## 3 Results and Discussion
### Specific Properties of the Multi-Walled CNT-K  
MWCNTs are a very versatile graphene-based material with sp2 character, forming single-walled or multi-walled tubes of different conformations and with a distinct delocalized \(\pi\)-electron system. Depending on how they are manufactured (e.g., a chemical vapor deposition with an iron-based catalyst), the resulting particles will have different properties, generally of high complexity. Therefore, it is important to characterize the nanotubes used here to be able to understand their role in the potential-controlled process and to identify changes in the MWCNT matrix due to environmental and electrical impacts. The morphological description of the CNT-K (Future Carbon GmbH, Germany) used here is provided on different scales (see Figure 1) and shows the altered configuration of the particle network in solution: CNT-K form spongy agglomerates at the macro level or a fibril network at the nano level. Moreover, the CNT-K stick together under pressure (like in the column) and create a uniform matrix (MWCNT matrix). Thus, a highly porous monolithic structure and a homogeneous particulate packed bed are present in the chromatographic column. Characteristic numbers are an asymmetry factor of 1.1 (describes the homogeneity of the packed bed); a HETP of 0.04 cm (represents the separation efficiency, see Equation S1); a column porosity of 0.4; and a total column porosity of 0.8 (see Figure S3 and Table S1). The description of the packed bed is extended using electrochemical methods, such as open circuit potential (ocp) measurements, which provide about +300 mV to +500 mV at neutral pH, depending on the arrangement of the CNT (of the matrix structure). This value is comparable to others in the literature [45; 46]. Thus, a lack of electrons exists in the passive state, and the particulate electrode turns out to be positively charged. In the presence of ions (10 mM phosphate buffer, pH = 7.2) the ocp measurement yields even higher positive potentials, showing a more pronounced positive charge for the CNT matrix.  
The single CNT-K tubes have an outer diameter between 20 and 40 nm, with a length up to hundreds of \(\mu\)m (Figure S4). The agglomerates are between 10 and 500 \(\mu\)m (Figure S5) and have pore sizes in the macro range. The specific surface area of the particulate material is around 200 m\({}^{2}\)/g, which is low compared to the single-walled CNT, with up to 1000 m\({}^{2}\)/g [47; 48]. However, the commercially available SWCNTs are 10 to 100 times more expensive than commercially available MWCNTs; moreover, no technology for a large-scale production of SWCNTs currently exists. The relatively small surface area of the MWCNT used may be caused by the agglomeration behavior of the CNT-K [47], limiting the access to the total CNT-K surface. Another possibility is that only the outer surface of a single nanotube is accessible, as around 85% of tubes are closed tubes (Figure S6). In literature, the values for the surface area of open or closed MWCNT are 300 m\({}^{2}\)/g or 150 m\({}^{2}\)/g [49] respectively, so the specific surface area of CNT-K with 200 m\({}^{2}\)/g is within an expected range. The fact that over 85% of the CNT-K tubes from the TEM pictures seem to be closed tubes leads to the conclusion that adsorption can  
Figure 1: Configuration of the MWCNT “CNT-K” (Future Carbon GmbH, Germany) at different scales. From left: (**a**) CNT-K agglomerate at macro scale (SEM, 2020\(\times\), [PERSON]); (**b**) surface of CNT-K agglomerates (SEM; 5000\(\times\), [PERSON]); (**c**) single CNT-K network at nano scale (TEM, 50,000\(\times\), Dr. [PERSON])take place exclusively on the outer MWCNT shell, which is important information for the adsorption capacity of static and dynamic adsorption experiments.