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PARTICLE SHAPE AND STRUCTURE ANALYSIS FROM THE SPATIAL INTENSITY PATTERN OF SCATTERED LIGHT USING DIFFERENT MEASURING DEVICES
PII: S0021-8502(99)00045-2
J. Aerosol Sci. Vol. 30, No. 10, pp. 1257}1270, 1999 1999 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0021-8502/99/$ - see front matter
PARTICLE SHAPE AND STRUCTURE ANALYSIS FROM THE SPATIAL INTENSITY PATTERN OF SCATTERED LIGHT USING DIFFERENT MEASURING DEVICES Bernd Sachweh,R* Holger Barthel,R Reinhard Polke,R Heinz UmhauerS and Helmut BuK ttner A R BASF AG, Engineering Research and Development, ZAT/R-L540, D-67056 Ludwigshafen, Germany S Mechanische Verfahrenstechnik und Mechanik, UniversitaK t Karlsruhe, Postfach 6980, D-76128 Karlsruhe, Germany A Mechanische Verfahrenstechnik und StroK mungsmechanik, UniversitaK t Kaiserslautern, Postfach 3049, D-67653 Kaiserslautern, Germany (First received 18 September 1998; and in ,nal form 27 October 1998)
Dedicated to Professor Fritz Ebert on his 60th birthday Abstract*The spatial intensity pattern of scattered light from nonspherical particles was investigated numerically and experimentally in order to obtain*beside size*sensitive shape information. The discrete dipole approximation (DDA) was used to calculate the light scattering pattern for some basic types of particle shapes. From these calculations the lower size limit where shape information can successfully be detected from light scattering was found at a size parameter of approximately 1. It can be even lower if elongated particles (cylinders) are present. For the exemplary studies three di!erent laboratory instruments available to the authors were utilized. The comparison of experimental and numerical results yielded good correlations, which con"rmed the selected theoretical approach. Thus, it is possible to develop experimental setups for speci"c applications only on basis of theoretical data. From the experiments we found that azimuthal scattering at a constant scattering angle is a promising setup for shape characterization, which can be adapted to speci"c applications with high #exibility. For supermicron particles the surface structure also contributes to the scattering pattern provided the characteristic size of surface elements substantially exceeds the wavelength of the light source. 1999 Elsevier Science Ltd. All rights reserved
I N T RO DU CT I O N
Manufacturing of disperse products requires the characterization of the disperse state in order to control the process and/or to obtain quality properties. One important physical property which has to be measured is the particle size. But there are other product properties such as the color strength of pigments which also depend on particle shape or surface structure. To the knowledge of the authors no on-line, in-line or in situ measuring techniques are available for these quantities. Such techniques are preferable whenever there is a risk of e!ecting the particles by the sampling as is the case for particles with high vapor/sublimation pressure, loose agglomerates or in corrosive gases. Optical methods are preferably employed for in situ measurements, most commonly based on di!raction techniques, which measure concentrations and size distributions of particle ensembles. However, there are advantages in using instruments that measure the intensity of light scattered by single particles in order to detect particle shape and structure, because the scattering intensity of single particles is more sensitive than the mean scattering intensity from ensemble measurements, where shape information is averaged due to di!erent orientations of the particles in the measuring volume. The present paper is a theoretical and experimental evaluation of di!erent options to obtain*in addition to particle size*shape and structure information from the light scattering data of single gasborne particles. The strong shape in#uence on the spatial
* Author to whom correspondence should be addressed. 1257
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scattering intensity pattern was measured for instance by Seger (1970), who investigated the di!raction patterns of single particles illuminated by laser light. Other experiments were conducted by Killinger and Zerull (1988), who investigated microwave scattering by nonspherical particles and by Umhauer et al. (1989, 1991), who contrary to other experimental studies used incident white light. If the scattering patterns for certain types of nonspherical particles were known, this information can be used to identify or at least distinguish, di!erent types of shapes, if some a priori information about the particles is available (Sachweh et al., 1995). Such information can then be used for example to quantify the fraction of hazardous particles in a mixed aerosol, if a speci"c shape is predominant for one particle component. Other examples are the presence of "brous particles in the working place environment, or coal particles in the atmosphere of mines. Another motivation for our investigations is the quanti"cation of the shape in#uence on the measuring accuracy of commercially available optical particle counters. This is important because the majority of industrial applications deal with nonspherical particles leading to a detector response which depends on the orientation of the individual particles. In the "rst section of this paper numerical calculations are presented which deliver the spatial intensity pattern of light scattered from single particles with di!erent size and shape. These calculations are based upon the discrete dipole approximation (DDA) developed by Draine (1988) and can advantageously be used to predict scattering patterns from submicron particles and to develop optical setups for new types of instruments. From these calculations the in#uence of particle shape on the scattering pattern can be quanti"ed and used to develop speci"c optical arrangements according to the measuring task. Further, a direct comparison between experimental and theoretical data is possible in order to verify the capabilities and limitations of existing laboratory instruments. In the experimental section of this paper three di!erent measuring setups (laboratory instruments) are presented which utilize the speci"c scattering pattern of nonspherical particles to derive shape information. The speci"c advantages of these instruments in shape characterization are discussed. Further, experimental results are presented which give hints at what size the structure of the particle surface signi"cantly contributes to the light scattering pattern. So far, the instruments presented in this paper cannot be used for in-line or in situ applications as demanded in the beginning of the section. However, the principal results of our investigations can be used to develop industrial types of instruments which ful"ll demands like in-line/in situ application or mechanical and chemical resistance. TH E OR Y AN D NU M ERI CAL CAL CULATI O N S
The scattering pattern of spherical particles with known optical properties which are illuminated by a plane, monochromatic wave can be calculated by the well-known solution of the Maxwell equations "rst derived by Mie (1908). However, this paper focuses on light scattering from nonspherical particles where Mie's solution fails. Therefore, a "nite element method, the discrete dipole approximation (henceforth DDA), was used to calculate the spatial intensity pattern for particles with arbitrary shape and orientation. The basic idea for this theoretical approach to the nonspherical scattering problem is based on the early "nding of Lorentz (1909), who showed that the dielectric properties of any substance are strongly correlated with the polarizability of its individual atoms. Based on this insight the DDA method was developed by Purcell and Pennypacker (1973), who composed an arbitrarily shaped scatterer from a "nite "eld of polarizable elements (dipoles). The single elements acquire dipole moments in response to the local electrical "eld. Further, the dipoles interact with one another via their electrical "eld. The correct calculation of the scattering "eld requires knowledge about the position and polarizability of the single dipoles. Draine et al. (1994) developed the computer code DDSCAT which was made available for scienti"c use as public domain software. This FORTRAN code enables the calculation of the scattering "eld on basis of the DDA method for (1) di!erent geometries (ellipsoid, cylinder, prism, etc.), (2) inhomogeneous optical structures and (3) arbitrary orientations (including averaging). The number N of dipoles depends on the required
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numerical accuracy d, the size parameter a and the complex refractive index m, which can be approximated by (Draine, 1988) N'(4n/3)"m"a
d \ "m" d \ . 1# 0.1 36n 0.1
(1)
The size parameter is de"ned as nd a" , j
(2)
where d is the particle diameter and j the wave length of the light source. The fractional accuracy d is de"ned as C (d)!C (d) + , d(d)" "" (3) C (d) + where C is the di!erential scattering cross section calculated for a sphere using either the DDA method or Mie's rigorous solution of Maxwell's equations for several scattering angles between 0 and 1803 and sphere diameters d. A sensitivity analysis was carried out by Draine and Flatau (1994) and by the authors for di!erent complex refractive indices m, size parameters a and scattering angles h. For a sphere with "m"(2 the scattering and absorption cross sections can be calculated to an accuracy of a few percent if the number of dipoles is chosen according to equation (1). Although equation (1) applies to spheres, the number of dipoles N for other convex shapes will only di!er by factors on the order of unity (Draine, 1988). This assumption could be con"rmed by our calculations for "nite length cylinders which are oriented with the cylinder axis perpendicularly to the illumination axis. For this case the results from the DDA method can be compared to van de Hulst's modi"cation of the solution of Maxwell's equations for in"nite length cylinders (van de Hulst, 1957), which showed relative deviations of less than 10% in the diameter regime below 5 km and length regime below 50 km. In Fig. 1 the required number of dipoles is plotted versus the particle size for various numerical accuracies d. The computing time strongly depends on the number of dipoles N, the number of scattering angles and orientations and the size parameter a. For N"8000, a"3.5, scattering angles between 0 and 1803 and azimuthal angles between 0 and 3603 (angular resolution of 0.253) the CPU time for a complete run on an IBM AIX V 4.1.5 amounts to 20,000 s. However, the DDA method is a powerful tool especially in the size
Fig. 1. Number of dipoles N as a function of size parameter a and accuracy d.
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parameter regime a(4, where 1000 dipoles might su$ce to obtain valid scattering data within an accuracy of 10%. The particle orientation with respect to the incident light is de"ned in a Cartesian coordinate system (&&lab frame''), in which the incident radiation (monochromatic plane wave) propagates in the #x-direction (see Fig. 2). An arbitrarily shaped scatterer, speci"ed by three unit vectors (a , a , a ), is centered at the origin of the lab frame and can be oriented in any position with respect to the axis of incidence by variation of the angles b, 0 and u. In order to quantify the in#uence of particle shape on the light scattering pattern, di!erent types of scatterers such as spheres, cubes and cylinders have been investigated using the DDA-method. As a result the spatial scattering patterns from single particles with a real refractive index of 1.5 illuminated by a frequency-doubled Nd : YAG-laser (j"532 nm) are shown in the polar diagrams in Fig. 3a}e. The vector of incident radiation is perpendicular to the paper plane with its positive direction towards the observer. Thus, the radial component de"nes the scattering angle h, where r"0 and r"R correspond to
scattering angles of 0 and 903, respectively. The azimuthal angle ' is described by concentric circles at a speci"c scattering angle with '"03 starting at the top of the diagram. Former experiments, e.g. by Sachweh et al. (1995) have shown that the variability in the azimuthal scattering pattern can be used to distinguish between di!erent particle shapes. For a sphere (Fig. 3a) with a diameter of 0.609 km the azimuthal scattering pattern is homogeneous if circular polarized laser light is used for illumination. For a cube (Fig. 3b) with a volume equivalent diameter d "0.609 km oriented with one side perpendicular to the incident radiation, the azimuthal scattering pattern exhibits increasing inhomogenieties at scattering angles larger than 503, whereas in the forward scattering regime less than 503 the azimuthal scattering is identical to that of a sphere. This result holds also true for any other particle orientation. We conclude that the di!raction dominated scattering is relatively insensitive to particle shape, if the particle size is on the order of the wave length of the incident light, here less than 0.5 km. If the dimension of the scatterer exceeds the wave length of light, the azimuthal scattering pattern is di!erent from a sphere also in the near forward scattering regime. This is demonstrated in Fig. 3c for a cube with d "1.5 km and the same orientation as the cube depicted in Fig. 3b. Another situation occurs if one geometrical dimension of the scatterer is much larger than the others (e.g. a cylindrical shape). For this case the scattering pattern will be di!erent from that of a sphere even if d is in the range of the wave length or smaller. This is shown in Fig. 3d where the scattering pattern from a cylinder with d "0.609 and aspect ratio"8 is plotted. The main scattering intensity is found around azimuthal angles of 90 and 2703. Fig. 3e exhibits the scattering pattern for a cylinder with d "0.005 km and an aspect ratio of 8. The size parameter a is calculated to 0.03 for this example. Light scattered from particles with a;1 is described by Rayleigh scattering where the shape in#uence can be neglected and scattering is supposed to be a volume e!ect only (van de Hulst, 1957). However, our calculations for a as small as 0.03 show that the scattering pattern from particles with one geometrical dimension exceeding
Fig. 2. Coordinate system for the scattering domain.
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Fig. 3. Scattering pattern from (a) sphere (d "0.609 km), (b) cube (d "0.609 km), (c) cube (d "1.5 km), (d) cylinder (d "0.609 km, aspect ratio"8), (e) cylinder (d "0.005 km, aspect ratio "8) (j"532 nm, m"1.5, 8000 dipoles).
the others by at least one order of magnitude still varies from the scattering pattern of a sphere. This result is of practical importance because it could be used to distinguish very small "brous particles (e.g. asbestos) from other particles. Thus, the detection of hazardous material in construction or working place areas is possible. We conclude from our calculations that for particles with a'3.5 shape in#uences the azimuthal scattering pattern at all scattering (polar) angles. For this case the forward
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scattering regime can advantageously be used to detect light, because the intensities are substantially higher as in the side or back scattering regime leading to better signal to noise ratios of the instruments. For a(3.5 only the side or back scattering regimes (polar angle '503) should be used in order to obtain sensitive shape information. However, if cylindrical particles have to be detected also the forward scattering regime can be used, as demonstrated in Fig. 3e. The size parameter limit in order to distinguish between di!erent shapes was estimated by Sachweh (1995) from experiments to be at a 3 (0.5 km for the used wave length) for a scattering angle h of 553. Recent investigations of Dick et al. (1998) show that this assessment was somewhat conservative because he obtained valid shape information in the side scattering regime (h"553) from particles down to a size parameter of 1.3 (0.2 km). OPT I CAL SE TU PS AN D M EA SU RIN G RES UL TS
1. Dual angle weighted nephelometer2aerosols (DA=N-A) A measuring method for distinction of di!erent particle shapes was realized by Sachweh et al. (1995) using a commercial instrument, the Dual Angle Weighted Nephelometer for aerosols (DAWN-A) developed by Wyatt et al. (1988). The detector head and a scheme of the measuring principle are shown in Fig. 4. Circularly polarized laser light is focused into the spherical measuring chamber. The aerosol beam entering from the top intersects the laser beam at the center of the measuring chamber. Scattered light is detected at a constant scattering (polar) angle of 553 and 8 azimuthal positions equally distributed between '"0 and 3603. The detection half-angle is only 1.253 so that a su$cient spatial resolution of the scattering pattern is obtained. An aerodynamic focusing nozzle was designed in order to reduce the size of the aerosol beam to 30% of the diameter of the laser beam. Thus, a nearly homogeneous illumination of at least 80% of the maximum intensity is realized although the radial intensity distribution of the laser beam is Gaussian. An experimental study was conducted by Sachweh et al. (1995) to investigate the response of the DAWN-A to spherical polystyrene latex (PSL), cubic like sodium chloride (NaCl) and irregularly shaped quartz particles covering a range of particle sizes, especially in the size range close to the wave length of the laser light (442 nm). In order to identify di!erent particle shapes the sphericity index, SPX, is introduced because it is di$cult to retrieve the geometrical sphericity as for instance de"ned by Wadell (1933) from light intensity measurements. The SPX is calculated from the relative standard deviation of all detector responses by
SPX( j)"1!
)
(m(i, j)!mN ( j)) G , (K!1)mN ( j)
Fig. 4. Detector head of the DAWN-A instrument.
(4)
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where K is the number of detectors (8), m (i, j) is the detector response from a single particle j at azimuthal detector position i and mN ( j)"1/K ) m(i, j) is the mean response from all G detectors. The SPX is 1 for perfect spheres and will decrease with increasing deviations from the spherical shape. Using SPX measurements for di!erent particle shapes an excellent distinction between spherical and nonspherical particles was possible. Although only few applications can bene"t from this information as mentioned in the introduction, it was proven that with a limited number of optical detectors a shape characterization is in principle possible. This "nding was a "rst important step towards development of more precise instruments for shape characterization. Theoretical calculations of the SPX distribution for nonspherical particles can be used to show the accuracy and limitations of the DAWN-A instrument in shape characterization. For a "rst test, measured data for NaCl-particles (Sachweh, 1995) are compared with theoretical data obtained by the DDA-method. Therefore, a cubic shape was de"ned for the calculations, which was the prevailing shape for the submicron NaCl particles used in our former experiments veri"ed by electron microscopy. But there are some limitations in the accuracy of shape characterization for the DDA calculations. Due to the particle generation mechanism by spray drying of NaCl containing droplets (1) the submicron particles exhibit rounded corners and (2) the supermicron particles consist of agglomerates of the cubic primary particles. Thus, some deviations between theory and experiments are to be expected. At least 100 arbitrary orientations were chosen for the calculations and each of the angles b and 0 (see Fig. 2) were uniformly varied between 0 and 903 in order to obtain every possible orientation of the cube. Figure 5 shows a comparison between the numerically derived data and experimental values for NaCl. The experimental values were taken as raw data from our earlier study (Sachweh et al., 1995) and evaluated again by applying a new specially developed digital "lter in order to obtain more precise results. For better comparison the cumulative number distribution was calculated from the theoretical and experimental data by introducing up to 128 SPX classes equally distributed between 0 and 1. All SPX data were summed up in the appropriate class yielding the SPX frequency number distribution which was used in a subsequent step in order to calculate the cumulative number distribution. While agreement is excellent at a particle size of 0.904 km, it worsens for the 0.695 and 1.167 km NaCl-particles. We explain this as follows: At smaller particle sizes the #uctuation of the scattered intensity is dampened due to the lower detection limit of the instrument, which is de"ned by the threshold level chosen to be slightly above the base noise. A part of the intensity distribution thus disappears in the noise, leading to higher experimental SPX
Fig. 5. Comparison between numerical and experimental SPX values for NaCl-particles.
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Fig. 6. Sphericity index distributions for quartz particles and polystyrene latex spheres.
values. For 1.167 km particles an increasing amount of agglomerates a!ects the measured result, which was not simulated at this time. From this result we conclude that agglomerated particles obviously look more spherical. Our earlier assumption that agglomerates are responsible for lower SPX values could not be con"rmed. Just the opposite seems to be valid: agglomerates of cubes look more spherical compared to a single cube. The capability of our speci"c DAWN-A setup to discriminate between di!erent particle shapes is demonstrated in Fig. 6, where the SPX distributions for quartz and PSL are plotted for 4 di!erent particle sizes. Due to the re-evaluation of the raw data from our earlier experiments an even better distinction between this two extreme shape classes is possible on basis of the SPX representation. If an SPX of 0.92 is used as the distinction value between the two shapes the fraction of particles which is erroneously identi"ed in the wrong shape class is less than 2%. 2 . FI BER AE RO SO L AN AL YZ ER (FAA)
The "ber aerosol analyzer (FAA) "rst introduced by Sachweh and Ebert (1995) was especially developed to distinguish between cylindrical "bers and other particles in a mixed aerosol. Furthermore, the instrument can be used to measure "ber diameter and length in case of a cylindrical shape, if the diameter is larger than 0.1 km and the length is smaller than 100 km. The optical setup is derived from the speci"c scattering pattern of cylinders with the cylinder axis oriented perpendicularly to the vector of incident radiation (refer to Fig. 3d and e). The main scattering intensity is con"ned to the azimuthal angular regime around 90 and 2703. The intensity distribution and the distances between the intensity modes are strongly dependent on the aspect ratio. Therefore, the variation in the scattering pattern can be used for length analysis if optical detectors are placed in a narrow distance in the azimuthal angular regime of 90 or 2703. The speci"c detector head of the FAA and the measuring principle are shown in Fig. 7. A diode pumped Nd : YAG-laser at a wave length of 532 nm operated in TEM mode is used for illumination. The laser beam enters the measuring chamber horizontally and leaves at the opposite side into a light trap to avoid re#ections within the measuring chamber. The aerosol beam enters from the top and crosses the laser beam in the center of the chamber. An aerodynamic focusing nozzle was designed which serves the following two functions: (1) A narrow particle beam is produced, which is much smaller than the diameter of the laser beam in order to ensure a homogeneous illumination for all particles. (2) The "bers are aligned parallel to the #ow lines due to a combination of shear and accelerating #ow in the focusing nozzle, so that the "ber axis is perpendicular to the illumination axis. The e$ciency
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Fig. 7. Detector head of the FAA instrument.
Fig. 8. Sphericity index distributions for glass "bers and spherical/nonspherical particles.
of "ber orientation and the retention of orientation during travel between nozzle exit and sensing volume were investigated by Barthel (1998), who found that 75% of the "bers longer than 8 km are aligned within a tilting angle of 23 which results in a relative measuring error of less than 10%. Eight optical detectors between azimuthal angles '"69 and 903 at a constant scattering angle h"553 are used by the presented measuring setup, where the scattered light is conducted by optical PMMA-"bers onto the cathodes of photomultiplier tubes. The electrical signals are digitized by an analog to digital converter and subsequently evaluated by software modules. The diagram in Fig. 8 shows experimental results for PSL, NaCl, quartz (electrical mobility diameter 0.7 km) and glass "bers (diameter+0.7 km, length 2}50 km) obtained from the "ber aerosol analyzer. Please note that the present detector con"guration enables a good distinction between "bers and non"bers using the SPX value. However, a reduced distinction capability results between PSL, NaCl and quartz. If PSL spheres and quartz particles have to be distinguished the error in shape characterization would be around 20% compared to the DAWN-A where it is less than 2%. Thus, the FAA is the ideal instrument in order to identify "ber particles in a externally mixed aerosol without speci"c sensitivity to other particle shapes. Provided the orientation of the "ber axis is perpendicular to the laser beam, a simpli"ed theoretical description of the light scattering pattern can be used. The van de Hulst
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Fig. 9. Length distribution of glass "bers obtained by the FAA and SEM.
modi"cation of the solution of Maxwell's equations for in"nite long cylinders can successfully be used in the azimuthal angular regime around 903 (Barthel et al., 1998). The advantage of this theory in comparison to DDA is the reduced computing time so that a set of calibration data can be performed within very short time. A sample of glass "bers were measured by the FAA and the data subsequently inverted by using calibration data from the van de Hulst theory. In order to verify the results a "lter was installed downstream the FAA to capture the glass "bers for alternative analysis by a scanning electron microscope (SEM). The cumulative number distribution of "ber lengths obtained by the FAA and an image analysis of the SEM-micrographs are plotted in Fig. 9. An excellent agreement between the median values of the cumulative number distributions is found. Due to the relatively large angular spacing of the azimuthal detectors "ber lengths greater than 10 km could not be resolved in this set of experiments. Please note, that "bers longer than 10 km are of course detectable by the current optical setup but added to the upper size class, so that no further length measurement is yet possible. However, a theoretical calculation for a future redesign of the measuring chamber will enable a better resolution, so that "ber lengths up to 100 km might be characterized. 3 . O PT ICA L P ART I CL E CO U N TE R ( O PC)
Another set of experiments was conducted by Umhauer et al. (1991, 1996), who analyzed the in#uence of shape and surface structure for supermicron particles on the measuring accuracy of an optical particle counter (OPC). The OPC with a purely optically de"ned measuring volume uses white light for illumination and detects scattered light from individual particles at a mean scattering angle of 903 (Fig. 10a). In contrast to the DAWN-A and FAA, which measured at 8 di!erent scattering angles simultaneously during the passage of a single particle, the OPC is provided with only one scattering detector at 903 scattering angle. Therefore, the same particle has to be moved repeatedly through the measuring volume thereby undergoing rotation in order to detect the entire shape spectrum. A special measuring chamber was developed (Fig. 10b) for this purpose. A charged particle is introduced into an alternating electrical "eld created by two conical electrodes as proposed by MuK ller (1960) and Straubel (1981). The particle is held in phase by the electrical "eld and oscillates about the center of the electrodes where the measuring volume of the OPC is projected. If the amplitude of the electrical "eld is large enough, the particle traverses the entire measuring volume. Further, a rotation is induced due to the di!erent moments resulting from the nonspherical shape. Thus, with each passage another side of the particle is detected by the OPC. The result is a distribution of
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Fig. 10. Detector head of the optical particle counter (a) and measuring chamber (b).
scattered light signal heights whose width depends on the material properties. High-speed micro-photographs were taken from the same particle in order to verify the orientation during passing the measuring volume and the proper working of the electrodynamical suspension.
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Fig. 11. Sphericity index versus particle size for di!erent quartz, limestone and pollen particles.
Although the intention of this research study was to obtain a measure for the ambiguities in the measuring signal of the OPC if nonspherical particles are present, SPX values can also be calculated from the present measuring results to evaluate shape and structure in#uences by the introduced SPX representation. Therefore, the SPX is calculated according to equation (4) from 1000}2000 passages through the measuring volume leading to a high statistical accuracy of the measuring results. Figure 11 shows the SPX plotted versus the volume equivalent diameter for quartz, limestone and pollen particles, respectively. The quartz particles exhibit an increasing SPX with decreasing particle size. In contrast to the former measurements done with the DAWN-A (Sachweh et al., 1995) this e!ect was not observed and SPX was found to be constant for di!erent particle sizes. Provided a comparable nonspherical shape, another particle characteristic must in#uence the scattering pattern. This led us to the conclusion that beside the shape the internal and surface structure are important, especially for larger particles. Quartz particles have highly re#ecting surface elements which become important for the scattering pattern at larger particle sizes, because the size of these areas substantially exceed the wave length of the light. The surface structure of limestone particle does not show this e!ect and consequently the SPX was found to be nearly constant for di!erent particle sizes. Note that the SPX is relatively high at about 0.88 but a clear distinction to spheres, which normally give SPX'0.95 is possible. Figure 12 shows an electron micrograph from the investigated pollen particles (Helianthus annuus) which nearly look spherical although the surface shows small stings with a diameter of approximately 1 km. Due to their nature only a small size spectrum is available for this type of particles so that SPX values only in a narrow size regime could be investigated. The current particles with an equivalent sphere diameter of approximately 30 km deliver SPX values of nearly 1. Thus, the stings are not visible in the experimental scattering pattern. From these results we conclude that the surface structure of particles must exceed the wavelength of the illuminating light substantially (like for quartz particles) in order to contribute signi"cantly to the scattering pattern. SU MM ARY
The scattering pattern of single particles can be used in order to obtain sensitive shape information, which is*beside size*an important information for the properties of particulate products. A theoretical investigation was carried out based on the discrete dipole approximation (DDA), which is an excellent software tool to predict the scattering pattern of arbitrary particle shapes in any orientation. Because of the extensive computing time, the
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Fig. 12. Electron micrograph of pollen &&Helianthus annuus''.
practicability of this method is limited to the size parameter regime below 4, if extensive theoretical studies like calibration data have to be performed. Numerical data for some basic particle shapes (sphere, cube, cylinder) were used in order to predict the shape in#uence on the scattering pattern. This information can on the one hand be used to design new optical instruments which are capable to deliver shape information. On the other hand, existing optical instruments can be investigated for their measuring accuracy if nonspherical particles are present. We found theoretically for very small particles (a"0.03) with one dimension exceeding the other dimensions by at least one order of magnitude (e.g. a cylindrical shape) that the scattering pattern is still di!erent compared to a sphere. This was a surprising result, because particles which scatter in the Rayleigh regime are supposed to look spherical, because they are much smaller than the wavelength of the used light source. This is important for practical applications, because very small "brous particles (asbestos "bers) can still be identi"ed by their scattering pattern and clearly distinguished from other particle shapes provided the scattering intensity is high enough to be measurable by common optical detectors. For some exemplary studies three di!erent laboratory measuring devices available to the authors were investigated experimentally for their speci"c advantages in shape characterization in the submicron and the supermicron size regime: (1) An equal distribution of detectors between azimuthal angles from 0 to 3603 (DAWN-A) at a constant scattering angle is highly e$cient for the identi"cation of di!erent particle shapes. (2) Using a similar optical setup at azimuthal angles around 903 (FAA) the identi"cation of "bers in an externally mixed aerosol and the characterization of length and diameter of the "bers is possible. (3) A white light counter equipped with an electrodynamical suspension is suitable for shape and structure analysis of supermicron particles ('20 km). It was shown from experimental data that the latter becomes important especially in this size regime, because the dimension of the structure elements substantially exceed the wavelength of the light. On the contrast, a surface structure on the order of only 1}2 times the wavelength of the illuminating light was not found to be detectable in the scattering pattern.
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REF ER E NCE S Barthel, H. (1998) Personal communication. Barthel, H., Sachweh, B. and Ebert, F. (1998) Measurement of airborne mineral "bers using a new di!erential light scattering device. Meas. Sci. ¹echnol. 9 (2), 210}220. Dick, W. D., Ziemann, P. J., Huang, P.-F. and McMurry, P. H. (1998) Optical shape fraction measurements of submicron laboratory and atmospheric aerosols. Meas. Sci. ¹echn. 9 (2), 183}196. Draine, B. T. (1988) The discrete dipole approximation and its application to interstellar graphite grains. Astrophys. J. 333, 848}872. Draine, B. T. and Flatau, P. J. (1994) discrete dipole approximation for scattering calculations. J. Opt. Soc. Am. A 11, 1491}1499. van de Hulst, H. C. (1957) ¸ight Scattering by Small Particles. Dover Publications, New York. Killinger, R. T. and Zerull, R. H. (1988) E!ects of shape and orientation to be considered for optical particle sizing. Proc. Int. Symp. on Optical Particle Sizing: ¹heory and Practice, Plenum Press, New York, pp. 419}429. Mie, G. (1908) BeitraK ge zur Optik truK ber Medien. Ann. Physik 25, 377}445. MuK ller, A. (1960) Theoretische Untersuchungen uK ber das Verhalten geladener Teilchen in Sattelpunkten elektrischer Wechselfelder. Annalen der Physik 7, 208}218. Purcell, E. M. and Pennypacker, C. R. (1973) Scattering and absorption of light by nonspherical dielectric grains. Astrophys. J. 186, 705}714. Sachweh, B. A., Dick, W. D. and McMurry, P. H. (1995) Distinguishing between spherical and nonspherical particles by measuring the variability in azimuthal light scattering. Aerosol Sci. ¹echnol. 23, 373}391. Sachweh, B. A. and Ebert, F. (1995) In situ measurement of airborne "bers using a new di!erential light scattering device. Abstracts of the 14th Annual Meeting of the American Association for Aerosol Research. Seger (1970) Automatische Formerkennung an kleinen Teilchen. Arbeitstagung Schwebsto!technik, Batelle Institut, Frankfurt. Straubel, H. (1981) Elektro-optische Messung von Aerosolen. ¹echnisches Messen 48, 199}210. Umhauer, H. (1989) Streulicht-PartikelgroK {en-ZaK hlanalyse als Methode fuK r in situ-Messungen in Gas-PartikelStroK mungen. ¹echnisches Messen 56 (5), 213}221. Umhauer, H. and Bottlinger, M. (1991) E!ect of particle shape and structure on the results of single-particle light-scattering size analysis. Appl. Opt. 30, 4980}4986. Umhauer, H. (1996) Experimentelle Untersuchungen zur GroK {enbestimmung von biologischen Partikeln durch Streulichtmessung, Martin Schnaiter, Diploma thesis 1993, Publication in preparation. Wadell (1933) Geology 41, 310. Wyatt, P. J. et al. (1988) Appl. Opt. 27 (2), 217}221.
J. Aerosol Sci. Vol. 30, No. 10, pp. 1257}1270, 1999 1999 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0021-8502/99/$ - see front matter
PARTICLE SHAPE AND STRUCTURE ANALYSIS FROM THE SPATIAL INTENSITY PATTERN OF SCATTERED LIGHT USING DIFFERENT MEASURING DEVICES Bernd Sachweh,R* Holger Barthel,R Reinhard Polke,R Heinz UmhauerS and Helmut BuK ttner A R BASF AG, Engineering Research and Development, ZAT/R-L540, D-67056 Ludwigshafen, Germany S Mechanische Verfahrenstechnik und Mechanik, UniversitaK t Karlsruhe, Postfach 6980, D-76128 Karlsruhe, Germany A Mechanische Verfahrenstechnik und StroK mungsmechanik, UniversitaK t Kaiserslautern, Postfach 3049, D-67653 Kaiserslautern, Germany (First received 18 September 1998; and in ,nal form 27 October 1998)
Dedicated to Professor Fritz Ebert on his 60th birthday Abstract*The spatial intensity pattern of scattered light from nonspherical particles was investigated numerically and experimentally in order to obtain*beside size*sensitive shape information. The discrete dipole approximation (DDA) was used to calculate the light scattering pattern for some basic types of particle shapes. From these calculations the lower size limit where shape information can successfully be detected from light scattering was found at a size parameter of approximately 1. It can be even lower if elongated particles (cylinders) are present. For the exemplary studies three di!erent laboratory instruments available to the authors were utilized. The comparison of experimental and numerical results yielded good correlations, which con"rmed the selected theoretical approach. Thus, it is possible to develop experimental setups for speci"c applications only on basis of theoretical data. From the experiments we found that azimuthal scattering at a constant scattering angle is a promising setup for shape characterization, which can be adapted to speci"c applications with high #exibility. For supermicron particles the surface structure also contributes to the scattering pattern provided the characteristic size of surface elements substantially exceeds the wavelength of the light source. 1999 Elsevier Science Ltd. All rights reserved
I N T RO DU CT I O N
Manufacturing of disperse products requires the characterization of the disperse state in order to control the process and/or to obtain quality properties. One important physical property which has to be measured is the particle size. But there are other product properties such as the color strength of pigments which also depend on particle shape or surface structure. To the knowledge of the authors no on-line, in-line or in situ measuring techniques are available for these quantities. Such techniques are preferable whenever there is a risk of e!ecting the particles by the sampling as is the case for particles with high vapor/sublimation pressure, loose agglomerates or in corrosive gases. Optical methods are preferably employed for in situ measurements, most commonly based on di!raction techniques, which measure concentrations and size distributions of particle ensembles. However, there are advantages in using instruments that measure the intensity of light scattered by single particles in order to detect particle shape and structure, because the scattering intensity of single particles is more sensitive than the mean scattering intensity from ensemble measurements, where shape information is averaged due to di!erent orientations of the particles in the measuring volume. The present paper is a theoretical and experimental evaluation of di!erent options to obtain*in addition to particle size*shape and structure information from the light scattering data of single gasborne particles. The strong shape in#uence on the spatial
* Author to whom correspondence should be addressed. 1257
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scattering intensity pattern was measured for instance by Seger (1970), who investigated the di!raction patterns of single particles illuminated by laser light. Other experiments were conducted by Killinger and Zerull (1988), who investigated microwave scattering by nonspherical particles and by Umhauer et al. (1989, 1991), who contrary to other experimental studies used incident white light. If the scattering patterns for certain types of nonspherical particles were known, this information can be used to identify or at least distinguish, di!erent types of shapes, if some a priori information about the particles is available (Sachweh et al., 1995). Such information can then be used for example to quantify the fraction of hazardous particles in a mixed aerosol, if a speci"c shape is predominant for one particle component. Other examples are the presence of "brous particles in the working place environment, or coal particles in the atmosphere of mines. Another motivation for our investigations is the quanti"cation of the shape in#uence on the measuring accuracy of commercially available optical particle counters. This is important because the majority of industrial applications deal with nonspherical particles leading to a detector response which depends on the orientation of the individual particles. In the "rst section of this paper numerical calculations are presented which deliver the spatial intensity pattern of light scattered from single particles with di!erent size and shape. These calculations are based upon the discrete dipole approximation (DDA) developed by Draine (1988) and can advantageously be used to predict scattering patterns from submicron particles and to develop optical setups for new types of instruments. From these calculations the in#uence of particle shape on the scattering pattern can be quanti"ed and used to develop speci"c optical arrangements according to the measuring task. Further, a direct comparison between experimental and theoretical data is possible in order to verify the capabilities and limitations of existing laboratory instruments. In the experimental section of this paper three di!erent measuring setups (laboratory instruments) are presented which utilize the speci"c scattering pattern of nonspherical particles to derive shape information. The speci"c advantages of these instruments in shape characterization are discussed. Further, experimental results are presented which give hints at what size the structure of the particle surface signi"cantly contributes to the light scattering pattern. So far, the instruments presented in this paper cannot be used for in-line or in situ applications as demanded in the beginning of the section. However, the principal results of our investigations can be used to develop industrial types of instruments which ful"ll demands like in-line/in situ application or mechanical and chemical resistance. TH E OR Y AN D NU M ERI CAL CAL CULATI O N S
The scattering pattern of spherical particles with known optical properties which are illuminated by a plane, monochromatic wave can be calculated by the well-known solution of the Maxwell equations "rst derived by Mie (1908). However, this paper focuses on light scattering from nonspherical particles where Mie's solution fails. Therefore, a "nite element method, the discrete dipole approximation (henceforth DDA), was used to calculate the spatial intensity pattern for particles with arbitrary shape and orientation. The basic idea for this theoretical approach to the nonspherical scattering problem is based on the early "nding of Lorentz (1909), who showed that the dielectric properties of any substance are strongly correlated with the polarizability of its individual atoms. Based on this insight the DDA method was developed by Purcell and Pennypacker (1973), who composed an arbitrarily shaped scatterer from a "nite "eld of polarizable elements (dipoles). The single elements acquire dipole moments in response to the local electrical "eld. Further, the dipoles interact with one another via their electrical "eld. The correct calculation of the scattering "eld requires knowledge about the position and polarizability of the single dipoles. Draine et al. (1994) developed the computer code DDSCAT which was made available for scienti"c use as public domain software. This FORTRAN code enables the calculation of the scattering "eld on basis of the DDA method for (1) di!erent geometries (ellipsoid, cylinder, prism, etc.), (2) inhomogeneous optical structures and (3) arbitrary orientations (including averaging). The number N of dipoles depends on the required
Optical particle shape and structure measurements
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numerical accuracy d, the size parameter a and the complex refractive index m, which can be approximated by (Draine, 1988) N'(4n/3)"m"a
d \ "m" d \ . 1# 0.1 36n 0.1
(1)
The size parameter is de"ned as nd a" , j
(2)
where d is the particle diameter and j the wave length of the light source. The fractional accuracy d is de"ned as C (d)!C (d) + , d(d)" "" (3) C (d) + where C is the di!erential scattering cross section calculated for a sphere using either the DDA method or Mie's rigorous solution of Maxwell's equations for several scattering angles between 0 and 1803 and sphere diameters d. A sensitivity analysis was carried out by Draine and Flatau (1994) and by the authors for di!erent complex refractive indices m, size parameters a and scattering angles h. For a sphere with "m"(2 the scattering and absorption cross sections can be calculated to an accuracy of a few percent if the number of dipoles is chosen according to equation (1). Although equation (1) applies to spheres, the number of dipoles N for other convex shapes will only di!er by factors on the order of unity (Draine, 1988). This assumption could be con"rmed by our calculations for "nite length cylinders which are oriented with the cylinder axis perpendicularly to the illumination axis. For this case the results from the DDA method can be compared to van de Hulst's modi"cation of the solution of Maxwell's equations for in"nite length cylinders (van de Hulst, 1957), which showed relative deviations of less than 10% in the diameter regime below 5 km and length regime below 50 km. In Fig. 1 the required number of dipoles is plotted versus the particle size for various numerical accuracies d. The computing time strongly depends on the number of dipoles N, the number of scattering angles and orientations and the size parameter a. For N"8000, a"3.5, scattering angles between 0 and 1803 and azimuthal angles between 0 and 3603 (angular resolution of 0.253) the CPU time for a complete run on an IBM AIX V 4.1.5 amounts to 20,000 s. However, the DDA method is a powerful tool especially in the size
Fig. 1. Number of dipoles N as a function of size parameter a and accuracy d.
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parameter regime a(4, where 1000 dipoles might su$ce to obtain valid scattering data within an accuracy of 10%. The particle orientation with respect to the incident light is de"ned in a Cartesian coordinate system (&&lab frame''), in which the incident radiation (monochromatic plane wave) propagates in the #x-direction (see Fig. 2). An arbitrarily shaped scatterer, speci"ed by three unit vectors (a , a , a ), is centered at the origin of the lab frame and can be oriented in any position with respect to the axis of incidence by variation of the angles b, 0 and u. In order to quantify the in#uence of particle shape on the light scattering pattern, di!erent types of scatterers such as spheres, cubes and cylinders have been investigated using the DDA-method. As a result the spatial scattering patterns from single particles with a real refractive index of 1.5 illuminated by a frequency-doubled Nd : YAG-laser (j"532 nm) are shown in the polar diagrams in Fig. 3a}e. The vector of incident radiation is perpendicular to the paper plane with its positive direction towards the observer. Thus, the radial component de"nes the scattering angle h, where r"0 and r"R correspond to
scattering angles of 0 and 903, respectively. The azimuthal angle ' is described by concentric circles at a speci"c scattering angle with '"03 starting at the top of the diagram. Former experiments, e.g. by Sachweh et al. (1995) have shown that the variability in the azimuthal scattering pattern can be used to distinguish between di!erent particle shapes. For a sphere (Fig. 3a) with a diameter of 0.609 km the azimuthal scattering pattern is homogeneous if circular polarized laser light is used for illumination. For a cube (Fig. 3b) with a volume equivalent diameter d "0.609 km oriented with one side perpendicular to the incident radiation, the azimuthal scattering pattern exhibits increasing inhomogenieties at scattering angles larger than 503, whereas in the forward scattering regime less than 503 the azimuthal scattering is identical to that of a sphere. This result holds also true for any other particle orientation. We conclude that the di!raction dominated scattering is relatively insensitive to particle shape, if the particle size is on the order of the wave length of the incident light, here less than 0.5 km. If the dimension of the scatterer exceeds the wave length of light, the azimuthal scattering pattern is di!erent from a sphere also in the near forward scattering regime. This is demonstrated in Fig. 3c for a cube with d "1.5 km and the same orientation as the cube depicted in Fig. 3b. Another situation occurs if one geometrical dimension of the scatterer is much larger than the others (e.g. a cylindrical shape). For this case the scattering pattern will be di!erent from that of a sphere even if d is in the range of the wave length or smaller. This is shown in Fig. 3d where the scattering pattern from a cylinder with d "0.609 and aspect ratio"8 is plotted. The main scattering intensity is found around azimuthal angles of 90 and 2703. Fig. 3e exhibits the scattering pattern for a cylinder with d "0.005 km and an aspect ratio of 8. The size parameter a is calculated to 0.03 for this example. Light scattered from particles with a;1 is described by Rayleigh scattering where the shape in#uence can be neglected and scattering is supposed to be a volume e!ect only (van de Hulst, 1957). However, our calculations for a as small as 0.03 show that the scattering pattern from particles with one geometrical dimension exceeding
Fig. 2. Coordinate system for the scattering domain.
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Fig. 3. Scattering pattern from (a) sphere (d "0.609 km), (b) cube (d "0.609 km), (c) cube (d "1.5 km), (d) cylinder (d "0.609 km, aspect ratio"8), (e) cylinder (d "0.005 km, aspect ratio "8) (j"532 nm, m"1.5, 8000 dipoles).
the others by at least one order of magnitude still varies from the scattering pattern of a sphere. This result is of practical importance because it could be used to distinguish very small "brous particles (e.g. asbestos) from other particles. Thus, the detection of hazardous material in construction or working place areas is possible. We conclude from our calculations that for particles with a'3.5 shape in#uences the azimuthal scattering pattern at all scattering (polar) angles. For this case the forward
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scattering regime can advantageously be used to detect light, because the intensities are substantially higher as in the side or back scattering regime leading to better signal to noise ratios of the instruments. For a(3.5 only the side or back scattering regimes (polar angle '503) should be used in order to obtain sensitive shape information. However, if cylindrical particles have to be detected also the forward scattering regime can be used, as demonstrated in Fig. 3e. The size parameter limit in order to distinguish between di!erent shapes was estimated by Sachweh (1995) from experiments to be at a 3 (0.5 km for the used wave length) for a scattering angle h of 553. Recent investigations of Dick et al. (1998) show that this assessment was somewhat conservative because he obtained valid shape information in the side scattering regime (h"553) from particles down to a size parameter of 1.3 (0.2 km). OPT I CAL SE TU PS AN D M EA SU RIN G RES UL TS
1. Dual angle weighted nephelometer2aerosols (DA=N-A) A measuring method for distinction of di!erent particle shapes was realized by Sachweh et al. (1995) using a commercial instrument, the Dual Angle Weighted Nephelometer for aerosols (DAWN-A) developed by Wyatt et al. (1988). The detector head and a scheme of the measuring principle are shown in Fig. 4. Circularly polarized laser light is focused into the spherical measuring chamber. The aerosol beam entering from the top intersects the laser beam at the center of the measuring chamber. Scattered light is detected at a constant scattering (polar) angle of 553 and 8 azimuthal positions equally distributed between '"0 and 3603. The detection half-angle is only 1.253 so that a su$cient spatial resolution of the scattering pattern is obtained. An aerodynamic focusing nozzle was designed in order to reduce the size of the aerosol beam to 30% of the diameter of the laser beam. Thus, a nearly homogeneous illumination of at least 80% of the maximum intensity is realized although the radial intensity distribution of the laser beam is Gaussian. An experimental study was conducted by Sachweh et al. (1995) to investigate the response of the DAWN-A to spherical polystyrene latex (PSL), cubic like sodium chloride (NaCl) and irregularly shaped quartz particles covering a range of particle sizes, especially in the size range close to the wave length of the laser light (442 nm). In order to identify di!erent particle shapes the sphericity index, SPX, is introduced because it is di$cult to retrieve the geometrical sphericity as for instance de"ned by Wadell (1933) from light intensity measurements. The SPX is calculated from the relative standard deviation of all detector responses by
SPX( j)"1!
)
(m(i, j)!mN ( j)) G , (K!1)mN ( j)
Fig. 4. Detector head of the DAWN-A instrument.
(4)
Optical particle shape and structure measurements
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where K is the number of detectors (8), m (i, j) is the detector response from a single particle j at azimuthal detector position i and mN ( j)"1/K ) m(i, j) is the mean response from all G detectors. The SPX is 1 for perfect spheres and will decrease with increasing deviations from the spherical shape. Using SPX measurements for di!erent particle shapes an excellent distinction between spherical and nonspherical particles was possible. Although only few applications can bene"t from this information as mentioned in the introduction, it was proven that with a limited number of optical detectors a shape characterization is in principle possible. This "nding was a "rst important step towards development of more precise instruments for shape characterization. Theoretical calculations of the SPX distribution for nonspherical particles can be used to show the accuracy and limitations of the DAWN-A instrument in shape characterization. For a "rst test, measured data for NaCl-particles (Sachweh, 1995) are compared with theoretical data obtained by the DDA-method. Therefore, a cubic shape was de"ned for the calculations, which was the prevailing shape for the submicron NaCl particles used in our former experiments veri"ed by electron microscopy. But there are some limitations in the accuracy of shape characterization for the DDA calculations. Due to the particle generation mechanism by spray drying of NaCl containing droplets (1) the submicron particles exhibit rounded corners and (2) the supermicron particles consist of agglomerates of the cubic primary particles. Thus, some deviations between theory and experiments are to be expected. At least 100 arbitrary orientations were chosen for the calculations and each of the angles b and 0 (see Fig. 2) were uniformly varied between 0 and 903 in order to obtain every possible orientation of the cube. Figure 5 shows a comparison between the numerically derived data and experimental values for NaCl. The experimental values were taken as raw data from our earlier study (Sachweh et al., 1995) and evaluated again by applying a new specially developed digital "lter in order to obtain more precise results. For better comparison the cumulative number distribution was calculated from the theoretical and experimental data by introducing up to 128 SPX classes equally distributed between 0 and 1. All SPX data were summed up in the appropriate class yielding the SPX frequency number distribution which was used in a subsequent step in order to calculate the cumulative number distribution. While agreement is excellent at a particle size of 0.904 km, it worsens for the 0.695 and 1.167 km NaCl-particles. We explain this as follows: At smaller particle sizes the #uctuation of the scattered intensity is dampened due to the lower detection limit of the instrument, which is de"ned by the threshold level chosen to be slightly above the base noise. A part of the intensity distribution thus disappears in the noise, leading to higher experimental SPX
Fig. 5. Comparison between numerical and experimental SPX values for NaCl-particles.
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Fig. 6. Sphericity index distributions for quartz particles and polystyrene latex spheres.
values. For 1.167 km particles an increasing amount of agglomerates a!ects the measured result, which was not simulated at this time. From this result we conclude that agglomerated particles obviously look more spherical. Our earlier assumption that agglomerates are responsible for lower SPX values could not be con"rmed. Just the opposite seems to be valid: agglomerates of cubes look more spherical compared to a single cube. The capability of our speci"c DAWN-A setup to discriminate between di!erent particle shapes is demonstrated in Fig. 6, where the SPX distributions for quartz and PSL are plotted for 4 di!erent particle sizes. Due to the re-evaluation of the raw data from our earlier experiments an even better distinction between this two extreme shape classes is possible on basis of the SPX representation. If an SPX of 0.92 is used as the distinction value between the two shapes the fraction of particles which is erroneously identi"ed in the wrong shape class is less than 2%. 2 . FI BER AE RO SO L AN AL YZ ER (FAA)
The "ber aerosol analyzer (FAA) "rst introduced by Sachweh and Ebert (1995) was especially developed to distinguish between cylindrical "bers and other particles in a mixed aerosol. Furthermore, the instrument can be used to measure "ber diameter and length in case of a cylindrical shape, if the diameter is larger than 0.1 km and the length is smaller than 100 km. The optical setup is derived from the speci"c scattering pattern of cylinders with the cylinder axis oriented perpendicularly to the vector of incident radiation (refer to Fig. 3d and e). The main scattering intensity is con"ned to the azimuthal angular regime around 90 and 2703. The intensity distribution and the distances between the intensity modes are strongly dependent on the aspect ratio. Therefore, the variation in the scattering pattern can be used for length analysis if optical detectors are placed in a narrow distance in the azimuthal angular regime of 90 or 2703. The speci"c detector head of the FAA and the measuring principle are shown in Fig. 7. A diode pumped Nd : YAG-laser at a wave length of 532 nm operated in TEM mode is used for illumination. The laser beam enters the measuring chamber horizontally and leaves at the opposite side into a light trap to avoid re#ections within the measuring chamber. The aerosol beam enters from the top and crosses the laser beam in the center of the chamber. An aerodynamic focusing nozzle was designed which serves the following two functions: (1) A narrow particle beam is produced, which is much smaller than the diameter of the laser beam in order to ensure a homogeneous illumination for all particles. (2) The "bers are aligned parallel to the #ow lines due to a combination of shear and accelerating #ow in the focusing nozzle, so that the "ber axis is perpendicular to the illumination axis. The e$ciency
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Fig. 7. Detector head of the FAA instrument.
Fig. 8. Sphericity index distributions for glass "bers and spherical/nonspherical particles.
of "ber orientation and the retention of orientation during travel between nozzle exit and sensing volume were investigated by Barthel (1998), who found that 75% of the "bers longer than 8 km are aligned within a tilting angle of 23 which results in a relative measuring error of less than 10%. Eight optical detectors between azimuthal angles '"69 and 903 at a constant scattering angle h"553 are used by the presented measuring setup, where the scattered light is conducted by optical PMMA-"bers onto the cathodes of photomultiplier tubes. The electrical signals are digitized by an analog to digital converter and subsequently evaluated by software modules. The diagram in Fig. 8 shows experimental results for PSL, NaCl, quartz (electrical mobility diameter 0.7 km) and glass "bers (diameter+0.7 km, length 2}50 km) obtained from the "ber aerosol analyzer. Please note that the present detector con"guration enables a good distinction between "bers and non"bers using the SPX value. However, a reduced distinction capability results between PSL, NaCl and quartz. If PSL spheres and quartz particles have to be distinguished the error in shape characterization would be around 20% compared to the DAWN-A where it is less than 2%. Thus, the FAA is the ideal instrument in order to identify "ber particles in a externally mixed aerosol without speci"c sensitivity to other particle shapes. Provided the orientation of the "ber axis is perpendicular to the laser beam, a simpli"ed theoretical description of the light scattering pattern can be used. The van de Hulst
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Fig. 9. Length distribution of glass "bers obtained by the FAA and SEM.
modi"cation of the solution of Maxwell's equations for in"nite long cylinders can successfully be used in the azimuthal angular regime around 903 (Barthel et al., 1998). The advantage of this theory in comparison to DDA is the reduced computing time so that a set of calibration data can be performed within very short time. A sample of glass "bers were measured by the FAA and the data subsequently inverted by using calibration data from the van de Hulst theory. In order to verify the results a "lter was installed downstream the FAA to capture the glass "bers for alternative analysis by a scanning electron microscope (SEM). The cumulative number distribution of "ber lengths obtained by the FAA and an image analysis of the SEM-micrographs are plotted in Fig. 9. An excellent agreement between the median values of the cumulative number distributions is found. Due to the relatively large angular spacing of the azimuthal detectors "ber lengths greater than 10 km could not be resolved in this set of experiments. Please note, that "bers longer than 10 km are of course detectable by the current optical setup but added to the upper size class, so that no further length measurement is yet possible. However, a theoretical calculation for a future redesign of the measuring chamber will enable a better resolution, so that "ber lengths up to 100 km might be characterized. 3 . O PT ICA L P ART I CL E CO U N TE R ( O PC)
Another set of experiments was conducted by Umhauer et al. (1991, 1996), who analyzed the in#uence of shape and surface structure for supermicron particles on the measuring accuracy of an optical particle counter (OPC). The OPC with a purely optically de"ned measuring volume uses white light for illumination and detects scattered light from individual particles at a mean scattering angle of 903 (Fig. 10a). In contrast to the DAWN-A and FAA, which measured at 8 di!erent scattering angles simultaneously during the passage of a single particle, the OPC is provided with only one scattering detector at 903 scattering angle. Therefore, the same particle has to be moved repeatedly through the measuring volume thereby undergoing rotation in order to detect the entire shape spectrum. A special measuring chamber was developed (Fig. 10b) for this purpose. A charged particle is introduced into an alternating electrical "eld created by two conical electrodes as proposed by MuK ller (1960) and Straubel (1981). The particle is held in phase by the electrical "eld and oscillates about the center of the electrodes where the measuring volume of the OPC is projected. If the amplitude of the electrical "eld is large enough, the particle traverses the entire measuring volume. Further, a rotation is induced due to the di!erent moments resulting from the nonspherical shape. Thus, with each passage another side of the particle is detected by the OPC. The result is a distribution of
Optical particle shape and structure measurements
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Fig. 10. Detector head of the optical particle counter (a) and measuring chamber (b).
scattered light signal heights whose width depends on the material properties. High-speed micro-photographs were taken from the same particle in order to verify the orientation during passing the measuring volume and the proper working of the electrodynamical suspension.
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Fig. 11. Sphericity index versus particle size for di!erent quartz, limestone and pollen particles.
Although the intention of this research study was to obtain a measure for the ambiguities in the measuring signal of the OPC if nonspherical particles are present, SPX values can also be calculated from the present measuring results to evaluate shape and structure in#uences by the introduced SPX representation. Therefore, the SPX is calculated according to equation (4) from 1000}2000 passages through the measuring volume leading to a high statistical accuracy of the measuring results. Figure 11 shows the SPX plotted versus the volume equivalent diameter for quartz, limestone and pollen particles, respectively. The quartz particles exhibit an increasing SPX with decreasing particle size. In contrast to the former measurements done with the DAWN-A (Sachweh et al., 1995) this e!ect was not observed and SPX was found to be constant for di!erent particle sizes. Provided a comparable nonspherical shape, another particle characteristic must in#uence the scattering pattern. This led us to the conclusion that beside the shape the internal and surface structure are important, especially for larger particles. Quartz particles have highly re#ecting surface elements which become important for the scattering pattern at larger particle sizes, because the size of these areas substantially exceed the wave length of the light. The surface structure of limestone particle does not show this e!ect and consequently the SPX was found to be nearly constant for di!erent particle sizes. Note that the SPX is relatively high at about 0.88 but a clear distinction to spheres, which normally give SPX'0.95 is possible. Figure 12 shows an electron micrograph from the investigated pollen particles (Helianthus annuus) which nearly look spherical although the surface shows small stings with a diameter of approximately 1 km. Due to their nature only a small size spectrum is available for this type of particles so that SPX values only in a narrow size regime could be investigated. The current particles with an equivalent sphere diameter of approximately 30 km deliver SPX values of nearly 1. Thus, the stings are not visible in the experimental scattering pattern. From these results we conclude that the surface structure of particles must exceed the wavelength of the illuminating light substantially (like for quartz particles) in order to contribute signi"cantly to the scattering pattern. SU MM ARY
The scattering pattern of single particles can be used in order to obtain sensitive shape information, which is*beside size*an important information for the properties of particulate products. A theoretical investigation was carried out based on the discrete dipole approximation (DDA), which is an excellent software tool to predict the scattering pattern of arbitrary particle shapes in any orientation. Because of the extensive computing time, the
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Fig. 12. Electron micrograph of pollen &&Helianthus annuus''.
practicability of this method is limited to the size parameter regime below 4, if extensive theoretical studies like calibration data have to be performed. Numerical data for some basic particle shapes (sphere, cube, cylinder) were used in order to predict the shape in#uence on the scattering pattern. This information can on the one hand be used to design new optical instruments which are capable to deliver shape information. On the other hand, existing optical instruments can be investigated for their measuring accuracy if nonspherical particles are present. We found theoretically for very small particles (a"0.03) with one dimension exceeding the other dimensions by at least one order of magnitude (e.g. a cylindrical shape) that the scattering pattern is still di!erent compared to a sphere. This was a surprising result, because particles which scatter in the Rayleigh regime are supposed to look spherical, because they are much smaller than the wavelength of the used light source. This is important for practical applications, because very small "brous particles (asbestos "bers) can still be identi"ed by their scattering pattern and clearly distinguished from other particle shapes provided the scattering intensity is high enough to be measurable by common optical detectors. For some exemplary studies three di!erent laboratory measuring devices available to the authors were investigated experimentally for their speci"c advantages in shape characterization in the submicron and the supermicron size regime: (1) An equal distribution of detectors between azimuthal angles from 0 to 3603 (DAWN-A) at a constant scattering angle is highly e$cient for the identi"cation of di!erent particle shapes. (2) Using a similar optical setup at azimuthal angles around 903 (FAA) the identi"cation of "bers in an externally mixed aerosol and the characterization of length and diameter of the "bers is possible. (3) A white light counter equipped with an electrodynamical suspension is suitable for shape and structure analysis of supermicron particles ('20 km). It was shown from experimental data that the latter becomes important especially in this size regime, because the dimension of the structure elements substantially exceed the wavelength of the light. On the contrast, a surface structure on the order of only 1}2 times the wavelength of the illuminating light was not found to be detectable in the scattering pattern.
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