## 2 Results and Discussion
### Characteristics of Synthesized REEIIPs and Hybrid Materials
The spectrum in Figure 1e shows multiple broad and overlapping absorption bands indicative of a chemically diverse surface. The most prominent feature is a broad absorption band centered around 3300-3400 cm\({}^{-1}\), commonly associated with O-H stretching vibrations, which may originate from hydroxyl groups introduced during the oxidative pretreatment or polymerization steps. This band may also include N-H stretching from amide or amine groups, indicating the incorporation of nitrogen functionalities, possibly through monomers used during polymer imprinting. The region between 2800 and 3000 cm\({}^{-1}\) reveals a weaker, yet discernible, set of bands corresponding to aliphatic C-H stretching vibrations, suggesting the presence of saturated alkyl chains from the polymer backbone. These features are characteristic of methylene (-CH\({}_{2}\)-) and methyl (-CH\({}_{3}\)) groups, likely derived from the vinyl group in monomers. The sharp band near 1650 cm\({}^{-1}\) is typically attributed to C=O stretching in amide or carboxylic acid groups. Bands around 1570-1620 cm\({}^{-1}\) could correspond to aromatic C=C stretching or the asymmetric stretching of carboxylate groups. Absorptions in the 1000-1300 cm\({}^{-1}\) range are assigned to C-O, C-N, or C-O-C stretching, indicative of ether linkages. The spectral complexity in this fingerprint region confirms that the pristine CNTs were successfully functionalized with a chemically rich polymer matrix capable of molecular imprinting. The broad bands and overlap suggest a heterogeneous environment typical of non-crystalline polymer networks. Figure 1f of MWCNT-GdIIPs displays a more defined and sharper IR spectrum, indicating a higher degree of chemical order or more consistent functional group incorporation. Most notably, the spectrum exhibits a strong and narrow absorption band around 1720 cm\({}^{-1}\), which is characteristic of C=O stretching in ester or carboxylic acid groups. This is a key signature for the successful grafting of functional monomers to the CNT surface. Compared to the pristine-imprinted sample, the O-H/N-H stretching region around 3400 cm\({}^{-1}\) appears narrower and less intense, possibly indicating fewer free hydroxyl groups on CNTs or more extensive hydrogen bonding within the polymer network. The C-H stretching region (2800-3000 cm\({}^{-1}\)) remains present, confirming the aliphatic C-H stretching vibrations, suggesting the presence of saturated alkyl chains from the polymer backbone. Multiple peaks are evident near 1200-1450 cm\({}^{-1}\), which can be attributed to C-N, C-O, and C-C stretching as well as CH\({}_{2}\)/CH\({}_{3}\) bending vibrations. The region around 1600 cm  
also likely includes N-H bending or aromatic C=C stretching, reflecting the imprinted polymer's chemical framework. The increased spectral resolution and the pronounced carbonyl peak confirm that the grafting approach has led to a well-defined and chemically robust imprinted surface on the CNTs. These structural features enhance the material's potential for selective ion recognition, likely improving the sensitivity and selectivity of obtained materials. The synthesized membranes were also studied by various techniques, like XRD, TGA, SEM, X-ray micro-tomography, VSM, DMA, and the mechanical technique. Selected results of the XRD analysis of pure and hybrid membranes with additions of various MWCNTs are presented in Figure 2.  
The synthesized polymers were also characterized by X-ray diffraction (XRD), and the results are presented in Figure 2a. Here, we can see that this is a typical structure of semicrystalline polymers with some weak peaks associated with the introduced REE ions, usually around the angle 2 theta 42-45\({}^{\circ}\), that indicates reduction in crystallinity due to polymer chain crosslinking and additive dispersion. In the case of REE sensitive adsorption membranes (Figure 2b,c), characteristic broad peaks originating from the polymer and graphite were found.