On the detailed modelling of high temperature nanoparticles synthesis
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1 On the detailed modelling of high temperature nanoparticles synthesis Prof. The 9 th International Conference on Chemical Kinetics (ICCK) Department of Chemical Engineering and Biotechnology 2 nd JULY 2015
2 Co-authors My Students: Special thanks to Prof Bill Green Daniel Nurkowski Philipp Burger Weerapong Phadungsukanan Shradda Shekar William Menz Markus Sander Richard West Raphael Shirley Jethro Akroyd Sebastian Mosbach (Alastair Smith) 2
3 Titania nanoparticles Titianium dioxide or titania (TiO 2 ) White pigment > 6.05 Mt (2013) / year (~70% of global pigment market) Wide range of applications Wet and flame aerosol methods Images from 3
4 Silicon nanoparitcles 4
5 Silica nanoparticles What are SiNP? Network of Si-O bonds such that Si:O = 1:2 Why are they important? Support material for functional/composite nanoparticles, catalysis Bio-medical applications, drug delivery Optics, optoelectronics, photoelectronics 5 Fabrics, clothes
6 Why model this? Precursor(TEOS) Aerosol reactor Silica nanoparticles Industrial Scale Molecular Scale P 1 atm T K What are the optimal process conditions? What are the final product properties? What is the final particle size distribution? What happens in the gas-phase? How do gas-phase precursors form the particles? How do these particles grow? How to describe the overall system from first-principles? 6
7 General aim: An improved understanding of the formation processes Understand how to control the quality of the particles Chemical processes Particle processes Development of methods for a systematic (and automated) model generation Images from and 7
8 Precursor chemistry 8
9 Titania gasphase chemistry 9
10 Introduction Titanium tetra-chloride (TiCl 4 ) Ti Cl Oxidation of TiCl 4 Richard H. West, Gregory J. O. Beran, William H. Green, and, Journal of Physical Chemistry A 111, (18), , (2007) 10
11 Introduction Titanium tetra-isopropoxide or TTIP (Ti(OC 3 H 7 ) 4 ) H C Ti O Right image from Buerger, Nurkowski, Kraft et al. Journal of Physical Chemistry A in press 11
12 Methodology 12
13 Methodology Journal of Physical Chemistry A in press 13
14 Species generation 14
15 Species generation 1. Single isopropoxide functional group with a Ti centre 2. Choose bonds to be broken Fragment Fragment 3. Break bonds and remove hydrocarbon fragments 4. Ti-containing fragment Journal of Physical Chemistry A in press 15
16 Species generation Possible site 2 Sub-valent site Possible site 1 Double bond Sub-valent site Possible site 1 Possible site 2 5. Identify possible site for hydrogen addition 6. Add hydrogens to all combinations of sites; some sites are left as radical sites Double bond 7. Add to set of possible hydrocarbon branches 8. Repeat until all possible branches are generated Journal of Physical Chemistry A in press 16
17 Species generation 9. Generate candidate species by selecting all combinations of branches, including empty branches Double bond Double bond combine Double bond Double bond Journal of Physical Chemistry A in press 17
18 Results: Species generation 4,477,456 candidate species Textual representation using molecular descriptors No electronic structure calculations performed 211,876 unique candidate species Exclusion of duplicates 981 selected candidate species Exclusion of carbon-containing radicals with more than one sub-valent sites 18
19 Electronic structure calculations 19
20 Optimised geometries Journal of Physical Chemistry A in press 20
21 Electronic structure calculations Density functional theory (DFT) at the B97-1/6-311+G(d,p) level of theory Internal rotor treatment Symmetrical rotors θ θ Hindrance potential Asymmetrical rotors Barrier height Fourier coefficients Symmetry number Torsional angle 21
![Hindered rotors Torsional energy barrier, V(θ) [kj mol -1 ] θ α θ](/docs-images/92/107880809/images/22-2.jpg "Torsional angle, θ [ ] Geometry Rotational angle 0 24 48 72 96 120")
22 Hindered rotors Torsional energy barrier, V(θ) [kj mol -1 ] θ α θ Torsional angle, θ [ ] Geometry Rotational angle
23 Hindrance potentials Journal of Physical Chemistry A in press 23
24 Thermodynamic property calculations 24
25 Thermochemical property calc. Partition functions are used to describe the statistical properties of a system Individual contributors are assumed to be independent Translational (T) Vibrational (V) Rotational (R) Electronic (E) Internal rotation (I) Internal rotation Used to calculate thermodynamic properties (C p, S, H) Journal of Physical Chemistry A in press 25
26 Equilibrium composition 26
27 Equilibrium composition Journal of Physical Chemistry A in press 27
28 Computational costs TransVibRotElec (per species): Geometry calculations: 68.5 h Frequency calculations: 19.2 h TVRE (total): 9.6 yr + I C /I T (additional costs): 20.8 yr Hardware: Intel(R) Xeon(R) CPU 3.00GHz / 8GB nodes 8 cores per node Journal of Physical Chemistry A in press 28
29 Current work Apply the methods to the TiCl 4 system and refine the existing detailed gas-phase model Original work Extended species set O 2 /TiCl 4 mixture (50/50 mol%) at 3 bar 29
30 Molehub Phadungsukanan, Kraft, Townsend, Murray-Rust, Journal of Cheminformatics 4, 15, (2012) 30
31 Tetraethoxysilane TEOS Central silicon attached to 4-ethoxy branches Vibrations and rotations within the molecule Many possible ways of bond breaking, many possible reactions Preferred precursor because relatively inexpensive and halidefree. Nurkowski, Klippenstein, Kraft et al., Zeitschrift fuer Physikalische Chemie, 229, (5) (2015) Nurkowski, Buerger, Kraft, et al Proceedings of the Combustion Institute 35, , (2015) 31
32 Reaction mechanism 32
33 Model derivation Input Automatic generation of possible reactions Reaction Rules 1. OC 2 H 5 2. OCH 3 /OCH 2 3. OC 2 H 4 4. OCHCH 3 5. O/OH 6. OCH=CH 2 33
34 Model derivation Input Automatic generation of possible reactions Reaction Rules 1. OC 2 H 5 2. OCH 3 /OCH 2 3. OC 2 H 4 4. OCHCH 3 5. O/OH 6. OCH=CH 2 N. M. Marinov, International Journal of Chemical Kinetics, (1999). 34
35 Model derivation 87 kcal/mol 104 kcal/mol Analogy 89 kcal/mol 101 kcal/mol Bond energies taken from: doi: /j100007a056 doi: / doi: /jp104759d 35
36 Model derivation Output: Reaction list Rates initially taken from analogous ethanol channels + N. M. Marinov, 1998 C 2 Chemistry provide decomposition channels for various hydrocarbon species 177 species, 2039 reactions 36
37 Flux and sensitivity analysis Flux analysis t end t 0 reactions R 1 : Si R n : Si Sensitivity analysis Si(OH)4 37
38 Flux and sensitivity analysis Important pathways & species 0.5% of TEOS in Ar T= 1500 K and P= 1 bar 38
39 Important pathways & species Most sensitive reactions 39
40 Important pathways & species Most sensitive reactions + other important reactions 40
41 Transition state theory Rate constants prediction Reactions with barriers - Traditional transition state theory (TST) Reactions without barriers - Variational transition state theory (VTST) 41
42 Reactions with barriers Silica Ethanol Rate constants in both systems are similar Rate constants are within a factor of ~2 with respect to 42 various modelling data
43 Reactions without barriers Chosen reactions Silica Ethanol 43
44 Reactions without barriers Silica Ethanol Rate constants for silica and ethanol are similar (within a factor of ~1.5-2) Much better agreement with literature data for ethanol rate constants, factor of ~2 Nurkowski, Klippenstein, Kraft et al., Zeitschrift fuer Physikalische Chemie, 44 Volume 229, Issue 5 (May 2015)
45 Optimisation Theory Experimental data exp exp η = η0 ± σ exp Model response with paramaters x η = η( x) x = ( ) with x,...,x K 1 and x = x 0 + cξ with uncertainty factor c and standard normally distributed ξ For a simple linear model, K=1 η ( x ) = A + B x η ( x, c, ξ ) A + B( x + cξ ) = ( x 0 ) = E[ η( x0, c ξ )] = A + B x0 σ ( c ) = Var( η( x0, c, ξ )) = B c µ, A. Braumann, P. L. W. Man, and M. Kraft. Ind. Eng. Chem. Res., 49: ,
46 Experimental validation (a) J. Herzler, J. A. Manion, and W. Tsang. Single-Pulse Shock Tube Study of the decomposition of tetraethoxysilane and Related Compounds. J. Phys. Chem. A, 101, ,
47 Reactor Plot Conclusion from kinetic model: Si(OH) 4 is the predominant gas-phase precursor 47
48 Particle model 48
49 Type Space ( ) 49
50 1. Inception H O H O H Si H H O H O H O + Si O Si O H O H O O H H [ monomers ] O O H H H O Si O O H H O -H 2 O H H H O O O Si Si O O O H [primary particle ] H H O Si(OH) 4 molecules undergo dehydration to form particles. These particles change in size and shape through their lifetime Inception increases the number of particles in the system. Shekar, Kraft, et al. Chemical Engineering Science 70,54-66, (2012) 50,
51 2. Surface Reaction Si(OH)4 from gas-phase reacts on a particle surface. 51
52 2. Rounding due to surface reaction Surface reaction alters the common surface between different primaries of a particle: 52
53 3. Coagulation Particles collide and stick to each other. 53
54 4. Intra-particle reaction Adjacent OH sites react with each other to form Si- O-Si bonds. 54
55 5. Sintering Sintering calculated on a primary particle-level & alters composition. 55
56 Particle model parameter estimation Unknown parameters Objective function: Parameter estimation method: Sobol sequences followed by simultaneous perturbation stochastic approximation 56
57 Particle model parameter estimation T. Seto, A. Hirota, T. Fujimoto, M. Shimada, and K. Okuyama. Sintering of Polydisperse Nanometer-Sized Agglomerates, Aerosol Sci. Tech., 27, ,
58 Particle model validation T = 900 o C T = 1500 o C T = 1750 o C 58
59 Simulation for industrial conditions Precursor + Fuel +Air Isothermal Batch Reactor (T = 1500 K, P = 1 atm) Sensitive applications of SiNP require highly specific properties TEOS decomposition Formation of Si(OH) 4 Particle formation 59
60 Simulation results Mean Diameter 20-40nm Low Standard deviation dc 60
61 Simulation results TEOS decomposition rate High surface activity 61
62 Desirable process zones Catalysis / functional materials / fillers 62
63 Desirable process zones Drug delivery / bio-medical applications 63
64 Silicon parameter estimation 64
65 Introduction: particle synthesis William J. Menz, Kraft, et al. Journal of Aerosol Science 76, , (2014) William J. Menz, Kraft, Combustion and Flame 160, , (2013) William J. Menz Kraft, Aerosol Science and Technology 47, , (2013) 65
66 Particle type space 66
67 Fully-coupled model 67
68 Parameter estimation: the adjusted parameters 68
69 Parameter estimation: case study 69
70 Parameter estimation: objective function 70
71 Parameter estimation: initial optimisation 71
72 Parameter estimation: visualised 72
73 Parameter estimation: model results 73
74 Parameter estimation: HDMR response surface 74
75 Parameter estimation: HDMR sensitivities 75
76 Parameter estimation: sensitivity analysis 76
77 Parameter estimation: bubble plots (2) 77
78 Acknowledgements 78
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