# A Quantitative Method for Characterizing of Structures' Debris Release

Maiqi Xiang, Martin Morgeneyer, Olivier Aguerre-Chariol, Caroline Lefebvre, Florian Philippe, Laurent Meunier, Christophe Bressot

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Maiqi Xiang, Martin Morgeneyer, Olivier Aguerre-Chariol, Caroline Lefebvre, Florian Philippe, et al. A Quantitative Method for Characterizing of Structures' Debris Release. Eng, 2025, 6 (7), pp.157. 10.3390/eng6070157. ineris-05163325

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Article

# A Quantitative Method for Characterizing of Structures' Debris Release

Maiqi Xiang<sup>1,2,3</sup>, Martin Morgeneyer<sup>2,* ID</sup>, Olivier Aguerre-Chariol<sup>3</sup>, Caroline Lefebvre<sup>4 ID</sup>, Florian Philippe<sup>2,3</sup>, Laurent Meunier<sup>3</sup> and Christophe Bressot<sup>3 ID</sup>

## Abstract

The characterization of airborne submicrometric composite structures' debris is a challenge in the field of environmental monitoring and control. The work presented here aims to develop a new quantitative method to measure elemental mass concentrations via particle sampling and Transmission Electron Microscopy—Energy-Dispersive X-ray Spectroscopy (TEM-EDS). The principle is to collect airborne particles on a porous TEM grid, then add a certain mass of reference particles, and compare the relative mass percentages of elements from reference and sample particles via EDS. Diverse pairs of airborne particles (RbCl, CsCl, NaCl, SrCl<sub>2</sub>, Ga(NO<sub>3</sub>)<sub>3</sub>, braking particles) were deposited on one TEM grid, and the experimental elemental mass ratios were measured by EDS and compared with the theoretical values. Results show that the quantitative and homogeneous collection of reference particles, such as RbCl, on the TEM grid could be suitable. For all the tested conditions, the absolute deviations between the theoretical elemental mass ratios and the experimental ratios remain lower than 8%. Thus, the mass concentration of Fe from the braking aerosol is calculated as 107 µg/m<sup>3</sup>. Compared to the cumbersome real-time instrument, this new method for mass characterization appears to be convenient, and requires a short time of aerosol sampling at the workplace. This approach ensures safety and practicability when assessing, e.g., the exposure risk of hazardous materials.

**Keywords:** mass quantification; TEM-EDS; airborne nanoparticle deposition; TEM grid; exposure assessment

## 1. Introduction

Nanoparticles, Nano-Objects and their Aggregates and Agglomerates (NOAA) or submicrometric particles are often released from commercial consumer products such as building materials, tires, or brakes, which could present risks over their fate to workers, consumers, and the environment [1–6]. Exposure assessment plays a significant role in risk assessment to protect workers and consumers from hazards. The exposure assessment of such particles remains challenging because of their difficulties in sampling, measurement, and characterization [7,8]. It is crucial to know the released particles' characteristics, including their size, shape, number, mass, and composition.

<figure><img src="image_2.png" /></figure>

check for
updates

Academic Editor: Rajinder Pal

Received: 31 May 2025

Revised: 26 June 2025

Accepted: 7 July 2025

Published: 10 July 2025

**Citation:** Xiang, M.; Morgeneyer, M.; Aguerre-Chariol, O.; Lefebvre, C.; Philippe, F.; Meunier, L.; Bressot, C. A. *Quantitative Method for Characterizing of Structures' Debris Release.* *Eng. 2025*, *6*, 157. https://doi.org/10.3390/eng6070157

**Copyright:** © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

<footnote n="1">1 College of Geographical Sciences, Shanxi Normal University, Taiyuan 030000, China; maiqi.xiang@outlook.com</footnote>

<footnote n="2">2 Génie de Procédés Industriels, Sorbonne Universités, Université de Technologie de Compiègne (UTC), F-60200 Compiègne, France</footnote>

<footnote n="3">3 Direction des Risques Chroniques, Institut National de l'Environnement Industriel et des Risques (INERIS), F-60550 Verneuil en Halatte, France; christophe.bressot@ineris.fr (C.B.)</footnote>

<footnote n="4">4 Service d'Analyse Physico-Chimique, Sorbonne Universités, Université de Technologie de Compiègne (UTC), F-60200 Compiègne, France</footnote>

<footnote>* Correspondence: martin.morgeneyer@utc.fr</footnote>
Elemental analysis is a process where a sample of some material is analyzed for its elemental composition. It can be qualitative and quantitative. Quantitative analysis mostly focuses on determining the percentage (mass %) of each element present. In addition, monitoring of absolute element concentration in various types of sample matrices is an important research theme in the field of pollution and health hazards. Some methods can be used to determine the absolute concentration of the element. Gravimetric analysis [9] is a primary method that can be used on a wide range of particle samples, after it has been weighed and calculated using the known molecular formulae. However, the weight increase requires the independence of environmental conditions. Besides the standalone wet chemical methods shown in a lab, spectroscopy-based apparatuses [10,11] are also used for quantitative analysis, such as Atomic Absorption Spectroscopy (AAS), Atomic Emission Spectroscopy (AES), and Ionized Coupled Plasma Atomic Emission Spectroscopy (ICP-AES). However, digestion or atomizing is a requirement to analyze the solid particles using these instruments. X-ray fluorescence-based apparatuses [12] like PX-375 are able to monitor elemental mass concentration from airborne particles but the apparatus is cumbersome and expensive, which needs to be used in the workplace. In addition, those techniques do not provide information on the size or shape of airborne objects.

EDS is a reliable and common way of analyzing fine particles and quantifying the element composition [13,14]. Coupled with TEM or SEM, it is a high-resolution tool that offers the possibility of physical, chemical, morphological characterization, single-particle analysis [15–18], and distinguishing nanomaterials from background [19,20]. However, the elemental quantitative analysis by EDS only gives the percentage of the elemental mass concentration. An easy method to obtain the absolute mass information will better meet the characterization requirement.

The sampling of airborne particles for EDS analysis can be carried out by TEM grid-equipped Mini Particle Sampler (MPS). This sampling technique has turned out to be portable and easy to use [7], and does not require energy-consuming tools, such as an electrostatic precipitator [21]. Particles are collected on the TEM grid by filtration. They have been verified to absorb negligible amounts of water vapor and to have low background contamination levels [22]. TEM grids consist of a holey carbon film and a copper mesh, as shown in Figure 1. The sampling efficiency of this technique has been improved and quantified through several studies [23,24]. This technique can be used to achieve the personal or static sampling of fine particles [23]. It has been employed in a wide range of applications such as occupational hygiene, consumer or environmental exposure assessment, powder technology, and hazardous material characterization [7,25–27].

<figure><img src="image_3.png" /><figcaption>**Figure 1.** Concept diagram of the TEM grid-equipped MPS.</figcaption></figure>

This work aims to develop a standard method for absolute mass quantification of chemical elements present in the airborne pollutants by collecting the tested aerosol and reference particles on one TEM grid by MPS sampling system and comparing the mass percentages of elements by EDS. Combined with microscopical analysis, the size, shape, number, and composition of the collected airborne particles can be observed and quantified. The mass of the element on the TEM grid is independent of the temperature and humidity
during analysis. Compared to the cumbersome on-line instruments, this elemental mass characterization method appears to be handy requiring only a short time of aerosol sampling at workplace. Long-term exposure could necessitate dilution apparatus to avoid particle deposition excess. Complicated sample preparation for microscopical analysis is not a requirement since particles can be directly collected homogeneously on the TEM grids [28].

## 2. Materials and Methods

### 2.1. Materials

Three types of "Quantifoil" holey carbon film 400 copper mesh TEM grids (Agar Scientific, Rotherham, UK) were used: 1.2/1/3, 2/2, and 2/1 for collecting particles. The structural characteristics of the carbon film are shown in Table 1. The TEM grid dimensions and the pore size variations are fitted to efficiently collect the different particles.

<table><caption>**Table 1.** Structural characteristics of the carbon film.</caption><thead><tr><td>Grid Type</td><td>Pore Size, µm</td><td>Pore Pitch, µm</td><td>Porosity, %</td></tr></thead><tbody><tr><td>1.2/1.3</td><td>1.2</td><td>1.2</td><td>18.1</td></tr><tr><td>2/2</td><td>2</td><td>2</td><td>19.6</td></tr><tr><td>2/1</td><td>2</td><td>1</td><td>34.9</td></tr></tbody></table>

Two kinds of particles were deposited on the same TEM grid, one is the reference material, and the second is the "unknown specimen".

#### 2.1.1. Known Aerosol and Validation of the Protocol

Five kinds of airborne salt particles were used as candidates of reference materials: CsCl (purity: 99.5%), RbCl (purity: 99.5%), SrCl₂ (purity: 99.99%), Ga(NO₃)₃ (purity: 99.9%), and NaCl (purity: 99.5%). The first four salts were potential references since elements Cs, Rb, Sr, and Ga are rare in ambient air with low toxicity. The following tests involving the five salts aimed to establish the effectivity of the generated aerosols and their performance in aerosol physics. The sampling efficiencies were compared with those already established in previous articles [28,29].

The aerosols were deposited in pairs on the same grid they were also prepared from one salt to check different deposition conditions for TEM observations. Since the quantities of the particles deposited on the grids are known, it is possible to check whether the chemical species obtained by EDS are indeed those expected. It is also possible to determine the most adequate salt having the closest performance in accordance with the laws of aerosol physics and thus the best candidate for the reference material.

#### 2.1.2. Unknown Aerosol

Those five kinds of salts were also supposed as unknown specimens (named as "pseudo-unknown specimens"): CsCl, RbCl, SrCl₂, Ga(NO₃)₃, and NaCl for calculating the theoretical elemental mass ratio (shown in Section 2.3). In addition, aerosol released by the friction of a brake pad and a braking disk [30] was used as another unknown specimen to test the developed method with a real-life aerosol. The used commercial disk was made of pearlitic cast iron with lamellar graphite.

### 2.2. Methods

The "unknown specimen" that needs to be characterized was deposited on a TEM grid (Step 1). After loading with a specific number and mass of reference nanoparticles (Step 2) on the same grid, the mass percentages of the deposited elements were compared
by EDS mapping. The mass of element involved in the unknown aerosol can be calculated by the mass percentage and the mass of reference element, as described in Figure 2. The set-up for depositing particles and the microscopical analysis are described below.

<figure><img src="image_4.png" /><figcaption>Figure 2. Schematic drawing of the method. The aerosol is sampled and then quantitatively analysed.</figcaption></figure>

### 2.2.1. Experimental Set-Up

#### Set-Up for Step 1: Sampling of Unknown Aerosol

As introduced before, for calculating the theoretical elemental mass ratio, CsCl, RbCl, SrCl₂, Ga(NO₃)₃, and NaCl were used as “pseudo-unknown specimens”. Braking aerosol was tested as a real unknown aerosol. The samplings of the salt particles and braking particles are explained below in detail.

##### a. Set-up for Step 1a: sampling of pseudo-unknown aerosol (salt particles)

The experimental design of the set-up for salt particle deposition is shown in Figure 3. A membrane dryer generated clean, dry, and compressed air. Polydisperse aerosol was generated by spray drying salt solution (CsCl, RbCl, SrCl₂, Ga(NO₃)₃ or NaCl) using an atomizer (PALAS AGK 2000, Palas, Karlsruhe, Germany). A 5–20 mmol/L salt solution concentrations were set for comparison. An applied pressure of 0.8 bar was selected for the atomizer. Two silica gel dryers removed water drops, and the humidity was hence below 5%. The extra airflow was emitted through a HEPA filter. Monodisperse nano aerosols were produced by an electrostatic classifier (3082, TSI), which includes a neutralizer (3088) and a nano Differential Mobility Analyzer (DMA 3085 A, TSI, Marseille, France). The aerosolized particles were neutralized by a radioactive source (TSI 3087) upstream of the filter. The neutralizer was utilized first to establish an equilibrium charge state on the particles, with known percentages of particles carrying no charge, single charge, and multiple charges associated with positive and negative polarities entering the DMA [31,32]. Valves were utilized for inducing the flow to two symmetrically placed MPS, one with a TEM grid installed, as shown in Figure 3. The particle number was measured by a Condensation Particle Counter (CPC 3787, TSI, Marseille, France). A flowrate of 0.6 L/min was set for the CPC pumping. The particle number deposited on the TEM grid (Nₘₐpositioₙ) was calculated based on the particle numbers upstream (Nₐuₚ) and downstream (Nₐdₐwn), which counted by CPC in the conditions of without the TEM grid, and with the TEM grid, respectively.

$$N_{deposition} = N_{up} - N_{down} \qquad (1)$$
<figure><img src="image_5.png" /><figcaption>Figure 3. Concept diagram of the experimental set-up.</figcaption></figure>

The collection efficiency of the TEM grid E was calculated as:

$$E = 1 - \frac{N_{\text{down}}}{N_{\text{up}}} \qquad (2)$$

Here, the particle number and collection efficiency were checked using the three-stage method. That is,

Stage 1: Counting without TEM grid sampling yields the upstream particle number $N_{up}$

Stage 2: Counting with TEM grid sampling yields the downstream particle number $N_{down}$

Stage 3: Counting without TEM grid sampling (repetition of Stage 1)

Measurement data from Stage 3 was used to check the aerosol's stability during the measurements by comparing them to those from Step 1. Ignoring the particle losses in the tubes, the particle number measured without the TEM grid was the number of particles generated from the atomizer. Particles with mobility diameters of 60–100 nm were deposited due to their higher sampling efficiencies compared to smaller particles [28]. Before depositing a different type of particles, purified water was filled in the atomizer bottle to clean the tubes and the instrumentation for at least 15 min.

b. Set-up for Step 1b: sampling of a real-life aerosol (braking particles)

Aerosol released by the friction of the brake pad and the braking disk was collected on a 1.2/1.3 TEM grid by MPS. The samplings were carried out on the developed bench presented in previous works [30]. The sampling flow was 0.3 L/min, and the sampling time was 7 min. The size distribution of braking particles was characterized by an SMPS (Scanning mobility particle sizer) and an APS (Aerodynamic Particle sizer). Braking particles were in the submicrometric/micrometric range [30]. SMPS measured particles smaller than 523 nm and APS measured particles with size between 523 nm and 10 µm. The instrumentations classified particles based on their size. Particle shape was approximated as a sphere.

Set-Up for Step 2: Sampling of Reference Aerosol (Salt Particles)

Since CsCl, RbCl, SrCl₂, Ga(NO₃)₃, and NaCl particles were used as potential reference materials, the set-up was the same as that of Step 1a: sampling of salt particles.

2.2.2. Microscopical Analysis of the Sampled Airborne Particles from Steps 1 and 2

Particles collected on the TEM grids (reference and unknown particles) were analyzed by a Scanning TEM (STEM) performed on a JEOL JEM 2100F microscope with a Centurio silicon drift detector for ultra-fast atomic elementary maps, which collected the X photons from the sample with the largest solid angle on the market up to 1 steradian; and by a JEOL JEM 1400 plus TEM with an Oxford 30 mm² atmospheric thin window silicon drift detector. The resolution of the EDS map and line scan ranges from 1.4 nm to 4 nm. The acceleration voltage was 200 kV. TEM provided micrographs with the size, shape, as well as distribution of deposited particles. EDS, measuring the average element percentage composition of a region by mapping, was performed by expanding the beam to cover a large grid area, which made a great deal of sense in obtaining unbiased elemental distribution information about
the sample. A long acquisition time of X-ray map and ZAF correction moved qualitative analysis to quantitative analysis [33].

The experimental mass ratio of the reference element, e.g., Rb and element present in the unknown aerosol, e.g., Fe was defined as the ratio of the mass percentage of those two elements measured by EDS. A total of 21 squares located on the grid with a magnification of x 20000 were analyzed, as Figure 4 shows. The EDS analysis allowed removing the elements involved in the detector of TEM, such as Si; and in the TEM grid, such as Cu and C. A 15 min elemental mapping was carried out in each square to enable high precisions.

<figure><img src="image_6.png" /><figcaption>Figure 4. A TEM grid with 21 squares with uniform spaces. The positions are numbered from 1 to 21.</figcaption></figure>

The TEM images were analyzed by the open-source program ImageJ (version 1.41 h) and origin pro-9.0 software (MA, USA, open-source version) to obtain the particle size distribution. In addition, an SEM (JEOL-2100F, JEOL Ltd., Tokyo, Japan) coupled with a QUANTAX EDS has been used to help analyze the existing elements in the unknown specimen.

## 2.3. Determination of the Theoretical Elemental Mass Ratio

Besides the elemental mass ratios measured by EDS, the mass ratios of the chemical elements present in the reference aerosol to the chemical elements present in the unknown aerosols were calculated for validity of the present method. The here so-called “theoretical elemental mass ratio” was defined as the ratio of masses of elements, i.e., mass of reference element divided by mass of unknown element.

### 2.3.1. Mass Ratio Between Elements Involved in Reference Salt Particles and Pseudo-Unknown Salt Particles

Salt particles, including pseudo-unknown and reference ones were deposited on the same TEM grid. The mass of the element, such as Rb, deposited on the TEM grid was quantified by the particle deposition number ($N_{deposition}$), particle size and shape, and element molar mass:

$$m_{Rb} = N_{RbCl(deposition)} \times \left( \rho_{RbCl} \times V_{RbCl} \times \frac{M_{Rb}}{M_{RbCl}} \right) \quad (3)$$

where $\rho$ is the particle density; $M$ is the molar mass; and $V$ is the volume of a single particle.

For pseudo-unknown particle and reference particle deposition, i.e., RbCl and CsCl deposition, the theoretical mass ratio between elements Rb and Cs was calculated as $m_{Rb}/m_{Cs}$.

### 2.3.2. Mass Ratio Between Elements Involved in Reference Salt Particles and Braking Particles

The mass of the braking particles ($m_{br}$) sampled on the TEM grid was estimated by the size distribution of generated aerosol which had been measured by the SMPS and APS, the TEM grid theoretical sampling efficiency (shown in Equation (2)), and the
approximate particle density from literature [30]. According to previous works [28,34], the theoretical efficiencies are consistent with the experimental values. Supposing that for size interval [i], the total particle number measured by SMPS was $N_{upbr}$ [i], and TEM grid sampling efficiency was $E_{[i]}$. The mass of braking particles deposited on the TEM grid can be estimated as:

$$m_{br} = N_{upbr[1]} \times E_{[1]} \times (\rho_{br} \times V_{br[1]}) + N_{upbr[2]} \times E_{[2]} \times (\rho_{br} \times V_{br[2]}) + \dots + N_{upbr[i]} \times E_{[i]} \times (\rho_{br} \times V_{br[i]}) + \dots \quad (4)$$

The mass of elements involved in the braking particles can be estimated by the mass of braking particles and element percentages. The theoretical mass ratio between the reference element, e.g., Rb and the unknown element x was estimated as $m_{Rb}/m_{x}$. The only elements which are not detectable by this approach are the carbon, the copper being a central membrane constituent. Some others grids are constituted by gold or nickel instead of copper enable copper quantification. Silicium is a constituent of the EDS detector itself, making the low concentration detection of this element more difficult.

### 3. Results and Discussions

#### 3.1. Qualitative and Quantitative Analysis of Reference Particles

##### 3.1.1. Reproducibility, Repeatability, and Stability of Reference Particle Deposition

Reproducibility and Repeatability of the Deposited Particle Number and Collection Efficiency

Samplings of (a) 12 repetitions for depositing 60 nm RbCl particles generated from 10 mmol/L RbCl solution; (b) 6 repetitions for depositing 60 nm CsCl particles generated from 10 mmol/L CsCl solution; and (c) 9 repetitions for depositing 60 nm CsCl particles generated from 20 mmol/L CsCl solution were carried out in different days. The sampling upstream and downstream lasted for 1–30 min. Then, 1.2/1.3-type TEM grids were used. The average particle number upstream and downstream per second, the average deposited particle number per second, and the collection efficiency in three sampling conditions are shown in Figure 5. The mean value and standard deviations (SD) are indicated.

<figure><img src="image_7.png" /><figcaption>**Figure 5.** Particle number upstream ($N_{up}$), particle number downstream ($N_{down}$), deposited particle number ($N_{deposition}$), and collection efficiency ($E$) for depositing (a) 60 nm RbCl particles generated from 10 mmol/L RbCl solution; (b) 60 nm CsCl particles generated from 10 mmol/L CsCl solution; and (c) 60 nm CsCl particles generated from 20 mmol/L CsCl solution.</figcaption></figure>
The results show that particle number upstream and downstream, deposited particle number do not change their order of magnitude along the repetitions for all three sampling conditions. The differences among the repetitions are caused by the biases of applied pressure and salt concentration of atomizer, pore size, and porosity of TEM grids. The collection efficiencies are almost constant in sampling conditions (a), (b), and (c), with standard deviations of 4%, 4%, and 5%, respectively.

## Variations in the Particle Number During Sampling

Figure 6 shows the changes in particle numbers detected by CPC with time for four tests. The particle number was recorded every second. Then, 60 nm RbCl or CsCl nanoparticles generated from 10 mmol/L RbCl or CsCl solutions were collected on the 1.2/1.3-TEM grids. A 5–30 min sampling period without TEM grid (Stage 1) was carried out firstly for each test. After collecting particles with TEM grids for 30 min (Stage 2), the particle number upstream was measured again for 5 min (Stage 3). The mean and standard deviation of each data set for sampling with TEM grid and without TEM grid have been added. Particle number for sampling with TEM grid and without TEM grid have been fitted, respectively. The results of linear regression and the product-moment correlation coefficients (r) are shown in Table 2.

<figure><img src="image_8.png" /><figcaption>**Figure 6.** Variations in particle number with time for sampling without and with TEM grid.</figcaption></figure>

<table><caption>**Table 2.** Linear regression formula and the r value for sampling without and with TEM grid. x: time (s); y: particle number.</caption><thead><tr><th></th><th>Sampling Without TEM Grid (Stage 1)</th><th>Sampling with TEM Grid (Stage 2)</th></tr></thead><tbody><tr><td>RbCl 1st test</td><td>Y = 76,570 + 2.769x; r = 0.93293</td><td>Y = 36,402 - 0.102x; /</td></tr><tr><td>RbCl 2nd test</td><td>Y = 75,298 + 5.303x; r = 0.99534</td><td>Y = 42,912 + 3.453x; r = -0.98166</td></tr><tr><td>RbCl 3rd test</td><td>Y = 10,812 - 0.234x</td><td>Y = 51,576 - 1.254x</td></tr><tr><td>CsCl test</td><td>Y = 90,080 - 0.834x</td><td>Y = 35,075 - 1.454x</td></tr></tbody></table>
The results show differences for both particle number upstream and downstream (up to 26.45% upstream and 30.86% downstream) depending on the RbCl sampling employed. When re-opening the atomizer, even if the sampling condition is the same, there is a bias towards the atomizer's applied pressure since it is manually controlled which also brings uncertainties [29]. Therefore, depositing particles once is recommended for avoiding the above errors.

In each test, the particle number upstream and downstream are quasi-constant with low standard deviations. The difference between measurement data of Stages 1 and 3 are 8.41%, 13.25%, 0.46%, and 1.43%, respectively, for the four tests.

## Stability of the Set-Up During Long-Term Depositions

Both 2 h and 9 h deposition have been tested to check the stability of set-up. A total of 5 min of samplings before and after deposition were carried out for establishing the constancy of particle number and collection efficiency. CsCl particles were generated from 20 mmol/L salt solution and 60 nm particles were selected from the DMA. Then, 1.2/1.3-type TEM grids were used to capture the particles. Figure 7 shows the differences between the first 5 min and last 5 min sampling of particle number upstream and downstream, deposited particle number, as well as the collection efficiency for (a) 2 h and (b) 9 h deposition, respectively.

<figure><img src="image_9.png" /><figcaption>**Figure 7.** Stabilities of particle number upstream ($N_{up}$), particle number downstream ($N_{down}$), deposited particle number ($N_{deposition}$), and collection efficiency (E) during (a) 2 h; and (b) 9 h deposition.</figcaption></figure>

The results show that both the particle number upstream and downstream decrease a little bit between the first 5 min and the last 5 min deposition. The number of deposited particles and collection efficiency are stable. The differences in deposited particle number and collection efficiency between the first 5 min and last 5 min are 11.57% and 6.62% for 2 h deposition; and 3.04% and 5.94% for 9 h deposition, respectively.

Regardless of the sampling condition, aerosol deposition is easy to be achieved, and the number of deposited particles is easy to be reproduced due to the stability of the set-up. For long-term depositions, samplings of a few minutes in Stages 1 and 3 can be used to calculate the average particle number upstream thanks to its linear relationship. Long-term of big particle deposition may reduce the pore size, which can slightly modify the air flow through the grid [35,36].
### 3.1.2. TEM Analysis of Reference Particles

Besides the particle number, particle size and shape were taken into account for the mass calculation of the reference elements. Figure 8 shows the representative TEM images of different depositions. The different conditions have been explained in Table 3. The size distributions of deposited particles were obtained by counting at least 500 particles from different sample regions using ImageJ. The mean and standard deviation of the particle diameter have been marked.

<figure><img src="image_10.png" /><figcaption>**Figure 8.** TEM images of (a) 5 min 60 nm RbCl and 10 min 60 nm CsCl; (b) 5 min 60 nm RbCl and 5 min 60 nm Ga(NO₃)₃; (c) 3 min 60 nm CsCl; (d) 40 s 100 nm NaCl; (e) 3 min 100 nm SrCl₂; and (f) 9 h 60 nm CsCl particle deposition. The pink curve and the red histogram showcase the particle size distributions.</figcaption></figure>
<table><caption>**Table 3.** Different depositing conditions (a) to (f) for TEM observations.</caption><thead><tr><th></th><th></th><th>(a)</th><th>(b)</th><th>(c)</th><th>(d)</th><th>(e)</th><th>(f)</th></tr></thead><tbody><tr><td>TEM grid</td><td></td><td>1.2/1.3</td><td>1.2/1.3</td><td>1.2/1.3</td><td>1.2/1.3</td><td>2/1</td><td>1.2/1.3</td></tr><tr><td rowspan="3">1st deposition</td><td>particle</td><td>RbCl</td><td>RbCl</td><td>CsCl</td><td>NaCl</td><td>SrCl<sub>2</sub></td><td>CsCl</td></tr><tr><td>salt concentration</td><td>10 mmol/L</td><td>10 mmol/L</td><td>10 mmol/L</td><td>20 mmol/L</td><td>5 mmol/L</td><td>20 mmol/L</td></tr><tr><td>size from DMA</td><td>60 nm</td><td>60 nm</td><td>60 nm</td><td>100 nm</td><td>100 nm</td><td>60 nm</td></tr><tr><td></td><td>time</td><td>5 min</td><td>5 min</td><td>3 min</td><td>40 s</td><td>3 min</td><td>9 h</td></tr><tr><td rowspan="3">2nd deposition</td><td>particle</td><td>CsCl</td><td>Ga(NO<sub>3</sub>)<sub>3</sub></td><td></td><td></td><td></td><td></td></tr><tr><td>salt concentration</td><td>10 mmol/L</td><td>10 mmol/L</td><td></td><td></td><td></td><td></td></tr><tr><td>size from DMA</td><td>60 nm</td><td>60 nm</td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>time</td><td>5 min</td><td>5 min</td><td></td><td></td><td></td><td></td></tr></tbody></table>

Particles observed here are homogeneously distributed on the porous TEM grid. For 9 h deposition shown in Figure 8f, particles are agglomerated, especially on the pores' edges, showing that the pore wall deposition due to interception plays a significant role in the particle collection [35,36]. Moreover, the edges of SrCl₂ particles are blurred when analyzing the samples after several days due to their hygroscopicity, as shown in Figure 8e. They are, therefore, not acceptable references.

Results show that the sizes observed by microscopy are similar to those selected by DMA. The standard deviation is less than 20 nm for 60 nm particles and less than 22 nm for 100 nm particles. Figure 8a shows that RbCl and CsCl particles have expected sizes with a narrow distribution (59 ± 12 nm). According to Figure 8b, RbCl and Ga(NO₃)₃ particles have a mean diameter of 53 nm, which is slightly smaller than the selected value from DMA. Ga(NO₃)₃ particles have a strict sphere shape. For CsCl and NaCl particles, bigger sizes (mean of 65 and 104 nm) are observed compared with the selected sizes (60 and 100 nm). Particles tend to be spherical when smaller than 60 nm, and cubical when larger than 100 nm, as shown in Figure 8c,d. One possible reason is that big particles are better crystallized than small ones, therefore tend to be cubic.

## 3.2. Elemental Mass Ratio Obtained by EDS

STEM-EDS analysis was used to compare the mass percentages between two deposited elements and calculate the experimental elemental mass ratios. This part shows a representative result of EDS analysis in the conditions of (3.3.1): particle depositions of two kinds of salts; and (3.3.2): particle deposition of salt and braking aerosol.

### 3.2.1. RbCl and CsCl Description of Particle Deposition

Using two salts, for example, 60 nm RbCl and CsCl, particles were deposited on a 1.2/1.3 TEM grid for 5 min. Both salt concentrations were 10 mmol/L. Figure 9a,b are STEM images of Square 8 before and after 15 min mapping. Comparing these two images, particles have not been destroyed after mapping. Particles showing a high dispersion in shape and size are observed on the carbon films but also at the hole edges. Figure 9c,d show Rb and Cs mapping images. Both elements Rb and Cs are homogeneously distributed on the carbon film. Between 1 and 10 keV, two peaks of elemental Rb located at 1–2 keV and several peaks for the Cs element in the 2–6 keV range have been observed, as shown in Figure 9e. Rb is a useful reference since it has fewer spectra peaks. From quantitative data, the mass ratio of elements Rb and Cs is around 33:67.

According to the quantitative analysis of the grid, the mass percentages of Rb or Cs are similar for all 21 squares, as shown in Table 4. The sample was approximately 46% of the Rb mass and 54% of the Cs mass. The standard deviation is 7.59%. The reference particles are proven to be homogeneously distributed on the grid.
<figure><img src="image_11.png" /><figcaption>**Figure 9.** STEM images: before mapping (a), after 15 min mapping (b); EDS elemental mapping images of Rb (c), Cs (d); and spectra analysis with quantification results (e) of Square 8 on a TEM grid loaded with RbCl and CsCl particles. Green peaks indicate L X-ray from Rb and Cs shell.</figcaption></figure>

<table><caption>**Table 4.** Experimental mass percentages of elements Rb and Cs in 21 squares of the TEM grid.</caption><thead><tr><th>Number of Square</th><th>% Mass of Rb</th><th>% Mass of Cs</th></tr></thead><tbody><tr><td>1</td><td>50</td><td>50</td></tr><tr><td>2</td><td>48</td><td>52</td></tr><tr><td>3</td><td>46</td><td>54</td></tr><tr><td>4</td><td>37</td><td>63</td></tr><tr><td>5</td><td>47</td><td>53</td></tr><tr><td>6</td><td>42</td><td>58</td></tr><tr><td>7</td><td>35</td><td>65</td></tr><tr><td>8</td><td>33</td><td>67</td></tr><tr><td>9</td><td>35</td><td>65</td></tr><tr><td>10</td><td>56</td><td>44</td></tr><tr><td>11</td><td>54</td><td>46</td></tr><tr><td>12</td><td>54</td><td>46</td></tr><tr><td>13</td><td>42</td><td>58</td></tr><tr><td>14</td><td>44</td><td>56</td></tr><tr><td>15</td><td>53</td><td>47</td></tr><tr><td>16</td><td>38</td><td>62</td></tr><tr><td>17</td><td>47</td><td>53</td></tr><tr><td>18</td><td>50</td><td>50</td></tr><tr><td>19</td><td>58</td><td>42</td></tr><tr><td>20</td><td>56</td><td>44</td></tr><tr><td>21</td><td>48</td><td>52</td></tr><tr><td>Mean</td><td>46</td><td>54</td></tr><tr><td>SD</td><td>7.59</td><td>7.59</td></tr></tbody></table>
### 3.2.2. RbCl and Braking Partsicles Description of Particle Deposition

Braking particles were sampled for 7 min on the TEM grid, and 60 nm RbCl particles were subsequently deposited for 30 min, as reference. STEM-EDS analysis confirms that the braking aerosol mostly consists of Fe, as shown in Figure 10 (Cu, another present element, appears because of the supported copper grid), which is consistent with the literature [37].

<figure><img src="image_12.png" /><figcaption>**Figure 10.** The elemental composition of braking aerosol by SEM-EDS analysis. The red line represents the cps over energy.</figcaption></figure>

Figure 11a,b are STEM images of Square 1 before and after 15 min EDS mapping. A high particle dispersion in shape and size is observed, and particles have not been destroyed during mapping. Figure 11c–h show C, O, Cl, Fe, Cu, and Rb mapping images. The mapping indicates that elements Rb, Cl, and C are homogeneously distributed on the carbon film. Among them, element C is present in the carbon film. Elements Rb and Cl are deposited as RbCl reference particles. It is also noticed that the large braking particles visible on the STEM BF image are rich in Fe, Cu, and O. However, since Cu also is a component of the mesh grid, we cannot provide any quantitative information on this element related to the braking aerosol. In addition, light elements are challenges for EDS quantitative analysis because of the inaccuracy of the absorption correction. Therefore, even if O is usually present in the braking aerosol as metal oxide [38], the quantification information is unavailable. In this case, element Fe is only quantified. Figure 12 shows spectra analysis with quantitative results. The mass ratio between elements Fe and Rb in this square is 90/10.

Table 5 shows the mass percentages of elements Rb and Fe measured by EDS mapping for 21 squares. Removing other elements, the sample was approximately 8% of the Rb mass and 92% of the Fe mass. The standard deviation is 4.13%.
<figure><img src="image_13.png" /><figcaption>**Figure 11.** STEM images: before mapping (a), after 15 min mapping (b); and EDS elemental mapping images of C (c), O (d), Cl (e), Fe (f), Cu (g), and Rb (h) of Square 1 on a TEM grid loaded with RbCl and braking particles.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Figure 12.** Spectra analysis with quantitative results.</figcaption></figure>

<table><caption>**Table 5.** Experimental mass percentages of elements Fe and Rb in 21 squares of the TEM grid.</caption><thead><tr><td>Number of Square</td><td>% Mass of Rb</td><td>% Mass of Fe</td></tr></thead><tbody><tr><td>1</td><td>10</td><td>90</td></tr><tr><td>2</td><td>7</td><td>93</td></tr><tr><td>3</td><td>7</td><td>93</td></tr><tr><td>4</td><td>3</td><td>97</td></tr><tr><td>5</td><td>3</td><td>97</td></tr><tr><td>6</td><td>13</td><td>87</td></tr></tbody></table>
<table><caption>Table 5. *Cont.*</caption><thead><tr><th>Number of Square</th><th>% Mass of Rb</th><th>% Mass of Fe</th></tr></thead><tbody><tr><td>7</td><td>10</td><td>90</td></tr><tr><td>8</td><td>9</td><td>91</td></tr><tr><td>9</td><td>4</td><td>96</td></tr><tr><td>10</td><td>3</td><td>97</td></tr><tr><td>11</td><td>9</td><td>91</td></tr><tr><td>12</td><td>3</td><td>97</td></tr><tr><td>13</td><td>5</td><td>95</td></tr><tr><td>14</td><td>1</td><td>99</td></tr><tr><td>15</td><td>14</td><td>86</td></tr><tr><td>16</td><td>5</td><td>95</td></tr><tr><td>17</td><td>17</td><td>83</td></tr><tr><td>18</td><td>10</td><td>90</td></tr><tr><td>19</td><td>9</td><td>91</td></tr><tr><td>20</td><td>10</td><td>90</td></tr><tr><td>21</td><td>9</td><td>91</td></tr><tr><td>Mean</td><td>8</td><td>92</td></tr><tr><td>SD</td><td>4.13</td><td>4.13</td></tr></tbody></table>

### 3.3. Comparison Between Experimental Mass Ratio and Theoretical Mass Ratio

The mass ratio of the reference element and the element present in the pseudo-unknown aerosol was investigated for different couples of particles. The experimental mass ratio and the theoretical mass ratio were compared and concluded in this part. RbCl is the reference particle, thus Rb is the reference element. The comparisons were carried out in the conditions of (3.4.1): particle depositions of RbCl and another salt; and (3.4.2): particle deposition of RbCl and braking aerosol.

#### 3.3.1. Mass Ratio Between Elements Involved in RbCl Particles and Pseudo-Unknown Salt Particles

Three couples of salt particles were deposited on the TEM grids:

1. RbCl and CsCl,

2. RbCl and NaCl,

3. RbCl and $Ga(NO_3)_3$

RbCl serves as a reference and the other salt as pseudo-unknown particles. The theoretical elemental mass ratios and the ratios detected by EDS of those couples (Rb:Cs, Rb:Na, and Rb:Ga) were compared. The particle number and volume of the two deposited compounds allow determining the theoretical elemental mass ratios. The experimental elemental mass ratio measured by EDS is the average of values in 21 squares. Then, 1.2/1.3-, 2/1-, and 2/2-type TEM grids were used for collecting 60 or 100 nm particles. Next, a 3–30 min deposition was carried out. The results of theoretical elemental mass ratios and experimental ratios are shown in Table 6.

Table 6 shows that the theoretical elemental mass ratios are close to experimental ratios measured by EDS for all the tested conditions. Absolute deviation is determined as the difference between theoretical mass percentage and experimental mass percentage of element Rb. They are lower than 8%. The aerosol deposition turned out to be a valuable
method to characterize the mass of elements in the aerosol deposited on a TEM grid by adding a certain weight of reference element to the grid.

<table><caption>**Table 6.** Comparison between the theoretical and experimental mass ratio of two kinds of elements. Rb is considered as the reference.</caption><thead><tr><th rowspan="2">Elements and Size</th><th colspan="8">Rb:Cs</th><th colspan="2">Rb:Na</th><th>Rb:Ga</th></tr><tr><th colspan="4">60 nm</th><th colspan="4">100 nm</th><th colspan="2">100 nm</th><th>60 nm</th></tr></thead><tbody><tr><td>Theoretical mass ratio</td><td>68/32</td><td>79/21</td><td>62/38</td><td>65/35</td><td>65/35</td><td>63/37</td><td>62/38</td><td>26/74</td><td>36/64</td><td>31/69</td><td>54/46</td></tr><tr><td>Experimental mass ratio</td><td>75/25</td><td>75/25</td><td>54/46</td><td>58/42</td><td>70/30</td><td>57/43</td><td>69/31</td><td>33/67</td><td>37/63</td><td>33/67</td><td>55/45</td></tr><tr><td>Absolute deviation (%)</td><td>7</td><td>4</td><td>8</td><td>7</td><td>5</td><td>6</td><td>7</td><td>7</td><td>1</td><td>2</td><td>1</td></tr></tbody></table>

### 3.3.2. Mass Ratio Between Elements Involved in RbCl Particles and Braking Particles

The mass of element Rb deposited on the grid is calculated as:

$$ 
\begin{aligned}
m_{\text{Rb}} &= N_{\text{RbCl}} \times \left( \rho_{\text{RbCl}} \times V_{\text{RbCl}} \times \frac{M_{\text{Rb}}}{M_{\text{RbCl}}} \right) \\
&= 8.564 \cdot 10^7 \times \left( 2.8 \times \frac{4}{3}\pi (3 \cdot 10^{-6})^3 \times \frac{85.47}{120.92} \right) = 1.917 \cdot 10^{-8} \text{ g} = 0.01917\mu\text{g}
\end{aligned}
\quad (5) $$

Figure 13 is the size distribution of braking particles characterized by SMPS and APS, which shows a mode of around 1 µm. SMPS measures particles smaller than 523 nm and APS measures particle size between 523 nm and 20 µm. The measured pore size and porosity of the used TEM grid are 1.2592 µm and 0.1896, respectively. According to the compositions of braking aerosols, Fe and its oxides (Fe₂O₃, Fe₃O₄) are expected [37]. The density of the braking particles is in the range of those of the compounds and the simple substances: (5.17–7.874 g/cm³) with a mean of 6.5 g/cm³. According to flowrate, particle density, pore size, and porosity, the theoretical sampling efficiencies of TEM grid for each size are calculated by the theoretical models [28]. According to the size distribution of generated aerosol and the sampling efficiency, the size distribution of particles deposited on the TEM grid is estimated. The mass of braking particles deposited on the TEM grid is estimated to be 3.83 µg by combining the size distribution of particles deposited on the TEM grid and density. Grigoratos and Martini's data on chemical elements from brake particle emissions give a %Fe range between 12% and 48% with an average of 30% [38].

<figure><img src="image_15.png" /><figcaption>**Figure 13.** Size distribution of generated braking aerosol assessed with SMPS and APS.</figcaption></figure>

The estimated mass of Fe from braking particles and deposited on the grid is 1.1508 µg when using this average percentage, i.e., 30% w/w.
The theoretical mass percentage of element Fe is estimated as 98%. The absolute deviation between the estimated ratio and the experimental ratio is 6%.

According to the EDS elemental mass ratio and the mass of Rb (see Table 5), the mass of element Fe deposited on the TEM grid is:

$$m_{\text{Fe}} = m_{\text{Rb}} \times (92/8) = 0.2205 \, \mu\text{g} \qquad (6)$$

The mass concentration of Fe in the released braking aerosol can be calculated by combining the aerosol sampling efficiency, flowrate, and time. The sampling efficiency of the used TEM grid is equal to 98.14%. Knowing that the sampling flow and the sampling time are evaluated, respectively, at 0.3 L/min and 7 min, the mass concentration is estimated as:

$$m'_{\text{Fe}} = \frac{m_{\text{Fe}}/0.9814}{0.3 \times 7} = 1.07 \times 10^{-7} \, \text{g/L} = 0.107\mu\text{g/L} \qquad (7)$$

# 4. Uncertainties and Expectations

As discussed above, the elemental mass ratio detected by STEM-EDS between two kinds of individual particles deposited on one TEM grid is consistent with the theoretical value, which has proved the validity of the current method for quantifying the elements in a particulate aerosol. The uncertainty sources involved in the method are analyzed and some requirements for the method application are advised.

## 4.1. Uncertainty Sources

The method for elemental mass characterization is adding quantitative reference particles to the TEM grid loaded with unknown aerosol and comparing them with reference particles using EDS. The sources of uncertainties are size, shape, density, number of deposited reference particles, EDS quantification, and aerosol distribution.

### 4.1.1. Size and Shape of Reference Particles

DMA is used to select particles by their electrical mobility. Besides the mobility, the diameter of particles exiting from the DMA also depends on the particle's charge number. Singly charged particles with the chosen mobility diameter and bigger particles with multiple charges were generated. For small particles (<100 nm), the singly charged particles were much more than the multiply charged particles [39], so most of the generated particles were monodisperse.

Particle shape brings uncertainty to the theoretical mass calculation. DMA selects size using electrical mobility diameter, which assumes a spherical shape. For non-spherical particles, mobility diameter is a function of particle shape and orientation. It is the cross-sectional area perpendicular to particle motion, which determines the drag on the particle and electrical mobility. Additionally, due to the impact of DMA's electric field, if non-spherical particles align such that their minimum cross-section is perpendicular to the motion direction, their mobility diameter will be less than their volume equivalent diameter.

### 4.1.2. Density and Purity of Reference Particles

Impurities are counted as reference particles when using impure salt, and cause other peaks during EDS spectra analysis. Salt particles such as $Ga(NO_3)_3$ particles tend to be hydrated in their natural state, which also brings uncertainties since the number of crystal water and the density of deposited particles are uncertain. The density of $Ga(NO_3)_3$ used in the calculations is 6.44 g/cm³, which is the density of $Ga(NO_3)_3 \cdot H_2O$.
### 4.1.3. Number of Reference Particles

The number of particles generated from the atomizer brings uncertainties to the theoretical particle mass. Moreover, the upstream and downstream sampling is manually controlled by two valves, which may bring errors to the deposition time. CPC counting efficiency also brings uncertainty. For a sample of 10,000 particles, the statistical precision is 99%. The uncertainty from CPC counting noise can be modeled as a multivariate Gaussian distribution identified from experiments when counting number concentration bigger than 1000/cm³ [40]. At 100 particles, the statistical uncertainty increases to 10% and significantly influences aerosol concentration. The totalizer allows increased count accuracy at low particle concentrations by use of a longer sample time.

### 4.1.4. Particle Distribution

Reference particles overloading on the TEM grid will interfere with TEM analyses. Alternatively, if the loading is too sparse, an accurate assessment of the particle characteristics may not be possible. The distribution of pollutant aerosol is also a source of uncertainty in the applications.

### 4.1.5. Uncertainty of EDS Quantitative Analysis

The quantitative analysis depends on the method and correction. The thickness of the sample biases the EDS result due to uncertainty in the ZAF correction. A low counting statistic is another primary source of error in most analytical electron microscopy quantifications.

### 4.1.6. Braking Particle Sampling

The mass concentration of Fe in the braking aerosol is derived from the mass of Fe on the TEM grid, sampling efficiency, flowrate, and sampling time. Normally, the sampling is controlled by a pump after the TEM grid, the flowrate of flow that goes through the TEM grid may be a little smaller than the specified flowrate, which brings uncertainty. The sampling efficiency is assumed to correspond to the mode of the braking particle size, which also brings uncertainty. The manual sampling time control is also a source of uncertainty.

## 4.2. Requirements and Expectations

Considering the sources of uncertainties, the following requirements will meet a better application of this method, regarding aerosol sampling, types of reference and unknown aerosol, and EDS analysis.

### 4.2.1. Aerosol Sampling

Regarding the TEM grid sampling, 1.2/1.3-type grid and a high flowrate are recommended for a high sampling efficiency. For reference particle sampling, nano-scale particles in the 60–100 nm sizes show higher efficiency and higher deposition number for MPS sampling [28]. Considering the CPC counting efficiency, a 0.8 bar applied pressure of the atomizer, a salt concentration of at least 10 mmol/L, and a sampling time of at least 2 min are advised for depositing enough reference particles. Depositing the reference particles at once is another requirement to avoid more uncertainties. For unknown particle sampling, the sampling efficiency is important for the estimation of elemental mass concentration in the unknown aerosol, which is assumed to be the efficiency at the mode size. Here, the size distribution is derived from data from SMPS/APS. For further use, the mode size could be easily found according to the TEM images. The sampling efficiency for particles bigger than the pore size of the TEM grid (1.2 µm for 1.2/1.3-type TEM grid) is 100%. For particles with sizes smaller than the pore size, the programming for estimating the sampling efficiency
has been added to the appendix. Using MATLAB 9.10, or other programs, the results could
be simply processed.

4.2.2. Reference Aerosol and Unknown Aerosol

60 nm RbCl spherical particles are good references, as they remain non-hydrated and non-hygroscopic. It is a non-ubiquitous compound and shows low toxicity. A few spectra peaks are exhibited in EDS analysis. While the shape of RbCl tends to be spherical when small (≤60 nm) and cubical when big (≥100 nm), hence strictly spherical particles with high purity are recommended as an improvement. For quantifying non-spherical objects, like fiber, the size is difficult to predict which prevents the quantitation. For ensuring a quantitative analysis, the non-spherical object is defined as at most 20% of the population in a mixed aerosol, as a criterion. If those particles reach this limitation, a semi-quantitative approach instead of a quantitative one is used here.

4.2.3. EDS Quantitative Analysis

The best way to minimize mistakes in EDS characterization is to use thin specimens, higher-brightness sources, large electron probes, and $C_s$-correction of the probe [33]. A long acquisition time or high counting statistic of the X-ray map also promotes mass percentage quantification [33]. A short waiting time between deposition and analysis is also advised.

Some chemical elements are excluded from this analytical method like C, Cu, present in the carbon film-coated copper grid, or Si due to the use of Silicon-based detectors. Light elements cannot be quantified as well due to the limitation of EDS analysis. The targeted chemical element(s) or the reference element should be enough to make it possible to compare the mass. Since the biggest absolute deviation of 8% between the theoretical elemental mass ratio and the experimental ratio measured by EDS is found, the mass percentage of the reference element or element to be determined in the range of 16–84% (2 times the deviation is reserved) is treated a valid characterization.

**5. Conclusions**

A method to quantitatively determine the mass of elements in particulate aerosol was developed by depositing the unknown aerosol and quantitative reference particles on a TEM grid. An MPS and an SMPS were used for the particle sampling and quantitative deposition. EDS mapping allows quantifying the mass of elements in the unknown aerosol by comparing it with that of the reference element. Diverse pairs of airborne particles (RbCl, CsCl, NaCl, SrCl₂, Ga(NO₃)₃, braking particles) were deposited. The use of an own defined standard has been preferred to compensate for sensitivity variations due to matrix and signal drift.

Results show that 60 nm RbCl spherical particle is a good reference for its rarity in usual airborne particles and its low toxicity. They remain non-hydrated, non-hygroscopic, and few spectra peaks are exhibited in EDS analysis. The reference particle deposition, even a long-term deposition, is easy to be achieved and the measured values such as deposited particle number are easy to be reproduced. TEM images show that the sizes of deposited particles are similar to those selected by DMA, with a narrow distribution. X-ray analysis for 21 squares on the grid shows that the mass percentages of reference and test elements are similar in each square. For all the tested conditions, the absolute deviations between the theoretical elemental mass ratios and the experimental ratios measured by EDS are less than 8%. Using this method, the mass concentration of Fe in the released braking aerosol is calculated as 107 µg/m³.

Despite the limitations, such as the limit to quantitative analysis for light elements C and O, the consistency between the theoretical elemental mass ratio and the experimental
value measured by EDS verifies that the proposed method turns out to be the proper manner for determining the mass (concentration) of elements in the unknown aerosol. Using this new method, only an easy aerosol sampling is needed at the workplace for mass characterization. The approach ensures safety, adaptability, and practicability for mass characterization in exposure assessment of particle emissions.

**Author Contributions:** Methodology, M.M. and F.P.; Software, C.B.; Validation, M.M.; Formal analysis, M.X.; Investigation, M.M.; Data curation, O.A.-C. and C.L.; Writing—review and editing, M.M.; Visualization, L.M.; Funding acquisition, C.B. and M.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** We acknowledge the financial support of the CSC (China Scholarship Council) for the scholarship and allow us to perform this work in good conditions. The French Ministry for Ecology and ADEME agency funding AQACIA project D-brake (no. 2166D0017) is also gratefully acknowledged.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data is contained within the article.

**Acknowledgments:** The authors gratefully acknowledge our respective institutions for making this transdisciplinary project possible. In addition, the authors also thank ASFERA (French Association for Studies and Research on Aerosols for awarding this work with the Jean Bricard Prize.

**Conflicts of Interest:** The authors declare no conflicts of interest.

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