## 2 Materials and Methods  
The model compounds used in this work were pyrocatechol (99%, Changzhou Winsun Import & Export Co., Ltd, Changzhou, Jiangsu, China), guaiaicol (\(\geq\) 98%, Alfa Aesar, Karlsruhe, Germany), vanillic acid (97%, Sigma-Aldrich, Buchs, Switzerland) and ferulic acid (98%, Alfa Aesar, Karlsruhe, Germany). No further purification of these compounds was conducted in this work. Nanosized cerium dioxide (99.5%, S\({}_{\rm Ar}\) = 71 m\({}^{2}\)/g, Alfa Aesar, Karlsruhe, Germany) was pre-calcined at 500 \({}^{\circ}\)C for 2 h to remove organic matter.  
A series of samples, P/CeO\({}_{2}\), G/CeO\({}_{2}\), VA/CeO\({}_{2}\), and FA/CeO\({}_{2}\), with concentrations of phenolic compounds of 0.1, 0.3, 0.6, 0.9, and 1.2 mmol/g were prepared. The concentration range of 0.1-1.2 mmol/g was selected based on previous studies [49]. According to [49], the maximum adsorption values for cinnamic acid and its derivatives, including ferulic acid, are almost equal and amount to \(\approx\) 2.9 \(\times\) 10\({}^{-4}\) mol/g irrespective of the differences in the reaction sites of their molecules. The samples were prepared by impregnation of 100 mg of CeO\({}_{2}\) with 2 mL of P, G, VA, and FA solutions in ethanol. The suspensions were stirred for several minutes and then dried at room temperature in the air.  
Infrared spectra were recorded on a Thermo Nicolet Nexus FT-IR instrument (Thermo Nicolet Corporation, Madison, WI, USA) within the range of 4000-400 cm\({}^{-1}\), working in diffuse reflection mode. The resolution was 4 cm\({}^{-1}\), scanning speed--0.5 cm/s, and number of scans--50. Before the FTIR studies, pure CeO\({}_{2}\) and samples P/CeO\({}_{2}\), G/CeO\({}_{2}\), VA/CeO\({}_{2}\), and FA/CeO\({}_{2}\) were mixed with KBr (\(\geq\) 99%, Alfarus, Kyiv, Ukraine) (1:10). KBr was pre-calcined for 2 h at 500 \({}^{\circ}\)C. Pure phenolic compounds were mixed with KBr in a ratio of 1:100.  
The TPD MS-experiment was performed on an MX-7304 monopole mass spectrometer (Electron, Sumy, Ukraine) with electron ionization, re-equipped for thermal desorption measurements [45; 46; 50]. At the beginning of the experiment, a sample weighing 10-20 mg was placed in a quartz-molybdenum ampoule and pumped out at room temperature to a pressure of \(\sim\)5 \(\times\) 10\({}^{-5}\) Pa. The rate of programmed linear heating was 0.17 \({}^{\circ}\)C/s. Heating was increased from room temperature to 750 \({}^{\circ}\)C. Volatile products of thermolysis entered the ionization chamber of the mass spectrometer and were ionized and fragmented under the action of electrons. The range of the investigated masses was 1-210 a.m.u. The total number of mass spectra recorded during the experiment reached \(\sim\)240. The slow heating of the sample and the high pumping rate of volatile thermolysis products made it possible to neglect diffusion effects. Under such conditions, the intensity of the ion current was proportional to the rate of desorption.  
Kinetic parameters of the chemical reactions and processes of the lignin model compound on the nanoceria surface (temperature of the maximum desorption rate T\({}_{\text{max}}\), reaction order \(n\), activation energy \(E^{\prime\prime}\), pre-exponential factor \(v_{0}\), and change of activation entropy \(\Delta S^{\prime\prime}\)) were calculated from the TPD-MS data by an in-house computer program using the linear form of the Arrhenius equation [45; 46; 50].  
Thermogravimetric analysis, differential thermogravimetric analysis (DTG), and differential thermal analysis (DTA) were performed using a TGA/DTA analyzer (Q-1500D, Hungary). Samples weighing 100 mg were heated from room temperature to 1000 \({}^{\circ}\)C. The heating rate was 10 \({}^{\circ}\)C/min in an air atmosphere.