Abstract
Energetic nanomaterials have gained prominence in the development of solid-state propellants, explosives and pyrotechnics. Such interests stem from kinetically controlled ignition processes in nanoscale regimes resulting from larger specific surface areas, metastable structures and small diffusion length scales at fuel-oxidizer interfaces. To this end, numerous works have investigated the energetic properties of a large class of metal nanoparticles (NPs) that include Al, Si and Ti. Gas-phase synthesis of metal NPs involve rapid cooling of supersaturated metal vapor (monomers) that initiates free-energy-driven collisional process including condensation/evaporation, and finally, leads to nucleation and the birth of a stable critical cluster. This critical cluster subsequently grows via competing coagulation/coalescence processes while undergoing interfacial reactions including surface oxidation . A fundamental understanding of the thermodynamics and kinetics of these processes can enable precise controlling of the synthesis process parameters to tailor their sizes, morphology, composition and structure, which, in turn, tune their surface oxidation and, energetic properties. The complexity and extremely diverse time scales make experimental studies of these processes highly challenging. Thus, hi-fidelity computational tools and modeling techniques prove to be powerful for detailed mechanistic studies of these processes in an efficient and robust manner. The current chapter focuses on computational studies of fate, transport and evolution of metal NPs grown via aerosol routes. The chapter starts with the discussion on gas-phase homogeneous nucleation, and nucleation rates of critical clusters, followed by kinetic Monte-Carlo (KMC) based studies on non-isothermal coagulation/coalescence processes leading finally to the mass transport phenomena involving oxidation of fractal-like NPs.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Renie J et al (1982) Aluminum particle combustion in composite solid propellants. Purdue University, West Lafayette, Ind
Bakhman N, Belyaev A, Kondrashkov YA (1970) Influence of the metal additives onto the burning rate of the model solid rocket propellants. Phys Combust Explos 6:93
Chiaverini MJ et al (1997) Instantaneous regression behavior of HTPB solid fuels burning with GOX in a simulated hybrid rocket motor. Int J Energ Mat Chem Propul 4(1–6)
Mench M, Yeh C, Kuo K (1998) Propellant burning rate enhancement and thermal behavior of ultra-fine aluminum powders(Alex). Energ Mat-Prod, Process Charac 30–1
Ritter H, Braun S (2001) High explosives containing ultrafine aluminum ALEX. Propellants, Explos, Pyrotech 26(6):311–314
Ilyin A et al (2002) Characterization of aluminum powders I. Parameters of reactivity of aluminum powders. Propellants Explos Pyrotech 27(6):361–364
Brousseau P, Anderson CJ (2002) Nanometric aluminum in explosives. Propellants, Explos, Pyrotech 27(5):300–306
Weiser V, Kelzenberg S, Eisenreich N (2001) Influence of the metal particle size on the ignition of energetic materials. Propellants, Explos, Pyrotech 26(6):284–289
Pantoya ML, Granier JJ (2005) Combustion behavior of highly energetic thermites: nano versus micron composites. Propellants, Explos, Pyrotech 30(1):53–62
Pivkina A et al (2004) Nanomaterials for heterogeneous combustion. Propellants, Explos, Pyrotech 29(1):39–48
van der Heijden AEDM et al (2006) Processing, application and characterization of (ultra)fine and nanometric materials in energetic compositions. Shock Compression Condens Matter Pts 1 and 2 845:1121–1126
Rai A et al (2006) Understanding the mechanism of aluminium nanoparticle oxidation. Combust Theor Model 10(5):843–859
Mason BA et al (2013) Combustion performance of several nanosilicon-based nanoenergetics. J Propul Power 29(6):1435–1444
Piekiel NW et al (2013) Combustion and material characterization of porous silicon nanoenergetics. In: 26th Ieee international conference on micro electro mechanical systems (Mems 2013) p 449–452
Thiruvengadathan R et al (2012) Combustion characteristics of silicon-based nanoenergetic formulations with reduced electrostatic discharge sensitivity. Propellants, Explos, Pyrotech 37(3):359–372
Prakash A, McCormick AV, Zachariah MR (2005) Synthesis and reactivity of a super-reactive metastable intermolecular composite formulation of Al/KMnO4. Adv Mat 17(7):900–
Perry WL et al (2004) Nano-scale tungsten oxides for metastable intermolecular composites. Propellants, Explos, Pyrotech 29(2):99–105
Perry WL et al (2007) Energy release characteristics of the nanoscale aluminum-tungsten oxide hydrate metastable intermolecular composite. J Appl Phys 101(6)
Berner MK, Zarko VE, Talawar MB (2013) Nanoparticles of energetic materials: synthesis and properties (review). Combust Explosion Shock Waves 49(6):625–647
Prakash A, McCormick AV, Zachariah MR (2005) Tuning the reactivity of energetic nanoparticles by creation of a core-shell nanostructure. Nano Lett 5(7):1357–1360
Zhang KL et al (2007) Synthesis of large-area and aligned copper oxide nanowires from copper thin film on silicon substrate. Nanotechnology 18(27)
Prakash A, McCormick AV, Zachariah MR (2004) Aero-sol-gel synthesis of nanoporous iron-oxide particles: A potential oxidizer for nanoenergetic materials. Chem Mater 16(8):1466–1471
Subramanian S et al (2008) Nanoporous silicon based energetic materials, DTIC Document
Blobaum KJ et al (2003) Deposition and characterization of a self-propagating CuOx/Al thermite reaction in a multilayer foil geometry. J Appl Phys 94(5):2915–2922
Ma E et al (1990) Self-propagating explosive reactions in Al/Ni multilayer thin-films. Appl Phys Lett 57(12):1262–1264
Gen M, Ziskin M, Petrov I (1959) A study of the dispersion of aluminium aerosols as dependent on the conditions of their formation. Doklady Akademii Nauk SSSR 127(2):366–368
Kwon YS et al (2003) Passivation process for superfine aluminum powders obtained by electrical explosion of wires. Appl Surf Sci 211(1–4):57–67
Kwon YS et al (2007) Properties of powders produced by electrical explosions of copper-nickel alloy wires. Mater Lett 61(14–15):3247–3250
Sarathi R, Sindhu TK, Chakravarthy SR (2007) Generation of nano aluminium powder through wire explosion process and its characterization. Mater Charact 58(2):148–155
Tillotson TM et al (2001) Nanostructured energetic materials using sol-gel methodologies. J Non-Cryst Solids 285(1–3):338–345
Jacobson MZ, Turco RP (1995) Simulating condensational growth, evaporation, and coagulation of aerosols using a combined moving and stationary size grid. Aerosol Sci Technol 22(1):73–92
Biswas P et al (1997) Characterization of iron oxide-silica nanocomposites in flames. 2. Comparison of discrete-sectional model predictions to experimental data. J Mater Res 12(3):714–723
Landgrebe JD, Pratsinis SE (1990) A discrete-sectional model for particulate production by gas-phase chemical-reaction and aerosol coagulation in the free-molecular regime. J Colloid Interface Sci 139(1):63–86
Lehtinen KEJ, Zachariah MR (2001) Self-preserving theory for the volume distribution of particles undergoing Brownian coagulation. J Colloid Interface Sci 242(2):314–318
Girshick SL, Chiu CP (1989) homogeneous nucleation of particles from the vapor-phase in thermal plasma synthesis. Plasma Chem Plasma Process 9(3):355–369
Panda S, Pratsinis SE (1995) Modeling the synthesis of aluminum particles by evaporation-condensation in an aerosol flow reactor. Nanostruct Mater 5(7–8):755–767
Prakash A, Bapat AP, Zachariah MR (2003) A simple numerical algorithm and software for solution of nucleation, surface growth, and coagulation problems. Aerosol Sci Technol 37(11):892–898
Mukherjee D, Prakash A, Zachariah MR (2006) Implementation of a discrete nodal model to probe the effect of size-dependent surface tension on nanoparticle formation and growth. J Aerosol Sci 37(10):1388–1399
Zachariah MR, Carrier MJ (1999) Molecular dynamics computation of gas-phase nanoparticle sintering: a comparison with phenomenological models. J Aerosol Sci 30(9):1139–1151
Yasuoka K, Matsumoto M (1998) Molecular dynamics of homogeneous nucleation in the vapor phase. I. Lennard-Jones fluid. J Chem Phys 109(19):8451–8462
Lummen N, Kraska T (2005) Molecular dynamics investigation of homogeneous nucleation and cluster growth of platinum clusters from supersaturated vapour. Nanotechnology 16(12):2870–2877
Li ZH et al (2007) Free energies of formation of metal clusters and nanoparticles from molecular simulations: Al-n with n = 2–60. J Phys Chem C 111(44):16227–16242
McGreevy RL (2001) Reverse Monte Carlo modelling. J Phys-Condens Matter 13(46):R877–R913
Mukherjee D, Sonwane CG, Zachariah MR (2003) Kinetic Monte Carlo simulation of the effect of coalescence energy release on the size and shape evolution of nanoparticles grown as an aerosol. J Chem Phys 119(6):3391–3404
Gillespie DT (1975) Exact method for numerically simulating stochastic coalescence process in a cloud. J Atmos Sci 32(10):1977–1989
Liffman K (1992) A direct simulation Monte-Carlo method for cluster coagulation. J Comput Phys 100(1):116–127
Kruis FE, Maisels A, Fissan H (2000) Direct simulation Monte Carlo method for particle coagulation and aggregation. AIChE J 46(9):1735–1742
Efendiev Y, Zachariah MR (2002) Hybrid Monte Carlo method for simulation of two-component aerosol coagulation and phase segregation. J Colloid Interface Sci 249(1):30–43
Mukherjee D, Wang M, Khomami B (2012) Impact of particle morphology on surface oxidation of nanoparticles: a kinetic Monte Carlo based study. AIChE J 58(11):3341–3353
Auer S, Frenkel D (2001) Prediction of absolute crystal-nucleation rate in hard-sphere colloids. Nature 409(6823):1020–1023
Valeriani C et al (2007) Computing stationary distributions in equilibrium and nonequilibrium systems with forward flux sampling. J Chem Phys 127(11)
Allen RJ, Valeriani C, Ten Wolde PR (2009) Forward flux sampling for rare event simulations. J Phys-Condens Matter 21(46)
Katz JL et al (1976) Condensation of a supersaturated vapor. III. The homogeneous nucleation of CCl4, CHCl3, CCl3F, and C2H2Cl4. J Chem Phys 65(1):382–392
Katz JL (1970) Condensation of a Supersaturated Vapor. I. The homogeneous nucleation of the n-alkanes. J Chem Phys 52(9):4733–4748
Oxtoby DW (1992) Homogeneous nucleation: theory and experiment. J Phys: Condens Matter 4(38):7627
Rusyniak M et al (2001) Vapor phase homogeneous nucleation of higher alkanes: dodecane, hexadecane, and octadecane. 1. Critical supersaturation and nucleation rate measurements. J Phys Chem B 105(47):11866–11872
Finney EE, Finke RG (2008) Nanocluster nucleation and growth kinetic and mechanistic studies: a review emphasizing transition-metal nanoclusters. J Colloid Interface Sci 317(2):351–374
Schmitt JL (1981) Precision expansion cloud chamber for homogeneous nucleation studies. Rev Sci Instrum 52(11):1749–1754
Wagner P, Strey R (1981) Homogeneous nucleation rates of water vapor measured in a two-piston expansion chamber. J Phys Chem 85(18):2694–2698
Hameri K, Kulmala M (1996) Homogeneous nucleation in a laminar flow diffusion chamber: the effect of temperature and carrier gas on dibutyl phthalate vapor nucleation rate at high supersaturations. J Chem Phys 105(17):7696–7704
Anisimov MP, Hameri K, Kulmala M (1994) Construction and test of laminar-flow diffusion chamber–homogeneous nucleation of Dbp and N-hexanol. J Aerosol Sci 25(1):23–32
Wyslouzil BE et al (1991) Binary nucleation in acid water-systems. 2. Sulfuric-acid water and a comparison with methanesulfonic-acid water. J Chem Phys 94(10):6842–6850
Viisanen Y, Kulmala M, Laaksonen A (1997) Experiments on gas-liquid nucleation of sulfuric acid and wafer. J Chem Phys 107(3):920–926
Fisk JA et al (1998) The homogeneous nucleation of cesium vapor. Atmos Res 46(3–4):211–222
Ferguson FT, Nuth JA (2000) Experimental studies of the vapor phase nucleation of refractory compounds. V. The condensation of lithium. J Chem Phys 113(10):4093–4102
Zhang RY et al (2012) Nucleation and growth of nanoparticles in the atmosphere. Chem Rev 112(3):1957–2011
Lu HM, Jiang Q (2005) Size-dependent surface tension and Tolman’s length of droplets. Langmuir 21(2):779–781
Lai SL et al (1996) Size-dependent melting properties of small tin particles: nanocalorimetric measurements. Phys Rev Lett 77(1):99–102
Tomanek D, Schluter MA (1986) Calculation of magic numbers and the stability of small Si clusters. Phys Rev Lett 56(10):1055–1058
Boustani I et al (1987) Systematic ab initio configuration-interaction study of alkali-metal clusters: Relation between electronic structure and geometry of small Li clusters. Phys Rev B 35(18):9437
Li ZH, Truhlar DG (2008) Cluster and nanoparticle condensation and evaporation reactions. Thermal rate constants and equilibrium constants of Al(m) + Al(n−m) <-> Al(n) with n = 2–60 and m = 1–8. J Phys Chem C 112(30):11109–11121
Girshick SL, Agarwal P, Truhlar DG (2009) Homogeneous nucleation with magic numbers: aluminum. J Chem Phys 131(13)
Wyslouzil BE, Seinfeld JH (1992) Nonisothermal homogeneous nucleation. J Chem Phys 97(4):2661–2670
Barrett JC (2008) A stochastic simulation of nonisothermal nucleation. J Chem Phys 128(16)
Domilovsky ER, Lushnikov AA, Piskunov VN (1979) Monte-Carlo simulation of coagulation processes. Izvestiya Akademii Nauk Sssr Fizika Atmosfery I Okeana 15(2):194–201
Debry E, Sportisse B, Jourdain B (2003) A stochastic approach for the numerical simulation of the general dynamics equation for aerosols. J Comput Phys 184(2):649–669
Garcia A et al (1987) A Monte Carlo method of coagulation. Phys A 143:535–546
Smith M, Matsoukas T (1998) Constant-number Monte Carlo simulation of population balances. Chem Eng Sci 53(9):1777–1786
Efendiev Y, Zachariah MR (2003) Hierarchical hybrid Monte-Carlo method for simulation of two-component aerosol nucleation, coagulation and phase segregation. J Aerosol Sci 34(2):169–188
Davari SA, Mukherjee D (2017) Kinetic Monte Carlo simulation for homogeneous nucleation of metal nanoparticles during vapor phase synthesis. AIChE J. Accepted. doi:10.1002/aic.15887
Pratsinis SE (1998) Flame aerosol synthesis of ceramic powders. Prog Energy Combust Sci 24(3):197–219
Mench MM et al (1998) Comparison of thermal behavior of regular and ultra-fine aluminum powders (Alex) made from plasma explosion process. Combust Sci Technol 135(1–6):269–292
Ozaki Y, Ichinose N, Kashū S (1992) Superfine particle technology. Springer, Berlin
Megaridis CM, Dobbins RA (1990) Morphological description of flame-generated materials. Combust Sci Technol 71(1–3):95–109
Friedlander SK (1977) Smoke, dust and haze: Fundamentals of aerosol behavior. Wiley-Interscience, New York, vol 333, p 1
Lehtinen KEJ, Zachariah MR (2001) Effect of coalescence energy release on the temporal shape evolution of nanoparticles. Phys Rev B 63(20)
Windeler RS, Lehtinen KEJ, Friedlander SK (1997) Production of nanometer-sized metal oxide particles by gas phase reaction in a free jet. 2. Particle size and neck formation - Comparison with theory. Aerosol Sci Technol 27(2):191–205
Windeler RS, Friedlander SK, Lehtinen KEJ (1997) Production of nanometer-sized metal oxide particles by gas phase reaction in a free jet. 1. Experimental system and results. Aerosol Sci Technol 27(2):174–190
Tsantilis S, Pratsinis SE (2000) Evolution of primary and aggregate particle-size distributions by coagulation and sintering. AIChE J 46(2):407–415
Ehrman SH, Friedlander SK, Zachariah MR (1998) Characteristics of SiO2/TiO2 nanocomposite particles formed in a premixed flat flame. J Aerosol Sci 29(5–6):687–706
Schweigert IV et al (2002) Structure and properties of silica nanoclusters at high temperatures. Phys Rev B 65(23)
Kruis FE et al (1993) A simple-model for the evolution of the characteristics of aggregate particles undergoing coagulation and sintering. Aerosol Sci Technol 19(4):514–526
Xing YC, Rosner DE (1999) Prediction of spherule size in gas phase nanoparticle synthesis. J Nanopart Res 1(2):277–291
Freund HJ, Bauer SH (1977) Homogeneous nucleation in metal vapors. 2. Dependence of heat of condensation on cluster size. J Phys Chem 81(10):994–1000
Lehtinen K, Zachariah M (2001) Energy accumulation during the coalescence and coagulation of nanoparticles. Phys Rev B 63(20):205402
Zachariah MR, Carrier MJ, BlaistenBarojas E (1996) Properties of silicon nanoparticles: a molecular dynamics study. J Phys Chem 100(36):14856–14864
Koch W, Friedlander SK (1990) The effect of particle coalescence on the surface-area of a coagulating aerosol. J Colloid Interface Sci 140(2):419–427
Wu MK et al (1993) Controlled synthesis of nanosized particles by aerosol processes. Aerosol Sci Technol 19(4):527–548
Martin DL, Raff LM, Thompson DL (1990) Silicon dimer formation by three-body recombination. J Chem Phys 92(9):5311–5318
Yaws C (1994) Handbook of vapor pressure. Gulf Pub. Co., Houston
Buffat P, Borel JP (1976) Size effect on the melting temperature of gold particles. Phys Rev A 13(6):2287
Tandon P, Rosner DE (1999) Monte Carlo simulation of particle aggregation and simultaneous restructuring. J Colloid Interface Sci 213(2):273–286
Iida T et al (2000) Equation for estimating viscosities of industrial mold fluxes. High Temp Mater Processes (London) 19(3–4):153–164
Hansen K, Campbell EEB (1998) Thermal radiation from small particles. Phys Rev E 58(5):5477–5482
Kumar S, Tien CL (1990) Dependent absorption and extinction of radiation by small particles. J Heat Transfer-Trans Asme 112(1):178–185
Tomchuk PM, Tomchuk BP (1997) Optical absorption by small metallic particles. J Exp Theor Phys 85(2):360–369
Altman IS et al (2001) Experimental estimate of energy accommodation coefficient at high temperatures. Phys Rev E 64(5)
Bohren CF, Huffman DR (1983) Absorption and scattering by a sphere. Absorption Scattering Light Small Part 82–129
Siegel R, Howel J (1992) Thermal radiation heat transfer. Hemisphere Publishing Corp, Washington DC
Rosner DE, Yu SY (2001) MC simulation of aerosol aggregation and simultaneous spheroidization. AIChE J 47(3):545–561
Norris JR (1999) Smoluchowski’s coagulation equation: uniqueness, nonuniqueness and a hydrodynamic limit for the stochastic coalescent. Ann Appl Probab 9(1):78–109
Kostoglou M, Konstandopoulos AG (2001) Evolution of aggregate size and fractal dimension during Brownian coagulation. J Aerosol Sci 32(12):1399–1420
Gooch JRV, Hounslow MJ (1996) Monte Carlo simulation of size-enlargement mechanisms in crystallization. AIChE J 42(7):1864–1874
Shah BH, Ramkrishna D, Borwanker JD (1977) Simulation of particulate systems using concept of interval of quiescence. AIChE J 23(6):897–904
Friedlander SK, Wu MK (1994) Linear rate law for the decay of the excess surface-area of a coalescing solid particle. Phys Rev B 49(5):3622–3624
Vemury S, Kusters KA, Pratsinis SE (1994) Time-lag for attainment of the self-preserving particle-size distribution by coagulation. J Colloid Interface Sci 165(1):53–59
Rosner DE (2005) Flame synthesis of valuable nanoparticles: Recent progress/current needs in areas of rate laws, population dynamics, and characterization. Ind Eng Chem Res 44(16):6045–6055
Strobel R, Pratsinis SE (2007) Flame aerosol synthesis of smart nanostructured materials. J Mater Chem 17(45):4743–4756
Bapat A et al (2004) Plasma synthesis of single-crystal silicon nanoparticles for novel electronic device applications. Plasma Phys Controlled Fusion 46:B97–B109
Holunga DM, Flagan RC, Atwater HA (2005) A scalable turbulent mixing aerosol reactor for oxide-coated silicon nanoparticles. Ind Eng Chem Res 44(16):6332–6341
Kommu S, Wilson GM, Khomami B (2000) A theoretical/experimental study of silicon epitaxy in horizontal single-wafer chemical vapor deposition reactors. J Electrochem Soc 147(4):1538–1550
Gelbard F, Tambour Y, Seinfeld JH (1980) Sectional representations for simulating aerosol dynamics. J Colloid Interface Sci 76(2):541–556
Frenklach M, Harris SJ (1987) Aerosol dynamics modeling using the method of moments. J Colloid Interface Sci 118(1):252–261
Whitby ER, McMurry PH (1997) Modal aerosol dynamics modeling. Aerosol Sci Technol 27(6):673–688
Kommu S, Khomami B, Biswas P (2004) Simulation of aerosol dynamics and transport in chemically reacting particulate matter laden flows. Part I: algorithm development and validation. Chem Eng Sci 59(2):345–358
Garrick SC, Lehtinen KEJ, Zachariah MR (2006) Nanoparticle coagulation via a Navier-Stokes/nodal methodology: Evolution of the particle field. J Aerosol Sci 37(5):555–576
Tsantilis S, Pratsinis SE (2004) Soft- and hard-agglomerate aerosols made at high temperatures. Langmuir 20(14):5933–5939
Wu MK, Friedlander SK (1993) Enhanced power-law agglomerate growth in the free-molecule regime. J Aerosol Sci 24(3):273–282
Maricq MM (2007) Coagulation dynamics of fractal-like soot aggregates. J Aerosol Sci 38(2):141–156
Zurita-Gotor M, Rosner DE (2002) Effective diameters for collisions of fractal-like aggregates: Recommendations for improved aerosol coagulation frequency predictions. J Colloid Interface Sci 255(1):10–26
Schmid HJ et al (2006) Evolution of the fractal dimension for simultaneous coagulation and sintering. Chem Eng Sci 61(1):293–305
Zhou L et al (2008) Ion-mobility spectrometry of nickel nanoparticle oxidation kinetics: application to energetic materials. J Phys Chem C 112(42):16209–16218
Dikici B et al (2009) Influence of aluminum passivation on the reaction mechanism: flame propagation studies. Energy Fuels 23:4231–4235
Wang CM et al (2009) Morphology and electronic structure of the oxide shell on the surface of iron nanoparticles. J Am Chem Soc 131(25):8824–8832
Rai A et al (2004) Importance of phase change of aluminum in oxidation of aluminum nanoparticles. J Phys Chem B 108(39):14793–14795
Sun J, Pantoya ML, Simon SL (2006) Dependence of size and size distribution on reactivity of aluminum nanoparticles in reactions with oxygen and MoO3. Thermochim Acta 444(2):117–127
Trunov MA et al (2005) Effect of polymorphic phase transformations in Al2O3 film on oxidation kinetics of aluminum powders. Combust Flame 140(4):310–318
Aumann CE, Skofronick GL, Martin JA (1995) Oxidation behavior of aluminum nanopowders. J Vac Sci Technol, B 13(3):1178–1183
Park K et al (2005) Size-resolved kinetic measurements of aluminum nanoparticle oxidation with single particle mass spectrometry. J Phys Chem B 109(15):7290–7299
Mukherjee D, Rai A, Zachariah MR (2006) Quantitative laser-induced breakdown spectroscopy for aerosols via internal calibration: application to the oxidative coating of aluminum nanoparticles. J Aerosol Sci 37(6):677–695
Alavi S, Mintmire JW, Thompson DL (2005) Molecular dynamics simulations of the oxidation of aluminum nanoparticles. J Phy Chem B 109(1):209–214
Vashishta P, Kalia RK, Nakano A (2006) Multimillion atom simulations of dynamics of oxidation of an aluminum nanoparticle and nanoindentation on ceramics. J Phys Chem B 110(8):3727–3733
Zhang F, Gerrard K, Ripley RC (2009) Reaction mechanism of aluminum-particle-air detonation. J Propul Power 25(4):845–858
Trunov MA et al (2006) Oxidation and melting of aluminum nanopowders. J Phys Chem B 110(26):13094–13099
Xiong Y, Pratsinis SE (1993) Formation of agglomerate particles by coagulation and sintering. 1. A 2-dimensional solution of the population balance equation. J Aerosol Sci 24(3):283–300
Mandelbrot BB (1983) The fractal geometry of nature 173 (Macmillan)
Meakin P, Witten TA (1983) Growing interface in diffusion-limited aggregation. Phys Rev A 28(5):2985–2989
Schmidtott A (1988) New approaches to insitu characterization of ultrafine agglomerates. J Aerosol Sci 19(5):553–563
Buffat P, Borel JP (1976) Size effect on melting temperature of gold particles. Phys Rev A 13(6):2287–2298
Levenspiel O (1999) Chemical reaction engineering. Ind Eng Chem Res 38(11):4140–4143
German RM (1996) Sintering theory and practice. Wiley, New York
Assael MJ et al (2006) Reference data for the density and viscosity of liquid aluminum and liquid iron. J Phys Chem Ref Data 35(1):285–300
Paradis P-F, Ishikawa T (2005) Surface tension and viscosity measurements of liquid and undercooled alumina by containerless techniques. Jpn J Appl Phys 44:5082–5085
Sarou-Kanian V, Millot F, Rifflet JC (2003) Surface tension and density of oxygen-free liquid aluminum at high temperature. Int J Thermophys 24(1):277–286
Blackburn PE, Buchler A, Stauffer JL (1966) Thermodynamics of vaporization in the aluminum oxide-boron oxide system. J Phys Chem 70(8):2469–2474
Polyak EV, Sergeev SV (1941) Compt Rend (Doklady) Acad Sci URSS 33
Samsonov G (1982) The oxide handbook. Springer, New York
Jensen JE et al (1980) Brookhaven national laboratory selected cryogenic data notebook, U.S.D.O.E. Brookhaven National Laboratory Associated Universities Inc., Editor. Brookhaven national Laboratory Associated Universities: UptUUpton, NY
Munro RG (1997) Evaluated material properties for a sintered alpha-alumina. J Am Ceram Soc 80(8):1919–1928
Weast RC (1989) CRC handbook of chemistry and physics. CRC Press, Boca Raton, FL
Astier M, Vergnon P (1976) Determination of the diffusion coefficients from sintering data of ultrafine oxide particles. J Solid State Chem 19(1):67–73
Acknowledgements
Figures, tables and discussions within Sects. 3 and 4 were in part or whole adapted/reprinted from the journal articles, J. Chem. Phys. 119, 3391 (2003) [44] and AIChE J., 58,3341 (2012) [49] with the author’s (D. Mukherjee’s) copyright permission from AIP publishing and Wiley Online respectively.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Mukherjee, D., Davari, S.A. (2017). Computational Modeling for Fate, Transport and Evolution of Energetic Metal Nanoparticles Grown via Aerosol Route. In: Shukla, M., Boddu, V., Steevens, J., Damavarapu, R., Leszczynski, J. (eds) Energetic Materials. Challenges and Advances in Computational Chemistry and Physics, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-319-59208-4_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-59208-4_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-59206-0
Online ISBN: 978-3-319-59208-4
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)