## 3 Results and Discussion
### Morphology and Characterization of the CuBTC@PET Membranes
#### 3.1.3 CuBTC@PET Morphology Study  
Figure 5 shows SEM images of PET@CuBTC composite fiber membranes under different growth cycles of PET fiber membranes, where CuBTC is produced by bonding Cu\({}^{2+}\) with three -COOH groups above the ligand BTC to produce a regularly arranged metal-organic skeleton. During the layer-by-layer growth of CuBTC on the surface of PET fibers, the Cu\({}^{2+}\) is bonded with the -COOH groups at the ends of the PET molecular chains first, followed by a further increase in the size of the skeleton in subsequent cycles. COOH is followed by a layer-by-layer bonding arrangement of Cu\({}^{2+}\) with the ligand in subsequent cycling cycles, and the skeleton size is further increased. Figure 5a shows that the CuBTC crystals grow more uniformly in size on the fiber surface at three cycles, but there are still many vacancies on the fiber surface where the crystal layer does not grow. The size of the skeleton gradually increases as the growth cycle increases. Figure 5b shows that in five cycles, when the crystal growth is uniform, the PET fiber surface is covered by the crystal layer, the skeleton size is moderate, and the PET fiber size is more compatible, and the overall fiber morphology is maintained. In Figure 5b, when increased to seven cycles, the skeleton size increases, the skeletons stack on top of each other to grow, the fiber gap is gradually filled by the skeleton, and the crystal size does not match the size of the fiber, resulting in the composite fiber stacking being too dense. Figure 5b shows that when the growth cycle is further increased to nine cycles, the skeleton size is too large and extremely mismatched with the fiber size. The PET fiber substrate was exposed to only a small amount of crystal growth embedded between the fibers, which may be due to the gradual growth of the skeleton on different fibers into one, where the chemical bond between PET and CuBTC could not withstand the shear force generated by its gravity and the relative motion between the fibers, which resulted in the shedding of the skeleton and the exposure of part of the fiber surface. In summary, for the in situ growth of CuBTC on PET fibers in this study, the CuBTC@PET composite fibers under the five-cycle condition have excellent surface morphology. Figure 6 shows the SEM images of the unswollen recrystallized PET fibers under the same in situ growth parameters. As can be seen from Figure 6a, the CuBTC crystals are unevenly distributed and small in size under the three-cycle condition, which is because  
Figure 5: SEM images of CuBTC@PET composite fibers under different growth cycles: (**a**) three cycles, (**b**) five cycles, (**c**) seven cycles, (**d**) nine cycles. the anchoring of Cu\({}^{2+}\) to the PET substrate determines the subsequent growth of CuBTC, and thus the contact area of the fiber with the solution determines the growth density of CuBTC. Without recrystallization, the fibers have a smaller specific surface area, providing fewer binding sites for Cu\({}^{2+}\), and the binding of Cu\({}^{2+}\) to PET is relatively poor, so there is not enough Cu\({}^{2+}\) and ligand to achieve a larger distribution of more homogeneous CuBTC crystals for nucleation. By observing Figure 6b,c, it can be seen that the crystal size further increases as the growth period increases to five and then seven cycles, and the size distribution becomes non-uniform compared to that under the same period in Figure 5. This is because CuBTC crystals have different nucleation rates, and in different cycles, some fresher nuclei are formed on the fiber surface in the subsequent cycles due to the uneven and insufficient bonding of Cu\({}^{2+}\) to the PET surface in the previous cycles, so different sizes of CuBTC particles grow, resulting in an uneven coating after the first five cycles, and the trend with the increase in the number of cycles becomes more and more obvious.