### 1. Introduction

### 2. Material and Methods

### 2.1. Materials

_{max}of 590 nm, and chemical formula C

_{25}H

_{30}N

_{3}Cl was purchased from Sigma–Aldrich. To prepare the stock solution of CV (1,000 mg L

^{−1}), 250 ml of distilled water was used to dissolve 273.8 mg of CV. In all experiments, Deionized water was applied. Also, chlorosulfonic acid (CSA, HSO

_{3}Cl, 97% wt), dimethylformamide (DMF, C

_{3}H

_{7}NO, 99% wt), HCl, and NaOH (0.1 mol L

^{−1}) were obtained from Merck. Also, the rice bran, which is a side product of the rice milling industry, was gathered from a grinding mill.

### 2.2. Adsorbent Preparation

### 2.3. Characterization of MRB

### 2.4. Batch Experiments Studies

^{−1}) was studied while other parameters were kept constant. The kinetic study was carried out by altering the contact time from 2 to 60 min. Additionally, the temperature varied between 279 and 328 K to analyze thermodynamic parameters.

### 2.5. Experimental Design and Optimization

^{−1}), and adsorbent dosage (B: 0.2–2 g L

^{−1}) were selected as independent variables for the predicted response (Y), and it was also considered as dependent outputs. According to BBD, a set of 17 runs was administered, involving five centered points with three parameters at three levels, and the results were presented in Table S1.

##### (2)

$$Y={b}_{0}+\sum _{i=1}^{n}{b}_{i}{x}_{i}+\sum _{i=1}^{n}{b}_{ii}{{x}_{i}}^{2}+\sum _{i\ne 1}^{n}{b}_{ij}{x}_{i}{x}_{j}$$_{i}and x

_{j}indicates are the independent variables as coded levels, Y is the response, b

_{ij}, b

_{ii}, b

_{i}, and b

_{0}are the interaction, quadratic, linear, and intercept coefficients, respectively, and n is the number of independent variables [38]. The reliability of the fitted model and the statistical significance were evaluated by the correlation coefficient R

^{2}, analysis of variance (ANOVA), and P-value.

### 3. Results and Discussion

### 3.1. MRB Characterization

^{−1}. These new bands are related to the S–O bond, which confirms that rice bran modification using chlorosulfonic acid was successful [41]. Adsorption band in the range of approximately 2,800–3,300 cm

^{−1}can be assigned to hydroxyl groups, which is related to its organic matters such as hemicellulose, protein, and lignin. [42, 43]. The peak at 2,921 cm

^{−1}, which belongs to MRB, is almost vanished, demonstrating organic matters of raw rice bran were eliminated by CSA in the process of adsorbent synthesis.

### 3.2. Analysis of Variance (ANOVA)

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$$\begin{array}{l}\text{Y}=45.9295+1.4073\times \text{T}+55.7759\times \text{Ads}-0.09609\times \\ \text{CV}+0.14065\times \text{T}\times \text{Ads}+0.0004763\times \text{T}\times \text{CV}+\\ 0.02209\times \text{Ads}\times \text{CV}-0.0236*{\text{T}}^{2}-15.6112\times {\text{Ads}}^{2}\end{array}$$^{2}and the anticipated R

^{2}values supports the model’s precision [44]. Fig. 3 (a) represents the normal probability of residuals for the removal efficiency of CV by MRB. It shows the symmetrical arrangement of experimental data within the level of confidence for the quadratic model [45].

^{−1}, contact time of 42.75 min, and adsorbent dosage of 2 g L

^{−1}.

### 3.3. pH Effect on The Removal Efficiency

^{+}ions and CV to occupy the active sites of MRB because sulfate group of MRB keeps its charge even in acidic medium. As a consequence, the removal efficiency was constan in pH range of 2–7. The pH

_{PZC}value confirmed these explanations. When pH goes up from 7 to 10, the removal efficiency increased because of precipitation of CV at the high concentration of OH

^{−}.

### 3.4. Ions Effect

^{+}, NO

_{3}

^{−}, Na

^{+}, SO

_{4}

^{2−}, Ca

^{2+}, Mg

^{2+}, HCO

_{3}

^{−}and Cl

^{−}on CV removal by MRB was studied (Fig. 4 (b)).To compare the impact of different ions on the CV removal process, eight samples and a control sample were used. The control sample marked as A in the chart. Ca

^{2+}and Mg

^{2+}ions compete with CV for active adsorption sites because of their positive charges; therefore, thereby decreasing the removal efficiency. Na

^{+}and K

^{+}also present positive charge as Calcium and Magnesium. In Fig. 4, we can observe a small reduction in dy removal in the presence of Na

^{+}and K

^{+}ions. However, for Ca

^{2+}and Mg

^{2+}, this reduction was more evident, because these ions are divalent, while Na

^{+}and K

^{+}are monovalent, showing low ineraction with positive active sites. The other ions did not affect the dye removal.

### 3.5. Equilibrium Studies

_{L}) in the Langmuir model, for different initial concentration of CV, was calculated in the range of 0.11 to 0.5, suggesting a favorable process for adsorption of CV by MRB. It is known that a nearly zero value for 1/n

_{f}calculated by the Freundlich model suggests a more heterogeneous surface for the adsorbent [49]. In this experiment, the calculated value was 0.473, which was consistent with this concept. The calculated values for maximum capacity corresponding to Dubinin-Radushkevich, Radke-Prausnitz, UT, and Langmuir isotherms were 404, 600, 603, and 600 mg g

^{−1}, respectively. It should be noted that the calculated values of UT and Radke-Prausnits were equal and very close to the Langmuir model result. The values of the Dubinin-Radushkevich model was far below the experimental results.

### 3.6. Kinetic Studies

^{−1}). Residual root-mean-square error (RMSE), the result of kinetic parameters, the linear form of these kinetics, chi-square test (χ

^{2}), and the coefficients of determination (R

^{2}) are shown in Table 3 [27, 51]. According to χ

^{2}, R

^{2}, and RMSE, liquid film diffusion and pseudo-first-order models were not sucessful in fitting experimental data, while the Elovich model showed a good fit for it. Also, it should be noted that the intra-particle diffusion model was better than the pseudo-second-order model. The experimental data and predicted data using kinetic models are indicated in Fig. S3. It is clear that Elovich and intra-particle diffusion models were well described all data.

^{−1}), the k

_{2}(2.18 × 10

^{−4}to 9.69 × 10

^{−5}g mg

^{−1}min

^{−1}) decreased, so it can be concluded that adsorption is slower at lower concentration of CV.

_{t}/q

_{e})) versus t should be a straight line if the film diffusion is the rate determining step. Also, the plot of q

_{t}against t

^{1/2}passing through the origin if the intraparticle diffusion act as the only rate-limiting step [47]. Otherwise, the adsorption kinetics may be controlled by film diffusion and intraparticle diffusion simultaneously. It was seen that in our experiment, the plotted line dose not pass through the origin, so both intraparticle diffusion and film diffusion are the rate-controlling step. Furthermore, the constant of intraparticle diffusion (k

_{dif}) increased by increasing dye concentration, as an outcome of the rise in the driving force.

### 3.7. Thermodynamic Study

^{−1}K

^{−1}), standard free energy ΔG (J mol

^{−1}) and standard enthalpy ΔH (J mol

^{−1}), the thermodynamic analysis was directed in CV removal by MRB at various temperature (279–328k) using following equations:

^{−1}K

^{−1}). The thermodynamic constants (ΔG, ΔS, and ΔH) are given in Table S3 [51]. The adsorption of CV by MRB is an endothermic physisorption because the enthalpy (ΔH) value was positive and less than 40 Jmol

^{−1}K

^{−1}[35]. The ΔS of adsorption had positive value since the randomness increased in the solid/solution interface. A negative amount of ΔG displays CV removal using MRB is a spontaneous reaction.

### 3.8. Desorption Study

^{−1}). After the adsorption process, MRB was separated from the CV solution, then it was mixed with HCl (0.5 mol L

^{−1}) and shaken for 30 min. Subsequently, the resulting mixture was washed with deionized water. As Fig. S4 shows, five cycles of adsorption/desorption reduce the dye removal efficiency by 10%, which shows the excellent ability of regenerated MRB in CV removal.

### 3.9. Comparision of The Capacities of MRB with Other Materials for The CV Removal

### 4. Conclusions

_{2}) decreased. The most important properties of MRB include high adsorption capacity (603 mg g

^{−1}) as well as the low cost and recoverability. The results of this study show that MRB has a high ability to eliminate CV from polluted effluents. Producing the adsorbent from MRB seems a proper replacement for conventional disposal methods.