1 / 19

Coalescence - Agenda

Coalescence - Agenda. What if particles are liquid, or are solid but temperatures are high enough, solid state diffusion can occur? Koch and Friedlander, coalescence limited approach Effect of partice internal pressure on coalescence rate. How about finite coalescence rate?

javan
Download Presentation

Coalescence - Agenda

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Coalescence - Agenda • What if particles are liquid, or are solid but temperatures are high enough, solid state diffusion can occur? • Koch and Friedlander, coalescence limited approach • Effect of partice internal pressure on coalescence rate

  2. How about finite coalescence rate? Important for particle growth in steep T gradients, e.g. flames sintering complete chemical reaction particles grow by between collisions fast compared to collision/sintering particle formation times sintering incomplete between collisions particles are necked important characteristics: characteristic times: • primary particle size • time between particle • extent of agglomeration collisions • time required for particle coalescence

  3. necked unagglomerated agglomerated t time coalesce t collision residence time Characteristic times and particle morphology Characteristic times depend on concentration of particles and on material properties Desired degree of agglomeration depends on application

  4. Motivations • Models of nanoparticle growth important: • reactor/process design • understanding/predicting formation of unwanted • byproducts of combustion. • Models of particle growth for silica overpredict primary • particle size if instantaneous coalescence is assumed • (see for example Ulrich G.D., Milnes, B.A., and Subramanian, N.S., • Combustion Sci. Technol. 14, 243 (1976)). • Models of particle growth for silica underpredictprimary • particle size of finite coalescence times based upon bulk • viscosity are used (see Xiong, Y. Akhtar M.K., and Pratsinis S.E., J. • Aerosol Sci., 24, 301, (1993), Ehrman, S.H., Friedlander S.K., and • Zachariah, M.R., J. Aerosol Sci., 29, 687 (1998)).

  5. Further motivation • Because of high surface area to volume ratio, pressure • inside nanoparticles may be very high. • For materials which coalesce by viscous flow, rate is • dominated by viscosity, an extremely temperature • and pressure sensitive variable. • Unlike typical crystalline materials, diffusivity of O2- • and Si4+ ions in liquid silica increases with increasing • pressure, resulting in a decrease in mobility (viscosity) • with increasing pressure. • Goal • Incorporate this information into a traditional collision/ • sintering model of aerosol growth.

  6. Collision/sintering see Koch and Friedlander, 1990; Friedlander and Wu, 1994; Lehtinen et al., 1996 flame generated silica particles • a = surface area of aerosol • assumptions • no barrier to nucleation • coalescence is rate-limiting • gives solution for particle size • after long residence times • initial rate of growth important TEM - S.H. Ehrman

  7. Characteristic coalescence time for viscous flow tc = dp[2] Frenkel (1945) J.Phys. 9,385. s h = viscosity dp = particle diameter s = surface tension What does this mean, viscosity in a nanoparticle? Especially a rapidly colliding and coalescing nanoparticle. Chemical bonds rapidly forming and breaking.

  8. As evidence of atomistic behavior in silica: viscosity related to diffusivity, D through Stokes-Einstein relationship:  = kT [4] Dl has been observed experimentally for mixed silicates by Shimizu and Kushiro(1984) Geochim. Cosmochim. Acta. 48, 1295. l = volume of oxygen anion Coalescence as atomistic process: Coalescence via solid state diffusion mechanism [3] Friedlander and Wu, Phys. Rev. B, 49, 3622 (1994) vp = particle volume s = surface tension D = solid state diffusivity vo = volume of diffusing species

  9. Pressure inside nanoparticles Laplace Equation Pi Pi - Pa = 4s[1] dp s = surface tension dp = particle diameter Pi = internal pressure Pa = ambient pressure Pa Pi for 3 nm diameter silica particle ~ 2000 atmospheres! (~ 0.2 gigaPascals) • May result in phase and transport • behavior different from P = 1 atm.

  10. -E PV - ö æ D D exp a = d ç ÷ kT o ø è Effect of P on diffusivity • For crystalline systems, diffusivity has exponential • dependance on pressure as well as temperature: Ed = activation energy for diffusion, J molecule -1 Va = activation volume for diffusion, cm3 molecule -1 [5] • For typical crystalline materials, increasing pressure • leads to decreasing diffusivity. Va is positive, ~ equal • to volume of diffusing species.

  11. The special case of silica • It has been observed experimentally for pure silica and • for some mixed silicates (NaAlSi2O6, Na2Si4O9) and • also in molecular dynamics simulations of pure silica - • up to a certain pressure Pcritical , diffusivity of oxygen • and silicon ions increasesas pressure increases. • Va in Eq. 5 is negative! Vaestimates range from volume of oxygen ion to volume of SiO4 tetrahedra • references: Shimizu and Kushiro Geochim. Cosmochim. Acta, 48, 1295 (1984). • Tsuneyuki and Matsui Phys. Rev. Let. 74, 3198 (1995) . • Poe et al. Science, 276, 1245 (1997). • Aziz et al., Nature, 390, 596 (1997).

  12. Why? Pressure Facilitated Diffusion (c) After decompression, tetrahedral framework rearranged, and diffusion has taken place. (a) Silicon ( ) in tetra- hedral coordination, pressure = 1 atm. (b) As pressure increases, up to Pcritical, areas of higher coordinated silicon form locally. Method proposed by Tsuneyuki and Matsui (1995) Phys. Rev. Let. 74, 3197.

  13. Effect of P on D, for silica Diffusivity Pressure Pcritical P < Pcritical = activation energy for diffusion related to activation energy for forming higher coordinated silica. P > Pcritical = activation energy related to activation energy for formation of tetragonal silica. Pcritical estimates range from 1 to 10 gPa as reference point, for limiting case of 1 SiO4 tetrahedra, Pi = 0.3 GPa

  14. dp kT 3 E t ö exp æ = d ÷ lsvo ç c 128D kT ø è o dp kT 3 t = lsvo c 128D o tc as function of T and P tc (dp, T) from equation [3] incorporating T dependance of diffusivity [6] tc (dp, P,T) ù è s é 4 æ P + ú ç ê ç ç E V a ç d + ú combining eqn’s [1], [3], and [5] to include effect of internal pressure on D ê [7] exp æ p è ú d a ê ú ê kT ë û Ed = 5.44 x 10-19 J molecule-1 (328 kJ/mole) Rodriguez-Viejo et al. (1993) Appl. Phys. Lett. 63, 1906. Do = 1.1 x 10-2 cm2 sec-1 , ibid. vo = 6.9cm3 (based upon diameter of oxygen ion, 2.8 A) Pa = 1 atm (1.013 bars) s = 0.3 J m-2 Kingery et al. (1976) Introduction to Ceramics Va =19.2 cm3 mole-1, Aziz et al., Nature, 390, 596 (1997)

  15. Enhanced coalescence rate for particles in initial stages of growth

  16. da dt -1 (a - as) = tc dvp dt 0.31 vp tc = Model Results, Improvements! Collision/sintering model for final primary particle size: [8] Koch and Friedlander (1990) J. Colloid Interface Sci.140,419. In terms of particle volume for the case of two particles coalescing at one time, [9] Lehtinen et al. (1996) J. Colloid Interface Sci. 182,606. Linear temperature profile and plug flow velocity profile: T(x) = 1720 K - 106 x x in cm [10] Ehrman et al. (1998) J. Aerosol Sci. 29, 687.

  17. Particle growth for various coalescence times Atomistic, with effect of pressure Atomistic, No effect of pressure Viscous flow

  18. Summary/Conclusions • Magnitude of the pressure dependence appears to be • significant • Including pressure dependence increases rate of growth in • initial stages. Effect becomes stronger as temperature • decreases. • Predictions of particle size made with collision/sintering • model are closer to experimental values when effect of • pressure is included. • Though still not in quantitative agreement with experimental • values, results from this study suggest effect of internal • pressure is importantfor silica (and possibly other materials) • and should be considered when estimating material • properties of nanoparticles.

  19. Discussion - outlook You’d better know temperature. Coalescence very T sensitive. Recent developments from Zachariah group (2003) - energy from heat released by reduction of surface area, heats particle above background gas T, and leads to quicker coalescence. Surface tension as a function of T also may important Still need better estimates of surface tension as function of particle size Impurities may affect coalescence

More Related