## 2 Results and Discussion
### Characteristics of Synthesized REEIIPs and Hybrid Materials
The Nd-selective membranes were characterized by enhanced thermal properties compared to the modified chitosan, even for pure NdIIPs, which were stable until 480 \({}^{\circ}\)C. After the introduction of modified MWCNTs (Figure 3b-d), namely with ion-imprinted polymer NdIIPs, their thermooxidative stability improved, and they were stable up to 590 \({}^{\circ}\)C. An increase in the thermooxidative stability after the introduction of modified MWCNTs was also observed for the Gd-sensitive membranes, i.e., the membranes with the addition of 2 wt.% MWCNT-GdIIPs were stable up to 730 \({}^{\circ}\)C. So, these hybrid membranes were characterized by enhanced thermal stability, which increased with the rise in MWCNT addition. The newly developed membranes were studied by rheological analysis using the dynamic mechanical method (DMA), which allowed us to characterize their viscoelastic properties in wide temperature ranges. Three parameters were used to describe the rheological properties, namely the storage modulus, E\({}^{\prime}\), the loss modulus, E\({}^{\prime\prime}\), and the loss coefficient tan \(\delta\) (Figure 4). The temperature dependencies of E\({}^{\prime}\), E\({}^{\prime\prime}\), and tan \(\delta\) provided information on the mobility of polymer chains. At lower temperatures, local movements related to low-amplitude motions of chain segments or within the lateral groups (\(\beta\) relaxations) could be observed. At higher temperatures, however, molecular movements related to glass transition (\(\alpha\) relaxations) were observed, and their occurrence could be associated with substantial changes in the mechanical properties of materials. As can be seen in Figure 4b,c, the relaxation process is associated with peaks near 95-110 \({}^{\circ}\)C for all hybrid membranes. However, the tan \(\delta\) peak was observed at higher temperatures in the range from 110 to 120 \({}^{\circ}\)C. Figure 4a shows significantly higher values of E\({}^{\prime}\) for membranes with a larger MWCNT content. This phenomenon could be caused by the higher number of nanoparticles in the polymer matrix, whose stiffness was much higher than that of the polymer matrix. With the increase in nanoparticle addition, the distance between them decreased, thus leading to the formation of more complex 3D microstructures with higher storage modules E\({}^{\prime}\) (almost twice). The modification of chitosan with aldehyde and the introduction of second REEIIPs resulted in a decrease in the glass transition temperature (from 140 \({}^{\circ}\)C for chitosan [44] to around 110 \({}^{\circ}\)C). Additionally, the introduction of modified MWCNTs caused a further decrease in the glass transition temperature (94 \({}^{\circ}\)C for E\({}^{\prime\prime}\) and around 110 \({}^{\circ}\)C for tan \(\delta\)). Moreover, the highest E\({}^{\prime\prime}\) values were noted for the PrIIPs membrane with the highest addition of 5 wt.% MWCNT-PrIIPs (almost double growth), which meant that it had the best resistance to elastic deformation. The increase in E\({}^{\prime}\) and E\({}^{\prime\prime}\) with temperature suggested enhanced thermal-mechanical stability in hybrid materials. So, the introduction of MWCNT-REEIIP additives significantly reinforced the polymer matrix and improved strength, stiffness, and ductility--critical for membrane durability under mechanical and thermal stress. Due to the potential future applications of the newly developed adsorption membranes for the recovery of REEs from extracts, it was important to examine their mechanical properties, such as tensile strength (Rm), Young's modulus (E), and elongation at break. Selected results are presented in Table 1 and Figure 5. It was found that the mechanical properties of membranes consisting of two REEIIPs were comparable, with the Nd-selective membrane exhibiting slightly higher values of the tested parameters (from 10 to 20%).