## 4 Conclusions  
A finite element analysis-based model (based on COMSOL Multiphysics software) allowed efficient simulation of TWA air sampling of VOCs using retracted SPME fibers. It was possible to model the effects of sampling time, coating type (including adsorptive coatings for the first time) and composition, diffusion coefficient, the distribution constant, the internal diameter of a protecting needle and diffusion path on the recovery of analytes, their concentration profiles in the air inside protecting needle, and the coating. The advantages of such a simulation compared to an experiment are: (1) time and cost savings; (2) lower uncertainty and the possibility to discover minor impacts of sampling parameters on its performance; and (3) the possibility to understand and optimize a sampling process in greater detail. The results of this research allowed disclosing potential sources of the apparent departure from [PERSON]'s law of a diffusion-based model used for quantification of VOCs with retracted SPME. It was established that sampling by porous coatings with high affinity to the analyte (Car/PDMS) is affected by the saturation of the fiber tip and slow diffusion of analytes in the coating. Highest recoveries are achieved for analytes having lowest diffusion coefficients and highest affinities to a coating. The increase of an internal diameter of a protecting needle from 24 to 23 ga allows proportionally greater responses to be obtained at similar recoveries. The most important parameter of a sampling process that users can control is a retraction depth. The increase of \(Z\) allows slowing down the sampling and achieving higher recoveries of analytes. In this study, at \(Z\) = 40 mm and constant analyte concentration in a sampled air, recoveries of studied analytes reached 86-93% compared to 65-82% at \(Z\) = 10 mm. The developed model allowed simulation of the worst sampling case when analyte concentrations significantly drop in the middle of sampling. For the first time, it has been proven that at such sampling conditions and \(Z\) = 40 mm, recoveries of analytes can drop by \(\sim\)10%, while at \(Z\) = 10 mm by \(\sim\)15%. According to the results of the simulation, it is optimal to conduct sampling of studied VOCs using a 23 ga Car/PDMS assembly at \(Z=40\) mm. Expected detection limits at these parameters are about \(1\)\(\upmu\)g\(\cdot\)m\({}^{-3}\). Alternative geometries of a protective TWA SPME sampling devices could be used to increase recoveries of analytes. Sampling using 0.75-mm I.D. SPME GC liner at \(Z=67\) mm provides similar recoveries compared to sampling using a protecting needle at \(Z=40\) mm, but it provides greater amounts of analytes extracted and lower detection limits. To achieve greater recovery, part of the liner should have narrower I.D. (e.g., 0.34 mm). The increase of the diameter of the extraction zone where the coating is located results in a more uniform distribution of analytes, which should lead to faster desorption, less pronounced peak tailing and greater accuracy. Specific sampler parameters should be selected for particular sampling time and environmental conditions (temperature and atmospheric pressure) using the developed model. The methodology used in this study could also be used for more accurate and simpler calibration of the method. It can be used to model the sampling of other environments (process gases, water) by retracted SPME fibers. Further modification of this model could allow simulation of soil and soil gas sampling. The following are available online at [[http://www.mdpi.com/1420-3049/23/11/2736/s1](http://www.mdpi.com/1420-3049/23/11/2736/s1)]([http://www.mdpi.com/1420-3049/23/11/2736/s1](http://www.mdpi.com/1420-3049/23/11/2736/s1)), Video S1: COMSOL_TWA_SPME.