# Optimization of Time-Weighted Average Air Sampling by Solid-Phase Microextraction Fibers Using Finite Element Analysis Software

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{−3}; n—amount of an analyte extracted by a coating, mol; Z—diffusion path length (distance between the needle opening to the tip of the retracted fiber), m; A—internal cross-section area of a protecting needle, m

^{2}; D—gas-phase molecular diffusion coefficient for a VOC, m

^{2}·s

^{−1}; t—sampling time, s.

## 2. Results and Discussion

#### 2.1. Time-Weighted Average (TWA) Sampling Profiles of Benzene from Air Using Different Coatings

#### 2.2. Effect of the Diffusion Coefficient and Distribution Constant on Sampling of Analytes by 85-µm Carboxen/Polidimethylsiloxane Coating

#### 2.3. Effect of a Protecting Needle Gauge Size

#### 2.4. Effect of Diffusion Path (Z) at Constant Analyte Concentration in Sampled Air

^{−3}(0.641 μmol·m

^{−3}) and t = 100,000 s, 23 ga Car/PDMS assembly extracts ~100 pg of benzene. For GC-mass spectrometry (MS), the detection limit of benzene is less than 2 pg [28] meaning that the detection limit will be ~1 µg·m

^{−3}, which is five times lower than the maximum permissible annual average concentration of benzene in ambient air in the European Union (5 µg·m

^{−3}). In other countries, permissible concentrations are even higher.

#### 2.5. Effect of Diffusion Path (Z) at Variable Analyte Concentration in Sampled Air (Worst-Case Scenario)

^{−3}in the middle of the extraction process (Figure 7). Desorption of toluene was not observed because it has the highest distribution constant among all studied analytes. However, the toluene sampling rate after the drop of its concentration in sampled air was lower than theoretical. Recoveries of analytes at Z = 10 mm dropped from 65–82 to 52–70%, at Z = 20 mm from 78–90 to 67–79%, at Z = 30 mm from 85–93 to 73–82, at Z = 40 mm from 86–93 to 75–82% (Figure 7). Only at Z = 40 mm, it was possible to keep recovery of all analytes above 75%. Thus, if possible, for greater accuracy, sampling must be arranged so that no significant drop in concentration takes place. Such a drop can be observed, e.g., if the end of sampling is planned for the night when VOCs concentrations in ambient air are typically lower due to much lower road traffic and other human activities. Also, using shorter sampling times can minimize the risk of the reverse diffusion when ambient concentrations are predicted to drop significantly.

#### 2.6. Alternative Geometries for TWA SPME Sampling

^{®}passive air sampler [29], which provide a greater surface area of an adsorbent available for the diffusive air sampling.

## 3. Materials and Methods

#### 3.1. General Parameters of Modeling

^{−6}and 10

^{−10}m

^{2}·s

^{−1}, respectively [30]. Distribution constant (K

_{d}) for benzene and common SPME coatings was set to 150,000 (85 µm Car/PDMS) [31], 8300 (65 µm PDMS/DVB) [31], and 301 (PDMS) [5]. For dichloromethane, acetone and toluene, distribution constants between 85 µm Car/PDMS coating and air were set to 72,000, 71,000 and 288,000, respectively [31].

^{®}(Supelco, Bellefonte, PA, USA) fibers with a core diameter of 130 µm. For 85 µm Car/PDMS and 65 µm PDMS/DVB, total fiber diameters were set to 290 and 270 µm, respectively. Calculations were conducted for 24- and 23 ga coatings having internal diameter of 310 and 340 µm, respectively.

^{−3}, which corresponds to 50 µg·m

^{−3}of benzene.

#### 3.2. Sampling Using Absorptive Coatings

_{1}and Flux

_{2}, respectively) at the boundaries (marked by red lines in Figure 11) were simulated using the equation, previously proposed by Mackay and Leinonen [32] for the water−air interface:

^{−1}; C

_{a}and C

_{f}—concentrations of an analyte in air and coating at the boundary layer, respectively, mol·m

^{−3}; K

_{d}—distribution constant for a VOC between SPME coating and air.

^{−1}. A further increase of the flux coefficient did not affect the results of the modeling.

#### 3.3. Sampling Using Adsorptive Coatings

^{2}·s

^{−1}for benzene, toluene, acetone, and dichloromethane, respectively). The approach proposed by Mocho and Desauziers [33] involving Knudsen diffusion in micro-pores was also tested. However, it was later rejected for model simplification because the diffusion of analytes inside coating is mainly driven by molecular diffusion inside macro-pores. The presence of PDMS binder was not considered in the model because: (1) it has much weaker affinity to analytes than Carboxen; and (2) the layer of PDMS in the coating is very thin and should not affect the diffusion of analytes [5]; (3) there is not enough published information about the exact structure of the coating.

_{p}, m

^{3}·kg

^{−1}) calculated as a dimensionless distribution constant divided by a coating density (K

_{d}/ρ). Coating porosities (ε = 0.685 for Car/PDMS and 0.775 for PDMS/DVB) were calculated using intra-particle porosities (0.37 for Car, and 0.55 for DVB [34]) and inter-particle porosity. The exact value of the latter is proprietary and not available in the open literature. Taking into account, the spherical shape of particles and available scanning electron microscope (SEM) photos, the inter-particle porosity of both coatings was set to the maximum possible value (0.50). A particle porosity (ε) was calculated as the total volume of pores (0.78 mL for Car, and 1.54 mL for DVB) divided by the total volume of one gram of material (2.13 mL for Car, and 2.78 mL for DVB). Densities of the coatings were calculated using free fall densities of the particles (470 kg·m

^{−3}for Car, and 360 kg·m

^{−3}for DVB) [34] and inter-particle porosity. Effective diffusion coefficients were calculated during the calculations by the COMSOL software using the Tortuosity model [33]:

## 4. Conclusions

^{−3}.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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Sample Availability: Samples of the compounds are not available from the authors. |

**Figure 1.**The typical procedure of time-weighted average sampling and analysis using retracted solid-phase microextraction fiber.

**Figure 2.**Benzene sampling profiles from ambient air (T = 298 K, Z = 10 mm, 24 ga needle, p = 1 atm, C

_{benzene}= 0.641 μmol·m

^{−3}) obtained using different fiber coatings. The ideal case pertains to Equation (1).

**Figure 3.**Concentrations of benzene in diffusion path air (

**a**) and coating (

**b**) of the retracted solid-phase microextraction (SPME) device after 100,000 s of time-weighted average (TWA) air sampling at Z = 10 mm.

**Figure 4.**Effect of sampling time of TWA recoveries of analytes having different diffusion coefficients and distribution constants using 85-µm Car/PDMS fiber (T = 298 K, Z = 10 mm, 24 ga needle, p = 1 atm, C = 0.641 μmol·m

^{−3}).

**Figure 5.**Effect of protecting needle gauge size concentration profile of benzene in the Car/PDMS coating after 100,000 s sampling.

**Figure 6.**Effect of diffusion path length on recoveries of four analytes (C = 0.641 µmol·m

^{−3}) after sampling for 100,000 s using 23 ga Car/PDMS fiber assembly.

**Figure 7.**Sampling (Z = 10 mm) profiles (

**a**) of four analytes from air having their varying concentrations (C

_{0–49,000 s}= 1.176 μmol·m

^{−3}, C

_{49,000–51,000 s}= 1.176–0.1176 μmol·m

^{−3}, C

_{51,000–100,000 s}= 0.1176 μmol·m

^{−3}) and recoveries of analytes (

**b**) at t = 100,000 s and different Z.

**Figure 8.**Alternative geometries for TWA SPME sampling: (

**a**) used by Tursumbayeva [18], and (

**b**) proposed in this research to minimize sources of deviation from Fick’s law of diffusion calibration.

**Figure 9.**Effect of TWA SPME sampling geometry on recoveries (t = 100,000 s, C

_{0–49,000 s}= 1.176 μmol·m

^{−3}, C

_{49,000–51,000 s}= 1.176–0.1176 μmol·m

^{−3}, C

_{49,000–100,000 s}= 0.1176 μmol·m

^{−3}).

**Figure 10.**Profiles of analyte concentration in the Car/PDMS coating after sampling ambient air (C

_{0–49,000 s}= 1.176 μmol·m

^{−3}, C

_{49,000–51,000 s}= 1.176–0.1176 μmol·m

^{−3}, C

_{49,000–100,000 s}= 0.1176 μmol·m

^{−3}) for 100,000 s using the geometry presented in Figure 8a.

**Figure 11.**The geometry of SPME device (retracted inside a protective needle for TWA sampling) used for modeling. Note: red lines indicate the boundaries between air and coating.

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**MDPI and ACS Style**

Kenessov, B.; Koziel, J.A.; Baimatova, N.; Demyanenko, O.P.; Derbissalin, M.
Optimization of Time-Weighted Average Air Sampling by Solid-Phase Microextraction Fibers Using Finite Element Analysis Software. *Molecules* **2018**, *23*, 2736.
https://doi.org/10.3390/molecules23112736

**AMA Style**

Kenessov B, Koziel JA, Baimatova N, Demyanenko OP, Derbissalin M.
Optimization of Time-Weighted Average Air Sampling by Solid-Phase Microextraction Fibers Using Finite Element Analysis Software. *Molecules*. 2018; 23(11):2736.
https://doi.org/10.3390/molecules23112736

**Chicago/Turabian Style**

Kenessov, Bulat, Jacek A. Koziel, Nassiba Baimatova, Olga P. Demyanenko, and Miras Derbissalin.
2018. "Optimization of Time-Weighted Average Air Sampling by Solid-Phase Microextraction Fibers Using Finite Element Analysis Software" *Molecules* 23, no. 11: 2736.
https://doi.org/10.3390/molecules23112736