## 3 Results
### Comparison of MAE and HRE  
Figure 4a presents the extraction yield profiles of two methods over time, illustrating distinct patterns. Experiments were conducted at atmospheric pressure and under optimal conditions (214.24 W with MAE), with the yield defined as the percentage of polyphenol crude extract from cinnamon leaves mass-extracted relative to the initial mass of cinnamon leaves. The extraction kinetics for both microwave-assisted extraction (MAE) and heat reflux extraction (HRE) reveal four key phases [26,27]. The initial \"zero phase\" is the heating stage, where the temperature increases from room temperature to methanol boiling point.  
Phase 1 shows a rapid yield increase as polyphenol is extracted from the surface of plant cells, accounting for approximately 57% of the total yield with MAE and 51% with HRE. In Phase 2, the yield rises further due to the internal diffusion of antioxidant compounds from within the particles to the surrounding medium, driven by thermal conduction within plant cells; this phase adds about 43% to the MAE total yield and 47% to that of HRE. Phase 3 is when a plateau or equilibrium is reached, with a steady yield indicating the end of MAE, which is typically reached between 20 and 25 min; with HRE, this is between 25 and 30 min.  
Phase 3 represents a plateau or equilibrium, where the extraction yield stabilizes, signaling the completion of the extraction process. For MAE, this phase is typically reached between 20 and 25 min, with higher extraction efficiency compared to HRE, where the plateau is reached between 25 and 30 min. MAE is more efficient, as it reaches the plateau phase faster, requiring less time to achieve a high extraction yield, making it a quicker and more effective method than other techniques.  
The HRE profile (also shown in Figure 4a-d) shows similar phases but differs from MAE. Its heating stage takes longer, as it heats both the plant material and the water. Phase 1 yields only 7.75% within the first 5 min, with a lower antioxidant yield than MAE (9.30%). At 25 min, the values of responses in MAE are higher than in HRE, with 16.30 \(\pm\) 0.10% for extraction yield, 37.07 \(\pm\) 0.66 mg GAE/g for TPC, 19.17 \(\pm\) 0.42 mg QE/g for TPC, and 113.43 \(\pm\) 0.26 \(\upmu\)g/mL for the IC\({}_{50}\) of DPPH scavenging.  
The energy required for the extraction processes, calculated based on the power consumption of heat reflux extraction (HRE) and microwave-assisted extraction (MAE) during their complete extraction periods, is 63 Wh for HRE and 60 Wh for MAE (Figure 4e). This demonstrates a considerable energy saving of 4.7% with MAE, underscoring its cost efficiency compared to HRE. In terms of energy consumption in extraction methods, the MAE method presents significant advantages over HRE, including a 6-8% reduction in energy consumption. This enhanced efficiency is largely attributed to its considerably shorter extraction time, with MAE reaching the plateau phase far more quickly than HRE.  
We found typical extraction curves for both methods, highlighting changes in yield over time. While both methods follow a similar pattern, they differ in yield rate and extraction time. This suggests that the MAE mechanism benefits from microwave irradiation, which heats polar molecules within plant cells outward, aided by the synergy of heat and mass transfer. The rapid yield increase in Phase 1 typically represents the rapid release of target compounds from the plant matrix. During this initial phase, microwave energy causes localized heating, which disrupts cell walls, resulting in the quick release of polyphenols into the solvent. A key difference between MAE and HRE is MAE's ability to rapidly reach high polyphenol yields and hence high antioxidant activity [28]. This efficiency likely results from microwaves' stronger extraction potential, which combines heat and mass transfer effects in a synergistic way.