Langmuir 1991,7, 1807-1814
1807
Particle Formation and Growth in Single-Stage Aerosol Reactors Hung V. Nguyent and Richard C. Flagan' Department of Chemical Engineering, California Institute of Technology, Pasadena, California 91125 Received August 24,1990. In Final Form: March 7,1991 The feasibility of producing dense particles of a refractory material controlled by reaction of a vapor precursor has been examined experimentally and theoretically. Previous experiments that generated dense, spherical particles of silicon have been repeated with one modification. The peak temperature in the reactor was lowered to minimize sintering of any agglomerates formed early in the reactor. Agglomerate particles were generated with a peak reactor temperature of 1070K. Raising the peak temperature to 1473 K resulted in nearly complete densification within a hot zone residence time of approximately 1 s. These results suggest that the dense particles previously reported resulted from sintering rather than vapor deposition. A simple model was used to probe the role of coagulation theoretically. Even with severely constrained reaction rates, a high concentration of fine particles was produced in the initial burst of nucleation. Coagulation plays a major role in the subsequent particle growth. The particles formed early in the reactor are efficient scavengers for clusters produced later, so only small clusters are formed after the initial nucleation burst for the conditions modeled. To suppress agglomeration, the number concentration produced by homogeneous nucieation must be reduced before entering the primary growth stage of the reactor. The use of a separate seed generation stage would be preferable to the single-stage reactor for particle growth by vapor deposition. 1. Introduction
Engineering applications of ceramic materials place severe demands on the starting powders from which the parts are created. The properties of the ceramic parts, such a8 fracture toughness, are highly dependent on the building blocks, the powder materials from which they are made. Consolidation of small,dense particles tends to form green compacts with few large pores. If the powder contains agglomerates, large pores may be generated due to bridging. These large pores reduce the green density and may cause substantial density variation across the compact. Large pores and inhomogeneous porosity in the green compact are a major cause of the highly variable structural properties of ceramic parts. Furthermore, kmg sintering times are required for complete densification when large pores are present. If the pores are too large, complete densification of the compact may become impractical. Pores that remain after densification are the points of origin of cracks, causing parts to fail under stress far below those predicted for a homogeneous material. Smaller ceramic precursor particles reduce sintering times and make smaller pore sizes attainable, although the handling of ultrafine particles is both difficult and expensive. Moreover, their high surface area to volume ratios makes such powders very susceptible to surface contamination. For these reasons, ceramic powders are presently limited to particles larger than about 0.1 pm diameter. Powders consisting of solid, roughly equiaxed, nonagglomerated, submicrometerparticles with controlled size distribution are thought to be ideal for the production of uniform high density green compacts of ceramics and other powder-based materials.' A variety of methods have been used to produce such powders. Colloidal methods such as the sol-gel process can produce highly uniform, nonagglomerated particles, although the range of composition is limited primarily to
*Towhom correspondence should be addressed. Present addreae: IBM Almaden Research Center, San Jose,CA. (1) Bowen, H. K. Mater. Sci. Eng. 190,44,1.
metal oxides.2*aSynthesis by aerosol routes has also been used to produce high-quality powders. Thermal plasma processes are used commercially to synthesize a broad range of powders for ceramics and other applications. Reasonably uniform silicon, silicon nitride, and silicon carbide have been generated by laser-induced reactions.4Jj Oxide particles are produced by vapor-phase oxidation of metal halides in flame synthesis.@ A variety of materials have been produced by externally heated aerosol reactors. High-quality silicon powders have been obtained by the thermal pyrolysis of si1ane.O The reaction of silane and ammonia in a heated tube produces silicon nitride.10 Vapor precursor powder synthesis begins with gas-phase chemical reactions that produce condensible vapors from more volatile precursors. High supersaturations are readily achieved due to the low saturation vapor pressure of ceramic materials, so large numbers of particles are generated by homogeneous nucleation. These particles grow by the combined effects of vapor deposition (physical condensation and/or surface reaction), small molecular cluster deposition, and coagulation both with large clusters and with similarly sized particles. Growth by chemical or physical vapor deposition has been proposed as a way to produce dense, nonagglomeratedparticles. Low-temperature silane pyrolysis under conditions that seed particles grow at essentially constant number concentration has, however, produced low-density particles.11 This has been (2) Barringer, E. A.; Bowen, H. K. Commun. Am. Ceram. SOC.1982,
66, c-199.
(3) Gobet, J.; Matejevic, E. J. Colloid Interface Sci. 1984,100, 655. (4) Cannon, W. R;Danforth,S. C.;Flint, J. H.; Haggerty, J. S.;Marra,
R. A. J. Am. Ceram. SOC.1982,65,324. (5) Cannon, W. R.; Danforth, S. C.;Haggerty, J. S.;Marra, R. A. J. Am. Ceram. SOC.1982,66, 330. (6) Ulrich, G. D. Combwt. Sci. Technol. 1971,4,47. (7) Ulrich,G. D.; Ines, B. A. M.; Subramanian, N. S. Combwt. Sci. Technol. 1976,14,243. (6) Ulrich,G. D.;Subramanian,N. A. Combwt. Sci. Technol. 1977,17, 119. (9) Wu, J. J.; Nguyen, H. V.; F an, R. C. hngmuir 1987,9,266. (10) Prochazka, S.; Greakovich!% Am. Ceram. SOC.Bull. 1978, 57, 579. (11) Wu, J. J.; Flagan, R. C. J. Appl. Phys. 1987,62, 1365.
0743-7463/91/2407-l807$02.50/0 (8 1991 American Chemical Society
1808 Langmuir, Vol. 7, No. 8, 1991
attributed to growth by cluster deposition. Growth by coagulation creates low-density flocs unless the temperature is high enough that the agglomerates sinter completely. Thus, dense particles can be generated either by "vapor" deposition or by sintering of agglomerates, but low density particles can result from either process under some circumstances. The time required for sintering increases with spherule size, so the maximum size of particles that can be fully densified by sintering in the short time available in aerosol reactors is limited for refractory materials. On the other hand, the growth of dense particles by vapor and cluster deposition can be achieved only by simultaneous suppression of homogeneous nucleation and cluster growth. This control of particle formation is extremely difficult to achieve for refractory materials. Since homogeneous nucleation of refractory materials generally produces large numbers of small particles, coagulation is usually a major contributor to particle growth. Wu et al.9 have proposed a method for the production of high-quality powders by vapor-phase precursors using a single-stage, multizone thermal reactor. Their recipe involves generating particles much smaller than the desired particle size by homogeneous nucleation while keeping the number concentration low enough to suppress growth by coagulation. The chemical reactions that lead to gasto-particle conversion must then be carried out at gradually increasing but controlled rates such that the particles are grown by deposition of the reaction products and new particle formation is suppressed. Uniformly sized, dense spherical particles of silicon were synthesized in a singlestage silane pyrolysis reactor operated in this mannerag It can be shown that particle growth in these experiments was influenced by both vapor and cluster deposition and coagulation. The reported number concentration at the reactor outlet was N = 4.6 X lo9 cmm8. The residence time, f R , in the reactor was approximately 1.5 8. Assuming that the particles were monosized, the coagulation rate coefficient for 0.1-pm particles is on the order of 9, = 1 X lo4 cm3 s-l. The characteristic time for coagulation at the reactor outlet, r c = 2 f @No= 0.5 s, is comparable to the reactor residence time. The characteristic time for coagulation within the reactor was probably shorter than this estimate because the concentration used for this estimate represents those particles that remain after coagulation has depleted their number. Thus, it appears likely that coagulation contributed significantly to the particle growth in the single stage reactor experiments. Since dense, spherical particles were reported, the agglomerates produced by coagulation must have sintered completely. Given the high peak temperatures of those experiments (1523K), such sintering cannot be ruled out. For development of thermal reactor technologies for the synthsis of refractory ceramic materials, it is important that the mechanism of particle growth by understood and controlled. The direct production of more refractory ceramic materials, such as silicon nitride in single-stage, multizone reactors is feasible only if dense particles can be grown directly by vapor and cluster deposition since densification of agglomerate particles a t practical reactor temperatures is likely to be too slow. In this work, the experiments of Wu et al.9were repeated with the temperature of the final zone kept low to minimize agglomerate sintering. If the particles do, in fact, grow by vapor deposition, then we would expect solid particles to be generated, even a t low peak temperatures. On the other hand, the low temperature should ensure the survival of any aggregate particles that are formed, thereby revealing
Nguyen and Flagan STATIC MIXERS SILANE ond N 1 T R C G E N . v MIXTURE ZONE I ZONE 2 ZONE 3
ZONE 4
ZONE 5
Figure 1. Schematic of the single-stage,five heating zone aerosol reactor used to produce silicon articles by silane pyrolysis. The transpiredwall dilution system used to minimize thermophoretic deposition of the product particles is enlarged.
the role of coagulation in particle growth. These experiments were accompanied by simulation of particle formation and growth to substantiate the inferred growth mechanism. 2. Experimental Section
Figure 1 showsthe single-stage reactor used in the experiments. It consists of a 1.1 cm i.d., 100 cm long quartz tube, with a total heated length of 55 cm. A total of five heating zones were used to produce a smoothly varying temperature profiie along the reactor length. The first three zones were each 5 cm long and were separated by 1cm of insulation to ensure smooth temperature profiles. These zones were heated with nichrome resiatence wire heating elements to temperatures up to 1370 K. The final two zones were 20 and 15 cm long, respectively, capable of achieving temperatures as high as 1770 K using silicon carbide heating elements. Again, the zones were separatedby insulation. Low silane concentration reactant gases were prepared by mixing dilute silane (1% in No Matheson)with additionalhighpurity nitrogen (99.996%)that had been passed over hot copper shavings for additional oxygen removal. The resulting mixture was introduced into the top of the reactor tube. The total flow rate was 1 L min-l f 6% for all silane concentrations. The temperaturesof the heating zones were controlledto achieve smoothly varying wall temperature profiles such as those illustrated in Figure 2. The profiie used on the previous experiments on the same reactor by Wu et al.9 is illustrated by the open points. The aerosol stream exiting from the bottom of the reactor tube was cooled by dilution with high-purity nitrogen that was transpiredthrough a porous, sinteredstainless steeltube (Figure 1, insert). This served the dual purposes of reducing both the particle number concentration and the gas temperature and minimizing both lose by thermophoreticdeposition ontothe cold wall and coagulation. The resulting aerosolmixture was further diluted with the recirculating dilution system shown in Figure 3. The two dilution stages reduced the number concentration of particles to a level compatible with conventional aerosol instruments. The size distributions of the product aerosol were measured over the size range from 20 to 300 nm by using a differential mobility analyzer (DMA, TSI Model 3071)with a condensation nuclei counter (CNC,TSI Model 3760) as a detector. In the DMA, a =Kr source is used to generate bipolar gas io- that attach to particles. The particles are then classified by their drift velocity in an electric field. Particles within a particular mobility range are extracted from the DMA and counted with the CNC. The mobility distribution was obtained by making a seriesof number concentration measurements at differentelectric field strengths. The sizedistribution wasdeterminedby inverting
Langmuir, Vol. 7, No. 8, 1991 1809
Particle Formation and Growth
4
Sample in
I I/Thot
A
Y, I-
10
20
30
50
40
60
Copper rod quid nitrogen
70
z (cm) Figure2. Measured wall temperature profiles corresponding to peak reactor temperatures of 1073 K (solid points) and 1523 K (open points). AEROSOL FLOW
-dlbFINE FILTER
Figure4. Schematic of the thermophoretic sampling probe used to obtain samples for TEM imaging of individual particles.
DILUTION NITROGEN
CIRCULATING DEVICE
COARSE FILTER
4
Figure 3. Schematic of the recirculating dilution system. the mobility distribution data with the routine MICRON.^^ The portions of the inverted distributions outaide the range that is directly measurable by the DMA were truncated, and the geometricmean diameters were computed based on the resultant distributions. The DMA/CNC combination provides only 'information regarding the mobility equivalent size of the particles, i.e., the electrostatic force to aerodynamic drag ratio, not their morphologies. Particle samples collected on Teflon filters were dispersed in water and placed on grids for examination under a transmission electron microscope (TEM). Microscopic analysis revealed the nature of the primary particles (spherules) rather than the agglomerates. Due to additional agglomerationof particles during the TEM grid preparation, the aggregatestructures could not be determined unambiguously. The sizes of the spherules were determined manually from electron micrographs. If the particles were solid single spheres, the mean mobility diameter computed from the DMA/CNC measurements would be the same as the mean primary particle diameter measured by the TEM, but as will be shown below, the two sizes differed markedly. Micrographs of the product particles were also obtained by using a thermophoretic TEM sampling probe (Figure 4). This probe allowed for direct collection of the particles exiting the reactor on the TEM grids,thereby eliminatingthe need todisperse collected particles in water and facilitating direct observations of particle structure. In the probe, the aerosol stream is heated, (12) Wolfenbarger, J. K.;Seinfeld,J. H.J. Aerosol Sci. 1990,22,227.
- 10
100
lo00
DP (nm)
Figure5. Particle size distributions measured for different initial SiHd concentrations with a peak reactor temperature of 1073 K. Sizes presented are mobility equivalent diameters. then impinged on a TEM grid that is mounted on the end of a copper rod. The other end of the rod was cooled by immersion in either liquid Nz or ice water. The sharp temperature gradient in the boundary layer of the stagnation point flow causes the particles to be driven from the hot gas onto the cold grid by thermophoresis. The number of particles collected on the TEM grid was controlled by adjusting the temperature gradient and collection time. The number of particles per unit grid area (number density) was kept low so that the structuresof individual particles could be determined.
3. Experimental Results Typical particle size distributions measured at the reactor outlet are shown in Figure 5. Duplicate measurement are presented for two different initial silane concentrations. For each reactant concentration, the size distributions agree closelyin size and number. The general shapes of the size distributions are similar in each case. Increasing the reactant concentration leads to larger apparent particle sizes.
Nguyen and Flagan
1810 Langmuir, Vol. 7, No. 8, 1991
1 0
-0-
0.01
mean diameter (DMA) primary diameter (TEM)
0.1
1
Initial SiH, conc. (“A)
Figure 6. Variation in the mean particle size as a function if the initial SiH4 concentration. Compared are the mean mobility diameter measured by using the DMA and the mean primary particle size measured by TEM.
The variation in the mean particle size with reactant concentration is shown in Figure 6. Both the mean mobility equivalent diameters and the spherule sizes determined by transmission electron microscope analysis of the particles collected by the Teflon filters are presented. The mobility equivalent particle size is 2 to 10times higher than that determined by microscopy for the silane concentrations studied. This large discrepancy indicates that the product particles are aggregates of the smaller structures. The mobility equivalent size increased significantly with initial silane concentration, while the fine structure or primary particle size remained relatively constant. The thermophoretic samplingprobe was usedto examine the structure of individual particles. Figure 7a shows a typical particle collected during reaction of 0.17 % silane. It is a chain agglomerate composed of approximately 19 nm diameter spherules and is typical of the particles collected with a low peak reactor temperature of 1070 K. From this structure, we may conclude that coagulation played a major role in the particle growth, leading to the formation of the aggregates. Furthermore, it is apparent that the particles have not fused completely within the 0.3 s residence in the reactor. Additional experiments were performed with higher peak temperatures to examine the possible role of particle fusion in the previous experiments of Wu et aL9 Parts b and c of Figure 7 show the particle structures that resulted when the peak temperature is raised to 1273 and 1473 K, respectively. It appears that aggregates like that shown in Figure 7a have undergone substantial, but not complete, coalescence. Hence, the dense particles previously reported with peak reactor temperatures of 1573 K likely resulted from coalescence of aggregate particles formed early in the reactor. The product number concentration variation with reactant concentration is shown in Figure 8. A 50-fold increase in the initial silane concentration resulted in a modest 35% increase in the total number concentration at the reactor outlet. This weak dependence of the number concentration with reactant loading is also consistent with the growth of particle primarily by coagulation. The
u.-
Ulll
Figure 7. TEM micrographs of silicon particles produced with an initial SiH4 concentration of 0.17 96 and a peak temperature of (a) 1073 K, (b) 1273 K, and (c) 1473 K.
number of particles predicted for a coagulating free molecular aerosol with the self-preserving particle size distribution13 for the silane concentration in 0.018% , assuming an average reactor temperature of 910K, is 2.82 X lo8~ m - ~ This . is in close agreement with the measured value of 1.57 X 108cm-3, particularly when it is noted that the theory assumes that the particles are dense spheres rather than the the aggregate structures that are apparently present in the low-temperature regions of the reactor. 4. Theory The particle structure observed with low peak temperature strongly suggests that coagulation played a crucial role in particle growth. A modeling effort was undertaken (13)Lai, F. S.; Friedlander, S. K.;Pich, J.; Hidy, G. M. J. Cotloid Interface Sci. 1972,39, 395.
Langmuir, Vol. 7, No. 8,1991 1811
Particle Formation and Growth
to substantiate this conclusion. Availablemodels of aerosol dynamics do not fully describe the evolution of an aerosol in which aggregates coalesce slowly. Most models of aerosol dynamics assume that particles coalesce instantly upon aggregation. Hence all particles are commonly assumed to be dense spheres.14 The diffusivities and collision cross sections of spherical particles are wellknown. Although the structures of noncoalescingparticles can be predicted by using diffusion-limited aggregation or cluster-cluster aggregation models,16J6 data on diffusivities and collision cross sections are lacking. Moreover, the influence of finite coalescence rates on particle growth has not been described theoretically. Recognizing these limitations, we shall use an approximate solution to the aerosol dynamic equation based on dense, spherical particles to probe the particle behavior in single-stage aerosol reactors. The simplified reaction coagulation (SRC)modeP was used to simulatethe aerosol evolution. This is an integral model representing the aerosol size distribution with two modes. The fine mode followsthe evolution of fine particles and clusters, i.e., the new particle produced by homogeneous nucleation. The second mode describes the behavior of the seed particles. In the original SRC model, mass is added to the fine mode directly from the reaction source. Here, a separate monomer balance is added to the model to better account for the condensation of the condensible vapors onto the particles. Mass is introduced into the fine mode by the monomer-monomer coagulation and by condensation of the monomers onto the fine particles (which is equivalent to coagulation of the monomer with the fine particles) and is removed by the seed particles. Because of the very low vapor pressure of Si at the conditions of interest here, mass loss by evaporation is neglected. Mass is added to the seed mode by coagulationof seeds with both monomers and fine particles. The two modes are followed by the number and mass concentrations N Hand MH,and NSand Ms,respectively, where the subscript H represents the homogeneousnucleation or fine mode and S the seed mode. For the present purposes, wall losses are neglected, and the aerosol and temperature are assumed to be uniformly distributed across the reactor tube. It is also assumed that, when two particles collide, they stick and form a single, dense new particle. A set of seven nonlinear differential equations is sufficient to follow the aerosol evolution
u ZP
cP-dT = - h,(T,-T) dz D,
(7)
with initial conditions at z = zo (14) &ield, J. H.Air Pollution; Wiley: New York, 1986. (15) Merlin, P.; Witten, T. A., Jr. Phys. Reu. A: Gen. Phys. 198S, 28,
2986.
(16) Meekin, P. J. Colloid Interface Sci. 1986,112, 187. (17) Wu,J. J.; Nguyen, H.V.; Flagen, R. C.; Okuyama, K.;Kousaka, Y. AIChE J. 1988,34, 1249.
NH MH = 0 (8) Ns = Nm (9) Ms = Mm (10) T = To (11) where K1, K ~ HKls, , K H , KHS,and Ks represent the coagulation coefficients. CAis the precursor concentration, R is the time varying reaction rate, and f i is~the average mass of a particle in the fine mode evaluated by =MH/NH and u,, are the reactor diameter, bulk gas density, heat capacity, and average velocity, respectively. T and T,are the gas and wall temperatures. h, is the average local heat transfer coefficient. NAVis the Avogadroconstant. From the steady-state one-dimensional continuity equation
D g ,p, C ,,
d
-&(U,P)
=0
Equations 1-7 become
u.$(
): = RNAv - K I N t- KIHNINH- KlsNINs (14) -(-) d N H = i K 1 N : - i K H N H 2 - K H s N H N s(15)
u"pdz
p
The detailed decomposition kinetics of silane involves many elementary reactions. The rate-limiting step is18
-.
SiH, + M SiH, + H, + M (19) with subsequent reactions rapidly leading to Si formation. Firsborder kinetics was assumed in the model calculations. The following pseudo-first-orderrate expression was used for conversions up to 1 % l8~9
[SiH,] mol cm-' s-l (20) where [MI is the total molar concentration of gas in the system (silane plus background gas) expressed in units of mol ~ m - ~For . conversions from 1% to depletion of the reactant, a first-order rate expression in silane reported by White et al.18 was used. The rate constant for this range was k = 1o12.Be-26768/?' s-l (21) Back reactions due to H2, which have been observed for conversions beyond 40% ,were neglected, as have surface reactions. (18) White, R.T.;Eapinc-Ron, R.L.;Ragen, D. 8.; Ring, M. A.; end ONeal, H.E.Int. J. Chem. Kinet. 1986,17,1029. (19) h e l l , J. H.;Walsh, R.Proc. R. SOC.London, Ser. A 1966,299, 543.
Nguyen and Flagan
1812 Langmuir, Vol. 7, No. 8, 1991 1o’O
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Initial Silane Concentration (YO)
Figure 8. Variation in the total particle number concentration measured at the reactor outlet using the DMS as a function of the initial SiH, concentration.
Two approaches were used to simulate the aerosol evolution. In the first approach (approach A), the aerosol remains as a single mode (fine mode) throughout the simulation. In the second approach (approach B), the aerosol starts out with a single mode, the fine particles formed by homogeneous nucleation. Once the number concentration in the fine mode reaches a local maximum, the fine particles are relabeled seed particles, and the size distribution is represented by two modes. The resulting calculations illustrate the ability of the seed particles to suppress new particle formation and the extent to which the particles formed early in the reactor grow by coagulation. Calculations were performed for the conditions of our experiments. The wall temperature profile was assumed to vary linearly from the midpoint of one zone to the next. The reactor inlet and outlet were at room temperature. 5. Model Rssults Figure 9a shows the predicted variation in the number concentration with axial position in the reactor for an initial silane concentration of 0.018%. Particle formation begins approximately 20 cm from the reactor inlet. The number concentration rises rapidly, peaking at about 35 cm from the reactor inlet. At this point, the two representations of the particle dynamics diverge. The single mode description (approach A) shows a gradual decrease in the number concentration, the result of the competition between coagulation of the nuclei formed early in the reactor and the formation of new nuclei from monomers. Accelerating the reaction in the downstream region leads to a second brief burst of new particle formation. With the precursor depleted, coagulation dominates the aerosol dynamics in the region downstream of this second nucleation burst. Because coagulation determines the ultimate number concentration of growing particles, the uncertainty in the reaction is not likely to significantly influence the total number of particles generated or general conclusions about the role of nucleation and coagulation in the dynamics of particles in single-stage aerosol reactors. The gas-phase reaction rate will, however, influence the particle size because the mean particle size is directly coupled to the amount of material reacted.
0.1 ~
.
.
.
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.
.
.
.
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.
.
.
.
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.
.
.
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.
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~
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z (cm) Figure 9. Predictions of particle formation and growth as a function of axial position in the reactor for 0.018% Si& wing approachesA (singlemode) and B (twomode): (a) total number concentration; (b) average particle size.
The two-mode representation of the aerosol dynamics (approach B)treats the particles formed early in the reactor as seed particles and probes the ability of these seeds to suppress further new particle formation. The seed concentration decreases quickly due to coagulation, with additional fine particle formation increasing the total number concentration above that of the single mode description after a short delay. The discontinuity seen in Figure 9a results from the arbitrary splitting of the two modes and is not physically significant. The number of the fine particles rapidly reaches a limiting value beyond which the concentration decreases slightly due to the combined effects of new nuclei formation and lossof nuclei by coagulation with other nuclei and with the seed particles. Late in the process there is a second burst in the fine
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Particle Formation and Growth 1o'O
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Langmuir, Vol. 7, No.8, 1991 1813 4
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Initial Silane Conc. ("A) Figure 10. Comparison of the calculated and measured total number concentrations at the reactor outlet as a function of the initial SiH, concentration. particle formation. That event is followed by the rapid loss of all of the fine mode particles by coagulation with the seed particles. The small increase in the seed mode concentration near the reactor outlet is due to the cooling of the gas, resulting in an increase in the gas density, which increases the particle number concentration (the reactants are consumed completely in the hot zone between 20 and 80 cm from the reactor inlet). The number concentration predicted by the singlemode model is approximatelytwice that by the two-mode model. Figure 9b shows the variation of particle size. The single mode calculation shows a gradual increase in the particle size from atomic dimensions until late in the reaction, where the second burst of new particle formation occurs. At that point, the mean particle size decreases slightly. Particles are not expected to decrease in size. Rather, the decrease in the mean size results from fast production of large numbers of very small particles. The two-mode model eliminates this computation artifact from the particles that account for the bulk of the aerosol mass. The seed particles grow continuously. The fine particles are seen to be small clusters, containing fewer than 13 atoms throughout the reactor. They are continuously being formed by monomer-monomer collisions and rapidly lost by coagulation with the seed particles. Thus, the apparent gradual decrease in the fine particle size after the initial nucleation burst is representative of the size to which the particles can grow before being lost to the seeds. During the second burst, the fine clusters grow to their largest size, slightly smaller than 1 nm. The rapid scavenging of the fine particles by the seeds limits their growth to sizes far below the mean size. Figure 10 compares calculations and experimental observations of the variation in the final number concentration with reactant concentration. The measured values at low silane concentration are lower than the predicted, and the sensitivity of the number concentration to the precursor level is somewhat greater than predicted by either model. The concentration dependence is weak, however, and the absolute concentrations agree well. Figure 11 compares the number mean mobility equivalent size at the reactor outlet with the predictions. The average size increases significantly with increasing silane
0.01
0.1
1
Initial SiH, Conc. (%)
Figure 11. Comparison of the calculated and measured mass mean diameters as a function of the initial SiH, concentration.
concentration, and the model calculations are in quite close agreement with the measured values, particularly given the differences in the structures produced experimentally with low peak reactor temperatures and the spherical shape assumed in the models. The measured particle size distribution is based on the "mobility equivalent diameter" which may differ significantly from the mass-based diameter obtained from the model. The average sizes predicted by the two-mode model are larger than those by the single mode. The predicted sizes are larger than the measured mean size for small silane concentrations, but are smaller for higher silane concentrations. This may be due to wall losses. At low silane concentrations, the particles produced are small and cannot compete for the condensible vapors as efficiently as the larger particles formed at higher reactant concentrations. The particles generated at these temperatures are low-density agglomerates; thus, as long as losses are not important, the measured mean sizes are expected to be larger than those computed based on the assumption of spherical shape. 6. Conclusions
The present experimental results suggest that the dense silicon particles produced in a single-stage multizone thermal reactor by Wu et al.g resulted not for vapor and cluster deposition on the nuclei generated early in the reaction but rather from sintering of the agglomerates formed by coagulation of like-sized particles. Model predictions further support this conclusion,indicating that coagulation plays a major role in particle growth throughout the reactor. To eliminate coagulation of the "seed" particles formed by nucleation early in the reactor, the seed number concentration must be reduced to a sufficiently low level that the characteristic time for self-coagulation of those seed particles, when they are large, becomes long compared to the residence time in the active portion of the reactor.
1814 Langmuir, Vol. 7, No. 8, 1991
While this might be accomplished by allowing a long time for coagulation after seed formation, when the particles are still very small, the use of a separate reactor stage for seed particle formation would allow coagulation to be quenched by dilution as demonstrated by Alam and F1aganm in the growth of large particles. Even though agglomerateparticles were generated,their fine structure revealsthat significantcoalescencehastaken place. The predicted fine cluster size is below 1nm in all (20) Alam, M.K.;Flagan, R. C.Aerosol Sci. Technol. 1986,5, 237.
Nguyen and Flagan
cases. Most of the mass deposita on the seeds in the form of fine particles rather than monomers. The fine structure sizesrange from 13 to 19nm, indicating that the deposited material has coalesced substantially, although incompletely. Acknowledgment. This work was supported by the National ScienceFoundation, Grant Number CBT-881306. The help of Carol Garland in the electron microscopy is greatly appreciated.
