Application of the Fe3O4/ alginate/ diatomite nano-adsorbent for the adsorption of palladium and cyanide from wastewater: optimisation, kinetic and equilibrium studies

ABSTRACT In this research, the adsorption rates of cyanide and palladium onto Fe3O4/alginate/diatomite nano-adsorbent (FADA) were evaluated. The co-precipitation technique was applied to synthesis of FADA. The response surface methodology (RSM) was employed to investigate the relation between input-independent factors (initial pollutant concentration, contact time, FADA dosage and pH) and one dependent output response (removal efficiency). The best model was selected based on the results of the ANOVA analysis.SO model due to R2 of 0.929 and the insignificant lack of fit (0.12) for cyanide and also R2 of 0.98 and the insignificant lack of fit (0.12) for palladium was selected as an appropriate model for adsorption of both pollutants. Therefore, prediction and optimisation of the adsorption of the pollutants onto FADAwere done based on SO model. The best conditions for the adsorption of cyanide (95.65%) and palladium (92.66%) onto FADA were obtainedat (pH, 5.45; palladium concentration, 15.13 mg L−1; contact time, 104.8 min and FADA dosage, 0.98 g L−1) and (pH,7.0; cyanide concentration, 4.88 mg L−1; contact time, 91.06 min and FADA dosage, 2.05 g L−1), respectively. Investigation of the non-linear isotherm models indicated adsorptions of cyanide (R2 = 0.995) and palladium (R2 = 0.999) ontoFADA have reasonably fit to the Sips model.The maximum adsorption capacities of cyanide and palladium per mass unit of FADA were 208.55 mg g−1 and 60.2 mg g−1, respectively.The pseudo-first-order (R2 = 0.99) and the intra-particle diffusion (R2 = 0.96) were found to agreement well with the adsorption experimental data obtained for cyanide and palladium, respectively. Results indicated the sorption reactions of cyanide and palladium onto FADA were endothermic and exothermic, respectively.The present study indicated diatomite magnano composite boosted with alginate polymer beads due to high operating groups and also a high surface-to-volume ratio and porosity can be applied as an efficient adsorbent for the removal of cyanide and palladium from aqueous solutions.


Introduction
The presence of pollutants in the environment can pose irreparable dangers to plants, animals and humans [1,2].Palladium is widely used in industrial catalysts, automobiles, pharmaceuticals, and hydrogen storage devices [3][4][5].Recycle and reuse of palladium in secondary resources due to its high economic value and also high popularity in industry can be too beneficial [6,7].Also, the health effects including skin and eye irritations, kidney disorders, bone cancers, paralysis and breathing disorders related to presence of the palladium in water sources and food chain have been proved.Cyanide as one of the most hazardous chemicals, can be produced during the incomplete combustion polyurethane, melamine, silk and etc.Also, the presence of cyanide in the pharmaceutics, petrochemical photography and electroplating industry effluents has been proven [8].Therefore, the presence of this pollutant(cyanide)in the environment can be threaten seriously the public health [3].The health effects of cyanide on human are including: mutagen, headache, dizziness, carcinogen nerve damage and hypoxia [9][10][11].Therefore, removal of the these pollutants from industrial effluents prior to discharge into the environment is very essential [12,13].Removal of metals from aqueous solutions by the conventional treatment methods, due to their non-biodegradable nature and stability in the environment is difficult and sometimes impossible.The conventional wastewater treatment processes such as coagulation and flocculation are not effective methods for removing cyanide and palladium.These methods usually produce significant amounts of sludge.Much researches have been done on the removal of cyanide and palladium.Alkalisation, chlorination, air oxidation and membrane processes such as reverse osmosis, electrodialysis and adsorption were also considered as cyanide and palladium removal methods.However, the application of these methods due to problems such as the high chemical and energy consumption, higher operational costs as well as low efficiency has been limited.In the recent years, several studies have been conducted on the use of ecofriendly adsorbents in the removal of metals from aqueous solutions.The advantages of using these absorbents are included abundant resources, low cost, easy usage, ecofriendly, economic, scientific and social importance [14][15][16].Most of the methods used to remove these pollutants are not economically affordable and are unacceptable from an environmental point of view [17,18].Adsorption process can be considered as an acceptable method due to easy operation low cost, high diversity and efficiency [19][20][21].However, some adsorbents used to adsorb these pollutants have low adsorption capacity and high regeneration cost [22].Diatomite is a biological silica that is produced from a kind of sea algae containing 70 to 90% silica [23].Diatomite is non-toxic and has a high surface-to-volume ratio and porosity.This bio silica enhances the adsorption strength of the adsorbent [24].Given that to separation and recycling of absorbent in the adsorption process is critical; therefore, combining of the magnetite nanostructure (Fe 3 O 4 ) with absorbents can be very useful for this purpose [25,26].Alginic acid, also called align, is a polysaccharide distributed widely in the cell walls of brown algae that is hydrophilic and forms a viscous gum when is hydrated.With metals such as sodium and calcium, its salts are known as alginates.Its colour ranges from white to yellowish-brown.It is sold in filamentous, granular, or powdered forms.Alginate due to high operating groups, surface area and chemical stability [27] can be applied to enhance the adsorbent performance [28].Therefore, in this research, the adsorption performances of cyanide and palladium onto Fe 3 O 4 /alginate/diatomite nano-adsorbent (FADA) were evaluated.Schematic of alginate structure is presented in Figure 1.
In order to minimise operational costs and time, it is essential application of an optimisation method on an industrial scale.The response surface methodology due to depict of the interactive effects of all the involved parameters and also the high precision and reliability can be proper to this purpose.Therefore, in the present study, optimisation and modelling of the pollutants adsorption onto FADA was investigated by RSM multivariable method and with using R software.After analysing of experimental data by RSM method, data optimisation was done using the Solver method.Then study of non-linear kinetic and isotherm models based on the results obtained from Solver method was done to identify the possible adsorption mechanism [29,30].Alginate and diatomite are inexpensive and available compounds for the preparation of nano-adsorbent.In addition, a suitable absorbent must have five conditions, the prepared adsorbent in this research be included these capabilities in comparison to other adsorbents: I) simple synthesis, II) the ability to separate from the liquid environment (magnetic feature), III) regeneration capability, IV) high adsorption rate after regeneration cycle, V) adsorbent does not have toxicity for the environment.Furthermore, no relevant study has yet been reported on the utilising of Fe 3 O 4 /alginate/diatomite composite for the removal of cyanide and palladium.Considering the interesting characteristics of Fe 3 O 4 , alginate and diatomite, the present research was aimed at exploring the prepared Fe 3 O 4 /alginate/diatomite composite for efficient adsorption of cyanide and palladium under the optimised conditions of the parameters (including pollutant concentration, contact time, pH and adsorbent dosage).

Synthesis of FADA nanocomposite
The synthesis of FADA was included two steps: production of magnetite nanoparticles by co-precipitation technique and then preparing of the FADA nanocomposites.To prepare of the magnetite nanoparticles, 0.023 M FeSO 4 .7H 2 O and 0.046 M FeCl 3 .6H 2 O were dissolved into 150 mL deionised water.Nitrogen gas was used to remove air from the mixture.In the following, 20 mL of ammonium hydroxide was added to the iron mixture under vigorous stirring (for 20 min).Then, 3 mL epichlorohydrin was mixed with iron solution.The mixture was heated to 75°C for 1 h and then was cooled to room temperature.The obtained Fe 3 O 4 nano-particles were washed with deionised water and ethanol and then were dried in an oven at 60°C for 24 h.In the following, for preparing of the FADA, 1 g of diatomite was mixed with 1 g of Fe 3 O 4 nano-particles and the achieved compound was added in the flask containing 1 g of sodium alginate and 100 mL of acetic acid solution (1 M).The FADA granular were formed with adding of 100 mL of NaOH and ethanol with ratio of 4:1 into flask.Then the FADA granular formed were washed by distilled water and were dried at the environment temperature [31].

FADA adsorbentcharacterization
Several techniques were applied to determine textural properties, surface morphology, and functional groups of FADA nanocomposite.X-ray diffraction (XRD) patterns using CuKα radiation and operated at 40 kV and 30 mA at 2θ range of 10-80°, was used to determine the nature of crystallinity of FADA [32].A Fourier Transform Infrared (FTIR) spectrophotometer (Perkin Elmer-spectrum 65, USA) using KBr disc method at wave number range of 400-4000 cm −1 was used to identify the functional group type of FADA adsorbent.The surface morphology and composition of the prepared FADA adsorbent was investigated by capturing high field emission scanning electron microscopy using a FESEM-ESCAN device (model Mira III, Czech Republic) equipped with an X-ray energy spectroscopy (EDX) under vacuum stable.Thermo gravimetric analysis (TGA) in the temperature range of 30 to 800°C was done to investigate weight losses occurred during synthesis ofFADA nanocomposite.The BET adsorption-desorption test at 77 K (Belsorp mini, Japan) was applied, to examine the specific surface area, pore total volume and the pore average diameter [33].

Batch adsorption experiments and analytical method
The experiments were performed intermittently in the batch scale.The stock solution was prepared separately from palladium chloride and potassium cyanide.Deionised water was used to prepare the desired solution.The stock solution was prepared weekly [34].The desired concentrations were prepared from the stock solution.The pH of the solution was adjusted to the desired range (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12).Then a certain amount of adsorbent (0.02 to 2.5 g L −1 ) was added in the flask containing 100 mL of the solution.After a certain period of time, the sample was taken from the solution and was analysed to check the residual amount of pollutants.It should be noted the all tests for palladium chloride and potassium cyanide were performed separately.The pH was measured with a pH metre (Aqua lytic (AL15)).The temperature was adjusted by incubator shaker.After separation of FADA composite by employing a magnet (1.4 T), samples were analysed for residual pollutant concentration using ICP-OES spectrometer detection.A schematic of the tests steps is provided in Figure 2.

Factorial experimental design and optimisation of the parameters
RSM using R software is a useful tool to state the combined effect of independent inputs and response variable.Four variables of pH, pollutant concentration, contact time and FADA dosage were entered in R software and the design of experimental runs was done based on central composite design (CCD)method [30].The values of the used independent variables for designing of CCD runs were tabulated in Tables 1, 2. The independent response related to each run was obtained in the laboratory and these responses were entered in the software.Then the coding data was done and the coded data were adapted to three RSM models (first-order response-surface (FO), two-way interactions (TWI) and full second-order (SO)).The best model was selected based on the results of the ANOVA analysis (model with insignificant lack-of-fit, a lower akaike information criterion (AIC) and a higher multiple R-squared) [35][36][37].The regression analysis was performed on the selected model and these results were entered in designing the final formula.Finally, the optimisation process was done using solver method and based on the stationary point in the original units.

Characterisation results
Morphological of FADA (Figure 3(a)) reveals a homogeneous and porosity structure than sodium alginate, diatomite and Fe 3 O 4 .EDAX spectrum taken from the FADAwas given weight ratios of O (40.05%), Mg (0.48%), Al (1.98%), Si (47.62%),K (0.31%), Fe (6.21%) and     [25,38,39].These results indicated diatomite and Fe 3 O 4 were successfully coated into sodium alginate (Figure 3(b)).According to thermo gravimetric analysis on the FADA nanocomposite (Figure 3(c)), it was observed nanocomposite is stable up to 80°C.The weight loses of FADA nanocomposite occurred at 200°C and dropped sharply at 800°C.This phenomenon can be related to presence of alginate in the FADA structure; as at 200°C and 700°C, about 3% and 10% of FADA structure was decomposed, respectively.The BET analysis showed a specific surface area of 63.44 m 2 /g, pore total volume of 1.343 cm 3 /g and the pore average diameter of 24.605 nm for the synthesised nanocomposite.

Fitting a response-surface model, regression analysis and optimisation process
Experimental data were fitted with the three models (FO, TWI and SO) and the best model was selected based on ANOVA analysis.The results obtained for each model were tabulated in Tables 3, 4. Based on Tables 3, 4, SO model because of insignificant lack-offit, a lower AIC and a higher multiple R-squared was selected as the best model and indicated satisfactory agreement with the experimental data obtained for both pollutants.Therefore, prediction and optimisation of the both pollutants adsorption onto FADA was done based on SO model.According to ANOVA analysis (Table S1 in the supporting information),the effective terms in cyanideandpalladiumadsorption ontoFADA were (a 1 , a 2 , a 3 , a 4 , a 3 : a 4 , a 1 2 , a 3 2 , a 4 2) and (a 1 , a 2 , a 3 , a 4 , a 1 : a 2 , a 1 : a 3 , a 1 : a 4 , a 2 : a 3 , a 2 : a 4 ,a 1 ^2, a 2 ^2, a 3 ^2, a 4 ^2), respectively.Also,  the regression analysis results (Table S2 (a)in the supporting information) indicated terms of (a 3 , a 4 , a 3 : a 4 ) and (a 1 , a 1 ^2, a 3 ^2 and a 4 ^2) have intensifying and reducing effects in the palladium adsorption onto FADA, respectively; while according to Table S2 (b) in the supporting information, the synergistic and oppositional terms in the cyanide adsorption onto FADA were (a 3 , a 4 , a 1 : a 2 , a 2 : a 3 , a 2 : a 4 , a 1 ^2) and (a 1 , a 2 , a 1 : a 3 , a 1 : a 4 , a 3 : a 4 , a 2 ^2, a 3 ^2, a 4 ^2), respectively.According to regression analysis, the final equations in terms of the coded factors were presented in Equations ( 1) to (2).
Coded factors for the removal of cyanide: Coded factors for the removal of palladium: According to the obtained results from solver analysis, the maximum removal rates of the cyanide and palladiumonto FADA were achieved under the selected conditions of (pH, 5.45; palladium concentration, 15.13 mg L −1 ; contact time, 104.8 min; FADA dosage, 0.98 g L −1 ) and (pH, 7.0; cyanide concentration, 4.88 mg L −1 ; contact time, 91.06 min; FADA dosage, 2.05 g L −1 ), respectively.

Perspective plots of the pollutant adsorption onto FADA
The interactive effects of the independent variables on removal performance of cyanide and palladium were investigated by perspective plotting (Figure 4).The effects of FADA dosage (0.5 to 2.5 g L −1 ) and reaction time (30 to 110 min), on the adsorption of cyanideontoFADA were simultaneously monitored (Figure 4).As portrayed in Figure 4, changes in the FADA dosage can directly affect the uptake capacity of the adsorbent.As shown in Figure 4, at a fixed time (40 min), pH of 5.45, and initial cyanide concentration of 6 mg L −1 , with an increase in FADAdosage from 0.5 to 2 g L −1 , the removal performance was increased and reached from 40% to 80%.This phenomenon is agreement with increase in the number of active sites and the availability for cyanide absorption (increasing adsorption capacities) with increasing FADA dose.Althoughany improvement in FADA performance did not observed in the adsorbent dosage above 2 g L −1 , probably due to saturation of the binding sites (for a given mass of the adsorbent, the surfacebinding sites on the adsorbent are fixed).The effect of the interaction between pH (2 to 12) and time (5-200 min) on the palladium adsorption onto FADAat initial palladium concentration of 25.64 and adsorbent dosage of 0.51 g L −1 was further investigated in the present study (Figure 5(a)).As portrayed in (Figure 5(a)),at a fixed time (50 min), increasing pH from 2.0 to 7.0 did not affect the removal performance of palladium, while removal efficiency decreased from 70% to 50% as pH increased above 7.0.The zero point of charge (pH zpc ) ofFADA (not shown) was determined 9.0.Therefore, it was proved adsorption of palladium onto FADA is independent of electrostatic attraction force (because FADA surface was positive at pH below 9.0) and the predominant mechanism for the removal of palladium is likely physical.Also, the proceeding of the sorption process by the formation of inner-sphere surface complexes on the surface of the sorbent can be the other mechanism for the adsorption of palladium onto FADA at the pHs below 7.0.The effects of pH (2 to 12)and initial palladium concentration (1 to 55 mg L −1 ) on the adsorption of palladium over FADAwere simultaneously surveyed at constant FADA dosage of 0.51 g L −1 within 102.5 min (Figure 5(b)).As can be seen in Figure 5(b), at a fixed pH of 4.0, an increase in initial palladium concentration from 10 to 40 mg L −1 was caused a decrease in the adsorption efficiency from 85% to 70%.This decrease in the removal performance can be due to saturation of the binding sites on the FADA surface and lack of participate of internal part of the adsorbent for the palladium sorption [40].Moreover, the interaction effect of palladium concentration (10-50 mg L −1 ) and time (5-200 min) as the significant parameters in the removal of palladium by FADAwas investigated.As can be seen from Figure 5(c), at a fixed initial concentration of palladium (10 mg L −1 ), an increase incontact time from 5 to 120 improved the removal performance from 74% to 82% (for a fixed adsorbent dose of 0.51 g L −1 and a pH of 6.0), while increase of the time to over 100 min was resulted to gradually decrease in the removal efficiency.The physical adsorption mechanism resulting fixing of the surface-binding sites on the adsorbent after 100 min, can be reason for this matter.As shown inFigure 5(d),at a fixed initial palladium concentration (10 mg L −1 ), improvement in the removal performance from 70% to 95% with increasing of FADA dosage from 0.2 to 0.8 g L −1 , can be in agreement with an increase in number of sorption sites and adsorption capacity as a higher amount of adsorbent should be used.Also, increment in removal performance with increasing of adsorbent dosage (0.2 to 0.8 g L −1 ) at a fixed pH of 4.0 can be due to an increase in the given mass of the adsorbent that this manner is in agreement with an increase in adsorption capacities [41] (Figure 5(e)).

Description of the reaction between adsorbate and adsorbent using two and three parameters-nonlinear isotherm models
The two and three parameters-nonlinear isotherm models were applied to describe distribution of cyanide and palladium molecules between the liquid phase and the solid phase (Table S3 in the supporting information) .The correlation coefficient (R 2 ), the chi-square statistic (X 2 ), the residual root mean square error (RMSE), the average percentage error (APE) and residual sum of squares (RSS) were used to evaluate the goodness-of-fit of the isotherms and kinetics (Table S4 in the supporting information).If kinetic or isotherm model data be in the good adjustment with the experimental data; the values of RMSE, X 2 , APE and RSS will be a small number, while a high correlation coefficient will be observed.
The Langmuir model states the adsorption of a pollutant on the adsorbent is monolayer, independent and uniform, while the Freundlich model is based on the non-uniform, uneven and multi-molecular adsorption.Tamkin recommends for adsorption processes to see heat loss throughout the adsorption process.The Dubinin-Radushkevich isotherm describes the dependence of the adsorption characteristic curve on the porous structure of the adsorbent.Jovanovic model is the same as that considered by Langmuir with considering of the some mechanical contacts between pollutant and adsorbent surfaces.The Langmuir (for cyanide) and Jovanovic (for palladium)models indicated highest R 2 and lowest values of RMSE, X 2 , APE and RSS than two-parameter isotherm models.The Khan Isotherm model is a general model that describes experimental data with the least percentage of average adsorption error of some pollutants from aqueous solutions and is based on the comparison of several multi-component adsorption isotherms.When a K is equal to unit, the Khan model is reduced to the Langmuir isotherm.An a K value of 0.27 showed that the Khan model could not be expressed in terms of the Langmuir isotherm.The amount of q m obtained for the Khan model showed a large difference with the calculated values for Langmuir, Jovanovic and Sips models.Due to the fact that the Sips model (Langmuir-Freundlich model) has a limited limit for the adsorption of contaminants with high concentrations, so it is based on solving the problem of increasing the adsorbed material by increasing the concentration.The Redlich-Peterson model is combination of the Langmuir and Freundlich models assuming the hybrid adsorption mechanism and does not follow ideal monolayer adsorption [42].The value of g lies between 0 and 1.At the higher concentrations of pollutants, model becomes limited (g lower than 1), therefore, the Redlich-Peterson model is reduced to the Freundlich model.When the g value equals to 1, Redlich-Peterson model is reduced to the Langmuir model and when the g equals to 0, the equation is reduced to Henry's law.The experimental data and the non-linear forms of the isotherm models portrayed in Figure 6.As presented in Tables 5, 6 and Figure 6, cyanide and palladium adsorption experimental data were in a good agreement with Sips model.It should be noted that Sips model is suitable for predicting heterogeneous surfaces and for monolayer adsorption at high concentrations of adsorbent.The q ms (q max ) calculated from the Sips model (208.55 mg g −1 ) related to cyanide adsorption was approximately two times values obtained for two-parameter isotherm models including Langmuir, Dubinin-Radushkevich and Jovanovic models [43].Also, the Sips model designed for cyanide and palladium adsorption, indicated highest R 2 and lowest values of RMSE, X 2 , APE and RSS than two and three-parameter isotherm models; as the Sips model indicated the best fit with experimental data obtained for cyanide and palladium removals.The q ms (q max ) calculated from the Sips model related to palladium adsorption was 60.2 mg g −1 .Therefore, adsorption of palladium onto FADA at high concentration is related to Langmuir model, whereas the adsorption process at low concentrations of palladium is based on the Freundlich model [44].The adsorption capacities (q max ) of the various materials for the uptake of palladium and cyanide were displayed in Table 7.

Description of the adsorption kinetic of cyanide and palladium onto FADA by the nonlinear models
The non-linear sorption kinetics of pseudo-first order, pseudo-second order and intraparticle diffusion were employed to investigate the adsorption mechanism and reaction pathway (Table S5 in the supporting information).Tables 8, 9 and Figure 7, presents the results of related to kinetic studies.According to the obtained results, the pseudo-firstorder and the intra-particle diffusion (pore diffusion) models were found to agree well with the adsorption experimental data obtained for cyanide and palladium, respectively [42].The pseudo-first order kinetic model declares the sorption capacity of solids has the main role in the pollutant adsorption assuming adsorption of the one pollutant molecule onto one sorption site on the adsorbent surface [52].The pseudo-second order kinetic model reveals adsorption of pollutant molecules onto sorption sites on the adsorbent surface is based on a chemical adsorption (such as sharing or exchange of electrons between the sorbent and the sorbate).Elovich model is a suitable model to study of the chemical adsorption kinetic of pollutants on heterogeneous materials.It describes as the amount of pollutants absorbed decreases the adsorbent capacity decreases.Therefore, it can be useful to describe the adsorption of pollutants from the aqueous solutions [53,54].Boyd's model deals with adsorption by the adsorbent surface (film diffusion) or particle transport within the adsorbent pores (adsorption is controlled by particle diffusion) [55].By plotting B t versus t, if the line passes through the centre, the particle diffusion mechanism will dominate, and if it does not pass through the origin, the surface mechanism will superior.
As shown in Tables 8, 9, Figure 7 and Figure 8, it was found intra-particle diffusion is involved in the palladium adsorption process and it can be the sole rate-limiting step.Also, two steps including external surface adsorption (steeper portion) and intra-particle or pore diffusion (sharper portion) are involved in the adsorption of palladium onto FADA (Figure 8) [42].Considering that the plot of q t against t 1/2 of does not pass through the origin, it can be said that the adsorbent surface (film diffusion) is the superior mechanism.This was confirmed by the Boyd diagram (not shown).Thus, intra-particle diffusion is the dominant mechanism for the adsorption of palladium onto FADA but it is not the sole rate controlling step.Also according to results presented in Tables 8, 9 and Figure 7, the  sorption capacity of solids has the main role in the cyanide adsorption assuming adsorption of the one cyanide molecule onto one sorption site on the adsorbent surface [44].

Thermodynamic studies of palladium and cyanide
The temperature influence on cyanide and palladium adsorption onto FADA was investigated in the range of 293-323 °K.The Gibbs free energy (ΔG° (kJ mol −1 )) as the fundamental criterion of spontaneity was calculated from the following equation: Also the parameters of enthalpy (ΔH 0 (kJ mol −1 )) and entropy (ΔS 0 (kJ mol −1 K −1 )) were determined from the following equation: Thermodynamic parameters were tabulated in the Tables 10, 11.As tabulated in Table 10, the values of ΔH 0 > 0, ΔS0 > 0 and ΔG<0 indicated the sorption reaction of cyanide onto FADA was endothermic, an increase in the randomness at the solid/liquid interface during the sorption process and a spontaneous sorption, respectively.Also according to Table 11, the values of ΔH 0 < 0, ΔS0 < 0 and ΔG<0 indicated the palladium sorption reaction onto FADA was exothermic, a decrease in the randomness at the solid/liquid interface during the sorption process and a spontaneous sorption, respectively.

Desorption studies
One of the most important points in the adsorption process is the long-term stability of the adsorbents during the adsorption and desorption cycles [56].For this purpose, the regeneration and the reusability experiments of palladium and cyanide onto FADA composite were done during six consecutive cycles and the results were presented in Figure 8.At the end of each step, the adsorbent used was magnetically separated and after rinsing with hydrochloric acid and neutralising with sodium hydroxide was used for the next process.After each cycle's adsorption process, the desorption percentages (%) were calculated by using Eq. ( 5) [25]: As portrayted in Figure 9, the regeneration efficiencies of FADA composite applied for cyanide in the 1 st and 6 th runs were 95.65% and 79.2%, respectively (Figure 9  a regeneration efficiencies of 92.66% and 75.44% were observed for the 1 st and 6 th runsduring adsorption of palladium by FADA composite, respectively (Figure 9 (b)).
The decrease in adsorbent efficiency in the adsorption of pollutants may be related to the gradual loss of active sites on the adsorbent surface [57]during washing with hydrochloric acid and neutralisation with sodium hydroxide [58].Another reason may be related to the irreversible blockage of some adsorption sites.

Conclusion
The response surface methodology (RSM) using R software was chosen as an efficient method for the optimisation of cyanide and palladium adsorption onto FADA.SO model (with R 2 of 0.9807, F-statistic of 105.1 on 14 and 29 DF, lack of fit of 0.0753 and AIC of 19.15 for palladium) and (with R 2 of 0.9296, F-statistic of 37.73 on 7 and 20 DF, lack of fit of 0.128085 and AIC of 130.73 for cyanide) was selected as the best model for predicting of the both pollutants.According to the obtained results from solver analysis, the maximum removal rates of the cyanide (95.65%) and palladium (92.66%) were achieved under the selected conditions of (pH, 5.45; palladium concentration, 15.13 mg L −1 ; contact time, 104.8 min; FADA dosage, 0.98 g L −1 ) and (pH, 7.0; cyanide concentration, 4.88 mg L −1 ; contact time, 91.06 min; FADA dosage, 2.05 g L −1 ), respectively.Based on the Sips model, the maximum adsorption capacities of cyanide and palladium per mass unit of FADA were 208.55 and 60.2 mg g −1 , respectively.The pseudo-first-order (R 2 = 0.99) and the intraparticle diffusion (R 2 = 0.96) were found to agreement well with the adsorption experimental data obtained for cyanide and palladium, respectively.The sorption reactions of cyanide and palladium onto FADA were endothermic and exothermic, respectively.

Figure 2 .
Figure 2. Schematic of the tests steps.

Figure 4 .
Figure 4.The perspective plot: the effect of adsorbent and time on theFADA performance in the removal of cyanide.

Figure 5 .
Figure 5.The perspective plots: the interaction effect of time and pH (a), pH and concentration (b), time and concentration(c), adsorbent and concentration (d) and adsorbent and pH (e) in the removal performance of palladium onto theFADA.

Figure 6 .
Figure 6.Fitting of equilibrium data onto two-three parameters isotherm models (a) cyanide (b) palladium.

Table 1 .
Actual and coded values of independent variables used for experimental design (palladium).
Na (3.35%) (not shown).The obtained results of EDAX indicated the presence of sodium alginate, diatomite and Fe 3 O 4 in the FADA structure.IR spectrum ofFADA was characterised as follows (cm −1 ): 1453 (symmetrical tensile vibrations of the carboxylate anions),

Table 2 .
Actual and coded values of independent variables used for experimental design (cyanide).

Table 3 .
Comparison of the different models of RSM for fitting response-surface model (palladium).

Table 4 .
Comparison of the different models of RSM for fitting a response-surface model (cyanide).

Table 5 .
Parameters of related to the isotherm models study (cyanide).

Table 6 .
Parameters of related to the isotherm models study (palladium).

Table 7 .
The adsorption capacities (q max ) of the various materials for the uptake of palladium and cyanide.

Table 8 .
Parameters of the kinetic models for the adsorption of cyanide ontoFADA.

Table 9 .
Parameters of the kinetic models for the adsorption of palladium onto FADA.

Table 10 .
Thermodynamic parameters for the adsorption of cyanide onto the FADA nanocomposite.

Table 11 .
Thermodynamic parameters for the adsorption of palladium onto the MPIDC.