## 2 Results and Discussion  
### Time-Weighted Average (TWA) Sampling Profiles of Benzene from Air Using Different Coatings  
A sampling of VOCs from the air via retracted SPME has been described using a simplified form of the Fick's first law of diffusion (Equation (1)). However, this equation works only when a SPME fiber acts as a \"zero sink\" sorbent. Modeling using COMSOL Multiphysics software (methodology is provided in the Materials and Methods section) allowed obtaining sampling profiles for benzene (Figure 2). Closer inspection of Figure 2 illustrates that none of the studied coatings behave as \"zero sink\" sorbent adhering to Equation (1), an effect amplified by extended sampling time. After 100,000 s of sampling, Carboxen/polydimethylsiloxane (Car/PDMS), polydimethylsiloxane/divinylbenzene (PDMS/DVB), and polydimethylsiloxane (PDMS) extracted 77, 38 and 2.7%, respectively, of the theoretically required for a passive sampling technique. Even if sampling time is decreased to 10,000 s, recoveries for these three SPME fiber coatings were 91, 69 and 12.6%, respectively. At sampling time 1000 s, recoveries were 97, 88 and 32% for Car/PDMS, PDMS/DVB and PDMS, respectively. One possible explanation for the departure from Equation (1) is that it can be caused by the increase of the analyte concentration in the air near the fiber tip (Figure 3a), which is directly proportional to the analyte concentration in the fiber tip continuously increasing during the sampling. The increase of analyte concentration in the air near the fiber tip results in the decrease of the analyte flux (i.e., the number of moles of analyte entering protecting needle per cross-sectional area and time) from the sampled air with time. This affects the sampling rate (i.e., number of moles of an analyte extracted by a coating per unit of time), which was previously assumed to be constant [3; 4; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. SPME fiber coating can affect the apparent rate of sampling. This was previously assumed to be negligible. According to Figure 3, Car/PDMS is the most efficient coating for TWA sampling of benzene because it provides the highest benzene extraction effectiveness indicated by the highest distribution constant. However, sampling by this coating is limited by the slow diffusion of an analyte via pores of the adsorbent (Figure 3b). At sampling time 100,000 s, the closest 1 mm of the Car/PDMS coating to the needle opening contains 41% of the total extracted analyte. Benzene concentration in the fiber tip is about 500 times higher than in its other end (furthest from the needle opening). For PDMS/DVB coating, the concentration in the tip is only about 24% higher. Slower diffusion of benzene via pores of Car/PDMS fiber is caused by the higher affinity of benzene to the surface of the solid phase (higher distribution constant), and lower porosity. Such non-uniform distribution of analytes in the Car/PDMS may be the reason of their slow desorption after TWA sampling and highly tailing peaks, particularly for most volatile analytes, which cannot be cold-trapped and refocused in a column front without cryogens. This problem also decreases the accuracy of the method. The accuracy of the model was validated by increasing the pore diffusion coefficient of benzene inside Car/PDMS coating by three orders of magnitude. In this case, the benzene sampling profile was the same as predicted by Equation (1). This also confirms that an analyte diffusion coefficient inside a coating affects sampling profile and the accuracy of its quantification using TWA SPME. The model has also been validated in the 3D mode of COMSOL software, which is much slower compared to 2D (Video S1: COMSOL_TWA_SPME). The difference between the results of 2D and 3D modeling were below 2%, which confirms the accuracy of the 2D model. Figure 2: Benzene sampling profiles from ambient air (\(T=298\) K, \(Z=10\) mm, 24 ga needle, \(p=1\) atm, \(C_{benzene}=0.641\)\(\upmu\)mol\(\cdot\)m\({}^{-3}\)) obtained using different fiber coatings.