## 3 SPME Process
### Quantitation
#### 3.5.4 Diffusion-based Calibration  
The diffusion coefficient is essential for description of kinetic processes of SPME [22]. Recently various diffusion-based calibration methods have been developed [22]. They were developed based on [PERSON]'s first law of diffusion, the interface model, the cross-flow model and the kinetic process of absorption/adsorption and desorption [22]. Main applications are in on-site sampling, comprising grab sampling and long-term monitoring [22].  
[PERSON]'s first law is applicable to calibration when diffusion paths are well-defined [22]. The main applications are air and water sampling. Fiber-retracted SPME devices are used in which the analyte molecules access the fiber coating only by means of diffusion through the static air/water gap between the needle opening and the fiber coating. In air, the diffusion of the molecules is fast and the length of the diffusion path can be adjusted [191]. These kinds of samplers were applied for time-weighted average (TWA) sampling of several analytes in air [56, 184]. For water sampling, a commercially SPME fiber assembly was developed and used for monitoring polycyclic aromatic hydrocarbons (PAHs) in water [185].  
In the case of a poorly defined or unknown diffusion path for on-site sampling (when the SPME fiber is inserted directly into the air or water sample, the interface model and cross-flow model can be used for calibration. However, these models are limited to the linear sampling regime and a constant convection of air/water [22]. Applying these calibration methods requires a controlled velocity of air/water [22]. The Interface model was developed by [PERSON] _et al_. [186] and applied for sampling of volatile organic compounds (VOC) in air. The cross-flow model was developed by [PERSON] _et al_. [187].  
_Kinetic calibration_ is based on a diffusion-controlled mass transfer model proposed by [PERSON] [43, 44]. The underlying assumption of this dynamic model is that there is a linearly proportional relationship between the adsorbed analyte and its initial concentration in the sample matrix. Based on this model two calibration methods of SPME, the kinetic calibration with standard or in-fiber standardization technique [192] and the standard-free kinetic calibration [190] were proposed. The applicability of this technique for TWA water sampling was established by both theoretical derivations and field trials [188, 189]. Furthermore this method has become more convenient and applicable through the single point calibration [193]. Kinetic calibration with standards in the extraction phase can be applied to grab sampling as well as long-term monitoring [22]. Due to the loss of the standard during sampling this calibration method may not work in some fast sampling situations. For fast on-site and _in vivo_ analysis, a standard-free kinetic calibration method was developed [190]. With this calibration method, all analyses can be directly calibrated with only two samplings and can be quantified without bearing in mind of reaching equilibrium in the system. The method was validated for identification of PAHs and BTEX in a standard aqueous solution and a standard gas flow-through system [190]. Compared with the previous calibration methods for rapid on-site analysis by SPME this method does not require a standard to calibrate the extraction. The total amount of the extracted analytes can be quantified without bearing in mind of reaching equilibrium in the system [190].