This work presents an apparatus that measures near-forward two-dimensional elastic scattering patterns of single aerosol particles and proposes a two-angle extension of the Guinier law to analyze these patterns. The particles, which approximately range from 2 to 8 micrometers in size, flow through the apparatus in an aerosol stream. A spatial filtering technique separates the near-forward portion of the patterns from the illumination light. Contours intended to represent the geometrical profile of the particles are generated from the patterns using the extension of the Guinier law. The analysis is applied to spherical and nonspherical particles, and the resulting contours are found to be consistent with particle shape only for spherical particles.
© 2010 OSA
Electromagnetic scattering is a well-established technique that can potentially be used to characterize the physical properties of aerosol particles. Typically, the primary properties of interest include particle size, shape, and composition. With this information, it can be possible to discriminate between certain particle types present in an aerosol . For example, an important application in defense-related contexts is the detection of aerosolized biological weapons agents within a background of naturally occurring harmless particles. Optical scattering techniques are particularly well suited for such applications because the particles can be examined in in situ, eliminating the need to collect and scrutinize them manually. For example, the Two-Dimensional Angular Optical Scattering (TAOS) experiments of Aptowicz et al. demonstrate that single-particle measurements collected from an urban aerosol can be qualitatively classified into general shape categories . More quantitative determination of particle size and shape solely form such two-dimensional (2D) patterns has proved difficult thus far. Although possible in principle, such characterization suffers in practice from miss-alignment of optical elements, beams, and particle streams, causing aberration of the patterns, in addition to the nonunique and potentially ambiguous results of the pattern interpretations.
The difficulties associated with these previous efforts motivate the exploration of alternative pattern measurement and interpretation techniques. Guinier analysis is one such technique that is widely applied to single and many-particle systems lacking a preferred orientation, such as trapped spherical-particles, randomly oriented colloids, and carbon soot aggregates [5, 7, 8]. In these applications, the scattering pattern over a single angle is measured near the forward direction. This yields a scattering curve from which the Guinier law provides an estimate of the particle, or aggregate, radius of gyration. Although useful as an overall sizing technique, this analysis does not typically supply information relating to the shape of the particle, which can be sufficient information for many applications.
Very little work exists establishing the usefulness of Guinier analysis to characterize single particles in fixed orientations using their 2D scattering patterns [9–11]. The purpose of this paper is to describe experiments intended to extend the analysis to such patterns with the goal of obtaining both size and shape estimates. The experimental apparatus is able to capture the 2D patterns surrounding the forward direction from single aerosol particles in a flowing stream. A generalization of the single-angle Guinier law to two angles, i.e., to 2D, is proposed and applied to the measured patterns. The result is the generation of a contour presumed to represent the outline of a particle’s geometrical profile along the forward direction. While this analysis is successful in generating contours for spherical particles, there is a systematic distortion in the contours for nonspherical particles, yielding contours that are clearly not representative of the true particle shapes.
2. Scattering apparatus
Figure 1 shows a schematic of the experimental apparatus. Aerosol particles are produced from aqueous solutions using distilled water via an aspiration aerosol generator (ROYCO instruments inc., Model 256) or by aerosolizing powders using an Erlenmeyer flask. Both generators are shown in the inset diagrams in Fig. 1. The aspiration generator forms droplets from an aqueous solution, which are then dried as they travel to a nozzle in the scattering volume. The result is an aerosol consisting of solid particles of the solute material. The size of the particles produced by the aspiration generator, while typically polydisperse, is roughly controlled by the concentration of the solute, which is adjusted to yield particles ∼ 1 – 5μm in size. The Erlenmeyer generator aerosolizes powders as follows: A small sample of the material is placed in the flask, which is then sealed by a stopper. Two aluminum tubes pass through the stopper; one delivers pressurized air to the flask, blowing the material around, while the other tube allows some of the airborne particles to exit the flask and then be transferred to the scattering apparatus. This aerosol generator typically produces a larger variation of particle sizes. Scattering measurements are done only on particles in the ∼ 1 – 10μm size range due to limitations imposed by the spatial filter described below. Several solute materials are used in the aspiration generator: riboflavin, sodium chloride, borosilicate glass, and polystyrene latex microspheres (Duke Scientific Corp.). Kaolinite powder is used in the Erlenmeyer generator. These materials are selected to provide particles of various morphologies, which is seen in the scanning electron microscope (SEM) images in Fig. 2.
The dried aerosol is guided by plastic tubing to a nozzle that narrows it to a stream approximately one mm in diameter. The nozzle opening is positioned vertically about one cm above an eduction tube that removes the aerosol. Particles in the stream traverse the intersection of two crossed diode-laser beams as shown in Fig. 1. These beams, which have different wavelengths of 637 and 657 nm, respectively, are used as an optical trigger that senses the presence of a particle and defines the so-called trigger volume . When a particle intersects the beam crossing, both wavelengths of light are scattered simultaneously. This light is imaged onto two photomultiplier tubes (PMT) (Hamamatsu Corp., Model H6780-02) through diode-laser line filters, each selected to pass only one of the diode-laser wavelengths. In this way, each PMT is sensitive to only one of the diode-laser wavelength. The passage of a particle through the trigger volume corresponds to a signal generated by each PMT, typically several mV in magnitude. The signals are then amplified (ORTEC model 570) to several V, see the block diagram in Fig. 1. Following this, the signals are discriminated by a quad single-channel analyzer (ORTEC model 850), which rejects all signals outside of an adjustable magnitude-window. This stage acts as a squelch, eliminating electronic noise and trigger signals associated with particles much larger than the size range of interest. Next, the signals are passed to analog processors (Stanford Research Systems, model SR 235), which condition the signal for input to an AND logic unit (ORTEC model CO4020). If there is coincidence of the signals from both PMTs, the AND unit outputs a TTL-level signal that fires a Q-switched Nd:YAG laser (Spectra Physics Lasers, Inc., model Y70-532Q) producing a linearly-polarized pulse of approximately 70 ns at the Nd:YAG second-harmonic wavelength of 532 nm.
The near-forward region of a particle’s 2D scattering pattern is collected using a simple spatial-filtering arrangement, also shown in Fig. 1. The Nd:YAG illumination pulse is brought to a gentle focus by a long focal-length lens (25 mm dia., f = 400 mm) labeled (i) in Fig. 1. The waist of this focus beam is less than one mm in diameter and enters a black anodized aluminum tube roughly one mm in diameter and two mm in length. This tube is glued to the center of a 52 mm diameter anti-reflection coated glass window, and acts as an absorption beam stop preventing the passage of the illumination light. Before arriving at this beam stop, the illuminating light passes through the aerosol stream at the point where the trigger beams intersect. In this way, the scattered light around the forward direction passes through the window, while the unscattered portion does not. Hence, the stop-window combination acts as a spatial filter removing the illumination beam from the particle’s scattering pattern. By using the long focal-length lens to focus the illumination beam into the stop, and by positioning the stop several cm from the aerosol stream, the light illuminating a particle is mostly collimated across the transverse area of the beam occupied be the particle. This means that plane-wave illumination can be assumed during analysis of the scattering patterns below.
Once the scattering pattern passes through the spatial filter, it is collimated by lens (e) in Fig. 1 (52 mm dia., f = 75 mm, achromat), which is located one focal length from the scattering volume. Following this, the pattern passes through a second lens (52 mm dia., f = 150 mm), focusing the pattern into the opening of an iris located at the lens’ back focal plane. This iris acts as a second spatial filter eliminating stray light: Because the particles are small, several micrometers in size, the overall intensity of their scattering patterns is similar to that of dust floating in the vicinity of the scattering volume or stuck to the surface of the lenses. Without this second spatial filter, scattering from these dust particles overwhelms the pattern from the aerosol particle. After the iris, the pattern is collimated by a final lens (25 mm dia., f = 45 mm, achromat), where it is recorded by a Charged Coupled Device (CCD) camera (Finger Lakes Instrumentation, LLC, model ML 0081909).
To enable quantitative analysis of the scattering patterns, a relationship is needed between each CCD pixel in the pattern (x,y) and the corresponding scattering angles (θ,ϕ). The angles (θ,ϕ) are the polar and azimuthal angles, respectively, where θ is measured from the propagation direction of the illumination beam and ϕ is measured from the polarization direction of the beam. The pixel-angle relationship is achieved by placing an 8μm diameter precision pinhole at the trigger beam intersection. The pattern collected by the CCD is then compared to the pattern expected from circular-aperture diffraction theory given in .
3. Survey of single particle patterns
Figure 3 shows an array of nine single-particle patterns obtained with the apparatus. The dark spot in the center of each pattern is the shadow created by the beam stop of the spatial filter, which eliminates the particle-illuminating Nd:YAG beam. The forward-scattering direction is at the center of this shadow. The polar angle occupied by this shadow is ∼ 2 degrees, while that of the pattern is ∼ 17 degrees. Thus the scattering patterns are collected over the 2D angular range of 2 ≲ θ ≲ 17 and 0 ≤ ϕ ≤ 360 degrees.
Pattern (a) in Fig. 3 corresponds to a mixture of purified water and 2.5 μm diameter borosilicate glass microspheres (Duke Scientific, Corp.) in the aspiration aerosol generator. The particle producing this pattern is a single microsphere initially contained within a droplet that dries on its way to the scattering volume, thus leaving the bare solid particle. The pattern in (b) is similar, except the particles in the aspirator solution are 4.3μm diameter polystyrene microspheres. An image of one of these particles is show in (c) of Fig. 2. Patterns (c)–(e) in Fig. 3 are produced by kaolinite particles aerosolized by the Erlenmeyer generator. The pattern in (f) corresponds to a sodium chloride crystal that forms from a droplet of salt solution produced by the aspiration generator that dries and crystallizes en route to the scattering volume. Patterns (g)–(i) correspond to riboflavin crystals formed likewise. Examples of both the salt and riboflavin particles are shown in Fig. 2.
Many of the patterns in Fig. 3 can be qualitatively grouped according to their general shape and symmetry. For example, patterns (a) and (b) display the azimuthal symmetry indicative of spherical particles. Patterns (g)–(i) have a banded structure with two orthogonal planes of reflection symmetry, which is indicative of a fiber-like particle, for example. The remaining patterns show more complexity and are more difficult to relate to any specific morphology. The interest now is to establish if more quantitative information, specifically relating to size and shape, can be harvested from these patterns by applying an extension of the Guinier law.
4. Two-dimensional extension of Guinier analysis
Guinier’s law is an approximate relationship between the decay of a particle’s randomly oriented forward-scattering peak and its radius of gyration Rg, e.g., see . The law is formulated in terms of the magnitude of the scattering wave vector q, which is the difference between the incident and scattered wave vectors; its magnitude is related to the polar scattering angle θ asEq. (2) to the near-forward portion of a scattering curve, one is able to estimate , and thus estimate the particle size. For example, if the particle is a sphere of radius R, then , see .
The derivation of the Eq. (2), as it relates to a single particle, assumes that the particle takes on all orientations. The final scattering measurement is then described by the average of all fixed-orientation scattering curves. This rotational averaging erases the azimuthal-angle dependence, resulting in the single angle expression of Eq. (2). Physically, the law originates from the onset of destructive interference between the farthest separated regions within the particle along the q direction, see e.g. . In this way it allows information related to the overall particle size to be connected to the scattering curve’s decrease from the forward direction. However, the particles in this work are effectively frozen in fixed orientations since they are illuminated by a single pulse from the Nd:YAG laser. This leads to the proposition that the Guinier law may still be useful for analysis of fixed-orientation scattering patterns given that it is properly generalized from one (θ) to two (θ,ϕ) scattering-angles.
The proposed extension begins by analyzing a scattering pattern on a polar-coordinate grid in the qx-qy plane, where the origin of the grid resides at the forward direction. The portion of the scattering pattern lost by the shadow caused by the spatial filter is reconstructed using interpolation following . A one-dimensional scattering curve can then be associated with each radial of the grid. Equation (2) is applied to each of the curves, except now Rg is regarded as an undefined length ρ presumed to relate to the particle’s shape in its particular orientation. The collection of the end-points of these radii generates a contour, and the hypothesis then, is that the contour represents the particle’s profile along the forward direction.
As an initial example of this new analysis, consider Fig. 4. The riboflavin pattern labeled (g) in Fig. 3 is shown here on the left, except the pixels are expressed in terms of their scattering wave vector components, qx and qy. These components are determined from the pinhole-calibration pixel-angle mapping described in Sec. 2 combined with Eq. (1). The polar-coordinate grid is divided into π/4 segments in the azimuthal angle ϕ. Eight points on the contour are identified, labeled qa-qh, where each corresponds to the scattering angle θ at which the intensity decreases to 2/3 of its value in the forward direction, i.e., the inverse of Eq. (2). This corresponds to the substitution qa = 1/ρa, qb = 1/ρb, etc., in Eq. (2). Shown on the right in Fig. 4 are the points ρa-ρh that generate the contour resulting from this substitution.
The above procedure is applied to the patterns in Fig. 3 to generate corresponding contours, each of which are shown with matching labels (a)–(i) in Fig. 5. By comparing these figures, one can see that patterns (a) and (b) in Fig. 3 have approximate azimuthal symmetry and yield mostly circular contours in Fig. (5), which is consistent with the glass and polystyrene particles used in the aerosol, recall Sec. 3. Moreover, the diameter of these contours approximately matches the manufacturer-provided diameter and is consistent with the SEM image in Fig. 2. Patterns (c) and (f) display a lesser degree of azimuthal symmetry, yet produce mostly circular contours implying sphere-like particle morphologies. These patterns are produced by Kaolinite and salt particles, respectively, each of which is generally nonspherical.
Contours (d), (e), and (g)–(i) in Fig. 5 are unexpected: Each is peanut-like in shape, yet the particles corresponding to them are kaolinite for (d) and (e), and riboflavin for (g)–(i). Kaolinite typically forms irregular particle-shapes and the SEM image in Fig. 2b shows that the riboflavin crystals are fiber like. Thus, the peanut-like contours are inconsistent with the likely morphology of these particles.
Some insight to the origin of the peanut-like contour is provided by Fig. 4. Suppose that the elliptical pattern in Fig. 4(a) were stretched along its horizontal axis of symmetry, which is roughly along the qx-axis, while not being deformed along the perpendicular direction, i.e., the qy-axis. The result would be a banded pattern that would qualitatively correspond to a long fiber-like particle oriented with its symmetry axis along that of the pattern. Consequently, the points labeled qa and qe would move toward larger values along ±qx. The inverse relationship between the components of q and ρ proposed above would then cause the points ρa and ρe to move toward the origin in Fig. 4(b). The points qc, qg, ρc, and ρg however, would remain unaffected. Consequently, the waist in the peanut-like contour would pinch-in toward the origin, resulting in two touching sphere-like contours for the particle profile. Given that this deformation produces a pattern consistent with a fiber-like particle, it becomes clear that the simple hypothesis proposed above to determine particle profiles using the Guinier law is incomplete.
There are several examples of work extending the traditional Guinier analysis to two-dimensions that find results similar to those above [9–11]. In each case, they demonstrate that the application of the Guinier law to a two-dimensional anisotropic pattern does not, in general, identify particle shape. Specifically,  finds that for small angle x-ray scattering (SAXS) the near-forward portion of the pattern is always elliptical for particles with uniaxial shapes. Thus, in some cases the Guinier analysis can provide information relating to the particle’s aspect ratio. It is not clear however, how this conclusion relates to the results above since the particles here do not satisfy the assumptions valid for SAXS due to their much larger refractive index under 532 nm illumination. Moreover, it seems probable that the proposed 2D extension of the Guinier law may not differentiate between different-shaped particles with similar-shaped geometrical profiles. For example, consider a prolate and oblate spheroidal particle; each is different in shape, yet both can be oriented to yield identical profiles along the forward direction.
The measurements presented here demonstrate that near-forward two-dimensional scattering patterns can be collected from single aerosol particles in a flow-through apparatus. Despite the apparent shortcomings of the two-dimensional extension of the Guinier law, the analysis of these patterns is able to provide size information for spherical particles. It is possible that further work could establish additional useful information in these patterns. For example, the shape of the two-dimensional forward scattering peak may be useful to differentiate between particle-shape classes, i.e., differentiate between spherical particles, fiber-like, etc.
The authors are thankful for assistance provided by James Sumner for the SEM images, advice provided by Dave Ligon, and helpful discussions with Chris Sorensen. This work was funded by the United States Defense Threat Reduction Agency.
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