# Synthesis of Iron Doped Zeolite Imidazolate Framework-8 and Its Remazol Deep Black RGB Dye Adsorption Ability

Authors: Mai Thi Thanh; Tran Vinh Thien; Vo Thi Thanh Chau; Pham Dinh Du; Nguyen Phi Hung; Dinh Quang Khieu
Journal: Journal of Chemistry
 (2017)

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## Abstract

Zeolite imidazole framework-8 (ZIF-8) and the iron doped ZIF-8 (Fe-ZIF-8) were synthesized by the hydrothermal process. The obtained materials were characteristic of X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), scanning electron microscope (SEM), nitrogen adsorption/desorption isotherms, and atomic absorption spectroscopy (AAS). The results showed that the obtained Fe-ZIF-8 possessed the ZIF-8 structure with a large specific area. ZIF-8 and Fe-ZIF-8 were used for the removal of Remazol Deep Black (RDB) RGB dye from aqueous solutions. The various factors affecting adsorption such as pH, initial concentration, contact time, and temperature were investigated. The results showed that the introduction of iron into ZIF-8 provided a much larger adsorption capacity and faster adsorption kinetics than ZIF-8 without iron. The electrostatic interaction andπ-π interaction between the aromatic rings of the RDB dye and the aromatic imidazolate rings of the adsorbent were responsible for the RDB adsorption. Moreover, the coordination of the nitrogen atoms and oxygen in carboxyl group in RDB molecules with the Fe2+ ions in the ZIF-8 framework played a vital role for the effective removal of RDB from aqueous solution.


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## Body

## 1. Introduction

It is well-known that textile industries, pulp mills, and dyestuff manufacturing discharge a considerable amount of colored wastewaters, which has provoked serious environmental concerns all over the world [1]. Its removal is therefore of prime importance. Owing to their complicated chemical structures, dyes are difficult to treat with municipal waste treatment operations. There are many treatment processes such as chemical precipitation, membrane filtration, and alum coagulation of which adsorption is considered the most effective method widely employed to treat wastewater containing different classes of dyes.Nearly 60% of the dyes used in textile plants are azo dyes which are classified as mono-, di-, tri-, and tetra-azo dyes, with the azo groups mainly bound to the benzene and naphthalene rings. Remazol Deep Black (denoted as RDB) RGB is a common diazo reactive dye in aqueous solutions and widely used in textile industries [2]. It is stable and hardly biologically degradable due to the presence of aromatic rings. Thus, much research attention has been paid to how to eliminate RDB from aqueous solutions. Various processes including adsorption, electrochemistry, and biosorption for RDB treatment have been reported. Soloman et al. [2] studied the electrochemical degradation of hydrolyzed Remazol Black. Performance of the batch recirculation system was comparatively better than the other rector configurations studied, with respect to capacity utilization and energy consumption. Cardoso et al. [3] used Brazilian pine-fruit shells(Araucaria angustifolia) in natural form and as adsorbents for the removal of RDB textile dye from aqueous effluents, with a maximum sorption capacity of 74.6 mg g−1. Biosorption of the azo dye by growing fungi (Aspergillus flavus) was investigated in batch reactors. The nearly complete removal of dye was found at initial concentration up to 250 mg/L and at pH 4.5 which was used as working pH value for removal of dye in all the batch studies. The removal of chemical oxygen demand (COD) was found to be 90% at 100 mg/L initial concentration of dye [4].Metal-organic frameworks (MOFs) are hybrid materials with ordered three-dimensional frameworksvia strong metal-ligand bonds between metal cations and organic linkers [5]. Since their discoveries, MOFs have received significant attention in their potential applications in gas storage [6–13], separation [14, 15], and heterogeneous catalysis [16–19]. The zeolitic imidazolate framework (ZIF) materials have zeolite like topologies and belong to an important class of MOFs materials with interesting adsorption, separation, and catalytic properties [20–23]. Among them, ZIF-8 [Zn(2-methylimidazole)2·2H2O] constructed from 2-methylimidazole ligands and Zn(II) center ions exhibits higher thermal and chemical stability than other MOFs [24]. Many studies show that ZIF-8 exhibited efficient removal of arsenic and organic pollutants from aqueous solutions. Jiang et al. [25] reported that ZIF-8 as a novel adsorbent for fast removal of 1H-benzotriazole and 5-tolyltriazole with regard to adsorption isotherms, kinetics, thermodynamics, desorption, and adsorbent regeneration. Lin and Chang [26] reported that the adsorption capacity of ZIF-8 was much higher than that of fly ash, activated carbon, zeolites, and so forth, showing its promising potential for the removal of humic acid. P-Arsanilic acid which is widely used as feeding additive in the poultry and pork industries to enhance the feeding efficiency was efficiently removed by using ZIF-8 as an adsorbent [27]. ZIF-8 exhibited the high arsenate/arsenite adsorption (up to 50 mg·g−1 for As(II) and 60 mg·g−1 for As(V)) [28]. Zheng et al. [29] reported a free solvent synthesis of core-shell Fe3O4@zeolitic imidazolate frameworks-8 (ZIF-8)via two steps. The introduction of magnetic iron oxide into ZIF-8 facilitated the separation of adsorbents by the magnetic field. Fe3O4@ZIF-8 showed good adsorption properties for methylene blue, with a maximum adsorption capacity of 20.2 mg g−1. According to these studies, ZIF-8 not only is highly stable in water but also exhibits promisingly high adsorption capacities. Owing to these features, ZIF-8 should be promising and feasible adsorbents to organic pollutants from aqueous solutions. On the other hand, in addition to being a catalyst, iron species can act as adsorptive sites for adsorption processes. The combination of iron and ZIF-8 (denoted as Fe-ZIF-8) is expected to provide a novel adsorbent due to large accessible surface area and abundant active surface sites.In this study, the introduction of iron into ZIF-8 by a one-step process was performed with the aim of improving its adsorption ability. Fe-ZIF-8 was used as an adsorbent for removing RDB dye. In addition, the dye adsorption over ZIF-8 was performed for comparison. The iron oxide incorporated into the ZIF-8 framework significantly enhanced a RDB adsorption capacity compared to bare ZIF-8. A possible adsorption mechanism was suggested, based on adsorption at various pH values and surface charges on Fe-ZIF-8.


## 2. Experimental

### 2.1. Materials

Zinc nitrate hexahydrate (Zn(NO3)2·6H2O, Daejung, Korea, ≥99%), iron(II) sulfate heptahydrate (FeSO4·7H2O, Merck, Germany > 99%), methanol (CH3OH, Merck, Germany), and 2-methylimidazole (C4H6N2, Sigma-Aldrich, USA, 99%) were utilized in this paper. Remazol black B RGB (C26H21N5Na4O19S6, molecular weight = 991.82) was obtained from Thuy Duong Textile Company, Vietnam. The structure of RDB is shown in Scheme 1.Scheme 1
The structure of RDB molecule.


### 2.2. Preparation of ZIF-8 and Iron Doped ZIF-8 (Fe-ZIF-8)

ZIF-8 and Fe-ZIF-8 were synthesized as in [30, 31]. Briefly, 2.8 mmol of zinc(II) and iron(II) (molar ratio of Fe/Zn = 0/10 or 1/9) were dissolved in 1.4 mmol of methanol. A solution consisting of 64.4 mmol of 2-methylimidazole and 1.4 mol of methanol was added to the Zn-Fe based solution and vigorously stirred for 24 hs at ambient temperature. Nitrogen was bubbled through the solution to minimize the oxidation reaction of Fe(II) to Fe(III) species. Finally, this solution was centrifuged at 300 rpm and washed thoroughly with methanol. This washing procedure was repeated 3 times. The resultant crystals were dried overnight at 120°C. The obtained samples with the molar ratio of Fe(II)/(Zn(II) + Fe(II)) being 0/10 and 1/10 were named ZIF-8 and Fe-ZIF-8, respectively. In the obtained samples, ZIF-8 was white and Fe-ZIF-8 was light brown.


### 2.3. Determination of the Point of Zero Charge

The pH at the potential of zero charge (pHPZC) of ZIF-8 and Fe-ZIF-8 was measured by the pH drift method [32]. To a series of 100 mL flasks, 5 mL of 0.1 M NaCl solution and 40 mL of distilled water were added. The initial pH value (pHi) of the solution was adjusted from 2.3 to 12.0 by adding either 0.1 M NaOH or 0.1 M HCl. The total volume of solution in each flask was made exactly as 50 mL by adding distilled water. The 0.01 M NaCl solutions with different pH values were obtained. Nitrogen was bubbled through the solution to eliminate the dissolved CO2. Then, 0.02 grams of the sample was added to each flask and mixtures were sealed and shaken for 24 hours; then the final pH (pHf) of solution was recorded. The plot of ΔpH=pHi-pHf versus initial pHi was conducted. The point of intersection of curve with abscissa, at which ΔpH = 0, provided pHPZC.


### 2.4. Adsorption Kinetics Study

Experiments were conducted in a batch process. The 3 L plastic beaker was equipped with a stainless steel flat blade impeller using an electric motor to stir the dye solution. Samples (ZIF-8 or Fe-ZIF-8) (0.4 g) were vigorously mixed with 1000 mL of RDB solution in the beaker at a fixed temperature. Ten millilitres of solution was drawn at preset intervals of time through tap and the solid was removed by centrifuging process. The residual dye concentrations were determined using UV-Vis spectrophotometry. The experiments were conducted with various RDB concentrations ranging from 30 to 50 ppm. The amount of the dye adsorbed by the adsorbent was calculated by the following equation:(1)qt=VCo-Ctm,where qt is the amount of dye adsorbed per unit of adsorbent amount (mg g−1) at t time, Co the initial dye concentration (mg L−1), Ct the dye concentration (mg L−1) after the batch adsorption procedure, V the volume of dye solution (L), and m the mass (g) of the adsorbent. It is reasonably assumed that the adsorption of dye from solution follows reversible first-order kinetics. The heterogeneous equilibrium between dye in solution and solid adsorbent is illustrated as follows [32]:(2)dyesolution⇄k2k1dyeadsorbent,where k1 and k2 are the forward and backward rate constants, respectively.The equilibrium constant,K0, defined as k1/k2 could be expressed [26](3)K0=k1k2=C0-CeCe,where C0 and Ce are dye concentrations (mg L−1) at initial and equilibrium time, respectively, and the others are described above.Pseudo-first-order kinetic of adsorption was investigated by Natarajan-Khalaf equation [33]:(4)ln⁡CoCt=kadst,where kads is the rate constant of adsorption process.The slope of the linear plot ofln⁡Co/Ct versus t will provide the value of kads.Based on the relaxation method [34, 35], kads could be expressed as(5)kads=k1+k2.Then, the forward and backward rate constants could be derived from (3) and (5).The kinetics of diffusion was studied by Webber’s intraparticle-diffusion model. Webber’s intraparticle-diffusion model is described in the following equation [36, 37]:(6)qt=kp·t1/2+I,where kp is intraparticle-diffusion rate constant (mg g−1 min−0.5) and I the intercept which reflects the layer boundary effect.The analysis of the multilinearity in pore and film-diffusion plot using Webber’s plot was conducted by using piecewise linear regression proposed by Malash and El-Khaiary [38].In this method, the experimental data could be fixed for one, two, or three linear segments’ line by Webber’s model.One linear segment’s line:Y=B+AX (two parameters).Two linear segments’ line:Y=B+AX+C(X-D)∗sign(X-D) (four parameters).Three linear segments’ line:Y=B+AX+CX-D∗signX-D+EX-F∗sign(X-F) (six parameters),where the values of A, B, C, D, E, and F are estimated by nonlinear regression. D and F called breakpoints are the boundaries between the segments. The Microsoft Excel “sign” function is defined as follows:(7)signX-a=1ifx>a0ifx=a-1ifx<a.The example for the two linear segments’ equation was expressed as follows:(8)Y=B-CD+XA+CifX>DB+ADifx=DB+CD+XA-Cifx<D.Then the linear equation of the first segment is y=a1x+b1, where b1=B+CD and a1=A-C.Then the linear equation of the second segment isy=b2x+a2, where b2=B-CD and a2=A+C.Nonlinear regression determines the model’s parameters by the least squares method. This is calculated by minimizing the sum of squared deviations,SSES, by numerical optimization techniques using Solver function in Microsoft Excel. The function for minimization is(9)SSES=∑1Nyexp-yest2,where yexp is experimental datum and yest is the value estimated by model.The determination coefficient,R2, is obtained by the expression(10)R2=1-SSESSSET,where SSET is the total sum of squares equal to ∑1Nyexp-ymean2 (ymean is the mean value of y).The comparison of models was based on Akaike’s Information Criterion (AIC) [38–40]. The AICc determines how well the data support each model. The value of AIC can be positive or negative. The model with the lowest AICs score is most likely correct. The AICc (for a small size sample) is calculated for each model from the following equations:(11)AICc=Nln⁡SSETN+2Np+2NpNp+1N-Np-1,where N is the number of experimental points and Np is the parameter sum of model.


### 2.5. Thermodynamic and Isothermal Studies

Experimental procedure was conducted as an adsorption kinetics study. However, the temperature of the process was fixed at 298, 308, and 318 K. The activation energy,Ea, was determined by Arrhenius equation [35]:(12)k=Ae-Ea/RT,where k is the rate constant equal to the rate constant kads in Natarajan and Khalaf equation, A the frequency factor, R gas constant (8.315 J mol−1 K−1), and T absolute temperature in Kelvin.Taking the natural logarithm of both sides of (12), one obtains(13)ln⁡k=-EaRT+ln⁡A.By linear plotting ln k versus 1/T, the Ea could be obtained from slope (-Ea/R).Thermodynamic parameters of activation can inform whether or not the adsorption process follows an activated complex or is prior to the final adsorption. Thermodynamic parameters of activation including the enthalpy (ΔH#), entropy ΔE#, and free energy Gibbs ΔG# of activation for RBB adsorption kinetics were obtained by applying Eyring equation [41, 42].The Eyring equation in its thermodynamic version is as follows:(14)k=kbThe-ΔG/RT=kbTheΔS#/R·e-ΔH#/RT,where k is the rate constant equal to the rate constant kads in Natarajan-Khalaf equation, the kb (1.3807 × 10−23 J K−1) the Boltzmann constant, and h (6.621 × 10−34 J s) the Planck constant.Taking the natural logarithm of both sides of (14), Eyring equation in linear form was obtained:(15)ln⁡kT=ln⁡kbh+ΔS#R-ΔH#RT.By linear plotting ln⁡(k/T) versus 1/T, ΔS# and ΔH# were obtained from the slope (ΔH#/T) and y-intercept [ln⁡(kb/h)+(ΔS#/R)].The Gibbs free energy of activation can be obtained by(16)ΔG#=ΔH#-TΔS#.In order to assess if the adsorption process is spontaneous or not, the thermodynamic parameters of adsorption are needed. The standard Gibbs free energy of adsorption (ΔG0) is given by the expression [35, 43](17)ΔG0=ΔH0-TΔS0,where ΔG0, ΔH0, and ΔS0 are the standard Gibbs free energy, enthalpy, and entropy, respectively.Δ
G
0 is given by van’t Hoff’s equation:(18)ΔG0=-RTln⁡Kd,where Kd is the distribution coefficient of the solute ions and equals (qe/Ce) [27, 44, 45], and the others are described above.By replacing (18) with (17), one obtains(19)ln⁡Kd=-ΔH0RT+ΔS0R.The value of ΔH0 and ΔS0 was determined from the slope and intercept of the linear plot of ln⁡Kd versus 1/T.The adsorption isotherms were developed at 25°C. The adsorption time was conducted for 24 hours to confirm saturation. Thereafter supernatant liquid was collected by centrifugation and the final dye concentrations were determined using UV-Vis spectrophotometry.The experimental data were analyzed according to the Freundlich and Langmuir models.Langmuir Isotherm. The Langmuir equation is valid for monolayer sorption onto the surface. It could be expressed as follows [37, 46]:(20)qe=KL·qmom·Ce1+KL·Ce,where qmom is the maximum monolayer capacity amount (mg g−1), KL is Langmuir equilibrium constant (L mg−1), and the others are described above.The essential characteristics of the Langmuir isotherm can be expressed in terms of a dimensionless constant separation factor,RL, which is performed as(21)RL=11+Co·KL,where the value of RL indicates the type of isotherm: unfavorable (RL>1), linear (RL=1), favorable (0<RL<1), or irreversible (RL=0) [47].Freundlich Isotherm. Freundlich equation is an empirical relation based on the adsorption of adsorbates onto the heterogeneous surface. It is represented as follows [48, 49]:(22)qe=KF·Ce1/n,where KF is the Freundlich constant, which is a measure of adsorption capacity and n an empirical parameter related to the nature and strength of the adsorption process. A large value of n means that the surface is heterogeneous. For values in the range 1<n<10, adsorption is favorable. Values of n between 2 and 10 represent good adsorption processes, whereas 1<n<2 indicates that adsorption capacity is only slightly suppressed at lower equilibrium concentrations [50].The parameters of models ((20) and (22)) were estimated by nonlinear regression method using Solver function in Microsoft Excel. To quantitatively compare the applicability of each model, apart from the regression coefficient (R2), the Chi-square test (χ2) was calculated as follows [51]:(23)χ2=∑qe,exp-qe,est2qe,est,where qe,exp and qe,est are the adsorption capacity at the equilibrium experimental condition and adsorption capacity estimated by model, respectively.A small value ofχ2 indicates that the data obtained from the model is consistent with the experimental value.


### 2.6. Characterization of Materials

The powder X-ray diffraction (XRD) patterns were recorded by a D8 Advance, Bruker (Germany) with CuKα radiation (λ=1.5406 Å). The morphology of the obtained sample was determined by scanning electron microscope (SEM) using SEM JMS-5300LV (Japan). The specific surface area of the sample was determined by nitrogen adsorption/desorption isotherms using a Micromeritics 2020 volumetric adsorption analyzer system (USA). Thermal behaviors of the obtained materials were analyzed by means of thermal analysis (TG-DTA) using Labsys TG Setaram (France). The element analysis was conducted by atomic absorption spectrometry (AAS) using AA6800 Shimazu (Japan). Visible spectrophotometry was measured by Lambda 25 Spectrophotometer, PerkinElmer (Singapore) at λmax of RDB dye (600 nm).


## 2.1. Materials

Zinc nitrate hexahydrate (Zn(NO3)2·6H2O, Daejung, Korea, ≥99%), iron(II) sulfate heptahydrate (FeSO4·7H2O, Merck, Germany > 99%), methanol (CH3OH, Merck, Germany), and 2-methylimidazole (C4H6N2, Sigma-Aldrich, USA, 99%) were utilized in this paper. Remazol black B RGB (C26H21N5Na4O19S6, molecular weight = 991.82) was obtained from Thuy Duong Textile Company, Vietnam. The structure of RDB is shown in Scheme 1.Scheme 1
The structure of RDB molecule.


## 2.2. Preparation of ZIF-8 and Iron Doped ZIF-8 (Fe-ZIF-8)

ZIF-8 and Fe-ZIF-8 were synthesized as in [30, 31]. Briefly, 2.8 mmol of zinc(II) and iron(II) (molar ratio of Fe/Zn = 0/10 or 1/9) were dissolved in 1.4 mmol of methanol. A solution consisting of 64.4 mmol of 2-methylimidazole and 1.4 mol of methanol was added to the Zn-Fe based solution and vigorously stirred for 24 hs at ambient temperature. Nitrogen was bubbled through the solution to minimize the oxidation reaction of Fe(II) to Fe(III) species. Finally, this solution was centrifuged at 300 rpm and washed thoroughly with methanol. This washing procedure was repeated 3 times. The resultant crystals were dried overnight at 120°C. The obtained samples with the molar ratio of Fe(II)/(Zn(II) + Fe(II)) being 0/10 and 1/10 were named ZIF-8 and Fe-ZIF-8, respectively. In the obtained samples, ZIF-8 was white and Fe-ZIF-8 was light brown.


## 2.3. Determination of the Point of Zero Charge

The pH at the potential of zero charge (pHPZC) of ZIF-8 and Fe-ZIF-8 was measured by the pH drift method [32]. To a series of 100 mL flasks, 5 mL of 0.1 M NaCl solution and 40 mL of distilled water were added. The initial pH value (pHi) of the solution was adjusted from 2.3 to 12.0 by adding either 0.1 M NaOH or 0.1 M HCl. The total volume of solution in each flask was made exactly as 50 mL by adding distilled water. The 0.01 M NaCl solutions with different pH values were obtained. Nitrogen was bubbled through the solution to eliminate the dissolved CO2. Then, 0.02 grams of the sample was added to each flask and mixtures were sealed and shaken for 24 hours; then the final pH (pHf) of solution was recorded. The plot of ΔpH=pHi-pHf versus initial pHi was conducted. The point of intersection of curve with abscissa, at which ΔpH = 0, provided pHPZC.


## 2.4. Adsorption Kinetics Study

Experiments were conducted in a batch process. The 3 L plastic beaker was equipped with a stainless steel flat blade impeller using an electric motor to stir the dye solution. Samples (ZIF-8 or Fe-ZIF-8) (0.4 g) were vigorously mixed with 1000 mL of RDB solution in the beaker at a fixed temperature. Ten millilitres of solution was drawn at preset intervals of time through tap and the solid was removed by centrifuging process. The residual dye concentrations were determined using UV-Vis spectrophotometry. The experiments were conducted with various RDB concentrations ranging from 30 to 50 ppm. The amount of the dye adsorbed by the adsorbent was calculated by the following equation:(1)qt=VCo-Ctm,where qt is the amount of dye adsorbed per unit of adsorbent amount (mg g−1) at t time, Co the initial dye concentration (mg L−1), Ct the dye concentration (mg L−1) after the batch adsorption procedure, V the volume of dye solution (L), and m the mass (g) of the adsorbent. It is reasonably assumed that the adsorption of dye from solution follows reversible first-order kinetics. The heterogeneous equilibrium between dye in solution and solid adsorbent is illustrated as follows [32]:(2)dyesolution⇄k2k1dyeadsorbent,where k1 and k2 are the forward and backward rate constants, respectively.The equilibrium constant,K0, defined as k1/k2 could be expressed [26](3)K0=k1k2=C0-CeCe,where C0 and Ce are dye concentrations (mg L−1) at initial and equilibrium time, respectively, and the others are described above.Pseudo-first-order kinetic of adsorption was investigated by Natarajan-Khalaf equation [33]:(4)ln⁡CoCt=kadst,where kads is the rate constant of adsorption process.The slope of the linear plot ofln⁡Co/Ct versus t will provide the value of kads.Based on the relaxation method [34, 35], kads could be expressed as(5)kads=k1+k2.Then, the forward and backward rate constants could be derived from (3) and (5).The kinetics of diffusion was studied by Webber’s intraparticle-diffusion model. Webber’s intraparticle-diffusion model is described in the following equation [36, 37]:(6)qt=kp·t1/2+I,where kp is intraparticle-diffusion rate constant (mg g−1 min−0.5) and I the intercept which reflects the layer boundary effect.The analysis of the multilinearity in pore and film-diffusion plot using Webber’s plot was conducted by using piecewise linear regression proposed by Malash and El-Khaiary [38].In this method, the experimental data could be fixed for one, two, or three linear segments’ line by Webber’s model.One linear segment’s line:Y=B+AX (two parameters).Two linear segments’ line:Y=B+AX+C(X-D)∗sign(X-D) (four parameters).Three linear segments’ line:Y=B+AX+CX-D∗signX-D+EX-F∗sign(X-F) (six parameters),where the values of A, B, C, D, E, and F are estimated by nonlinear regression. D and F called breakpoints are the boundaries between the segments. The Microsoft Excel “sign” function is defined as follows:(7)signX-a=1ifx>a0ifx=a-1ifx<a.The example for the two linear segments’ equation was expressed as follows:(8)Y=B-CD+XA+CifX>DB+ADifx=DB+CD+XA-Cifx<D.Then the linear equation of the first segment is y=a1x+b1, where b1=B+CD and a1=A-C.Then the linear equation of the second segment isy=b2x+a2, where b2=B-CD and a2=A+C.Nonlinear regression determines the model’s parameters by the least squares method. This is calculated by minimizing the sum of squared deviations,SSES, by numerical optimization techniques using Solver function in Microsoft Excel. The function for minimization is(9)SSES=∑1Nyexp-yest2,where yexp is experimental datum and yest is the value estimated by model.The determination coefficient,R2, is obtained by the expression(10)R2=1-SSESSSET,where SSET is the total sum of squares equal to ∑1Nyexp-ymean2 (ymean is the mean value of y).The comparison of models was based on Akaike’s Information Criterion (AIC) [38–40]. The AICc determines how well the data support each model. The value of AIC can be positive or negative. The model with the lowest AICs score is most likely correct. The AICc (for a small size sample) is calculated for each model from the following equations:(11)AICc=Nln⁡SSETN+2Np+2NpNp+1N-Np-1,where N is the number of experimental points and Np is the parameter sum of model.


## 2.5. Thermodynamic and Isothermal Studies

Experimental procedure was conducted as an adsorption kinetics study. However, the temperature of the process was fixed at 298, 308, and 318 K. The activation energy,Ea, was determined by Arrhenius equation [35]:(12)k=Ae-Ea/RT,where k is the rate constant equal to the rate constant kads in Natarajan and Khalaf equation, A the frequency factor, R gas constant (8.315 J mol−1 K−1), and T absolute temperature in Kelvin.Taking the natural logarithm of both sides of (12), one obtains(13)ln⁡k=-EaRT+ln⁡A.By linear plotting ln k versus 1/T, the Ea could be obtained from slope (-Ea/R).Thermodynamic parameters of activation can inform whether or not the adsorption process follows an activated complex or is prior to the final adsorption. Thermodynamic parameters of activation including the enthalpy (ΔH#), entropy ΔE#, and free energy Gibbs ΔG# of activation for RBB adsorption kinetics were obtained by applying Eyring equation [41, 42].The Eyring equation in its thermodynamic version is as follows:(14)k=kbThe-ΔG/RT=kbTheΔS#/R·e-ΔH#/RT,where k is the rate constant equal to the rate constant kads in Natarajan-Khalaf equation, the kb (1.3807 × 10−23 J K−1) the Boltzmann constant, and h (6.621 × 10−34 J s) the Planck constant.Taking the natural logarithm of both sides of (14), Eyring equation in linear form was obtained:(15)ln⁡kT=ln⁡kbh+ΔS#R-ΔH#RT.By linear plotting ln⁡(k/T) versus 1/T, ΔS# and ΔH# were obtained from the slope (ΔH#/T) and y-intercept [ln⁡(kb/h)+(ΔS#/R)].The Gibbs free energy of activation can be obtained by(16)ΔG#=ΔH#-TΔS#.In order to assess if the adsorption process is spontaneous or not, the thermodynamic parameters of adsorption are needed. The standard Gibbs free energy of adsorption (ΔG0) is given by the expression [35, 43](17)ΔG0=ΔH0-TΔS0,where ΔG0, ΔH0, and ΔS0 are the standard Gibbs free energy, enthalpy, and entropy, respectively.Δ
G
0 is given by van’t Hoff’s equation:(18)ΔG0=-RTln⁡Kd,where Kd is the distribution coefficient of the solute ions and equals (qe/Ce) [27, 44, 45], and the others are described above.By replacing (18) with (17), one obtains(19)ln⁡Kd=-ΔH0RT+ΔS0R.The value of ΔH0 and ΔS0 was determined from the slope and intercept of the linear plot of ln⁡Kd versus 1/T.The adsorption isotherms were developed at 25°C. The adsorption time was conducted for 24 hours to confirm saturation. Thereafter supernatant liquid was collected by centrifugation and the final dye concentrations were determined using UV-Vis spectrophotometry.The experimental data were analyzed according to the Freundlich and Langmuir models.Langmuir Isotherm. The Langmuir equation is valid for monolayer sorption onto the surface. It could be expressed as follows [37, 46]:(20)qe=KL·qmom·Ce1+KL·Ce,where qmom is the maximum monolayer capacity amount (mg g−1), KL is Langmuir equilibrium constant (L mg−1), and the others are described above.The essential characteristics of the Langmuir isotherm can be expressed in terms of a dimensionless constant separation factor,RL, which is performed as(21)RL=11+Co·KL,where the value of RL indicates the type of isotherm: unfavorable (RL>1), linear (RL=1), favorable (0<RL<1), or irreversible (RL=0) [47].Freundlich Isotherm. Freundlich equation is an empirical relation based on the adsorption of adsorbates onto the heterogeneous surface. It is represented as follows [48, 49]:(22)qe=KF·Ce1/n,where KF is the Freundlich constant, which is a measure of adsorption capacity and n an empirical parameter related to the nature and strength of the adsorption process. A large value of n means that the surface is heterogeneous. For values in the range 1<n<10, adsorption is favorable. Values of n between 2 and 10 represent good adsorption processes, whereas 1<n<2 indicates that adsorption capacity is only slightly suppressed at lower equilibrium concentrations [50].The parameters of models ((20) and (22)) were estimated by nonlinear regression method using Solver function in Microsoft Excel. To quantitatively compare the applicability of each model, apart from the regression coefficient (R2), the Chi-square test (χ2) was calculated as follows [51]:(23)χ2=∑qe,exp-qe,est2qe,est,where qe,exp and qe,est are the adsorption capacity at the equilibrium experimental condition and adsorption capacity estimated by model, respectively.A small value ofχ2 indicates that the data obtained from the model is consistent with the experimental value.


## 2.6. Characterization of Materials

The powder X-ray diffraction (XRD) patterns were recorded by a D8 Advance, Bruker (Germany) with CuKα radiation (λ=1.5406 Å). The morphology of the obtained sample was determined by scanning electron microscope (SEM) using SEM JMS-5300LV (Japan). The specific surface area of the sample was determined by nitrogen adsorption/desorption isotherms using a Micromeritics 2020 volumetric adsorption analyzer system (USA). Thermal behaviors of the obtained materials were analyzed by means of thermal analysis (TG-DTA) using Labsys TG Setaram (France). The element analysis was conducted by atomic absorption spectrometry (AAS) using AA6800 Shimazu (Japan). Visible spectrophotometry was measured by Lambda 25 Spectrophotometer, PerkinElmer (Singapore) at λmax of RDB dye (600 nm).


## 3. Results and Discussion

### 3.1. Characterization of ZIF-8 and Fe-ZIF-8

Figure1 shows XRD patterns of ZIF-8 and Fe- ZIF-8. The XRD pattern of ZIF-8 in this work agreed well with patterns from [30, 31]. There was a well-defined diffraction (011) at two theta = 7.16° in the XRD pattern of ZIF-8, indicating that the crystallinity of ZIF-8 in this work was relatively high. The XRD patterns of Fe-ZIF-8 also exhibited characteristic peaks of ZIF-8 and no characteristic peaks of iron oxides were observed. However, intensity of these diffractions decreases as a certain amount of iron was doped into the ZIF-8 framework.Figure 1
XRD patterns of ZIF-8 and Fe-ZIF-8.SEM images of ZIF-8 and Fe-ZIF-8 are presented in Figure2. Morphology of ZIF-8 consisted of spherical particles with a diameter around 100 nm while the irregular shapes of Fe-ZIF-8 with sizes around 0.1–100 nm were observed. The introduction of iron into ZIF-8 caused a significant change in morphology of ZIF-8.Figure 2
SEM observations of ZIF-8 and Fe-ZIF-8.
(a)
(b)The zinc and iron compositions were analyzed by AAS. The results are presented in Table1. Iron percentage in the final product (0.116) was higher than the original (0.100). The pH of the synthesized gel was around 4.5. Then iron(II) was likely to incorporate completely into ZIF-8; however, possibly Zn(II) was partly dissolved in the solution. This is reason why there was an increase in the percentage of iron in the final product.Table 1
Chemical composition of ZIF-8 and Fe-ZIF-8 analyzed by AAS and XPS.
Adsorbent
AAS
XPS
Zn(mol/g)
Fe(mol/g)
Molar ratio(Fe/(Zn + Fe))
Initial molar ratio(Fe/(Zn + Fe))
Fe(II)(%)
Fe(III)(%)
ZIF-8
0.043
—
0
—
—
—
Fe-ZIF-8
0.038
0.005
0.116
0.100
100
0.000The XPS spectra indicated a chemical state of element, that is, iron (Fe2p) and zinc (Zn2p). The peak of Zn 2p1/2 (1044 eV) and Zn2p3/2 (1020.96 eV) observed for both samples confirmed the existence of Zn(II) (Figure3). For ZIF-8, the peak of Fe 2p3/2 was inconspicuous, indicating that iron was a very minor component (in fact, it could not be detected). Only peak Fe2p3/2 for Fe(II) at 709.98 eV was detected implying the main iron in Fe-ZIF-8 was Fe(II). The percentage of oxidation state of iron, calculated from peak areas, was listed in Table 1. It was worth noting that the initial iron source of Fe(III) was also tested to incorporate into ZIF-8 but the solid product was not obtained. This means that the presence of Fe(III) in the initial synthesized mixture was not favorable for the formation of ZIF-8 structure.Figure 3
XPS Fe2p and Zn2p core level spectra of ZIF-8 (a) and Fe-ZIF-8 (b).
(a)
(b)Based on ZIF-8 with space group ofI4-3m [52] the cell parameter of ZIF-8 and Fe-ZIF-8 was expressed by(24)1d2=h2+k2+l2a2,where d is spacing distance, a is cell parameter, and h,k,l are Miller indexes of diffraction planes.The cell parameter of ZIF-8 (16.800 Å) and Fe-ZIF-8 (16.977 Å) seems to be unchangeable. Since the charge and radii of Zn2+ (0.75 Å) and Fe2+ (0.74 Å) are similar, it is likely that Fe(II) can substitute Zn(II) in ZIF-8 or disperse highly in ferrous forms.Figure4 shows the nitrogen adsorption/desorption isotherms of ZIF-8 and Fe-ZIF-8. All samples exhibited type IV with H4 which is characteristic of mesoporous materials. Fe-ZIF-8 possessed a shape which is different from ZIF-8 at high relative pressure. This result suggests that the porous structure was distorted due to the incorporation of iron oxides. ZIF-8 exhibited a high specific surface area of 1380 m2·g−1 (calculated by BET model), which was similar to that found in the previous literature [30, 31, 53].Figure 4
Nitrogen adsorption/desorption isotherms of ZIF-8 and Fe-ZIF-8.The introduction of iron oxide into ZIF-8 lowered the specific surface area, the pore diameter, and the pore volume. The specific surface areas are 1380 and 1243 m2·g1 for ZIF-8 and Fe-ZIF-8, respectively (see Table 2). This also gave evidence of the encapsulation of iron oxides within the pores of framework, which brought about the lowering of accessible void space for N2 gas molecules.Table 2
Textural properties of ZIF-8 andFe-ZIF-8.
Adsorbent
1
S
B
E
T (m2/g)
2
S
L
a
n
g
m
u
i
r (m2/g)
3
D
p
o
r
e (nm)
4
V
p
o
r
e (cm3/g)
ZIF-8
1383
1909
3.34
1.16
Fe-ZIF-8
1243
1599
2.06
0.64
1
S
B
E
T: specific surface area calculated by BET model; 2SLangmuir: specific surface area calculated by Langmuir model; 3Dpore: pore diameter calculated by BJH model; 4Vpore: pore volume.The thermal stability of materials was tested by TG-DTA. ZIF-8 and Fe-ZIF-8 were found to be highly stable up to 220°C and 250°C. Beyond this temperature the framework slowly started to decompose and a flat valley was obtained till 700°C (Figure5). The incorporation of iron in ZIF-8 seems to make the materials more stable. This behavior was also observed as TiO2 is doped in ZIF-8 [54].Figure 5
TGA-DTA of ZIF-8 and Fe-ZIF-8.The stability of ZIF-8 in water with different pHs was also studied. Figure6 presents XRD patterns of ZIF-8 which were soaked in water with pH from 2 to 12. The pH of the solution was adjusted by NaOH 0.01 M or HCl 0.01 M. The crystallinity of ZIF-8 nanoparticles was retained well at pH > 3–12, which proved that ZIF-8 was stable in aqueous solutions with pHs in the range of 3–12.Figure 6
XRD diffraction patterns of the ZIF-8 soaked in water with different pHs (mZIF-8/Vsolution = 0.1 g/ 30 ml, pH = 2–12; socking time: 24 hours).


### 3.2. A Study on RDB Adsorption onto ZIF-8 and Fe-ZIF-8

#### 3.2.1. Effect of Initial RDB Concentration

The experimental results for adsorption at various concentrations (30–50 mg·L−1) with contact time are shown in Figure 7. As seen from Figure 7, the adsorption capacity of adsorbent increases as initial dye concentrations go up. The RDB adsorption of Fe-ZIF-8 was higher than that of ZIF-8 in the same initial concentration. The adsorption capacity of RDB onto ZIF-8 increased from 30.20 to 42.14 mg g−1 and that onto Fe-ZIF-8 increased from 50.36 to 76.79 mg g−1 as the initial concentrations increased from 30 to 50 mg g−1. The initial dye concentration provided a critical driving force to overcome all the mass transfer resistance of RDB between the aqueous solution and the adsorbent surface [55]. As a result, high initial RDB concentration might promote the adsorption process. Figure 7 indicates that the adsorption of RDB was fast in the earlier stage (0–100 minutes) and gradually reached the equilibrium. It is found that the time required to obtain the adsorption equilibrium was around 250 minutes.Figure 7
Effect of contact time on the adsorption of RDB by ZIF-8 and Fe-ZIF-8 (CRDB = 30–50 mg·L−1, adsorbent = 0.2 g, and initial pH = 8.2; VRDB = 500 ml, temperature = 30°C, and stirring rate = 500 rpm).Due to the porosity of ZIF-8 and Fe-ZIF-8, intraparticle diffusion was expected in the adsorption process. This was examined by plotting RDB uptake,qt against the square root of time, t1/2 as (6). If intraparticle diffusion is the rate-limiting step this plot will give a straight line and an intercept equal to zero. However, previous studies by various researchers showed that these plots represent multilinearity [56]. This application often suffers uncertainties caused by the multilinear nature of their plot. Therefore, the confidence intervals for parameters are determined to estimate their uncertainties. If the 95% confidence interval of y-intercept does not contain zero or it varies from this negative/positive value to another, y-intercept is significantly different from zero. It is concluded that the line does not pass through the origin or vice versa (in this study the SPSS-version 21 was used to calculate the confidence interval).Piecewise linear regression proposed by Malash and El-Khaiary [38] was applied to analyze multilinearity of Webber’s plot. Since increasing the number of linear segments leads to an increase in the number of regression parameters, a decrease in SSET naturally follows. For this reason, SSET solely cannot be used to assess the goodness of fit for models. The well-known statistical method for model comparison is Akaike’s Information Criterion (AIC) [38, 57]. This method advises which model is more likely to be correct. The smaller AIC value indicates a more compatible model. For example, Figure 8 illustrates experimental data and piecewise linear regression lines with initial concentration 50 mg L−1 for ZIF-8 and Fe-ZIF-8. The experimental points seem to be close to regression lines for two or three linear segment lines. We could not estimate visually which one is more likely correct. The values of AICc for RDB adsorption onto ZIF-8 are 89.47 and 16.05 and 22.46 for one-segment, two-segment, and three-segment models, respectively. Those for RDB adsorption onto Fe-ZIF-8 are 98.65 and 6.67 and 10.01 for one-segment, two-segment, and three-segment models, respectively. It is decided to accept the model with two linear segments as the correct model because of the lowest value of AICc in this model.Figure 8
Plot of piecewise linear regression for one, two, and three segments’ based Webber’s model (CRDB = 50 mg·L−1; madsorbent = 0.2 g;V = 500 mL; temperature = 30°C; stirring rate = 500 rpm).A comparison of models based onAICc is presented in Table 3. Table 3 shows that Webber’s model analyzed two segments linear regression provided the lowest AICc compared to one- or three-segment models. In conclusion, the experimental data best fit with the two segments’ linear regression model. Results of piecewise two linear segments’ regression for different initial concentrations are shown in Table 4. For illustration, for 50 mg L−1 concentration of ZIF-8 in Figure 8, the intercepts of the first line in the Webber plot were −10.19 with 95% confidence interval (−12.28 to −8.10). This value of the intercept was significantly different from zero. It means the line did not pass through the origin. The similar behaviors were observed for all the other cases. These results indicate that the adsorption of RDB dye onto ZIF-8 or Fe-ZIF-8 in the first stage was controlled by film diffusion (e.g., surface adsorption and liquid film diffusion) while the second was assigned to intraparticle diffusion [57–59]. The breakpoints (see Table 4) reflect the adsorption process moving from one mechanism to another. The times of phase transition calculated by the square of breakpoints varied from 36 to 100 minutes. The adsorption could be divided into two distinct phases by the time of phase transition: (i) main adsorption of RDB molecules within 0–100 minutes of the contact times: this process was rather slow compared to other adsorbents [40, 57] in which the fast and instantaneous adsorption was observed; since the pore sizes of Fe-ZIF-8 or ZIF-8 are around 1 nm [45], the adsorption of RDB with four benzene rings in which each has a critical dimension of around 0.662 nm [60] on ZIF-8 limited the diffusion of the RDB molecule to the inner pore structure; however, abundant active adsorption sites could be obtained at its external surface, which is helpful to the adsorption of dye molecules; (ii) a gradual attainment of the equilibrium where only about 5–10% of the adsorption was encountered. This is due to the utilization of the all active sites on the adsorbent surface. The first linear segment indicated a boundary layer effect while the second linear segment was assigned to intraparticle diffusion [58, 59].Table 3
Comparison of piecewise linear regression for one, two, and three linear segments by AIC.
Adsorbent
C
R
D
B mg·L−1
One linear segment’s regression
Two linear segments’ regression
Three linear segments’ regression
SSE
R
2
AIC
SSE
R
2
AIC
SSE
R
2
AIC
ZIF-8
30
247.07
0.905
62.72
82.93
0.968
39.30
82.93
0.968
45.34
40
736.84
0.858
91.13
189.35
0.964
60.77
189.35
0.964
66.78
50
619.32
0.884
89.47
33.91
0.994
16.05
33.91
0.995
22.46
Fe-ZIF-8
30
835.06
0.650
94.38
54.13
0.977
28.51
54.14
0.977
34.23
40
2070.79
0.973
117.99
317.80
0.967
72.76
317.80
0.967
80.24
50
984.31
0.846
98.65
23.73
0.996
6.77
21.33
0.997
10.01Table 4
Results of piecewise regression for the two linear segments for ZIF-8 and Fe-ZIF-8 (the values in parentheses are at a 95% confidence level).
Adsorbent
Concentration(mg·L−1)
Break point (minute0.5)
The first linear segment
The second linear segment
Intercept 1
Slope 1
Intercept 2
Slope 2
ZIF-8
30
5.92
−2.83(−5.11 : −0.55)
4.68
19.16(17.58 : 20.74)
0.75
40
7.07
−10.29(−17.10 : −3.47)
4.83
27.06(25.29 : 28.83)
0.67
50
8.94
−10.19(−12.28 : −8.10)
5.58
34.85(32.21 : 37.49)
0.52
Fe-ZIF-8
30
9.49
22.58(20.16 : 25.00)
3.85
78.07(75.00 : 81.15)
−1.97
40
10.00
8.13(2.64 : 13.63)
6.82
98.79(93.99 : 103.59)
−2.26
50
8.94
25.38(23.59 : 27.16)
6.01
80.15(78.58 : 81.72)
−0.15The rate parameter,kp, increases with an increase in initial concentrations. However, the effect of initial RDB on rate parameters was irregular for RDB adsorption onto Fe-ZIF-8. The irregularity of kp could be related to that fact that iron incorporated caused the heterogeneity of ZIF-8 structure.The experimental data usually exhibit the multilinear plots, two or more stages influencing the adsorption process. In the statistical method, the piecewise linear regression is relevant to analyzing the data with multilinearity instead of the conventional graphical analysis [61] that might misidentify objective break points or numbers of segments.As seen from Figure9, a possible desorption might occur where the RDB uptake appears to fluctuate or even drop a little. This behavior could be attributed to either a reversible adsorption or a back diffusion controlling mechanism [62]. Thepseudo-first- or second-order kinetic models of Lagergren [33] or Ho and McKay [63], respectively, have been widely used to investigate the formal kinetics of adsorption processes [12, 27, 40, 64]. However, the present experimental data could not apply to these models due to reversible adsorption. In the present study, thepseudo-first-order kinetics model of Natarajan-Khalaf was used to analyze the experimental data. The rate constant, kads, for the adsorption of dye was determined from the slope of Natarajan-Khalaf’s plots. The results are listed in Table 5. The high coefficient of determination R2 (0.973–0.998) implies that this model was compatible with the experimental data. The rate constant of adsorption is separated into the rate of forward and reverse adsorption. The rate constants for the forward and reverse process are also presented in Table 5. It is clear that the adsorption kinetics can be significantly improved by the introduction of iron into the ZIF-8. As shown in Table 5 the rate constants for adsorption could be increased approximately 5 times by Fe-ZIF-8 and the kinetics with Fe-ZIF-8 were faster than that with ZIF-8.Table 5
Rate constants for the adsorption and the rate constants for the forward and reverse process and equilibrium constants at different concentrations for ZIF-8 and Fe-ZIF-8.
Adsorbent
C
R
D
B (mg/L)
k
a
d
s
k
1
k
2
K
o
R
2
ZIF-8
30
0.0023
0.0009
0.0014
0.6429
0.995
40
0.0025
0.0009
0.0016
0.5625
0.998
50
0.0046
0.0015
0.0031
0.4839
0.990
Fe-ZIF-8
30
0.0115
0.0077
0.0038
2.0263
0.991
40
0.0122
0.0081
0.0041
1.9756
0.991
50
0.0184
0.0113
0.0071
1.5915
0.980Figure 9
Effect of temperature on adsorption of RDB dye onto ZIF-8 (a) and Fe-ZIF-8 (b) (CRDB = 30–50 mg·L−1, mZIF-8 = 0.2 g, VRDB = 500 ml, and stirring rate: 500 ppm).
(a)
(b)Adsorption thermodynamics was conducted by varying the temperature from 298 K to 318 K as shown in Figure9.The thermodynamic parameters including activation energy,Keq, k1, and k2 are presented in Table 6. The results showed that equilibrium adsorption capacity, qeq, of both adsorbents increased with an increase in temperature which indicated that the process was endothermic. The equilibrium adsorption capacity of Fe-ZIF-8 is higher than that of ZIF-8 for each corresponding temperature. The increasing rate constant with an increase in temperature suggests that temperature favors the adsorption process for the fast rate to proceed. The equilibrium constant, Keq, for Fe-ZIF-8 and ZIF-8 changed in the range of 1.3–1.8 and 3.4–5.7, respectively, as temperature varied from 298 to 318 K. It is worth noting that Keq in the case of Fe-ZIF-8 is higher and increases much faster than that in the case of ZIF-8. The activation energy refers to the minimum amount of energy that must be overcome to proceed with the adsorption. Ea for ZIF-8 and Fe-ZIF-8 was 48.27 kJ and 12.51 kJ, respectively. Lower Ea for Fe-ZIF-8 indicated that Fe-ZIF-8 was more favorable for RDB adsorption than ZIF-8. Low activation energy (below 42 kJ mol−1) implies diffusion controlled process because the temperature dependence of pore diffusivity is relatively weak and the diffusion process refers to the movement of the solute to an external surface and not diffusivity of material along microspore surfaces in a particle [65]. Ea with ZIF-8 is slightly higher than 42 kJ mol−1. However, a reversible adsorption was observed as shown in Figure 9, indicating that the rate-limiting step in this case involved a physical-chemical mechanism and not purely physical or chemical one. Therefore the RDB adsorption onto ZIF-8 was also considered a diffusion controlled process and so is the RDB adsorption onto Fe-ZIF-8.Table 6
Activation energy, equilibrium and rate constants for RDB dye adsorption, and rate constants for forward and reverse process of RDB adsorption onto ZIF-8 and Fe-ZIF-8.
Absorbent
Temp.(K)
K
e
q
q
e
q (mg·g−1)
k
1 (×103)(min−1)
k
2 (×103)(min−1)
k
a
d
s (×103)(min−1)
R
2
E
a (kJ·mol−1)
R
2
ZIF-8
298
1.272
28.89
0.890
1.800
2.700
0.990
48.270
0.991
308
1.570
43.94
1.914
2.692
4.606
0.988
318
1.842
53.02
3.908
5.304
9.212
0.973
Fe-ZIF-8
298
3.401
62.92
11.361
7.063
18.424
0.988
12.507
0.972
308
4.079
77.50
12.851
7.876
20.727
0.994
318
5.864
87.64
17.761
7.572
25.333
0.991The activation parameters calculated using Eyring equation are presented in Table7. This would express whether the adsorption process follows an active complex prior to the final sorption. The coefficient of determination was high for both ZIF-8 and Fe-ZIF-8 although the Eyring equation is not strictly linear with respect to 1/T [66]. The negative value of ΔS∗ (−29.44 J K−1 mol−1 for ZIF-8 and −153.40 J K−1·mol−1 for Fe-ZIF-8) suggests a possibility of an associative chemisorption through the formation of an activated complex between RDB molecule and adsorbent [47], [63]. Also the negative value of ΔS# normally reflects that no significant change occurs in the internal structure of the adsorbent during the adsorption process [41, 66]. The values for ΔH# (52. 03 kJ.mol−1 for ZIF-8 and 9.94 for Fe-ZIF-8) suggest that these reactions are endothermic. The large, positive ΔG# in both RDB adsorptions onto ZIF-8 and Fe-ZIF-8 imply that these reactions require energy to convert reactants to the product and as the energy requirement is satisfied the reaction proceeds. Typically, ΔG# value relates to the adsorption rate. The rate increases as ΔG# decreases [41, 42]. This is seen when comparing the data from Tables 6 and 7. In Table 6, the rate constant, kads, of Fe-ZIF-8 is higher than that of ZIF-8. Table 7 describes the trend for ΔG# in which the Fe-ZIF-8 has the lower ΔH# value than ZIF-8.Table 7
Activation parameters for RDB dye adsorption onto ZIF-8 and Fe-ZIF-8.
Adsorbent
Temperature(K)
Δ
S
# (J·mol−1·K−1)
Δ
H
# (kJ·mol−1)
Δ
G
# (kJ·mol−1)
R
2
ZIF-8
298
−29.44
52.03
60.80
0.999
308
61.10
318
61.39
Fe-ZIF-8
298
−153.40
9.94
55.66
0.960
308
57.19
318
58.73The thermodynamic parameters,ΔH0,ΔS0, and ΔG0, of system were determined using van’t Hoff equation to assess the spontaneity of adsorption process. In Table 8, the results show that the adsorption process using ZIF-8 and Fe-ZIF-8 was endothermic as indicated by the positive sign of the ΔH0 value. The positive value of ΔS0 indicates the increasing randomness at the solid-liquid interface during the adsorption of RDB molecules on the adsorbent [43]. The negative values of ΔG0 suggest the spontaneous RDB adsorption of RDB on ZIF-8 or Fe-ZIF-8. The more negative value at higher temperatures implies that the spontaneity increases with a temperature increase. As the Gibbs free energy change is negative and accompanied by the positive standard entropy change, the adsorption reaction is spontaneous with high affinity. Consistent with the findings in the kinetics, more negative values of ΔG0 with Fe-ZIF-8 were obtained compared to that with ZIF-8. Again, this confirmed the important role of iron in ZIF-8 in enhancing the RDB capacity.Table 8
Thermodynamic parameters for the adsorption of RDB dye onto ZIF-8 and Fe-ZIF-8.
Absorbent
Δ
G
0 (kJ)
Δ
H
0 (kJ)
Δ
S
0 (J)
R
2
298 K
308 K
318 K
ZIF-8
−0.599
−1.359
−1.615
16.033
55.795
0.983
Fe-ZIF-8
−1.092
−3.600
−4.677
51.639
170.000
0.980


#### 3.2.2. Effect of pH

One of the important parameters controlling the adsorption process is pH. Figure10 shows the effect of pH on the removal of RBB dye from aqueous solutions. The behaviors of pH effect for RDB adsorption onto ZIF-8 and Fe-ZIF-8 were similar. However, the RDB adsorption capacity of Fe-ZIF-8 was higher than that of ZIF-8. In general, the RDB adsorption capacity of adsorbents was observed to increase significantly with an increase in pH from 2.2 to 6, followed by a slight increase in pH from 6 to 10 and it decreased significantly in further pH increase. The values of pHZPC for ZIF-8 and Fe-ZIF-8 determined by pH drift method were around 9.2 and 9.8, respectively, and are in accordance with previous results [25, 27, 67] (the inset in Figure 10). The value of pHZPC indicates that the surface of the adsorbent is positively charged when pH of the solution is below pHZPC, while the surface of adsorbent becomes negatively charged at pH of the solution above pHZPC.Figure 10
Effect of pH on the adsorption of RDB by ZIF-8 and Fe-ZIF-8 (CRDB = 50 mg·L−1; mAdsorbent = 0.02 g;V = 50 mL; shaking time = 24 h; Temp. = 30°C).As seen in Scheme1, molecular structure of RDB consists of two groups of –SO3- and –SO4-, a group of NH2. Commonly, equilibrium of RDB in water is expressed as in Scheme 2.Scheme 2
Equilibrium of RDB in water.Therefore, the higher pH is the more the equilibrium of (22) shifts to the right. With regard to the correlation of the electronic charges of the adsorbent/adsorbate and solution pH values, it can be presumed that there might be an electrostatic interaction between the positively charged ZIF-8 surface and the negatively charged site of RDB increase as pH of solution increases up to pHZPC. The adsorption capacity of ZIF-8 and Fe-ZIF-8 started to decrease significantly at pH >  ~10.2, which was probably due to the electrostatic repulsion of negatively charged RDB and negative ZIF-8. In addition, the low stability of ZIF-8 framework in pH lower than 3 also contributes to the low RDB adsorption capacity (see Figure 6). This electrostatic interaction mechanism is similar to the adsorption mechanism for phthalic acid [67] and p-arsanilic acid on ZIF-8 [27]. In addition, the hydrophobic and π-π interaction between the aromatic rings of the RDB and the aromatic imidazole rings of the ZIF-8 framework is also thought to contribute to the RDB adsorption capacity.The increasing RDB uptake of Fe-ZIF-8 is probably due to the adsorption through other mechanisms addition to the electrostatic interaction. The enhanced adsorbed amount with Fe-ZIF-8 probably resulted from an increased number of adsorption iron sites. It is likely that the coordination of the nitrogen atoms and oxygen in RDB molecules to the Fe2+ ions in the ZIF-8 framework is responsible for the more efficient adsorption compared with bare ZIF-8. From this discussion the possible mechanisms of RDB adsorption onto ZIF-8 or Fe-ZIF-8 were illustrated in Figure 11.Figure 11
The proposed mechanism of RDB adsorption onto ZIF-8 or Fe-ZIF-8 at pH <pHZPC. 2-Melm: 2-methylimidazole.


#### 3.2.3. Isotherm Adsorption Studies

The study of adsorption isotherms is helpful in determining the adsorption capacities for removal at certain dyes at fixed temperature. In the present work, the equilibrium experiments were operated as if the initial concentration (C0=50 mg·L−1) was kept constant and the absorbent weight varied between 0.005, 0.007, 0.01, 0.12, 0.015, 0.017, and 0.020 g. The experimental data were analyzed according to the nonlinear form of Langmuir and Freundlich model. Figure 12 presents the experimental points and nonlinear regression curves of Langmuir and Freundlich models. The parameters of models are listed in Table 9. However, the maximum adsorption capacity is not obtained in Freundlich equation. Halsey [68] supposed that the maximum adsorption capacity, qm, by Freundlich equation could be expressed:(25)qm=limCe→C0⁡KFCe1/n.qm calculated based on Freundlich equation is also shown in Table 9.Table 9
The parameters of Langmuir and Freundlich models.
Adsorbent
Langmuir model
Freundlich model
K
L (L·mg−1)
q
m
o
m (mg·g−1)
R
2
χ
2
N
K
F (mg· g−1·mg·L−1)n
q
m (mg·g−1)
R
2
χ
2
ZIF-8
0.594
133.76
0.974
0.254
7.800
82.344
127.35
0.878
1.209
Fe-ZIF-8
0.568
193.56
0.958
2.340
4.434
92.015
222.33
0.961
2.399Figure 12
Langmuir and Freundlich isotherm models of adsorption RDB dye onto ZIF-8 and Fe-ZIF-8 (CRDB = 50 mg·L−1;V = 40 mL; madsorbent = 0.005–0.020 g; pH = 8.2; shaking time = 24 hours).The determination coefficient(R2) and the Chi-square test (χ2) for assessing the compatibility of experimental data with the isothermal models are listed in Table 9. The high value of R2 and low χ2 suggest that the isothermal data of ZIF-8 could be well represented by the Langmuir model. This implies a monolayer adsorption for ZIF-8. For Fe-ZIF-8 both models exhibited similar values of R2 and χ2. Moreover, favorable characteristic parameters of RL for Langmuir isotherm and n for Freundlich isotherm were 0<RL=0.034<1 and 2<n=4.43<10, which indicated that both isotherms were favorable. These results confirmed that the equilibrium data of RDB adsorption onto Fe-ZIF-8 could be well fitted by the two adsorption isotherm models. This result indicated a monolayer adsorption and the existence of heterogeneous surface in Fe-ZIF-8. It is worth noting that maximum monolayer adsorption capacity, qmom, for ZIF-8 is much higher than that for ZIF-8. It was concluded that the introduction of iron into ZIF-8 enhanced the RDB adsorption onto Fe-ZIF-8 in terms of kinetics and isotherm adsorption.K
L in Langmuir model is the equilibrium constant and describes the relation between kinetics and thermodynamics. Then, KL in Langmuir model is thought to be equivalent to Ko. However, the relation of KL and Ko (K0=k1/k2) (see Table 5) was not clear in our study. It is explained by that fact that in the solid-liquid adsorption system KL in the Langmuir model no longer reflects the equilibrium constant as its original meaning. In our previous study [40], as isothermal adsorption experiments were operated with constant initial concentration C0 and variable weights of adsorbent, we found that the obtained parameters of Langmuir and Freundlich models also increase as the initial concentration increases, which should be constant at certain temperature. It is thought that these parameters turn out to be empirical coefficients rather than fixed parameters at a certain temperature.


#### 3.2.4. Reusability of ZIF-8 and Fe-ZIF-8

To estimate the reusability of ZIF-8 and Fe-ZIF-8 for the removal RDB, the used adsorbents were regenerated by sonication assisted washing with 10−3 M NaOH solution for 6 h and drying for 24 hours at 100°C and then exploited to adsorb RDB. The adsorption capacity of the regenerated ZIF-8 and Fe-ZIF-8 are presented in Figure 13. Although the RDB adsorption decreased gradually with an increase in desorption cycles, the regenerated adsorbents still exhibited good performance for their adsorption. After the desorption for three cycles, the RDB adsorption capacity of by ZIF-8 and Fe-ZIF-8 reached 90% and 95% of the adsorption of the initial material, respectively. The XRD patterns of adsorbents after the three cycles seem unchangeable (see Figure 14), indicating that the adsorbents were stable in this condition.Figure 13
Effect of regeneration cycles of ZIF-8 and Fe-ZIF-8 adsorbents on the adsorption of RDB (VRDB = 125 mL; CRDB = 50 mg L−1; adsorbent/VRDB = 0.05 g/125 mL; shaking time = 10 hours).Figure 14
The XRD patterns of ZIF-8 and Fe-ZIF-8 adsorbents after the three cycles.


## 3.1. Characterization of ZIF-8 and Fe-ZIF-8

Figure1 shows XRD patterns of ZIF-8 and Fe- ZIF-8. The XRD pattern of ZIF-8 in this work agreed well with patterns from [30, 31]. There was a well-defined diffraction (011) at two theta = 7.16° in the XRD pattern of ZIF-8, indicating that the crystallinity of ZIF-8 in this work was relatively high. The XRD patterns of Fe-ZIF-8 also exhibited characteristic peaks of ZIF-8 and no characteristic peaks of iron oxides were observed. However, intensity of these diffractions decreases as a certain amount of iron was doped into the ZIF-8 framework.Figure 1
XRD patterns of ZIF-8 and Fe-ZIF-8.SEM images of ZIF-8 and Fe-ZIF-8 are presented in Figure2. Morphology of ZIF-8 consisted of spherical particles with a diameter around 100 nm while the irregular shapes of Fe-ZIF-8 with sizes around 0.1–100 nm were observed. The introduction of iron into ZIF-8 caused a significant change in morphology of ZIF-8.Figure 2
SEM observations of ZIF-8 and Fe-ZIF-8.
(a)
(b)The zinc and iron compositions were analyzed by AAS. The results are presented in Table1. Iron percentage in the final product (0.116) was higher than the original (0.100). The pH of the synthesized gel was around 4.5. Then iron(II) was likely to incorporate completely into ZIF-8; however, possibly Zn(II) was partly dissolved in the solution. This is reason why there was an increase in the percentage of iron in the final product.Table 1
Chemical composition of ZIF-8 and Fe-ZIF-8 analyzed by AAS and XPS.
Adsorbent
AAS
XPS
Zn(mol/g)
Fe(mol/g)
Molar ratio(Fe/(Zn + Fe))
Initial molar ratio(Fe/(Zn + Fe))
Fe(II)(%)
Fe(III)(%)
ZIF-8
0.043
—
0
—
—
—
Fe-ZIF-8
0.038
0.005
0.116
0.100
100
0.000The XPS spectra indicated a chemical state of element, that is, iron (Fe2p) and zinc (Zn2p). The peak of Zn 2p1/2 (1044 eV) and Zn2p3/2 (1020.96 eV) observed for both samples confirmed the existence of Zn(II) (Figure3). For ZIF-8, the peak of Fe 2p3/2 was inconspicuous, indicating that iron was a very minor component (in fact, it could not be detected). Only peak Fe2p3/2 for Fe(II) at 709.98 eV was detected implying the main iron in Fe-ZIF-8 was Fe(II). The percentage of oxidation state of iron, calculated from peak areas, was listed in Table 1. It was worth noting that the initial iron source of Fe(III) was also tested to incorporate into ZIF-8 but the solid product was not obtained. This means that the presence of Fe(III) in the initial synthesized mixture was not favorable for the formation of ZIF-8 structure.Figure 3
XPS Fe2p and Zn2p core level spectra of ZIF-8 (a) and Fe-ZIF-8 (b).
(a)
(b)Based on ZIF-8 with space group ofI4-3m [52] the cell parameter of ZIF-8 and Fe-ZIF-8 was expressed by(24)1d2=h2+k2+l2a2,where d is spacing distance, a is cell parameter, and h,k,l are Miller indexes of diffraction planes.The cell parameter of ZIF-8 (16.800 Å) and Fe-ZIF-8 (16.977 Å) seems to be unchangeable. Since the charge and radii of Zn2+ (0.75 Å) and Fe2+ (0.74 Å) are similar, it is likely that Fe(II) can substitute Zn(II) in ZIF-8 or disperse highly in ferrous forms.Figure4 shows the nitrogen adsorption/desorption isotherms of ZIF-8 and Fe-ZIF-8. All samples exhibited type IV with H4 which is characteristic of mesoporous materials. Fe-ZIF-8 possessed a shape which is different from ZIF-8 at high relative pressure. This result suggests that the porous structure was distorted due to the incorporation of iron oxides. ZIF-8 exhibited a high specific surface area of 1380 m2·g−1 (calculated by BET model), which was similar to that found in the previous literature [30, 31, 53].Figure 4
Nitrogen adsorption/desorption isotherms of ZIF-8 and Fe-ZIF-8.The introduction of iron oxide into ZIF-8 lowered the specific surface area, the pore diameter, and the pore volume. The specific surface areas are 1380 and 1243 m2·g1 for ZIF-8 and Fe-ZIF-8, respectively (see Table 2). This also gave evidence of the encapsulation of iron oxides within the pores of framework, which brought about the lowering of accessible void space for N2 gas molecules.Table 2
Textural properties of ZIF-8 andFe-ZIF-8.
Adsorbent
1
S
B
E
T (m2/g)
2
S
L
a
n
g
m
u
i
r (m2/g)
3
D
p
o
r
e (nm)
4
V
p
o
r
e (cm3/g)
ZIF-8
1383
1909
3.34
1.16
Fe-ZIF-8
1243
1599
2.06
0.64
1
S
B
E
T: specific surface area calculated by BET model; 2SLangmuir: specific surface area calculated by Langmuir model; 3Dpore: pore diameter calculated by BJH model; 4Vpore: pore volume.The thermal stability of materials was tested by TG-DTA. ZIF-8 and Fe-ZIF-8 were found to be highly stable up to 220°C and 250°C. Beyond this temperature the framework slowly started to decompose and a flat valley was obtained till 700°C (Figure5). The incorporation of iron in ZIF-8 seems to make the materials more stable. This behavior was also observed as TiO2 is doped in ZIF-8 [54].Figure 5
TGA-DTA of ZIF-8 and Fe-ZIF-8.The stability of ZIF-8 in water with different pHs was also studied. Figure6 presents XRD patterns of ZIF-8 which were soaked in water with pH from 2 to 12. The pH of the solution was adjusted by NaOH 0.01 M or HCl 0.01 M. The crystallinity of ZIF-8 nanoparticles was retained well at pH > 3–12, which proved that ZIF-8 was stable in aqueous solutions with pHs in the range of 3–12.Figure 6
XRD diffraction patterns of the ZIF-8 soaked in water with different pHs (mZIF-8/Vsolution = 0.1 g/ 30 ml, pH = 2–12; socking time: 24 hours).


## 3.2. A Study on RDB Adsorption onto ZIF-8 and Fe-ZIF-8

### 3.2.1. Effect of Initial RDB Concentration

The experimental results for adsorption at various concentrations (30–50 mg·L−1) with contact time are shown in Figure 7. As seen from Figure 7, the adsorption capacity of adsorbent increases as initial dye concentrations go up. The RDB adsorption of Fe-ZIF-8 was higher than that of ZIF-8 in the same initial concentration. The adsorption capacity of RDB onto ZIF-8 increased from 30.20 to 42.14 mg g−1 and that onto Fe-ZIF-8 increased from 50.36 to 76.79 mg g−1 as the initial concentrations increased from 30 to 50 mg g−1. The initial dye concentration provided a critical driving force to overcome all the mass transfer resistance of RDB between the aqueous solution and the adsorbent surface [55]. As a result, high initial RDB concentration might promote the adsorption process. Figure 7 indicates that the adsorption of RDB was fast in the earlier stage (0–100 minutes) and gradually reached the equilibrium. It is found that the time required to obtain the adsorption equilibrium was around 250 minutes.Figure 7
Effect of contact time on the adsorption of RDB by ZIF-8 and Fe-ZIF-8 (CRDB = 30–50 mg·L−1, adsorbent = 0.2 g, and initial pH = 8.2; VRDB = 500 ml, temperature = 30°C, and stirring rate = 500 rpm).Due to the porosity of ZIF-8 and Fe-ZIF-8, intraparticle diffusion was expected in the adsorption process. This was examined by plotting RDB uptake,qt against the square root of time, t1/2 as (6). If intraparticle diffusion is the rate-limiting step this plot will give a straight line and an intercept equal to zero. However, previous studies by various researchers showed that these plots represent multilinearity [56]. This application often suffers uncertainties caused by the multilinear nature of their plot. Therefore, the confidence intervals for parameters are determined to estimate their uncertainties. If the 95% confidence interval of y-intercept does not contain zero or it varies from this negative/positive value to another, y-intercept is significantly different from zero. It is concluded that the line does not pass through the origin or vice versa (in this study the SPSS-version 21 was used to calculate the confidence interval).Piecewise linear regression proposed by Malash and El-Khaiary [38] was applied to analyze multilinearity of Webber’s plot. Since increasing the number of linear segments leads to an increase in the number of regression parameters, a decrease in SSET naturally follows. For this reason, SSET solely cannot be used to assess the goodness of fit for models. The well-known statistical method for model comparison is Akaike’s Information Criterion (AIC) [38, 57]. This method advises which model is more likely to be correct. The smaller AIC value indicates a more compatible model. For example, Figure 8 illustrates experimental data and piecewise linear regression lines with initial concentration 50 mg L−1 for ZIF-8 and Fe-ZIF-8. The experimental points seem to be close to regression lines for two or three linear segment lines. We could not estimate visually which one is more likely correct. The values of AICc for RDB adsorption onto ZIF-8 are 89.47 and 16.05 and 22.46 for one-segment, two-segment, and three-segment models, respectively. Those for RDB adsorption onto Fe-ZIF-8 are 98.65 and 6.67 and 10.01 for one-segment, two-segment, and three-segment models, respectively. It is decided to accept the model with two linear segments as the correct model because of the lowest value of AICc in this model.Figure 8
Plot of piecewise linear regression for one, two, and three segments’ based Webber’s model (CRDB = 50 mg·L−1; madsorbent = 0.2 g;V = 500 mL; temperature = 30°C; stirring rate = 500 rpm).A comparison of models based onAICc is presented in Table 3. Table 3 shows that Webber’s model analyzed two segments linear regression provided the lowest AICc compared to one- or three-segment models. In conclusion, the experimental data best fit with the two segments’ linear regression model. Results of piecewise two linear segments’ regression for different initial concentrations are shown in Table 4. For illustration, for 50 mg L−1 concentration of ZIF-8 in Figure 8, the intercepts of the first line in the Webber plot were −10.19 with 95% confidence interval (−12.28 to −8.10). This value of the intercept was significantly different from zero. It means the line did not pass through the origin. The similar behaviors were observed for all the other cases. These results indicate that the adsorption of RDB dye onto ZIF-8 or Fe-ZIF-8 in the first stage was controlled by film diffusion (e.g., surface adsorption and liquid film diffusion) while the second was assigned to intraparticle diffusion [57–59]. The breakpoints (see Table 4) reflect the adsorption process moving from one mechanism to another. The times of phase transition calculated by the square of breakpoints varied from 36 to 100 minutes. The adsorption could be divided into two distinct phases by the time of phase transition: (i) main adsorption of RDB molecules within 0–100 minutes of the contact times: this process was rather slow compared to other adsorbents [40, 57] in which the fast and instantaneous adsorption was observed; since the pore sizes of Fe-ZIF-8 or ZIF-8 are around 1 nm [45], the adsorption of RDB with four benzene rings in which each has a critical dimension of around 0.662 nm [60] on ZIF-8 limited the diffusion of the RDB molecule to the inner pore structure; however, abundant active adsorption sites could be obtained at its external surface, which is helpful to the adsorption of dye molecules; (ii) a gradual attainment of the equilibrium where only about 5–10% of the adsorption was encountered. This is due to the utilization of the all active sites on the adsorbent surface. The first linear segment indicated a boundary layer effect while the second linear segment was assigned to intraparticle diffusion [58, 59].Table 3
Comparison of piecewise linear regression for one, two, and three linear segments by AIC.
Adsorbent
C
R
D
B mg·L−1
One linear segment’s regression
Two linear segments’ regression
Three linear segments’ regression
SSE
R
2
AIC
SSE
R
2
AIC
SSE
R
2
AIC
ZIF-8
30
247.07
0.905
62.72
82.93
0.968
39.30
82.93
0.968
45.34
40
736.84
0.858
91.13
189.35
0.964
60.77
189.35
0.964
66.78
50
619.32
0.884
89.47
33.91
0.994
16.05
33.91
0.995
22.46
Fe-ZIF-8
30
835.06
0.650
94.38
54.13
0.977
28.51
54.14
0.977
34.23
40
2070.79
0.973
117.99
317.80
0.967
72.76
317.80
0.967
80.24
50
984.31
0.846
98.65
23.73
0.996
6.77
21.33
0.997
10.01Table 4
Results of piecewise regression for the two linear segments for ZIF-8 and Fe-ZIF-8 (the values in parentheses are at a 95% confidence level).
Adsorbent
Concentration(mg·L−1)
Break point (minute0.5)
The first linear segment
The second linear segment
Intercept 1
Slope 1
Intercept 2
Slope 2
ZIF-8
30
5.92
−2.83(−5.11 : −0.55)
4.68
19.16(17.58 : 20.74)
0.75
40
7.07
−10.29(−17.10 : −3.47)
4.83
27.06(25.29 : 28.83)
0.67
50
8.94
−10.19(−12.28 : −8.10)
5.58
34.85(32.21 : 37.49)
0.52
Fe-ZIF-8
30
9.49
22.58(20.16 : 25.00)
3.85
78.07(75.00 : 81.15)
−1.97
40
10.00
8.13(2.64 : 13.63)
6.82
98.79(93.99 : 103.59)
−2.26
50
8.94
25.38(23.59 : 27.16)
6.01
80.15(78.58 : 81.72)
−0.15The rate parameter,kp, increases with an increase in initial concentrations. However, the effect of initial RDB on rate parameters was irregular for RDB adsorption onto Fe-ZIF-8. The irregularity of kp could be related to that fact that iron incorporated caused the heterogeneity of ZIF-8 structure.The experimental data usually exhibit the multilinear plots, two or more stages influencing the adsorption process. In the statistical method, the piecewise linear regression is relevant to analyzing the data with multilinearity instead of the conventional graphical analysis [61] that might misidentify objective break points or numbers of segments.As seen from Figure9, a possible desorption might occur where the RDB uptake appears to fluctuate or even drop a little. This behavior could be attributed to either a reversible adsorption or a back diffusion controlling mechanism [62]. Thepseudo-first- or second-order kinetic models of Lagergren [33] or Ho and McKay [63], respectively, have been widely used to investigate the formal kinetics of adsorption processes [12, 27, 40, 64]. However, the present experimental data could not apply to these models due to reversible adsorption. In the present study, thepseudo-first-order kinetics model of Natarajan-Khalaf was used to analyze the experimental data. The rate constant, kads, for the adsorption of dye was determined from the slope of Natarajan-Khalaf’s plots. The results are listed in Table 5. The high coefficient of determination R2 (0.973–0.998) implies that this model was compatible with the experimental data. The rate constant of adsorption is separated into the rate of forward and reverse adsorption. The rate constants for the forward and reverse process are also presented in Table 5. It is clear that the adsorption kinetics can be significantly improved by the introduction of iron into the ZIF-8. As shown in Table 5 the rate constants for adsorption could be increased approximately 5 times by Fe-ZIF-8 and the kinetics with Fe-ZIF-8 were faster than that with ZIF-8.Table 5
Rate constants for the adsorption and the rate constants for the forward and reverse process and equilibrium constants at different concentrations for ZIF-8 and Fe-ZIF-8.
Adsorbent
C
R
D
B (mg/L)
k
a
d
s
k
1
k
2
K
o
R
2
ZIF-8
30
0.0023
0.0009
0.0014
0.6429
0.995
40
0.0025
0.0009
0.0016
0.5625
0.998
50
0.0046
0.0015
0.0031
0.4839
0.990
Fe-ZIF-8
30
0.0115
0.0077
0.0038
2.0263
0.991
40
0.0122
0.0081
0.0041
1.9756
0.991
50
0.0184
0.0113
0.0071
1.5915
0.980Figure 9
Effect of temperature on adsorption of RDB dye onto ZIF-8 (a) and Fe-ZIF-8 (b) (CRDB = 30–50 mg·L−1, mZIF-8 = 0.2 g, VRDB = 500 ml, and stirring rate: 500 ppm).
(a)
(b)Adsorption thermodynamics was conducted by varying the temperature from 298 K to 318 K as shown in Figure9.The thermodynamic parameters including activation energy,Keq, k1, and k2 are presented in Table 6. The results showed that equilibrium adsorption capacity, qeq, of both adsorbents increased with an increase in temperature which indicated that the process was endothermic. The equilibrium adsorption capacity of Fe-ZIF-8 is higher than that of ZIF-8 for each corresponding temperature. The increasing rate constant with an increase in temperature suggests that temperature favors the adsorption process for the fast rate to proceed. The equilibrium constant, Keq, for Fe-ZIF-8 and ZIF-8 changed in the range of 1.3–1.8 and 3.4–5.7, respectively, as temperature varied from 298 to 318 K. It is worth noting that Keq in the case of Fe-ZIF-8 is higher and increases much faster than that in the case of ZIF-8. The activation energy refers to the minimum amount of energy that must be overcome to proceed with the adsorption. Ea for ZIF-8 and Fe-ZIF-8 was 48.27 kJ and 12.51 kJ, respectively. Lower Ea for Fe-ZIF-8 indicated that Fe-ZIF-8 was more favorable for RDB adsorption than ZIF-8. Low activation energy (below 42 kJ mol−1) implies diffusion controlled process because the temperature dependence of pore diffusivity is relatively weak and the diffusion process refers to the movement of the solute to an external surface and not diffusivity of material along microspore surfaces in a particle [65]. Ea with ZIF-8 is slightly higher than 42 kJ mol−1. However, a reversible adsorption was observed as shown in Figure 9, indicating that the rate-limiting step in this case involved a physical-chemical mechanism and not purely physical or chemical one. Therefore the RDB adsorption onto ZIF-8 was also considered a diffusion controlled process and so is the RDB adsorption onto Fe-ZIF-8.Table 6
Activation energy, equilibrium and rate constants for RDB dye adsorption, and rate constants for forward and reverse process of RDB adsorption onto ZIF-8 and Fe-ZIF-8.
Absorbent
Temp.(K)
K
e
q
q
e
q (mg·g−1)
k
1 (×103)(min−1)
k
2 (×103)(min−1)
k
a
d
s (×103)(min−1)
R
2
E
a (kJ·mol−1)
R
2
ZIF-8
298
1.272
28.89
0.890
1.800
2.700
0.990
48.270
0.991
308
1.570
43.94
1.914
2.692
4.606
0.988
318
1.842
53.02
3.908
5.304
9.212
0.973
Fe-ZIF-8
298
3.401
62.92
11.361
7.063
18.424
0.988
12.507
0.972
308
4.079
77.50
12.851
7.876
20.727
0.994
318
5.864
87.64
17.761
7.572
25.333
0.991The activation parameters calculated using Eyring equation are presented in Table7. This would express whether the adsorption process follows an active complex prior to the final sorption. The coefficient of determination was high for both ZIF-8 and Fe-ZIF-8 although the Eyring equation is not strictly linear with respect to 1/T [66]. The negative value of ΔS∗ (−29.44 J K−1 mol−1 for ZIF-8 and −153.40 J K−1·mol−1 for Fe-ZIF-8) suggests a possibility of an associative chemisorption through the formation of an activated complex between RDB molecule and adsorbent [47], [63]. Also the negative value of ΔS# normally reflects that no significant change occurs in the internal structure of the adsorbent during the adsorption process [41, 66]. The values for ΔH# (52. 03 kJ.mol−1 for ZIF-8 and 9.94 for Fe-ZIF-8) suggest that these reactions are endothermic. The large, positive ΔG# in both RDB adsorptions onto ZIF-8 and Fe-ZIF-8 imply that these reactions require energy to convert reactants to the product and as the energy requirement is satisfied the reaction proceeds. Typically, ΔG# value relates to the adsorption rate. The rate increases as ΔG# decreases [41, 42]. This is seen when comparing the data from Tables 6 and 7. In Table 6, the rate constant, kads, of Fe-ZIF-8 is higher than that of ZIF-8. Table 7 describes the trend for ΔG# in which the Fe-ZIF-8 has the lower ΔH# value than ZIF-8.Table 7
Activation parameters for RDB dye adsorption onto ZIF-8 and Fe-ZIF-8.
Adsorbent
Temperature(K)
Δ
S
# (J·mol−1·K−1)
Δ
H
# (kJ·mol−1)
Δ
G
# (kJ·mol−1)
R
2
ZIF-8
298
−29.44
52.03
60.80
0.999
308
61.10
318
61.39
Fe-ZIF-8
298
−153.40
9.94
55.66
0.960
308
57.19
318
58.73The thermodynamic parameters,ΔH0,ΔS0, and ΔG0, of system were determined using van’t Hoff equation to assess the spontaneity of adsorption process. In Table 8, the results show that the adsorption process using ZIF-8 and Fe-ZIF-8 was endothermic as indicated by the positive sign of the ΔH0 value. The positive value of ΔS0 indicates the increasing randomness at the solid-liquid interface during the adsorption of RDB molecules on the adsorbent [43]. The negative values of ΔG0 suggest the spontaneous RDB adsorption of RDB on ZIF-8 or Fe-ZIF-8. The more negative value at higher temperatures implies that the spontaneity increases with a temperature increase. As the Gibbs free energy change is negative and accompanied by the positive standard entropy change, the adsorption reaction is spontaneous with high affinity. Consistent with the findings in the kinetics, more negative values of ΔG0 with Fe-ZIF-8 were obtained compared to that with ZIF-8. Again, this confirmed the important role of iron in ZIF-8 in enhancing the RDB capacity.Table 8
Thermodynamic parameters for the adsorption of RDB dye onto ZIF-8 and Fe-ZIF-8.
Absorbent
Δ
G
0 (kJ)
Δ
H
0 (kJ)
Δ
S
0 (J)
R
2
298 K
308 K
318 K
ZIF-8
−0.599
−1.359
−1.615
16.033
55.795
0.983
Fe-ZIF-8
−1.092
−3.600
−4.677
51.639
170.000
0.980


### 3.2.2. Effect of pH

One of the important parameters controlling the adsorption process is pH. Figure10 shows the effect of pH on the removal of RBB dye from aqueous solutions. The behaviors of pH effect for RDB adsorption onto ZIF-8 and Fe-ZIF-8 were similar. However, the RDB adsorption capacity of Fe-ZIF-8 was higher than that of ZIF-8. In general, the RDB adsorption capacity of adsorbents was observed to increase significantly with an increase in pH from 2.2 to 6, followed by a slight increase in pH from 6 to 10 and it decreased significantly in further pH increase. The values of pHZPC for ZIF-8 and Fe-ZIF-8 determined by pH drift method were around 9.2 and 9.8, respectively, and are in accordance with previous results [25, 27, 67] (the inset in Figure 10). The value of pHZPC indicates that the surface of the adsorbent is positively charged when pH of the solution is below pHZPC, while the surface of adsorbent becomes negatively charged at pH of the solution above pHZPC.Figure 10
Effect of pH on the adsorption of RDB by ZIF-8 and Fe-ZIF-8 (CRDB = 50 mg·L−1; mAdsorbent = 0.02 g;V = 50 mL; shaking time = 24 h; Temp. = 30°C).As seen in Scheme1, molecular structure of RDB consists of two groups of –SO3- and –SO4-, a group of NH2. Commonly, equilibrium of RDB in water is expressed as in Scheme 2.Scheme 2
Equilibrium of RDB in water.Therefore, the higher pH is the more the equilibrium of (22) shifts to the right. With regard to the correlation of the electronic charges of the adsorbent/adsorbate and solution pH values, it can be presumed that there might be an electrostatic interaction between the positively charged ZIF-8 surface and the negatively charged site of RDB increase as pH of solution increases up to pHZPC. The adsorption capacity of ZIF-8 and Fe-ZIF-8 started to decrease significantly at pH >  ~10.2, which was probably due to the electrostatic repulsion of negatively charged RDB and negative ZIF-8. In addition, the low stability of ZIF-8 framework in pH lower than 3 also contributes to the low RDB adsorption capacity (see Figure 6). This electrostatic interaction mechanism is similar to the adsorption mechanism for phthalic acid [67] and p-arsanilic acid on ZIF-8 [27]. In addition, the hydrophobic and π-π interaction between the aromatic rings of the RDB and the aromatic imidazole rings of the ZIF-8 framework is also thought to contribute to the RDB adsorption capacity.The increasing RDB uptake of Fe-ZIF-8 is probably due to the adsorption through other mechanisms addition to the electrostatic interaction. The enhanced adsorbed amount with Fe-ZIF-8 probably resulted from an increased number of adsorption iron sites. It is likely that the coordination of the nitrogen atoms and oxygen in RDB molecules to the Fe2+ ions in the ZIF-8 framework is responsible for the more efficient adsorption compared with bare ZIF-8. From this discussion the possible mechanisms of RDB adsorption onto ZIF-8 or Fe-ZIF-8 were illustrated in Figure 11.Figure 11
The proposed mechanism of RDB adsorption onto ZIF-8 or Fe-ZIF-8 at pH <pHZPC. 2-Melm: 2-methylimidazole.


### 3.2.3. Isotherm Adsorption Studies

The study of adsorption isotherms is helpful in determining the adsorption capacities for removal at certain dyes at fixed temperature. In the present work, the equilibrium experiments were operated as if the initial concentration (C0=50 mg·L−1) was kept constant and the absorbent weight varied between 0.005, 0.007, 0.01, 0.12, 0.015, 0.017, and 0.020 g. The experimental data were analyzed according to the nonlinear form of Langmuir and Freundlich model. Figure 12 presents the experimental points and nonlinear regression curves of Langmuir and Freundlich models. The parameters of models are listed in Table 9. However, the maximum adsorption capacity is not obtained in Freundlich equation. Halsey [68] supposed that the maximum adsorption capacity, qm, by Freundlich equation could be expressed:(25)qm=limCe→C0⁡KFCe1/n.qm calculated based on Freundlich equation is also shown in Table 9.Table 9
The parameters of Langmuir and Freundlich models.
Adsorbent
Langmuir model
Freundlich model
K
L (L·mg−1)
q
m
o
m (mg·g−1)
R
2
χ
2
N
K
F (mg· g−1·mg·L−1)n
q
m (mg·g−1)
R
2
χ
2
ZIF-8
0.594
133.76
0.974
0.254
7.800
82.344
127.35
0.878
1.209
Fe-ZIF-8
0.568
193.56
0.958
2.340
4.434
92.015
222.33
0.961
2.399Figure 12
Langmuir and Freundlich isotherm models of adsorption RDB dye onto ZIF-8 and Fe-ZIF-8 (CRDB = 50 mg·L−1;V = 40 mL; madsorbent = 0.005–0.020 g; pH = 8.2; shaking time = 24 hours).The determination coefficient(R2) and the Chi-square test (χ2) for assessing the compatibility of experimental data with the isothermal models are listed in Table 9. The high value of R2 and low χ2 suggest that the isothermal data of ZIF-8 could be well represented by the Langmuir model. This implies a monolayer adsorption for ZIF-8. For Fe-ZIF-8 both models exhibited similar values of R2 and χ2. Moreover, favorable characteristic parameters of RL for Langmuir isotherm and n for Freundlich isotherm were 0<RL=0.034<1 and 2<n=4.43<10, which indicated that both isotherms were favorable. These results confirmed that the equilibrium data of RDB adsorption onto Fe-ZIF-8 could be well fitted by the two adsorption isotherm models. This result indicated a monolayer adsorption and the existence of heterogeneous surface in Fe-ZIF-8. It is worth noting that maximum monolayer adsorption capacity, qmom, for ZIF-8 is much higher than that for ZIF-8. It was concluded that the introduction of iron into ZIF-8 enhanced the RDB adsorption onto Fe-ZIF-8 in terms of kinetics and isotherm adsorption.K
L in Langmuir model is the equilibrium constant and describes the relation between kinetics and thermodynamics. Then, KL in Langmuir model is thought to be equivalent to Ko. However, the relation of KL and Ko (K0=k1/k2) (see Table 5) was not clear in our study. It is explained by that fact that in the solid-liquid adsorption system KL in the Langmuir model no longer reflects the equilibrium constant as its original meaning. In our previous study [40], as isothermal adsorption experiments were operated with constant initial concentration C0 and variable weights of adsorbent, we found that the obtained parameters of Langmuir and Freundlich models also increase as the initial concentration increases, which should be constant at certain temperature. It is thought that these parameters turn out to be empirical coefficients rather than fixed parameters at a certain temperature.


### 3.2.4. Reusability of ZIF-8 and Fe-ZIF-8

To estimate the reusability of ZIF-8 and Fe-ZIF-8 for the removal RDB, the used adsorbents were regenerated by sonication assisted washing with 10−3 M NaOH solution for 6 h and drying for 24 hours at 100°C and then exploited to adsorb RDB. The adsorption capacity of the regenerated ZIF-8 and Fe-ZIF-8 are presented in Figure 13. Although the RDB adsorption decreased gradually with an increase in desorption cycles, the regenerated adsorbents still exhibited good performance for their adsorption. After the desorption for three cycles, the RDB adsorption capacity of by ZIF-8 and Fe-ZIF-8 reached 90% and 95% of the adsorption of the initial material, respectively. The XRD patterns of adsorbents after the three cycles seem unchangeable (see Figure 14), indicating that the adsorbents were stable in this condition.Figure 13
Effect of regeneration cycles of ZIF-8 and Fe-ZIF-8 adsorbents on the adsorption of RDB (VRDB = 125 mL; CRDB = 50 mg L−1; adsorbent/VRDB = 0.05 g/125 mL; shaking time = 10 hours).Figure 14
The XRD patterns of ZIF-8 and Fe-ZIF-8 adsorbents after the three cycles.


## 3.2.1. Effect of Initial RDB Concentration

The experimental results for adsorption at various concentrations (30–50 mg·L−1) with contact time are shown in Figure 7. As seen from Figure 7, the adsorption capacity of adsorbent increases as initial dye concentrations go up. The RDB adsorption of Fe-ZIF-8 was higher than that of ZIF-8 in the same initial concentration. The adsorption capacity of RDB onto ZIF-8 increased from 30.20 to 42.14 mg g−1 and that onto Fe-ZIF-8 increased from 50.36 to 76.79 mg g−1 as the initial concentrations increased from 30 to 50 mg g−1. The initial dye concentration provided a critical driving force to overcome all the mass transfer resistance of RDB between the aqueous solution and the adsorbent surface [55]. As a result, high initial RDB concentration might promote the adsorption process. Figure 7 indicates that the adsorption of RDB was fast in the earlier stage (0–100 minutes) and gradually reached the equilibrium. It is found that the time required to obtain the adsorption equilibrium was around 250 minutes.Figure 7
Effect of contact time on the adsorption of RDB by ZIF-8 and Fe-ZIF-8 (CRDB = 30–50 mg·L−1, adsorbent = 0.2 g, and initial pH = 8.2; VRDB = 500 ml, temperature = 30°C, and stirring rate = 500 rpm).Due to the porosity of ZIF-8 and Fe-ZIF-8, intraparticle diffusion was expected in the adsorption process. This was examined by plotting RDB uptake,qt against the square root of time, t1/2 as (6). If intraparticle diffusion is the rate-limiting step this plot will give a straight line and an intercept equal to zero. However, previous studies by various researchers showed that these plots represent multilinearity [56]. This application often suffers uncertainties caused by the multilinear nature of their plot. Therefore, the confidence intervals for parameters are determined to estimate their uncertainties. If the 95% confidence interval of y-intercept does not contain zero or it varies from this negative/positive value to another, y-intercept is significantly different from zero. It is concluded that the line does not pass through the origin or vice versa (in this study the SPSS-version 21 was used to calculate the confidence interval).Piecewise linear regression proposed by Malash and El-Khaiary [38] was applied to analyze multilinearity of Webber’s plot. Since increasing the number of linear segments leads to an increase in the number of regression parameters, a decrease in SSET naturally follows. For this reason, SSET solely cannot be used to assess the goodness of fit for models. The well-known statistical method for model comparison is Akaike’s Information Criterion (AIC) [38, 57]. This method advises which model is more likely to be correct. The smaller AIC value indicates a more compatible model. For example, Figure 8 illustrates experimental data and piecewise linear regression lines with initial concentration 50 mg L−1 for ZIF-8 and Fe-ZIF-8. The experimental points seem to be close to regression lines for two or three linear segment lines. We could not estimate visually which one is more likely correct. The values of AICc for RDB adsorption onto ZIF-8 are 89.47 and 16.05 and 22.46 for one-segment, two-segment, and three-segment models, respectively. Those for RDB adsorption onto Fe-ZIF-8 are 98.65 and 6.67 and 10.01 for one-segment, two-segment, and three-segment models, respectively. It is decided to accept the model with two linear segments as the correct model because of the lowest value of AICc in this model.Figure 8
Plot of piecewise linear regression for one, two, and three segments’ based Webber’s model (CRDB = 50 mg·L−1; madsorbent = 0.2 g;V = 500 mL; temperature = 30°C; stirring rate = 500 rpm).A comparison of models based onAICc is presented in Table 3. Table 3 shows that Webber’s model analyzed two segments linear regression provided the lowest AICc compared to one- or three-segment models. In conclusion, the experimental data best fit with the two segments’ linear regression model. Results of piecewise two linear segments’ regression for different initial concentrations are shown in Table 4. For illustration, for 50 mg L−1 concentration of ZIF-8 in Figure 8, the intercepts of the first line in the Webber plot were −10.19 with 95% confidence interval (−12.28 to −8.10). This value of the intercept was significantly different from zero. It means the line did not pass through the origin. The similar behaviors were observed for all the other cases. These results indicate that the adsorption of RDB dye onto ZIF-8 or Fe-ZIF-8 in the first stage was controlled by film diffusion (e.g., surface adsorption and liquid film diffusion) while the second was assigned to intraparticle diffusion [57–59]. The breakpoints (see Table 4) reflect the adsorption process moving from one mechanism to another. The times of phase transition calculated by the square of breakpoints varied from 36 to 100 minutes. The adsorption could be divided into two distinct phases by the time of phase transition: (i) main adsorption of RDB molecules within 0–100 minutes of the contact times: this process was rather slow compared to other adsorbents [40, 57] in which the fast and instantaneous adsorption was observed; since the pore sizes of Fe-ZIF-8 or ZIF-8 are around 1 nm [45], the adsorption of RDB with four benzene rings in which each has a critical dimension of around 0.662 nm [60] on ZIF-8 limited the diffusion of the RDB molecule to the inner pore structure; however, abundant active adsorption sites could be obtained at its external surface, which is helpful to the adsorption of dye molecules; (ii) a gradual attainment of the equilibrium where only about 5–10% of the adsorption was encountered. This is due to the utilization of the all active sites on the adsorbent surface. The first linear segment indicated a boundary layer effect while the second linear segment was assigned to intraparticle diffusion [58, 59].Table 3
Comparison of piecewise linear regression for one, two, and three linear segments by AIC.
Adsorbent
C
R
D
B mg·L−1
One linear segment’s regression
Two linear segments’ regression
Three linear segments’ regression
SSE
R
2
AIC
SSE
R
2
AIC
SSE
R
2
AIC
ZIF-8
30
247.07
0.905
62.72
82.93
0.968
39.30
82.93
0.968
45.34
40
736.84
0.858
91.13
189.35
0.964
60.77
189.35
0.964
66.78
50
619.32
0.884
89.47
33.91
0.994
16.05
33.91
0.995
22.46
Fe-ZIF-8
30
835.06
0.650
94.38
54.13
0.977
28.51
54.14
0.977
34.23
40
2070.79
0.973
117.99
317.80
0.967
72.76
317.80
0.967
80.24
50
984.31
0.846
98.65
23.73
0.996
6.77
21.33
0.997
10.01Table 4
Results of piecewise regression for the two linear segments for ZIF-8 and Fe-ZIF-8 (the values in parentheses are at a 95% confidence level).
Adsorbent
Concentration(mg·L−1)
Break point (minute0.5)
The first linear segment
The second linear segment
Intercept 1
Slope 1
Intercept 2
Slope 2
ZIF-8
30
5.92
−2.83(−5.11 : −0.55)
4.68
19.16(17.58 : 20.74)
0.75
40
7.07
−10.29(−17.10 : −3.47)
4.83
27.06(25.29 : 28.83)
0.67
50
8.94
−10.19(−12.28 : −8.10)
5.58
34.85(32.21 : 37.49)
0.52
Fe-ZIF-8
30
9.49
22.58(20.16 : 25.00)
3.85
78.07(75.00 : 81.15)
−1.97
40
10.00
8.13(2.64 : 13.63)
6.82
98.79(93.99 : 103.59)
−2.26
50
8.94
25.38(23.59 : 27.16)
6.01
80.15(78.58 : 81.72)
−0.15The rate parameter,kp, increases with an increase in initial concentrations. However, the effect of initial RDB on rate parameters was irregular for RDB adsorption onto Fe-ZIF-8. The irregularity of kp could be related to that fact that iron incorporated caused the heterogeneity of ZIF-8 structure.The experimental data usually exhibit the multilinear plots, two or more stages influencing the adsorption process. In the statistical method, the piecewise linear regression is relevant to analyzing the data with multilinearity instead of the conventional graphical analysis [61] that might misidentify objective break points or numbers of segments.As seen from Figure9, a possible desorption might occur where the RDB uptake appears to fluctuate or even drop a little. This behavior could be attributed to either a reversible adsorption or a back diffusion controlling mechanism [62]. Thepseudo-first- or second-order kinetic models of Lagergren [33] or Ho and McKay [63], respectively, have been widely used to investigate the formal kinetics of adsorption processes [12, 27, 40, 64]. However, the present experimental data could not apply to these models due to reversible adsorption. In the present study, thepseudo-first-order kinetics model of Natarajan-Khalaf was used to analyze the experimental data. The rate constant, kads, for the adsorption of dye was determined from the slope of Natarajan-Khalaf’s plots. The results are listed in Table 5. The high coefficient of determination R2 (0.973–0.998) implies that this model was compatible with the experimental data. The rate constant of adsorption is separated into the rate of forward and reverse adsorption. The rate constants for the forward and reverse process are also presented in Table 5. It is clear that the adsorption kinetics can be significantly improved by the introduction of iron into the ZIF-8. As shown in Table 5 the rate constants for adsorption could be increased approximately 5 times by Fe-ZIF-8 and the kinetics with Fe-ZIF-8 were faster than that with ZIF-8.Table 5
Rate constants for the adsorption and the rate constants for the forward and reverse process and equilibrium constants at different concentrations for ZIF-8 and Fe-ZIF-8.
Adsorbent
C
R
D
B (mg/L)
k
a
d
s
k
1
k
2
K
o
R
2
ZIF-8
30
0.0023
0.0009
0.0014
0.6429
0.995
40
0.0025
0.0009
0.0016
0.5625
0.998
50
0.0046
0.0015
0.0031
0.4839
0.990
Fe-ZIF-8
30
0.0115
0.0077
0.0038
2.0263
0.991
40
0.0122
0.0081
0.0041
1.9756
0.991
50
0.0184
0.0113
0.0071
1.5915
0.980Figure 9
Effect of temperature on adsorption of RDB dye onto ZIF-8 (a) and Fe-ZIF-8 (b) (CRDB = 30–50 mg·L−1, mZIF-8 = 0.2 g, VRDB = 500 ml, and stirring rate: 500 ppm).
(a)
(b)Adsorption thermodynamics was conducted by varying the temperature from 298 K to 318 K as shown in Figure9.The thermodynamic parameters including activation energy,Keq, k1, and k2 are presented in Table 6. The results showed that equilibrium adsorption capacity, qeq, of both adsorbents increased with an increase in temperature which indicated that the process was endothermic. The equilibrium adsorption capacity of Fe-ZIF-8 is higher than that of ZIF-8 for each corresponding temperature. The increasing rate constant with an increase in temperature suggests that temperature favors the adsorption process for the fast rate to proceed. The equilibrium constant, Keq, for Fe-ZIF-8 and ZIF-8 changed in the range of 1.3–1.8 and 3.4–5.7, respectively, as temperature varied from 298 to 318 K. It is worth noting that Keq in the case of Fe-ZIF-8 is higher and increases much faster than that in the case of ZIF-8. The activation energy refers to the minimum amount of energy that must be overcome to proceed with the adsorption. Ea for ZIF-8 and Fe-ZIF-8 was 48.27 kJ and 12.51 kJ, respectively. Lower Ea for Fe-ZIF-8 indicated that Fe-ZIF-8 was more favorable for RDB adsorption than ZIF-8. Low activation energy (below 42 kJ mol−1) implies diffusion controlled process because the temperature dependence of pore diffusivity is relatively weak and the diffusion process refers to the movement of the solute to an external surface and not diffusivity of material along microspore surfaces in a particle [65]. Ea with ZIF-8 is slightly higher than 42 kJ mol−1. However, a reversible adsorption was observed as shown in Figure 9, indicating that the rate-limiting step in this case involved a physical-chemical mechanism and not purely physical or chemical one. Therefore the RDB adsorption onto ZIF-8 was also considered a diffusion controlled process and so is the RDB adsorption onto Fe-ZIF-8.Table 6
Activation energy, equilibrium and rate constants for RDB dye adsorption, and rate constants for forward and reverse process of RDB adsorption onto ZIF-8 and Fe-ZIF-8.
Absorbent
Temp.(K)
K
e
q
q
e
q (mg·g−1)
k
1 (×103)(min−1)
k
2 (×103)(min−1)
k
a
d
s (×103)(min−1)
R
2
E
a (kJ·mol−1)
R
2
ZIF-8
298
1.272
28.89
0.890
1.800
2.700
0.990
48.270
0.991
308
1.570
43.94
1.914
2.692
4.606
0.988
318
1.842
53.02
3.908
5.304
9.212
0.973
Fe-ZIF-8
298
3.401
62.92
11.361
7.063
18.424
0.988
12.507
0.972
308
4.079
77.50
12.851
7.876
20.727
0.994
318
5.864
87.64
17.761
7.572
25.333
0.991The activation parameters calculated using Eyring equation are presented in Table7. This would express whether the adsorption process follows an active complex prior to the final sorption. The coefficient of determination was high for both ZIF-8 and Fe-ZIF-8 although the Eyring equation is not strictly linear with respect to 1/T [66]. The negative value of ΔS∗ (−29.44 J K−1 mol−1 for ZIF-8 and −153.40 J K−1·mol−1 for Fe-ZIF-8) suggests a possibility of an associative chemisorption through the formation of an activated complex between RDB molecule and adsorbent [47], [63]. Also the negative value of ΔS# normally reflects that no significant change occurs in the internal structure of the adsorbent during the adsorption process [41, 66]. The values for ΔH# (52. 03 kJ.mol−1 for ZIF-8 and 9.94 for Fe-ZIF-8) suggest that these reactions are endothermic. The large, positive ΔG# in both RDB adsorptions onto ZIF-8 and Fe-ZIF-8 imply that these reactions require energy to convert reactants to the product and as the energy requirement is satisfied the reaction proceeds. Typically, ΔG# value relates to the adsorption rate. The rate increases as ΔG# decreases [41, 42]. This is seen when comparing the data from Tables 6 and 7. In Table 6, the rate constant, kads, of Fe-ZIF-8 is higher than that of ZIF-8. Table 7 describes the trend for ΔG# in which the Fe-ZIF-8 has the lower ΔH# value than ZIF-8.Table 7
Activation parameters for RDB dye adsorption onto ZIF-8 and Fe-ZIF-8.
Adsorbent
Temperature(K)
Δ
S
# (J·mol−1·K−1)
Δ
H
# (kJ·mol−1)
Δ
G
# (kJ·mol−1)
R
2
ZIF-8
298
−29.44
52.03
60.80
0.999
308
61.10
318
61.39
Fe-ZIF-8
298
−153.40
9.94
55.66
0.960
308
57.19
318
58.73The thermodynamic parameters,ΔH0,ΔS0, and ΔG0, of system were determined using van’t Hoff equation to assess the spontaneity of adsorption process. In Table 8, the results show that the adsorption process using ZIF-8 and Fe-ZIF-8 was endothermic as indicated by the positive sign of the ΔH0 value. The positive value of ΔS0 indicates the increasing randomness at the solid-liquid interface during the adsorption of RDB molecules on the adsorbent [43]. The negative values of ΔG0 suggest the spontaneous RDB adsorption of RDB on ZIF-8 or Fe-ZIF-8. The more negative value at higher temperatures implies that the spontaneity increases with a temperature increase. As the Gibbs free energy change is negative and accompanied by the positive standard entropy change, the adsorption reaction is spontaneous with high affinity. Consistent with the findings in the kinetics, more negative values of ΔG0 with Fe-ZIF-8 were obtained compared to that with ZIF-8. Again, this confirmed the important role of iron in ZIF-8 in enhancing the RDB capacity.Table 8
Thermodynamic parameters for the adsorption of RDB dye onto ZIF-8 and Fe-ZIF-8.
Absorbent
Δ
G
0 (kJ)
Δ
H
0 (kJ)
Δ
S
0 (J)
R
2
298 K
308 K
318 K
ZIF-8
−0.599
−1.359
−1.615
16.033
55.795
0.983
Fe-ZIF-8
−1.092
−3.600
−4.677
51.639
170.000
0.980


## 3.2.2. Effect of pH

One of the important parameters controlling the adsorption process is pH. Figure10 shows the effect of pH on the removal of RBB dye from aqueous solutions. The behaviors of pH effect for RDB adsorption onto ZIF-8 and Fe-ZIF-8 were similar. However, the RDB adsorption capacity of Fe-ZIF-8 was higher than that of ZIF-8. In general, the RDB adsorption capacity of adsorbents was observed to increase significantly with an increase in pH from 2.2 to 6, followed by a slight increase in pH from 6 to 10 and it decreased significantly in further pH increase. The values of pHZPC for ZIF-8 and Fe-ZIF-8 determined by pH drift method were around 9.2 and 9.8, respectively, and are in accordance with previous results [25, 27, 67] (the inset in Figure 10). The value of pHZPC indicates that the surface of the adsorbent is positively charged when pH of the solution is below pHZPC, while the surface of adsorbent becomes negatively charged at pH of the solution above pHZPC.Figure 10
Effect of pH on the adsorption of RDB by ZIF-8 and Fe-ZIF-8 (CRDB = 50 mg·L−1; mAdsorbent = 0.02 g;V = 50 mL; shaking time = 24 h; Temp. = 30°C).As seen in Scheme1, molecular structure of RDB consists of two groups of –SO3- and –SO4-, a group of NH2. Commonly, equilibrium of RDB in water is expressed as in Scheme 2.Scheme 2
Equilibrium of RDB in water.Therefore, the higher pH is the more the equilibrium of (22) shifts to the right. With regard to the correlation of the electronic charges of the adsorbent/adsorbate and solution pH values, it can be presumed that there might be an electrostatic interaction between the positively charged ZIF-8 surface and the negatively charged site of RDB increase as pH of solution increases up to pHZPC. The adsorption capacity of ZIF-8 and Fe-ZIF-8 started to decrease significantly at pH >  ~10.2, which was probably due to the electrostatic repulsion of negatively charged RDB and negative ZIF-8. In addition, the low stability of ZIF-8 framework in pH lower than 3 also contributes to the low RDB adsorption capacity (see Figure 6). This electrostatic interaction mechanism is similar to the adsorption mechanism for phthalic acid [67] and p-arsanilic acid on ZIF-8 [27]. In addition, the hydrophobic and π-π interaction between the aromatic rings of the RDB and the aromatic imidazole rings of the ZIF-8 framework is also thought to contribute to the RDB adsorption capacity.The increasing RDB uptake of Fe-ZIF-8 is probably due to the adsorption through other mechanisms addition to the electrostatic interaction. The enhanced adsorbed amount with Fe-ZIF-8 probably resulted from an increased number of adsorption iron sites. It is likely that the coordination of the nitrogen atoms and oxygen in RDB molecules to the Fe2+ ions in the ZIF-8 framework is responsible for the more efficient adsorption compared with bare ZIF-8. From this discussion the possible mechanisms of RDB adsorption onto ZIF-8 or Fe-ZIF-8 were illustrated in Figure 11.Figure 11
The proposed mechanism of RDB adsorption onto ZIF-8 or Fe-ZIF-8 at pH <pHZPC. 2-Melm: 2-methylimidazole.


## 3.2.3. Isotherm Adsorption Studies

The study of adsorption isotherms is helpful in determining the adsorption capacities for removal at certain dyes at fixed temperature. In the present work, the equilibrium experiments were operated as if the initial concentration (C0=50 mg·L−1) was kept constant and the absorbent weight varied between 0.005, 0.007, 0.01, 0.12, 0.015, 0.017, and 0.020 g. The experimental data were analyzed according to the nonlinear form of Langmuir and Freundlich model. Figure 12 presents the experimental points and nonlinear regression curves of Langmuir and Freundlich models. The parameters of models are listed in Table 9. However, the maximum adsorption capacity is not obtained in Freundlich equation. Halsey [68] supposed that the maximum adsorption capacity, qm, by Freundlich equation could be expressed:(25)qm=limCe→C0⁡KFCe1/n.qm calculated based on Freundlich equation is also shown in Table 9.Table 9
The parameters of Langmuir and Freundlich models.
Adsorbent
Langmuir model
Freundlich model
K
L (L·mg−1)
q
m
o
m (mg·g−1)
R
2
χ
2
N
K
F (mg· g−1·mg·L−1)n
q
m (mg·g−1)
R
2
χ
2
ZIF-8
0.594
133.76
0.974
0.254
7.800
82.344
127.35
0.878
1.209
Fe-ZIF-8
0.568
193.56
0.958
2.340
4.434
92.015
222.33
0.961
2.399Figure 12
Langmuir and Freundlich isotherm models of adsorption RDB dye onto ZIF-8 and Fe-ZIF-8 (CRDB = 50 mg·L−1;V = 40 mL; madsorbent = 0.005–0.020 g; pH = 8.2; shaking time = 24 hours).The determination coefficient(R2) and the Chi-square test (χ2) for assessing the compatibility of experimental data with the isothermal models are listed in Table 9. The high value of R2 and low χ2 suggest that the isothermal data of ZIF-8 could be well represented by the Langmuir model. This implies a monolayer adsorption for ZIF-8. For Fe-ZIF-8 both models exhibited similar values of R2 and χ2. Moreover, favorable characteristic parameters of RL for Langmuir isotherm and n for Freundlich isotherm were 0<RL=0.034<1 and 2<n=4.43<10, which indicated that both isotherms were favorable. These results confirmed that the equilibrium data of RDB adsorption onto Fe-ZIF-8 could be well fitted by the two adsorption isotherm models. This result indicated a monolayer adsorption and the existence of heterogeneous surface in Fe-ZIF-8. It is worth noting that maximum monolayer adsorption capacity, qmom, for ZIF-8 is much higher than that for ZIF-8. It was concluded that the introduction of iron into ZIF-8 enhanced the RDB adsorption onto Fe-ZIF-8 in terms of kinetics and isotherm adsorption.K
L in Langmuir model is the equilibrium constant and describes the relation between kinetics and thermodynamics. Then, KL in Langmuir model is thought to be equivalent to Ko. However, the relation of KL and Ko (K0=k1/k2) (see Table 5) was not clear in our study. It is explained by that fact that in the solid-liquid adsorption system KL in the Langmuir model no longer reflects the equilibrium constant as its original meaning. In our previous study [40], as isothermal adsorption experiments were operated with constant initial concentration C0 and variable weights of adsorbent, we found that the obtained parameters of Langmuir and Freundlich models also increase as the initial concentration increases, which should be constant at certain temperature. It is thought that these parameters turn out to be empirical coefficients rather than fixed parameters at a certain temperature.


## 3.2.4. Reusability of ZIF-8 and Fe-ZIF-8

To estimate the reusability of ZIF-8 and Fe-ZIF-8 for the removal RDB, the used adsorbents were regenerated by sonication assisted washing with 10−3 M NaOH solution for 6 h and drying for 24 hours at 100°C and then exploited to adsorb RDB. The adsorption capacity of the regenerated ZIF-8 and Fe-ZIF-8 are presented in Figure 13. Although the RDB adsorption decreased gradually with an increase in desorption cycles, the regenerated adsorbents still exhibited good performance for their adsorption. After the desorption for three cycles, the RDB adsorption capacity of by ZIF-8 and Fe-ZIF-8 reached 90% and 95% of the adsorption of the initial material, respectively. The XRD patterns of adsorbents after the three cycles seem unchangeable (see Figure 14), indicating that the adsorbents were stable in this condition.Figure 13
Effect of regeneration cycles of ZIF-8 and Fe-ZIF-8 adsorbents on the adsorption of RDB (VRDB = 125 mL; CRDB = 50 mg L−1; adsorbent/VRDB = 0.05 g/125 mL; shaking time = 10 hours).Figure 14
The XRD patterns of ZIF-8 and Fe-ZIF-8 adsorbents after the three cycles.


## 4. Conclusion

The iron doped zeolite imidazolate framework-8 was synthesized by hydrothermal process. Ferrous ion as an iron source could be directly introduced into ZIF-8 to form Fe-ZIF-8 (molar mole of Fe/(Fe + Zn) = 0.116). The ferrous ions could replace partially Zn(II) in ZIF-8 structure or exist in amorphous species. The ZIF-8 was stable in aqueous solutions with pH in ranging from 3 to 12 for 24 hours. Both ZIF-8 and Fe-ZIF-8 were used to study the RDB adsorption. The results show that the introduction of iron into ZIF-8 significantly enhanced the RDB adsorption capacity compared to bare ZIF-8. The study based on Webber’s intraparticle diffusion shows that the adsorption process with ZIF-8 and Fe-ZIF-8 tended to follow two stages in which the first stage was film-diffusion and the second was an intraparticle-diffusion process. The kinetic parameters based on Arrhenius and Eyring equation proved that the introduction of iron into ZIF-8 provided a much larger adsorption capacity and faster adsorption kinetics than ZIF-8. In addition to the electrostatic interaction mechanism and the hydrophobic andπ-π interaction between the aromatic rings of the RBB dye and the aromatic imidazole rings of the adsorbent for ZIF-8, the coordination of the nitrogen atoms and oxygen in carboxyl group in RDB molecules to the Fe2+ ions in the ZIF-8 framework might explain why Fe-ZIF-8 has a higher RBD adsorption capacity than ZIF-8. The experimental data for ZIF-8 were well correlated by Langmuir model while those for Fe-ZIF-8 were well fitted to both Langmuir and Freundlich models. The maximum monolayer adsorption capacity for Fe-ZIF-8 (193.56 mg−1·g−1) was approximately 1.4 times higher than that for ZIF-8 (133.76 mg−1·g−1).



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