Highly efficient magnetic phosphoric acid modified defatted Chlorella vulgaris algae (MDCV/ 𝐅𝐞 𝟑 𝐎 𝟒 ) as a novel biosorbent for methylene blue removal

A novel biosorbent based on defatted Chlorella vulgaris (DCV) as a by-product of the biofuel industry was considered as an economical and inexpensive biosorbent in the form of magnetic modified defatted Chlorella vulgaris (MDCV/Fe3O4) for methylene blue (MB) removal. The lipid extraction was performed on raw Chlorella vulgaris (RCV). Phosphoric acid was selected as a DCV modifier. During acid modification, the variables affecting the biosorption capacity and the residual algae such as temperature (30-70 ℃ ), the contact time of DCV with acid (3-9 hr), the concentration of acid (2-6 mol/L), and the ratio of acid volume to DCV (30-70 mL/g) were investigated and optimized using Minitab-18 software. The modified defatted Chlorella vulgaris (MDCV) was prepared by acidification of DCV under optimal conditions. MDCV/ Fe 3 O 4 was prepared using the co-precipitation method for easy and low-cost separation of biosorbent. The XRD, FTIR, SEM, EDS, BET, and VSM analyses were performed to identify the structures and characteristics of RCV, DCV, MDCV, and MDCV/ Fe 3 O 4 . Some experiments were designed using Minitab-18 software to investigate the effects of temperature (5-45 ℃ ), contact time (30-90 min), biosorbent dosage (15-45 mg), initial concentration of MB (20-100 mg/L), and pH (5-9) on the biosorption capacity of MDCV/ Fe 3 O 4 . The kinetic, isothermal and thermodynamic parameters were investigated on MDCV/ Fe 3 O 4 . Results: O 4 was calculated in the amount of 32.44 mg/g. According to the positive values of ∆G and negative values of ∆H (-46.56 kJ/mol) and ∆S (-0.17 kJ/mol.K), the biosorption of MB on MDCV/ Fe 3 O 4 was non-spontaneous, exothermic with a decrease in irregularity. Modifications such as lipid extraction, improved this and Comparison characteristics species confirmed its high isothermal and thermodynamic studies were also performed.

has been reported in Equations 1-2. Ineffective variables were removed to increase the suitability of the models with experimental data [33].  ANOVA results of recent regression are reported in Table 2. The calculated Fisher distributions of both models are greater than their critical values. Also, the P-values of them are less than 0.05.
Therefore, the compatibility of the models with data is proven. The adjusted determination coefficients of models Y 1 and Y 2 are 91.34% and 96.14%, respectively. So, it can be concluded that no other effective variable has been ignored [33].  Table 3, the P-values of all coefficients of the effective variables in Y 1 analysis is less than 0.05. Since the coefficients of interactions of X 2 and X 4 with other variables are significant, they can not be ignored. Regarding the response of Y 2 , all variables except X 4 are significant [33]. ). Therefore, it can be concluded that the cubic crystal structure of iron oxide is well-formed [32,36].

Fourier Transform Infrared (FTIR)
The results of FTIR analysis for RCV, DCV, MDCV, and MDCV/Fe 3 O 4 are shown in Fig. 2. In all samples, the broad peak was observed in the range of 3400 -1 cm . It shows the tensile vibrations of the hydroxyl bond ( O-H ), the amide groups ( N-H ), and the presence of the water molecules [29]. The peaks around 2926 -1 cm are associated with symmetrical and asymmetric tensional vibrations C-H in aliphatic groups such as CH , 2 CH , and 3 CH [29]. The intensity of this peak is highest in RCV and almost the same in other samples. In RCV, a peak was observed in 2855 -1 cm , indicating 2 CH and 3 CH bonds in fatty acids. It confirms the presence of lipids in the structure of RCV that was removed after the lipid extraction process due to the removal of fatty acids [37]. CO mineral compounds such as carbonates. In general, small peaks in the wavelength regions below 600 -1 cm are related to the tensile vibrations of organic and mineral halogen compounds such as KCl [40]. About the sample of MDCV/Fe 3 O 4 , a wide peak is observed in the region of 571 -1 cm , which indicates the Fe-O vibrations, so the magnetic property of this sample is confirmed [32].  Fig. 3a, the crystalline structure of the RCV is heterogeneous. According to Fig. 3b, no significant changes in algae structure occurred after lipid extraction. Chloroform and methanol can enter cell tissue without serious damages to the cell walls [41]. Based on Fig. 3c, phosphoric acid modification has caused severe structural changes. The crystalline structure of DCV has been transformed into an amorphous structure with a uniform and relatively homogeneous surface. Also, the particle size has increased compared to the previous ones. The formation of cavities and bulges on the surface of MDCV is an important factor in increasing the biosorption of dye pollutants [41,42]. Fig. 3d shows the uniform coverage of the MDCV surface by iron oxide particles and the formation of a spherical crystalline structure [43].

Energy-Dispersive X-ray Spectroscopy (EDS)
The EDS analysis was performed to obtain the elements of RCV, DCV, MDCV, and MDCV/Fe 3 O 4 that is shown in Fig. 4. Percentages of elements are reported in Table 5. The highest weight percentages in RCV and DCV are related to carbon and oxygen. Other elements such as nitrogen, sodium, magnesium, aluminum, calcium, phosphorus, sulfur, chlorine, potassium, and silicon are also found with a lower weight. According to the results, after magnetization, about 38% of the weight of MDCV/Fe 3 O 4 is related to the iron elements. Therefore, the weight ratio of the MDCV: Fe 3 O 4 (1:1) is almost confirmed.

Brunauer-Emmett-Teller (BET)
The BET analysis was performed for RCV, DCV, MDCV, and MDCV/Fe 3 O 4 . Features such as specific surface area, average pore size, and porosity volume of samples were investigated in Table   6. The specific surface area of DCV and MDCV increased about 2 and 15 times, respectively, compared to RCV. The decrement in specific surface area of MDCV/Fe 3 O 4 compared to its nonmagnetic type was due to the coverage of some of its pores with iron particles. Nevertheless, the specific surface area of MDCV/Fe 3 O 4 compared to RCV has increased about 11 times. Thus, the appropriate modification process is confirmed on Chlorella vulgaris algae to prepare an easily separable biosorbent while increasing its specific surface area [43].   with no remanent magnetization and coercivity. It indicated the strong magnetic response to the different magnetic fields in paramagnetic materials. Therefore, they were easily separable by an external magnetic field and did not stick together when the magnetic field was removed [47]. The saturation magnetization of Fe 3 O 4 and MDCV/Fe 3 O 4 were 78.64 emu/g and 38.89 emu/g, respectively, which were suitable compared to the magnetic adsorbent derived from Chlorella vulgaris reported by M. Govarthanan [48]. The decrease in MDCV/Fe 3 O 4 magnetization relative to Fe 3 O 4 was due to changes in particle size, irregular bonding of particles, and surface spin disorientation [49,50].

Biosorption analysis
Experimental results for biosorption analysis are reported in Table 7. Based on Equation 3, the multiple regression analysis of experimental data with 95% probability was used to study the effect of each parameter on the biosorption capacity of MDCV/Fe 3 O 4 , kinetics, isotherms, and thermodynamic models. Ineffective variables were removed to increase the suitability of the models with experimental data.
The compatibility of the models with data is proven by the ANOVA results of recent regression.
Based on Table 8, the calculated Fisher distributions is greater than its critical value. Also, the Pvalue is less than 0.000. The adjusted determination coefficient of model Y is 98.35% [51]. According to Table 9, the P-values of all coefficients of the effective variables in Y analysis are less than 0.05. Since the coefficients of interactions of X 2 2 and X 1 X 4 are significant, X 1 and X 2 can not be ignored [51].

Effect of contact time
The biosorption capacity of MDCV/Fe 3 O 4 was plotted in Fig. 8a. The biosorption capacity is zero at the beginning of the process. It reaches the maximum levels during the first five minutes. Then, it decreases over time and reaches equilibrium mode. This phenomenon is called repulsion. It occurs when large biosorption surface areas are available and rapidly covered by MB molecules in the first few minutes [52][53][54]. Eventually, the system reaches equilibrium after a while of biosorption and desorption. In the first minutes, the higher MB concentration, due to the high driving forces of mass transfer, increase the biosorption capacity. So the highest MB removal efficiency appears in the first minutes before the time of equilibrium. After reaching equilibrium, the removal efficiency of MB by MDCV/Fe 3 O 4 at initial concentrations of 20, 60, and 100 mg/L are about 63%, 37% and 37%, respectively.

Effect of pH
The pH of the solution significantly affects the relationship between biosorbent and adsorbate. On the other hand, the interactions of hydrogen ions, Van der Waals forces, and the propagation of cavities, also affect the biosorption rate. As can be seen in Fig. 8b, the amounts of biosorption capacity in pH 3 to 7 increased from 17.6 to 25 mg/g and then it decreased to 13 mg/g as the pH increased to 9. The cell wall of Chlorella vulgaris contains a large number of functional groups, carboxylic acid. Therefore, at low pH, cell wall ligands are protonated and the H + also increases.
As a result, the biosorption capacity decreased due to the competition between H + and cationic molecules of MB. As the pH increased and OH − formed, more ligands, such as the amino and carboxyl functional groups, were exposed to the attraction between OH − and MB cationic molecules. The competition between H + and MB also decreased, so the biosorption capacity of

Effect of the initial concentration of MB
Changes in the biosorption capacity and removal efficiency of MB are calculated according to the changes in the initial concentration of MB and reported in Fig. 8d. By changing the initial concentration of MB from 20 to 100 mg/L, the biosorption capacity has increased from 8.5 to 25 mg/g, due to mass transfer-driving forces. As mentioned in the previous section, the removal efficiency of MB is directly related to the number of active sites of the biosorbent. Therefore, at a constant biosorbent dosage, with increasing the initial concentration of MB, the active sites of the biosorbent decrease and lead to the reduction in removal efficiency from 63% to 37% [60].

Effect of temperature
As mentioned in the ANOVA analysis section, the temperature does not significantly affect the biosorption capacity relative to temperature indicates that the biosorption process is entropically rather than enthalpically driven [62].

Biosorption kinetics
Kinetic trends and their parameters are reported in Fig. 9 and Table 10. Due to the downward trend in biosorption capacity over time, the pseudo-first-order model cannot be examined [63].

Biosorption isotherms
Comparing the results of Fig. 10 and Table 11

Biosorption thermodynamic
The Van't Hoff plot of versus 1/ is shown in Fig. 11. The calculated thermodynamic parameters are reported in Table 12. Positive values of ∆ indicate the non-spontaneous biosorption of MB onto MDCV/ 3 4 , which grows with increasing temperature [50]. The result of changes in the energy of the biosorption and desorption has led to a negative amount of ∆ . As a result, the biosorption process of MB on MDCV/ 3 4 is exothermic [68].  is good. Although this amount is lower than some biosorbents such as biochars and their activated carbons, it is promising and even higher compared to some green, red, and brown algae with similar modifications. On the other hand, few studies have been done on the modified dry Chlorella vulgaris. Therefore, this study offers a useful approach in MB biosorption with maximum removal efficiency during the shortest time. Gracilaria parvispora -83.08 [73] Palm leaflets -72.3 [77] Palm frond base -70.87 [77] Cystoseira barbatula -38.61 [78] Raw wet Chlorella vulgaris -10.142 [79] Annona squmosa seed Sulfuric acid activation 8.52 [80] S. dimorphus -6 [81] Defatted algal biomass of S.dimorphus (DAB) Lipid extraction 7.73 [81] Sulfuric acid pretreated DAB Sulfuric acid pretreatment 7.80 [81] Raw posidonia oceanica fibres -5.56 [82] Caulerpa racemosa var. cylindracea -5.23 [83] This work Lipid extraction Phosphoric acid modification Magnetization 32.44 -

Conclusion
In this work, Chlorella vulgaris algae was examined to remove MB from wastewater. This study showed that lipid extraction could provide a good opportunity to use algae residues after the esterification process as an economic biosorbent. Optimization of the variables in the phosphoric acid modification process ensured the maximization of the biosorption capacity and residual defatted algae. Finally, the modified defatted algae were magnetized for easy and low-cost

Materials
Chlorella vulgaris algae were obtained from the Biotechnology Laboratory, Faculty of Chemical

Biosorbent preparation
Raw Chlorella vulgaris algae (RCV) was first washed several times with distilled water to remove impurities and dried at 45℃ for 24 hr. Then it was powdered with mortar.

Lipid extraction
Lipid extraction of RCV was performed by ultrasonic cell destruction and Soxhlet extraction setup [84]. First, 10 g of RCV was mixed with 10 mL of methanol. Then it was sonicated with the frequency of 28 kHz at room temperature for 40 minutes. The sonicated RCV was then transferred to a cartridge and placed inside the Soxhlet setup. As a solvent mixture, 285 mL of chloroform:methanol (1:2 v/v) was poured into the flask according to Bligh & Dyer method [85].
Extraction was carried out for 24 hr at 65℃. The defatted Chlorella vulgaris (DCV) was washed several times with distilled water to remove the remaining solvent and dried at 50℃ for 24 hr. Dry DCV was powdered with a mortar and used for the next steps. Where m 1 and m 2 are the mass of DCV (mg) before and after acid treatment, respectively. Considering the last responses, the regression, and the variance analysis (ANOVA) were done using Minitab-18 software. Optimal conditions were calculated in the maximum amount of both responses and DCV was modified in those conditions [33].

Biosorption analysis
The biosorption of MB on MDCV/Fe 3 O 4 was performed in a batch using an incubator at 200 rpm.
The effect of variables such as temperature (X 1 ), contact time (X 2 ), biosorbent dosage (X 3 ), initial concentration of MB (X 4 ), and pH (X 5 ) were investigated. NaOH and HCl 0.1M were used to regulate the pH. The experiments were performed using the CCD by RSM involving 29 runs with 3 central points and 10 axial points (α = 1). The coded and uncoded conditions specified by the experimental design are shown in Table 15. The final concentration of MB was obtained using a UV-Visible spectrophotometer at λ max =665 nm [89]. Biosorption capacity (mg/g) and removal percentage (%) were calculated based on the following Equations: Where C 0 and C t are the initial and final concentrations of MB (mg/L), respectively. V is the volume of the dye pollutant (L) and m is the biosorbent dosage (g).
Regression, and variance analysis (ANOVA) of the biosorption capacity of MDCV/Fe 3 O 4 were done using Minitab-18 software.

Statistical analysis
The design of the experiments was done by using the central compound design (CCD) of the response surface methodology (RSM). The responses were considered based on the quadratic functions with the interaction of the variables affecting them according to Equation 7. Also, the levels of variables are based on Equation 8 [90].
Where β i shows the coefficients of the parameters of the quadratic function, z i and x i are real and coded values, respectively. ∆z i is the distance between the value of the center point and the next or previous levels. β d is the major coded value for each variable. z i 0 is the real value of the center point.
The relation between the total sum of the square (SS Total ), the sum of the square due to regression (SS Reg ), and errors (SS Error ) is based on Equation 9. The equations for calculating the sum of squares and the mean sum of squares of the data are shown in Table 16. The matching of the regression model and experimental data is determined by using the calculated Fisher distribution (F calc. ), the critical Fisher distribution (F c ), the probability value (P-value), and the adjusted determination coefficient (R adj. 2 ), as shown in Equations 10-13 [90]. The statistical calculations are also based on the probability of 95% (α = 0.05).
. = (10) Where n and p are the numbers of observations and parameters of the model, respectively. Table (16) -Analysis of variance for a fitted mathematical model to an experimental data using multiple regression [90] Variation source Sum of the square Degree of freedom Mean sum of the square

Biosorption kinetics
Kinetic studies were performed to evaluate the reaction rate, equilibrium time, equilibrium capacity, and biosorption process behavior. For this purpose, the models such as pseudo-secondorder and intraparticle diffusion were used according to Equations 19-20, which are shown in Table   17. Intraparticle diffusion = 0.5 + (20) q t vs. t 0.5 Calculating k id and C through the slope and intercept [92] Biosorption isotherms The trend of equilibrium biosorption capacity (q e ) according to the equilibrium concentration of MB (C e ) is investigated using biosorption equilibrium isotherms. The datasets were calculated in different initial concentrations of MB at constant temperatures over time. In each step, q e was calculated using the biosorption capacity of MDCV/Fe 3 O 4 . Then C e was calculated using C 0 and q e at each run. Langmuir, Freundlich, and Temkin isotherms were examined using Equations 21-24 reported in Table 18 [67,93,94].

Biosorption thermodynamics
The thermodynamics of biosorption of MB on MDCV/Fe 3 O 4 were studied at temperatures of 278, 298, and 317 K. Gibbs free energy change (∆G), enthalpy change (∆H), and entropy change (∆S) were calculated according to the following Equations: ∆°= − ln( ) In the above equations, R is the gas constant (J/mol.K), T is the temperature of the process (K), ρ is water density (g/mL), K F is the Freundlich constant (( properties. The UV-Visible spectrophotometer was also used to determine the MB concentration.