Removal of Crystal Violet by Using Reduced-Graphene-Oxide-Supported Bimetallic Fe/Ni Nanoparticles (rGO/Fe/Ni): Application of Artificial Intelligence Modeling for the Optimization Process

Reduced-graphene-oxide-supported bimetallic Fe/Ni nanoparticles were synthesized in this study for the removal of crystal violet (CV) dye from aqueous solutions. This material was characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM) coupled with energy dispersive spectroscopy (EDS), Raman spectroscopy, N2-sorption, and X-ray photoelectron spectroscopy (XPS). The influence of independent parameters (namely, initial dye concentration, initial pH, contact time, and temperature) on the removal efficiency were investigated via Box–Behnken design (BBD). Artificial intelligence (i.e., artificial neural network, genetic algorithm, and particle swarm optimization) was used to optimize and predict the optimum conditions and obtain the maximum removal efficiency. The zero point of charge (pHZPC) of rGO/Fe/Ni composites was determined by using the salt addition method. The experimental equilibrium data were fitted well to the Freundlich model for the evaluation of the actual behavior of CV adsorption, and the maximum adsorption capacity was estimated as 2000.00 mg/g. The kinetic study discloses that the adsorption processes can be satisfactorily described by the pseudo-second-order model. The values of Gibbs free energy change (ΔG0), entropy change (ΔS0), and enthalpy change (ΔH0) demonstrate the spontaneous and endothermic nature of the adsorption of CV onto rGO/Fe/Ni composites.


Introduction
Crystal violet (CV) as a cationic dye belongs to the class of triphenylmethane dyes, which is used for different purposes, such as dermatological agents, biological staining, textile dying, and paper printing [1][2][3]. Colored dyes create issues in the ecosystem as they are not only nonbiodegradable, toxic, mutagenic, and carcinogenic but also reduce light penetration and affect the photosynthetic activity of aquatic life [4][5][6]. CV is commonly stable when discharged into waste water owing to the complex aromatic molecular structure; therefore, it is imperative to remove this dye from waste water [7,8].
In this work, response surface methodology (RSM), ANN-GA, and ANN-PSO were applied to optimize and predict the process conditions for the maximum removal efficiency of CV removal from aqueous solutions. Parameters investigated for the CV removal include the effect of initial dye concentration, initial pH, contact time, and temperature. The rGO/Fe/Ni composites were synthesized by the co-precipitation method and characterized though X-ray diffraction (XRD), scanning electron microscopy (SEM) in conjunction with energy dispersive spectroscopy (EDS), Raman spectroscopy, N 2 -sorption, and X-ray photoelectron spectroscopy (XPS). The zero point of charge (pH ZPC ) of rGO/Fe/Ni composites was determined by using the salt addition method. The isotherm models of Freundlich, Langmuir, Temkin, and Dubinin-Radushkevich (D-R) were adopted to analyze the experimental data. Adsorption kinetics were examined by using pseudo-first-order, pseudo-second-order, intraparticle diffusion, and Elovich models. In addition, thermodynamics parameters (Gibbs free energy change, entropy and enthalpy changes) were calculated using the Van't Hoff equation.

Materials
All reagents and chemicals used in this work were of analytical grade, including H 2 SO 4, FeSO 4 ·7H 2 O, NiCl·6H 2 O, NaBH 4 , HCl, and NaOH. Crystal violet (molecular formula: C 25 H 30 N 3 Cl, molecular weight = 408 g/mol, λ max = 583 nm) used in this work was supplied by Tianjin Kemio Chemical Co., Tianjin, China ( Figure 2, Table 1). The stock solution of this dye (1000 mg/L) was prepared with deionized water. Graphite powder (particle diameters < 30 µm) was purchased from Sinopharm Chemical Reagent (Beijing, China).   [30]. Quantities of 2.0 g graphite powder and 0.5 g NaNO 3 were placed into 40 mL H 2 SO 4 in a 500 mL beaker under continuous stirring. Then, 5.0 g KMnO 4 was slowly added and stirred for 2 h below 20 • C. After this, the temperature of the solution was raised to 35 • C and kept for 30 min during the above-mentioned process. Subsequently, the reaction mixture was heated to 98 • C and allowed to react for 15 min under stirring. Finally, H 2 O 2 (30 wt %) was added to the reaction mixture, and the yellow-brown graphite oxide solution was washed several times with diluted HCl (5 wt %) and deionized water. The resultant nanoparticles were obtained by centrifugation, then dried at 60 • C for 48 h in vacuum.

Synthesis of Fe/Ni Nanoparticles and rGO/Fe/Ni Composites
The rGO/Fe/Ni composites were synthesized by the co-precipitation method [31]. FeSO 4 ·7H 2 O solution and NiCl·6H 2 O solution were added into GO solution using ultrasonication for about 2 h. The mixture was then stirred for 12 h. After this, 5.2 g NaBH 4 dissolved in 50 mL of deionized water was added to the mixture. The black precipitate was obtained via centrifugation with three deionized water and ethanol washing cycles, and then dried at 50 • C under a vacuum for 24 h before characterization. Furthermore, Fe/Ni nanoparticles were also prepared similarly to rGO/Fe/Ni composites without adding the GO.

Characterization of the Prepared Nanomaterials
X-ray diffraction patterns of Fe/Ni and rGO/Fe/Ni were obtained using a Philips Analytical X-ray (Lelyweg 1 7602, EA, Almelo, The Netherlands) with a Cu Kα X-ray source (generator tension 40 kV, current 40 mA) in the range of 5-90 • . The morphology and dimensions of these materials were characterized by scanning electron microscopy (Quanta F250, FEI, Hillsboro, OR, USA) coupled with energy dispersive spectroscopy. Raman measurements were performed by using LabRAM HR800 spectroscopy recorded at a 532 nm laser source (Horiba Jobin Yvon, Paris, France). The specific surface areas of Fe/Ni nanoparticles and rGO/Fe/Ni composites were determined using the N 2 adsorption/desorption isotherms at 77 K (Brunauer-Emmett-Teller (BET) Quadrasorb SI, Quantachrome Instruments, Boynton Beach, FL, USA). The Fe/Ni and rGO/Fe/Ni composites were characterized by X-ray photoelectron spectroscopy using an ESCALAB 250Xi spectrometer (Thermo Electron Corporation, Waltham, MA, USA).

Determination of the Zero Point of Charge
The pH of an aqueous solution is an important factor that may influence the adsorption process. The zero point of charge (ZPC) is defined as the pH value where a net surface charge equal to zero is indicated [32]. The pH ZPC of rGO/Fe/Ni composites was determined by using the salt addition method [33]. A quantity of 30 mL of NaCl (0.05 mol/L) solution was added to several 100 mL Erlenmeyer flasks. Initial pH (pH i ) values of NaCl solutions were adjusted over a range from 2 to 10 by adding 0.1 mol/L HCl and NaOH. pH i values of solutions were then accurately recorded, and 50 mg of each adsorbent was added to each flask. Suspensions were shaken at 298 K for 48 h. The suspensions were centrifuged at 4500 rpm for 5 min, and the final pH (pH f ) values of the suspensions were recorded. The value of pH ZPC is the point where the curve of ∆pH (pH f -pH i ) versus pH i crosses the line equal to zero while pH ZPC was determined by the intersection point of the curve.

Experiments
The removal of CV by rGO/Fe/Ni composites was studied in a batch system. Conical flasks with volume 100 mL were used for mixing 20 mg rGO/Fe/Ni with 50 mL of solution of known CV concentration, initial pH, temperature, and contact time. The solutions were agitated with a thermostatically controlled shaker at 200 rpm. The initial pH values were adjusted by the addition of 0.1 mol/L HCl or 0.1 mol/L NaOH to conduct the batch experiments at the desired pH. The isotherm study was carried out with different initial concentrations of CV from 200 to 1000 mg/L, keeping the other variables constant. The kinetic study was done by varying time from 5 to 24 min. For the thermodynamic study, the temperature was varied from 298 to 318 K. Then, the adsorbents were separated by centrifugation, and the final concentration of CV was analyzed by measuring a UV-visible spectrophotometer at λ max of 583 nm. The percentage removal (Y) and the amount of CV removal at equilibrium, q e (mg/g), were calculated by the following equations: where C i (mg/L) and C f (mg/L) are the initial and final CV concentrations in solution, respectively; v is the volume of the solution (mL); and m is the dosage of the adsorbent (mg).

Box-Behnken Design (BBD)
The Box-Behnken Design (BBD), as one of the designs for experiments of response surface methodology (RSM), was used to investigate the combined effects of independent variables, namely, initial dye concentration (X 1 ), initial pH (X 2 ), contact time (X 3 ), and temperature (X 4 ), with the minimum number of combinations for the four factors mentioned above [34]. A total of 29 experiments, involving the four operating parameters at three levels and five replications of the central point, were devised by BBD. This model will also give the maximum removal efficiency of CV under optimum conditions. Each independent variable has 3 levels designated as −1, 0, and +1 for low, middle, and high values, respectively ( Table 2). The relationship of the independent variables and the percentage decolorization of CV is described by the second-order polynomial where Y is the removal efficiency of CV; X i (i = 1-4) are noncoded variables; and β j (j = 0-14) are the regression coefficients for intercept, linear, quadratic, and interaction effects, respectively (i = j). ANNs are capable of machine learning and pattern recognition, which can solve problems like learning, thinking, remembering, and reasoning. The artificial neurons are the basic elements of ANNs, and consist of many simple computational elements that are connected to each other. The "network" is defined as the structure in which the neurons act simultaneously in a group. In the present study, a three-layer feed-forward perceptron ANNs with a back-propagation (BP) algorithm was established for modeling purposes [35]. This network consists of an input layer, hidden layers, and an output layer. All input weights were summed to create the output through the activation function [36] (Figure 3). The tangent sigmoid transfer function (tansig) (Equation (7)) was used in the input-hidden layer, whereas the linear transfer function (purelin) (Equation (8)) was adopted in the output layer. All the input and output were normalized within uniform range (0.1-0.9) during training of the network. Normalization of the input data was done using the following equation: where x i is the corresponding scaled variable for an input variable (x); likewise, x min and x max are the minimum and maximum values of the variable, respectively.
In Equations (5) and (6), x i is the value of a neuron in the input layer, w ij is the corresponding connection weight between neuron i in the input layer and neuron j in the hidden layer, W i is the connection weight, and θ is called the bias. The tangent sigmoid (tansig) function and linear transfer function (purelin) were used between the input and hidden layers and between the hidden and output layers, respectively.
The output was produced by the weight and bias of neurons through the activation function using the following equation: where Y, f, and sum represent the output, activation function, and all weights and biases in hidden layer or output layer, respectively.
The relative influence of the individual variable was calculated by the following Garson equation [37,38]: where I ab is the relative importance of the jth input variable to the output variable; w x is the connection weight; and a, e, and b are the number of neurons in the input layer, hidden layer, and output layer, respectively.

Optimization Using ANN-GA and ANN-PSO Models
GA is considered a useful method for solving optimization problems using the MATLAB 2015a software. PSO, as a new method, is able to accomplish the same goal as GA [39]. GA is inspired by the biological evolutionary process employing Darwin's theory of survival of the fittest [40]. The optimization of GA begins with random solutions called population strings or chromosomes. Each of the chromosomes (combinations of four genes, X 1 , X 2 , X 3 , and X 4 ) usually is represented as a binary string, which is evaluated by an objective function for their fitness [41]. In this process, GA uses three main types of rules (i.e., selection, crossover, and mutation) to create the new generation from the current population until one chromosome has the best fitness and thus is taken as the best solution to the problem. The values of the GA parameters for population size, number of generations, crossover rate, and mutation probability were 20, 100, 0.8, and 0.01. PSO was firstly proposed by Kennedy and Eberhart. This metaheuristic method is inspired by the social behavior of birds flocking and fish schooling for searching for food [42]. PSO is started with a swarm of particles randomly positioned in multidimensional search space. Every particle is the solution to the problem, which has two characteristics, namely, velocity and position. These particles have a memory and it is helpful to keep track of its previous best position. The position corresponding to the best fitness is known as personal best and global best. After the completion of each iteration, the position of particles is adjusted based on its own historical behavior and neighbors. The particles continue to move in the search space until the maximum iteration number or the desired value of the objective function was reached. The operating parameters were the swarm size (20), maximum iteration (50), personal learning coefficient (2), global learning coefficient (2), minimum inertia weight (0.3), and maximum inertia weight (0.9).

Characterization of Fe/Ni Nanoparticles and rGO/Fe/Ni Composites
The XRD patterns of the GO, Fe/Ni nanoparticles, and rGO/Fe/Ni composites are shown in  The morphology of Fe/Ni and rGO/Fe/Ni was characterized by using SEM ( Figure 5). Fe/Ni nanoparticles aggregated together tightly were observed ( Figure 5a). As shown in Figure 5b, the Fe/Ni nanoparticles are homogeneously dispersed well on the rGO surface, which imply an inhibiting effect on the Fe/Ni nanoparticle aggregation. The spectra of EDS also illustrate the presence of Ni as shown in Figure 6a,b. nZVI was synthesized by Wang et al., and the average diameter of this material is 80 nm [44]. In this study, the particle sizes of Fe/Ni nanoparticles and rGO/Fe/Ni composites are 44-81 nm and 26-68 nm in diameter, and the average diameters of Fe/Ni nanoparticles and rGO/Fe/Ni composites are approximately 66 nm and 42 nm, respectively (Figure 7a,b). These results indicate that Ni can effectively prevent the aggregation of nZVI, and the Fe/Ni nanoparticles can be dispersed onto the rGO surface.   Raman spectroscopy can be used as an effective method to identify the degree of graphitization and structural changes in the GO-based nanomaterials. The spectra of the GO, rGO, and rGO/Fe/Ni are shown in Figure 8, which exhibit the characteristic D and G bands centered at 1345 and 1587 cm −1 , respectively. The D band is a structural disorder originated from the breathing mode of A 1g symmetry, whereas the G band is of E 2g symmetry induced by the inplane vibrations of sp 2 bond atoms [45]. The intensity ratio of the D to G bands (I D /I G ) is often used as a measure of defect levels in graphene-based materials. The intensity of I D /I G increases from 0.98 for GO to 1.07 for rGO and then to 1.38 for rGO/Fe/Ni composites. This phenomenon could be attributed to the decrease in the sp 2 cluster size, perhaps caused by the creation of defects owing to the presence of iron atoms on the surface of the rGO. The surface area of Fe/Ni nanoparticles and rGO/Fe/Ni composites was measured using a BET analyzer, and the surface area of these materials was calculated to be 3.70 and 43.31 m 2 /g ( Figure 9). It is noted that the surface area of rGO/Fe/Ni composites is significantly higher than that of Fe/Ni nanoparticles. This is attributed to the satisfactory dispersion of Fe/Ni on the surface of rGO. The results of X-ray photoelectron spectroscopy (XPS) show that the binding energies at 284.6, 554.6, 720.6, and 860.8 eV are attributed to C1s, O1s, Fe2p, and Ni2p, respectively (Figure 10a). The Fe2p spectra consist of 2p 1/2 and 2p 3/2 peaks, which are located at 710.55 and 725.37 eV. The binding energies of the shake-up satellite (2p 3/2 and 2p 1/2 ) at 719.94 eV and 724.88 eV indicate the existence of Fe 2+ and Fe 3+ [45]. A weak peak at 707.5 eV corresponding to Fe 0 was observed in both the Fe/Ni and rGO/Fe/Ni (Figure 10b,c). The intensity of the Fe 0 peak in the rGO/Fe/Ni is stronger than that of the Fe/Ni particles, indicating that rGO might decrease the oxidation degree of Fe/Ni.

The Zero Point of Charge of rGO/Fe/Ni Composites
The behavior of CV adsorption on rGO/Fe/Ni composites was studied over a broad range of pH (2)(3)(4)(5)(6)(7)(8)(9)(10). It is worth noting that an obvious increase in the removal efficiency of CV by rGO/Fe/Ni composites was observed with the increase in pH of the solution (Figure 11a). The pH zpc value of this material is 3.5 (Figure 11b). For pH > pH zpc , the rGO/Fe/Ni composite surface will possess negative charge, which is in favor of the adsorption of CV [46,47]. For pH < pH zpc , this material's surface is charged positively [48]. These results are in accordance with the effect of pH on the removal efficiency of CV.

Experimental Results
The BBD of RSM was applied to visualize the effect of various independent parameters, namely, initial pH, temperature, contact time, and initial concentration, on the dependent parameter (removal efficiency of CV). Experimental data and predicted values for the removal of CV from aqueous solution are listed in Table 3. A multivariate analysis was performed to describe the relationship between dependent parameters and independent parameters; the fitted model equation is shown as follows.
The plot of normal probabilities versus the residual values shows that the points of residuals on the plot follow a straight line, confirming the normality of the error distribution ( Figure 12). The value of the determination coefficient (R 2 = 0.9701) demonstrates that the predicted values were in agreement with experimental values (Figure 13). Three-dimensional response surface plots (a, b, c, d, e, and f) indicate the combined effect of initial pH and initial concentration, contact time and initial concentration, temperature and initial concentration, contact time and initial pH, temperature and initial pH, and temperature and contact time. It is evident that the maximum removal efficiency was recorded at high pH and low initial concentration ( Figure 14). As shown in Figure 15, the value of final pH is higher than that of initial pH. This may be ascribed to the increased negative charge on the surface of rGO/Fe/Ni composites. Since the pH zpc of rGO/Fe/Ni composites is 3.5, the adsorption of CV was also enhanced when pH > pH zpc .     Analysis of variance (ANOVA) was applied to examine the quality of the fitted model. If the values of p are less than 0.05, then the model terms have a statistically significant role on the CV removal (Table 4). Therefore, it can be concluded that the variables X 2 , X 3 , X 4 , X 1 X 3 , X 2 X 3 , and X 1 2 are all statistically significant model terms. The F values represent the significance of operating parameters on the CV removal by rGO/Fe/Ni composites, based on which the order for the importance of operating parameters is as follows: X 2 > X 3 > X 4 > X 1 . This model has a good suitability due to its high F-values and nonsignificant lack of fit.

BP-ANN Model
The experimental data used in the BP-ANN model were collected in this study from BBD. Of the whole data set, 80% (1-24) was used for training and 20% (25)(26)(27)(28)(29) was used for testing ( Table 5). The value of R 2 (0.9998) of the BP-ANN model indicates the best prediction ability for testing and training in this network ( Figure 16). The number of neurons (N) in the hidden layer was determined according to the minimum mean square error (MSE) of the neural network. In order to determine the optimum number of neurons in the hidden layer, the number of nodes was examined by varying from 1 to 10. The values of MSE were used as the error function ( Figure 17). As can be seen in Figure 18, the ANN architecture with 3 neurons in the hidden layer appeared to be the optimal topology for training. The influence for each input variable on the output variable was calculated by the Garson equation using the weight and bias (Table 6). It was reported that temperature gives the highest percentage contribution to the decolorization of CV with 36.27% followed by 20.23% of initial concentration, 35.95% of initial pH, and 7.54% of contact time (Table 7).     Table 6. The weights and biases of BP-ANN in input-hidden layers (w i and b i ) and hidden-output layer (w j and b j ).

Prediction by BBD, ANN-PSO, and ANN-GA
The optimum values of independent parameters for BBD are 3.0 for pH, 40.6 • C for temperature, contact time of 18.0 min, and initial concentration of 368.9 mg/L. The maximum removal efficiency predicted under this condition was 88.2%, while the corresponding experimental value was 75.8% ( Table 8). The maximum percentage decolorization predicted by using ANN-PSO model is 88.0%, and the corresponding experimental value is 84.5% (Figure 19). The performance of the ANN-GA model indicates that the prediction removal efficiency is 86.9% under the following condition: pH of 3.3, temperature of 36.1 • C, contact time of 15.8 min, and initial concentration of 331.2 mg/L ( Figure 20). The absolute errors between the predicted and experimental results are 12.4, 3.5, and 5.6 for the BBD, ANN-PSO, and ANN-GA models, respectively. It was found that ANN-PSO was suitable for the prediction of CV removal by rGO/Fe/Ni composites. Table 8. Comparison between the predicted percentage decolorization of CV by using BBD, ANN-particle swarm optimization (PSO), and ANN-genetic algorithm (GA) models and the experimental results.

Isotherm Studies
The adsorption data for the CV onto rGO/Fe/Ni nanocomposites were fitted to Langmuir, Freundlich, Temkin, and Dubinin-Radushkevich (D-R) models. The isotherm studies were performed under contact time of 18 min, pH of 5, and temperature of 25 • C with initial dye concentration of CV ranging from 200 to 1000 mg/L in order to provide an insight into the adsorption characteristics of rGO/Fe/Ni composites. The Freundlich isotherm assumes that the adsorption occurs on a heterogeneous surface with a multilayer adsorption mechanism, which is expressed as follows [49]: log q e = log k f + 1/n log c e (12) where q e is the amount of CV adsorbed (mg/g); c e is the equilibrium concentration of CV (mg/L); and K f and n are constants affecting the adsorption capacity and intensity of adsorption, respectively, with value closer to zero with the rising heterogeneous nature of the surface (1/n < 1 indicates normal Langmuir isotherm while 1/n above 1 indicates bimechanism and cooperative adsorption). The Langmuir isotherm describes the adsorption process occurring in a single layer (forming a molecular monolayer) of the adsorbent surface, and was employed for the calculation of the maximum capacity of adsorption (q max ). A plot of 1/q e versus 1/c e was used to obtain the Langmuir equilibrium isotherm. The Langmuir isotherm equation in linear form is given as follows [50]: where c 0 and c e are the initial and final dye concentration (mg/L), respectively; q e is the amount of CV at equilibrium (mg/g); q m is the maximum adsorption capacity; K L is the Langmuir constant (L/mg); and R L is the separation factor that indicates the adsorption nature to be either unfavorable (R L > 1), linear (R L = 1), favorable (0 < R L < 1), or irreversible (R L = 0) [51]. The Temkin isotherm considers that the heat of adsorption for all molecules in the phase will decrease linearly with coverage owing to adsorbent-adsorbate interaction [52,53].
where B is related to the heat of adsorption, while A (L/g) is the binding constant responding to the maximum binding energy at equilibrium; c e and q e have the same meanings as mentioned above.
The Dubinin-Radushkevich (D-R) isotherm was applied to estimate whether the adsorption process has a physical or chemical mechanism [54,55]. The linear form of the D-R isotherm is presented as the following equations [56,57]: ln q e = ln q max − αε 2 (16) where c e , q e , and q max have the same meanings as mentioned above; T is the absolute solution temperature (K); R is the universal gas constant, 8.314 (J/mol K); α is a constant energy (mol 2 /J 2 ); and ε is the Polanyi potential. The value of E gives information about the adsorption mechanism: physical or chemical. If it lies between 8 and 16 kJ/mol, the adsorption process is controlled by a chemical mechanism, while a value of E smaller than 8 kJ/mol indicates that the adsorption process was physisorption [58]. The calculated isotherm parameters for the adsorption of CV onto rGO/Fe/Ni composites are presented in Table 9. The value of K F for the Freunlich model was 98.7 and the 1/n was found to be 0.4572, demonstrating that the adsorption of CV onto the rGO/Fe/Ni composites was a favorable process. The values of R L (7.8 × 10 −6 -3.9 × 10 −5 ) are in the range of 0-1, indicating that the process is favorable, which corroborates the K F values of the Freunlich isotherm. The value of the Langmuir isotherm constant (K L ) is 128.8 L/mg. The maximum adsorption capacity from the Langmuir isotherm was calculated to be 2000 mg/g. The mean adsorption energy value of CV was 0.2 KJ/mol, implying that the adsorption of CV by rGO/Fe/Ni composites was mostly chemisorption. The value of R 2 for the Freundlich isotherm (0.9700) was higher than those for the Langmuir (0.9483), Temkin (0.9094), and D-R (0.7339) isotherms. The values of the adsorption isotherm constants n and R 2 indicate that the experimental values are well fitted to the Freundlich model. As given in Table 10, the removal capacity of the rGO/Fe/Ni composites is significantly higher than that of other materials. The excellent CV removal capacity of rGO/Fe/Ni composites is an important advantage for environmental remediation.

Kinetics Studies
A study on the kinetics was applied to describe the solute uptake rate and the rate-controlling step of the process for the CV adsorption onto rGO/Fe/Ni composites. The experimental data were fitted to the pseudo-first-order, pseudo-second-order, intraparticle diffusion, and Elovich kinetic models.
The pseudo-first-order kinetic model is presented by the relation of Lagergren, which states that the adsorption rate of vacant sites is proportional to the number of occupied sites, and the equations can be described by the following form [64,65]: where q e (mg/g) and q t (mg/g) are the adsorption capacity at equilibrium and at time t (min), respectively, and k 1 (min/1) is the first-order rate constant. The pseudo-second-order model can be represented in the following form [66]: where k 2 is the pseudo-second-order rate constant (g/mg/min), and the adsorption rate constants (k 2 ) can be determined experimentally by plotting of t/q t versus t.
To study the adsorption mechanism, the kinetic data of adsorption were fitted into intraparticle diffusion and Elovich equations. The intraparticle diffusion model was described by Weber and Morriss, and can be used to investigate the rate-limiting step for CV adsorption onto rGO/Fe/Ni composites [67,68]: where k 3 is the rate constant of intraparticle diffusion (mg/g min 1/2 ), and the value of B is proportional to the boundary layer [69]. The Elovich model implies multilayer adsorption and assumes that the adsorption sites increase exponentially during the adsorption process; this equation can be written as follows [70]: where α (mg/g/min) is the initial adsorption rate and β (g/mg) is the desorption constant, which is related to the extent of surface coverage and activation energy for chemisorption. The values of parameters obtained from these models are presented in Table 11. From the values of R 2 , it can be concluded that the experimental data are well fitted to the pseudo-second-order kinetic model in contrast with the pseudo-first-order, intraparticle diffusion, and Elvoich kinetics. This implicates that the adsorption is of a chemical nature.

Thermodynamics Studies
In order to investigate the effect of temperature on the adsorption of CV, experiments were carried out at four different temperatures: 298, 308, 318, and 328 K. The amount of adsorption was increased from 946.21 to 1087.04 mg/g with the increase in temperature. Kc was calculated using the following equation [71]: The enthalpy change ∆H 0 (kJ/mol) and entropy change ∆S 0 (J/mol/K) for the adsorption of CV were calculated from the slope and intercept of the plot of ln(K c ) v/s 1/T, and these parameters can be obtained from the Van't Hoff equation [72]: The values of Gibbs free energy (∆G 0 ) was computed from the following equation: Values of ∆G 0 for the adsorption of CV onto rGO/Fe/Ni composites in this work were found to be −5.0850, −5.9120, −6.5544, and −6.9719 kJ/mol at 293, 303, 313, and 323 K, respectively (Table 12). The negative values of ∆G 0 demonstrate the spontaneous nature of the adsorption process. In addition, by plotting a graph of ln K c versus 1/T, the values of ∆H 0 and ∆S 0 can be obtained from the slopes and intercepts ( Figure 21). The positive ∆H 0 value suggests the endothermic nature of the adsorption process that is supported by the increase in removal efficiency with increasing temperature [73]. A positive value of entropy change was observed, which corresponded to the increase of randomness at the solid/liquid interface in the adsorption process [74]. The positive values of ∆S 0 and ∆H 0 show that the interaction of rGO/Fe/Ni composites with CV is basically entropy driven [75].

Conclusions
The results of this study demonstrate that rGO/Fe/Ni composites can be used effectively for the removal of CV from aqueous solutions. This material was synthesized by using the co-precipitation method, and characterized by XRD, SEM, EDS, Raman spectroscopy, N 2 -sorption, and XPS. Operating parameters such as initial concentration, initial pH, contact time, and temperature were investigated with the aid of BBD, ANN-GA, and ANN-PSO models to predict the optimum conditions and the maximum removal efficiency. The high value of R 2 (0.9998) for the BP-ANN model indicates the best prediction ability. The absolute errors between predicted and experimental results were 12.4 for BBD, 5.6 for ANN-GA, and 3.5 for ANN-PSO. The existence of the high degree of agreement between the predicted results and experimental results indicate that the ANN-PSO could be used effectively for the evaluation and optimization of the effects of the independent variables on the removal efficiency of CV. Since the pH zpc of rGO/Fe/Ni composites is 3.5, the adsorption of CV was enhanced when pH > pH zpc . The maximum adsorption capacity from the Langmuir isotherm was calculated to be 2000 mg/g. The value of R 2 for the Freundlich isotherm (0.9700) was higher than those for the Langmuir (0.9483), Temkin (0.9094), and D-R (0.7339) isotherms. The experimental data is well fitted to the pseudo-second-order kinetic model. The negative values of ∆G 0 illustrate the spontaneous nature in the range of temperature studied (293-323 K). The positive values of ∆S 0 and ∆H 0 show that the interaction of rGO/Fe/Ni composites with CV is basically entropy driven. Further studies should be performed concerning the zeta potential and the oxidation-reduction potential of nanomaterials, as well as the removal of two dyes simultaneously.