## 2 Results and Discussion
### In-Solution Characterization of PDA-Coated Adsorbent Materials: UV-Vis Spectra
Passing from 1 to 2 layers of PDA, nano/microfractures and nano/micropores appeared on the material surface. In order to investigate the PDA organization on PVP-co-S, smaller areas, 60 \(\upmu\)m \(\times\) 60 \(\upmu\)m, were measured by AFM, as shown in Figure 5. PVP-co-S morphology had a roughness that strongly decreased from 62 nm to 3.6 nm when the number of PDA layers was increased. Specifically, one layer of PDA yielded PDA aggregation phenomena on the PVP-co-S surface (PVP-co-S/PDA+), while uniform coverage was achieved by doubling the PDA quantity (PVP-co-S/PDA++). The zoomed 5 \(\upmu\)m \(\times\) 5 \(\upmu\) topographic image of the PVP-co-S/PDA++ highlighted that PDA forms nanoparticles with a size of \(\sim\)80 nm that covered the PVP-co-S surface uniformly. Moreover, phase images of the PVP-co-S/PDA++ were homogeneous, indicating a homogeneous PDA surface coverage. Combining AFM and SEM measurements, we found that one PDA layer did not significantly affect the integrity of the PVP-co-S, and PDA did not cover it uniformly. The addition of a second PDA layer significantly affected the integrity of the PVP-co-S, increasing its porosity and, moreover, yielding uniform PVP-co-S coverage. Figure 5: **(a)** Scanning electron microscopy images of pure PVP-co-S, PVP-co-S/PDA+ and PVP-co-S/PDA++ films with different magnification (scale bars (left to right): 100, 20 \(\upmu\)m). **(b)** The corresponding 60 \(\upmu\)m \(\times\) 60 \(\upmu\)m topographic and phase images. For PVP-co-S/PDA++, zoomed 5 \(\upmu\)m \(\times\) 5 \(\upmu\)m images are also shown. Roughness (RMS) values are reported. The modifications induced by the second layer of PDA, together with the hydrophobic nature of PVP-co-S, adjuvated by its poly-catechol and poly-hydroxy-indole moieties, suggest, contrary to the case of DE, an improved capacity for entrapment of chemicals or pollutants. In order to derive the optical properties (refractive index and extinction coefficient) of pure PVP-co-S film and its thickness, and to quantitatively evaluate the PDA incorporation (%volume fraction) along the film thickness, PVP-co-S films with and without PDA deposited on glass were characterized by spectroscopic ellipsometry. DE samples, due to their high roughness, were not eligible for reflection measurements and were not characterized by spectroscopic ellipsometry. Figure 6a shows experimental ellipsometric spectra of the pseudo-refractive index, n, and extinction coefficient, k, of pure PVP-co-S, PVP-co-S/PDA+ and PVP-co-S/PDA++ deposited on glass. For PVP-co-S/PDA+, a broad peak at -310 nm appeared and became stronger after doubling the number of PDA layers, a clear indication of PDA incorporation into the films (in agreement with absorption spectra in Figure 2b). In order to estimate the optical properties of the pure PVP-co-S film from the ellipsometric measurements, a simple substrate/PVP-co-S film/air model where the optical properties of pure PVP-co-S film were derived through a Tauc-Lorentz dispersion equation with a layer thickness of 121 nm \(\pm\) 10 nm, which was consistent with the maximum peak-to-valley distance, Rp-v, within the 60 \(\upmu\)m \(\times\) 60 \(\upmu\)m scanned area (shown in Figure 4b) from AFM. Figure 6b shows the spectra of the refractive index, n, and extinction coefficient, k, of the PVP-co-S layer derived by the ellipsometric analysis. Four main absorption bands, at 330 nm, 406 nm, 564 nm and 710 nm, were found, all shifted to larger wavelengths  
Figure 6: (**a**) Ellipsometric spectra of the pseudorefractive index, n (scattered filled points) and pseudoextinction coefficient, k (scattered empty points) of films of pure PVP-co-S (squares), PVP-co-S/PDA+ (rhombuses) and PVP-co-S/PDA++ (circles) deposited on glass. Structural models obtained by ellipsometric analysis at the bottom. In the ellipsometric models, the film thickness and the composition (% volume) of the bottom and top of the graded films in terms of volume fractions are shown.