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Abstract
Accurate characterization of the asymmetry parameter g is of crucial importance for radiative transfer calculations. Here, we present a portable light scattering (PLS) device designed for in situ, real-time, and contact-free measurements of the particle phase function. The integration time is 20ms for each measurement. Using this device, we measured g values for laboratory-generated brown (organic) carbon aerosol and soot, and commercially available Arizona Road Dust. For the three types of aerosol, the g values were 0.664 ± 0.002, 0.506 ± 0.004, and 0.701 ± 0.020, respectively. The smallest angle our PLS device approaches is 0.7°, which is an order of magnitude smaller than that of commercial nephelometers, thus facilitating more accurate determination of g.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The asymmetry parameter g is the weighted average of the normalized scattered intensity with the cosine of the scattering angle and thus describes the directionality of the scattered light from particles [1,2]. It can be considered as the ratio of the light scattered in the forward direction over that of the backward direction. By definition, g ranges between −1 and 1 (i.e. 1 ≥ g ≥ −1). If the scattering is isotropic, g = 0. When g > 0, forward scattering dominates; when g < 0, backward scattering dominates. Being able to determine where the scattered light is directed is important for many systems; for example, how much incident solar radiation is scattered back into space by aerosol plumes. Thus, accurate values of g are essential in many radiative transfer schemes and climate models to assess aerosol forcing of climate [1,2].
A mathematical description of light scattering from a particle or group of particles is simply given by the particle’s 4 by 4 Mueller matrix operating on the incident beam’s Stokes vector [3,4]. The first element of the Mueller matrix is S11, the phase function which represents the angular distribution of the scattered light intensity as a function of the scattering angle θ. It is normalized so that the integral of the scattered light is equal to 1. The parameter g defined by integrating S11 with the cosine operator over scattering angles
A common way to determine g in many experimental and field settings is by using an integrating nephelometer with a backscatter shutter [5]. The nephelometer measures the backscatter fraction b which is then related to g empirically [6–10]. The limitation of this method arise from the smallest angle a nephelometer can approach, which is typically ~7°, thereby leading to a significant truncation error in b especially for large (≥1 μm) particles.
Digressing from the conventional nephelometer-based way of determining g, we have developed a state-of-the-art portable light scattering (PLS) device with the angle detection range 0.7° to 162° to directly measure this parameter. By assuming S11 to remain constant at θ≤0.7° (Rayleigh regime), we determine g using Eq. (1) by integrating S11 over the angle range 0° to 162°.
2. Instrument design
Figure 1 shows the schematic diagram of our PLS device – it occupies a 15” x 15” ‘shoebox’ like area, which makes it highly portable. To measure S11, the vertically polarized CW 532 nm incident laser beam (Coherent 1261780) passes through a 1/4 λ wave plate (Thorlabs WPQ10M-532) with its fast axis 45° from vertical to ensure the incident light is circularly polarized with the Stokes vector (1,0,0,1)T. The incident beam is directed to illuminate the aerosol sample flowing out of a 1/4” inner diameter copper tubing (i.e. out of the page in the figure). The scattered light is collected by two 512 channel detectors (Hamamatsu S3902-512Q). The scattered light from 0° to 9° is collected by a Fourier lens (AC254-050-A) and the unscattered light (the incident laser beam) is focused by the Fourier lens to a waist. At the waist, a mirror (Lenox Laser AL-45-500) with a 500 µm diameter through-hole, oriented at 45° to the mirror normal axis allows the unscattered light to pass while the scattered light is reflected by the mirror. A small portion of the scattered light at small angles (0° ~0.7°) is lost through the mirror hole along with the unscattered light. The reflected scattered light is then collected by a lens (AC254-035-A-ML) to be projected onto the detector. The scattered light from 12° to 162° is collected by a custom elliptical mirror. The scattered light from 162° to 168° is omitted due to the weak signal and strong mirror edge effect. The intersection of the incident light and the aerosol is at the near focal point of the elliptical mirror; an iris with a 1.5 mm opening is placed at the far focal point where the scattered light is refocused and then thereafter the diverging scattered light is projected onto the second detector. Our device measures the scattered light at all angles simultaneously with an integration time of 20 ms corresponding to each measurement. This device allows for quick and efficient procurement of data, eliminates problems regarding aerosol flow stability, and makes the detection at small angles easier. The two detectors are connected to a data acquisition box, which feeds data collected from the detectors to a computer. This design is adapted from [11–13] albeit with a smaller dimension, finer angle resolution, and wider angle range leading to a precise determination of g.
Fig. 1 A schematic diagram of our portable static light scattering (PLS) device. This device occupies a footprint of 15” x 15” area and is designed to perform in situ, contact-free, real-time measurements of particle asymmetry parameter g.
Since our device measures the relative scattered intensity I(θ) from 0.7° to 162°, assuming I(θ) remains constant at θ≤0.7°, Eq. (1) can be modified as
Plotting the scattered intensity versus q, where q = (4π/λ)sin(θ/2), on a log-log scale reveals the Rayleigh, Guinier, and power law regimes, respectively [14–16]. From the Guinier regime, one can determine the particle radius of gyration Rg. Although this manuscript will not touch upon the size analysis aspect of particles, it should be noted that the smallest detection angle of our PLS device limits the Rg measurement to be less than 6.9 µm. It is reasonable to assume S11 remains constant at θ≤0.7° (Rayleigh regime) for particles with Rg less than 6.9 µm.3. Device benchmark test
Our device was benchmark tested using water droplets produced from a Collison 6-jet nebulizer (CH Technologies Inc., NJ, USA), similar to the one performed in [17]. With the knowledge of the size distribution of spherical water droplets generated at 137.9 kPa (20 psi) [18] and using Mie theory [19], we calculated the theoretical scattered intensity for comparison with the experimental data. Experimental data and theoretical calculations were in excellent agreement in both θ and q space, as shown in Figs. 2(a) and 2(b), respectively, except for the angle range 150° to 162°, where enhanced backscattering was observed. Our previous work (Fig. 2.5 in [13]) has shown the enhanced backscattering is a real effect and not due to calibration errors. Our smallest q detection limit is q = 0.15 µm−1 (~0.7°), which is limited by the hole-size of the pinhole mirror. By integrating the scattering intensity, we found g = 0.818 ± 0.005 for these water droplets, which matched well with theoretical predictions (g = 0.812) using Mie theory [19]. The two separate curves in each panel of Fig. 2 are from the two individual detectors. Note that the experimental g values reported in this figure and throughout this study have been obtained by averaging over multiple measurements of S11
Fig. 2 Water droplets for benchmark testing. The experimental and theoretical phase functions match well in both (A) q and (B) θ spaces. We found g = 0.818 ± 0.005 for these water droplets, in excellent agreement with theoretical predictions.
4. Measurement of carbonaceous and non-carbonaceous aerosol asymmetry parameter
We measured g using this device for laboratory-generated carbonaceous and non-carbonaceous particles. For generation of carbonaceous aerosol, 10 g of Alaskan peatland was burned under smoldering condition in a 21 m3 stainless steel chamber, described in detail in [20]. Smoldering peat fires produce spherical organic carbon particles that absorb light in the near-UV; hence, are commonly called brown carbon (BrC). One hour after the start of a burn, the emitted smoke aerosol were sampled from the chamber into an ‘iron lung’. The iron lung is made of a 16-gallon static-control flexible drum liner (McMaster-Carr 9772T43) that is inserted in a 10-gallon steel drum (McMaster-Carr 4115T12) consisting of a sample port on the lid. Aerosol sample can be inhaled and exhaled through the sample port by adjusting the pressure to the port. Two plastic windows are mounted on the sides of the drum for viewing purposes. Details on the iron lung design can be found in [21]. The exhaled smoke particles were directed to the scattering volume of our PLS device for measurement of S11; the flow rate was set to be 0.6 L/min. Simultaneous and parallel measurement of BrC aerosol number size distribution were performed using an scanning mobility particle sizer (TSI Inc.). Based on previous work, we estimated the complex refractive index m of BrC from Alaskan peat at λ = 532 nm to be 1.45 + 0.002i [20]. Combining the knowledge of m, the aerosol number size distribution, and spherical morphology, we determined the theoretical S11 using Mie theory. As seen in Fig. 3, the experimental and theoretical values of S11 match well. The experimental curve only includes the side scattering data because, for these sub-micron size particles, the forward scattering signal did not yield a decent signal-to-noise ratio. The side scattering intensity, however, begins to approach Rayleigh regime at small q, which is sufficient to determine g = 0.664 ± 0.002, assuming the intensity remains constant at θ≤12°. The uncertainty in g is appreciably small, primarily due to the use of the iron lung which significantly stabilizes the aerosol flow and produces highly repeatable g values. Compared to the theoretically predicted g = 0.702, the smaller value of the experimentally determined g is attributable to the enhanced backscattering signal, as shown in Fig. 3(b). Nonetheless, the measured g is still within 6% of the theoretical prediction assuming the BrC aerosol particles are perfect spheres. Notice that the scattering curve gets noisier at θ>75°, which is due to the low total particle number concentration (5.85 × 104/cm3). The signal corresponding to this sample can be considered just above the threshold detection limit. The number size distribution of this aerosol sample is shown as an inset in Fig. 3(b).
Fig. 3 The phase function of laboratory-generated brown (organic) carbon aerosol in (a) q and (b) θ spaces, respectively. The experimentally determined g = 0.664 ± 0.002 agree within 6% of the theoretical predictions of g = 0.702 made using Mie theory. The slight disagreement between both values could be attributed to the enhanced backscattering observed experimentally.
In addition to BrC aerosol, we experimentally measured g values for soot particles generated from a kerosene lamp in our laboratory. The experimental procedure was similar to the one for BrC aerosol involving the use of iron lung. The average g for these non-spherical aerosol (see inset of Fig. 4) was determined to be 0.506 ± 0.004.
Fig. 4 The phase function of soot particles from a kerosene lamp in (a) q and (b) θ spaces with SEM images shown in the insets. The asymmetry parameter was g = 0.506 ± 0.004.
For non-carbonaceous particle characterization, we purchased ultrafine Arizona Road Dust (AZRD) from Powder Technology Inc. AZRD is a type of standard dust used for filter testing. It is also used as a model analogue for atmospheric dust particles. AZRD particles were aerosolized using an aerosol generator. The design of the aerosol generator is described in [22]. In our experiment, 5g AZRD was loaded into the aerosol generator chamber. The outflowing aerosolized particles were directed to the scattering volume of our PLS device. The measured phase function of AZRD particles is shown in Fig. 5. The kink at q≈20 µm−1 is expected as the SEM images (inset figures of Fig. 5) show these particles to have semi-spherical symmetry [23]. The experimentally determined average g was 0.701 ± 0.020.
Fig. 5 The phase function of ultrafine Arizona Road Dust (AZRD) in (a) q and (b) θ spaces with corresponding particle SEM images shown in the insets. A kink occurs at q≈20 µm−1 due to the semispherical symmetry shape. The asymmetry parameter was g = 0.701 ± 0.020.
5. Truncation error of g
We have analyzed the truncation error of g as a function of particle size. Using Mie theory, we ran spherical particles of geometric mean radius from 0.5 µm to 25 µm with the same geometric standard deviation of 1.2. Figure 6(a) shows the normalized radius probability as a function of geometric mean normalized radius, and Fig. 6(b) shows the truncation error of g determined by our PLS device at λ = 532nm as a function of geometric mean radius for two refractive indices m = 1.33 (water) and 1.95 + 0.79i (soot). For a commercial nephelometer (the smallest angle ~7°) having three wavelengths, there are a few steps involved to determine g. First, a correction factor for the total scattering should be obtained from the scattering Angstrom exponent [24]. The corrected total scattering is used to calculate the backscatter fraction b which is then connect to g by the relationship given in [10]. This method can reduce the truncation error; however, it is only applicable for weakly absorbing submicron particles with the imaginary part of the refractive index 0~0.01. For supermicron particles, the correction factors have considerable uncertainties [24]. Our device circumvents this circuitous way of determining g by directly measuring this parameter for particles of any refractive index and size.
Fig. 6 (A) Normalized size distribution. (B) Truncation error of g as a function of geometric mean radius for refractive indices m = 1.33 and 1.95 + 0.79i.
6. Conclusion
We developed a novel portable light scattering device capable of directly measuring the particle asymmetry parameter g. The device was benchmark tested with water droplets. Using this device, we have characterized carbonaceous particles such as brown carbon from Alaskan peat smoldering and soot from a kerosene lamp, and non-carbonaceous particles such as ultrafine Arizona Road Dust. We determined their average g values to be 0.664 ± 0.002, 0.506 ± 0.004, and 0.701 ± 0.020, respectively. Being able to approach angles as small as 0.7° in the forward direction enables our device to accurately measure g in comparison to commercially available nephelometers.
Funding
National Science Foundation (NSF) (AGS-1455215, CBET-1511964, AGM-1261651, AGS-1649783); National Aeronautics and Space Administration (NASA) (NNX15AI66G).
Acknowledgments
We would like to thank Dr. Huafang Li at the Institute of Materials Science & Engineering, Washington University in St. Louis for helping us collect the SEM images and Dr. William R. Heinson for insightful theoretical discussions.
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