Efficient Removal of Siloxane from Biogas by Using β-Cyclodextrin-Modified Reduced Graphene Oxide Aerogels

In this study, β-cyclodextrin-modified reduced graphene oxide aerogels (β-CD-rGOAs) were synthesized via a one-step hydrothermal method and were used to remove hexamethyldisiloxane (L2) from biogas. The β-CD-rGOAs were characterized by the Brunner–Emmet–Teller technique, using Fourier-transform infrared spectroscopy, Raman spectrometry, scanning electron microscopy (SEM), contact angle measurements, and X-ray diffraction. The results of the characterizations indicate that β-CD was grafted onto the surface of rGOAs as a cross-linking modifier. The β-CD-rGOA had a three-dimensional, cross-linked porous structure. The maximum breakthrough adsorption capacity of L2 on β-CD-rGOA at 273 K was 111.8 mg g−1. A low inlet concentration and bed temperature facilitated the adsorption of L2. Moreover, the β-CD-rGOA was regenerated by annealing at 80 °C, which renders this a promising material for removing L2 from biogas.


Introduction
Biogas is an increasingly important renewable energy resource that is produced by the digestion of organic materials from sewage treatment plants and waste disposal sites; biogas is comprised primarily of methane (50-70%, v/v), one of the most widely used energy resources [1,2]. Apart from methane, the other main compound in biogas is CO 2 (30% to 50%, v/v), followed by other gases under 2% (e.g., oxygen, nitrogen, hydrogen sulfide, and siloxanes) [3,4]. Among these trace gases, siloxanes have the strongest adverse effect on the utilization of biogas due to the conversion of siloxanes into silicates and microcrystalline quartz during combustion [3], which contributes to abrasion of the inner surfaces of the combustion engine [5,6]. Therefore, the removal of siloxanes must be taken into consideration before biogas applications.
To date, several methods have been developed for removing siloxanes from biogas, including adsorption, absorption, deep chilling, biological treatment, and membrane separation [7][8][9][10]. Among these methods, deep chilling exhibits high removal efficiency and has been applied on an industrial scale; however, this method is too expensive to accept [11]. During absorption, the use of strong acids such as H 2 SO 4 or HNO 3 presents many disadvantages, including the corrosion of the equipment, by-and co-product generation, and a negative impact on health and the environment [12]. Regarding biodegradation, the removal efficiency is low, and long processing times are required [13]. Nevertheless, membrane separation is not considered to be a competitive treatment due to the selectivity

Chemicals and Reagents
β-cyclodextrin (β-CD, C42H70O35, Mw 1135 g mol −1 , ρ 1.614 g cm −3 , 99.0% purity, solid As reported herein, a β-CD-rGOA with a 3D structure was synthesized by using IGGO as a raw material via a one-step hydrothermal method. The resultant β-CD-rGOA was thoroughly characterized to determine the possible adsorption mechanism. Subsequently, to investigate the optimal adsorption performance of β-CD-rGOA for removing hexamethyldisiloxane (L2), batch experiments were designed, including the influence of the β-CD dosage, L2 inlet concentration, and bed temperature. Moreover, regeneration experiments were applied to evaluate the recyclability of β-CD-rGOA. The results indicate that β-CD-rGOA is highly promising in removing siloxanes from biogas.

Characterization
The morphology of the as-synthesized materials was characterized via scanning electron microscopy (SEM, S-4800, Hitachi, Tokyo, Japan) and with a Raman spectrometer (Renishaw, NewMills, UK). Transmission electron microscopy (TEM, H-7650, Hitachi, Tokyo, Japan) was used to characterize the fine structure of the materials. The X-ray diffraction (XRD, Bruker AXS, Karlsruhe, Germany) patterns were used to analyze the structural characteristics of the samples with a D8 ADVANCE X-ray source (Bruker AXS, Munich, Germany). The functional group composition was confirmed by Fourier-transform infrared (FTIR, Bruker Optics Co., Karlsruhe, Germany) spectroscopy from 400 to 4000 cm −1 with a Tensor 27 spectrometer (Bruker AXS, Karlsruhe, Germany). The N 2 adsorptiondesorption isotherms were measured with an aperture and specific surface area analyzer (Kubo × 1000, Beijing Builder Co., Ltd., Beijing, China) at 77 K and 10 −5 < P/P 0 < 1.0. The Brunner-Emmet-Teller (BET, Beijing Builder Co., Ltd., Beijing, China) specific surface areas (S BET ) were obtained, and the Barrett-Joyner-Halenda method was used to calculate the average pore size (D aver ) and total pore volume (V tot ). The water contact angle was investigated, to determine the hydrophobicity of the samples, with a contact angle/interface system (JY-PHb, Jinhe Instrument Manufacturing Co., Ltd., Nanjing, China). Gas chromatography with a hydrogen flame ionization detector (GC 9790, Fuli Analytical Instrument Co., Ltd., Wenling City, China) was used to observe the L2 concentration with a GDX-102 stationary-phase column (2.0 m long × 2.0 mm inner diameter). The detecting Nanomaterials 2022, 12, 2643 4 of 14 conditions were as follows: oven temperature, 200 • C, injector temperature, 250 • C, and detector temperature, 280 • C.

Adsorption and Regeneration
The L2 dynamic adsorption performance onto the adsorbents was evaluated based on a previous study [34]. The relevant parameters were as follows: L2 inlet concentration (C in ), 14.62 mg L −1 , gas flow rate (V g ), 50 mL min −1 (superficial velocity of 100 cm min −1 , cross-sectional area of 0.5 cm 2 ), and temperature (T), 20 • C. When the L2 outlet concentration (C out,t ) equaled C in , the adsorption reached saturation. The association between C out,t /C in and time (t) was used to express breakthrough curves that were used to describe the dynamic adsorption performance. Usually, the adsorption behavior was evaluated by the following two quantities: breakthrough time (t B , min) and breakthrough adsorption quantity (Q B , mg g −1 ). The breakthrough time was defined as the time in which C out,t /C in = 0.05, and Q B as the adsorption quantity was when the adsorption time was t B .
The adsorption capacity (Q t ), corresponding to t, was evaluated with Equation (1) [35]: where C in and C out,t are the inlet concentration (mg L −1 ) and outlet concentration (mg L −1 ) at adsorption time t (min), m (g) is the mass of adsorbent, and V g (L min −1 ) is the gas flow rate. By substituting C out,t /C in = 0.05 in Equation (1), Q B is obtained. When the β-CD-rGOAs were saturated with L2, the regeneration of the used β-CD-rGOAs was performed in a water bath at 80 • C under blowing nitrogen for 30 min. This adsorption-desorption was repeated 10× to evaluate the regenerative performance of the β-CD-rGOAs. The continuous adsorption-desorption cycle was repeated for the first 5 times, and an adsorption-desorption cycle was repeated daily for the next 5 times.

Mathematical Models
The Yoon-Nelson model was selected to predict the theoretical breakthrough adsorption capacity (Q B,th , mg g −1 ) and the theoretical breakthrough time (t B,th , min) and to better understand adsorption phenomena of L2 in the β-CD-rGOAs. The model is represented by Equation (2) [36]: where K YN is the Yoon-Nelson constant of the model, t is the adsorption time (min), and τ is the time when the ratio C out,t /C in = 0.5.
The model values (K YN and τ) of various adsorption experiments were obtained through simulation using Equation (2). The t B,th was obtained by the Equation (2) when the C out,t /C in ratio was 0.05.
Hence, substituting Equation (2) in Equation (1), the Q B,th at t B,th can be calculated. Figure S1 shows digital photos of β-CD-rGOHs and β-CD-rGOAs. After hydrothermal reduction, the hydrogels were prepared, indicating that reduction-induced self-assembly facilitated the formation of hydrogels. Figure 2 shows the nitrogen adsorption/desorption isotherms and the pore size distributions of IGGO, rGOA, and β-CD-rGOA-0.5. In accordance with the IUPAC classification, β-CD-rGOA-0.5 demonstrated the features of type IV isotherms with H3 hysteresis loops, which is indicative of a mesoporous structure [37]. Alternatively, IGGO and rGOA followed a type III isotherm with a macroporous or nonporous material and low BET surface area. Table 1 shows the textural parameters of IGGO and β-CD-rGOAs. The BET analysis indicates that the specific surface areas of IGGO, rGOA, β-CD-rGOA-0.25, β-CD-rGOA-0.5, and β-CD-rGOA-1 were 7.4, 55.2, 59.3, 163.5, and 112.3 m 2 g −1 , respectively. The increased BET area of β-CD-rGOAs was possible due to the reduction-induced self-assembly and β-CD crosslinking effect. With increasing β-CD loading, the BET area increased, and the porous structure was enhanced. The pore size distributions indicate that the primary pores of β-CD-rGOA-0.5 were within a diameter of 2-6 nm, which mainly contributed to the specific surface area. However, more β-CD caused a decrease in the surface area and total pore volume, which might be attributable to the excessive aggregation of β-CD [32]. Therefore, β-CD-rGOA-0.5 had an appropriate amount of β-CD. Based on the literature, a narrower mesoporous range facilitates L2 adsorption [38].

Effect of Modifier β-CD
β-CD-rGOA-0.5. In accordance with the IUPAC classification, β-CD-rGOA-0.5 demonstrated the features of type IV isotherms with H3 hysteresis loops, which is indicative of a mesoporous structure [37]. Alternatively, IGGO and rGOA followed a type III isotherm with a macroporous or nonporous material and low BET surface area. Table 1 shows the textural parameters of IGGO and β-CD-rGOAs. The BET analysis indicates that the specific surface areas of IGGO, rGOA, β-CD-rGOA-0.25, β-CD-rGOA-0.5, and β-CD-rGOA-1 were 7.4, 55.2, 59.3, 163.5, and 112.3 m 2 g −1 , respectively. The increased BET area of β-CD-rGOAs was possible due to the reduction-induced self-assembly and β-CD crosslinking effect. With increasing β-CD loading, the BET area increased, and the porous structure was enhanced. The pore size distributions indicate that the primary pores of β-CD-rGOA-0.5 were within a diameter of 2-6 nm, which mainly contributed to the specific surface area. However, more β-CD caused a decrease in the surface area and total pore volume, which might be attributable to the excessive aggregation of β-CD [32]. Therefore, β-CD-rGOA-0.5 had an appropriate amount of β-CD. Based on the literature, a narrower mesoporous range facilitates L2 adsorption [38].   Figure S2 shows a water droplet on the surface of a β-CD-rGOA-0.5 film, which indicates the strong hydrophobicity of the material. Table 1 shows the experimental values of the contact angle (θ) for the studied materials. The β-CD-rGOAs all exhibited high hydrophobicity, which is attributable to the removal of some oxygen-containing functional groups because of the hydrothermal reaction. Figure 3 shows SEM and TEM images of IGGO, rGOA, and β-CD-rGOA-0.5. IGGO had a relatively smooth surface with no wrinkles and holes. After hydrothermal reduction, the folds of rGOA and β-CD-rGOA-0.5 increased in number, and the surfaces were not smooth. Thinner lamellae and more pores can be identified in the SEM and TEM images, and are shown in Figure 3c-f. In contrast, β-CD-rGOA-0.5 exhibited more wrinkles than rGOA, implying that it may possess a higher specific surface area and larger pore volume, which could be due to the modification of the β-CD crosslinking effect.   Figure S2 shows a water droplet on the surface of a β-CD-rGOA-0.5 film, which indicates the strong hydrophobicity of the material. Table 1 shows the experimental values of the contact angle (θ) for the studied materials. The β-CD-rGOAs all exhibited high hydrophobicity, which is attributable to the removal of some oxygen-containing functional groups because of the hydrothermal reaction. Figure 3 shows SEM and TEM images of IGGO, rGOA, and β-CD-rGOA-0.5. IGGO had a relatively smooth surface with no wrinkles and holes. After hydrothermal reduction, the folds of rGOA and β-CD-rGOA-0.5 increased in number, and the surfaces were not smooth. Thinner lamellae and more pores can be identified in the SEM and TEM images, and are shown in Figure 3c-f. In contrast, β-CD-rGOA-0.5 exhibited more wrinkles than rGOA, implying that it may possess a higher specific surface area and larger pore volume, which could be due to the modification of the β-CD crosslinking effect. These folds could improve the surface area and increase the adsorption [39]. These results are consistent with the previous findings shown in Table 1. These folds could improve the surface area and increase the adsorption [39]. These results are consistent with the previous findings shown in Table 1.  Figure 4 shows XRD diagrams of IGGO, rGOA, and β-CD-rGOA-0.5. An extensive alteration of the structures was noted by the XRD patterns. A sharp diffraction peak at 11.6° in the IGGO pattern corresponded to the (001) plane, which reveals a highly ordered structure with interlayer spacing of about 7.6 Å [40]. Moreover, a narrow peak (100) centered at 42.7° was observed for IGGO, corresponding to the long range order in the graphitic planes. After hydrothermal reduction, the characteristic peak of IGGO disappeared, and characteristic diffraction peaks indexed to (002) facets of graphitic carbon for rGOA and β-CD-rGOA-0.5 at 24.9° and 23.4°, respectively; these corresponded to interlayer spacings of 3.7 and 3.9 Å, respectively [38]. The presence of the broad diffraction peak signified the disordered structure, and the loss of 42.7° could reflect the loss of planarity for rGOA and β-CD-rGOA-0.5. The interlayer spacing of the rGOA and β-CD-rGOA-0.5 were smaller than that of IGGO due to the removal of oxygen-containing functional groups and π-π interactions during self-assembly [38]. The interlayer spacing of β-CD-rGOA-0.5 was slightly larger than that of rGOA, which is attributable to the cross-linking modification of β-CD. When β-CD was introduced into the  Figure 4 shows XRD diagrams of IGGO, rGOA, and β-CD-rGOA-0.5. An extensive alteration of the structures was noted by the XRD patterns. A sharp diffraction peak at 11.6 • in the IGGO pattern corresponded to the (001) plane, which reveals a highly ordered structure with interlayer spacing of about 7.6 Å [40]. Moreover, a narrow peak (100) centered at 42.7 • was observed for IGGO, corresponding to the long range order in the graphitic planes. After hydrothermal reduction, the characteristic peak of IGGO disappeared, and characteristic diffraction peaks indexed to (002) facets of graphitic carbon for rGOA and β-CD-rGOA-0.5 at 24.9 • and 23.4 • , respectively; these corresponded to interlayer spacings of 3.7 and 3.9 Å, respectively [38]. The presence of the broad diffraction peak signified the disordered structure, and the loss of 42.7 • could reflect the loss of planarity for rGOA and β-CD-rGOA-0.5. The interlayer spacing of the rGOA and β-CD-rGOA-0.5 were smaller than that of IGGO due to the removal of oxygen-containing functional groups and π-π interactions during self-assembly [38]. The interlayer spacing of β-CD-rGOA-0.5 was slightly larger than that of rGOA, which is attributable to the cross-linking modification of β-CD. When β-CD was introduced into the β-CD-rGOAs, the crosslinking effect of more hydrogen bonds suppressed π-π restacking, which enlarged the interlamellar spacing. β-CD-rGOAs, the crosslinking effect of more hydrogen bonds suppressed π-π restacking, which enlarged the interlamellar spacing. Raman spectroscopy is frequently used to characterize the deficiencies in graphene-based materials ( Figure 5). The Raman spectra indicate two distinct characteristic peaks in IGGO, rGOA, and β-CD-rGOA-0.5 at 1600 and 1345 cm −1 , corresponding to the G and D peaks, respectively, of carbon materials. The G peak is the characteristic feature for graphite (sp 2 -hybridized carbon in-plane stretching vibration), and the D peak is due to the disordered carbon, including, e.g., sp 3 -hybridized carbon and dopant atoms. Usually, the D/G band intensity ratio (ID/IG) represents the degree of disorder in carbon [41]. The ID/IG of rGOA (0.95) and β-CD-rGOA-0.5 (0.98) indicate a noticeable increase compared with IGGO (0.83). This indicates that the hydrothermal reduction increased the number of defects and resulted in a low degree of carbonization. β-CD-rGOA-0.5 had a slightly higher value of ID/IG than rGOA, which indicates that introducing β-CD lead to an increase in the degree of defects. Because of the hydrogen bonding between β-CD and rGOA, the degree of graphitization was decreased, which led to a higher ID/IG ratio. The peaks located in the range of 2300-2800 cm −1 are the 2D bands, which are another characteristic peak of graphene [37]. In comparison with IGGO, rGOA and β-CD-rGOA-0.5 exhibited a fairly broad and up-shift 2D peak in the Raman spectrum, demonstrating its low-layer structure, which was consistent with the TEM results.   Raman spectroscopy is frequently used to characterize the deficiencies in graphenebased materials ( Figure 5). The Raman spectra indicate two distinct characteristic peaks in IGGO, rGOA, and β-CD-rGOA-0.5 at 1600 and 1345 cm −1 , corresponding to the G and D peaks, respectively, of carbon materials. The G peak is the characteristic feature for graphite (sp 2 -hybridized carbon in-plane stretching vibration), and the D peak is due to the disordered carbon, including, e.g., sp 3 -hybridized carbon and dopant atoms. Usually, the D/G band intensity ratio (I D /I G ) represents the degree of disorder in carbon [41]. The I D /I G of rGOA (0.95) and β-CD-rGOA-0.5 (0.98) indicate a noticeable increase compared with IGGO (0.83). This indicates that the hydrothermal reduction increased the number of defects and resulted in a low degree of carbonization. β-CD-rGOA-0.5 had a slightly higher value of I D /I G than rGOA, which indicates that introducing β-CD lead to an increase in the degree of defects. Because of the hydrogen bonding between β-CD and rGOA, the degree of graphitization was decreased, which led to a higher I D /I G ratio. The peaks located in the range of 2300-2800 cm −1 are the 2D bands, which are another characteristic peak of graphene [37]. In comparison with IGGO, rGOA and β-CD-rGOA-0.5 exhibited a fairly broad and up-shift 2D peak in the Raman spectrum, demonstrating its low-layer structure, which was consistent with the TEM results. β-CD-rGOAs, the crosslinking effect of more hydrogen bonds suppressed π-π restacking, which enlarged the interlamellar spacing. Raman spectroscopy is frequently used to characterize the deficiencies in graphene-based materials ( Figure 5). The Raman spectra indicate two distinct characteristic peaks in IGGO, rGOA, and β-CD-rGOA-0.5 at 1600 and 1345 cm −1 , corresponding to the G and D peaks, respectively, of carbon materials. The G peak is the characteristic feature for graphite (sp 2 -hybridized carbon in-plane stretching vibration), and the D peak is due to the disordered carbon, including, e.g., sp 3 -hybridized carbon and dopant atoms. Usually, the D/G band intensity ratio (ID/IG) represents the degree of disorder in carbon [41]. The ID/IG of rGOA (0.95) and β-CD-rGOA-0.5 (0.98) indicate a noticeable increase compared with IGGO (0.83). This indicates that the hydrothermal reduction increased the number of defects and resulted in a low degree of carbonization. β-CD-rGOA-0.5 had a slightly higher value of ID/IG than rGOA, which indicates that introducing β-CD lead to an increase in the degree of defects. Because of the hydrogen bonding between β-CD and rGOA, the degree of graphitization was decreased, which led to a higher ID/IG ratio. The peaks located in the range of 2300-2800 cm −1 are the 2D bands, which are another characteristic peak of graphene [37]. In comparison with IGGO, rGOA and β-CD-rGOA-0.5 exhibited a fairly broad and up-shift 2D peak in the Raman spectrum, demonstrating its low-layer structure, which was consistent with the TEM results.    1050 cm −1 (C-O-C stretching vibration in the epoxy groups) were observed, which indicates that IGGO has a large number of oxygen-containing groups on its surface [36]. After hydrothermal reduction, the C-O-C band at 1050 cm −1 and the C=O peak at 1727 cm −1 in the rGOA were no longer evident, which indicates that some of the oxygen-containing groups in IGGO underwent reduction. However, after adding β-CD, the FTIR spectra of β-CD-rGOA-0.5 indicate that, not only was the C=O peak absent, but the spectral features of β-CD were evident (the coupled C-O-C stretching/O-H bending vibrations at 1163 cm −1 and the coupled C-O/C-C stretching/O-H bending vibrations at 1050 cm −1 and 1112 cm −1 ), indicating the modification of rGOA with β-CD [41,42]. Moreover, the broader absorption of β-CD-rGOA-0.5 over the range of 3000-3750 cm −1 (high wavenumbers) was evident, which is indicative of hydrogen bond formation between rGOA and β-CD [43]. bration in the carboxyl groups, C-OH groups, and adsorbed-state water. In the IGGO spectrum, 2927 cm −1 (low-intensity stretching and bending vibrations from C-H), 1727 cm −1 (C=O stretching vibration in the carboxyl groups), 1600 cm −1 (C=C vibration of the graphene skeleton), and 1050 cm −1 (C-O-C stretching vibration in the epoxy groups) were observed, which indicates that IGGO has a large number of oxygen-containing groups on its surface [36]. After hydrothermal reduction, the C-O-C band at 1050 cm −1 and the C=O peak at 1727 cm −1 in the rGOA were no longer evident, which indicates that some of the oxygen-containing groups in IGGO underwent reduction. However, after adding β-CD, the FTIR spectra of β-CD-rGOA-0.5 indicate that, not only was the C=O peak absent, but the spectral features of β-CD were evident (the coupled C-O-C stretching/O-H bending vibrations at 1163 cm −1 and the coupled C-O/C-C stretching/O-H bending vibrations at 1050 cm −1 and 1112 cm −1 ), indicating the modification of rGOA with β-CD [41,42]. Moreover, the broader absorption of β-CD-rGOA-0.5 over the range of 3000-3750 cm −1 (high wavenumbers) was evident, which is indicative of hydrogen bond formation between rGOA and β-CD [43]. In accordance with the experimental results, a possible working mechanism was elucidated ( Figure 7). In a 180 °C hydrothermal enviroment, carbonyl groups can be efficiently reduced to hydroxyl groups, and the ring-opening reaction of an epoxy group occured to form a hydroxyl group. After the modification of β-CD on the rGOA surface, the π-π stacking between the graphene sheets can be weakened; with the hydroxyl group generated, the H-bonds would be increased. When hydroxyl segments at the edge and plane of rGOA interact through hydrogen bonding, a porous 3D structure is possibly facilitated. In this manner, β-CD-rGOA-0.5 can provide more active sites and channels, whereas the adsorption ability was increased. In accordance with the experimental results, a possible working mechanism was elucidated ( Figure 7). In a 180 • C hydrothermal enviroment, carbonyl groups can be efficiently reduced to hydroxyl groups, and the ring-opening reaction of an epoxy group occured to form a hydroxyl group. After the modification of β-CD on the rGOA surface, the π-π stacking between the graphene sheets can be weakened; with the hydroxyl group generated, the H-bonds would be increased. When hydroxyl segments at the edge and plane of rGOA interact through hydrogen bonding, a porous 3D structure is possibly facilitated. In this manner, β-CD-rGOA-0.5 can provide more active sites and channels, whereas the adsorption ability was increased. graphene skeleton), and 1050 cm −1 (C-O-C stretching vibration in the epoxy gro were observed, which indicates that IGGO has a large number of oxygen-contai groups on its surface [36]. After hydrothermal reduction, the C-O-C band at 1050 and the C=O peak at 1727 cm −1 in the rGOA were no longer evident, which indicates some of the oxygen-containing groups in IGGO underwent reduction. However, adding β-CD, the FTIR spectra of β-CD-rGOA-0.5 indicate that, not only was the peak absent, but the spectral features of β-CD were evident (the coupled Cstretching/O-H bending vibrations at 1163 cm −1 and the coupled C-O/C-C stretchin H bending vibrations at 1050 cm −1 and 1112 cm −1 ), indicating the modification of rG with β-CD [41,42]. Moreover, the broader absorption of β-CD-rGOA-0.5 over the r of 3000-3750 cm −1 (high wavenumbers) was evident, which is indicative of hydr bond formation between rGOA and β-CD [43]. In accordance with the experimental results, a possible working mechanism elucidated (Figure 7). In a 180 °C hydrothermal enviroment, carbonyl groups ca efficiently reduced to hydroxyl groups, and the ring-opening reaction of an epoxy g occured to form a hydroxyl group. After the modification of β-CD on the rGOA sur the π-π stacking between the graphene sheets can be weakened; with the hydr group generated, the H-bonds would be increased. When hydroxyl segments at the and plane of rGOA interact through hydrogen bonding, a porous 3D structu possibly facilitated. In this manner, β-CD-rGOA-0.5 can provide more active sites channels, whereas the adsorption ability was increased.  Figure 7. Working mechanism of hydrothermal reduction and crosslinking.

Comparison of Dynamic Adsorption Performances
The adsorption breakthrough curves by using the Yoon-Nelson model of the IGGO, rGOA, β-CD-rGOA-0.25, β-CD-rGOA-0.5, and β-CD-rGOA-1 (Figure 8) were tested at 20 • C, V g of 50 mL min −1 , and C in of 14.62 mg L −1 for comparing the dynamic adsorption performance. Table 2 shows the experimental adsorption values and the calculated model parameters. The high correlation coefficients (R 2 > 0.99) indicate that the Yoon-Nelson model fit well with the L2 dynamic adsorption onto β-CD-rGOAs. Thus, in the following discussion, the calculated theoretical parameter values (t B,th and Q B,th ) were used to compare and analyze the adsorption capacity of the β-CD-rGOAs. The L2 directly penetrated the IGGO, indicating that the IGGO had virtually no adsorption ability. Furthermore, the adsorption performance among the β-CD-rGOAs was ranked as β-CD-rGOA-0.5 > β-CD-rGOA-1 > β-CD-rGOA-0.25 > rGOA, and the β-CD-rGOA-0.5 exhibited the maximum breakthrough time and adsorption capacity, with t B,th and Q B,th values of 11.03 min and 88.7 mg g −1 , respectively. To determine the factors that are responsible for the β-CD-rGOA adsorption capacity, the relationships between Q B,th and S BET , V tot , and the contact angle were evaluated (Figure 9). The linear regression equation was y = a + bx. Some important statistical data were shown in Table S2. Specifically, the closer R 2 is to 1, the better the linear relationship; the smaller the standard deviation, the more precise the data. Accordingly, the correlation coefficient (R 2 ) values for Q B,th -S BET , Q B,th -V tot , and Q B,th -contact angle were 0.9953, 0.9507, and 0.8563, respectively. Therefore, it can be broadly concluded that S BET and V tot were the predominant factors that affected the L2 adsorption capacity, while contact angle also has a certain degree of positive correlation [38].
The adsorption breakthrough curves by using the Yoon-Nelson mode rGOA, β-CD-rGOA-0.25, β-CD-rGOA-0.5, and β-CD-rGOA-1 (Figure 8) we °C, Vg of 50 mL min −1 , and Cin of 14.62 mg L −1 for comparing the dynam performance. Table 2 shows the experimental adsorption values and t model parameters. The high correlation coefficients (R 2 > 0.99) indicate th Nelson model fit well with the L2 dynamic adsorption onto β-CD-rGOAs following discussion, the calculated theoretical parameter values (tB,th an used to compare and analyze the adsorption capacity of the β-CD-rGOA rectly penetrated the IGGO, indicating that the IGGO had virtually no ad ity. Furthermore, the adsorption performance among the β-CD-rGOAs w β-CD-rGOA-0.5>β-CD-rGOA-1>β-CD-rGOA-0.25> rGOA, and the β-CDhibited the maximum breakthrough time and adsorption capacity, with values of 11.03 min and 88.7 mg g −1 , respectively. To determine the facto sponsible for the β-CD-rGOA adsorption capacity, the relationships betw SBET, Vtot, and the contact angle were evaluated (Figure 9). The linear regres was y = a + bx. Some important statistical data were shown in Table S2. Sp closer R 2 is to 1, the better the linear relationship; the smaller the standard more precise the data. Accordingly, the correlation coefficient (R 2 ) values QB,th-Vtot, and QB,th-contact angle were 0.9953, 0.9507, and 0.8563, respective it can be broadly concluded that SBET and Vtot were the predominant factor the L2 adsorption capacity, while contact angle also has a certain degr correlation [38].

Influence of Inlet Concentration and Bed Temperature
Inlet concentration is a significant factor influencing the adsorption process [44]. Figure 10 shows the curve of the tB,th and QB,th change over Cin. The tB,th decreased exponentially with Cin. However, QB, th values presented, at first, an increasing trend and then a decreasing one in the concentration series experiment. As reported [45,46], it might be related to the co-action of the adsorption driving force of L2 molecules (positive correlation to Cin) and the accessibility of adsorption sites (negative correlation to Cin), which could portend L2 adsorption behavior during industrial application. Bed temperature is another important factor that affects the L2 adsorption efficiency. Breakthrough curves fitted by the Yoon-Nelson model of L2 adsorption on β-CD-rGOA-0.5 at different bed temperatures (0-55 °C) were shown in Figure 11, and the details of the calculated results by the Yoon-Nelson model were presented in Table  3. There was a tendency that, the higher the bed temperature, the shorter the tB,th, indi-

Influence of Inlet Concentration and Bed Temperature
Inlet concentration is a significant factor influencing the adsorption process [44]. Figure 10 shows the curve of the t B,th and Q B,th change over C in . The t B,th decreased exponentially with C in . However, Q B,th values presented, at first, an increasing trend and then a decreasing one in the concentration series experiment. As reported [45,46], it might be related to the co-action of the adsorption driving force of L2 molecules (positive correlation to C in ) and the accessibility of adsorption sites (negative correlation to C in ), which could portend L2 adsorption behavior during industrial application.

Influence of Inlet Concentration and Bed Temperature
Inlet concentration is a significant factor influencing the adsorption process [44]. Figure 10 shows the curve of the tB,th and QB,th change over Cin. The tB,th decreased exponentially with Cin. However, QB, th values presented, at first, an increasing trend and then a decreasing one in the concentration series experiment. As reported [45,46], it might be related to the co-action of the adsorption driving force of L2 molecules (positive correlation to Cin) and the accessibility of adsorption sites (negative correlation to Cin), which could portend L2 adsorption behavior during industrial application. Bed temperature is another important factor that affects the L2 adsorption efficiency. Breakthrough curves fitted by the Yoon-Nelson model of L2 adsorption on β-CD-rGOA-0.5 at different bed temperatures (0-55 °C) were shown in Figure 11, and the details of the calculated results by the Yoon-Nelson model were presented in Table  3. There was a tendency that, the higher the bed temperature, the shorter the tB,th, indi- Bed temperature is another important factor that affects the L2 adsorption efficiency. Breakthrough curves fitted by the Yoon-Nelson model of L2 adsorption on β-CD-rGOA-0.5 at different bed temperatures (0-55 • C) were shown in Figure 11, and the details of the calculated results by the Yoon-Nelson model were presented in Table 3. There was a tendency that, the higher the bed temperature, the shorter the t B,th , indicating that low temperature was beneficial to the adsorption of L2 on β-CD-rGOA-0.5. The results revealed that the L2 adsorption on β-CD-rGOA-0.5 was exothermic. The maximum breakthrough adsorption capacity (111.8 mg g −1 ) of L2 on β-CD-rGOA-0.5 was observed at a temperature of 0 • C, C in of 14.62 mg L −1 , and V g of 50 mL min −1 .

Recycling Performance of β-CD-rGOA-0.5
The recycling performance is a key factor for evaluating practical applicatio adsorbent [47]. Thus, the spent β-CD-rGOA-0.5 was assessed via thermal treatme °C for 30 min, and, subsequently, through five adsorption-desorption cycles. F shows the adsorption breakthrough curves for L2 of β-CD-rGOA-0.5 after each tion, and Figure S3 shows that there is no residual L2 on the β-CD-rGOA-0 continuous cycles. These results indicate that β-CD-rGOA-0.5 can be completely or recycled. Therefore, the as-prepared β-CD-rGOA-0.5 is a promising candida number of applications on an industrial scale.

Recycling Performance of β-CD-rGOA-0.5
The recycling performance is a key factor for evaluating practical applications of an adsorbent [47]. Thus, the spent β-CD-rGOA-0.5 was assessed via thermal treatment at 80 • C for 30 min, and, subsequently, through five adsorption-desorption cycles. Figure 12 shows the adsorption breakthrough curves for L2 of β-CD-rGOA-0.5 after each desorption, and Figure S3 shows that there is no residual L2 on the β-CD-rGOA-0.5 after continuous cycles. These results indicate that β-CD-rGOA-0.5 can be completely reused or recycled. Therefore, the as-prepared β-CD-rGOA-0.5 is a promising candidate for a number of applications on an industrial scale.

Conclusions
β-CD-rGOA-0.5, an efficient adsorbent material, was synthesized by a one-step h drothermal reaction with β-CD as a surface modification agent. The β-CD-rGOA-0.5 e hibited a stable, hierarchically porous, 3D structure because of the many hydrog bonds and the crosslinking effect. Furthermore, β-CD-rGOA-0.5 exhibited many use properties, including a high surface area (163.5 m 2 g −1 ), total pore volume (0.68 cm 3 g and water contact angle (128.4°). Moreover, the maximum breakthrough adsorption c pacity of L2 onto β-CD-rGOA-0.5 was 111.8 mg g −1 at a temperature of 0 °C, Cin of 14 mg L −1 , and Vg of 50 mL min −1 . In addition, the QB,th was strongly linearly proportional SBET, Vtot, and the contact angle, which indicates that the adsorption mechanism β-CD-rGOA-0.5 for L2 might depend on capillary condensation and the hydrophobic fect. Furthermore, the low bed temperature and inlet concentration resulted in high adsorption levels for β-CD-rGOA-0.5. Finally, the β-CD-rGOA-0.5 can be easily regen ated and reused multiple times by heating at 80 °C for 30 min. All of these characterist indicate that the β-CD-rGOA-0.5 exhibits prospects of industrial application. The prese study provided experimental evidence and a theoretical basis for the removal of siloxa from actual biogas. Next, we will investigate the effects of coexisting substances biogas on siloxane adsorption. Further studies directly addressing practical problem are needed.

Conclusions
β-CD-rGOA-0.5, an efficient adsorbent material, was synthesized by a one-step hydrothermal reaction with β-CD as a surface modification agent. The β-CD-rGOA-0.5 exhibited a stable, hierarchically porous, 3D structure because of the many hydrogen bonds and the crosslinking effect. Furthermore, β-CD-rGOA-0.5 exhibited many useful properties, including a high surface area (163.5 m 2 g −1 ), total pore volume (0.68 cm 3 g −1 ), and water contact angle (128.4 • ). Moreover, the maximum breakthrough adsorption capacity of L2 onto β-CD-rGOA-0.5 was 111.8 mg g −1 at a temperature of 0 • C, C in of 14.62 mg L −1 , and V g of 50 mL min −1 . In addition, the Q B,th was strongly linearly proportional to S BET , V tot , and the contact angle, which indicates that the adsorption mechanism of β-CD-rGOA-0.5 for L2 might depend on capillary condensation and the hydrophobic effect. Furthermore, the low bed temperature and inlet concentration resulted in high L2 adsorption levels for β-CD-rGOA-0.5. Finally, the β-CD-rGOA-0.5 can be easily regenerated and reused multiple times by heating at 80 • C for 30 min. All of these characteristics indicate that the β-CD-rGOA-0.5 exhibits prospects of industrial application. The present study provided experimental evidence and a theoretical basis for the removal of siloxane from actual biogas. Next, we will investigate the effects of coexisting substances in biogas on siloxane adsorption. Further studies directly addressing practical problems are needed.
Supplementary Materials: The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/nano12152643/s1, Figure S1: Photographs of the rGOHs and rGOAs; Figure S2: Image showing a water droplet on the surface of β-CD-rGOA-0.5 film; Figure S3: FTIR spectra of β-CD-rGOA-0.5 and desorbed β-CD-rGOA-0.5 after cycling; Table S1: Properties of aerogels with different sizes; Table S2: The statistical parameters of curves between Q B and S BET , Q B and V tot , Q B and θ for the rGOAs.