Excellent Performance and Feasible Mechanism of ErOx-Boosted MnOx-Modiﬁed Biochars Derived from Sewage Sludge and Rice Straw for Formaldehyde Elimination: In Situ DRIFTS and DFT

: To avoid resource waste and environmental pollution, a chain of ErO x -boosted MnO x - modiﬁed biochars derived from rice straw and sewage sludge (Er y Mn 1-y /BACs, where biochars derived from rice straw and sewage sludge were deﬁned as BACs) were manufactured for formaldehyde (HCHO) elimination. The optimal 15%Er 0.5 Mn 0.5 /BAC achieved a 97.2% HCHO removal efﬁciency at 220 ◦ C and exhibited favorable E HCHO and thermal stability in a wide temperature window between 180 and 380 ◦ C. The curbed inﬂuences of H 2 O and SO 2 offset the boosting effect of O 2 in a certain range. Er–Mn bimetallic-modiﬁed BACs offered a superior HCHO removal performance compared with that of BACs boosted using Er or Mn separately, owing to the synergistic effect of ErO x and MnO x conducive to improving the samples’ total pore volume and surface area, surface active oxygen species, promoting redox ability, and inhibiting the crystallization of MnO x . Moreover, the support’s hierarchical porous structure not only expedited the diffusion and mass transfer of reactants and their products but also elevated the approachability of adsorption and catalytic sites. Notably, these prominent features were partly responsible for the outstanding performance and excellent tolerance to H 2 O and SO 2 . Using in situ DRIFTS characterization analysis, it could be inferred that the removal process of HCHO was HCHO ad → dioxymethylene (DOM) → formate species → CO 2 + H 2 O, further enhanced with reactive oxygen species. The DFT calculation once again proved the removal process of HCHO and the strengthening effect of Er doping. Furthermore, the optimal catalytic performance of 15%Er 0.5 Mn 0.5 /BAC demonstrated its vast potential for practical applications.


Introduction
The robust growth of industrial activities in China's now mammoth economy has led to a rapid increase in the demand for coal, one of the main energy sources. Volatile organic compounds (VOCs) discharged in large quantities from coal-fired power stations are mainly composed of aldehydes, alkanes and alkenes, and chlorinated hydrocarbons [1,2].
In addition to posing a significant threat to human health, these pollutants also generate gas pollution, forming photochemical smog and secondary organic aerosols that contribute to the dangerous depletion of stratospheric ozone [3]. In particular, as a common VOC, HCHO has been classified as a Class A carcinogen by the World Health Organization, and it is also widely recognized as a hazard to human health [4,5]. Consequently, researchers have developed efficient methods to remove HCHO, among which adsorption, photocatalysis, condensation, catalytic oxidation, biological filtration, and other technologies have recently emerged [6,7]. Among these technological endeavors, catalytic oxidation is regarded as an environmentally friendly, economical, and promising solution [7]. It is known that the performance of catalysts is vital for the efficiency of oxidation reactions. In the past several decades of research, supported noble metals and supported transition metal oxides have been considered key catalysts for the adsorption and catalytic oxidation of HCHO [7,8]. A series of metal oxide supports, including MnO x , TiO 2 , CeO 2 , and FeO x and their composites, such as MnO x -CeO 2 , CeO 2 -Co 3 O 4 , and In 2 O 3 -SnO 2 , have been used in a wide range of studies on catalytic HCHO due to their excellent redox effects, the high dispersity of the supported metal oxides, and the metal-support interactions (MSIs) between the supports and the supported metal oxides [9][10][11]. However, applications of these common metal oxide supports are restricted owing to certain disadvantages, such as irregular shapes, unsuitable sizes, uneven structures, and high prices [12,13]. Against this backdrop, despite their own problems, biochar supports hold potential for HCHO removal because of their low prices, adjustable sizes, large specific surface areas, excellent hydrophobicity, and rich sources [14]. Biochars' hydrophilic and porous structures provide them not only with excellent supports to convert VOCs into CO 2 and H 2 O but also suitable mediums to remove a variety of gas pollutants, such as NO x , SO 2 and Hg 0 [15][16][17]. Unlike most commercial activated carbon, hierarchical porous biochars are mainly composed of mesopores and macropores and not micropores, which significantly reduces the influence of internal diffusion and mass transfer on catalytic oxidation and adsorption rates [2,18]. In addition, mesopores and macropores can be used as spacious rooms for active ingredient dispersion, providing channels for the transfer and diffusion of other active substances, such as electrons [18]. Therefore, researching new types of efficient and cheap hierarchical porous biochars has become a focus in the field of catalysis.
Unfortunately, the finite number of surface functional groups and limited active sites in pristine biochars are insufficient to remove various VOCs. It has been reported that loading noble metals or transition metal oxides onto biochars could significantly enhance their catalytic activity and adsorption capacity [19]. Compared with noble metals, transition metal oxides provide lower costs and stronger resistance to poisoning, making them attractive alternatives to improve biochars' activity [20]. In particular, manganese oxides have become a major research topic because of their rapid electron transfer, abundant oxygen vacancies, and variable valences [21,22]. Notably, manganese oxides are regarded as a promising class of transition metal oxides, with relatively large oxygen storage capacities and high activity during the removal of VOCs [23]. Based on previous studies, Mn's different valence states from −3 to +7 allow its oxides to provide abundant reactive oxygen species while it also transfers activated electrons into a mobile electron environment that increases redox reactions [24].
However, manganese oxides are still limited by their low resistance to SO 2 poisoning, thermal instability, excessive by-products, and other problems in practical industrial applications [25]. To improve the anti-SO 2 performance of Mn-based catalysts, it has become a promising method to modify the catalysts with other metal elements to exploit the synergistic effect between bimetallic oxides [26]. As a rare earth metal, Er (erbium) has often been used in various fields in modified catalysts because it does not completely occupy the 4f and empty 5d orbitals. For example, adding a small amount of Er doping could significantly augment the oxygen vacancy concentration and oxygen storage capacity of CeZr/TiO 2 catalysts, generating excellent anti-SO 2 performance and SCR activity [27]. In addition, the presence of Er oxide in a YAlO 3  catalytic activity [26]. According to studies, Er and its composite oxides have been applied in a series of metal-oxide-supported catalysts, but they have rarely been applied in catalysts with biochars as the supports and for HCHO elimination [26][27][28]. For the above reasons, using ErO x -boosted MnO x -modified biochars to improve catalytic activity is encouraged, albeit a few reports on the utilization of such catalysts to remove VOCs in simulated flue gas and the catalytic oxidation mechanism of HCHO with Er y Mn 1−y /BACs are still unclear. To shed light on this, a range of Er y Mn 1−y /BACs samples were investigated for HCHO removal in this novel work, emphasizing three aspects: (1) the performance and practical application of Er y Mn 1−y /BACs catalysts for HCHO removal; (2) the mechanism of HCHO removal by Er y Mn 1−y /BACs catalysts; and (3) the physicochemical properties and structural features of these catalysts, aiming to explore the relationship between the physicochemical properties and catalytic performance of Er y Mn 1−y /BACs as well as to develop a new and efficient catalyst for HCHO removal.

Sample Synthesis
Sewage sludge was collected from the Shuikoushan Industrial Sewage Treatment Plant, while rice straw was acquired from the outskirts of Hengyang City, Hunan Province, PR China. The biochars with sewage sludge, rice straw, and their combination as precursors were labeled as SAC, SAW, and BAC, respectively. The fabrication methods of the biochars have been described in detail in our past work [29]. The active ingredient precursors were manganese(II) acetate tetrahydrate or erbium(III) nitrate pentahydrate, while SAC, SAW, and BAC acted as the supports, in which the Mn-or Er oxide-modified catalysts were fabricated using the facile ultrasonic-assisted impregnation method. First, the desired precursors of erbium(III) nitrate pentahydrate or manganese(II) acetate tetrahydrate were uniformly dissolved in deionized water. Subsequently, the calculated amounts of the corresponding supports were impregnated in the precursor solutions for 25 h, undergoing ultrasonic sound treatment during the first 2 h. Lastly, the acquired samples were positioned in a drying oven until completely dried and then calcined at 450 • C for 5 h with constant N 2 protection. XEr y Mn 1−y /BAC catalysts were thus obtained, where X represents the mass fractions of the doping active metal oxides designated as 5%, 10%, 15%, and 20%. In addition, y and 1 − y represent the mole ratio of Er to Mn in the bimetallic oxides. 15%Er/BAC, 15%Mn/BAC, 15%Er 0.5 Mn 0.5 /SAC, and 15%Er 0.5 Mn 0.5 /SAW were also manufactured in the above manner.

Samples Characterization
First, a TriStarll3020 surface area porosity analysis tube (America Micromeritics, Georgia, GA, USA) was deployed to evaluate the pore parameters and specific surface areas of the samples. Scanning electron microscopy (SEM) photographs were obtained to analyze the surface morphologies and structures of the samples with a MIRA4 analyzer (TESCAN, Prague, Czech Republic). Transmission electron microscope (TEM) images were obtained with a Technai G2 F20 (FEI, Colombia MD USA) to view the samples' microstructures. Next, the X-ray diffraction (XRD) results of the components' dispersivity and crystallinity were obtained using a Bruker D8-Advance X-ray diffraction installation. H 2 temperature-programmed reduction (H 2 -TPR) was carried out using a Tianjin Xianquan TP-5080 automatic chemical adsorption instrument. The samples' chemical element states and chemical compositions were investigated with a Thermo ESCALAB 250XI Xray photoelectron spectrometer (America Thermo, Lexington, MA, USA). Finally, in situ diffuse reflectance infrared Fourier-transform spectroscopy (DRIFTS) for the samples was conducted with a Nicolet iz10 (Thermo Fisher, Lexington, MA, USA). Figure 1 shows the device sketch for evaluating the HCHO elimination performance, which consisted of the following three main sectors. The first component was the simulated Catalysts 2023, 13, 1222 4 of 24 flue gas supply system, where the simulative flue gas (SFG) contained 200.0 ± 2.0 ppm of HCHO, balanced N 2 , and 6% O 2 . Gaseous HCHO was prepared using a peristaltic pump to infuse a solution of 38 wt% HCHO into a polyethylene tube enclosed within a temperaturecontrolled heater. Moreover, the carrier gas of 80 mL/min N 2 carried the high-humidity gas-phase HCHO and passed through the condenser device to remove the gas-phase water vapor. The second component was a sustaining flow-fixed bed reactor. For each experiment, a 0.5 g sample was placed in a quartz tube (inner diameter = 10 mm; length = 1200 mm), and the total flow rate was maintained at 500 mL/min using a programmed heating tube furnace and various matching mass flow controllers, which corresponded to a gas hourly space velocity (GHSV) of approximately 64,000 h −1 . The corresponding gas components were plenarily mixed before entering the fixed bed reactor. The third component was the gas analyzer system, which included a PGM7340 analyzer (RAE Systems, San Francisco, CA, USA) and a PGA-650 analyzer (Phymetrix, Medford, NY, USA) to survey the HCHO and CO 2 concentrations, respectively. The required HCHO concentration was regularly checked to maintain stability for at least 30 min before the start of the test. In addition, trial tests were performed before the experiment to lessen interference from the instrument and exterior elements.  Figure 1 shows the device sketch for evaluating the HCHO elimination performance, which consisted of the following three main sectors. The first component was the simulated flue gas supply system, where the simulative flue gas (SFG) contained 200.0 ± 2.0 ppm of HCHO, balanced N2, and 6% O2. Gaseous HCHO was prepared using a peristaltic pump to infuse a solution of 38 wt% HCHO into a polyethylene tube enclosed within a temperature-controlled heater. Moreover, the carrier gas of 80 mL/min N2 carried the high-humidity gas-phase HCHO and passed through the condenser device to remove the gas-phase water vapor. The second component was a sustaining flow-fixed bed reactor. For each experiment, a 0.5 g sample was placed in a quartz tube (inner diameter = 10 mm; length = 1200 mm), and the total flow rate was maintained at 500 mL/min using a programmed heating tube furnace and various matching mass flow controllers, which corresponded to a gas hourly space velocity (GHSV) of approximately 64,000 h −1 . The corresponding gas components were plenarily mixed before entering the fixed bed reactor. The third component was the gas analyzer system, which included a PGM7340 analyzer (RAE Systems, San Francisco, CA, USA) and a PGA-650 analyzer (Phymetrix, Medford, NY, USA) to survey the HCHO and CO2 concentrations, respectively. The required HCHO concentration was regularly checked to maintain stability for at least 30 min before the start of the test. In addition, trial tests were performed before the experiment to lessen interference from the instrument and exterior elements.   The HCHO removal efficiency (E HCHO ) and CO 2 selectivity (S C ) were determined using the following formulae:  Table 1 overviews the physical properties of the primordial BAC and modified BACs, including total pore volumes, BET surface areas, and average pore diameters. Figure 2a depicts the N 2 adsorption/desorption isotherms of the samples. All the isotherms exhibit the typical IV with H3 hysteresis loops, revealing the existence of slit-shaped mesopores based on the IUPAC [30,31]. The primordial BAC exhibited the maximal BET surface area of 284.3071 m 2 /g and the highest total pore volume of 0.263 cm 3 /g. Both the specific surface areas and total pore volumes of the boosted samples decreased with the addition of the metal oxides. This might be due to sections of the existing pores being covered and destroyed by the loaded metal oxides [25]. The bimetallic-modified samples had higher specific surface areas than the mono-metallic-modified samples, and this phenomenon was attributed to the synergistic effect between Er and Mn oxides, which improves the dispersity of metal oxides [32,33]. The total pore volumes and specific surface areas of the Er 0.5 Mn 0.5 /BAC samples decreased as a result of the increase in the loading value. This phenomenon might be because of the agglomeration of metal oxides, and the blocking of more voids by Er and Mn oxides becomes increasingly significant with the increasing metal oxide loading value [29,30]. Combining the subsequent SEM analysis and the experimental results in Comparison of Catalytic Performance, the specific surface area was not the exclusive determinant of the samples' activity. Furthermore, the samples' pore size distribution curves in Figure 2b show that the pore volume characteristics of the prepared samples were mainly determined by micropores and mesopores. including total pore volumes, BET surface areas, and average pore diameters. Figure 2a depicts the N2 adsorption/desorption isotherms of the samples. All the isotherms exhibit the typical IV with H3 hysteresis loops, revealing the existence of slit-shaped mesopores based on the IUPAC [30,31]. The primordial BAC exhibited the maximal BET surface area of 284.3071 m 2 /g and the highest total pore volume of 0.263 cm 3 /g. Both the specific surface areas and total pore volumes of the boosted samples decreased with the addition of the metal oxides. This might be due to sections of the existing pores being covered and destroyed by the loaded metal oxides [25]. The bimetallic-modified samples had higher specific surface areas than the mono-metallic-modified samples, and this phenomenon was attributed to the synergistic effect between Er and Mn oxides, which improves the dispersity of metal oxides [32,33]. The total pore volumes and specific surface areas of the Er0.5Mn0.5/BAC samples decreased as a result of the increase in the loading value. This phenomenon might be because of the agglomeration of metal oxides, and the blocking of more voids by Er and Mn oxides becomes increasingly significant with the increasing metal oxide loading value [29,30]. Combining the subsequent SEM analysis and the experimental results in Comparison of Catalytic Performance, the specific surface area was not the exclusive determinant of the samples' activity. Furthermore, the samples' pore size distribution curves in Figure 2b show that the pore volume characteristics of the prepared samples were mainly determined by micropores and mesopores.

SEM and TEM Analysis
The SEM images of the primordial BAC and modified BACs are shown in Figure 3. The surface morphology and structure of the primordial BAC dramatically changed after the import of metal oxides. As demonstrated in Figure 3b, only a few agglomerates located in 5%Er 0.5 Mn 0.5 /BAC and most surfaces of 5%Er 0.5 Mn 0.5 /BAC were not completely used, allowing further loading with additional metal oxides. For 10%Er 0.5 Mn 0.5 /BAC, while part of the effective area was fully utilized, some of the surface of 10%Er 0.5 Mn 0.5 /BAC was not exploited. It was thought that more dispersed active metal oxides resulted in more adsorption or catalytic sites, thus improving catalytic activity [29,34]. Regarding 15%Er 0.5 Mn 0.5 /BAC, almost all surface areas were highly dispersed with metal oxides, with some agglomerating metal oxides and more agglomerates existing in 20%Er 0.5 Mn 0.5 /BAC. Consequently, the excess metal oxides destroyed some pre-existing pores due to more serious agglomerates [35,36]. This appearance also dovetailed with the frontal BET results. Furthermore, as revealed in Figure 3f, EDX was used to detect the rough element ratio of Er to Mn in 15%Er 0.5 Mn 0.5 /BAC. The Mn/Er atomic ratio in a particular morphology of 15%Er 0.5 Mn 0.5 /BAC was 0.93, which is almost equal to the theoretical Mn/Er atomic ratio in 15%Er 0.5 Mn 0.5 /BAC (Mn/Er = 1). The experiments demonstrated that Er and Mn were equally dispersed in 15%Er 0.5 Mn 0.5 /BAC and that ErO x was slightly more likely to agglomerate than MnO x . in 5%Er0.5Mn0.5/BAC and most surfaces of 5%Er0.5Mn0.5/BAC were not completely used, allowing further loading with additional metal oxides. For 10%Er0.5Mn0.5/BAC, while part of the effective area was fully utilized, some of the surface of 10%Er0.5Mn0.5/BAC was not exploited. It was thought that more dispersed active metal oxides resulted in more adsorption or catalytic sites, thus improving catalytic activity [29,34]. Regarding 15%Er0.5Mn0.5/BAC, almost all surface areas were highly dispersed with metal oxides, with some agglomerating metal oxides and more agglomerates existing in 20%Er0.5Mn0.5/BAC. Consequently, the excess metal oxides destroyed some pre-existing pores due to more serious agglomerates [35,36]. This appearance also dovetailed with the frontal BET results. Furthermore, as revealed in Figure 3f, EDX was used to detect the rough element ratio of Er to Mn in 15%Er0.5Mn0.5/BAC. The Mn/Er atomic ratio in a particular morphology of 15%Er0.5Mn0.5/BAC was 0.93, which is almost equal to the theoretical Mn/Er atomic ratio in 15%Er0.5Mn0.5/BAC (Mn/Er = 1). The experiments demonstrated that Er and Mn were equally dispersed in 15%Er0.5Mn0.5/BAC and that ErOx was slightly more likely to agglomerate than MnOx. The TEM images of 15%Mn/BAC, 15%Er/BAC, and 15%Er0.5Mn0.5/BAC at 50 nm and 5 nm are revealed in Figure 3, where visible lattice fringes appeared on the crystal nanoparticles. Figure 3g reveals that the particle size of 15%Mn/BAC was approximately 20 nm, and three lattice stripes of 0.2730 nm, 0.4267 nm, and 0.3564 nm were detected, which can be attributed to the MnO (0 2 1) phase, MnO2 (1 1 1) phase, and Mn3O4 (3 1 1) phase, respectively [25]. The particle size of 15%Er/BAC shown in Figure 3h was approximately The TEM images of 15%Mn/BAC, 15%Er/BAC, and 15%Er 0.5 Mn 0.5 /BAC at 50 nm and 5 nm are revealed in Figure 3, where visible lattice fringes appeared on the crystal nanoparticles. Figure 3g reveals that the particle size of 15%Mn/BAC was approximately 20 nm, and three lattice stripes of 0.2730 nm, 0.4267 nm, and 0.3564 nm were detected, which can be attributed to the MnO (0 2 1) phase, MnO 2 (1 1 1) phase, and Mn 3 O 4 (3 1 1) phase, respectively [25]. The particle size of 15%Er/BAC shown in Figure 3h was approximately 27 nm, and a lattice fringe of 0.2961 nm was determined to belong to the Er 2 O 3 (2 2 2) phase. In addition, the particle size of 15%Er 0.5 Mn 0.5 /BAC shown in Figure 3i was approximately 19 nm, which was lesser than that of 15%Er/BAC and 15%Mn/BAC, hinting that the incorporation of Er reduced the crystallinity and particle sizes of Mn/BAC to a certain extent, as only one lattice fringe of 0.2877 nm corresponding to ErMnO 3 (1 1 3) phases was observed. Moreover, the absence of lattice streaks matching other metallic components also proved that the Er and Mn species existed as amorphous species [37]. The 5 nm and 50 nm TEM images clearly show that the Er and Mn species were highly decentralized in 15%Er 0.5 Mn 0.5 /BAC or emerged as amorphous species.

H 2 -TPR Analysis
The redox reactions of the primordial BAC and modified BACs were analyzed using H 2 -TPR. As elucidated in Figure 4, the two overlapping peaks occurred at approximately 652 • C and 718 • C in the primordial BAC, and the peak centered at 652 • C might be due to the reduction in adsorbed oxygen on the surface, while the latter could be attributed to the gasification of the BAC [37]. The peaks at these two positions in the other modified BAC samples were due to the same cause. An additional peak for 15%Er/BAC appeared at 538 • C, possibly as a result of Er 2 O 3 participating in the redox reactions with the transformation into metallic erbium [38]. In addition, the first peak for 15%Mn/BAC at 417 • C can be ascribed to the reduction of MnO 2 -Mn 2 O 3 /Mn 3 O 4 and the second peak at 505 • C to the succedent reduction of Mn 3 O 4 -MnO [39,40]. Furthermore, three extra peaks were observed for 15%Er 0.5 Mn 0.5 /BAC. The two peaks below 500 • C were interpreted as being associated with the concurrent reduction of MnO 2 /Mn 2 O 3 to Mn 3 O 4 and Er 2 O 3 to Er, while the peak at approximately 540 • C might be associated with the conversion of Mn 3 O 4 to MnO [41]. extent, as only one lattice fringe of 0.2877 nm corresponding to ErMnO3 (1 1 3) phases was observed. Moreover, the absence of lattice streaks matching other metallic components also proved that the Er and Mn species existed as amorphous species [37]. The 5 nm and 50 nm TEM images clearly show that the Er and Mn species were highly decentralized in 15%Er0.5Mn0.5/BAC or emerged as amorphous species.

H2-TPR Analysis
The redox reactions of the primordial BAC and modified BACs were analyzed using H2-TPR. As elucidated in Figure 4, the two overlapping peaks occurred at approximately 652 °C and 718 °C in the primordial BAC, and the peak centered at 652 °C might be due to the reduction in adsorbed oxygen on the surface, while the latter could be attributed to the gasification of the BAC [37]. The peaks at these two positions in the other modified BAC samples were due to the same cause. An additional peak for 15%Er/BAC appeared at 538 °C, possibly as a result of Er2O3 participating in the redox reactions with the transformation into metallic erbium [38]. In addition, the first peak for 15%Mn/BAC at 417 °C can be ascribed to the reduction of MnO2-Mn2O3/Mn3O4 and the second peak at 505 °C to the succedent reduction of Mn3O4-MnO [39,40]. Furthermore, three extra peaks were observed for 15%Er0.5Mn0.5/BAC. The two peaks below 500 °C were interpreted as being associated with the concurrent reduction of MnO2/Mn2O3 to Mn3O4 and Er2O3 to Er, while the peak at approximately 540 °C might be associated with the conversion of Mn3O4 to MnO [41]. It was shown that in comparison with 15%Er/BAC and 15%Mn/BAC, the corresponding two reduction peaks of 15%Er0.5Mn0.5/BAC were at lower temperatures and showcased better redox abilities [26,41]. This could be due to the following two reasons. A synergistic effect occurred between ErOx and MnOx, which might have led to structural deformation and surface oxygen defects, thus favoring catalytic oxidation reactions [42]. Second, the Mn 4+ /Mn 3+ and Er 3+ /Er pairs expedited one another to form more surface oxygen vacancies, significantly accelerating reactant activation or increasing oxygen mobility [30,43]. Moreover, studies indicate that the inclusion of Er could enhance the low-temperature redox It was shown that in comparison with 15%Er/BAC and 15%Mn/BAC, the corresponding two reduction peaks of 15%Er 0.5 Mn 0.5 /BAC were at lower temperatures and showcased better redox abilities [26,41]. This could be due to the following two reasons. A synergistic effect occurred between ErO x and MnO x , which might have led to structural deformation and surface oxygen defects, thus favoring catalytic oxidation reactions [42]. Second, the Mn 4+ /Mn 3+ and Er 3+ /Er pairs expedited one another to form more surface oxygen vacancies, significantly accelerating reactant activation or increasing oxygen mobility [30,43]. Moreover, studies indicate that the inclusion of Er could enhance the low-temperature redox capacity of a catalyst, which is consistent with the results of these experiments. Therefore, this could explain why 15%Er 0.5 Mn 0.5 /BAC possessed outstanding catalytic activity at a lower temperature range [26,44].

XRD Analysis
XRD measurements were performed to probe into the crystal structures and chemical compositions of the primordial BAC and modified BACs, with the results displayed in Figure 5. Regarding the primordial BAC, nine diffraction peaks at 2θ = 26.60 • , 28 [25,37,42]. Interestingly, the peaks belonging to C and SiO 2 receded or disappeared with the introduction of erbium oxides or manganese oxides, demonstrating that the external structures of the supports were violently changed via the loading of the active metal oxides [37]. Moreover, this phenomenon also indicated a strong interaction between these oxides and the supports [37,45] [47]. Since the radii of Er 3+ (0.881 Å) are close to those of Mn 4+ (0.60 Å) and Mn 3+ (0.66 Å), Er ions might dissolve in the MnO 2 lattice [48]. Significantly, in comparison with 15%Mn/BAC and 15%Er/BAC, the interrelated peaks delegating the interaction between Er and Mn were broader and weaker in 15%Er 0.5 Mn 0.5 /BAC, indicating that they favored the generation of fewer amorphous surface species, which could have increased the dispersion of the metal oxides and accelerated surface oxygen vacancies, improving the catalytic performance of the samples [43].
XRD measurements were performed to probe into the crystal structures and chemical compositions of the primordial BAC and modified BACs, with the results displayed in Figure 5. Regarding the primordial BAC, nine diffraction peaks at 2θ = 26.60°, 28 [25,37,42]. Interestingly, the peaks belonging to C and SiO2 receded or disappeared with the introduction of erbium oxides or manganese oxides, demonstrating that the external structures of the supports were violently changed via the loading of the active metal oxides [37]. Moreover, this phenomenon also indicated a strong interaction between these oxides and the supports [37,45]. Regarding 15%Er/BAC, five peaks at 2θ = 20.6°, 40.1°, 47.2°, 56.5°, and 59.4° belonged to Er2O3 [46]. As for 15%Mn/BAC, four peaks at 2θ = 40.55°, 59.84°, 69.50°, and 73.80° were clearly observed, in which the peaks at 2θ = 59.84° and 73.8° corresponded to Mn3O4, and the peak at 2θ = 40.55° indicated the presence of MnO, whereas the peak at 2θ = 69.5° was assigned to MnO2. This phenomenon might be because different Mn species coexisted in these samples, showing faultless crystalline structures and distinct diffraction peaks. However, unlike 15%Er/BAC and 15%Mn/BAC, several characteristic peaks appeared in XEr0.5Mn0.5/BACs at 2θ = 47.16°, which were similar to ErMnO3 [47]. Since the radii of Er 3+ (0.881 Å) are close to those of Mn 4+ (0.60 Å) and Mn 3+ (0.66 Å), Er ions might dissolve in the MnO2 lattice [48]. Significantly, in comparison with 15%Mn/BAC and 15%Er/BAC, the interrelated peaks delegating the interaction between Er and Mn were broader and weaker in 15%Er0.5Mn0.5/BAC, indicating that they favored the generation of fewer amorphous surface species, which could have increased the dispersion of the metal oxides and accelerated surface oxygen vacancies, improving the catalytic performance of the samples [43].

XPS Analysis
XPS analysis was carried out on the primordial BAC and modified BAC samples to obtain information on the valence states and chemical compositions of the relevant elements. Figure 6a exhibits the three sub-peaks of the O 1s XPS spectra in these samples, where the peaks with lower binding energy values at 528.2-528.7 eV corresponded to lattice oxygen (O α ) and the peaks at approximately 529.7-530.1 eV were due to faintly bonded oxygen or chemisorbed oxygen (O β ), while the peaks at approximately 530.9-531.7 eV resulted from adsorbed water species (O s ) [49,50]. The primordial BAC lacked O α , an oxygen reservoir, and the metal oxide modification favored O α formation, thus enhancing the catalytic activity [32]. According to the SEM analysis, the metal oxides covered the surfaces of the samples in the loading and calcination stages, blocking the pre-existing type of oxygen, which offers a possible explanation for its disappearance. In addition, O β exhibited extremely high reactivity and fluidity in the catalytic oxidation reaction, demonstrating the distinguished catalytic activity of removing HCHO [37,40]. Compared with the unsalted 15%Er 0.5 Mn 0.5 /BAC, the O s ratio of used 15%Er 0.5 Mn 0.5 /BAC increased from 16 [51]. Therefore, it can be inferred that more reactive oxygen species were conducive to accelerating the catalytic activity of HCHO removal.
enhancing the catalytic activity [32]. According to the SEM analysis, the metal oxides covered the surfaces of the samples in the loading and calcination stages, blocking the preexisting type of oxygen, which offers a possible explanation for its disappearance. In addition, Oβ exhibited extremely high reactivity and fluidity in the catalytic oxidation reaction, demonstrating the distinguished catalytic activity of removing HCHO [37,40]. Compared with the unsalted 15%Er0.5Mn0.5/BAC, the Os ratio of used 15%Er0.5Mn0.5/BAC increased from 16.46% to 38.26%, while that of Oα and Oβ of used 15%Er0.5Mn0.5/BAC decreased from 38.33% and 45.21% to 34.76% and 26.98%, respectively, demonstrating the participation of Oα and Oβ in the catalytic oxidation reactions [51]. Therefore, it can be inferred that more reactive oxygen species were conducive to accelerating the catalytic activity of HCHO removal.   Figure 6b showcases the five sub-peaks of the C 1s XPS spectra, among which the generated characteristic peaks located at 282.5-282.9 eV, 283.8-284.2 eV, 284.9-285.8 eV, 287.3-287.8 eV, and 289.6-290.8 eV were related to graphitic carbon, carbon existing in alcohol or phenolic, carbonyl groups, carboxyl, or ester groups, and π-π* transitions in aromatic rings, respectively [9,52]. In addition, the loading of metal oxides resulted in a boom in the ratio of COOH to C-C, which likely resulted from the impregnation of acetate or nitrate precursor solutions, where the decrease in C-O could be attributed to the desorption of chemisorbed oxygen via high-temperature calcination under the N 2 atmosphere [9] . In the modified BACs, the proportion of functional C-O groups decreased and the proportion of total-oxygen-containing functional groups heightened after the reactions, which was a possible outcome of the oxidation of C-O by reactive oxygen species during the removal of HCHO [53].
The Mn 2p XPS spectra are revealed in Figure 6c, and the main finding is that the three peaks were located at 638. 5 3+ , and Mn 4+ in fresh 15%Er 0.5 Mn 0.5 /BAC all increased to different degrees, signaling that the incorporation of ErO x could expedite the increase in the Mn valence state and proving that redox reactions occurred between ErO x and MnO x . High-valence Mn, such as Mn 4+ , participating in the redox cycle might help improve the catalytic activity of the sample and accelerate the removal of HCHO [55]. In addition, the proportions of Mn 4+ /Mn 3+ , Mn 4+ + Mn 3+ , and Mn 4+ demonstrated a decreasing trend after the reactions, suggesting that Mn in the high-price state changed to a low-price state during the reactions. Figure 6d shows the Er 4d XPS spectra, wherein three peaks could be observed at 167.1-168.3 eV, 169.1-171.2 eV, and 173.6-178.2 eV. The first peak corresponded to Er 4d5/2, indicating that Er existed in the modality of Er 2 O 3 and, thus, in the state of Er 3+ occurring at this time, while the last peak had a higher peak binding energy at 173.6-178.2 eV corresponding to Er 4d3/2, which could be a result of the Er metal oxides [38,56,57]. The peak in the middle indicated that the metal Er was first oxidized to Er 2+ , but because of the relatively unstable electronic configuration, it was rapidly oxidized to Er 3+ [56]. Therefore, these values demonstrate that Er was successfully loaded onto the BAC samples and participated in the catalytic oxidation reaction in the Er 3+ mode. Such binding energy values of Er 4d are consistent with those in perovskites [36]. All these phenomena testify that at least part of the Er 2 O 3 transformed into the perovskite-like structure of ErMnO 3 , which is consistent with the H 2 -TPR analysis. This suggests that the addition of ErO x could change the morphological structure of the catalyst.

Effect of Molar Ratio of Er/Mn
The performances of the 15%ErMn/BAC samples with diverse molar ratios of Er/Mn for HCHO elimination at 100-380 • C are listed in Figure 7. A roughly similar trend was observed in the E HCHO of these samples. The E HCHO first showed noticeable growth with the rise in the reaction temperature from 100 • C to 220 • C and subsequently behaved in a slight downward trend with the continuous enhancement of the reaction temperature at 220-380 • C. The former finding can be interpreted as the increase in the reaction temperature providing more kinetic energy and facilitating the chemical adsorption and oxidation of HCHO [58]. Meanwhile, the decline in the E HCHO at excessively high temperatures could be caused by various reasons, such as the high temperatures inhibiting the physical adsorption of HCHO [37,59]. Another reason was the destruction of the BAC structure at high temperatures. In addition, vibrant metal oxides could catalytically oxidize the carbon matrix into H 2 O and CO 2 [25]. Moreover, it was found that the E HCHO of 15%Er 0.5 Mn 0.5 /BAC engendered the most outstanding performance in the 100-380 • C temperature range when the molar ratio of Er/Mn was 1:1. This optimal performance could be connected with the strongest synergistic effect between the two metal oxides with an appropriate molar ratio of Er/Mn [60,61]. Ultimately, 15%Er 0.5 Mn 0.5 /BAC showed the most outstanding performance at 220 • C in these samples, and its E HCHO content was 97.2%. high temperatures. In addition, vibrant metal oxides could catalytically oxidize the carbon matrix into H2O and CO2 [25]. Moreover, it was found that the EHCHO of 15%Er0.5Mn0.5/BAC engendered the most outstanding performance in the 100-380 °C temperature range when the molar ratio of Er/Mn was 1:1. This optimal performance could be connected with the strongest synergistic effect between the two metal oxides with an appropriate molar ratio of Er/Mn [60,61]. Ultimately, 15%Er0.5Mn0.5/BAC showed the most outstanding performance at 220 °C in these samples, and its EHCHO content was 97.2%.

Effects of Support Materials
The support materials derived from diverse raw materials showed distinctive surface functional groups and intrinsic pore structures in different proportions of micropores, mesopores, and macropores, which directly influenced the mass transfer and pervasion of reactants and product molecules, thus playing an imperative role in the catalytic reactions [12,62]. Figure 8 showcases the effects of the support materials from diverse precursors on HCHO removal at an identical loading and molar ratio of metal oxides at 100-380 °C. Throughout the entire heating process, 15%Er0.5Mn0.5/BAC exhibited a better EHCHO than 15%Er0.5Mn0.5/SAC and 15%Er0.5Mn0.5/SAW, which could be theoretically ascribed to 15%Er0.5Mn0.5/BAC neutralizing 15%Er0.5Mn0.5/SAW and 15%Er0.5Mn0.5/SAC. It is conceivable that the hierarchical porous structure of 15%Er0.5Mn0.5/BAC well regulated the proportions of micropores, mesopores, and macropores via the BAC support, which was more conducive to the mass transfer and diffusion of reactant and offspring molecules [31]. In addition, the EHCHO of 15%Er0.5Mn0.5/BAC and 15%Er0.5Mn0.5/SAW presented a decreasing trend with the increase in the reaction temperature at 220 and 300 °C, and 15%Er0.5Mn0.5/BAC's EHCHO dropped lower than 15%Er0.5Mn0.5/SAW's at high temperatures. This may have been caused by high temperatures destroying the active centers and pore structures of BAC and SAW, and the thermal stability of BAC was higher than that of SAW [62,63]. In contrast, according to the BET analysis, 15%Er0.5Mn0.5/BAC possessed better physicochemical characteristics, which were conducive to the diffusion and mass transfer of gas reactants, and exhibited the best HCHO abatement performance across the entire temperature range.

Effects of Support Materials
The support materials derived from diverse raw materials showed distinctive surface functional groups and intrinsic pore structures in different proportions of micropores, mesopores, and macropores, which directly influenced the mass transfer and pervasion of reactants and product molecules, thus playing an imperative role in the catalytic reactions [12,62]. Figure 8 showcases the effects of the support materials from diverse precursors on HCHO removal at an identical loading and molar ratio of metal oxides at 100-380 • C. Throughout the entire heating process, 15%Er 0.5 Mn 0.5 /BAC exhibited a better E HCHO than 15%Er 0.5 Mn 0.5 /SAC and 15%Er 0.5 Mn 0.5 /SAW, which could be theoretically ascribed to 15%Er 0.5 Mn 0.5 /BAC neutralizing 15%Er 0.5 Mn 0.5 /SAW and 15%Er 0.5 Mn 0.5 /SAC. It is conceivable that the hierarchical porous structure of 15%Er 0.5 Mn 0.5 /BAC well regulated the proportions of micropores, mesopores, and macropores via the BAC support, which was more conducive to the mass transfer and diffusion of reactant and offspring molecules [31]. In addition, the E HCHO of 15%Er 0.5 Mn 0.5 /BAC and 15%Er 0.5 Mn 0.5 /SAW presented a decreasing trend with the increase in the reaction temperature at 220 and 300 • C, and 15%Er 0.5 Mn 0.5 /BAC's E HCHO dropped lower than 15%Er 0.5 Mn 0.5 /SAW's at high temperatures. This may have been caused by high temperatures destroying the active centers and pore structures of BAC and SAW, and the thermal stability of BAC was higher than that of SAW [62,63]. In contrast, according to the BET analysis, 15%Er 0.5 Mn 0.5 /BAC possessed better physicochemical characteristics, which were conducive to the diffusion and mass transfer of gas reactants, and exhibited the best HCHO abatement performance across the entire temperature range.

Effects of Active Ingredients
The active ingredients and their loading values exerted important effects on the dispersion, aggregation, crystallization, and redox properties of the correlative metal oxides, which were closely related to the catalytic activities of the samples [39]. Figure 9a displays the effects of various ingredients on HCHO elimination in the primordial BAC and bimetallic-modified BAC samples with different loading values. It can be seen that the E HCHO of the modified BAC samples first showed a significant upward trend with the increase in the loading value and then exhibited a slight downward trend with the excessive loading of metal oxides. The former could be attributed to the uniform dispersion of the loaded metal oxides on the sample surfaces, providing a large number of adsorption or catalytic active sites, while the latter might be due to the more severe agglomeration caused by excess metal oxides, thus hiding voids and adsorption or catalytic activity sites. In addition, the E HCHO of XEr 0.5 Mn 0.5 /BACs increased continuously until the temperature reached 220 • C and dropped slightly as the reaction temperature increased further. 15%Er 0.5 Mn 0.5 /BAC showed the highest catalytic activity of 97.2% at 220 • C and consistently demonstrated the best performance throughout the phase, which was likely a consequence of the better dispersion of the Er and Mn oxides, more oxygen vacancies, and the preeminent properties of the prepared sample. The SEM results also confirmed the superior physical and chemical properties of 15%Er 0.5 Mn 0.5 /BAC. Considering the metal oxide loading value as a significant influencing factor for HCHO removal, 15%Er 0.5 Mn 0.5 /BAC was selected for a follow-up study in this work.

Effects of Active Ingredients
The active ingredients and their loading values exerted important effects on the dispersion, aggregation, crystallization, and redox properties of the correlative metal oxides, which were closely related to the catalytic activities of the samples [39]. Figure 9a displays the effects of various ingredients on HCHO elimination in the primordial BAC and bimetallic-modified BAC samples with different loading values. It can be seen that the EHCHO of the modified BAC samples first showed a significant upward trend with the increase in the loading value and then exhibited a slight downward trend with the excessive loading of metal oxides. The former could be attributed to the uniform dispersion of the loaded metal oxides on the sample surfaces, providing a large number of adsorption or catalytic active sites, while the latter might be due to the more severe agglomeration caused by excess metal oxides, thus hiding voids and adsorption or catalytic activity sites. In addition, the EHCHO of XEr0.5Mn0.5/BACs increased continuously until the temperature reached 220 °C and dropped slightly as the reaction temperature increased further. 15%Er0.5Mn0.5/BAC showed the highest catalytic activity of 97.2% at 220 °C and consistently demonstrated the best performance throughout the phase, which was likely a consequence of the better dispersion of the Er and Mn oxides, more oxygen vacancies, and the preeminent properties of the prepared sample. The SEM results also confirmed the superior physical and chemical properties of 15%Er0.5Mn0.5/BAC. Considering the metal oxide loading value as a significant influencing factor for HCHO removal, 15%Er0.5Mn0.5/BAC was selected for a follow-up study in this work. As illustrated in Figure 9b, the E HCHO of the Er-or Mn-modified samples demonstrated significant improvement compared with the primordial BAC. It was observed that the metal oxide loading greatly facilitated HCHO removal. 15%Er 0.5 Mn 0.5 /BAC demonstrated superior performance and a wider effective temperature range than that of single-loading samples. The synergistic effect of the bimetallic oxides was the main factor behind the enhancement in the bimetallic oxides' dispersity, the number of oxygen vacancies, surface active substances, and the redox ability [39,64].
It was clear that the reaction temperature was a key factor in the catalytic reactions for a given catalyst, and the corresponding active temperature range always behaved similarly. Before this, the catalytic activity was proportional to the temperature rise due to an increase in the catalytic activation energy [17]. There might be several reasons why the E HCHO decreased at high temperatures. Firstly, high temperatures can hamper the adsorption of reactant molecules [65]. Secondly, the catalytic oxidation of the carbon matrix by metal oxides leads to the structural destruction of the BAC [34,66].

Effect of O 2
As an indispensable gas component in the actual flue gas, O 2 significantly influenced the conversion of reactive oxygen species associated with the catalytic oxidation procedures of HCHO [12,32]. Figure 10 displays the influences of O 2 concentrations on HCHO elimination in 15%Er 0.5 Mn 0.5 /BAC at 220 • C. It was recognized that oxygen deficiency might impact the catalytic properties of the samples. Nevertheless, with a short supply of oxygen, 15%Er 0.5 Mn 0.5 /BAC performed relatively well in terms of the E HCHO due to the pre-existing lattice oxygen and chemisorbed oxygen both participating in the catalytic oxidation of HCHO [32,37]. XPS analysis demonstrated that residual O α and O β were on the surface of 15%Er 0.5 Mn 0.5 /BAC in a dearth of oxygen, which played a role in the catalytic oxidation of HCHO. Moreover, the E HCHO significantly increased when the oxygen content was raised to 3%, but the variation in the E HCHO was almost negligible as the O 2 concentration increased further. Ample gaseous oxygen to supplement the consumed O α and O β was essential for achieving an efficient HCHO removal performance [32,67]. Meanwhile, the oxygen vacancy and lattice defects on the surface of 15%Er 0.5 Mn 0.5 /BAC were conducive to the capture and transmission of O 2 , thus further facilitating HCHO removal [68,69]. The above phenomenon demonstrated that only 3% oxygen could result in a significant enhancement in HCHO removal, and the oxygen content in the industrial flue gas was generally greater than that, thus well fulfilling this requirement. As illustrated in Figure 9b, the EHCHO of the Er-or Mn-modified samples demonstrated significant improvement compared with the primordial BAC. It was observed that the metal oxide loading greatly facilitated HCHO removal. 15%Er0.5Mn0.5/BAC demonstrated superior performance and a wider effective temperature range than that of singleloading samples. The synergistic effect of the bimetallic oxides was the main factor behind the enhancement in the bimetallic oxides' dispersity, the number of oxygen vacancies, surface active substances, and the redox ability [39,64].
It was clear that the reaction temperature was a key factor in the catalytic reactions for a given catalyst, and the corresponding active temperature range always behaved similarly. Before this, the catalytic activity was proportional to the temperature rise due to an increase in the catalytic activation energy [17]. There might be several reasons why the EHCHO decreased at high temperatures. Firstly, high temperatures can hamper the adsorption of reactant molecules [65]. Secondly, the catalytic oxidation of the carbon matrix by metal oxides leads to the structural destruction of the BAC [34,66].

Effect of O2
As an indispensable gas component in the actual flue gas, O2 significantly influenced the conversion of reactive oxygen species associated with the catalytic oxidation procedures of HCHO [12,32]. Figure 10 displays the influences of O2 concentrations on HCHO elimination in 15%Er0.5Mn0.5/BAC at 220 °C. It was recognized that oxygen deficiency might impact the catalytic properties of the samples. Nevertheless, with a short supply of oxygen, 15%Er0.5Mn0.5/BAC performed relatively well in terms of the EHCHO due to the preexisting lattice oxygen and chemisorbed oxygen both participating in the catalytic oxidation of HCHO [32,37]. XPS analysis demonstrated that residual Oα and Oβ were on the surface of 15%Er0.5Mn0.5/BAC in a dearth of oxygen, which played a role in the catalytic

Effects of SO2 and H2O
The influences of SO2 and H2O on HCHO removal in 15%Er0.5Mn0.5/BAC are shown

Effects of SO 2 and H 2 O
The influences of SO 2 and H 2 O on HCHO removal in 15%Er 0.5 Mn 0.5 /BAC are shown in Figure 11. In most cases, SO 2 acted as an inhibitor in the removal of HCHO [42]. Compared with the pure SFG, the E HCHO demonstrated a significant downward trend when 300 ppm SO 2 was added, but this trend gently slowed down when the SO 2 increased to 600 and 900 ppm. The former trend can be interpreted in two ways: the first is that SO 2 might compete with HCHO or O 2 for limited adsorption/catalytic active sites, and the second is that SO 2 could readily react with metal oxides in the sample to form metal sulfates, which might cover the surface active sites or block the pores, as demonstrated by in situ DRIFTS [70,71]. The latter trend may be because the introduction of ErO x or MnO x could undermine the adsorption intensity of SO 2 on the sample surface, offsetting the inhibitory effect of SO 2 [31]. Likewise, H 2 O (g) also had a slight inhibitory effect on the E HCHO . Increasing H 2 O by 8% in the SFG reduced the E HCHO from 92.4% to 90.8%, indicating that 15%Er 0.5 Mn 0.5 /BAC possessed excellent H 2 O resistance resulting from the strong interaction between ErO x and MnO x and the hydrophobicity of BAC [72]. Equally, the inhibitory effect of H 2 O might be due to the competitive adsorption of the active sites between HCHO and H 2 O [73]. The combined additions of SO 2 and H 2 O exerted a greater passive effect on the E HCHO than the single addition of SO 2 or H 2 O. Nevertheless, under the action of SFG + 600 ppmSO 2 + 8%H 2 O, the E HCHO of 15%Er 0.5 Mn 0.5 /BAC only decreased by 4.5% from 92.4% to 87.9%, elucidating its excellent anti-SO 2 /H 2 O performance, which was possibly a result of the positive effect of gaseous H 2 O on HCHO potentially related to the active catalytic sites of HCHO [32]. Therefore, it was predicted that 15%Er 0.5 Mn 0.5 /BAC displayed exceptional SO 2 and H 2 O resistance in the practical flue gas component. The test results of the stability and selectivity of the 15%Er0.5Mn0.5/BAC catalyst for HCHO removal are presented in Figure 12. Under SFG conditions, the stability test of 15%Er0.5Mn0.5/BAC persisted for 30 h, while the EHCHO decreased from 96.6% to 93.9% in the first 6 h and then remained at approximately 93%. Adding 8%H2O or 300 ppm SO2 to the SFG also degraded the EHCHO to almost an identical extent, and their combination amplified this negative trend, which was consistent with the previous performance test analyses. The SC also exhibited an identical trend, albeit slightly stronger than that of the EHCHO, but the addition of both 8% H2O and 300 ppm SO2 impeded their conversion. Some intermediates, such as DOM and formate, were produced during the removal of HCHO, which was coherent with the results of the subsequent in situ DRIFTS. Eventually, under SFG + 8%H2O and 300 ppmSO2, the EHCHO and SC of 15%Er0.5Mn0.5/BAC were maintained at approximately 85% and 90%, demonstrating distinguished stability and selectivity. The test results of the stability and selectivity of the 15%Er 0.5 Mn 0.5 /BAC catalyst for HCHO removal are presented in Figure 12. Under SFG conditions, the stability test of 15%Er 0.5 Mn 0.5 /BAC persisted for 30 h, while the E HCHO decreased from 96.6% to 93.9% in the first 6 h and then remained at approximately 93%. Adding 8%H 2 O or 300 ppm SO 2 to the SFG also degraded the E HCHO to almost an identical extent, and their combination amplified this negative trend, which was consistent with the previous performance test analyses. The S C also exhibited an identical trend, albeit slightly stronger than that of the E HCHO , but the addition of both 8% H 2 O and 300 ppm SO 2 impeded their conversion. Some intermediates, such as DOM and formate, were produced during the removal of HCHO, which was coherent with the results of the subsequent in situ DRIFTS. Eventually, under SFG + 8%H 2 O and 300 ppmSO 2 , the E HCHO and S C of 15%Er 0.5 Mn 0.5 /BAC were maintained at approximately 85% and 90%, demonstrating distinguished stability and selectivity.
HCHO removal are presented in Figure 12. Under SFG conditions, the stability test of 15%Er0.5Mn0.5/BAC persisted for 30 h, while the EHCHO decreased from 96.6% to 93.9% in the first 6 h and then remained at approximately 93%. Adding 8%H2O or 300 ppm SO2 to the SFG also degraded the EHCHO to almost an identical extent, and their combination amplified this negative trend, which was consistent with the previous performance test analyses. The SC also exhibited an identical trend, albeit slightly stronger than that of the EHCHO, but the addition of both 8% H2O and 300 ppm SO2 impeded their conversion. Some intermediates, such as DOM and formate, were produced during the removal of HCHO, which was coherent with the results of the subsequent in situ DRIFTS. Eventually, under SFG + 8%H2O and 300 ppmSO2, the EHCHO and SC of 15%Er0.5Mn0.5/BAC were maintained at approximately 85% and 90%, demonstrating distinguished stability and selectivity.

Intermediates and Mechanism
As reflected in Figure 13, the HCHO reaction processes in the Er 0.5 Mn 0.5 /BAC catalyst at 90 min under different test conditions were studied using in situ DRIFTS spectra. The peak associated with molecularly adsorbed HCHO occurred at 1142 cm −1 within 10 min after introducing 200 ppm HCHO + 6%O 2 /N 2 [74]. In addition, the peak's intensity increased with the reaction time before decreasing slightly after 30 min. The ω(CH 2 ), ν(CH 2 ), and ν(C-O) of dioxymethylenes were reflected in bands located at 1061, 1014, and 809 cm −1 , respectively [74,75]. Following previous studies, it was documented that HCHO was first adsorbed on the sample surface by molecules and then fleetly oxidized into DOM by carbonyl electrophilic carbon combined with nucleophilic surface oxygen [76]. After 10 min, DOM bands were detected and increased with time, showing that the catalytic oxidation reaction of HCHO was still occurring. The paraformaldehyde (POM) produced by the adsorption corresponding to the peak value of 937 cm −1 was also rapidly accumulating and continuously generating DOM [75,76]. The amount of DOM reached a stable value as the production of DOM, and its further conversion attained a dynamic equilibrium at 40 min. Moreover, the slight adsorption bands at 1460 and 1385 cm −1 could be attributed to the ν as (COO − ) and ν s (COO − ) of formate species, while the ν as (CH) and ν s (CH) of formate species appeared at 2943 and 2825 cm −1 [77,78]. Previous studies have suggested that formates are often adsorbed on the surfaces of catalysts in three frameworks: monodentate, bridging, and bidentate (chelating), which are distinguishable by the frequency of spacings between ν s (COO − ) and v as (COO − ) [32]. The reduced intensity of the bands in the formate species indicated that the depletion of the formate species was expedited, and DOM oxidation was inhibited until equilibrium was reached after 40 min of the reaction proceeding. The peaks at 1656 cm −1 and 2334-2363 cm −1 were related to the formate species' oxidation reactions and conversion to H 2 O and CO 2 [41,77,79]. After 10 min of reaction, it was observed that the absorption of CO 2 reached the maximum value before fluctuating and decreasing. The former might have been caused by the rapid catalytic oxidation reaction of HCHO, while the latter was ascribed to the formation of POM blocking the adsorbed active sites, leading to the desorption of CO 2 in the catalyst [76]. The negative bands at 3484 cm −1 and 3690 cm −1 were generated by the depletion of hydroxyl(-OH) on the surface, and the adsorption of activated H 2 O molecules was continuously replenished by reactive oxygen species [79,80]. The peak at 685 cm −1 was attributed to the formation of metallic oxygen bands between Mn or Er ions and carboxyl(COO-), indicating that ErO x and MnO x could serve as active sites during the removal of HCHO [37]. The feasible reaction mechanisms of HCHO removal in 15%Er0.5Mn0.5/BAC were speculated following the characterization analyses and experimental results shown above. It was confirmed that the mechanism of the catalytic oxidation of HCHO by carbon materials supported with metal oxide catalysts followed the Mars-van Krevelen (MVK) mechanism [60]. In this study, catalytic oxidation gradually predominated over adsorption for HCHO removal with the increment in the reaction temperature and time, and the oxidation of HCHO was mainly attributed to the surface reactive oxygen species, including chemisorbed oxygen and lattice oxygen and free radicals on the surfaces of the catalysts, which were expressed as Oγ and OH, respectively. As reflected in Figure 14, HCHO was instantaneously captured by hydroxyl groups and other active sites on the surface of 15%Er0.5Mn0.5/BAC. In addition, combined with the results of DRIFTS and other characterization analyses, it was determined that the main gaseous products came from carbonate species and formate intermediates in the HCHO removal process. The latter's production was ascribed to the reaction of surface reactive oxygen species and HCHO to generate DOM, which, in turn, was rapidly oxidized to form formate species. The former's production can be explained by the loss of hydrogen bonds in the formic acid intermediate, further oxidized by the active hydroxyl group to unstable H2CO3, before being converted to CO2 and H2O (Equations (6)- (11)). The subsequent adsorption of HCHO or O2 was favorable toward H2O desorption, thus starting a new cycle of HCHO oxidation [81,82]. Throughout the reaction processes, gaseous O2 and H2O continuously replenished depleted reactive oxygen species while the redox cycle of Er 3+ /Er 2+ and Mn 4+ /Mn 3+ /Mn 2+ The feasible reaction mechanisms of HCHO removal in 15%Er 0.5 Mn 0.5 /BAC were speculated following the characterization analyses and experimental results shown above. It was confirmed that the mechanism of the catalytic oxidation of HCHO by carbon materials supported with metal oxide catalysts followed the Mars-van Krevelen (MVK) mechanism [60]. In this study, catalytic oxidation gradually predominated over adsorption for HCHO removal with the increment in the reaction temperature and time, and the oxidation of HCHO was mainly attributed to the surface reactive oxygen species, including chemisorbed oxygen and lattice oxygen and free radicals on the surfaces of the catalysts, which were expressed as O γ and OH, respectively. As reflected in Figure 14, HCHO was instantaneously captured by hydroxyl groups and other active sites on the surface of 15%Er 0.5 Mn 0.5 /BAC. In addition, combined with the results of DRIFTS and other characterization analyses, it was determined that the main gaseous products came from carbonate species and formate intermediates in the HCHO removal process. The latter's production was ascribed to the reaction of surface reactive oxygen species and HCHO to generate DOM, which, in turn, was rapidly oxidized to form formate species. The former's production can be explained by the loss of hydrogen bonds in the formic acid intermediate, further oxidized by the active hydroxyl group to unstable H 2 CO 3 , before being converted to CO 2 and H 2 O (Equations (6)- (11) [25,38]. The introduction of Er species increased the catalytic activity and changed the morphological structures of the catalysts, which was suitable for the TEM and H 2 -TPR results. In particular, the hierarchical porous structure of the BAC carrier with suitable ratios of micropores, mesopores, and macropores boosted the reaction paths, which not only furnished abundant surface functional groups but also facilitated the diffusion and mass transfer of reactants and products, thus improving the catalytic oxidation ability of HCHO. In summary, the specific pathways of removing HCHO by 15%Er 0.5 Mn 0.5 /BAC can be determined as follows. carrier with suitable ratios of micropores, mesopores, and macropores boosted the reaction paths, which not only furnished abundant surface functional groups but also facilitated the diffusion and mass transfer of reactants and products, thus improving the catalytic oxidation ability of HCHO. In summary, the specific pathways of removing HCHO by 15%Er0.5Mn0.5/BAC can be determined as follows.

DFT Calculation Method
To further clarify the mechanism and reaction process of the catalytic oxidation of HCHO in 15%Er 0.5 Mn 0.5 /BAC, current first principle DFT calculations were carried out using the Vienna Ab initio Simulation Package (VASP) with the projector augmented wave (PAW) method [83]. The commutative functional was treated employing the generalized gradient approximation (GGA) of the Perdew-Burke-Ernzerhof (PBE) functional. All calculations were conducted with spin polarizations. The energy cut-off value of the plane wave base expansion was set to 450 eV, and the force on each atom was less than 0.03 eV/Å, which was utilized as the convergence criterion of geometric relaxation. A 2 × 2 × 1 grid was used to sample k points in the Brillouin region. A convergence energy threshold of 10 −5 eV was adopted in the self-consistent calculations. The DFT-D3 method was utilized to take into account the van der Waals interaction [84]. A 15 Å vacuum was joined in the z direction to prevent the interaction from periodic structures.
The free energies were calculated using the following formula: ∆G = ∆E DFT + ∆E ZPE − T∆S, where ∆E DFT is the DFT electronic energy difference at each step, ∆E ZPE and ∆ S are the correction of zero-point energy and the change in entropy, respectively, acquired via vibration analysis, and T is the temperature (T = 300 K) [85].

HCHO Oxidation Reaction Path Diagram of MnO 2 and Er-MnO 2
To prove that Er doping contributed to the HCHO catalytic oxidation reaction and its mechanism, Figure 15 shows the reaction path and configuration of MnO 2−x (1 1 1) and Er-MnO 2−x (1 1 3) in the catalytic oxidation of HCHO, in which the structure and shape of each intermediate for the HCHO conversion to CO 2 and H 2 O are observed. In addition, the formaldehyde oxidation reaction paths of the Er-MnO 2 and MnO 2 structures were calculated, as shown in Figure 16. It can be seen that the MnO 2 structure was stronger than the Er-MnO 2 structure in the first step of formaldehyde adsorption activation, with an adsorption-free energy of −2.08 eV, while that of the Er-MnO 2 structure was only −0.53 eV. After a series of calculations, it was found that the rate determination step of the MnO 2 structure reaction was a CH 2 O 2 *→CO 2 * transfer step, and the rate determination step energy barrier was 0.95 eV, while the decisive step of the Er-MnO 2 structure reaction was an HCOO*→CO 2 * step, and the energy barrier of the decisive step was 0.80 eV. The reduction in the energy barrier of the decisive step indicates that the Er-MnO 2 structure promoted the formaldehyde oxidation process. This result is consistent with the in situ DRIFTS, and the incorporation of Er promoted the catalytic oxidation of HCHO to a certain extent.

Conclusions
A series of ErOx-boosted MnOx-modified biochars derived from rice straw and sewage sludge (EryMn1-y/BACs) were prepared using the facile ultrasonic-assisted impregnation method, and their HCHO removal activities were subsequently tested. The optimal 15%Er0.5Mn0.5/BAC displayed a 97.2% HCHO removal efficiency at 220 °C and excellent stability throughout the circulation experiment. The removal mechanism of HCHO in 15%Er0.5Mn0.5/BAC was systematically studied using BET, H2-TPR, SEM, TEM, XRD, in situ DRIFTS, XPS, and density-functional theory (DFT). The effects of O2, SO2, and H2O on HCHO removal in 15%Er0.5Mn0.5/BAC were tested, and the curbed influences of H2O and SO2 offset the boosting effect of O2 within a certain range. Er-Mn bimetallic-modified BAC offered a superior HCHO removal performance than that of Er-or Mn-boosted BAC, owing to the synergistic effect of ErOx and MnOx conducive to improving the samples' total pore volumes and surface areas, the surface active oxygen species, the promotion of redox ability, and the inhibition of the crystallization of MnOx. Moreover, the support's hierarchical porous structure not only expedited the diffusion and mass transfer of reactants and their products but also elevated the approachability of adsorption and catalytic sites. Notably, these prominent features were partly responsible for the outstanding performance and excellent tolerance to H2O and SO2. In situ DRIFTS showed the appearance of CO2 and H2O during the oxidation of HCHO to DOM and formate intermediates. The DFT calculations proved the removal process of HCHO and the strengthening effect of Er doping. Finally, this work provides direction and guidance for the future development of outstanding biochars-based catalysts for HCHO removal.

Conclusions
A series of ErO x -boosted MnO x -modified biochars derived from rice straw and sewage sludge (Er y Mn 1-y /BACs) were prepared using the facile ultrasonic-assisted impregnation method, and their HCHO removal activities were subsequently tested. The optimal 15%Er 0.5 Mn 0.5 /BAC displayed a 97.2% HCHO removal efficiency at 220 • C and excellent stability throughout the circulation experiment. The removal mechanism of HCHO in 15%Er 0.5 Mn 0.5 /BAC was systematically studied using BET, H 2 -TPR, SEM, TEM, XRD, in situ DRIFTS, XPS, and density-functional theory (DFT). The effects of O 2 , SO 2 , and H 2 O on HCHO removal in 15%Er 0.5 Mn 0.5 /BAC were tested, and the curbed influences of H 2 O and SO 2 offset the boosting effect of O 2 within a certain range. Er-Mn bimetallic-modified BAC offered a superior HCHO removal performance than that of Er-or Mn-boosted BAC, owing to the synergistic effect of ErO x and MnO x conducive to improving the samples' total pore volumes and surface areas, the surface active oxygen species, the promotion of redox ability, and the inhibition of the crystallization of MnO x . Moreover, the support's hierarchical porous structure not only expedited the diffusion and mass transfer of reactants and their products but also elevated the approachability of adsorption and catalytic sites. Notably, these prominent features were partly responsible for the outstanding performance and excellent tolerance to H 2 O and SO 2 . In situ DRIFTS showed the appearance of CO 2 and H 2 O during the oxidation of HCHO to DOM and formate intermediates. The DFT calculations proved the removal process of HCHO and the strengthening effect of Er doping. Finally, this work provides direction and guidance for the future development of outstanding biochars-based catalysts for HCHO removal.