## 2 Sample Extraction
### Headspace-Solid Phase Microextraction  
The first SPME application was presented in 1990 [72]. It is considered one of the most versatile sample preparation techniques currently available [73]. Its simplicity of optimization, high reproducibility, and low cost have made it widely accepted. Similar to liquid-liquid extraction, absorption extraction is also based on the distribution coefficient. The only difference is that the absorbent fibers are in a rubbery state at room temperature and therefore are solid. The final equilibrium sampling state can be expressed as:  
\[C_{0}\times V_{s}=C_{s}\times V_{s}+C_{G}\times V_{G}+C_{F}\times V_{F} \tag{3}\]  
The total amount of analytes in the sample is the original concentration (\(C_{0}\)) multiplied by the volume (\(V_{S}\)). After equilibrium is reached, it is the sum of the analyte amounts in each phase: \(C_{S}\times V_{S}\) for the sample phase, \(C_{G}\times V_{G}\) for the gas phase, and \(C_{F}\times V_{F}\) for the absorbent phase. \(C_{F}\times V_{F}\) represents the absorbed amount of an analyte in the fiber coating \(W_{F}\):  
\[C_{G}=\frac{W_{F}}{V_{F}\times K_{F/G}} \tag{4}\]  
\[C_{S}=\frac{W_{F}}{V_{F}\times K_{F/G}\times K_{G/S}} \tag{5}\]  
\(K_{G/S}\) and \(K_{F/G}\) are the distribution constants between the gas phase and the sample phase and between the fiber phase and the gas phase. Substituting the \(C_{G}\) and \(C_{S}\) in Equation (3), the absorbed amount in the fiber coating \(W_{F}\) is:  
\[W_{F}=\frac{C_{0}\times V_{S}\times V_{F}\times K_{F/G}\times K_{G/S}}{V_{F} \times K_{F/G}\times K_{G/S}+V_{G}\times K_{G/S}+V_{S}} \tag{6}\]  
HS-SPME is a highly automated technique. It allows direct sampling and does not require organic solvents [74]. HS-SPME-GC-MS has successfully measured a number of volatiles in beer, such as organic acids, carbonyl compounds, esters, alcohols, fatty acids, and monophechols. A detailed description of the coating materials used for SPME fiber is available in a review paper [75]. A method using multi-coated fiber (Divinylbenzene/Carboxen/Polydimethylsiloxane, DVB-CAR-PDMS) was applied to beer VOC analysis by [PERSON] [76]. In a recent study [41], 329 volatiles were determined from 19 types of lager beers by using DVB-CAR-PDMS fiber for extraction and bidimensional GC-MS for analysis. According to its principles, SPME extraction has some inherent disadvantages. Multiphase equilibria to be achieved in SPME systems are influenced by matrix effects [77]. In practice, SPME requires a certain amount of sampling time. The sample, headspace, and fiber phases are brought to an approximate equilibrium to minimize extraction bias. [78]. This requires sufficient sampling time. To overcome the long extraction time, many research groups have made improvements. The mass transfer efficiency of multiphase systems is significantly improved at high temperatures [79]. Cooling the fibers allows them to maintain good absorption in a thermal sample environment [80]. To improve the extraction efficiency and capacity of the SPME device, new geometries of the sorbent phase were used, like SPME Arrow and thin-film SPME (TF-SPME). By applying a larger extraction phase volume and molecular exchange surface area, higher analytical sensitivity and faster extraction speeds were achieved [73; 79]. Physical assistive technologies, like vacuum and ultrasound, have also been applied to SPME sampling. With the proper setup, the extraction processing can be faster, milder on temperature, more selective, and more sensitive [81; 82; 83; 84]. The basic principle and the method development strategy are well explained in a recent review [85]. It is worth noting that, in a complex system such as a fermented beverage, which contains hundreds or thousands of components, VOCs might compete for binding to the sorbent, affecting absorption. In this context, the role of ethanol is crucial since it is the most abundant volatile compound in fermented beverages and has been reported as an important interfering molecule during the HS-SPME extraction of minor compounds.