flame synthesis of inorganic nanoparticles Shraddha Shekar and Jethro Akroyd Markus KRAFT Karlsruhe 12 July 2010
Part 1
Introduction Precursor (TES) Mesoporous silica nanoparticles Aim: To answer the following questions What happens in the gas-phase? ow do gas-phase precursors form the particles? ow do these particles grow? ow to describe the overall system from first-principles?
Product : lica nanoparticles Mesoporous lica Nanoparticles: network of - bonds such that : = 1:2 Applications: Support material for functional/composite nanoparticles. ptics, optoelectronics, photoelectronics Catalysis Bio-medical applications, drug delivery
Industrial Flame Reactor Product (lica nanoparticles) Flame Spray Reactor P 1 atm T 1100-1500 K Aim: To describe the flame synthesis of silica nanoparticles Experiments (erzler et al / Seto et al / Pratsinis et al ) Model Precursor(TES) Fuel(ethanol+air) / Inerts(Ar)
Ab initio modelling Species generation Quantum Chemistry calculations Statistical Mechanics Thermochemistry calculation verall Model (T) S(T) C p (T) Equilibrium calculation Chemical Kinetics Population Balance Model
Equilibrium Plot Ref: W. Phadungsukanan, S. Shekar, R. Shirley, M. Sander, R.. West, and M. Kraft. First-principles thermochemistry for silicon species in the decomposition of tetraethoxysilane. J. Phys. Chem. A, 113, 9041 9049, 2009
Reaction kinetics Equilibrium ints towards the existence of stable intermediates & products. Intermediates () x (C 3 ) 4-x () y (C 2 5 ) 4-y Main Product () 4 Kinetics Reaction set generated to include all intermediates and products from equilibrium. Reactions obey Arrhenius law rate constant k = AT β e -Ea/RT Rate parameters (A, β, Ea) fitted to experimental values (a) (a) J. erzler, J. A. Manion, and W. Tsang. ngle-pulse Shock Tube Study of the decomposition of tetraethoxysilane and Related Compounds. J. Phys. Chem. A, 101, 5500-5508, 1997
ptimisation of Reaction rates The rate parameters have been fitted to shock-tube experimental data provided by erzler et al Step 1: Low discrepancy series To perform a pre-scan of parameters for 18 reactions. Step 2: Sensitivity Analysis To identify the 4 most sensitive parameters Uncertainties in model parameters for reactions R1 and R15 Step 3: Response Surface Methodology To estimate model uncertainties J. erzler, J. A. Manion, and W. Tsang. ngle-pulse Shock Tube Study of the decomposition of tetraethoxysilane and Related Compounds. J. Phys. Chem. A, 101, 5500-5508, 1997
Reaction Mechanism Species mole fractions versus time for an isothermal batch reactor. Initial composition was 10 mol % TES in Ar, T=1300 K and at atmospheric pressure. -reactions for TES decomposition pathway proposed in this work. The rates are fitted using LD sequences and RSM.
Flux Diagram & Sensitivity Analysis Flux Diagram. Shaded boxes identify the main reaction pathway. Normalised sensitivities of main products to different reactions. Identification of main reaction pathways
LI mechanism reduction full 79 species 401 reactions reduced 27 species 58 reactions Initial composition 250ppm TES in N2, T = 900 C P = 1 atm.
Gas-phase main reaction pathways 3 C C 2 2 C 2 C C 3 2 C C 2 2 C 3 C -C 2 4 3 C Reaction Pathway 1 3 C C 2 3 C 3 C -C 2 4 -C 2 4 2 C C 3 3 C C 3 3 C -C 2 4 C 3 3 C C 2 2 C 2 C 2 C C 2 3 C 3 C C C 2 2 C 3 -C 2 -C 2 4 C 4 3 -C 2 4 2 C C 2 2 C C 3 Reaction Pathway 2 C 3 3 C -C 2 4 C 2 C 3
Particle Model - 2 INCEPTIN SURFACE GRWT -n 2 () 4 molecules in gas-phase undergo inception to form a dimer (---). This dimer is considered to be the first particle. Particle growth then proceeds by subsequent removal of hydroxyl groups. n(-----)
Particle Model Surface growth New inception and surface growth steps have been incorporated in a previously developed stochastic particle model developed by Sander et al. (a) (a): M. Sander, R.. West, M. S. Celnik, and M. Kraft. A Detailed Model for the ntering of Polydispersed Nanoparticle Agglomerates, Aerosol Sci. Tech., 43, 978-989, 2009
Individual Jump Processes 1. Inception + [monomers] - 2 [primary particle] Process Rate: 2. Surface growth - 2 Process Rate:
Individual Jump Processes 3. Coagulation P j P k P i + 4. ntering (Viscous flow model)
The Algorithm 1. Set start time t t 0 and the initial system x x 0. 2. Calculate an exponentially distributed waiting time where U is a uniformly distributed random number, U Є (0; 1), and R tot is the total rate of all processes (surface reaction, coagulation and inception) defined for rates R i, i Є {coag,, inception, surfrxn} Ref: M. Sander, R.. West, M. S. Celnik, and M. Kraft. A Detailed Model for the ntering of Polydispersed Nanoparticle Agglomerates, Aerosol Sci. Tech., 43, 978-989, 2009
The Algorithm 3. Increment time variable t t+dt. 4. If t > t stop then end. 5. Update the sintering level for the time dt for all the particles. 6. Choose a process i according to the probability: 7. Perform process i. 8. Go to step 2. Ref: M. Sander, R.. West, M. S. Celnik, and M. Kraft. A Detailed Model for the ntering of Polydispersed Nanoparticle Agglomerates, Aerosol Sci. Tech., 43, 978-989, 2009
Model validation and analysis The sintering parameters (A, E and d p,min ) in the stochastic model are fitted to experimental data by Seto et al. (a) using a low discrepancy series. Due to the effect of sintering, the primary particle size increases and the collision diameter decreases with temperature. ntering increases as temperature increases reducing the collision diameters. At a temperature of about 2000 C, the collision diameter and primary diameter become identical and particles become spherical. Ref (a): T. Seto, A. irota, T. Fujimoto, M. Shimada, and K. kuyama. ntering of Polydisperse Nanometer-zed Agglomerates, Aerosol Sci. Tech., 27, 422-438, 1997
Particle size distribution Solid lines: Model Circles: Experiments (a) Ref (a): T. Seto, A. irota, T. Fujimoto, M. Shimada, and K. kuyama. ntering of Polydisperse Nanometer-zed Agglomerates, Aerosol Sci. Tech., 27, 422-438, 1997
Model produced TEM-like images Ref (a): T. Seto, A. irota, T. Fujimoto, M. Shimada, and K. kuyama. ntering of Polydisperse Nanometer-zed Agglomerates, Aerosol Sci. Tech., 27, 422-438, 1997
verall mechanism for particle formation Gas-phase reactions Particle formation Particle growth C 3 2 C 3 C 3 C C 2 3 C -2C C 2 4-2C 2 C 2 4 3 2 C C 3 3 C [monomer] C 3-2 2 [primary particle] -n 2 (----) n [lica particle] The gas-phase and particle model described above are coupled using an operator splitting technique to generate the overall model. Ref: S. Shekar, M. Sander, R. Riehl, A. J. Smith, A. Braumann, M. Kraft. Flame synthesis of silica nanoparticles from tetraethoxysilane, Technical Report 86, c4e-preprint Series, Computational Modelling Group, Cambridge, 2010
Conclusion 1. New kinetic model proposed which postulates silicic acid () 4 as the main product of TES decomposition. 2. A novel pathway proposed for the formation of silica nanoparticles via the interaction of silicic acid monomers. 3. Feasibility of using first-principles to gather a deeper understanding of complex particle synthesis processes.
Part 2
bjective Model turbulent reacting flow including particle formation We seek a practical method Engineering design tool Standard CFD (Computational Fluid Dynamics) codes Application to ongoing research
Difficulty Turbulent flows are unsteady Concentrations and temperature fluctuate CFD codes typically solve for average quantities Turbulent reaction models must solve average material and energy balances Mean reaction closure problem Average concentrations and temperature are not sufficient to calculate the average reaction rate
Common CFD reaction models Complex chemistry models Mean reaction closure problem ignored, so effectively assumes slow chemistry Eddy break up / hybrid kinetics Assumes irreversible reaction controlled by the slower of turbulent mixing and chemical reaction Flamelet models Assumes instantaneous reaction at a mixing interface between reactants
Transported PDF methods Alternative to solving for average quantities Joint composition probability density function (PDF) Describes the probability of all possible combinations of composition and temperature Applicable to all chemistry and all flows Reaction term is closed Further reading aworth (2009), doi:10.1016/j.pecs.2009.09.003
DQMoM DQMoM (Direct Quadrature Method of Moments) PDF is approximated using weighted fields Solve transport equations for the field system Deterministic method, compatible with off-the-shelf CFD BUT significant numerical problems We consider DQMoM-IEM Further reading Akroyd et al. (2010), doi:10.1016/j.ces.2009.11.010
DQMoM-IEM equations Derived from a closed joint PDF transport equation source term unsteady term turbulent diffusion term convection term standard CFD terms Further reading Akroyd et al. (2010), doi:10.1016/j.ces.2009.11.010
DQMoM-IEM algorithm perator splitting CFD code used to solve standard transport equation DQMoM-IEM solver developed for source term equation (micromixing, turbulent diffusion, reaction processes) Further reading Akroyd et al. (2010), doi:10.1016/j.ces.2009.11.010
DQMoM-IEM solver Analytic solver (N = 2 fields) Analytic solution of micromixing and turbulent diffusion Numerical integration of reaction General solver (N 2 fields) Numerical integration of all processes Further reading Akroyd et al. (2010), doi:10.1016/j.ces.2009.11.010
DQMoM-IEM validation Liquid phase test reaction in a turbulent jet k 1 >> k 2, yield of R is very sensitive to mixing Reproduce experimental and transported PDF data Further reading Akroyd et al. (2010), doi:10.1016/j.ces.2009.11.010 Akroyd et al. (2010), Technical Report 95, c4e-preprint Series, Cambridge
Validation 0.0066 m 0.004 m
Validation Predictions of the reaction yield 0.0066 m 0.004 m ± 0.5 Tsai and Fox (1994), doi:10.1016/0009-2509(94)00270-3 Li and Toor (1986), doi:10.1002/aic.690320809 References Akroyd et al. (2010), Technical Report 95, c4e-preprint Series, Cambridge
Comparison 0.0066 m 0.004 m Stochastic Fields method Monte Carlo PDF method for standard CFD milar to DQMoM-IEM, but Stochastic treatment of turbulent diffusion Fields no longer weighted Monte Carlo algorithm improved
Comparison 0.0066 m 0.004 m Yield (%) Yield without reaction closure (so equivalent to a typical complex chemistry model) N = 64 32 16 8 4 Circles Time-averaged yield Literature method Improved method Lines Loci of yield fluctuations Literature method Improved method Shading Difference between loci for the two methods Decreasing statistical error References Akroyd et al. (2010), Technical Report 95, c4e-preprint Series, Cambridge
Feasibility study Application of DQMoM-IEM to an industrial reaction Strong coupling Velocity field Combustion chemistry Particle size distribution We ignore the population balance for this study
Feasibility study Titania formation from titanium tetrachloride Fast, high temperature, corrosive reaction
Velocity field No reaction case 4 3 2 3
Temperature field No reaction case mean temperature (K) standard deviation (K)
Reaction case 1 Reaction at mean concentration and temperature ΔT (K) yield (%) reaction effectively stalls after 2 m
Reaction case 2 DQMoM-IEM, N = 2 ΔT (K) yield (%) sufficient heat release to sustain reaction
Reaction comparison What is going wrong with reaction case 1? Fluctuations in concentration and temperature ignored Results consistent with ideal reactor study What is going right with reaction case 2? DQMoM-IEM accounts for fluctuations Greater heat release due to non-linear chemistry Very significant impact on temperature field
Work in progress Include fully coupled particle processes Solve inception, surface growth and coagulation for each field using Method of Moments with Interpolative Closure Expect additional heat release from surface growth to be important for quantitative prediction of reaction yield Further reading Frenklach et al. (2002), doi:10.1016/s0009-2509(02)00113-6
Future development Couple CFD to first-principles solid phase model Detailed treatment of the solid phase Propose one-way coupling Solve for quantity of solid Ti 2 in CFD Extract gas-phase histories along streamlines Post process streamline to calculate detailed solid phase Spatially resolve solid phase by mapping back to CFD Refined solid phase process understanding
Conclusions DQMoM-IEM reaction closure implemented in CFD Applicable to all chemistry and all flows New solution algorithms developed Compatible with off-the-shelf CFD Propose spatially resolved solid phase models Fully coupled method of moments population balance Post process with a detailed solid phase model
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