## 1 Introduction  
Analysis of time-weighted average (TWA) concentrations of volatile organic compounds (VOCs) in outdoor and indoor (occupational) air is an important part of environmental monitoring programs aiming at chronic exposure or background concentrations. Such analysis is commonly conducted using gas chromatography (GC) in combination with various sampling and sample preparation approaches. Passive sampling is a common approach for determination of TWA concentrations because of its simplicity and low cost. However, most techniques require additional sample preparation and thermal desorption in a separate unit connected to a GC [1]. Solid-phase microextraction (SPME) is the only TWA sampling technique, that does not require additional stages and/or equipment [2]. It is based on sampling via the passive VOCs extraction by a fiber coating retracted inside a protecting needle followed by thermal desorption inside a GC injection port [3, 4]. Desorption of VOCs from the SPME coating is fast and does not require cryogenic or another type of focusing as is the case with whole air- or sorbent tube-based samples [5]. In the TWA mode, the SPME device with retracted fiber is deployed into a sampling location for the desired period (e.g., 24 h for daily average sampling), then isolated from possible interferences during storage and transport to a laboratory and analyzed (Figure 1). The method can be considered \"green\" because it fulfills all the requirements of green analytical chemistry [6, 7]. Calibration is relatively simple compared with a \"classic\" exposed SPME fiber that is subject to variable thickness of the boundary layer that affects the rate of extraction [8, 9]. TWA sampling by retracted SPME fibers is described by the simplified version of the [PERSON]'s law of diffusion [3]:  
\[\overline{C}\ =\ \frac{n\times Z}{A\times D\times t} \tag{1}\]  
where \(\overline{C}\)--TWA concentration of an analyte, mol\(\cdot\)m\({}^{-3}\); \(n\)--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\({}^{2}\cdot\)s\({}^{-1}\); \(t\)--sampling time, s.  
Equation (1) can also be interpreted by an extraction process, i.e., the amount of analyte extracted is proportional to TWA concentration outside of the SPME needle opening, needle opening area, sampling time, and the gas-phase molecular diffusion coefficient, and inversely proportional to retraction depth. Several important assumptions are made with the application of Equation (1) to TWA-SPME, i.e., (1) the fiber coating acts as a \"zero sink\" (without desorption of analytes) and does not affect the rate of sampling; (2) the SPME fiber coating is consistent and reliably responding to changing concentrations in the bulk gas-phase outside of the needle opening; and (3) the gas-phase concentration in the bulk are the same as at the face of the fiber needle opening. To date, all published research on TWA-SPME has used Equation (1) as the basis of quantification [3, 4, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19] of VOCs in an outdoor air, laboratory air, pyrolysis reactor air, engine exhaust, and process air. Equation (1) predicted measured gas concentrations with reasonable accuracy and precision. However, more evidence suggests that the discrepancies between the model and  
Figure 1: The typical procedure of time-weighted average sampling and analysis using retracted solid-phase microextraction fiber. experimental data exist. [PERSON] et al. [17] reported a significant departure from the zero-sink assumption and from Equation (1) suggesting \"apparent\" diffusion coefficient (\(D\)) dependent on both sampling time (\(t\)) and retraction depth (\(Z\)). [PERSON] et al. [11] reported significant differences in the extracted mass of naphthalene gas for different SPME coatings, i.e., that Equation (1) does not incorporate.