## 3 Results and Discussion
### Evaluation of the HS-BA\(\mu\)E/GC-MS Methodology  
#### 3.2.1 Optimization Assays  
After optimizing the instrumental system, experimental conditions for the HS-BA\(\mu\)E/GC-MS methodology were established (Figure 1). The assays were conducted via HS in 5 mL vials containing a standard mix of six target BVOCs: \(\alpha\)-pinene, \(\beta\)-pinene, limonene, 1,8-cineole, thymol, and caryophyllene oxide. As the HS-BA\(\mu\)E technology operates in two stages, i.e., microextraction in the gaseous phase followed by back-extraction in the liquid phase, an OVAT strategy was adopted to optimize parameters such as sorbent coating phase, equilibrium time and temperature, as well as solvent type and desorption time. One significant advantage of this methodology compared to others considered as reference methods (e.g., SPME) is the ease of selecting the best coating phase from a variety of available materials tailored to the target compounds involved [7]. For this study, four polymers (S-CN, S-DVB, HLB, and S-X) and four ACs (R, SX PLUS, CA1, and CN1) were tested. Figure 3a illustrates the comparison of efficiency achieved for all sorbent phases tested under standard experimental conditions, indicating that the ACs generally exhibit greater selectivity than the tested polymers, resulting in higher recoveries. Additionally, it can be observed from the same figure that while thymol is poorly recovered, caryophyllene oxide consistently shows a very good response. Based on the data obtained from the sorbent phase assays, three AC phases (R, CA1, and CN1) appear to offer the best selectivity for the six target BVOCs. These sorbents are nanoporous solids capable of efficiently retaining analytes in the gaseous phase through dispersive and/or electrostatic interactions. The R phase, characterized by ultramicropores (\(\leq\)0.7 nm) and supermicropores (0.7-2.0 nm), demonstrates the ability to retain molecules of various sizes. However, the CA1 and CN1 phases, containing only supermicropores, exhibit a preference for smaller-sized molecules such as the six target BVOCs under study. Furthermore, the results indicate that the chemical surface characteristics of the ACs play a crucial role. The R phase, with a neutral surface (pH\({}_{\text{PZC}}\) 6.50) and smaller pore size, appears to be ideal for retaining \(\alpha\)- and \(\beta\)-pinene. Conversely, CA1 and CN1 phases, with acidic surfaces (pH\({}_{\text{PZC}}\) 2.20 and 5.10, respectively) and larger pore sizes, exhibit enhanced retention of limonene and 1,8-cineole. On the other hand, the polymers studied can also retain the six target BVOCs, primarily through \(\pi\)-\(\pi\), dipole-dipole, hydrogen bonds, and ionic interactions, depending on particle size and surface area. Nevertheless, based on the results depicted in Figure 3a, since the CN1 phase exhibited the most acceptable RSDs and greater recovery efficiencies, it was selected to optimize the following parameters. Figure 2: Chemical structures of the target BVOCs studied in the present work, including five monoterpneoids (\(\alpha\)-pinene, \(\beta\)-pinene, limonene, 1,8-cineole, and thymol) and one sesquiterpenoid (caryophyllene oxide). The study subsequently evaluated the key parameters for microextraction in the gaseous phase, focusing on equilibrium time and temperature. Initially, five equilibrium times (1, 2, 3, 6, and 16 h) were tested to assess the retention of the six BVOCs, as depicted in Figure 3b. Analysis of the data revealed that the recovery performance increased up to 3 h, after which a significant decrease in recovery was observed. Extending the equilibrium time to 6 and 16 h resulted in a considerable decrease in recovery efficiencies due to the occurrence of the _wall-effect_ phenomenon. This phenomenon involves the adsorption of target compounds onto the inner walls of the glass vials over extended periods of time [7]. Furthermore, evaluation of thermostat effects (25, 35, and 55 \({}^{\circ}\)C) demonstrated that a temperature of 35 \({}^{\circ}\)C gave higher recovery yields for the target BVOCs.