Acid red 18 removal from aqueous solution by nanocrystalline granular ferric hydroxide (GFH); optimization by response surface methodology & genetic-algorithm

The need for fresh water is more than before by population growth, and industrial development have affected the quality of water supplies, one of the important reason for water contamination is synthetic dyes and their extensive use in industries. Adsorption has been considered as a common methods for dye removal from waters. In this study, Acid Red18 removal in batch mode by using Granular Ferric Hydroxide (GFH) was investigated. The GFH characterized by XRD, FESEM and FTIR analysis. Experiments were designed using RSM-CCD method. The maximum removal efficiency was obtained 78.59% at pH = 5, GFH dosage = 2 g/l, AR18 concentration = 77.5 mg/l and 85 min of contact time. Optimization with RSM and Genetic Algorithm carried out and is similar together. The non-linear adsorption Isotherm and kinetic fitted with Freundlich (R2 = 0.978) and pseudo-second-order (R2 = 0.989) models, respectively. Thermodynamic studies showed that the AR18 adsorption is endothermic process and GFH nature was found spontaneous.

Batch adsorption studies. Dye adsorption studies were performed in 100 ml glass Erlenmeyer flasks with 25 ml of dye solution. Desirable pH was adjusted by 0.1 N NaOH and HCL by Kent EIL7020 pH meter, a certain amount of adsorbent weighted and added to the dye solution and then samples were shaken at room temperature at 200 rpm. After that flask contents were centrifuged in 4500 rpm for 5 min in Universal Premium PIT320 model and the residual dye concentration read by spectrophotometer Perkin-Elmer lambda25. The amount of adsorbed dye onto the adsorbent surface was calculated by using the mass balance equation: C0 is the initial concentration of dye (mg/l), Ce is the residual concentration of dye (mg/l), M is the mass of adsorbents (g), V is the volume of AR18 solution (l).
Furthermore, dye removal efficiency was obtained from: Isotherm studies were carried out at different dye concentration, and the kinetic was determined at different contact time. Thermodynamic studies were performed at various temperatures for understand the nature of the process.
Experimental design. Design-Expert11 (Stat.Ease.Inc. Minneapolis, USA) software with Response Surface Methodology (RSM) package applied to design experimental runs and optimum conditions and the impact of various independent variables (pH, initial concentration, contact time, adsorbent dosage). Dye adsorption was evaluated by using central composite design (CCD) which can minimize the numbers of total experiments. Likewise, to determine a total number of runs the following equation is presented: N = 2 k + 2k + C 0 .
In which K is the number of experimental variables, 2 k is the cubic runs, 2k is the axial runs, and C 0 is the center point's runs 29 . CCD matrix and coded values of variables is shown in Tables 2 and 3. This approach was suggested 30 trials. The following are some of the benefits of this design:   Isotherm studies. Adsorption isotherms provide quantitative information on an adsorbent's adsorption capacity and behavior with the adsorbate 19 . Experimental data were analyzed and fitted to Freundlich, Langmuir, and Temkin isotherm models to achieve this goal.
Langmuir isotherm. The Langmuir isotherm is used to describe monolayer adsorption on a homogenous adsorbent surface 30 . The following equations reflect its nonlinear model: where q e is the amount of AR18 adsorbed per gram of GFH, C e is the dye concentration at equilibrium (mg/l), and q max is the maximum amount of Acid red18 adsorbed. The Langmuir equilibrium constant in l/mg is denoted by K L . Non-linear models were used to estimate the parameters.
Freundlich isotherm. Adsorption is not monolayer in the Freundlich isotherm, which is formulated for equilibrium on inhomogeneous surfaces 31 .
The nonlinear version of the Freundlich isotherm model is as follows: Adsorption capacity is represented by K F (l/mg), while adsorption intensity is represented by 1/n. The nonlinear plot of qe versus Ce and the linear plot of log qe vs. log Ce were utilized to calculate K F and n.  www.nature.com/scientificreports/ Temkin isotherm. A heterogeneous surface with adsorption sites with the same bond energy is studied in the Temkin isotherm model. A linear reduction in adsorption heat occurs in this isotherm due to the contact effects of the adsorbent and adsorbate on each other 31 . The following equation expresses the non-linear Temkin models: B is the isotherm constant (J/mol). The maximal bond energy (l/mg), the gas constant (8.314 J/mol K), the temperature in degrees Kelvin, and the heat of adsorption (J/mol) are all represented by the letters K T , R, T, and b.
Kinetic studies. The pace and mechanism of the reaction are revealed by a kinetic examination of the adsorption process 32 . Ion adsorption from solution has been studied using a variety of kinetic models. The adsorption kinetic of AR18 onto GFH was studied using pseudo-first order, pseudo-second order, and intraparticle diffusion kinetic models. These three models' nonlinear forms are written as: where q e (mg/g) is the adsorption capacity at equilibrium and q t (mg/g) is the adsorption capacity at time t. Adsorption rate constants are k 1 (/min) for pseudo-first-order kinetic, k 2 (g/mg min) for second-order kinetic, and k i (mg/g min 0.5 ) for intraparticle Diffusion kinetic 30 .
Thermodynamic study. Thermodynamic parameters include changes in the free energy of Gibbs (ΔG), enthalpy (ΔH o ), and entropy (ΔS). ΔG is free energy change (kJ/mol) can be calculated from the following equation where R is the universal gas constant (8.314 J/K mol), T is the absolute temperature (K). The distribution adsorption coefficient, Kc, is calculated from the following equation: where C 0 is the initial concentration (mmol/l), Ce is the equilibration concentration after centrifugation (mmol/l), V is the volume of the suspension (l), and m is the mass of adsorbent (g). The adsorption equilibrium constant (K) can be calculated by plotting lnK d versus Ce and extrapolating Ce to 0. The value of the intercept is that of lnK. ΔH o (J/mol-kJ/mol) and ΔS 0 (J/mol °K-kJ/mol K) according to Equation are calculated.
where ΔH 0 is the isosteric enthalpy change, ΔS is the entropy change, where ΔH 0 and ΔS 0 were obtained from the slope and intercept of the linear plot of lnK d against 1/T 32 . The number of tests for isotherm, kinetic and thermodynamic studies was selected in range, above which, the q e alter not significantly. In this regard, the number of tests was 8 for each kinetic model, 7 for each isotherm models, and 3 for thermodynamic study based on the temperatures selected.

Results and discussion
Granular ferric hydroxide characterization. XRD studies. X-ray diffraction of GFH was analyzed in the range of 2θ = 5-80° at 0.02 step size, and the result is shown in Fig. 3.
Akaganeite was found to be the main compound in GFH structure and also there was hematite in lower content. Baseline noise and peak broadening related to akaganeite reveals the poor crystallinity in GFH structure which is in line with previous reports on GFH characteristics that defined β-FeOOH as a poor crystallized similar to mineral akaganeite. akaganeite is a tetragonal mineral formed by a double chain octahedral 23 . On the other hand with existing a low amount of chloride in GFH sample, broadening of peaks in XRD is observable 23  FESEM. Figure 4a shows the surface morphology of GFH. It displays uniform round edge of GFH particles and also has a porous structure which can provide suitable adsorption sites for dye removal as shown in Fig. 4b these sites are appropriately filled with dye molecules, and sorbent particles have become more agglomerated. EDX analysis (Fig. 5) determined to contain elements in GFH. The result indicates that Fe and O are the two main constituent of GFH with 69 and 31% respectively.
Nonlinear Pseudo first order kinetic equation Nonlinear Pseudo second order kinetic equation: AR18 adsorption. Statistical analysis. In the present study, four different statistical models and their fitting with obtained experimental data were investigated. Quadratic model with and lack of fit 0.17 was suggested by software analysis. According to the presented data in a Table 4 Quadratic model with adjusted and predicted R 2 value 0.989 and 0.972 was the best-fitted model for AR18 removal by GFH.
Effect of experimental parameters on adsorption process. The effect of four different variable on AR18 adsorption were studied. From the Table 5, it can understand that pH, Dose, Initial concentration and time with the F-value 851,729,284,186 respectively had the most to the lowest effect on adsorption process efficiency. Also, the interaction of studied variable investigated in which AC showed the bigger F-value it means that the interaction  Predicted vs actual efficiency comparison is shown in Fig. 7a. As it can be seen, there was a good correlation between them. Also residual of runs was in the range of − 3 to 3, which is indicant of a close value to the predicted one (Fig. 7b).  www.nature.com/scientificreports/ Effect of pH. The negative coefficient of pH was indicative of decreasing removal efficiency with increase in pH; this can be explained that at acidic pH, the higher AR18 uptake will occur. Due to the presence of the large number of positive charges on the adsorbent's surface at lower pHs while on the other hand the AR18 Molecules are negatively charged and this lead to an Electrostatic sorption 2 The calculated pH ZPC value for GFH was determined 7.5-8 based on previous studies. The sorbent surface charge is more positive at pH < pH ZPC while at pH > pH ZPC the AR18 adsorption shows decrease, and as a consequence, the removal efficiency will be decreased.
Effect of initial dye concentration. One of the effective parameters on adsorption process in this study was the initial concentration of AR18. The impact of this parameter was studied. The result showed that with an increase in initial concentration of dye, the efficiency improved. It might be because of more availability of pollutant for adsorbent particles.   Understandably, GFH provides more surface area for adsorption of dye; besides, it was found that a higher amount of GFH, a higher removal efficiency could be achieved.
Effect of contact time. Contact time was found to be the less effective parameter in the adsorption process. The impact of contact time in present study was assessed from 10 to 110 min and the best removal efficiency obtained at 85 min of contact time (79%) whereas by increasing contact time from 10 to 60 min, uptake rate increased around 10%; generally, it can be said that the adsorption process of AR18 almost depends on pH and in nonacidic pH, the effect of time on the process was not found to be tangible. Figure 8 demonstrates the interaction effects of studied variables, (a,c) pH and adsorbent dose contours confirmed that decrease pH value from 11 to 3 and increase dose from 0.5 to 2.  www.nature.com/scientificreports/ Determining optimal settings. The optimum condition is the value of each variable in which the maximum uptake rate is obtained. These conditions were determined by the numerical optimization method. According to the software (RSM) the maximized efficiency expected to be 78.59% at pH = 5, adsorbent dose = 2 g/l, contact time = 85 min and initial AR18 concentration = 77.5 mg/l. The experimental RE under-designed optimum conditions was achieved 79.71%. Table 6 shows the range of prediction interval, which is 72.9-84.2%, the actual value for this investigation was 79.71%. Also optimization of the process parameters was accomplished by using the GA method. In this approach, the solutions created by one population are applied to generate a new population. The generation of the new population is continued to find a better solution or fitness value. The operation is sopped as the best fitness value shows no impressive improvement by the further populations and be approximately constant. The proposed approach was performed in the Matlab GA toolbox. (Matlab2018).
To optimize the RSM-CCD model based on the GA approach, the minimum and maximum levels of the independent variables were set at the upper and lower levels. As seen in Fig. 9, the results evidently show that the best fitness value was improved rapidly until about generation 50, and after that, shows no impressive improvement and be approximately constant because whose populations become close to the optimal point. As given in Fig. 9, the current best individuals plot demonstrates that the maximum removal efficiency of about 76.43% is achieved at the optimum condition.
Optimum condition based on GA results obtained pH = 5, Adsorbent dose = 2 g/l, Contact time = 81 min and Dye Concentration = 77.5 mg/l. These results was found very close to RSM Optimization method.
Isotherm studies. For better understating of adsorption mechanism, isotherm studies are essential. The equilibrium distribution of AR18 on GFH was found by isotherms, which were performed at seven different initial AR18 concentration with 2 g/l of adsorbent, at pH = 7 for 60 min of contact time at room temperature. In this study, three isotherm models were investigated included: Langmuir, Freundlich and Temkin, the model' . Also, the coefficient constants of each model are listed in the Table 7.    Table 7, adsorption data was better fit to Freundlich Isotherm. The maximum capacity for dye adsorption was found 29.13 mg/g while the adsorption energy was 1.175 which shows that the affinity of dye molecules on GFH is not such a strong binding because a higher k L value for adsorbent shows a stronger affiliation to sorbate. Also, the coefficient 1/n (generally 0-1) indicates the favorable adsorption of the adsorbate to the adsorbent. 37 The 1/n value tends to zero; the adsorbent surface is more heterogenic 38 . The affinity of the adsorption sites between AR18 and GFH is determined by R L constant, which is dimensionless.
The value of R L shows the nature of adsorption as follow: The Calculated R L value is between 0.14 and 0.54 as all of these values are between 0 and 1. It can understand that AR18-GFH have favorable adsorption. The non-linear fitting Isotherm models are presented in Fig. 10A. Kinetic studies. To understand adsorption mechanism and dye uptake rate, kinetic studies were investigated. Pseudo-first-order, Pseudo-second-order and Intra-particle diffusion models were used to analyze the adsorption kinetics. K 1 (g/mg min), K 2 (/min) and K dif (mg/g min 1/2 ) are the rate constants of pseudo-first-order, second order and Intra-particle diffusion models, respectively. In this study data of experiments was fit better   Fig. 10B. Result of Kinetics of this study is agreement with previous study 2,39,40 . The pseudo-firstorder kinetic assumes that the adsorption process is affected by the physiosorption, and the rate-limiting step in adsorption depends on collision between solute molecules of ions with unoccupied single sites at the surface of the adsorbent material The intraparticle diffusion kinetic assumes that the intraparticle diffusion of dye molecules on the adsorbent is the rate-limiting step in the adsorption process 41 . The pseudo-second-order kinetic assumes that the rate-limiting step of adsorption is chemisorption, which is probably ascribed to ion-exchange or sharing of electrons between adsorbents and adsorbate. Another assumption in this model is that the rate of occupation of adsorption sites is proportional to the square of the number of unoccupied sites 42,43 . Also, the intraparticle diffusion kinetic assumes that the intraparticle diffusion of dye molecules on the adsorbent is the rate-limiting step in the adsorption process 15 . parameters of Kinetic models is shown in Table 8.

Thermodynamics of adsorption.
Temperature is one of the factors affecting the adsorption process.
Thermodynamic studies help us to understand recognize the process as much as possible, as well as information about changes in the internal energy associated with adsorption and, thus, to take measures to increase the efficiency of adsorption. In this study, the efficacy of GFH in the removal of acid red 18 at temperatures (298, 293, and 303° K) was investigated. The thermodynamic parameters at three different temperatures are listed in Table 9. The enthalpy change (ΔH 0 ) obtained are Positive and demonstrates the endothermic nature the adsorption of Acid Red 18 onto GFH; this also supports the observed increase in the adsorption capacity of Acid Red 18 with increasing temperature so increasing temperature is favorable for the adsorption. The positive value of standard entropy change (ΔS) suggests stability, good affinity and decrease of randomness of Acid Red 18 by GFH in the whole removal process. The negative value of ΔG at all temperatures indicated that the adsorption was a spontaneous process. Additionally, the increase in absolute values of ΔG with increasing the temperature reveals that higher temperature facilitated the adsorption. In the Table 10 comparison of maximum adsorption capacity of Acid Red 18 and other adsorbents has been investigated.  Table 9. Thermodynamic parameters of AR18 adsorption onto the GFH.

Conclusion
In this study removal of Acid red 18 anionic dye by granular ferric hydroxide (GFH) with RSM-CCD method design with 30 runs investigated. The results showed GFH Nanocrystal can effectively reduce AR18 concentration in adsorption process (78.59%). Optimization of process performed with RSM and Genetic Algorithm method. Results of two procedure was very close together, RSM: 78.59% vs GA:76.43%. The adsorption process can be better fitted with Freundlich isotherm (R 2 = 0.98) and Pseudo-second-order (R 2 = 0.98) kinetic models. Maximum adsorption capacity determined 29.13 mg/g. Also thermodynamic studies indicated that the reaction process was endothermic and spontaneous. According to the obtained results, GFH can be considered as having a good efficiency in removing Acid red18 dye.

Data availability
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