Application of Taguchi method and response surface methodology into the removal of malachite green and auramine-O by NaX nanozeolites

In the present study, the simultaneous removal of malachite green (MG) and auramine-O (AO) dyes from the aqueous solution by NaX nanozeolites in a batch system is investigated. Taguchi method and response surface methodology (RSM) were used to optimize and model dye removal conditions. In order to do so, the effect of various factors (dyes concentration, sonication time, ionic strength, adsorbent dosage, temperature, and pH of the solution) on the amount of dye removal was evaluated by the Taguchi method. Then, the most important factors were chosen and modeled by the RSM method so as to reach the highest percentage of dye removal. The proposed quadratic models to remove both dyes were in good accordance with the actual experimental data. The maximum removal efficiencies of MG and AO dyes in optimal operating conditions were 99.07% and 99.61%, respectively. Also, the coefficients of determination (R2) for test data were 0.9983 and 0.9988 for MG and AO dyes, respectively. The reusability of NaX nanozeolites was evaluated during the adsorption process of MG and AO. The results showed that the adsorption efficiency decreases very little up to five cycles. Moreover, NaX nanozeolites were also applied as adsorbents to remove MG and AO from environmental water samples, and more than 98.1% of both dyes were removed from the solution in optimal conditions.


Experimental design. Taguchi method.
Taguchi is a method that reduces the number of experiments by minimizing the interference of uncontrolled factors, which is used as a mathematical technique. By creating orthogonal arrays and matching many factors, Taguchi identifies minor variables in the shortest amount of time. The orthogonal arrays are shown in Table 2. Factors studied include temperature (25-35 °C), solution pH (3)(4)(5)(6)(7)(8)(9), adsorbent (100-300 mg), ionic strength (0-6 w/v%), dye concentration (6-10 mg L -1 ) and sonication time (3-9 min). Applying the Taguchi method, only 27 experiments are required to obtain the optimal levels of the variables (Table 2), while the most accurate optimization method for a complete study of seven variables at three levels requires 2187 experiments (3 7 = 2187), which is practically time-consuming. Therefore, the Taguchi method can reduce the number of tests, reduce time, decrease costs, and determine important factors in a short time. Taguchi uses the signal-to-noise ratio in measurable amounts of qualitative characteristics according to the purpose of the experiments. The signal-to-noise ratio (S/N) is obtained by Eq. (1): In this equation, n is the number of experiments, and y is the response of the variables 44 .  www.nature.com/scientificreports/ Response surface methodology (RSM). RSM is a set of mathematical and statistical methods determining the relationship between one or more responses to several variables. In chemistry, many phenomena are modeled based on their theories. However, many phenomena do not have a satisfactory mathematical model due to their dependence on many controlling factors, unknown mechanisms, and mathematical complexity. In such cases, the use of experimental modeling methods such as the response level method is effective. In the central composite design (CCD)-based RSM, variables are examined at five levels. Low levels (-α) and high levels (+ α) are entered into the software by the operator, and the software provides other levels. According to the results obtained in the Taguchi method in "Taguchi method". Taguchi method, in this step, five factors that were of great importance were examined. These factors were the amount of adsorbent, dye concentration, sonication time, and pH solution ( Table 3). The percentage of dye removal was considered as the response variable. The equation that can be used in the response surface method is the polynomial quadratic equation. The responses must conform to Eq. (2) in order to use it.
Where k is the number of variables, β 0 is the model constant, β i are the coefficients of linear factors, β ij and β ii are the coefficients of the factors that interact with each other, ɛ the remaining values are related to random error, X i and X j are the variables 45 .
Analytical methods. In order to study the efficiency of NaX nanozeolites to remove MG and AO dyes, batch experiments were performed. The experiments were designed by the CCD method. For this reason, at room temperature, in a centrifuge tube, 25 mL of a solution containing both dyes (4 mg L −1 ) was added. Then, 347 mg of NaX nanozeolites were added to the sample solution. The pH of the solution was adjusted to 8. The solution was placed in an ultrasonic bath for 11.5 min and centrifuged at 3000 rpm for 5 min. Finally, the supernatant was removed and transferred to UV/Vis cells to determine the amount of residual concentration and to calculate the percentage of dye removal of MG and AO, and the adsorption of solutions for MG and AO was read at 620 nm and 430 nm, respectively. In these experiments, Eq. (3) was used to determine the percentage of dye removal.
C 0 and C are the initial and final concentrations of the desired dye in terms of mg L −1 , respectively 46 .

Results and discussion
Characterization of the NaX nanozeolites. Figure 2a shows the XRD pattern of the sample, and XRD analysis shows that high purity NaX zeolite phase without phase interference has been synthesized in the above phase method (JCPDS no. 39-0218) 47,48 . The average size of the crystals synthesized using the Scherer equation was in the range of 40-70 nm. The crystal size indicates that the synthesis of NaX zeolite in nanometer dimensions has been successful. Morphological analysis of NaX nanozeolites was performed using SEM. The SEM image of the synthesized zeolite sample (Fig. 2b) shows that the particle sizes are in the range between 50 and 150 nm. Also, the adsorption and desorption porosity was measured by the BET analysis. The BET surface area, calculated average particle size, and total pore volume of synthesized NaX nanozeolites were found as 852.5 m 2 /g, 69.42 nm, 0.304 cm 3 /g, respectively.
Determination of pH PZC . pH PZC is the point at which the adsorbent surface charge is neutral. Thus, at a pH above this point, the adsorbent surface has a negative charge, and at a lower pH, the surface charges become positive. In order to determine pH PZC , 10 mL of NaCl solution (0.1 M) was poured into separate test tubes, and the solutions were adjusted to different pH (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12). Hydrochloric acid (1 M) and sodium hydroxide (1 M) were used to adjust the pH. Then, 0.3 g of adsorbent was added to the solutions, and the samples were placed in a shaker at 150 rpm. After 24 h, the adsorbents were separated from the solution, and the solutions' pH was measured again. The pH PZC was found to be 6.5 (Fig. S1).
(2)  Table S1. The change in each of the factors indicates the importance of the factor in the process. In Table 4, the effect of each factor at each level was calculated independently by the software, and finally, according to the differences created in each factor, the importance of each was investigated. In MG and AO dye removal experiments, the amount of adsorbent has the first effect on the adsorption process, pH comes as the second factor, MG dye concentration the third, AO dye concentration the fourth, sonication time the, ionic strength the sixth, and finally the temperature is the seventh factor. Based on the results of Table 4, the variables of adsorbent amount, solution pH, dye concentration, and sonication time were selected as effective variables for optimization and modeling by the RSM method. Therefore, the variables of temperature and ionic strength were omitted. Because as shown in Fig. 3 and Table 4, the temperature has little effect on the process compared to other factors and was maintained at 25 °C in subsequent optimal experiments. Increasing ionic strength also reduces the adsorption of dyes by NaX nanozeolites. This can be attributed to preventing dye molecules from approaching the active sites of adsorption 49 . The same effect has been reported in the literature for some cationic dyes, such as the adsorption of methylene blue by sludge ash, methylene blue, and crystal violet by palm kernel fiber 50,51 .

Significant variable optimization by RSM.
In this section, Design Expert statistical software version 10 was used to execute the CCD design and analyze the resulting data. Software output includes main effects, their interactions, quadratic equation, and statistical graphs. To perform experiments by the CCD method, the software designed 32 experiments. Table 5 shows the order of these 32 experiments. Method of analysis in "Analytical methods". Analytical methods are provided. The answer to each row of the experiment is also given.
A reliable method for evaluating the quality of a matched model is the analysis of variance (ANOVA). In ANOVA, the share of variance of each factor is compared with the variance caused by random errors in measurement. In fact, the significance of regression can be examined through this comparison. Significance of regression is performed by comparing the regression variance to the variance of the residuals with the Fisher distribution (F-test). If this ratio is greater than the critical value of F, the mathematical model is consistent with the experimental data. If the calculated p-value for each of the factors is less than 0.05, it indicates the effectiveness of that factor, and if it is more than 0.05, it means that the change of that factor does not affect the values. The parameters for MG and AO dyes are given in Table 6. The correlation coefficients (R 2 ) were 0.9983 and 0.9988, and adj-R 2 were 0.9953 and 0.9967 for MG and AO, respectively. High values of R 2 and adj-R 2 confirm the model's ability to make a convincing estimate of the response.
As can be seen in Table 6, the value of p for linear and interaction factors is less than 0.05. From the value of p related to nonconformity, it can be deduced that the equation obtained is consistent with the experimental   (4) and (5).
In Eqs. (4) and (5) Residual diagrams help to interpret the results accurately. Assuming that the errors are normally distributed and independent of each other, residual probability diagrams (Fig. 4a,b) are an essential diagnostic tool to identify and explain systematic deviations. Also, the residual probability graph also shows that the error variance is homogeneous 28 . In this diagram, the closer the points are to the line, the less error there is. As shown in Fig. 4a,b are points close to the line. In Fig. 4c-f, the better the distribution of points at the top and bottom of the axis is the same (i.e., the probability of positive and negative error is the same, and the test error is not a systematic error). As shown in Fig. 4c-f, there is no systematic error. Figure 5 shows the three-dimensional diagrams of the interaction effect. Three-dimensional diagrams of surface response are a function of two independent parameters that keep all other parameters at constant levels. These diagrams can provide information about the relationship between the two parameters and are useful in understanding the main effects and interaction effects of the two parameters. Figure 5a shows the interaction of the two parameters of solution pH and the amount of adsorbent on MG dye removal. The MG dye removal goes up with increasing pH of the solution and increasing the amount of adsorbent. At pHs higher than pH PZC , which is 6.5 for NaX nanozeolites, the surface charge of the nanoparticles is negative. Thus, the adsorption of positively charged dye molecules due to electrostatic attraction increases. On the other hand, increasing the amount of adsorbent provides more adsorption sites for dye molecules to be adsorbed on the adsorbent surface. Therefore, the interaction of these two parameters, which causes the positive surface of nanoparticles and increases the adsorption sites, increases the adsorption. Similar results about an increase in the removal percentage with increasing pH (alkaline conditions or natural pH) and increasing the amount of adsorbent have also been reported for MG and AO dyes 33,52 . As shown in Fig. 5b,c, the amount of dye removal decreases with an increasing dye concentration of MG and AO. Decreasing the removal percentage at higher concentrations is due to the increase in dye concentration relative to the number of initial moles of dye available to the surface area. For a given amount of adsorbent, the total number of active sites available is constant, and as a result, the same amount of site absorbs the analyte, so as the initial dye concentration increases, the removal percentage decreases. Arabkhani and Asfaram (2020) used a novel three-dimensional magnetic polymer  www.nature.com/scientificreports/ aerogel for the removal of MG dye and achieved similar results to this stage of this study, stating that the removal efficiency decreases with increasing the initial dye concentration 6 . Figure 5d shows the effect of sonication time on the amount of AO dye removal. As it is known, with increasing sonication time, the amount of dye removal should increase. This is because with increasing time, there is more opportunity for the dye and adsorbent molecules to be exposed. In a study entitled "Rapid removal of Auramine-O (AO) and Methylene blue (MB) dyes from aqueous solutions using ZnS:Cu nanoparticles as the adsorbent, Asfaram et al. (2015) found similar results to the present study and showed that the removal efficiency increased with increasing sonication time 10 . Optimization. Optimization in chemistry is used effectively and economically to reduce cost and time in multi-response methods. For this reason, following investigating the factors affecting the removal of MG and AO dyes by the Taguchi method, the conditions for removing the dye from the solution by RSM were optimized. According to the experiments performed in Taguchi design, the most important factors affecting the removal of MG and AO dyes in the method are solution pH, adsorbent mass, sonication time, the concentration of MG and AO dyes. These items were evaluated as the main factors (independent variables) in the RSM statistical design. The software presented the optimal values of each parameter and the relevant tests were performed. All stages of the experiment were carried out according to the Analytical methods section. Optimal values and test results are shown in Table S2. It is observed that more than 99% of both dyes are removed from the solution by NaX nanozeolites in optimal conditions. www.nature.com/scientificreports/ Application to real samples. In order to study the efficiency of the method for the analysis of real samples, NaX nanozeolites were used as adsorbents to remove MG and AO from fish farms, tap water, and drinking water samples. For this reason, tests were performed in optimal conditions, in accordance with the method mentioned in "Analytical methods". Environmental water samples were used instead of distilled water. After spectrophotometric determination of the remaining amount of dye, the percentage of simultaneous removal for MG and AO dyes was more than 98.1% in environmental water samples (Table S3). This means that NaX nanozeolites can remove significant amounts of MG and AO from environmental water samples.
Interference studies. After obtaining the optimal conditions of effective parameters for removing the synchrony of MG and AO dyes, interference studies were carried out to evaluate the method's selectivity. In order to investigate the disturbance effect of different ions, different concentrations of disturbing ions were added to the solution and the steps were taken according to the method described in "Analytical methods". Also, Analytical methods were applied (Removal conditions: 347 mg of NaX nanozeolites, pH: 8, the concentration of both dyes 4 mg L −1 , centrifuge rate: 3500 rpm). The results are shown in Table S4. If the signal obtained in the presence of the disturbing ion differs by ± 5% from the signal in the absence of the disturbing ion, it indicates the degree of disturbance of the species on the decomposition signal. To determine the tolerance limit of the disturbing ion, a lower concentration of that species is examined to give an error value of ± 5%. According to the results, by adding almost high amounts of ions, no interference was observed on the decomposition signal. In this study and optimal conditions, the rate of dye removal in the presence of other ions was above 95%, which indicates the proper selectivity of NaX nanozeolites to both dyes despite the competitive effect of other ions. www.nature.com/scientificreports/ Desorption and reusability studies. The reuse of adsorbent could be considered as one of the important economic parameters. Therefore, the recyclability of NaX nanozeolites during the MG and AO adsorption process was evaluated. In this study, the NaX nanozeolites used were washed with 10 ml of methanol (0.01 M) and placed in an ultrasonic bath for 5 min. Finally, the amount of adsorption in each cycle was measured by spectrophotometry. The results in Fig. 6 show that up to 5 cycles, the adsorption efficiency decreases slightly. In general, this reduction can be due to adsorption degradation during adsorption-desorption cycles 53,54 .
Comparison of adsorbents. The efficiency of the proposed method was evaluated with other methods for removing MG and AO dyes. The results are given in Table 7. This study showed that the developed method, compared to other methods, provides high removal of contamination (dye) in a short time from water samples. This method also has other advantages, such as the low number of tests, low operating costs, and optimization in the best possible way to achieve the highest efficiency (percentage of paint removal).

Conclusion
The efficiency of NaX nanozeolites for simultaneous removal of malachite green (MG) and auramine-O (AO) dyes from aqueous solutions was investigated. The synthesized nanosorbents were characterized using SEM and XRD. The most important variables affecting the dye removal process were determined by the Taguchi method. These effective variables included solution pH, adsorbent mass, sonication time, MG, and AO dye concentrations and were optimized and modeled by CCD based on the RSM method. The optimal conditions obtained by RSM modeling included pH 8, ultrasound time of 11.5 min, an absorbent dose of 347 mg, and concentration of both dyes 4 mg L −1 , and the highest dye removal (more than %99) was obtained for both dyes. Quadratic models for dye determination were statistically compared with values of R 2 ˃ 0.99 and p < 0.0001, and the results showed that both models have reasonable accuracy. The results obtained for adsorption-desorption experiments showed that the adsorbent could be reused up to five times without a significant reduction in the percentage of dye removal. The methodmethod's efficiency for analyzing real samples containing MG and AO dyes also showed that the developed methodcould remove high amounts of dye contamination (%98.1) from complex samples.    www.nature.com/scientificreports/ Data availability Table 7. Comparison of the NaX nanozeolites with other adsorbents for removal MG and AO. a Metal organic framework-5 (MOF-5) and melamine-terephthaldehyde-based intergrade two imensional π-conjugated covalent organic framework (COF).