# Shape Discrimination of Individual Aerosol Particles Using Light Scattering

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Methods

#### 2.1. Experimental Setup

#### 2.2. Calculation Method of Scattered Light

#### 2.3. Sample Generation

_{a}of two aerosol particles both within 4 μm, and the size distribution of Oleic acid particles is slightly wider than that of rod-shaped Silicon dioxide particles.

## 3. Results and Discussion

#### 3.1. Extraction and Correction of the Spectral Signal

#### 3.1.1. Signal Extraction

#### 3.1.2. Correction of Light Intensity

#### 3.2. Screen the Time-of-Flight

#### 3.3. Modeling and Analysis

_{f}and AF

_{f}. The two parameters are similar to the asymmetry factor (A

_{f}) proposed by Kaye et al. [7], and can be expressed as follows:

_{f}, and AF

_{f}, respectively. The PLS-DA was carried out on the transformed spectral data, and the number of extracted principal components was set as one and two, respectively. The results are shown in Table 2. As can be seen from Table 2, after the nonlinear processing of the six independent variables, the ability of the prediction model to distinguish the shape of particulate matter and explain variables has been significantly improved. When the number of principal components was set to two, the corresponding result is better than that when the number of extracted principal components was set to one.

_{s}represents the predicted value of the model. Because the values of TOF1 of the aerosol samples detected in the experiment are all within 10 after central standardization, and the values of AP

_{f}and AF

_{f}range from 0 to 100 according to their definitions by combining the coefficients of each variable in Equation (8), it can be seen that the value of the first term is about two to three orders of magnitude smaller than the value of the second and third terms in this prediction model, indicating that the influence of TOF1 is very small and almost negligible compared to AP

_{f}and AF

_{f}. Therefore, to ensure that the predicted values of the models corresponding to different aerosol particles have the same range, the TOF1 variable is omitted for re-modeling, and the result is shown in Equation (9). By comparing Equation (8) with Equation (9), it can be seen that the difference between the coefficients of AP

_{f}and AF

_{f}in the two equations is extremely small. According to Equation (9), the value of F

_{s}ranges from −9.9722 to 203.8778. To conveniently identify and classify the shape of aerosol particles according to the value of F

_{s}, a simple mathematical transformation was carried out on Equation (9), and its value range was adjusted to 0~100. The transformed prediction model is shown in Equation (10).

_{s}corresponding to various aerosol samples (the interval between adjacent intervals is 4). It can be seen that the value of F

_{s}of spherical Oleic acid aerosol particles is generally small, and the value of F

_{s}at the highest point of its relative frequency histogram is 14. For rod-shaped Silicon dioxide aerosol particles, the value of F

_{s}is obviously higher than that of the Oleic acid aerosol particles, and the overall distribution is closer to the right side of the axis. The highest point of relative frequency histogram appears at F

_{s}is 54. Figure 11b represents the distribution trend of the cumulative frequency of the predicted value F

_{s}corresponding to the above aerosol samples. It can be seen that there is a significant difference between the distribution trend of cumulative frequency of Oleic acid aerosol particles and rod-shaped Silicon dioxide aerosol particles. Considering that some particles with unsatisfactory shapes may be produced during the preparation and generation, which will affect the shape classification of particulate matter, therefore, the values of F

_{s}of Oleic acid particles corresponding to the cumulative frequency of 80% and rod-shaped Silicon dioxide particles corresponding to the cumulative frequency of 20% can be considered as the distinguishing thresholds of spherical aerosol and rod-shaped aerosol, respectively (corresponding to F

_{s}= 18 and F

_{s}= 38, respectively). Because the abscissa in Figure 11 is the center value of each interval, the criteria for judging spherical aerosol particles and rod aerosol particles should be F

_{s}< 20 and F

_{s}> 36, respectively. When the value of F

_{s}of the particle is between 20 and 36, it can be considered as other non-spherical particles.

#### 3.4. Group by Particle Size

_{f}between the two aerosol particles is large, while the difference in AF

_{f}is small. With the increase of aerodynamic particle size, the difference in AF

_{f}between the two aerosol particles increases gradually, while the difference in AP

_{f}decreases significantly.

_{a}through the corresponding conversion equation, therefore, several monodisperse aerosol particles generated by the monodisperse aerosol generator FMAG1520 were used to calibrate the experimental device, and the results are shown in Figure 13a. The abscissa in Figure 13a represents the time-of-flight of the particle, and the ordinate represents its aerodynamic diameter. By referring to the fitting results of the calibration curve of the APS3321 device, the conversion equation between time-of-flight and aerodynamic diameter of the experimental device can be expressed as Equation (11):

_{f}and AF

_{f}variables in the model of each particle size segment. It can be seen that the relative values of Beta coefficients of the two variables are different in three particle size segments, and AP

_{f}has a greater influence on the model in the smaller particle size segment (D1), which shows that AP

_{f}has a better shape discrimination ability than AF

_{f}for particles in D1 segment. With the increase of particle size, the Beta coefficient of AP

_{f}decreases gradually, while the Beta coefficient of AF

_{f}shows an increasing trend. It shows that AF

_{f}is better than AP

_{f}in distinguishing the shape of aerosol particles in the larger particle size segment (D3) while the influence of the two parameters on the model is roughly equal in the D2 segment. In addition, it can be seen from Figure 13b that the results obtained by PLS-DA on the spectral data of aerosol particles are in good agreement with the calculated results under experimental conditions.

_{s}, the range of predicted values of each model was adjusted to 0~100 by Equations (12)–(14). Referring to the method of threshold selection in Section 3.3, the values of F

_{s}of Oleic acid droplets corresponding to the cumulative frequency of 80% and rod-shaped Silicon dioxide particles corresponding to the cumulative frequency of 20% were used as the thresholds for separating spherical aerosols from rod-shaped aerosols in each particle size segment.

#### 3.5. Preliminary Laboratory Validation

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Schematic diagram of scattering spectrum signal of single aerosol particle collected by oscilloscope.

**Figure 4.**(

**a**) Electron microscope image of rod-shaped Silicon dioxide particles synthesized by reversed-phase microemulsion method. (

**b**) Size distribution of aerosol samples.

**Figure 5.**Schematic diagrams and local enlarged schematic diagrams of original signal and denoised signal of single Oleic acid particle. (

**a**) The spectral signal corresponds to APD. (

**b**) The spectral signal corresponds to PMT.

**Figure 6.**The intensity distribution of scattered light from aerosol samples. (

**a**) Oleic acid aerosol particles. (

**b**) Rod-shaped Silicon dioxide aerosol particles.

**Figure 7.**Relative sizes of corrected scattered light intensity E1, E2, and E3 of two aerosol particles. (

**a**) Oleic acid aerosol particles. (

**b**) Rod-shaped Silicon dioxide aerosol particles.

**Figure 8.**The distribution of time-of-flight of Oleic acid particles and rod-shaped Silicon dioxide particles.

**Figure 9.**The AUC of Oleic acid particles and rod-shaped Silicon dioxide particles based on their time-of-flight.

**Figure 10.**The results of the AUC of the classification model and the Beta coefficient correspond to the respective variables when PLS-DA extracted different number of principal components. (

**a**,

**b**) ncomp = 1. (

**c**,

**d**) ncomp = 2. (

**e**,

**f**) ncomp = 3. (

**g**,

**h**) ncomp = 4. (

**i**,

**j**) ncomp = 5.

**Figure 11.**The distribution of F

_{s}of Oleic acid aerosol particles and rod-shaped Silicon dioxide aerosol particles. (

**a**) Relative frequency. (

**b**) Cumulative frequency.

**Figure 12.**Difference of light-scattering parameters between Oleic acid and rod-shaped Silicon dioxide particles under different aerodynamic particle sizes.

**Figure 13.**(

**a**) Conversion relationship between time-of-flight of aerosol particles and aerodynamic diameter. (

**b**) Beta coefficients of AP

_{f}variable and AF

_{f}variable of the models in different particle size segments.

**Figure 14.**Identification and classification results of various aerosol samples with different shape characteristics.

**Figure 15.**Electron microscope images of aerosol samples. (

**a**) 4# Silicon dioxide microspheres. (

**b**) 5# irregular Silicon dioxide particles. (

**c**) 7# Silicon oxide powder materials. (

**d**) 8# Silicon oxide powder materials. (

**e**) 9# Basic magnesium sulfate whiskers. (

**f**) 10# rod-shaped Silicon dioxide particles.

Evaluation Index | ncomp = 1 | ncomp = 2 | ncomp = 3 | ncomp = 4 | ncomp = 5 |
---|---|---|---|---|---|

PCTVAR of X | 0.3954 | 0.6165 | 0.7575 | 0.8659 | 0.9131 |

PCTVAR of Y | 0.4506 | 0.6390 | 0.6759 | 0.6864 | 0.6889 |

Evaluation Index | ncomp = 1 | ncomp = 2 |
---|---|---|

AUC | 0.9825 | 0.9828 |

PCTVAR of X | 0.7511 | 0.999 |

PCTVAR of Y | 0.7226 | 0.724 |

Evaluation Index | D1 | D2 | D3 |
---|---|---|---|

AUC | 0.9950 | 0.9905 | 0.9787 |

PCTVAR of X | 0.9991 | 0.9990 | 0.9856 |

PCTVAR of Y | 0.8515 | 0.7938 | 0.7029 |

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**MDPI and ACS Style**

Han, Y.; Ding, L.; Wang, Y.; Zheng, H.; Fang, L.
Shape Discrimination of Individual Aerosol Particles Using Light Scattering. *Sensors* **2023**, *23*, 5464.
https://doi.org/10.3390/s23125464

**AMA Style**

Han Y, Ding L, Wang Y, Zheng H, Fang L.
Shape Discrimination of Individual Aerosol Particles Using Light Scattering. *Sensors*. 2023; 23(12):5464.
https://doi.org/10.3390/s23125464

**Chicago/Turabian Style**

Han, Yan, Lei Ding, Yingping Wang, Haiyang Zheng, and Li Fang.
2023. "Shape Discrimination of Individual Aerosol Particles Using Light Scattering" *Sensors* 23, no. 12: 5464.
https://doi.org/10.3390/s23125464