A conservative model for high-throughput synthesis of nanoparticles in reacting gas flows

Considerable progress has been made over the past decades in the modeling of gas-phase synthesis of nanoparticles. However, when the nanoparticles mass fraction is large representing up to 50 % of the mixture mass fraction, some issues can be observed in the self-consistent modeling of the production process. In particular, enthalpy exchanges between gas and particle phases and differential diffusion between the two phases are usually neglected, since the particle mass fraction is generally very small. However, when high nanoparticle mass fractions are encountered, these simplifications may cause non conservation of the total enthalpy or the total mass. In the present paper, we propose a conservative model for nanoparticles production from gas-phase processes with a high throughput of nanoparticles. The model is derived in order to satisfy conservations of both enthalpy and mass and is validated on laminar one-dimensional premixed and non-premixed flames. In particular, it is shown that the enthalpy of the particle phase as well as the differential diffusion of the gas phase with respect to the particle phase cannot be generally neglected when the nanoparticles concentration is high to preserve the accuracy of the numerical results

A conservative model for high-throughput synthesis of nanoparticles in reacting gas flows

Considerable progress has been made over the past decades in the modeling of gas-phase synthesis of nanoparticles. However, when the nanoparticles mass fraction is large representing up to 50 % of the mixture mass fraction, some issues can be observed in the self-consistent modeling of the production process. In particular, enthalpy exchanges between gas and particle phases and differential diffusion between the two phases are usually neglected, since the particle mass fraction is generally very small. However, when high nanoparticle mass fractions are encountered, these simplifications may cause non conservation of the total enthalpy or the total mass. In the present paper, we propose a conservative model for nanoparticles production from gas-phase processes with a high throughput of nanoparticles. The model is derived in order to satisfy conservations of both enthalpy and mass and is validated on laminar one-dimensional premixed and non-premixed flames. In particular, it is shown that the enthalpy of the particle phase as well as the differential diffusion of the gas phase with respect to the particle phase cannot be generally neglected when the nanoparticles concentration is high to preserve the accuracy of the numerical results

Modélisation d'un plasma de silane-hydrogène avec dynamique de nanoparticules pour applications photovoltaïques.

This thesis addresses the modeling of silicon nanoparticle dynamics in radio-frequency capacitively-coupled silane plasma discharges for photovoltaic applications.A complete derivation of fluid equations for a two-temperature reactive polyatomic plasma has been achieved in the framework of the kinetic theory of gases. From an asymptotic analysis of the Boltzmann equation, the Chapman-Enskog method was applied to derive the zeroth-order “Euler-type” equations and the first-order “Navier-Stokes-type” equations. Expressions for transport fluxes have been obtained in terms of the macroscopic variables gradients, and associated transport coefficients have been derived.The multicomponent fluid plasma model thus derived has been simplified and implemented numerically in order to model a plasma enhanced chemical vapor deposition reactor as used for silicon thin films deposition. A software has been written in FORTRAN and validated against a benchmark model from the literature. The plasma model has then been applied to typical conditions for low temperature plasma enhanced silicon epitaxy. The main plasma species densities are in good agreement with existing experimental data. The influence of silane plasma chemistry on the DC bias voltage has also been investigated using “tailored voltage” asymmetric waveforms.The model has then been enriched with a sectional model accounting for size and charge of nanoparticles. An estimation of the accommodation coefficient of silane on nanoparticles was obtained from a comparison with existing experimental results. Results of the simulations confirm the critical role of positive ions in the deposition process.The model implemented in this work opens the path for a systematic study of the evolution of the plasma properties as a function of the process conditions and of the influence of nanoparticles on the plasma physicochemical properties.Cette thèse porte sur la modélisation de la dynamique des nanoparticules de silicium dans les plasmas de silane à couplage capacitif pour applications photovoltaïques.Une dérivation complète des équations fluides pour un plasma bi-température réactif polyatomique a été effectuée dans le cadre de la théorie cinétique des gaz. A partir d'une analyse asymptotique de l'équation de Boltzmann, la méthode de Chapman-Enskog a permis d'obtenir les équations d'ordre zéro en le nombre de Knudsen, qui correspondent au régime "Euler", et les équations d'ordre un qui correspondent au régime "Navier-Stokes-Fourier". La méthode fournit également une expression des flux de transport en termes des gradients des variables macroscopiques, ainsi que les coefficients de transports associés.Le modèle de plasma fluide multi-espèces ainsi dérivé a été simplifié et implémenté numériquement en vue de modéliser un réacteur de dépôt chimique en phase vapeur assisté par plasma utilisé pour le dépôt de couches minces de silicium. Un logiciel a été écrit en FORTRAN et validé numériquement à l'aide d'un "benchmark" issu de la littérature. Il a ensuite été mis en oeuvre dans les conditions typiques de l'épitaxie par plasma basse température. Les densités des principales espèces sont en accord avec les données expérimentales de la littérature. L'influence de la chimie du silane sur la tension d'auto-polarisation a également été étudiée, grâce à l'utilisation de formes d'ondes asymétriques sur mesure.Le modèle a ensuite été enrichi à l'aide d'un modèle sectionnel en taille et en charges pour les nanoparticules. La comparaison avec les résultats expérimentaux existants a permis d'estimer le coefficient d’accommodation du silane sur les nanoparticules. Les résultats obtenus confirment le rôle prépondérant des ions positifs dans le processus de dépôt.Le modèle développé dans cette thèse ouvre ainsi la voie à une étude systématique de l’évolution du plasma en fonction des conditions de dépôt et de l'influence des nanoparticules sur les propriétés physico-chimiques du plasma

Kinetic theory of two-temperature polyatomic plasmas

International audienceWe investigate the kinetic theory of two-temperature plasmas for reactive polyatomic gas mixtures. The Knudsen number is taken proportional to the square root of the mass ratio between electrons and heavy-species, and thermal non-equilibrium between electrons and heavy species is allowed. The kinetic non-equilibrium framework also requires a weak coupling between electrons and internal energy modes of heavy species. The zeroth-order and first-order fluid equations are derived by using a generalized Chapman-Enskog method. Expressions for transport fluxes are obtained in terms of macroscopic variable gradients and the corresponding transport coefficients are expressed as bracket products of species perturbed distribution functions. The theory derived in this paper provides a consistent fluid model for non-thermal multicomponent plasmas

Étude expérimentale et numérique de l'effet thermique d'une décharge à barrière diélectrique Numerical and experimental study of the thermal effect of a dielectric barrier discharge

International audienceIn this work, we compare experimental measurements with numerical simulations of the effect of a dielectric barrier discharge over a quiescent flow. The experimental and numerical temperature profiles agree well qualitatively.Dans ce travail, nous présentons des résultats expérimentaux et numériques sur l’effet d’une décharge à barrière diélectrique sur un écoulement au repos. Les profils de température expérimental et numérique sont en bon accord qualitatif

Importance of mass and enthalpy conservation in the modeling of titania nanoparticles flame synthesis

In most simulations of fine particles in reacting flows, including sooting flames, enthalpy exchanges between gas and particle phases and differential diffusion between the two phases are most often neglected, since the particle mass fraction is generally very small. However, when the nanoparticles mass fraction is very large representing up to 50 % of the mixture mass, the conservation of the total enthalpy and/or the total mass becomes critical. In the present paper, we investigate the impact of mass and enthalpy conservation in the modeling of titania nanoparticles synthesis in flames, classically characterized by a high conversation rate and consequently a high nanoparticles concentration. It is shown that when the nanoparticles concentration is high, neglecting the enthalpy of the particle phase may lead to almost 70 % relative error on the temperature profile and to relative errors on the main titania species mass fractions and combustion products ranging from 20 % to 100 %. It is also established that neglecting the differential diffusion of the gas phase with respect to the particle phase is also significant, with almost 15 % relative error on the TiO$_{2}$ mole fraction, although the effect on combustion products is minor

Accounting for hydrolysis in the modeling of titanium dioxide nanoparticle synthesis in laminar TiCl 4 flames

International audienceThe description of TiO 2 synthesis in TiCl 4 flames is most often based on phenomenological models that qualitatively reproduce experimental trends in terms of final production but they do not provide chemical insights into the actual kinetic pathways. Alternatively, thermodynamically-consistent detailed TiCl 4 oxidation kinetics are available. However, since they have been developed under dry conditions they still need to be challenged and validated when employed for flame synthesis where the presence of water molecules may potentially activate TiCl 4 hydrolysis. To derive accurate chemical descriptions for TiO 2 flame synthesis, it is essential to evaluate the possible contribution of TiCl 4 hydrolysis. For this, numerical simulations of TiO 2 flame synthesis in laminar flames are performed in this article using different chemical descriptions for TiCl 4 conversion into TiO 2. Detailed oxidation kinetics neglecting hydrolysis are shown to predict an extremely slow formation of TiO 2 particles in flames when O 2 concentration is small. As a consequence, a significant underestimation of the conversion yield is observed compared to experimental evidences and to trends deduced from phenomenological models. To correct this behaviour, a new scheme is proposed by combining a detailed oxidation kinetics with a five-reaction mechanism describing the first steps of TiCl 4 hydrolysis. Conversion of TiCl 4 is found to be faster and more efficient with this new combined scheme, leading to log-normal particle size distributions in agreement with the experimental data for nanoparticles flame synthesis

Impact of charged species transport coefficients on self-bias voltage in an electrically asymmetric RF discharge

International audienceIn this paper, we use a fluid model to simulate the excitation of a hydrogen radio-frequency discharge, and employ tailored voltage waveforms to assess the effect of charged species transport properties. Results of the fluid simulation are compared with experimental data and previous results obtained with a hybrid model. Several expressions for electron and ion transport coefficients are compared, and their impact on the self-bias potential is studied. The self-bias is shown to be insensitive to the choice of electron transport coefficients, while remarkably sensitive to variations in ion mobility. Besides, our results show that fluid models can be competitive with hybrid models, provided self-consistent ion transport models and rate constants are used

Simple experimental and analytical methods to estimate the power coupling efficiency in plasma discharges

International audienceA simple experimental method to estimate the power effectively absorbed by a plasma is presented. It relies on a thermal management study that is applied to the whole discharge system, providing the energy released by the plasma and lost by convection and radiation at the reactor walls. The methodology is illustrated in the case of H2 Electron Cyclotron Resonance microwave plasma. Nevertheless, this method can be extended to a variety of electrical discharge or feed gases. Using this method, an experimental coupling efficiency of ∼22 ± ∼8% was derived. In comparison, an analytical balance of the plasma power absorption yields a theoretical coupling efficiency of ∼28 ± ∼9%