Surface Modiﬁcations of Superparamagnetic Iron Oxide Nanoparticles with Polyvinyl Alcohol and Activated Charcoal as Methylene Blue Adsorbents

: As novel methylene blue adsorbents, polyvinyl alcohol and activated charcoal were used to modify the surface of superparamagnetic iron oxide nanoparticles. The adsorption capacity after 69 h was 26.50 ± 0.99–40.21 ± 1.30 mg/g, depending on the temperature (333.15, 310.15, and 298.15 K) and the initial concentration of methylene blue, which was between 0.017 and 0.020 mg/mL. Based on thermodynamics parameters, the adsorption process can be considered to be spontaneous endothermic physisorption. Kinetics studies show that the pseudo-second-order model was the best-ﬁtted model. Adsorption isotherm studies show that the best-ﬁtted models were the Langmuir, Langmuir, and Temkin and Pyzhev isotherm models when adsorbing MB at 333.15, 310.15, and 298.15 K, respectively.


Introduction
Although magnetic nanoparticles have various applications [1], water treatment is one of the most common applications [2][3][4][5].The magnetic property makes the separation processes easier, especially in solid-liquid phases [6], leading to their application in water treatment.Hence, magnetic separation processes are receiving more attention from researchers globally.Magnetic properties can be obtained from various magnetic nanoparticles (i.e., iron oxide nanoparticles-IONPs). IONPs have different types, including magnetite, superparamagnetic iron oxide nanoparticles, and Fe 3 O 4 (SPION).SPION, a hydrophobic material, can be synthesized via multiple methods, of which co-precipitation is the most rapid, with the highest yield of magnetite and a facile synthesis method due to the suppression of maghemite, despite several disadvantages such as agglomeration [1,[7][8][9].This might be caused by kinetic factors while crystals are growing during the nucleation and oxidation processes [1,[7][8][9].
In water treatment, the presence of SPION can ease the separation process when removing synthetic dyes from water due to their magnetic properties [6].While SPION nanoparticles have a large surface area, the adsorption capacity of synthetic dyes (i.e., methyl orange, Congo red, and methylene blue-MB) can be enhanced significantly when carbon-based materials are introduced (i.e., activated charcoal (AC), graphene oxide, and carbon nanotubes) due to their larger surface area, chemical structure (i.e., porosity), and superior adsorption capabilities [2,[10][11][12][13][14][15][16][17][18][19][20].For instance, the adsorption capacity of SPION is only 45.43 mg/g, while SPION/MWCNT, SPION@Carbon sheets, SPION/graphene oxide, and SPION/expanded graphite have adsorption capacities of 48.06, 95, 280.26, and 76.2 mg/g, respectively [21][22][23][24][25]. Recently, as an MB adsorbent, SPION has been modified using PVA and graphite, yielding SPION/PVA/GR [26].However, one of the more inexpensive carbon-based materials is activated charcoal (AC).Commercial AC, one of the most used adsorbents due to its high pore value, huge surface area, high surface reactivity, and suitable pore distribution caused by the carbonization activation processes, can be produced from multiple sources of agricultural waste [27][28][29].Hence, to improve the adsorption process of MB, which is a carcinogenic and toxic synthetic textile dye associated with cancer, skin disease, and mutations, modifying SPION with activated charcoal is necessary [30][31][32].Removing methylene blue from wastewater is necessary to protect the environment and human health [32].
Even though the phase separation process between solid and liquid can be easy when using magnetic activated charcoal as an MB adsorbent, to enhance the rate of degradation of the pollutants and alter the physical form of the adsorbents (i.e., to a membrane or thin film), polymers such as polyvinylpyrrolidone, polyacrylonitrile, or especially polyvinyl alcohol (PVA) can be introduced into the composite [33][34][35][36][37][38].Polymers can also affect the adsorption capacity of SPION-based MB adsorbents.For instance, SPION/chitosan/graphene oxide and SPION/PVA/chitosan/graphene oxide can have adsorption capacities of 30.01 and 36.4 mg/g, respectively [39,40].
This present study focuses on evaluating the potential of adsorbing MB onto SPION/ PVA/AC materials, which can be synthesized via simple, environmentally friendly, and inexpensive methods.Moreover, using SPION/PVA/AC, there is a potential to make a magnetic thin film composite adsorb MB.Additionally, this work chose a very low initial concentration of MB to test the possibility of removing MB from diluted MB wastewater at 298.15-333.15K.In this study, the characterization of SPION/PVA/AC and the quantitative method for adsorption experiments were adapted without any modifications similar to previous literature [26,40].However, the surface charge of SPION was determined using zeta potential measurements.Additionally, by adapting the same methods and calculations without any modifications, as in previous publications, the adsorption kinetics (pseudo-first and pseudo-second-order, simplified Elovich), adsorption isotherm (Langmuir, Dubinin-Raduskevich, Halsey, Tempkin and Pyzhev, and Halsey), and thermodynamic properties were evaluated [26,40].

Materials
From Xilong Scientific Co., Ltd.(Shantou, China), activated charcoal (AC) was bought.The remaining chemicals were used without any purification after being purchased from the same batch and companies as in the previous publication [26].

Synthesis
Solution A1-SPION synthesis: The synthesis process was adapted without any modifications from the previous publication [26].
Solution A2-SPION solution: Without any modifications, the SPION solution was prepared as in the previous publication [26].
Solution B-PVA solution: Without any modifications, the PVA solution was prepared as in the previous publication [26].
Solution C-AC solution: In 250 mL of deionized water, 12 g of dried AC was mixed for 1 h using sonication.
Solution D-SPION/PVA synthesis: Without any modifications, the SPION/PVA solution was prepared as in the previous publication [26].
Solution E-SPION/PVA/AC synthesis: To synthesize SPION/PVA/AC, solution C was initially mixed with solution D for 1 h.Then, the product was dried at 80 • C for 24 h.Solution G-Methylene blue stock solution: Without any modifications, the MB solution was prepared as in the previous publication [26].
Solution H-Methylene blue diluted solution: Without any modifications, this step was adapted from the previous literature [26].

Characterization of Adsorbent
Adapting from previous publications, after synthesizing SPION/PVA/AC, the FE-SEM, FTIR, XRD, BET, BJH, and VSM were used to characterize the adsorbents [26,40].Additionally, the zeta potential can determine the type of surface charge of SPION.

FE-SEM
As shown in Figure 1a, adapting from previous publications [26,40], the morphology of IONPs (iron oxide nanoparticles) was evaluated.The IONPs seem to be aggregated, which is similar to previous publications [1,26,40].
Solution H-Methylene blue diluted solution: Without any modifications, this ste was adapted from the previous literature [26].

Characterization of Adsorbent
Adapting from previous publications, after synthesizing SPION/PVA/AC, the FE SEM, FTIR, XRD, BET, BJH, and VSM were used to characterize the adsorbents [26,40 Additionally, the zeta potential can determine the type of surface charge of SPION.

FE-SEM
As shown in Figure 1a, adapting from previous publications [26,40], the morpholog of IONPs (iron oxide nanoparticles) was evaluated.The IONPs seem to be aggregated which is similar to previous publications [1,26,40].Using ImageJ software v.1.53t,as shown in Figure 1b, IONPs have the mean particl size of 23.3 ± 2.4 nm.The average IONPs size matched the results of previous publication [1,26].
As shown in Figure 2a, while IONPs seem to be invisible, at the 5 µm scale, AC was clearly visible.However, as the magnification increased, in Figure 2b,c, the IONPs, which are on the surface of AC, were clearly visible.With some findings, in the area that was heavily concentrated with IONPs at 500 nm, as shown in Figure 2c, the IONPs were aggregated.This phenomenon can be explained by PVA coating the outer surface of IONPs, as demonstrated in Figure 2d.However, the aggregation can also be caused by the infamous disadvantage of the synthesis method (co-precipitation).Hence, XRD and FTIR were used to confirm Figure 2d.As shown in Figure 2a, while IONPs seem to be invisible, at the 5 µm scale, AC was clearly visible.However, as the magnification increased, in Figure 2b,c, the IONPs, which are on the surface of AC, were clearly visible.With some findings, in the area that was heavily concentrated with IONPs at 500 nm, as shown in Figure 2c, the IONPs were aggregated.This phenomenon can be explained by PVA coating the outer surface of IONPs, as demonstrated in Figure 2d.However, the aggregation can also be caused by the infamous disadvantage of the synthesis method (co-precipitation).Hence, XRD and FTIR were used to confirm Figure 2d.

XRD Analysis
To confirm whether IONPs were SPION, XRD analysis was performed [26].As shown in Figure 3a, the peaks at 2θ positions of 18.28 • , 30.17As shown in Figure 2a, while IONPs seem to be invisible, at the 5 µm scale, AC w clearly visible.However, as the magnification increased, in Figure 2b,c, the IONPs, wh are on the surface of AC, were clearly visible.With some findings, in the area that w heavily concentrated with IONPs at 500 nm, as shown in Figure 2c, the IONPs were a gregated.This phenomenon can be explained by PVA coating the outer surface of ION as demonstrated in Figure 2d.However, the aggregation can also be caused by the in mous disadvantage of the synthesis method (co-precipitation).Hence, XRD and FT were used to confirm Figure 2d.

XRD Analysis
To confirm whether IONPs were SPION, XRD analysis was performed [26].shown in Figure 3a, the peaks at 2θ positions of 18.28°, 30.17°, 35.51°, 43.17°, 53.65°, 57.1 and 62.75° confirm that IONPs are magnetite-SPION [42].Moreover, the hkl indices th correspond to these 2θ positions are (220), ( 311), ( 400), ( 422), (511), and (440), which similar to the literature [43][44][45].Based on Figure 3a, using the Scherrer equation at a reflective peak 2θ of 35.51° [4 the shape factor of 0.89, and the SPION size were determined to be 23.2 nm.This res corresponds to the FE-SEM analysis.As shown in Figure 3b, the peaks of SPION/PVA/A have all the characteristic 2θ positions of SPION combining with the high-intensity pea Based on Figure 3a, using the Scherrer equation at a reflective peak 2θ of 35.51 • [46], the shape factor of 0.89, and the SPION size were determined to be 23.2 nm.This result corresponds to the FE-SEM analysis.As shown in Figure 3b, the peaks of SPION/PVA/AC have all the characteristic 2θ positions of SPION combining with the high-intensity peaks of AC and PVA, which indicated that SPION/PVA/AC was successfully constructed similar to Figure 2d.

FTIR
To determine types of bonds exists in the adsorbent, FTIR was used.The FTIR spectra were analyzed using the same instrument as the previous publication [26,40].As seen in Figure 4, IONP were confirmed to be SPIONs due to the distinctive peaks at 584 and 446 cm −1 [26,40,47].Additionally, as shown in Figure 4a, the wavelengths of 3419 and 1627 cm −1 also appear.These peaks were similar to previous publications [1,26,40,[48][49][50].
Magnetochemistry 2023, 9, x FOR PEER REVIEW 5 of 22 of AC and PVA, which indicated that SPION/PVA/AC was successfully constructed similar to Figure 2d.

Zeta Potential
To evaluate one of the nanoparticles' physical properties, the zeta potential can be considered.By providing the electrical state of charged interfaces between dispersed particles, the electrostatic interaction can be measured using zeta potential [60].The average zeta potential of SPION was 18.67 ± 6.16 mV at pH = 4-5, which was similar to other publications [61][62][63][64][65][66], and the nanoparticles were not stable in the colloid suspension [67].However, the relationship between the zeta potential and the colloidal stability of nanoparticles in dispersion is conflicting in the literature [60].However, based on the zeta potential reported above, the net charge of SPION nanoparticles was positive.

BJH Analysis
The adsorption-desorption isotherm in Figure 4b shows that starting at 0.1 p/po, the volume of the adsorbate uptake increases to a higher p/po.
From Figure 4b, a type IV isotherm can be seen.This can be interpreted that the adsorbent has a small amount of micropores (with a size between 2 and 50 nm) in its mesoporous structure [68,69].Additionally, the hysteresis loop can be considered H3 type, indicating that the adsorbents have a wide pore size distribution [41].As shown in Table 1, the SPION/PVA/AC's average pore diameter was shown.Additionally, as shown in Figures 3 and 4a, combining with the synthesis method similar to the literature, the IONPs that were used in this research can be considered as SPION [51][52][53][54].As shown in Figure 4a, the PVA has peaks at 851, 1097, 1378, 1443, 1653, 1737, 2941, and 3418 cm −1 , which correspond to the C-C stretching vibration, C=O stretching, C-H dormation vibration, CH 2 bending, C=O carbonyl stretch, C=O stretching vibrational band, CH 2 asymmetric stretching vibration, and O-H stretching vibration, respectively [26,[55][56][57][58].As shown in Figure 4a, the AC has peaks at 1634, and 3427 cm −1 , which correspond to the C=O stretching vibration and the O-H stretching vibration [59].In Figure 4a, SPION/PVA/AC has peaks at 3421, 2921, 1617, 1058, 677, 598, and 442 cm −1 .These peaks were similar to the peaks of SPION, PVA, and AC.Hence, Figure 2d can be considered to be the morphology of SPION/PVA/AC.

Zeta Potential
To evaluate one of the nanoparticles' physical properties, the zeta potential can be considered.By providing the electrical state of charged interfaces between dispersed particles, the electrostatic interaction can be measured using zeta potential [60].The average zeta potential of SPION was 18.67 ± 6.16 mV at pH = 4-5, which was similar to other publications [61][62][63][64][65][66], and the nanoparticles were not stable in the colloid suspension [67].However, the relationship between the zeta potential and the colloidal stability of nanoparticles in dispersion is conflicting in the literature [60].However, based on the zeta potential reported above, the net charge of SPION nanoparticles was positive.

BJH Analysis
The adsorption-desorption isotherm in Figure 4b shows that starting at 0.1 p/p o , the volume of the adsorbate uptake increases to a higher p/p o .
From Figure 4b, a type IV isotherm can be seen.This can be interpreted that the adsorbent has a small amount of micropores (with a size between 2 and 50 nm) in its mesoporous structure [68,69].Additionally, the hysteresis loop can be considered H3 type, indicating that the adsorbents have a wide pore size distribution [41].As shown in Table 1, the SPION/PVA/AC's average pore diameter was shown.In addition to determining the surface area of 751 m 2 /g, Table 1 also determines the total pore volume of the adsorbent to be 0.38 cm 3 /g and the average pore diameter of the SPION/PVA/AC to be 10 Å.
Based on the shape of the hysteresis loop in Figure 4c, the SPION/PVA/AC can be concluded to have superparamagnetic properties as well, even though the magnetization magnitude decreases significantly compared to bare SPION from 69.7 to 10.5 emu/g.This phenomenon can be explained similar to the FE-SEM results for PVA-coated SPION [75].From the FE-SEM, FTIR, and VSM analyses, as shown in Figure 2d, the structure of the adsorbent was proposed.

Loading Capacity of SPION/PVA/AC and Modelling
Using the same settings and instruments of UV-Vis spectrometry as in the literature, the MB concentration was quantified [26,40].As shown in Table 2, the measured MB concentration, Q t , %LC, and %EE of the adsorption process at 273.15, 303.15, and 333.15K can be calculated.1, SPION/PVA/AC has an adsorption capacity 3% higher than SPION/PVA/CS/GO [40] and SPION/CS/GO [39].However, SPION/PVA/ AC has slightly lower adsorption capacities than SPION (17.5%) [21], SPION/MWCNT (22%) [22], and SPION@Graphene (17.2%) [76].Despite these small changes in adsorption capacity, SPION/PVA/AC consists of cheaper materials compared to SPION/CS/GO, SPION/MWCNT, and SPION@Graphene.Hence, the benefits of low cost can outweigh the slight decreases in the adsorption capacities.When compared to SPION, despite its more expensive and smaller adsorption capacities, SPION/PVA/AC consists of PVA, which can further modify the physical form of the adsorbents (i.e., thin film).Additionally, after 24 h, at 333.15 K, in four different concentrations, at least 85% methylene blue was adsorbed, while only 55% methylene blue was adsorbed at 298.15 K.This shows that as the temperature increases, the loading amount, loading capacity, and entrapment efficiency increase significantly after 24 h.Hence, temperature has significant effects on adsorption capacity.
Due to the effect of temperature, the thermodynamic parameters were calculated and are given in Table 3.As shown in Table 3, a feasible and spontaneous adsorption process can be interpreted by ∆G < 0 [77][78][79][80][81].To further interpret the ∆G value, as the temperature increases, ∆G becomes more negative.This indicates that physical forces are the main factor in the adsorption process, and adsorption is more favorable at higher temperatures [77,82].In addition, the value of ∆S, which is greater than zero, indicates that during the adsorption process, the surface randomness increases and the MB and SPION/PVA/AC internal structures change [77][78][79][80][81]. Additionally, ∆H > 0 indicates that the adsorption process was endothermic, there was an occurrence of monolayer adsorption, and weak chemical forces between the adsorbents and MB exist [77][78][79][80][81].The endothermic adsorption process means that the adsorption degree increases as the temperature increases [80].The endothermic adsorption can be explained by the interaction between pre-adsorbed water and SPION/PVA/AC, which is stronger than the interaction between MB and SPION/PVA/AC [83].Hence, MB molecules have to compete for the active sites of SPION/PVA/AC against water molecules, resulting in the simultaneous adsorption-desorption of MB and water, yielding ∆H > 0 [84,85].The adsorption process can be considered to be physisorption if the ∆H > 40 kJ/mol [77,80].As shown in Table 3, as the indicator, the ∆H < 20 kJ/mol shows that Van der Waals forces dominate the physisorption interaction [86].Additionally, this value also indicates that the electrostatic interactions and forces of attraction were weak and the bonding between MB and the adsorbents was loose [87][88][89].After determining the relationship between temperature and adsorption capacities, the relationship between time and adsorption capacities were investigated (as shown in Table 4).
As shown in Table 4, the adsorption capacity increased as the temperature increases from 298.15 to 310.15 K, indicating an endothermic process, which is in accord with ∆H > 0 [77,78].However, the adsorption capacity decreased insignificantly as the temperature reached 333.15 K.This phenomenon might be due to the decrease in adsorption forces between the active sites of SPION/PVA/AC and MB [90,91] and the increase in mobility of MB ions [92].When increasing the initial MB concentration, the driving force of mass transfer is higher, leading to an increase in adsorption/loading capacity [93].After 25 h, at a temperature of 333.15 K, the loading capacity did not deviate much.This phenomenon can be caused by a decreased ratio between the free methylene blue molecules and the abundant free adsorption sites available [92,94].From Table 4, to have the highest adsorp-tion capacities, SPION/PVA/AC must be in contact with MB solution at the concentration of 0.02 mg/mL for 69 h at 310.15 K.After adsorbing almost all the methylene blue (%EE was close to 100%), values of loading amount (Q t ) and time (t) were used to calculate the adsorption kinetics using multiple kinetics models.As shown in Table 5 and Figure 5, at different adsorption conditions (i.e., temperature, time, and MB concentration), the pseudo-second-order and simplified Elovich kinetic model can determine the adsorption rate and the loading amount at equilibrium.As shown in Table 4, the adsorption capacity increased as the temperature increases from 298.15 to 310.15 K, indicating an endothermic process, which is in accord with ∆H > 0 [77,78].However, the adsorption capacity decreased insignificantly as the temperature reached 333.15 K.This phenomenon might be due to the decrease in adsorption forces between the active sites of SPION/PVA/AC and MB [90,91] and the increase in mobility of MB ions [92].When increasing the initial MB concentration, the driving force of mass transfer is higher, leading to an increase in adsorption/loading capacity [93].After 25 h, at a temperature of 333.15 K, the loading capacity did not deviate much.This phenomenon can be caused by a decreased ratio between the free methylene blue molecules and the abundant free adsorption sites available [92,94].From Table 4, to have the highest adsorption capacities, SPION/PVA/AC must be in contact with MB solution at the concentration of 0.02 mg/mL for 69 h at 310.15 K.After adsorbing almost all the methylene blue (%EE was close to 100%), values of loading amount (Qt) and time (t) were used to calculate the adsorption kinetics using multiple kinetics models.
As shown in Table 5 and Figure 5, at different adsorption conditions (i.e., temperature, time, and MB concentration), the pseudo-second-order and simplified Elovich kinetic model can determine the adsorption rate and the loading amount at equilibrium.As shown in Table 5, at 333.15, 310.15, and 273.15 K, out of all the mentioned kinetics models, the pseudo-second order can be considered to be the most fitted for SPION/PVA/AC due to the small χ 2 and R 2 values.The pseudo-second-order kinetic model, which is shown in Table 5, indicates that the adsorption mechanism is involved in chemisorption via electrons transferring (valence forces) between MB and the adsorbent [95][96][97][98][99].
As the temperature increased from 273.15 to 310.15 K, the k 2 values increased as well, indicating a faster adsorption rate at high temperatures [92].Moreover, depending on the adsorption conditions (i.e., adsorption contact time and adsorption amount), the MB adsorption rate decreases as time increases.This phenomenon can be caused by the conversion of MB to the MB + cationic form [77].
After 25 h, MB had a slight shift in the UV-VIS peak wavelength when the adsorption experiments were at T = 333.15K.However, at 298.15 K and 310.15 K, the phenomenon was not seen.The wavelength shift phenomenon can be seen and explained similarly to previous publications [26].
Comparing the obtained experimental and calculated equilibrium adsorption capacities (as shown in Tables 4 and 5), these values were much smaller compared to some literature [100][101][102][103][104][105][106][107][108] and much greater compared to other literature [89,93,[109][110][111][112].Similar to the previous publication, as shown in Table 6, various adsorption isotherm models, including isotherm constants, were determined [26].The adsorption experimental parameters can be fitted using all the above isotherm models, based on the R 2 values, except Langmuir at 298.15 K.However, as shown in Table 6, at 310.15 and 333.15 K, the best-fitted isotherm model is Langmuir due to the highest R 2 values.Similarly, at 298.15 K, the best-fitted isotherm model is Temkin and Pyzhev due to the highest R 2 value.As shown in Table 6, at 310.15 and 333.15 K, since 0 < average R L < 1 in the Langmuir adsorption isotherm models (as shown in Figure 6), the adsorption mechanism can be described as the attachment of MB onto the surface of SPION/PVA/AC, which is favorable [2,22].From the Langmuir isotherm model, the adsorbent's surface can be considered to be homogeneous, and MB was adsorbed as a monolayer [25,26].As shown in Figure 7, from the Frendlich isotherm model, at 333.15 K, the value indicates the non-favorable physical process [26].At 310.15 K, as is the closest to 0, the physical process was favorable.Moreover, the values of nF, which were smaller than 1 at T = 333.15K and 298.15 K, represent the poor adsorption characteristic, while at 310.15 K, the nF value was greater than 1, which indicates the good adsorption characteristic [77].Since > 1, the adsorption process has involved cooperative adsorption [26,102,113].Moreover, since nF < 1, with surface density, the bond energies increase [26,114].
Looking at the Dubinin-Radushkevich model, as shown in Figure 8, the R 2 value was greater than 0.5, which indicates that the adsorption between SPION/PVA/AC and methylene blue occurred in relevance with this isotherm at all temperatures [115].As shown in Figure 7, from the Frendlich isotherm model, at 333.15 K, the 1 n F value indicates the non-favorable physical process [26].As shown in Figure 7, from the Frendlich isotherm model, at 333.15 K, the value indicates the non-favorable physical process [26].At 310.15 K, as is the closest to 0, the physical process was favorable.Moreover, the values of nF, which were smaller than 1 at T = 333.15K and 298.15 K, represent the poor adsorption characteristic, while at 310.15 K, the nF value was greater than 1, which indicates the good adsorption characteristic [77].Since > 1, the adsorption process has involved cooperative adsorption [26,102,113].Moreover, since nF < 1, with surface density, the bond energies increase [26,114].
Looking at the Dubinin-Radushkevich model, as shown in Figure 8, the R 2 value was greater than 0.5, which indicates that the adsorption between SPION/PVA/AC and methylene blue occurred in relevance with this isotherm at all temperatures [115].At 310.15 K, as 1  n F is the closest to 0, the physical process was favorable.Moreover, the values of n F , which were smaller than 1 at T = 333.15K and 298.15 K, represent the poor adsorption characteristic, while at 310.15 K, the n F value was greater than 1, which indicates the good adsorption characteristic [77].Since 1 n F > 1, the adsorption process has involved cooperative adsorption [26,102,113].Moreover, since n F < 1, with surface density, the bond energies increase [26,114].
Looking at the Dubinin-Radushkevich model, as shown in Figure 8, the R 2 value was greater than 0.5, which indicates that the adsorption between SPION/PVA/AC and methylene blue occurred in relevance with this isotherm at all temperatures [115].Since KDR < 1, the surface heterogeneity increased due to the pore structure of SPION/PVA/AC and the interactions between SPION/PVA/AC and MB [26,116].Because E < 0, the sorption process is exothermic [117].When E is between 8 and 16 kJ/mol or E < 8 kJ/mol, the adsorption process that occurs can be chemical ion-exchange or physical adsorption, respectively [26,[118][119][120][121].Hence, from Figure 8, the sorption process can be considered to be physical adsorption.
On the other hand, at 298.15 K, the best-fitted adsorption isotherm model was Temkin and Pyzhev, as shown in Figure 9, with an R 2 value of 0.999.The Temkin and Pyzhev model shows that adsorption is characterized by a uniform distribution of binding energies, up to some maximum binding energy [122,123] Similar to the Freundlich isotherm model, the Halsey isotherm model can examine an adsorption system that has multilayered and heterogeneous surfaces with a uniform surface heat distribution [26,124].Hence, at 273.15 K, 310.15 K, and 333.15 K, the only model that is not the worst-fitted model is Halsey, as shown in Figure 10, and it has similar R 2 values as the Freundlich isotherm model.Since K DR < 1, the surface heterogeneity increased due to the pore structure of SPION/PVA/AC and the interactions between SPION/PVA/AC and MB [26,116].Because E < 0, the sorption process is exothermic [117].When E is between 8 and 16 kJ/mol or E < 8 kJ/mol, the adsorption process that occurs can be chemical ion-exchange or physical adsorption, respectively [26,[118][119][120][121].Hence, from Figure 8, the sorption process can be considered to be physical adsorption.
On the other hand, at 298.15 K, the best-fitted adsorption isotherm model was Temkin and Pyzhev, as shown in Figure 9, with an R 2 value of 0.999.Since KDR < 1, the surface heterogeneity increased due to the pore structure of SPION/PVA/AC and the interactions between SPION/PVA/AC and MB [26,116].Because E < 0, the sorption process is exothermic [117].When E is between 8 and 16 kJ/mol or E < 8 kJ/mol, the adsorption process that occurs can be chemical ion-exchange or physical adsorption, respectively [26,[118][119][120][121].Hence, from Figure 8, the sorption process can be considered to be physical adsorption.
On the other hand, at 298.15 K, the best-fitted adsorption isotherm model was Temkin and Pyzhev, as shown in Figure 9, with an R 2 value of 0.999.The Temkin and Pyzhev model shows that adsorption is characterized by a uniform distribution of binding energies, up to some maximum binding energy [122,123] Similar to the Freundlich isotherm model, the Halsey isotherm model can examine an adsorption system that has multilayered and heterogeneous surfaces with a uniform surface heat distribution [26,124].Hence, at 273.15 K, 310.15 K, and 333.15 K, the only model that is not the worst-fitted model is Halsey, as shown in Figure 10, and it has similar R 2 values as the Freundlich isotherm model.The Temkin and Pyzhev model shows that adsorption is characterized by a uniform distribution of binding energies, up to some maximum binding energy [122,123] Similar to the Freundlich isotherm model, the Halsey isotherm model can examine an adsorption system that has multilayered and heterogeneous surfaces with a uniform surface heat distribution [26,124].Hence, at 273.15 K, 310.15 K, and 333.15 K, the only model that is not the worst-fitted model is Halsey, as shown in Figure 10, and it has similar R 2 values as the Freundlich isotherm model.As shown in Table 6, at 333.15 K, since I 0, the intraparticle diffusion model can be considered to be not only intraparticle diffusion but also film diffusion [26,77].Additionally, from the data in Table 7 and Figure 11, as the kI values decrease while temperature increases, combining with the I values, the diffusion process (intraparticle and film) happened simultaneously [125][126][127].As shown in Table 6, at 333.15 K, since I = 0, the intraparticle diffusion model can be considered to be not only intraparticle diffusion but also film diffusion [26,77].
Additionally, from the data in Table 7 and Figure 11, as the k I values decrease while temperature increases, combining with the I values, the diffusion process (intraparticle and film) happened simultaneously [125][126][127].In addition to intraparticle diffusion, film diffusion, chemisorption, and physical adsorption, other adsorption mechanisms could include the electrostatic interaction of surface negative charge with the positively charged methylene blue, the hydrogen bonding, and the π-π* stacking with the aromatic ring of methylene blue [125][126][127].Moreover, the adsorption mechanisms can be controlled by external diffusion and boundary layer diffusion [77,88,128].Hence, the adsorption was not only controlled by the rate-control step but also by some of the kinetic models and intraparticle diffusion as well.In addition to intraparticle diffusion, film diffusion, chemisorption, and physical adsorption, other adsorption mechanisms could include the electrostatic interaction of surface negative charge with the positively charged methylene blue, the hydrogen bonding, and the π-π* stacking with the aromatic ring of methylene blue [125][126][127].Moreover, the adsorption mechanisms can be controlled by external diffusion and boundary layer diffusion [77,88,128].Hence, the adsorption was not only controlled by the rate-control step but also by some of the kinetic models and intraparticle diffusion as well.

Conclusions
Using polyvinyl alcohol and activated charcoal to modify the surface of superparamagnetic iron oxide nanoparticles, the materials can adsorb MB at 333.15, 310.15, and 298.15K with the adsorption capacity after 69 h ranging from 26.50 ± 0.99 to 40.21 ± 1.30 depending on the temperature and the initial concentration of methylene blue, which were between 0.017 and 0.020 mg/mL.The thermodynamic parameters indicate that the adsorption was endothermic, spontaneous, and physisorption.The adsorption capacity increased as temperature increased despite the physical change of methylene blue at 333.15 K based on the shift in the UV-VIS peak wavelength.Based on the adsorption kinetics (pseudo-second order) and the intraparticle diffusion model, the adsorption mechanism can be considered chemisorption and exothermic.The Langmuir, Langmuir, and Temkin-Pyzhev isotherm models were the best-fitted models at 333.15, 310.15, and 298.15 K, respectively.

Conclusions
Using polyvinyl alcohol and activated charcoal to modify the surface of superparamagnetic iron oxide nanoparticles, the materials can adsorb MB at 333.15, 310.15, and 298.15K with the adsorption capacity after 69 h ranging from 26.50 ± 0.99 to 40.21 ± 1.30 depending on the temperature and the initial concentration of methylene blue, which were between 0.017 and 0.020 mg/mL.The thermodynamic parameters indicate that the adsorption was endothermic, spontaneous, and physisorption.The adsorption capacity increased as temperature increased despite the physical change of methylene blue at 333.15 K based on the shift in the UV-VIS peak wavelength.Based on the adsorption kinetics (pseudo-second order) and the intraparticle diffusion model, the adsorption mechanism can be considered chemisorption and exothermic.The Langmuir, Langmuir, and Temkin-Pyzhev isotherm models were the best-fitted models at 333.15, 310.15, and 298.15 K, respectively.

Funding:
This research is funded by International University.VNU-HCM under grant number T2022-01-CEE.Institutional Review Board Statement: Not applicable.

Table 1 .
BJH and BET analyses of the SPION/PVA/AC samples.

Table 2 .
The Q t , %LC, and %EE after 24 h of adsorption.

Table 2 ,
comparing to Table

Table 6 .
Adsorption isotherms model constants and variables.

Table 7 .
The intraparticle diffusion model after 96 h.

Table 7 .
The intraparticle diffusion model after 96 h.