The collisional growth of soot particles at high temperatures

THE

COLLISIONAL

GROWTH OF SOOT PARTICLES TEMPERATURES

AT HIGH

S. C. GRAHAM Shell Research Limited, Thornton Research Centre, P.O. Box 1, Chester CH1 3SH, England

Recently, we have shown that the light-scattering behaviour of soot aerosols in incident shock flows (duration - 3 ms) at -1800 K is consistent with the predictions of free-molecule coagulation theory. However, agreement between theory and experiment is obtained only if it is assumed that the collisions between soot particles are coalescent in that the collision partners fuse completely after each collision to form a new spherical particle. The aim of the present study is to determine as directly as possible, whether the collisions that occur in the first 1-2 milliseconds following nucleation are indeed coalescent or chain forming. This was achieved from observations on soot aerosols generated in cycloheptatriene/argon shock-flows a t - 1 7 5 0 K using a laser light-scattering technique in which the polarization of the incident beam was modulated at - 2 0 kHz. The ratios of the absorbanees of the aerosol at 488 nm and 3.39 p,m were also measured to assess the relative proportions of true soot (I.R. absorbing) and polynuclear aromatics (I.R. transparent) in the condensed phase. The polarization modulation permitted the variation in the ratio of the differential light-scattering cross-sections of the aerosols, for light-scattered perpendicular and parallel respectively to the polarization direction of the linearly polarized incident beam, to be measured during the same shock flow, This ratio was observed to increase throughout the flow, showing that the scattering properties of the particles become more and more like those of isotropic spheres as time proceeds. This behaviour is the opposite of that predicted for chain-forming collisions. The small but significant scattering that is observed along the polarization direction of the incident beam is attributed to an intrinsic, rather than a shape anisotropy, that reflects the highly anisotropie nature of the polynuclear aromatics that are present in the particles.

Introduction

here is that isotropic spherical particles do not scatter light in this direction. 4 I n contrast, anisotropic a n d / o r non-spherical particles (inc l u d i n g particle chains) scatter light along the vibration direction with a n intensity that increases as the particles deviate increasingly from isotropie spheres.

We have recently developed 1-3 theoretical models of a coagulating aerosol whose behaviour agrees well with our optical measurements on soot aerosols. The models are based in part on the following assumptions that relate to the collision process: (i) the particles are spherical and perfectly sticky, (ii) when two particles collide, they coalesce a n d fuse completely to form a n e w spherical particle. Our aim here is to determine, as directly as possible, whether collisions between particles are "coalescent" (as assumed in our models) or chain-forming. To achieve this we have made a time-resolved study of the d e p e n d e n c e of the differential scattering cross-sections of the soot aerosols on the vibration direction of the electric vector of a linearly polarized incident laser beam. T h e u n d e r l y i n g principle

Experimental The soot aerosols were generated in incident shock flows of h y d r o c a r b o n / a r g o n mixtures at temperatures in the range 1700-1800 K. The shock tube and associated apparatus and techniques 1-3.5,6 have b e e n described elsewhere, apart from the polarization-modulation system described below. T h e same photomultiplier a n d associated detection system described elsewhere 1-3"6 was used to detect the light 663

664

SOOT FORMATION AND GROWTH

scattered perpendicular to an argon-ion laser beam at 488 nm. The polarization-dependence of the scattered light intensity was achieved by appropriate modulation of the polarization of the incident laser beam using an Electro Optic Developments modulator and associated drive amplifier. Briefly, the procedure adopted was as follows. The laser beam was " o n / o f f " modulated at ~40 kHz by a toothed disc driven by an air turbine, described previously, z This disc was equipped additionally with a light-emitting diode and associated detector mounted on a micrometer stub, itself mounted tangentially to the periphery of the toothed disc (Fig. 1). The reference signal from the L.E.D. was first transformed into a square wave of constant but adjustable amplitude. It was then halved in frequency before being used as the input signal of the linear voltage amplifier used to drive the electro-optic modulator. After appropriate alignment of the modulator crystal, the " o n / o f f " modulation and the polarization modulation were then synchronized by adjustment of the micrometer to compensate for the frequency-dependent phase lag between the output and input voltages of the drive amplifier. Correctly synchronized, successive "on" periods of the laser beam were alternately

vertically polarized (zero horizontal component) and elliptically polarized (predominantly horizontal) as illustrated in Fig. 2. Because the intensity of the scattered light reaching the photomultiplier P~ (Fig. 1) during the "vertical" half of the modulation cycle is extremely sensitive to any horizontally polarized component that may be present in the incident beam, the drive amplifier was fitted with a Zener diode to clamp the potential across the crystal to a constant value (nominally zero) as quickly as possible during this half of the modulation cycle. The diode clamp also ensured that the amplitude of the square wave input to the drive amplifier (Fig. 1) affected the output of the amplifier only during the "elliptical" half of the modulation cycle. The scattered light signal for a single shock flow (duration - 3 ms) generated three envelopes, which in increasing order of intensity corresponded to (a) emission only, (b) emission + "vertical" scattering, and (c) emission + "elliptical" scattering. For convenience, the three envelopes were used to calculate, for each shock flow, the variation in the corresponding polarization ratio, R~.~, defined as the ratio of the differential cross-sections of the soot aerosols for light scattered perpendicular to and parallel to the vibration direction of a

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SOOT PARTICLES AT HIGH TEMPERATURES

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Alignment and Calibration Procedures Before any measurements were made on incident shock flows, several alignment and calibration procedures were carried out. The most important of these are described below. With the shock t u b e w i n d o w s W I and W2 (Fig. 1) removed, the electro-optic crystal was rotated about the two axes normal to the laser b e a m until the beam e m i t t e d d u r i n g the diodec l a m p e d half of the m o d u l a t i o n cycle was as nearly linearly p o l a r i z e d as possible. The deviation from linear polarization was established by rotating the Glan-Taylor ana]yser (Fig. 1) through 180 ~. This gave a ratio of m a x i m u m to m i n i m u m transmitted light intensities during this rotation of - 6 0 0 : 1 . T h e shock tube w i n d o w s were then replaced so as to cause a m i n i m a l disturbance to the polarization characteristics of the beam. This proved a very tedious p r o c e d u r e because of the difficulties in screwing down the w i n d o w mountings without i m p a r t i n g a residual stress-induced b i r e f r i n g e n c e to the w i n d o w s themselves. T h e shock tube was then filled with argon (1 atm) and the polarization rotator (Fig. 1)

was adjusted m a n u a l l y until the polarization of the " d i o d e - c l a m p e d " b e a m was accurately vertical, giving a m i n i m u m in the moleeulal: Rayleigh scattering as detected b y the photom u l t i p l i e r Ps' The f o l l o w i n g calibration procedures were then carried out. The ratio, R ...... of the m a x i m u m to minim u m intensities of the Rayleigh scattering from the argon was d e t e r m i n e d d u r i n g a 180 ~ rotation of the polarization direction of the d i o d e - c l a m p e d beam. Next, the miqrometer stub setting, c h o p p e r speed, and a m p l i t u d e of the input square wave signal to the drive amplifier were all adjusted to give the optimum, correctly phased, m o d u l a t i o n of both b e a m polarization a n d a m p l i t u d e (Fig. 2) for use during an incident shock. The horizontal c o m p o n e n t of the b e a m d u r i n g the elliptical " u n c l a m p e d " half-cycle was then determined as the ratio, Rh, of the b e a m intensities as detected by the p h o t o m u l t i p l i e r PT (Fig. 1) with and without the G l a n - T a y l o r analyser in the beam. The significance of these calibration procedures is as follows. T h e m a x i m u m possib l e a m p l i t u d e m o d u l a t i o n of the light scattered b y the soot particles d u r i n g an incident shock that could be effected b y the above polarization m o d u l a t i o n of the incident beam is R,, m • Rh" T h e extent to w h i c h the intensity modulation

666

SOOT FORMATION AND GROWTH

of the scattered light falls short of this m a y be attributed to the asphericity a n d / o r anisotropy of the particles. Finally, the optical system was validated b y firing pure argon shocks with the Glan-Taylor analyser set to b l o c k vertically polarized light. Any spurious depolarization of the beam during the "vertical" half-cycle could thus b e readily detected b y monitoring the transmitted intensity reaching the photomultiplier~ JoT. Initially, spurious depolarizations were observed, attributable to transient stress-induced birefringence in the shock tube w i n d o w s generated b y the shock itself. They were successfully eliminated b y m o d i f y i n g the w i n d o w mountings 9

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Results Our initial p o l a r i z a t i o n - d e p e n d e n t measurements were made on shock flows at comparatively low temperatures (~1750 K) where the thermal emission at 488 nm is c o r r e s p o n d i n g l y weak and where we b e l i e v e a,6 the c o n d e n s e d phase to consist largely of l i q u i d p o l y n u e l e a r aromatic species that transform relatively slowly into soot. This provides a natural explanation for the occurrence of coalescent rather than chain-forming collisions a n d thus makes the direct test of this assumption of particular interest. The optical records for a c y e l o h e p t a t r i e n e / argon shock at 1760 K, where [C]tot,l, the total carbon concentration in the shock heated gases was 2.0 x 10 17 a t o n / c m 3, are shown in Fig. 3. The scattered light intensity ratio I ~ that w o u l d be o b s e r v e d if the scattering were measured truly p e r p e n d i c u l a r and parallel to the polarization direction of the linearly polarized beam is given b y

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where I , and I~ are the measured intensities during the elliptical a n d vertical m o d u l a t i o n cycles (Fig. 3a a n d 3b). The variations in I~1 d u r i n g the shock flow for this and other simitar shocks are illustrated in Fig. 4. This figure provides strong e v i d e n c e that the collisional process is coalescent rather than chain-forming because the formation and growth of chains w o u l d lead to a c o n t i n u i n g decrease in I 1 whereas we observe lower values of I,A at the onset of detectable scattering than at any time subsequently.

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FIG. 3. Oscilloscope traces of the variation in scattered and transmitted intensities at 488 nm and 3.39 jxm recorded during a cycloheptatriene/argon shock (No. 387) at 1750 K. The scattered light (h = 488 urn) was recorded at three different sensitivities to permit measurements to be made during both the elliptical "on" periods (labelled 1, 2 . . . in Figs. 3a and 3b) and the vertical "on" periods (labelled a, b . . . . in Fig. 3h) of the argon laser beam. The infra-red absorption at 3.39 pan (Fig. 3c) is obtained as the difference between the envelopes of successive "on" periods (upper envelope, emission + transmission) and "off" periods (lower envelope, emission only) of the 3.39 Ixm He/Ne laser beam. 6

SOOT PARTICLES AT HIGH TEMPERATURES Shock f r o n t ornvol I

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FIG. 4. A comparison between the experimentally determined variations in It. ~ during the shock flow for three cycloheptatriene/argon shocks (Figs. 4a, 4b and 4c), with that calculated (Fig. 4d) for anisotropic assembly of isotropic prolate ellipsoids of refractive index r~ = 1.51-0.52 i, similar to that of soot at 488 nm: (a) T = 1760 K, [C] total = 2.0 X 1017 atom/cm 3, R h = 0.67 and R .... = 107; (b) T = 1750 K, [C] total = 2.0 X 1017 atom/cm a, R h = 0.58 and R .... = 105; (c) T = 1730 K, [C]totaj = 2.0 x 1017 atom/cm 3, R h = 0.58 and R ..... = 102.

This last feature is particularly difficult to explain in terms of chain-forming collisions because the infra-red (3.39 bun) absorption profile'for shock No. 387 (Fig. 3c) shows that soot itself accounts for a small proportion, both of the total absorption at 488 ran, and of the total volume fraction of particulate material, 3 at, and shortly after the onset of detectable scattering. Even though the absorbance ratio A339~m/A488nm for this shock does increase throughout the shock flow, its value after 3 msec is still only 0.10 whereas the value calculated for soot 6 is - 0 . 1 9 . The results presented i n Fig. 4, however, do show that the "soot" particles do not have the same light scattering properties as isotropic spheres. Disregarding particle chains, we consider the following explanations. (i) For the sub-microscopic particles (diameter <40 nm) that are present in our shock flows, it may well be that the dimensions of the polynuclear aromatic molecules are sufficiently large in comparison with the particle diameter to confer an intrinsic anisotropy on the polarizability of a spherical particle, even in the absence of any turbostratic

ordering of different molecules within the particle. (ii) The fusing of two collision partners to form a true sphere may be slow enough that, at any instant, the incompletely fused particles make a significant contribution to I v, a n d yet still be fast enough to preclude chain formation. I n the absence of any model for (i) and (ii) above, from which to obtain "predicted" values of I~x, we assume 7 that both (i) and ( i i ) - - a n d indeed particle chains as w e l l - - a l l lead t o It.1 ratios that can be simulated by an isotropic assembly of identical isotropic ellipsoids of suitable eccentricity. The comparison between the experimentally determ i n e d values of I~1 and those calculated for prolate ellipsoids of various eccentricities is illustrated in Fig. 4 and provides some quantitative measure of the deviation of the observed scattering from that given b y isotropic spheres. The relatively large value (-2.5) of the major:minor axis ratio of the ellipsoids that generate the initial values argues somewhat against the slow fusion hypothesis (ii). There is, in addition, circumstantial evidence to suggest that intrinsic anisotropy (i) is responsible

668

SOOT FORMATION AND GROWTH

for the deviation that we observe from scattering by isotropie spheres. First, it is well e s t a b l i s h e d s that spherical, highly anisotropic, l i q u i d crystalline droplets (diameter/> 1 Ixm) can be formed d u r i n g the pyrolysis of aromatic hydrocarbons in the condensed phase. Secondly, it has b e e n suggested 9,x~that soot (carbon black) particles may b e formed d u r i n g the gas-phase p y r o l y s i s of aromatic hydrocarbons at lower temperatures ( - 1 4 0 0 K) via the p o l y m e r i z a t i o n / d e h y d r o g e n a t i o n of sub-microscopic liquid-crystalline droplets of molecular polynuclear aromatics. Finally, and most importantly, the o b s e r v e d initial increase in Ira (Fig. 4) provides strong evidence for the intrinsic anisotropy hypothesis, (i), because the presence of a given (anisotropic) molecular structure in a particle must surely give an intrinsic anisotropy that decreases with increasing particle size. W h e n two such particles collide and coalesce, the anisotropy will i n e v i t a b l y be reduced unless the anisotropic structures h a p p e n to be a l i g n e d parallel to each other. Conclusion We have shown h o w the measurement of polarization d e p e n d e n t scattered light intensities can provide v a l u a b l e information about the collisional process in rapidly coagulating aerosols generated in incident shock flows. O u r measurements on soot aerosols f o r m e d d u r i n g the pyrolysis of aromatic hydrocarbons at a temperature of --1750 K indicate that the particle collisions are coalescent rather than chain-forming. This is consistent with our i n d e p e n d e n t l y b a s e d conclusion 3'6 that the c o n d e n s e d phase in such systems consists largely of l i q u i d phase polynuclear aromatic species that are converted into soot relatively slowly.

We find, in addition, that the scattering b y the particles differs significantly from that given b y isotropie spherical particles. We attribute this difference largely to an intrinsic anisotropy of the (spherical) particles that reflects the f u n d a m e n t a l anisotropic character of the polynuclear aromatic structures w i t h i n them, rather than to particle asphericity.

Acknowledgments I should like to thank Mr. M. A. McLeod for invaluable assistance in operating the shock tube, S. Lea and F. Kelly for the construction of the polarization modulation system, and finally, Electro-Optic Developments for modifying their drive amplifier without charge.

REFERENCES 1. GraHAM,S. C. ANDHOMEa,J. B., Faraday Symposium, Chem. Soc., 7, 86 (1973). 2. GrahAM, S. C., HOMER, J. B. AND ROSEN~ELD,J. L. J., Proc. Roy. Soc. (London), A344, 259 (1975). 3. GrahAM, S. C., HOMER, J. B. ANDROSENFELD,J. L. J., Second Symposium (European) on Combustion, p. 374 (1975). 4. Van DE HULS'r, H. C., Light Scattering by Small Particles, p. 80, John Wiley, New York, 1957. 5. GrahAM, S. C. ANDHOMER,J. B., Ninth International Shock Tube Symposium, p. 712, Stanford University Press, 1973. 6. GraHAM, S. C., HOMEa, J. B. AND ROSENFELD,J. L. J., Tenth International Shock Tube Symposium, p. 621, 1975. 7. CLam; JONES, R., Phys. Rev., 68, 213 (1945). 8. Maasn, H., Preprints Symposia, Amer. Chem. Sot., Div. Pet. Chem. Inc., 20, 389 (1975). 9. MARSH,H., Carbon, 11,254 (1973). 10. DONNET,J. B., LAHAYE,J., VOET, A. ANDPaADO, G., Carbon, 12, 212 (1974).

COMMENTS Richard G. Gann, National Bureau of Standards, USA. It seems that a random orientation of oblate particles could produce a scattering profile similar to that for spherical particles. However, your observation of isotropic'seattering does uniquely point to some chain-like structure. Do you feel that an increased sensitivity to irregularity of shape could be obtained by imposing a transverse electric field

on your shock tube? This would tend to align the somewhat charged particles, thus enhancing your isotropic scattering components.

Author's Reply. We have computed the ratio of the differential scattering cross-sections for "light scattered perpendicular and parallel to the electric vector of the linearly polarized incident beam for

SOOT PARTICLES AT H I G H T E M P E R A T U R E S a randomly oriented assembly of oblate spheroids. In general, the greater the anisotropy of the particles within the isotropic assembly, the less anisotropie the scattering. An assembly of spherical, isotropic particles gives the most highly anisotropie scattering, with a scattering cross-section of zero in the direction of the electric vector of the incident beam. I do not think that the finite scattering observed along the electric vector of the incident beam can be ascribed to chain formation because the scattering becomes more anisotropic with time rather than less, i.e. more like that of an assembly of isotropie spheres. The imposition of an electric field on the shock heated gases would be expected to align anisotropic particles. This could be detected from both scattering and extinction measurements because the gas would exhibit linear dichroism.

Charles A. Garris, I.V.I.C., Ingenieria, Venezuela. Would you please comment on the dependence of your results on the scattering volume of your instrument and the particle density, i.e. if there exist many particle chains within the scattering volume simultaneously, will this lead to apparent isotropy? What would be observed if only a small part of a long-chain particle were within the scattering volume at a given instant?

Author's Reply. All our light scattering measurements were made on incident shock flows. The effective scattering volume is that volume swept by the 0.2mm diameter by 5ram long cylinder at the focus of the laser beam as the shocked gases flow through it at a typical velocity of 800 ms-1. Thus, the effective volume is about 8 x 10 -3 cm -3. The n u m b e r of particles in this effective volume is at least 2 x 107. Thus the scattering volume is effectively very large. If the n u m b e r of particles were small and the scattering influenced by part of a long chain being in this volume, one would expect to find a very "noisy" intensity of scattered light, very different from that we observed. As indicated in my reply to Dr. Gann, the scattering from an assembly of randomly oriented ellipsoids will be the more nearly isotropic the greater the anisotropy of the ellipsoids.

Richard C. Flagan, California Institute of Technology, USA. Would you define the terms and the model you have used to model soot growth?

Author's Reply. The models we have used are described in references 1, 2, 3, and 6 of the paper. They have been verified only for pyrolysis of aromatic hydrocarbons at total carbon concentrations

669

of 1-4 x 1017 a t o m / c m 3, temperatures of 17001850K, and times up to 3 ms. These models describe the growth of the particles rather than the conversion of the particulate material into soot. Basically we assume the particulate phase behaves as a liquid so that whenever particles collide, they coalesce to form a new spherical particle.

S. H. Bauer, Cornell University, USA. Could you tell us something about the assumptions you had to introduce to unscramble the product of the particle n u m b e r density and the mean square of the particle size which is obtained from the intensity of scattered light? I am aware that the m e a n volume and number density factors can be separated provided there is sufficient information on the complex index of refraction. Did you have to make any assumptions regarding the refractive index for your particles and the dependence of the index on wavelength and particle size? Author's Reply. The methods we used are described in references 2 and 6 of the paper and by Ref. 1 below. Very briefly, we have shown that the light absorbing species are, in general, mixtures of soot and molecular polynuclear aromatics that have identical specific absorptions at 488 nm, based on carbon content. Thus we are able to obtain the specific absorption of the condensed phase. We then find the complex index of refraction to be m4ssn m = 1.62 - 0.57i. We assume that m4ssn,~ is independent of particle size and make no assumptions about it at other wavelengths.

REFERENCES 1. GRAHAM,S. C. AND ROBINSON, A., J.: Aerq6ol Sci. 7, 261 (1976).

Henri Mitler, Harvard University, USA. Could you make some comments on the particle sizes as a function of time? Author's Reply. Typically for shock flows with T = 1750K - 1800K, and total carbon concentration of 2 • 1017 a t o m / c m 3, the particle diameter, computed from the mean particle volume reaches about 39nm some 2.5-3ms after the end of shock heating and at the end of the shock flow. For much of the time df//dt is approximately proportional to Q-s/8 so that dD/dt varies as D -a/2. This indicates that the rate of increase of particle diameter decreases very quickly.