## 2 Materials and Methods
### Materials
The thermal analysis of the samples was performed on a DTG 60H derivatograph (Shimadzu, Kyoto, Japan). TGA curves were recorded at a heating rate of 5 \({}^{\circ}\)C/min in air; the sample weight was 20-30 mg.  
Textural properties were studied by analyzing N\({}_{2}\) adsorption-desorption isotherms at \(-\)196.15 \({}^{\circ}\)C obtained on a Quantachrome NOVATOUCH LX4 adsorption analyzer equipped with long cells with a flask and an outer diameter of 9 mm. Before the analysis, the samples were degassed for 16 h at a temperature of 120 \({}^{\circ}\)C in accordance with IUPAC recommendations. The total pore volume (VT) and BET were calculated using the Quantachrome TouchWin\({}^{\text{TM}}\) software, version 1.22, in accordance with the procedure used in the works [34; 95]. Mossbauer spectroscopy was performed using the Express Mossbauer spectrometer MS1104 Em (Southern Federal University, Rostov-on-Don, Russian Federation). \(\alpha\)-Fe calibration was performed for all samples. The source of gamma quanta of Co\({}^{57}\). A set of Mossbauer spectra was produced at room temperature. The following designations are noted in the text: Is is an isomeric shift, mm/c; Qs is a quadrupole splitting, mm/c; H is the magnetic field on the Fe nuclei, mm/c; S is the area of the component; and G is the line width, mm/c. The reaction of phenol with oxygen in the presence of H\({}_{2}\)O\({}_{2}\) on PVP-stabilized CoFe\({}_{2}\)O\({}_{4}\) nanocomposites was carried out using the technique described in our previous articles [37; 58; 65] in a duck-type glass thermostatic reactor with intensive stirring (400 rpm), temperature heating, in an oxidizing oxygen atmosphere. To perform the experiments, 10 mL of phenol solution with an initial substrate concentration of 10 mmol/L was loaded into the reactor. Then, 0.02 g of the nanocomposite catalyst was added. The reactor was closed and purged with oxygen 3 times. Then, a given atmosphere (oxygen) was created in the reactor. The reactor was shaken until a constant volume of the gas phase was established within the experimental error, after which the remaining components of the system were quickly pressed through a glass tap. This moment was taken as the beginning of the reaction. The liquid volume in all experiments was 10 mL, and the gas volume was 180 mL. The temperature was maintained using a U-10 thermostat. The results were processed in coordinates W = f (Q), where W is the oxygen absorption rate (mol/L min) and Q is the amount of absorbed oxygen (mol/L). During the reaction, samples of the reaction mixture were periodically taken from the reactor (at the reaction moments of 0, 15, 30, 60, 90, and 120 min). The reaction mixture was analyzed by HPLC. HPLC was calibrated for the identification and quantification of many of the expected oxidized phenol intermediates (hydroquinone, p-nitropenol, resorcinol, p-benzoquinone, pyrocatechol, trans-muconic acid, and phenol) [92]. The concentration of phenol and its expected oxidized products (p-nitrocatechin, hydroquinone, p-nitrophenol, resorcinol, p-benzoquinone, pyrocatechin, trans-muconic acid, and phenol) was controlled by analyzing liquid aliquots taken during the reaction in the Jasco HPLC system at a wavelength of 246 nm (UV-2075 plus detector, Tokyo 193-0835, Japan). For this purpose, a biphenyl column and 0.3 mL-min\({}^{-1}\) (PU-2089 Plus, Tokyo 193-0835, Japan) mixture of acetonitrile (A) and acidified ultrapure water (B) H\({}_{3}\)PO\({}_{4}\) were used. The conversion of phenol (X\({}_{\text{PHOH}}\)) was calculated using Formula (1):  
\[\text{X}_{\text{PHOH}}\left(\%\right)=\left(\text{C}_{0\text{PHOH}}-\text{C}_ {\text{PHOH}}\right)/\text{C}_{0\text{PHOH}} \tag{1}\]  
where C\({}_{0}\) is the initial concentration of the substrate in the solution and C is the current concentration of the substrate. The concentration of H\({}_{2}\)O\({}_{2}\) in the solution was determined at a wavelength of 405 nm using a T70 spectrophotometer from PG instruments Ltd. (Lutterworth, UK).