Sander Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this authorM. Kraft Dr, M. Kraft Dr mk306@cam.ac.uk Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this author M. Celnik Dr., M. Celnik Dr. Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this authorT. Totton, T. Totton Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this authorA. Raj, A. Raj Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this authorM. Sander, M. Sander Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this authorM. Kraft Dr, M. Kraft Dr mk306@cam.ac.uk Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, United KingdomSearch for more papers by this author First published: 19 August 2009 https://doi.org/10.1002/cite.200950425AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume81, Issue8Special Issue: ProcessNet‐Jahrestagung und 27. Jahrestagung der BiotechnologenAugust, 2009Pages 1068-1068 ReferencesRelatedInformation

In this study the coagulation, condensation, and sintering of nanoparticles is investigated using a stochastic particle model. Each stochastic particle consists of interacting polydisperse primary particles that are connected to each other. In the model sintering occurs between each individual pair of neighboring primary particles. This is important for particles in which the range of the size of the primary particles varies significantly. The sintering time is obtained from the viscous flow model. The model is solved using a stochastic particle algorithm. The particles are represented in a binary tree that contains the connectivity as well as the degree of sintering information. Particles are forme, coagulate, sinter, and experience condensation according to known rate laws. The particle binary tree, along with it the degree of sintering, is updated after each time step according to the rates of the different processes. The stochastic particle method uses the technique of fictitious jumps and linear process deferment. The theoretical results are fitted against experimental values for the formation of SiO2 nanoparticles and computer generated TEM pictures are presented and compared to experiments.

Two new polycyclic aromatic hydrocarbon (PAH) surface processes are proposed, which can cause dehydrogenation and “rounding” of PAH molecules. The reaction pathways for both the processes involve decyclisation of a 6-member ring present on the PAH surface. 1,6-Hydrogen migration in the bay region formed by nearby carbon atoms provides an alternate route for both the processes to proceed. The energetics and kinetics of the proposed processes are investigated using density functional theory and transition state theory, respectively. The B3LYP functional with the 6-311++G(d,p) basis set is employed for the geometry optimisation and vibrational frequency analysis of the chemical species and the transition states. The current PAH growth mechanism is extended by including the new processes. A detailed PAH growth model, the kinetic Monte Carlo-aromatic site (KMC-ARS) model [Raj A, Celnik M, Shirley R, Sander M, Patterson R, West R, et al. A statistical approach to develop a detailed soot growth model using PAH characteristics. Combust Flame 2009;156:896–913] is used to study PAH growth with the extended mechanism. Computed ensembles are generated for large PAHs present in a C2H2 flame with 70–320 carbon atoms, and are compared to the experimentally observed ensembles. The inclusion of the new PAH processes in the chemical mechanism is found to improve the predicted composition of the large PAH molecules, especially for the PAHs with 70–200 carbon atoms.

Standard empirical atom-atom potentials are shown to be unable to describe the binding of PAH molecules in the variety of configurations seen in clusters. The main reason for this inadequacy is the lack of anisotropy in these potentials. We have constructed an anisotropic atom-atom intermolecular potential for the benzene molecule from first principles using SAPT (DFT) interaction energy calculations and the Williams-Stone-Misquitta method for obtaining molecular properties in distributed form. Using this potential as a starting point we have constructed a transferable anisotropic potential to model intermolecular interactions between polycyclic aromatic hydrocarbons (PAH). This new potential has been shown to accurately predict interaction energies for a variety of dimer configurations for four different PAH molecules including certain configurations which are poorly predicted with current isotropic potentials. It is intended that this potential will form the basis for further work on the aggregation of PAHs.

Tetraethoxysilane (TEOS) is used as a precursor in the industrial production of silica nanoparticles using thermal decomposition methods such as flame spray pyrolysis (FSP). Despite the industrial importance of this process, the current kinetic model of high-temperature decomposition of TEOS to produce intermediate silicon species and eventually form amorphous silica (alpha-SiO2) nanoparticles remains inadequate. This is partly due to the fact only a small proportion of the possible species is considered. This work presents the thermochemistry of practically all of the species that can exist in the early stages of the reaction mechanism. In order to ensure that all possible species are considered, the process is automated by considering all species that can be formed from the reactions that are deemed reasonable in the standard ethanol combustion model in the literature. Thermochemical data for 180 species (over 160 of which have not appeared in the literature before) are calculated using density functional theory with two different hybrid functionals, B3LYP and B971. The standard enthalpy of formation (Delta H-f(298.15K)degrees) values for these species are calculated using isodesmic reactions. It is observed that internal rotation may be important because the barriers to rotation are reasonably low. Comparisons are then made between the rigid rotor harmonic oscillator approximation (R-RHO) and the R-RHO with some of the vibrational modes treated as hindered rotors. It is found that full treatment of the hindered rotors makes a significant difference to the thermochemistry and thus has an impact on equilibrium concentrations and kinetics in this system. For this reason, all of the species are treated using the hindered rotor approximation where appropriate. Finally, equilibrium calculations are performed to identify the intermediates that are likely to be most prevalent in the high-temperature industrial process. Particularly, Si(OH)(4), SiH(OH)(3), SiH2(OH)(2), SiH3(OH), Si(OH)(3)(OCH3), Si(OH)(2)(OCH3)(2), the silicon dimers (CH3)(3)-SiOSi(CH3)(3) and SiH3OSiH3, and the smaller hydrocarbon species CH4, CO2, C2H4, and C2H6 are highlighted as the important species.

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 C2H2 and a C6H6 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.

An updated rate of O2 oxidation of one to four ring polyaromatic hydrocarbons in premixed flames is presented based on density function theory simulations of oxygen attack at different radical sites on various PAHs. The rate is in agreement with other rates found in the literature; however, it is several orders of magnitude lower than the currently accepted oxidation rate of multi-ring aromatic species, including soot. Simulations are presented of a premixed flame using this improved rate and a new advanced soot particle model, which is developed in this paper. This model includes unprecedented detail of the particles in the ensemble, including the aromatic content, C/H composition and primary-particle aggregate structure. The O2 oxidation rate calculated in this paper is shown to give a better prediction of particle number density and soot volume fraction for a premixed flame. The predicted particle size distributions are shown also to describe better the experimental data. Predicted C/H ratio and PAH size distributions are shown for the flame. Computed TEM-style images are compared to experimental TEM images, which show that the aggregate structure of the particles is well predicted.

Recent studies demonstrate that the decomposition of nitric oxide on a soot molecule forms surface nitrogen and oxygen. The surface nitrogen can be recombined to gaseous N2 while the surface oxygen desorbs from the soot molecule as CO. This non-catalytic conversion of gaseous NO into N2 is investigated using density functional theory, transition state theory and a kinetic Monte-Carlo (kMC) simulation. The results are validated against experiments. A mechanism for the conversion of NO to N2 on a soot surface is explored. The geometries of the intermediate stable species as well as the transition states were optimized to identify the different reaction steps. The forward and backward reaction rate of each intermediate reaction is calculated applying transition state theory. A kMC simulation using the current rates and intermediate species demonstrates feasible mechanisms for the conversion of NO to N2 on a soot surface. It is also suggested that a portion of NO is trapped on the soot surface and this increases during the reaction and blocks the active carbon sites inhibiting further reactions. By combining different theoretical techniques in a multi-scale model, we are able to describe the conversion of soot in the presence of NO accurately.