Measurement and Evaluation of Elastic Light Scattering from a Single Levitated Irregular Particle

This study introduced a convenient experimental method to measure and to evaluate the elastic light scattering from a single irregular particle. The particle levitation system was used to trap a particle and to maintain the particle at null position by utilizing electrodynamic balance. Moreover, the Raman spectroscopy was applied to observe the light scattering of a single particle. The influences of relative humidity on optical properties of particle were also discussed. For comparison with experimental results, the classical Lorenz-Mie theory was employed to compute the phase function of a single particle. The experimental results demonstrated that the measurements of light scattering were in approximate trend with the model. In particular, numerical simulation results showed that the scattering intensity was underestimated in backward scattering directions. Consequently, the effect of surface roughness and irregular morphology of particle might be resulted in deviations of backward scattering. Besides, the experiments suggested that while using the weighted average method to estimate the refractive index might cause some significant deviations of light scattering between measuring and modeling.


INTRODUCTION
Within the last few decades, scattering and absorption light of spherical particle which affect solar radiative forcing and/or visibility had been widely studied and were well understood (Charlson et al., 1992;Kiehl and Briegleb, 1993;Lee and Hsu, 1999;Chen et al., 2000;Friedlander, 2000;Lin et al., 2000;Watson et al., 2005;Lin et al., 2009;Lin et al., 2010;Wu et al., 2012;IPCC, 2013;Kim, 2015;Pu et al., 2015;Fukushima et al., 2016;Molnár et al., 2016). Though, light scattering or light absorption from irregular or non-spherical particle perseveres with a paradox. There were many types of this particle such as dust, mineral and soot aerosol, volcanic ash, snow crystal, and biological spore, etc. which could find in different environments. Further, the effects of irregular or non-spherical particle on electromagnetic scattering and remote-sensing recoveries had been extensively discussed in recent times (Volten et al., 1996;Li et al., 2004;Moreno et al., 2006;Liu and Mishchenko, 2007;Muñoz et al., 2010; Petrov et al., 2011;Hajihashemi and Jiang, 2013;Zubko et al., 2013;Bagheri et al., 2015;Milstein and Richardson, 2015;Wang et al., 2015;Yang et al., 2015). The size, shape, and surface texture characterization play an influential role in establishing the optical properties of the irregular or non-spherical particle which was often associated with many uncertainties. To neglect the nonsphericity of particle may cause a significant underestimation or overestimation of light scattering (Li et al., 2004;Yang et al., 2007). Modeling of light scattering from particle also plays an important role in determining optical characterization of aerosol. The Lorenz-Mie theory was a classical method to calculate the scattering properties of a single homogeneous particle. It was not only used to calculate scattering and absorption cross-sections but also the angular scattering for diameter of spherical particle, refractive index, and wavelength of incident light (De Leeuw and Lamberts, 1987;Ma, 2007;Li et al., 2012;Dlugach and Mishchenko, 2014;Han et al., 2014;Greengard et al., 2015;Briard et al., 2016). The phase function was dependent on the refractive index, the incident wavelength, and the particle size. Accordingly, the phase function could be utilized to calculate the particle diameter (Chang and Biswas, 1992;Gatherer et al., 2002;Hopkins et al., 2003;Mitchem et al., 2006;Symes et al., 2006;Davies et al., 2012;Haddrell et al., 2013). In addition, the chemical composition or mixing state of particle could influence the refractive index, size, and density, which in sequence directly affect their optical properties (Liu and Mishchenko, 2007;Gangl et al., 2008).
In order to recognize optical properties of particle, systematic measurements may first be accomplished on a single levitation particle under laboratory conditions. Investigation of single particle studies started in the early part of the twentieth century by using Millikan condenser to measure the elementary charge on the electron. Basing on the oil droplet experiment, the electrodynamic balance (EDB) had been used to capture and levitate a single particle in an electric field. Through this original study, many investigations as well as physical and chemical properties of single particle had been measured and demonstrated by utilizing different kinds of levitating technique such as electrostatic trapping, acoustic balance, and optical levitation (Millikan, 1935;Richardson et al., 1989;Davis and Bridges, 1994;Davis, 1997;Peng and Chan, 2001;Haddrell et al., 2005;Jarzembski and Tankosic, 2005;Mitchem et al., 2006;Nakajima, 2006;Tsai, 2007;Chan and Chan, 2007;Kelly et al., 2008;Kawamoto, 2009;Reid, 2009;Wills et al., 2009;Knox et al., 2010;Zaitone and Tropea, 2011;Davies et al., 2012;Haddrell et al., 2014).
Although many studies had discussed the optical characterization of irregular or non-spherical particle by using numerical simulation, few had been carried out on the determination by using experimental method. Hence, this study devised an automatic and useful experimental method; moreover, the comparison with the Lorenz-Mie theory model that could obtain the scattering function of a single irregular particle as well as capture optical properties related to particle size and refractive index.

MATERIALS AND METHODS
The experiments and simulations, described as following sections, experimental apparatus included three major systems, i.e., the automatically controlled electrodynamic balance (EDB) system, the charge coupled device (CCD) camera monitoring system, and the particle scattering measurement system. The specifications of refractive index for each test Polymethyl methacrylate (PMMA) and carbon particles were 1.49 and 2-i, respectively (Cariou et al., 1986;Hinds, 1999).

Simulation of Mie Scattering
In the following, a brief overview of the equations which were used in this study was given. The Mie scattering properties were computed by using the scattering amplitude functions i 1 and i 2 , which described the scattering at a particular angle with polarization perpendicular and parallel to the scattering plane, respectively. To consider a spherical particle falling into Mie size range that was illuminated with polarized light of intensity, the amplitude functions could be defined as following equations: where µ = cos θ scat , a k and b k were the Mie scattering coefficients and the functions π k (µ) and τ k (µ) contained the information about angular dependence. This numerical solution of the Mie regime particle was restricted to the size parameter regime ≤ 10 4 -10 5 (van de Hulst, 1981;Shah, 1992). Besides, the θ was the angle between the direction of the incident light and the scattered radiation. The angular functions π k (µ) and τ k (µ) could be defined as the simple recursive relations : starting from π 0 = 0 and π 1 = 1. The Mie coefficients a k and b k were defined as following functions: Their numerical evaluations and the more detailed descriptions could be found in standard references in Lorenz-Mie theory (van de Hulst, 1981;Bohren and Huffman, 1983;Davis and Schweiger, 2002;Wolfram and Thomas, 2012). Additionally, the subroutine DAMIE was used to calculate the scattering cross section of PMMA and carbon particle (Dave, 1968).

Automatically Controlled Electrodynamic Balance System
As shown in Fig. 1, an auto-controlled EDB system was used in this study. The factors of the custom-built EDB cell were shown in Table 1. The particle was illuminated with a 30 mW solid-laser (λ = 532 nm) and imaged on a monitor with a CCD camera using a zoom lens, so the particle's location upon entering the null position of the balance was monitored.
The EDB was combined alternating current (AC) electric fields with direct current (DC) electric fields in order to capture and levitate a single charged particle at the null position of the electric field. Because of the dry dispersion method used, the particles would ordinarily carry out one or more excess electrons through contact charging. The levitated particle was stabilized by charging of the alternating electric field (V ac ), specifically the amplitude and frequency of the central double-ring electrodes. Assuming that there was no loss of particle's charge, the mass of the particle was proportional to the inputted DC voltage (V dc ). By employing

Item
Unit DC electrode AC electrode The distance between upper and lower electrode (V dc ) The distance between central double-ring electrodes (V ac ) The voltage of alternating current (V ac ) The frequency of the V ac 12 mm in diameter 16 mm in diameter 20 mm 10 mm < 2000V, 1 mA 0.3 Hz-3 MHz the LabVIEW software, the position of levitated particle on the display provided system with feedback signal to adjust the V dc for saving particle at null position automatically.
A V ac was applied to the central double-ring electrodes, coming about a null potential at the geometric center of the alternating electric field. The alternating current potential of the balance was defined as following equation: where Ω = 2πf was angular frequency of the alternating potential and r was radius of the central double-ring electrodes.
A V dc was applied to upper and lower ring electrode to balance a charged particle with the gravitational force in the null position. Thus, the direct current potential was defined as following equation: where C 0 was a geometric factor, g was the acceleration of gravity, m was the mass of the particle, Z 0 was the separation distance of the upper and lower ring electrode, n was the number of elementary charges present on the particle, and q was the elementary charge (Davis, 1985;Jarzembski and Tankosic, 2005).

Light Scattering of Single Levitated Particles
The EDB cell was combined with a precision motorized rotation stage and these two devices were positioned at the same central line. This stage could rotate continuously through a full 360 degrees, and furthermore the range from 40 to 140 degrees was utilized in the experiment. Therefore, there had some restrictions on the measurement of the light scattering behavior that predominantly scattered forward or backward, it had to design another system which collects light by means of a fixed lens. The Raman spectroscopy (model QE65000, Ocean Optics, USA) was introduced to measure the scattering of the levitated particles undergoing experimental conditions. The specifications of the Raman spectroscopy were categorized in Table 2. In general, Raman spectroscopy provides information about molecular vibrations that could be used for identification or quantitation of particle's components. Nevertheless, it was utilized to measure and evaluate the elastic light scattering of particle in this study. The 532 nm line of a solid-laser with output power 30 mW was used as the source of excitation. Before the laser beam was passed through the EDB, it was sent through a polarizer to maintain its polarization. A collimator with a focal length of 10 mm and the diameter of 5 mm was used to collimate the scattering of the levitated particle. The solid angle aperture of the collimator was about 5.7 degrees. The collimator was set up on the precision motorized rotation stage which calibrated with a stepping motor driver. As the stage was controlled by a stepping motor driver, the respective scattering angles could be verified. The integration time of each observation was 30 seconds. All measurements were made at room temperatures of 20-25°C.

RESULTS AND DISCUSSION
The Figs. 2 and 4 demonstrated an experimental approach that provided insight into how particle size and refractive index affect the elastic scattering of PMMA and carbon particle. For comparison, numerical simulations based on the Lorenz-Mie theory were also displayed.
As demonstrated in Figs. 2(a), 2(b), and 2(c), the intensity of scattered light polarized perpendicular to the scatter plane was sensitive to scattering angle and particle diameter. Besides, as illustrated in Figs. 2(d), 2(e), and 2(f), the results showed the less oscillation in the forward scattering region that contributed by the parallel polarization of light. The results suggested that the larger particle contributes more oscillations and scattering intensity to the angular scattering curve (Ioannidou, 2005;Redmond et al., 2010;Zhang and Rubini, 2011;Dlugach et al. 2012;Sorensen et al., 2014).
In addition, the micro-structural morphology of the test particles was observed by Scanning Electron Microscope (SEM). At higher magnifications of 10000X, the structure and surface characteristic of PMMA particles could be clearly revealed. Fig. 3 showed SEM micrographs of PMMA particles with a diameter in about 5, 10, and 15 µm. As shown in Figs. 3(a), 3(b), and 3(c), most of the PMMA particles were spherical but some were concave and almost had a heavily wrinkled outer surface. The results demonstrated that the slightly deviations of backward scattering might be caused by the wrinkled surface characteristic of the particle (Li et al., 2004;Yang et al., 2007). For a carbon particle, as displayed in Fig. 4, the intensity of scattered light either polarized perpendicular or polarized parallel to the scatter plane was insensitive to scattering angle but particle diameter in some scattering regions. In contrast, as illustrated in Figs. 4(d), 4(e), and 4(f), the results showed the a few oscillations in the forward scattering region that contributed by the parallel polarization of light. The refractive index influenced scattering (or extinction) in the small particle size region more than in the coarse particle size region (Bäumer et al., 2008;Jung and Kim, 2008;Kostinski and Mongkolsittisilp, 2013).
The structure and surface characteristic of carbon particles was also observed by SEM at normal magnifications of 5000X. The Fig. 5 showed SEM micrographs of carbon particles with an aerodynamic diameter in about 5, 10, and 15 µm. As shown in Figs. 5(a), 5(b), and 5(c), most of the carbon particles were irregular, non-spherical and other small particles might agglomerate on the surface to effectively increase surface roughness.
Basing on the following equation, the aerodynamic diameter (d a ) could be translated into equivalent volume diameter (Hinds, 1999).
where ρ 0 was the standard particle density and ρ p was the carbon density, 433 kg m -3 which provided from manufacturer. The χ was dynamic shape factor. Additionally, it was important to note that the simulation might result in significant deviations in the overall scattering because of using aerodynamic diameter to replace equivalent volume diameter (d e ). Although the aerodynamic diameter was widely applied in aerosol science and technology, the equivalent volume diameter might be involved in optical properties. Consequently, it was interesting to note that the appearance of the varied backward scattering between numerical evaluations and experimental results because of the irregular structure or wrinkled surface characteristic of particle. Several theoretical and experimental studies also had shown that the non-spherical or irregular particle could lead to significant deviations in the scattering function calculated by the Lorenz-Mie theory, particularly at backward scattering directions (Curtis et al., 2007;Aptowicz et al., 2013).
According to the following equation, the initial value of the charge on a particle could be calculated (Hinds, 1999). Assuming there was no loss of the particle charge in the process which the particle diameter was increased with increasing relative humidity. By adjusting the DC voltage, the electrostatic force could be made to balance the force of gravity and the particle held stationary. At this moment, Correspondingly, by replacing the initial value of the particle charge as n, the variation of particle diameter could be determined in higher relative humidity. Hence, the variation of relative mass of the particle due to condensation or evaporation of water in response to the changes in ambient RH was determined by recording the V dc required to balance the weight of the particle. The specifications of parameter and refractive index were categorized in Table 3. The volume average and mass average refractive indices were separately calculated from the volumes and masses of the carbon and water.
As demonstrated in Figs. 6(a) and 6(b), the experimentally measured elastic scattering intensity was in good agreement of backward scattering but in the enhancement of forward scattering with numerical simulations. The experimental results also indicated the scattering intensity increased with the increasing of relative humidity. The trend of experimental results was similar with many studies (Yoon and Kim, 2006;Cheng et al., 2008;Deng et al., 2013;Liu et al., 2013;Pilinis et al., 2014).
Some studies also demonstrated that the scattering efficiency occurred an increasing behavior above 50% relative humidity and water uptake would not only change the refractive index but also particle size Lyamani et al., 2008;Li et al., 2011). Besides, it was  Fig. 6. The scattering intensity as a function of scattering angle for a carbon particle at relative humidity= 50 and 70%.
important to note that when using volume average method to estimate the effective refractive index of multicomponent or heterogeneous particle might cause some significant deviations between the theoretical and experimental result because of variations of the mixing state and the water distribution on the particle surface (Watson et al., 2008;Deng et al., 2013;Pilinis et al., 2014).
Furthermore, the hygroscopic characteristics of particle were important to both direct and indirect forcing of global climate and atmospheric visibility reduction phenomena. The forward scattering of the ambient aerosols was especially affected by water uptake (Balis et al., 2003;Gangl et al., 2008;Liu et al., 2008).

CONCLUSIONS
This automatically electrodynamic balance system might be not only conducted a steady levitation of single particle but also provided an advantage measurement of light scattering. The experimental results presented that the measurements of light scattering were in approximate trend with numerical simulations basing on the Lorenz-Mie theory. Furthermore, simulation results also indicated that the scattering intensity might be underestimated in backward scattering directions.
For a light-scattering material, like PMMA, the scattering intensity of perpendicular polarization was sensitive to angle; furthermore, parallel polarization provided less oscillation in the forward scattering regions. In addition, the larger particle contributed more oscillations and higher intensity to the scattering curve.
For a light-absorbing material, like carbon, the scattering intensity of perpendicular and parallel polarization was insensitive to scattering angle but particle diameter. By contrast, parallel polarization provided a few oscillations in the forward scattering regions. Accordingly, the results showed that the simulation might result in significant deviations in the overall scattering while using aerodynamic diameter to replace equivalent volume diameter. Besides, the results also showed that the scattering intensity increased with the increasing of relative humidity.
According to the micro-structural morphology, the results showed that the appearance of backward scattering was varied with the irregular structure or wrinkled surface characteristic. Moreover, the results suggested that while using the weighted average method to estimate the refractive index of heterogeneous particle might cause some significant deviations of light scattering between measuring and modeling.