## 3 Results and Discussion
### FTIR Analysis  
Figure 3 shows a sequence of FTIR spectra for TiO\({}_{2}\) NPs, PEG, TiO\({}_{2}\) coated with PEG, 2 ME, and composite TiO\({}_{2}\)-PEG-2 ME. In Figure 3a, the FTIR spectrum of TiO\({}_{2}\) NPs clearly shows tree bands. The first band is the broadest, and is observed at 3500 cm\({}^{-1}\), corresponding to the stretching vibration of the hydroxyl group O-H of the TiO\({}_{2}\) NPs. The second band is observed around 1630 cm\({}^{-1}\), corresponding to bending modes of water Ti-OH; the last is a prominent peak at 1383 cm\({}^{-1}\) related to Ti-O modes [26; 27]. In Figure 3b, the FTIR spectrum of PEG is shown. The peaks around 2888, 2920, and 2888 cm\({}^{-1}\) are attributed to the alkyl chain of polymer; the bands at 1342 and 1100 cm\({}^{-1}\) are due to C-H bending and C-O stretching vibration, respectively; and the band at 1242 cm\({}^{-1}\) corresponds to C-H twisting vibrations [16; 17; 26]. The IR spectrum of TiO\({}_{2}\)-PEG is given  
Figure 1: Schematic representation of the functionalization of PEG–TiO\({}_{2}\) and TiO\({}_{2}\)–PEG–2 ME (2 ME image is supported by [25]). (2 ME: 2-Methoxysestradiol; PEG: polyethylene glycol.) in Figure 3c, where new bands appear due to the presence of PEG (such as the bands around 2880, 1352, and 1105 cm\({}^{-1}\), corresponding to C-H stretching vibrations, C-H bending, and C-O stretching vibration); all these bands are shifted from their original position in PEG, exhibiting hydrogen-bonding nature and confirming PEG's interaction with the surface of TiO\({}_{2}\) NPs. Figure 3: Fourier-transform infrared (FTIR) spectra for (**a**) TiO\({}_{2}\); (**b**) PEG; (**c**) TiO\({}_{2}\)–PEG; (**d**) 2 ME, and (**e**) TiO\({}_{2}\)–PEG–2 ME. The magnified view of (**d**) and (**e**) on the right side shows the IR spectrum for TiO\({}_{2}\)–PEG–2 ME in the range 1800–1000 cm\({}^{-1}\); in this zone, it is possible to identify the peaks associated with aromatic ring C=C stretching vibration in of 2 ME (zone 1) and tree peak associated with the methoxy group O-CH\({}_{3}\) and the alcohol group C-OH (zone 2); these zones are showed in the upper right side in an schematic representation of the 2-Methoxyestradiol molecule. The color of spheres (gray, red and light gray) represent Carbon (C), Oxigen (O) and Hydrogen (H) atoms. Figure 2: Transmission electron microscopy (TEM) image of TiO\({}_{2}\) nanoparticles (NPs). The FTIR spectrum of 2 ME and functionalized TiO\({}_{2}\)-PEG NPs with 2 ME is given in Figure 3d,e. The FTIR spectrum of 2 ME alone is characterized by a number of characteristic bands occurring at 3417, 3182, 3000, 2963, 2907, 2809, and 1600 cm\({}^{-1}\), and in the ranges 1500-1400 cm\({}^{-1}\) and 1300-1000 cm\({}^{-1}\); the last bands are the fingerprint of 2 ME. The bands between 3417 and 3000 cm\({}^{-1}\) are due to hydroxyl stretching vibration bands. The band at 3000 cm\({}^{-1}\) belongs to the C-H bond stretching vibration. The bands at 2963, 2907, and 2809 cm\({}^{-1}\) correspond to stretching vibration of functional groups CH, CH\({}_{2}\), and CH\({}_{3}\). The vibration at 1600 cm\({}^{-1}\) corresponds to C=C bond stretching vibration in the aromatic ring (zone 1 in Figure 3). The bands in the range 1500-1400 cm\({}^{-1}\) are due to CH, CH\({}_{2}\), and CH\({}_{3}\) bending vibration and those in 1300-1200 cm\({}^{-1}\) correspond to vibration of the methoxy group O-CH\({}_{3}\) and the alcohol group C-OH (zone 2 in Figure 3). In the FTIR spectrum of TiO\({}_{2}\)-PEG\(-\)2 ME in Figure 3e, new bands belonging to 2 ME are observed--these bonds occurring mainly in the region 1525-1000 cm\({}^{-1}\). In this zone, we can distinguish peaks located at 1525 and 1420 cm\({}^{-1}\) (zone 2) corresponding to the bending vibration of functional groups CH, CH\({}_{2}\), and CH\({}_{3}\). These bands are shifted from their original position at 1526 and 1422 cm\({}^{-1}\) in pure 2 ME. In zone 1 we found bands appearing at 1260, 1232, and 1205 cm\({}^{-1}\), slightly shifted from their original position in 2 ME [20; 28].