Langmuir 1992,8, 1666-1670
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Measurement of the Fractal Dimension of Soot Using UV Laser Radiation Paul A. Bonczyk' and Robert J. Hall United Technologies Research Center, East Hartford, Connecticut 06108 Received December 13, 1991. I n Final Form: March 16, 1992 Accurate values were determined for the fractal dimension of soot particulates formed in a small, overventilated CaHdair diffusion flame. The experimentprincipally entailed measurementof the near forward to backward elastic scattering of UV laser light by the soot. Mass fractal dimensions were inferred from log-log plots of scattering versus the absolute value of the momentum transfer vector in the asymptotic, large scattering angle regime. The inferred dimensions were toward the low end of the reported range for soot. The scattering data were supplemented by measurements of optical extinction at the 266-nm laser wavelength, as well as extinction versus wavelength using a conventional lamp. The laser extinction data were used in evaluating particulate albedos, while the lamp data ruled out the possible interference of polycyclic aromatic hydrocarbon UV absorptions. The role of the primary monomer size in limiting the asymptotic range over which the fractal dimension may be determined is discussed.
Introduction In a recent work,l we determined the parameters which describe the in situ morphology and number of soot particulate clusters formed in a laboratory-scale diffusion flame. The morphology was taken to be fractal chains of monomer spherules, and the cluster structural parameters were determined from optical extinction and scattering measurements at visible, laser wavelengths. Values were obtained for the number and size of the spherules comprising each cluster, as well as the cluster number, radius of gyration, and fractal dimension. The results of this analysis were satisfactory save for the fractal dimension, whose numerical value could not be determined accurately. Thiswas due to insufficient range of the elastic scattering momentum transfer vector, which is inversely proportional to the wavelength of the incident 1ight.l More specifically, for visible laser sources with wavelength -0.5 pm, and typical soot cluster radii of gyration of -0.1 pm or less, the product of momentum transfer wave vector and cluster size is about 5 in the backscatter direction. Generally, this will not be large enough to achieve adequate access to the asymptotic regime, in which a log-log plot of scattered intensity vs momentum transfer wave vector will be linear, with a slope that unambiguously yields the mass fractal dimension. In this partially developedregime, attempts to determine a fractal dimension by least-squares fitting structure functions will be sensitive to the choice of cutoff function, which is not a desirable situation given the uncertainties associated with the latter. In slightly more detail, the nature of these functions is as follows. The structure function describes the spatial arrangement of the monomer spherules comprising the cluster and is closely related to the scattered light intensity. The "cutoff' refers to a modification of the monomer pair correlation function to account for monomer separations on the order of the cluster size; the form of the cutoff is usually exponential or Gaussian. The structure and correlation functions are closely related in that they are a Fourier transform pair. For a cluster of infinite size,the correlation function nominally has a r-(3-D)dependence on monomer separation, r, and mass fractal dimension, D. Making use of the indicated transform, the scattered intensity has a q-Ddependence on scattering wave vector, q. Even for a cluster of finite size, this latter dependence is essentially (1) Bonczyk, P.A.; Hall,R. J. Langmuir 1991, 7, 1274.
correct within the limits assigned to ea 2 below. Further, more detailed discussions ofihese issues have been given by Freltoft et aL2 and T e i ~ e i r a . ~ In this work, we have endeavored to overcome the difficulties mentioned above, and thereby arrive at a more reliably accurate value for the fractal dimension of the soot formed in our flame. To do so, the experimental approach has been altered such that the optical measurements are carried out in the UV region at 266 nm and not in the visible region at 514.5 nm as had been done earlier.' In this way, the momentum transfer vector was extended in the UV to values nearly twice those in the visible, which permits, as shown below, a more accurate determination of the fractal dimension. This 2X extension is optimal since, as will be shown, the role of the primary monomer size may make it futile to attempt to extend the measurements to much larger values of the momentum transfer vector, q. No concerted attempts were made here to reproduce values for the other cluster parameters determined earlier. Thus, results given here include the fractal dimension of soot at several different heights in the flame, as well as the a l b e d ~ As . ~ will be shown, knowledge of the latter makes it possible to rule out interparticle multiple scattering effects which could otherwise complicate data interpretation. Finally, using a conventional lamp as a light source, measurements of extinction versus wavelength were made at various heights in the flame in order to rule out any significant interference of polycyclic aromatic hydrocarbons (pcah) with the scattering from soot.
Experimental Section The apparatus used here is very similar to that shown in Figure 1of ref 1. The principal differenceis a laser,optics,and detectore appropriate for pulsed UV light measurements. A second difference is the use of both a laser and a lamp to make optical extindionmeasurements. Somedetails concerningthese changes are as follows. The UV light at 266 nm was derived from the frequency doubled output of a 2X Nd:YAG laser operating at 532 nm. The laser emits 10 ns long pulses at a repetition rate of 10 pulsesls. The typical energy of the unattanuatad light at (2) Freltoft, T.; Kjeme, J. K. Phys. Rev. B 1986, 33,269. (3) Teixeira, J. In On Growth and Form-Fractal and Non-Fractal Patterns in Physics; Stanley, H. E., Ostrowsky, N., Eds.; MartinNijhoff: Dordrecht, 1986; p 145. (4)Kerker, M. The Scattering of Light and Other Electromagnetic Radiation; Academic Press: New York, 1969.
0743-7463/92/2408-1666$03.00/00 1992 American Chemical Society
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Measurement of the Fractal Dimension of Soot 266 nm was 1-2 mJ. This output was attenuated by about 104 using suitable neutral density filters, and then focused into the flame with a 50 cm focal length quartz lens. The scattering and transmission of light were recorded by appropriate UV-sensitive photomultipliers coupled to boxcar type electronics. For the scattering, as earlier, the sample volume size was a function of the scattering angle, which had to be accounted for properly in the data reduction. At 90' the sample volume was a cylinder having a 0.20 mm diameter and 3.2 mm length. This length was longer than that used previously in order to compensate for reduced light collection efficiency in the UV. Due to the nearly two-dimensional character of the flame, this change caused no difficulty, the soot number and size being constant over said length. Another variation in this work was the use of a xenon lamp and spectrometer in place of the laser and related optoelectronics. The lamp and spectrometer were used to determine optical extinction in the 200-600 nm wavelength interval. The lamp arc was focused at the flame center, and then refocused onto the end face of a 0.2 mm diameter optical fiber. This was done with unity magnification image transfer; hence, the spatial resolution of the extinction measurements in a plane normal to the incident light direction was equal to the fiber diameter. The spectral bandpass of the V2-m spectrometer was roughly 0.8 nm, which was sufficiently small to record the largely featureless spectral extinction. Using the apparatus modifications described above, the measurements carried out in this work were as follows. With the ethylene/air diffusion flame set to operate exactly as earlier,l lamp extinction versus wavelength was measured at several differentheightsin the flame. This was followedby measurement of the intensities of the UV laser light scattered at 4 O intervals between 12 and 168'. Spurious scattering from optical components prevented data collection nearer 0 and 180O. In addition to the scattering, extinction of the 266-nm laser was measured as well;as mentioned, extinctionis fundamental to the evaluation of albedos. Both the scattering and extinction were determined at the horizontal center of the flame for severaldifferent heights. For all of the above measurements, the flame settings remained unchanged. Finally, Rayleigh measurements in room air were carried out in order to calibrate the scattered intensities, and corrections were arrived at for the attenuation of the scattered light passing between the center of the flame and its boundary. Since the burner was rotatable about its z-axis, the required corrections were evaluated directly from a series of extinction measurements. Dependingon scattering angle and height in the flame, the corrections ranged between 2 and 39%. Applying said corrections was essential to obtaining angular intensities free of distortion. These correctionsdo not account for possible additional distortions due to interparticle multiple scattering; however, the latter appears not to be significant in this work. Markers indicative of multiple scattering include large optical depth based on scattering, intracluster scattering (see below), and significant light depolarization; all of these were, however, negligibly small. Further discussion of these secondary issues is omitted in this short paper; details are available in ref 1.
Rssults The extinction data taken with the xenon lamp are summarized in Figure 1. The ordinates do not give the correct absolute values for the extinction coefficients. We have chosen to normalize the peak extinction to unity at each height and then to superimpose the data. In this way all the extinctions are seen to have a similar spectral dependence, with peak values near 300-350 nm. The correct absolute values of the peak spectral extinctions are (in cm-') 0.099, 0.171, 0.201, and 0.169 at 14, 17, 20, and 25 mm height, respectively. These values and the data in Figure 1may be used to obtain an absolute ordinate scale for each height. The scattering data taken with the 266-nm laser are shown in Figure 2. The ordinate is the log of the quantity n, (du/dQ), (in cm-' sr-9, where n. is the number density of soot clusters and (du/dQ),, in general a complex function
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Height nJlr (du/dQ)dQ,cm-l 0.0195 0.0450 0.0208 0.0184
extinction,cm-l 0.301 0.306 0.276 0.175
albedo 0.065 0.147 0.075 0.105
of cluster parameters, is the differential light scattering cross section. The abscissa is the log of the absolute value of the momentum transfer vector q (in pm-l). This parameter is related to the scattering angle 8 by q = (44x1 sin (8/2), where h is the wavelength of the incident and scattered light. For large clusters comprised of many spherules, the scattering vs q (or 8) is expected to exhibit significant dissymmetry. This is the case for the data at 20,25, and 28 mm in Figure 2. At 17 mm, dissymmetry is nearly absent, which indicates the presence there of small, Rayleigh-like particulates whose description in terms of fractals is inappropriate. The data in Figure 2 and measured optical extinctions at the laser wavelength may be used to evaluate the particulate albedos. These results are given in Table I. The indicated integration represents a summation of scattering over all measured angles and is the fraction of the extinction in column 2 which is due to scattering alone. Accordingly, the albedos, by definition? are obtained from (column 3)/(column 2). The resulting numerical values, while larger than the visible light values,' are smallenough to rule out the significantpresence of interparticle multiple scattering, as well as to validate in general the data reduction approach used here, which is based on the assumption of singly scattered light. The integrated scattering coefficient in column 3 of Table I was derived
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so that q2a2/3 0.04. It follows that the D can be determined from the slope of log (du/dQ)vs log (q) provided that R d > 1. To verify that this inequality holds, it is necessary to determine R,. This can be done by fitting a polynomial to (1) for low values of q. Keeping in mind that q A-l, such a fit will be less accurate for the UV data reported here; hence, we take R, to be equal to the values given for the ref 1 visible data. Then, D has been determined from a linear fit to all data points in Figure 3 for which R,q 1 2. The final values thus obtained for the fractal dimensions are D = 1.33,1.49, and 1.60 a t z = 20, 25, and 28 mm, respectively. The 25-mm value is probably most reliable, because the asymptotic range is limited at 20 mm, and the 28 mm data are "noisy" a t the largest scattering angles.
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Discussion This work rests on the assumption that the measured absorptionlextinction and scattering are due solely to soot particulates. It is well-known, however, that pcah molecules are present in measurable quantity in sooting flames6Jand that they have highUV absorption.8 It peaks around 220-250 nm for two- and three-ring compounds like naphthalene and phenanthrene and at 300 nm and higher for pcah with four or more rings like pyrene. Accordingly,the UV spectral absorption of the pcah should have two or more peaks, and indeed this was observed earlier.g In contrast, soot, much like carbon and graphite, exhibits asingle absorption peak near 300 nm.lo A further distinction between pcah and soot is that the pcah concentration peaks upstream from that of soot with some overlap present between them.7 With the preceding facta in mind, we made the measurements in Figure 1in order to detect any significant pcah presence. For the interval of interest here, i.e. z = 17-28 mm, this appears not to be the case since the extinctions in Figure 1 are single-peaked and retain their functional shape with height change. It should be apparent that the expression above for q is Bragg's law, in which a length scale q-' is related to a momentum transfer or scattering angle 8. The larger the variation in q, the more complete is the range of length scale probed as well as the potential description of a complex aggregate. Here, we have varied q-' from 0.02 to 0.2 pm and, in the parlance of fractals, have probed the Guinier region fully and the P o r d regime partially." More specifically, there are two breaks in the log-log plot of scattering vs q for an aggregate. The first is at Rd z 1, the second at aq z 1, with the slope between them being the mass fractal dimension, D,, of the cluster. In this work, we have probed up to aq = 0.37, or sufficient to determine D,, and in principle R,. Beyond the second break is a slope which may be used to determine the surface fractal dimension, D,,of the aggregates primary spherules. Although this region was not accessible to us, it has been probed by others in a butadienelair diffusion flame using small angle X-ray scattering (SAXS).12If the data in ref 12 are renormalized to conform to intensity vs q, and then combined with our data at 25 mm height, the (6) Chakraborty, B. B.; Long, R. Combuat. Flame 1968,12, 237. (7) Prado, G.; Garo, A.; KO,A.; Sarofim, A. In Twentieth Symposium (International) on Combustion; The Combustion Institute Pittaburgh, PA, 1984; p 989. (8) Clar, E. Polycyclic Hydrocarbons;Academic Press: London, 1974. (9) DAlessio, A,; Beretta, F.; Cavaliere, A.; Menna, P. In Soot in Combustion Systems and its Toxic Properties; Lahaye, J., Prado, G., Eds.; Plenum: New York, 1983; p 355. (10) Vaglieco, B. M.; Beretta, F.; D'Alessio, A. Combust. Flame 1990, 79, 259. (11) Schaefer, D. W.; Hurd, A. J. Aerosol Sci. Technol. 1990,12,876. (12) England, W. A. Combust. Sci. Technol. 1986, 46, 83.
Langmuir, Vol. 8, No. 6, 1992 1669
Measurement of the Fractal Dimension of Soot -4
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result shown in Figure 4 is obtained. The SAXS data seem to make a transition from the mass fractal to the Porod regime a t the point where our laser data end. Since scattered intensity in the Porod region is -q+j+Ds,13 the slope at large q is -4.06 = -6 + D,, from which D,= 1.94. This fractal dimension is indicative of a smooth monomer surface, at least down to length scales of about 30 A, a result that may be relevant to kinetic analysis of soot growth and oxidation rates. Although the ref 12 data are for a flame different than ours, it is likely that the soot morphologies are quite similar. The finite size of the monomers places an upper limit on the q range that is useful for mass fractal determination. A typical monomer radius of 10 nm (=0.01 pm), for example, will create a knee in the scattering curve at q 100 pm-l. One might be able to extend the asymptotic range achieved in these experiments by about a factor of 2, depending on the primary spheroid size, but it seems unlikely that the asymptotic mass fractal regime will exist over even 1 orderof-magnitude for typical soot sizes. As an aside, we note that the slope of the X-ray data at the smallest q values is-1.53, but inasmuch as only two data points are available, this cannot be taken as a reliable D value. In addition to this work, other measurements of the fractal dimension of flame-generated particulates have been reported. These include soot'4 and silica15 particulates formed by the combustion of hydrocarbon fuels and silicon compounds, respectively. A complete tabulation of these results is available in ref 14. Those which interest us are for soot and are as follows: D = 1.5-1.6, CzHdair diffusion flame, transmission electron microscope (TEM) grid collection and analysis;16 CHd02 premixed flame, quartz probe sampling, D = 1.62 f 0.06 and 1.72 f 0.10 from light scattering (flask sample) and TEM analysis, respectively;" D = 1.6 f 0.15, CHd02 premixed flame, in situ light scattering analysis;18CzHdair diffusion flame, thermophoretic probe sampling and TEM analysis, D = 1.62 f 0.04 and 1.74 f 0.06 at z = 15 mm and r (radius) = 3.1 and 3.7 mm, re~pectively;'~ CnHJair diffusion flame, in situ light scattering analysis, D = 1.55, 1.52, and 1.45 atz = 20,25, and 28 mm, respectively, usingan exponential cutoff and least-squares fitting of a model structure
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(13) Hurd, A. J.; Schaefer, D. W.; Martin, J. E. Phys. Reu. A 1987,35, 2361. (14) Megaridis, C. M.;Dobbins,R. A. C o m b u t . Sci. Technol. 1990,71, 95. (15) Hurd, A. J.; Flower, W. L. J.Colloid Interface Sci. 1988,122,178. (16) Samson, R. J.; Mulholland, G. W.; Gentry, J. W. Langmuir 1987, 3, 272. (17) Zhang, H. X.; Sorensen, C. M.; Ramer, E. R.; Olivier, B. J.; Merklin, J. F. Langmuir 1988,4, 867.
function.' Although the preceding results are interesting and deserve acknowledgment, it is unclear to what extent comparisons with this work may be made. Only ref 18 and our earlier work' use an in situ light scattering analpis, and achieving agreement between in situ and TEM analyses is subject to q ~ e s t i 0 n . lMoreover, ~ the flame in ref 18 is dissimilar from that used here in ref 1. Accordingly, all that may be said is that the fractal dimensions given here are broadly consistent with previous values and that they have been determined via an approach that is insensitive to choice of structure function. Our best estimate of the fractal dimension, the D = 1.49 value from the 25-mm measurements, lies toward the low end of the reported range of values. It is essentially identical to the value reported in ref 15 for silica soot. With such a value for the fractal dimension, our inferred cluster parameters retain the desirable property, as previously noted in ref 1 and by Dobbins et al.,19 that the total monomer density is approximately constant with height. With a larger value of D, such as 1.78, this constraint is not obeyed.' These results appear to indicate that there is no universal value for the fractal dimension of soot which is valid in every sooting flame; but more and better data are required for this to be stated with certainty. The flame in this work is identical to that used earlier by us for measurements at 514.5 nm.' More specifically, the burner and fuel/air flow settings are the same, and the height of the flame, as determined with a cathetometer, is unchanged within f1/2 mm. Despite this equality, there was a slight difference in the behavior of light scattering vs height a t 514.5 and 266 nm. In Figure 3 of ref 1, the angularly resolved scattering at 514.5 nm peaks a t z = 25 mm. Equivalently, in Table I of ref 1 the integrated scattering peaks there as well with the value of 5.00 X cm-l. In this work, the preceding peaks are seen in Figure 1 and Table I to occur at z = 20 mm, the integrated scattering having the value of 4.50 X cm-l. The large difference in the magnitude of the integrated scattering is not a concern since it scales as X-4.20 The difference in the peak positions is a concern, but presently lacks an adequate explanation. In seeking an explanation, we investigated the possible role of intracluster multiple scattering. In the fractal scattering analysis of Berry and Percival,5 a criterion is presented for estimating the importance of such multiple scattering for scalar waves. Numerical evaluation of this criterion for UV light and the ref 1 cluster parameters indicates, however, that such multiple scattering should be of marginal importance, just as it was for visible light. It is also to be noted that the monomer size parameters for UV light should remain in the Rayleigh range. In the absence of attenuation, the laser used here emits 10-nspulses with 2 mJ of energy at 266 nm. This light, when focused in the flame to a 0.02 cm beam diameter, has an intensity of -6 X lo8W/cm2. Using this intensity, we initially observed the scattering at z = 20 mm to be isotropic. This may be interpreted as resulting from vaporization of the soot particulates by the intense pulses, thereby producing secondary particulates of significantly reduced size. These are, then, Rayleigh scatterers, or close to it, and cause the light to scatter isotropically. This
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(18) Gangopadhyay,S.; Elminyawi, I.; Sorensen, C. M. Appl. Opt. 1991, 33, 4859. (19) Dobbins, R. A.; Santoro, R. J.; Semerjian, H. C. In Twenty-Third Symposium (International)on Combustion; The Combustion Institute: P-itGburgh, PA, 1990; p 1525. (20) Kerker, M. The Scattering of Light and Other Electromagnetic Radiation; Academic Press: New York, 1969; p 88.
1670 Langmuir, Vol. 8,No.6, 1992 effect has been observed previously by DaschPz1who estimated a 0.2 J/cm2laser fluence threshold for it, a value easily exceeded by the -6 J/cm2 determined from parameters given immediately above. These observations emphasizethe need to adequately attenuate intense,pulsed laser light used in the sizing of particulates via light scattering. In our case, attenuations of 3 to 4 orders-of(21) Dasch, C. J. Appl. Opt. 1984,23, 2209.
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magnitude were needed to achieve insensitivity of dissymmetry measurements to source intensity. Preliminary results of our work were presented earlier.22
Acknowledgment. We thank Dr. W. A. England for transmitting the SAXS data taken at the AERE Harwell Laboratory (U.K.). (22) Hall,R. J. Presentation (unpublished) at the American Association of Aerosol Research Annual Meeting, Travis City, MI, Oct 7-11, 1991.
