Ultralight, Mechanically Enhanced, and Thermally Improved Graphene-Cellulose-Polyethyleneimine Aerogels for the Adsorption of Anionic and Cationic Dyes

Graphene-cellulose-polyethyleneimine aerogels (GA-MCC-PEI) were prepared using a simple, environmentally friendly method to remove anionic and cationic dyes in water. Graphene-cellulose hydrogels were prepared using a hydrothermal method and then immersed in a polyethyleneimine aqueous solution for 48 h to obtain graphene-cellulose-polyethyleneimine hydrogels, which were then freeze-dried. The light and porous composite aerogels had a good compression resistance, and the maximum allowable pressure of the graphene-cellulose-polyethyleneimine aerogel with a cellulose content of 43% was 21.76 kPa, which was 827 times its weight. Adsorption of the anionic dye amaranth and the cationic dye methylene blue by the graphene-cellulose-polyethyleneimine aerogel was satisfactorily modeled using the Langmuir isothermal equation, indicating monolayer adsorption. When the cellulose content was 39%, the equilibrium adsorption capacities of the composite aerogel for amaranth and methylene blue were 369.37 mg/g and 237.33 mg/g, respectively. This graphene-cellulose-polyethyleneimine aerogel can be used to remove dye pollutants in water to maintain ecological balance, thus broadening the application space of aerogel materials, that is, as adsorbents in different environments.


Introduction
Dyes in water can adversely affect ecosystems and human health. Adsorption has become one of the most effective wastewater treatment methods because of its low cost, simple operation, and high efficiency [1][2][3]. Graphene aerogels are porous (porosity can reach more than 99%), which can provide sufficient transport channels for the diffusion of pollutants when they are adsorbed to improve the adsorption efficiency of adsorbents [4,5]. Graphene aerogels also have the advantages of strong flexibility, ultra-low density, porous structure, ideal specific surface area, and high adsorption capacity, and are able to be used as adsorbents in different environments [6,7]. However, owing to the van der Waals and π-π interactions between graphene sheets, irreversible stacking and agglomeration occur, which negatively affects the mechanical properties and pore structure of graphene aerogels, thus limiting their practical applications. Moreover, aerogels composed of a single material do not have multiple functions [8][9][10][11][12]. Therefore, other functional materials have been incorporated into graphene aerogels to address the above-mentioned problems. Multicomponent composite aerogels with high mechanical strengths and adsorption capacities have high practical value.
Cellulose has numerous advantages, including good hydrophilicity, non-toxicity, biodegradability, biocompatibility, and low density. Importantly, cellulose has multiple binding sites on its surface for hydroxyl and hydrogen bonds, which can serve as linkage high-temperature reaction ends. The high-temperature reaction ends when the green color changes to reddish-brown. At this time, 30 wt.% hydrogen peroxide solution was dropped into the mixed solution until no bubbles appeared. Finally, the obtained solution was sonicated for 30 min, and a higher purity GO solution was obtained after precipitation, centrifugation, and dialysis.

Preparation of Graphene-Cellulose-Polyethyleneimine Aerogel (GA-MCC-PEI)
First, 3 g of PEI solid was dissolved in 30 mL of deionized water and the mixture was stirred at a temperature of 80-100 • C for 2 h to obtain a completely dissolved 9 wt.% PEI aqueous solution. This process was repeated to prepare six groups of 9 wt.% PEI aqueous solution. Then 25 g/L GO solution was prepared by stirring 250 mg graphene oxide (GO) powder evenly in 10 mL deionized water. This process was repeated to prepare six groups of 25 g/L GO solution. Different amounts of cellulose powder (0 mg, 100 mg, 200 mg, 300 mg, 400 mg, and 500 mg) were added to each GO solution and the mixtures were stirred for 3 h to obtain a GO solution and graphene oxide-cellulose (GO-MCC) mixtures. A 25 mL PTFE-lined hydrothermal reactor was used to install these six groups of mixed solutions. All hydrothermal reactors were heated at 180 • C for 12 h to obtain graphene (GA) hydrogels and graphene-cellulose (GA-MCC) hydrogels. The six hydrogels were immersed in 9 wt.% PEI aqueous solution for 48 h to obtain a graphene-PEI (GA-PEI) hydrogel and graphene-cellulose-PEI (GA-MCC-PEI) hydrogels. In the process of freezing all hydrogels, first, use liquid nitrogen freezing, then, use a freeze dryer. GA Table 1.

Characterization Method
The mass of the composite aerogel sample was weighed by an electronic balance. Scanning electron microscope (SEM) images were measured by QUANTA200. X-ray diffraction (XRD) measurements were performed using an XRD-6100 with a scan range of 5-60 • and a scan speed of 5 • /min. The specific surface area and pore structure of the composite aerogel were obtained by an ASAP2460 automatic specific surface area and porosity analyzer. For the compression test of the composite aerogel, the sample was cut into a cylindrical shape with a height of 0.5 cm and completed on a dynamic thermal analyzer model */DMA242E Artemis. Thermogravimetric analysis (TG) is a test performed using a 209 F3 Thermogravimetric Analyzer. A PE lambda 750 UV-Vis spectrophotometer was used to verify the adsorption properties of the composite aerogels for dyes. Fourier transform infrared spectroscopy (FTIR) was obtained using a Spectrum 400 instrument. Deionized water was used as the reference solution. Seven different concentrations of the amaranth solution and methylene blue solution were set up, and the maximum absorbance was measured using an ultraviolet-visible (UV-vis) spectrophotometer at wavelengths of 552 nm and 664 nm for amaranth and methylene blue, respectively. Each experiment was repeated three times under the same conditions.
The general property parameters of dyes are shown in Table 2. The adsorption capacity of the sample for dyes is calculated as Formula (1) [26].
Formula: q e is the equilibrium adsorption capacity (mg/g). C 0 is the initial concentration of solvent (mg/L) before adsorption. C e is the concentration of solvent (mg/L) when the adsorption equilibrium is reached. V is the volume of solvent (L). W is the quality of adsorbent (g).

Adsorption Equilibrium Equation
In this paper, the Langmuir isothermal adsorption equation and the Freundlich isothermal adsorption equation were introduced, and the data on adsorption performance were analyzed using the curve-fitting method of these two equations.
Langmuir adsorption isotherm is an ideal monolayer adsorption model. The equation can be expressed as [29]: The equation can be transformed into: Formula: q e (mg/g) is the adsorption capacity of adsorbent at equilibrium. Concentration of C e (mg/L) at equilibrium. k L (L/mg) is the Langmuir isothermal adsorption constant, which describes the binding ability of the target to the adsorption site on the adsorbent. The greater the value, the greater the affinity between the adsorbate and the adsorbent is. Q m (mg/g) is the saturated adsorption capacity of adsorbent.
Langmuir isothermal adsorption equation can also be used to describe the adsorption process by dimensionless R L , the expression is [29]: Freundlich adsorption equation is a multi-molecular layer adsorption model. The equation can be expressed as [29]: Formula: Q e (mg/g) is the adsorption amount of adsorbent at equilibrium; concentration of Ce (mg/L) at equilibrium. K F and 1/n are Freundlich isothermal equilibrium adsorption constants. The larger the K F value, the larger the adsorption capacity. The larger the value of 1/n, the greater the adsorption strength. If 0.1 < 1/n < 0.5, this means that the adsorption process is spontaneous and easy.

Results
According to the SEM images of the GA-MCC-PEI aerogels, GA-MCC-PEI- (1,3,5) had irregular and densely packed pores. As shown in Figure 1a-f, rod-shaped cellulose was interspersed between the graphene sheets and formed a tightly packed structure with the graphene sheets. As shown in Figure 1c,f, the composite aerogel containing 43.11% cellulose (GA-MCC-PEI-5) had a greater number of pores and pores with thicker walls than the composite aerogel containing 31.12% cellulose (GA-MCC-PEI-3). The porous structure of the composite aerogels can provide sufficient transport channels for the diffusion of dyes when they are adsorbed to improve the adsorption efficiency of the adsorbent. Moreover, the tight connections between graphene and cellulose can enhance the mechanical properties of composite aerogels. Formula: Qe (mg/g) is the adsorption amount of adsorbent at equilibrium; concentration of Ce (mg/L) at equilibrium. KF and 1/n are Freundlich isothermal equilibrium adsorption constants. The larger the KF value, the larger the adsorption capacity. The larger the value of 1/n, the greater the adsorption strength. If 0.1 < 1/n < 0.5, this means that the adsorption process is spontaneous and easy.

Results
According to the SEM images of the GA-MCC-PEI aerogels, GA-MCC-PEI-(1, 3, 5) had irregular and densely packed pores. As shown in Figure 1a-f, rod-shaped cellulose was interspersed between the graphene sheets and formed a tightly packed structure with the graphene sheets. As shown in Figure 1c,f, the composite aerogel containing 43.11% cellulose (GA-MCC-PEI-5) had a greater number of pores and pores with thicker walls than the composite aerogel containing 31.12% cellulose (GA-MCC-PEI-3). The porous structure of the composite aerogels can provide sufficient transport channels for the diffusion of dyes when they are adsorbed to improve the adsorption efficiency of the adsorbent. Moreover, the tight connections between graphene and cellulose can enhance the mechanical properties of composite aerogels. As shown in Figure 2, the Brunauer-Emmett-Teller (BET) isotherms of the GA-PEI and GA-MCC-PEI-3 aerogels both showed characteristics of type IV physical adsorption. As shown in Figure 2, the Brunauer-Emmett-Teller (BET) isotherms of the GA-PEI and GA-MCC-PEI-3 aerogels both showed characteristics of type IV physical adsorption. Therefore, both the GA-PEI and GA-MCC-PEI-3 aerogels had typical mesoporous structures, which concurred with the dense porous structure revealed in the SEM images. The H3type hysteresis regression line indicated that voids formed between the mesopores and wrinkled, wide, slit-like voids accumulated in the graphene layer, which induced nitrogen gas eruption during the desorption process [30]. A dense void structure is beneficial because it allows the composite aerogels to achieve the desired adsorption effect quickly and efficiently. Nanomaterials 2022, 12, x FOR PEER REVIEW 6 of 1 Therefore, both the GA-PEI and GA-MCC-PEI-3 aerogels had typical mesoporous struc tures, which concurred with the dense porous structure revealed in the SEM images. Th H3-type hysteresis regression line indicated that voids formed between the mesopore and wrinkled, wide, slit-like voids accumulated in the graphene layer, which induced n trogen gas eruption during the desorption process [30]. A dense void structure is benef cial because it allows the composite aerogels to achieve the desired adsorption effec quickly and efficiently. As shown in Table 3, both the GA-PEI and GA-MCC-PEI-(1-5) aerogels had larg specific surface areas, and as the MCC content increased, the specific surface area of th aerogel first increased and then decreased. Among them, GA-MCC-PEI-4 (MCC-39%) ha the largest specific surface area (92.32 m 2 /g). Because MCC is a filler with a high specif surface area and its linkages with GA and PEI increase the density of the composite aero gel, the specific surface area of the composite material gradually increases as the MC content increases [31]. However, when the MCC content is too high (such as GA-MCC PEI-5), the porous structure of the composite aerogel collapses, thus decreasing the spe cific surface area. In addition, when the density of the composite material is too large, th void volume in the aerogel may also reduce, thus slightly decreasing the specific surfac area of the material. The specific surface area of GA-PEI (MCC-0%) was lower than tha of GA-MCC-PEI-5 (MCC-43%), indicating that the linkages between cellulose and th other components, graphene and PEI, serve to optimize the porous structure of the com posite aerogel. Moreover, the dense void structure enhances the adsorption capacity o the graphene-cellulose-PEI ternary composite aerogel. As shown in Figure 3., the FTIR spectrum of the GO aerogel contained peaks at 173 cm −1 and 1630 cm −1 corresponding to the stretching vibration of the C=O bond at the edg of GO and the bending vibration of the -COOH and -OH bonds, respectively [32]. Thes two peaks were significantly weakened or even disappeared in the FTIR spectra of th GA-PEI and GA-MCC-PEI-(1, 3, 5) aerogels. Moreover, a peak (1566 cm −1 ) correspondin to the stretching vibration of the C=C bond of GA appeared in the composite aeroge which indicated that GO was reduced to GA during the preparation of the composite ae ogel [33]. The FTIR spectra of the MCC and GA-MCC-PEI-(1, 3, 5) aerogels containe peaks corresponding to the O-H vibrational contraction (3239 cm −1 ) and C-H vibrationa As shown in Table 3, both the GA-PEI and GA-MCC-PEI-(1-5) aerogels had large specific surface areas, and as the MCC content increased, the specific surface area of the aerogel first increased and then decreased. Among them, GA-MCC-PEI-4 (MCC-39%) had the largest specific surface area (92.32 m 2 /g). Because MCC is a filler with a high specific surface area and its linkages with GA and PEI increase the density of the composite aerogel, the specific surface area of the composite material gradually increases as the MCC content increases [31]. However, when the MCC content is too high (such as GA-MCC-PEI-5), the porous structure of the composite aerogel collapses, thus decreasing the specific surface area. In addition, when the density of the composite material is too large, the void volume in the aerogel may also reduce, thus slightly decreasing the specific surface area of the material. The specific surface area of GA-PEI (MCC-0%) was lower than that of GA-MCC-PEI-5 (MCC-43%), indicating that the linkages between cellulose and the other components, graphene and PEI, serve to optimize the porous structure of the composite aerogel. Moreover, the dense void structure enhances the adsorption capacity of the graphene-cellulose-PEI ternary composite aerogel. As shown in Figure 3., the FTIR spectrum of the GO aerogel contained peaks at 1730 cm −1 and 1630 cm −1 corresponding to the stretching vibration of the C=O bond at the edge of GO and the bending vibration of the -COOH and -OH bonds, respectively [32]. These two peaks were significantly weakened or even disappeared in the FTIR spectra of the GA-PEI and GA-MCC-PEI-(1, 3, 5) aerogels. Moreover, a peak (1566 cm −1 ) corresponding to the stretching vibration of the C=C bond of GA appeared in the composite aerogel, which indicated that GO was reduced to GA during the preparation of the composite aerogel [33]. The FTIR spectra of the MCC and GA-MCC-PEI-(1, 3, 5) aerogels contained peaks corresponding to the O-H vibrational contraction (3239 cm −1 ) and C-H vibrational contraction (1456 cm −1 ). These characteristic peaks of cellulose indicated that MCC was incorporated into the GA-MCC-PEI aerogels [34]. With the increase in MCC content, the O-H peak (3200-3500 cm −1 ) and C-H peak (1456 cm −1 ) shifted, indicating that the O-H and C-H groups in the composite aerogel were connected to form hydrogen bonds. In the spectra of both the GA-PEI and GA-MCC-PEI aerogels, the peak at 1566 cm −1 corresponding to the bending vibration of the -NH bond of the secondary amine indicated that PEI was successfully integrated into the composite aerogels [35].
Nanomaterials 2022, 12, x FOR PEER REVIEW 7 contraction (1456 cm −1 ). These characteristic peaks of cellulose indicated that MCC incorporated into the GA-MCC-PEI aerogels [34]. With the increase in MCC content O-H peak (3200-3500 cm −1 ) and C-H peak (1456 cm −1 ) shifted, indicating that the O-H C-H groups in the composite aerogel were connected to form hydrogen bonds. In spectra of both the GA-PEI and GA-MCC-PEI aerogels, the peak at 1566 cm −1 corresp ing to the bending vibration of the -NH bond of the secondary amine indicated tha was successfully integrated into the composite aerogels [35]. Thermogravimetric analyses (Figure 4) of the GA-PEI and GA-MCC-PEI-(1, 3, 5) ogels revealed mass losses. The mass loss occurred in the temperature range of 230 °C and was insignificant at temperatures below 200 °C. For all samples, the mass los curred during three main stages. When the temperature is 0~200 °C, the weight loss o composite aerogel samples is less than 15%, which is the first stage of thermogravim indicating that residual water in the pores of the aerogel was removed, whereas the ple itself did not suffer a mass loss. This result concurred with the SEM and BET re in that the composites contain a dense pore structure. When the temperature is 200 °C, all the composite aerogels have a significant mass loss, which is the second stag thermogravimetric. The mass loss ranged from 24% to 38%, suggesting pyrolysis of c lose and decomposition of hydrogen bonds [36]. The third stage occurred at 450-70 and the mass loss ranged from 25% to 35%, indicating that the residual carbon was ox tively degraded into gaseous substances with low molecular weights [37]. Thermogravimetric analyses (Figure 4) of the GA-PEI and GA-MCC-PEI-(1, 3, 5) aerogels revealed mass losses. The mass loss occurred in the temperature range of 230-450 • C and was insignificant at temperatures below 200 • C. For all samples, the mass loss occurred during three main stages. When the temperature is 0~200 • C, the weight loss of all composite aerogel samples is less than 15%, which is the first stage of thermogravimetric, indicating that residual water in the pores of the aerogel was removed, whereas the sample itself did not suffer a mass loss. This result concurred with the SEM and BET results in that the composites contain a dense pore structure. When the temperature is 200-420 • C, all the composite aerogels have a significant mass loss, which is the second stage of thermogravimetric. The mass loss ranged from 24% to 38%, suggesting pyrolysis of cellulose and decomposition of hydrogen bonds [36]. The third stage occurred at 450-700 • C, and the mass loss ranged from 25% to 35%, indicating that the residual carbon was oxidatively degraded into gaseous substances with low molecular weights [37].   [38]. In general, the thermal stability of the composite aerogel can be maximized by controlling the MCC content, and good thermal stability can widen the application space of composite aerogels in the field of adsorption.
As shown in Figure 5, there was only one peak (11.6°) in the XRD pattern of the GO aerogel, which corresponded to the (002) plane of GO [39]. According to the Bragg equation, the interlayer spacing (d) was 0.76 nm. In the XRD patterns of the GA-PEI and GA-MCC-PEI-(1, 2, 4) aerogels, there were no characteristic peaks of GO. A peak at 22.4° corresponding to the characteristic peak of GA was observed [40]. The calculation showed that its interlayer spacing was 0.39 nm. Therefore, GO was completely reduced to GA, which agreed with the FTIR results. A characteristic peak (16.5°) of MCC appeared in the XRD pattern of the GA-MCC-PEI-(1, 2, 4) aerogels, corresponding to the 10Ῑ facet of MCC [41]. As the MCC content increased, the characteristic peak of MCC increased in intensity and the graphene peak shifted to the left. Therefore, a large number of oxygen-containing functional groups was removed during the reduction of GO, and graphene sheets were re-stacked under the action of π-π interactions, despite MCC inserted between graphene sheets reducing the stacking effect of π-π interactions.  [38]. In general, the thermal stability of the composite aerogel can be maximized by controlling the MCC content, and good thermal stability can widen the application space of composite aerogels in the field of adsorption.
As shown in Figure 5, there was only one peak (11.6 • ) in the XRD pattern of the GO aerogel, which corresponded to the (002) plane of GO [39]. According to the Bragg equation, the interlayer spacing (d) was 0.76 nm. In the XRD patterns of the GA-PEI and GA-MCC-PEI-(1, 2, 4) aerogels, there were no characteristic peaks of GO. A peak at 22.4 • corresponding to the characteristic peak of GA was observed [40]. The calculation showed that its interlayer spacing was 0.39 nm. Therefore, GO was completely reduced to GA, which agreed with the FTIR results. A characteristic peak (16. [38]. In general, the thermal stability of the composite aerogel can be maximized by controlling the MCC content, and good thermal stability can widen the application space of composite aerogels in the field of adsorption. As shown in Figure 5, there was only one peak (11.6°) in the XRD pattern of the GO aerogel, which corresponded to the (002) plane of GO [39]. According to the Bragg equation, the interlayer spacing (d) was 0.76 nm. In the XRD patterns of the GA-PEI and GA-MCC-PEI-(1, 2, 4) aerogels, there were no characteristic peaks of GO. A peak at 22.4° corresponding to the characteristic peak of GA was observed [40]. The calculation showed that its interlayer spacing was 0.39 nm. Therefore, GO was completely reduced to GA, which agreed with the FTIR results. A characteristic peak (16.5°) of MCC appeared in the XRD pattern of the GA-MCC-PEI-(1, 2, 4) aerogels, corresponding to the 10Ῑ facet of MCC [41]. As the MCC content increased, the characteristic peak of MCC increased in intensity and the graphene peak shifted to the left. Therefore, a large number of oxygen-containing functional groups was removed during the reduction of GO, and graphene sheets were re-stacked under the action of π-π interactions, despite MCC inserted between graphene sheets reducing the stacking effect of π-π interactions. facet of MCC [41]. As the MCC content increased, the characteristic peak of MCC increased in intensity and the graphene peak shifted to the left. Therefore, a large number of oxygencontaining functional groups was removed during the reduction of GO, and graphene sheets were re-stacked under the action of π-π interactions, despite MCC inserted between graphene sheets reducing the stacking effect of π-π interactions.
As shown in Figure 6a, the GA-PEI aerogel and GA-MCC-PEI-(1-5) aerogels all had a cylindrical structure (radius of 1.1 cm and height of 2.48-2.86 cm) and a porous surface before compression testing. Height maps of the GA-PEI aerogel and GA-MCC-PEI-(1-5) aerogels are shown in Figure 6b-g. When the MCC content in composite aerogels increases gradually, their height also increases. As shown in Figure 6h-m, when the GA-PEI and GA-MCC-PEI-(1-5) aerogels were subjected to a pressure of 500 g (approximately 553 times their own weight), the composite aerogel did not break or crush and the height did not change significantly. Therefore, the GA-PEI and GA-MCC-PEI aerogels exhibited excellent anti-compression properties. As shown in Figure 6a, the GA-PEI aerogel and GA-MCC-PEI-(1-5) aerogels all had a cylindrical structure (radius of 1.1 cm and height of 2.48-2.86 cm) and a porous surface before compression testing. Height maps of the GA-PEI aerogel and GA-MCC-PEI-(1-5) aerogels are shown in Figure 6b-g. When the MCC content in composite aerogels increases gradually, their height also increases. As shown in Figure 6h-m, when the GA-PEI and GA-MCC-PEI-(1-5) aerogels were subjected to a pressure of 500 g (approximately 553 times their own weight), the composite aerogel did not break or crush and the height did not change significantly. Therefore, the GA-PEI and GA-MCC-PEI aerogels exhibited excellent anti-compression properties. Due to the porosity of aerogels, there is more demand for improving their mechanical properties. As shown in Figure 7a,b, the height of the GA-PEI and GA-MCC-PEI-(1-5)  As shown in Figure 6a, the GA-PEI aerogel and GA-MCC-PEI-(1-5) aerogels all had a cylindrical structure (radius of 1.1 cm and height of 2.48-2.86 cm) and a porous surface before compression testing. Height maps of the GA-PEI aerogel and GA-MCC-PEI-(1-5) aerogels are shown in Figure 6b-g. When the MCC content in composite aerogels increases gradually, their height also increases. As shown in Figure 6h-m, when the GA-PEI and GA-MCC-PEI-(1-5) aerogels were subjected to a pressure of 500 g (approximately 553 times their own weight), the composite aerogel did not break or crush and the height did not change significantly. Therefore, the GA-PEI and GA-MCC-PEI aerogels exhibited excellent anti-compression properties. Due to the porosity of aerogels, there is more demand for improving their mechanical properties. As shown in Figure 7a  Due to the porosity of aerogels, there is more demand for improving their mechanical properties. As shown in Figure 7a,b, the height of the GA-PEI and GA-MCC-PEI-(1-5) aerogels changed when they were subjected to a pressure of 500 g (approximately 553 times their own weight). Moreover, as the MCC content increased, the height change of the composite aerogel decreased. Among them, GA-MCC-PEI-5 (MCC content of 43%) exhibited the smallest change in height under compression. Therefore, the addition of MCC enhances the mechanical properties of the composite by promoting the formation of hydrogen bonds among PEI, GA, and MCC, as supported by the XRD and FTIR results. As shown in Figure 7c,d, at low MCC contents, the density of the composite aerogel was low and the internal pores were large, and thus the deformation was high. As the MCC content increased, the density of the composite aerogel increased and the size of the pores decreased. The tighter the arrangement of the aerogel, the greater the pressure it can withstand. This also shows that the hydrogen bonding among MCC, GA, and PEI can enhance the mechanical properties of the composites. As shown in Figure 6d, GA-MCC-PEI-5 (MCC-43%) with the highest MCC content had the largest Young's modulus and was able to withstand a maximum stress of 21.76 kPa, approximately 827 times its weight. exhibited the smallest change in height under compression. Therefore, the addition of MCC enhances the mechanical properties of the composite by promoting the formation of hydrogen bonds among PEI, GA, and MCC, as supported by the XRD and FTIR results. As shown in Figure 7c,d, at low MCC contents, the density of the composite aerogel was low and the internal pores were large, and thus the deformation was high. As the MCC content increased, the density of the composite aerogel increased and the size of the pores decreased. The tighter the arrangement of the aerogel, the greater the pressure it can withstand. This also shows that the hydrogen bonding among MCC, GA, and PEI can enhance the mechanical properties of the composites. As shown in Figure 6d, GA-MCC-PEI-5 (MCC-43%) with the highest MCC content had the largest Young's modulus and was able to withstand a maximum stress of 21.76 kPa, approximately 827 times its weight.  Table 4 shows the maximum allowable pressure of composite aerogels prepared from graphene, cellulose, and PEI reported in recent years. These values were lower than those (21.76 kPa) of GA-MCC-PEI-5 (MCC-43%), which was attributed to the hydrogen bonding between graphene, cellulose, and PEI. This shows that for porous aerogel materials, by reasonably adjusting the content of MCC, GA, and PEI to control the number of hydrogen bonds in the composite material, a composite aerogel with ideal mechanical properties can be obtained.  Table 4 shows the maximum allowable pressure of composite aerogels prepared from graphene, cellulose, and PEI reported in recent years. These values were lower than those (21.76 kPa) of GA-MCC-PEI-5 (MCC-43%), which was attributed to the hydrogen bonding between graphene, cellulose, and PEI. This shows that for porous aerogel materials, by reasonably adjusting the content of MCC, GA, and PEI to control the number of hydrogen bonds in the composite material, a composite aerogel with ideal mechanical properties can be obtained. The SEM and BET results show that the composite aerogel has a dense mesoporous structure and can be applied to the adsorption of dyes in water. Therefore, the GA-MCC-PEI-4 aerogel (MCC-39%) with the largest specific surface area among the composite aerogels was selected for the adsorption tests. As shown in Figure 8a-f, droplets of amaranth and methylene blue (0.1 g/L solutions) were adsorbed by GA-MCC-PEI-4 within 2 s. The traces of dye remaining in the petri dishes indicated that GA-MCC-PEI-4 had a greater adsorption capacity for amaranth than for methylene blue. In particular, compared with the methylene blue traces, there were fewer amaranth traces and they were lighter in color. Dripping of methylene blue into amaranth (Figure 8g-i), dripping of amaranth into methylene blue (Figure 8j-l), and adjacent dripping of the two dyes (Figure 8m,n) revealed that the dry GA-MCC-PEI-4 aerogel adsorbed the dyes within 2 s. A comparison of Figure 8i,l also indicated that GA-MCC-PEI-4 had a greater adsorption capacity for amaranth. In particular, compared with the methylene blue traces, there were fewer amaranth traces and they were lighter in color after the adsorption time of 2 s. Similarly, as shown in Figure 8m-o, GA-MCC-PEI-4 had a greater adsorption capacity for amaranth than for methylene blue. Amaranth and methylene blue solutions (same concentrations) were dropped adjacently into a petri dish with GA-MCC-PEI-4 placed in the middle for adsorption. After 2 s (Figure 8o), it was clear that the composite aerogel had a stronger adsorption capacity for amaranth than for methylene blue. In summary, the GA-MCC-PEI-4 composite aerogel had obvious adsorption capacity for cationic dye methylene blue and anionic dye amaranth, but it had a better adsorption effect on amaranth. The porous structure of the composite aerogel is the reason for the adsorption of these two dyes, so it has a physical adsorption effect on amaranth dye and methylene blue dye. Furthermore, GA-MCC-PEI-4 composite aerogels (PEI-12.4%) contain higher cationic PEI and have a stronger and more sensitive affinity to the anionic dye amaranth. When composite aerogels were used to adsorb the amaranth dye, chemical adsorption also occurred. In short, the adsorption process of GA-MCC-PEI on the cationic dye methylene blue is mainly the physical adsorption process caused by the interaction In summary, the GA-MCC-PEI-4 composite aerogel had obvious adsorption capacity for cationic dye methylene blue and anionic dye amaranth, but it had a better adsorption effect on amaranth. The porous structure of the composite aerogel is the reason for the adsorption of these two dyes, so it has a physical adsorption effect on amaranth dye and methylene blue dye. Furthermore, GA-MCC-PEI-4 composite aerogels (PEI-12.4%) contain higher cationic PEI and have a stronger and more sensitive affinity to the anionic dye amaranth. When composite aerogels were used to adsorb the amaranth dye, chemical adsorption also occurred. In short, the adsorption process of GA-MCC-PEI on the cationic dye methylene blue is mainly the physical adsorption process caused by the interaction between the adsorbate and the adsorbent molecule, and its adsorption on the anionic dye amaranth occurs as both physical and chemical adsorption. Chemical adsorption is the adsorption of electron transfer, exchange, or common between adsorbate molecules and atoms (or molecules) on the solid surface to form adsorption chemical bonds. This is also why when composite aerogels make contact with the cationic dye methylene blue and the anionic dye amaranth at the same time, they tend to adsorb more amaranth dyes before reaching their maximum adsorption capacity.
As shown in Figure 9a,b, as the concentrations of amaranth and methylene blue increased, the corresponding absorbance values also increased. The fitted standard curves of absorbance versus concentration for the two dyes had correlation coefficient (R 2 ) values that were greater than 0.99. Therefore, these standard curves were used in subsequent concentration calculations. of absorbance versus concentration for the two dyes had correlation coefficient (R 2 ) values that were greater than 0.99. Therefore, these standard curves were used in subsequent concentration calculations. As shown in Figure 9c,d, the adsorption capacities of GA-PEI (MCC-0%), GA-MCC-PEI-2 (MCC-26%), and GA-MCC-PEI-4 (MCC-39%) for amaranth and methylene blue were significantly affected by the pH value. In particular, the adsorption capacities of the aerogels for the anionic dye amaranth decreased as the pH increased, whereas the adsorption capacities of the aerogels for the cationic dye methylene blue increased as the pH increased. When GA-MCC-PEI adsorbs the anionic dye amaranth, the adsorption amount of amaranth dye can be divided into three parts with the change in PH. A PH between 2 and 4 is a high adsorption area, a PH between 4 and 8 is a transition area, and a PH between 8 and 10 is a low adsorption area. When GA-MCC-PEI adsorbs methylene blue, the adsorption amount of methylene blue dye can also be divided into three parts with the change in PH. A PH between 2 and 4 is a low adsorption area, a PH between 4 and 8 is a transition area, and a PH between 8 and 10 is a high adsorption area. In low-pH environ- As shown in Figure 9c,d, the adsorption capacities of GA-PEI (MCC-0%), GA-MCC-PEI-2 (MCC-26%), and GA-MCC-PEI-4 (MCC-39%) for amaranth and methylene blue were significantly affected by the pH value. In particular, the adsorption capacities of the aerogels for the anionic dye amaranth decreased as the pH increased, whereas the adsorption capacities of the aerogels for the cationic dye methylene blue increased as the pH increased. When GA-MCC-PEI adsorbs the anionic dye amaranth, the adsorption amount of amaranth dye can be divided into three parts with the change in PH. A PH between 2 and 4 is a high adsorption area, a PH between 4 and 8 is a transition area, and a PH between 8 and 10 is a low adsorption area. When GA-MCC-PEI adsorbs methylene blue, the adsorption amount of methylene blue dye can also be divided into three parts with the change in PH. A PH between 2 and 4 is a low adsorption area, a PH between 4 and 8 is a transition area, and a PH between 8 and 10 is a high adsorption area. In low-pH environments, excessive H + inhibits the release of cations, resulting in the weak adsorption capacity of the aerogels for the cationic dye methylene blue. In contrast, in low-pH environments, excessive H + promotes the release of anions and thus the adsorption of anionic dyes (amaranth). Therefore, as the pH increased, the adsorption capacity of the aerogel changed in opposite directions for anionic dyes (amaranth) and cationic dyes (methylene blue).
As shown in Figure 9c,d, the equilibrium adsorption capacity of the aerogel for the dyes increased as the MCC content increased. As the MCC content increased, the pores in the composite aerogel increased in number and decreased in size, thus increasing the adsorption capacity. In addition, the equilibrium adsorption capacity of the composite aerogel was higher for anionic dyes (amaranth) than for cationic dyes (methylene blue) irrespective of the MCC content and the pH environment because of the high affinity of cationic PEI in the composite aerogel for anionic dyes, which also confirmed the results shown in Figure 8g-o. GA-MCC-PEI-4 (MCC-39%) had the maximum adsorption capacity for both dyes, with an equilibrium adsorption amount of 369.37 mg/g (pH = 2) for amaranth and 237.33 mg/g (pH = 10) for methylene blue. Table 5 shows the maximum adsorption capacities of composites prepared from cellulose, graphene, and PEI for amaranth dye and methylene blue dye in recent years, which are all lower than that of GA-MCC-PEI-4 (MCC-39%) for amaranth (369.37 mg/g) and methylene blue (237.33 mg/g). Therefore, the adsorption capacity of a composite aerogel can be improved by regulating the content of cellulose in the composite to optimize the porous structure of the aerogel. As shown in Figure 10, the adsorption curves of GA-PEI (MCC-0%), GA-MCC-PEI-2 (MCC-26%), and GA-MCC-PEI-4 (MCC-39%) were fitted to the Langmuir and Freundlich isothermal equations with good R 2 values. Among them, the initial concentrations of the composite aerogels for the adsorption of the two dyes were determined by pre-experiment. It is the initial concentration corresponding to the maximum absorption of composite aerogels under certain conditions (pH = 7, room temperature).
As shown in Table 6, the Freundlich isothermal equation showed good fitting with the experimental data (R 2 > 0.9). The Freundlich isotherm is used to describe adsorption processes that occur on heterogeneous surfaces and active sites with different energies based on multilayer adsorption and equilibrium [60]. Adsorption strength n is used to describe the inhomogeneity of the adsorption surface [61]. The greater the value of 1/n, the greater the adsorption strength of the adsorbate. When 0.1 < 1/n < 0.5, the adsorption process is able to proceed. K F describes the adsorption capacity of the adsorption process. The larger the value, the larger the adsorption capacity of the adsorbate [62,63]. The 1/n of the composite aerogel GA-MCC-PEI for the adsorption of the amaranth or methylene blue solutions was between 0.1 and 0.5. Moreover, with the increase in the MCC content in the composite aerogels, the values of 1/n and KF gradually increased. For the composite aerogels with the same MCC content, the values of 1/n and K F corresponding to the absorption of the amaranth dye are higher than those corresponding to the absorption of the methylene blue dye. This indicates that the adsorption process of the GA-MCC-PEI composite aerogel for the two dyes is beneficial. Moreover, with the increase in the MCC content in the composite aerogel, its absorption capacity is stronger. The absorption capacity of the GA-MCC-PEI composite aerogel for the amaranth dye was better than that for the methylene blue dye. As shown in Table 6, the Freundlich isothermal equation showed good fitting with the experimental data (R 2 > 0.9). The Freundlich isotherm is used to describe adsorption processes that occur on heterogeneous surfaces and active sites with different energies based on multilayer adsorption and equilibrium [60]. Adsorption strength n is used to describe the inhomogeneity of the adsorption surface [61]. The greater the value of 1/n, the greater the adsorption strength of the adsorbate. When 0.1 < 1/n < 0.5, the adsorption process is able to proceed. KF describes the adsorption capacity of the adsorption process. The larger the value, the larger the adsorption capacity of the adsorbate [62,63]. The 1/n of the composite aerogel GA-MCC-PEI for the adsorption of the amaranth or methylene blue solutions was between 0.1 and 0.5. Moreover, with the increase in the MCC content in the composite aerogels, the values of 1/n and KF gradually increased. For the composite aerogels with the same MCC content, the values of 1/n and KF corresponding to the absorption of the amaranth dye are higher than those corresponding to the absorption of the methylene blue dye. This indicates that the adsorption process of the GA-MCC-PEI composite aerogel for the two dyes is beneficial. Moreover, with the increase in the MCC content in the composite aerogel, its absorption capacity is stronger. The absorption capacity of the GA-MCC-PEI composite aerogel for the amaranth dye was better than that for the methylene blue dye. The Langmuir equation showed a good fitting with the experimental data (R 2 > 0.99), which was greater than the corresponding R 2 value fitted by the Freundlich isothermal equation. Therefore, the Langmuir adsorption model described the adsorption isotherms better than the Freundlich adsorption model, indicating that monolayer adsorption of the two dyes occurred in all the composite aerogel samples. The dimensionless R L values of the Langmuir equation (Table 6) were greater than 0 and less than 1, indicating that all the adsorption processes were spontaneous. Moreover, as the MCC content increased, both the isothermal adsorption constant k L and saturated adsorption capacity Q m of the composite aerogel increased. This shows that with the increase in the MCC content in the composite aerogel, its absorption capacity is stronger. The GA-MCC-PEI-4 (MCC-39%) aerogel with the largest specific surface area had the best adsorption capacity because the density of the pores in the composite aerogel was optimal at an MCC content of 39%. For the composite aerogels with the same MCC content, the isothermal adsorption constant k L and saturated adsorption capacity Q m corresponding to the amaranth dye absorption were higher than those corresponding to the methylene blue dye absorption. All samples showed a greater adsorption capacity for the anionic dye amaranth than for the cationic dye methylene blue because of the high affinity of cationic PEI in the composite aerogel for anionic dyes.

Conclusions
In this work, a preparation method for ternary composite aerogels composed of graphene, cellulose, and PEI was demonstrated. Ultra-lightweight graphene-cellulose-PEI aerogels (GA-MCC-PEI) with a dense mesoporous structure on the surface and with high mechanical strength, good thermal stability, and significant adsorption capacity for both anionic and cationic dyes were prepared. Inside the composite aerogel, hydrogen bonds formed among cellulose, graphene, and PEI. Cellulose was successfully inserted between the graphene sheets, which played a role in preventing the π-π stacking of the graphene sheets. The GA-MCC-PEI aerogel with an MCC content of 43% (mass of 0.91 g) was able to withstand a pressure of up to 21.76 kPa, equivalent to 827 times the mass of the aerogel. As the cellulose content increased, the mechanical properties of the composite aerogel were enhanced. Adsorption tests revealed that the GA-MCC-PEI composite aerogel had a significant adsorption capacity for the anionic dye amaranth and the cationic dye methylene blue. Moreover, fitting of the adsorption isotherms using the Langmuir isothermal equation yielded high correlation coefficients, indicating monolayer adsorption. Among the prepared aerogels, GA-MCC-PEI-4 (MCC-39%) had the largest adsorption capacity for both dyes, with an equilibrium adsorption capacity of 369.37 mg/g and 237.33 mg/g for amaranth and methylene blue, respectively. The prepared graphene-cellulose-PEI aerogel can be used to remove dye pollutants in water to maintain ecological balance, thus broadening the application space of aerogel materials, that is, as adsorbents in different environments.
Funding: This research was financially sponsored by the Fundamental Research Funds for the Central Universities (2572019BB05) for its support.

Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Data Availability Statement:
The data that support the findings of this study are available from the corresponding author upon reasonable request.