Metal-Organic Framework-101 ( MIL-101 ) : Synthesis , Kinetics , Thermodynamics , and Equilibrium Isotherms of Remazol Deep Black RGB Adsorption

In the present paper, the synthesis of metal-organic framework-101 (MIL-101) and Remazol Deep Black RGB (RDB) adsorption on MIL-101 were demonstrated.-e kinetics of RDB adsorption onMIL-101 was studied usingWeber’s intraparticle diffusionmodel and the pseudo-firstand pseudo-second-order kinetic models. Particularly, the statistical method of piecewise linear regression andmultinonlinear regression was employed to analyse the adsorption data according to the previously mentioned kinetic models. -e results indicated that the adsorption process followed the three-step pseudo-first-order kinetic equation, which was consistent with the results of the intraparticle diffusion model with three linear segments. -is model best described the experimental data. In addition, the adsorption isotherm data were studied using five adsorption models, namely, Langmuir, Freundlich, Redlich–Peterson, Toth, and Sips in nonlinear forms, and the Langmuir model is the most appropriate for the experimental data. -e values of energies of activation of adsorption were calculated, and they revealed that the adsorption process was of endothermic chemical nature. A statistical comparison using Akaike information criterion to estimate the goodness of fit of the kinetic and isotherm models was presented.


Introduction
It is well known that wastewater from textile industries, pulp mills, and dyestuff manufacturing has been a potential threat to environment [1,2].Various treatment processes such as physical separation, chemical oxidation, and biological degradation have been widely investigated to remove dyes from wastewaters [3].Among these processes, adsorption technology is considered as one of the most competitive methods because it does not require high operating temperature and has a simple operation as well as low cost, and several coloring materials can be removed simultaneously [4].
MIL-101 has demonstrated good performance in storage and adsorption of gas such as hydrogen storage [5], adsorption of CO 2 and CH 4 [6], and long-chain alkanes [7].However, there are very few reports studying the adsorption of dyes from aqueous solutions [8][9][10].MOFs in general and MIL-101 in particular exhibit high efficiency for adsorption of dyes from aqueous solutions due to their unique structures such as large surface areas, ordered porosity, and high density of adsorption sites (anion and cation).MIL-101 demonstrates excellent adsorption properties for dyes, such as methyl orange (MO), xylenol orange (XO), and uranine.For expanding applications of MIL-101, studying the adsorption of this material for Remazol Deep Black RGB (denoted as RDB) used widely in dye industry will be a concern of this work.
Azo dyes with an azo group are widely used in many textile industries due to their low cost, high solubility, and stability.
ese dyes and their intermediate products are toxic, carcinogenic, and mutagenic to aquatic life.Remazol Deep Black RGB is a common diazo reactive dye, widely used in textile industries [11].It is stable and hard to degrade biologically due to the presence of aromatic rings.us, RDB removal from textile wastewater has drawn much attention among researchers.Several techniques including adsorption, electrochemistry, and biosorption for RDB treatment have been reported.Soloman et al. [11] applied the electrochemical treatment to hydrolyze Remazol Black.ey demonstrated that the performance of the batch recirculation system was better than other reactor con gurations studied in terms of capacity utilization and energy consumption.Brazilian pine-fruit shells (Araucaria angustifolia) in their natural form were used as an adsorbent for the removal of RDB dye from aqueous e uents [12].A biosorption process to discard azo dyes by fungi (Aspergillus avus) was investigated in batch reactors [13].Ninety percent of the dye in a 100 mg/L solution was removed.Recently, anh et al. [14] reported that iron doping to ZIF-8 signi cantly enhances RDB adsorption capacity.Fe-ZIF-8 also exhibits photocatalytic degradation of RDB under visible light [15].
Batch adsorption studies focus on two main trends: (i) designing and optimizing experiments with the evaluation of the in uence of the experimental variables-this approach enables to estimate the magnitude of the in uence of the factors a ecting the process and their interactions [16]-and (ii) kinetics, thermodynamics, and equilibrium isotherm adsorption studies [14,17].For the latter, several models are used to study adsorption kinetics and isotherms.
e parameters in these models are calculated with linear or nonlinear regression approaches.However, the number of parameters in each mode is di erent.For example, the Langmuir isotherm model contains two parameters, while the Redlich-Peterson isotherm model has three parameters.It is obvious that the greater the number of model parameters, the lower the relative errors (REs) or the sum of squared errors (SSEs).erefore, the model compatibility needs to be evaluated including SSEs or REs and the number of model parameters as well as the experimental points.However, in the majority of current publications, the goodness of t for models is estimated based on only the REs or SSEs.To the best of our knowledge, the research on this issue is limited.
In the present study, MIL-101 was employed as an adsorbent for removing RDB dye.e e ects of initial concentration, adsorbent particle size, agitation speed, temperature, and pH on the adsorption behavior of RDB onto MIL-101 were investigated.e adsorption kinetic and isothermal studies and the goodness of t for models were addressed.

Apparatus.
e powder X-ray di raction (XRD) pattern was recorded by means of a D8 Advance (Bruker, Germany) with CuKα radiation (λ 1.5406 Å). e morphology of the obtained samples was determined using transmission electron microscope (TEM) on JEOL JEM-2100F.e speci c surface area of the samples was determined by means of nitrogen adsorption/desorption isotherms using a Micromeritics 2020 volumetric adsorption analyzer system.Visible spectrophotometry was measured by using Lambda 25 Spectrophotometer (PerkinElmer, Singapore) at λ max of RDB dye (600 nm).

Preparation of MIL-101.
MIL-101 was synthesized from chromium (III) nitrate nonahydrates, H 2 BDC, and HF using the hydrothermal method [18].ree samples of MIL-101 with di erent molar ratios of HF/H 2 BDC 0.00, 0.25, and 0.75 were prepared.In a typical procedure, a mixture of 10 mmol of H 2 BDC, 12.5 mmol of Cr(NO 3 ) 3 •9H 2 O, x mmol of HF (x 0.00, 0.25, and 0.75), and 350 mmol of H 2 O was heated in a Te on-lined stainless steel autoclave at 200 °C for 8 h.e resulting green solid was ltered and then washed with ethanol in a Soxhlet apparatus for around 12 h to completely remove the unreacted amount of H 2 BDC. e obtained MIL-101 was denoted as MHF0 for the molar ratio of HF/H 2 BDC 0, MHF0.25 for 0.25, and MHF0.75 for 0.75.

Adsorption Kinetic and ermodynamic
Studies.Kinetic studies were carried out in a 3 L plastic beaker.is beaker was equipped with a stainless steel at-blade impeller using an electric motor to stir the dye solution and a tap near the bottom to withdraw the liquid at any time.MIL-101 (0.50 g) was mixed thoroughly with 1000 mL of the dye solution in the beaker at room temperature.10 mL of the mixture was withdrawn periodically, and MIL-101 was removed by using a centrifuge.e nal dye concentration was determined using the spectrophotometric method.e adsorption capacity of the adsorbent was calculated according to the following formula: where q t is the adsorption capacity (mg•g −1 ) at t time, C 0 is the initial dye concentration (mg•L −1 ), C t is the dye concentration (mg•L −1 ) at time t, V is the volume of dye solution (L), and m is the mass of the adsorbent (g).
For the adsorption isotherm study, an amount of 30, 40, 50, 60, 70, 80, 90, and 110 mg of MIL-101 was added to 8 stopper 250 mL Erlenmeyer flasks containing 100 mL of 100 mg/L RDB solution.e flasks were then placed into a shaker bath at 28 ± 1 °C for 24 hours.ereafter, the supernatant liquid was separated by centrifugation and the final dye concentration was determined with the method mentioned above.
In order to study formal and diffusion kinetics, Weber's intraparticle diffusion model and pseudo-first-and pseudosecond-order kinetic models were used.Weber's intraparticle diffusion model is described as in the following equation [19]: where k i is intraparticle diffusion rate constant (mg•g −1 •min −0.5 ) and I is the intercept which represents the thickness of the boundary layer.
If intraparticle diffusion is the rate-limiting step, then the plot of q versus t 0.5 will give a straight line with a slope that equals k i and an intercept equal to zero.
e pseudo-first-and pseudo-second-order kinetic models in the nonlinear form are expressed as follows [20]: where q t and q e are the adsorption capacity at time t (min) and at equilibrium time, respectively, k 1 is the rate constants of the pseudo-first-order model (min −1 ), and k 2 is the rate constant of the pseudo-second-order kinetic model (g•mg −1 •min −1 ).
For the thermodynamic study, the experiments were conducted in the same way as in the adsorption kinetics study.However, the adsorption temperature was fixed at 298, 308, 318, and 328 K. e activation energy, E a , was determined using the Arrhenius equation [21]: where k is the rate constant, A is the frequency factor, R is the gas constant (8.314J mol −1 •K −1 ), and T is the absolute temperature in Kelvin.Taking the natural logarithm of both sides of (4), one obtains By linearly plotting ln k versus 1/T, one could obtain E a from the slope (−E a /R).
In order to evaluate whether the adsorption process is spontaneous, the adsorption thermodynamic parameters are needed.e standard Gibbs free energy of adsorption (ΔG 0 ) is given by the following expression: where ΔG 0 , ΔH 0 , and ΔS 0 are the change of standard Gibbs energy, enthalpy, and entropy, respectively.
ΔG 0 is given by the van't Hoff equation: where K d is the distribution coefficient of the solute ions and equal to q e /C e [22,23] and the others are described earlier.
By replacing ( 6) to (7), one obtains e value of ΔH 0 and ΔS 0 is calculated from the slope and intercept of the linear plot of ln K d versus 1/T.

Adsorption Isotherm Study.
Experimental data were analysed according to five isotherm models by Langmuir, Freundlich, Redlich-Peterson, Sips, and Toth.
Langmuir isotherm: Langmuir model is valid for monolayer sorption onto the surface.It could be expressed as follows [24]: where q m is the maximum monolayer capacity amount (mg•g −1 ), K L is the equilibrium constant, q e is the equilibrium adsorption capacity (mg•g −1 ), and C e is the equilibrium concentration of adsorbate (mg•L −1 ).
Freundlich isotherm: e Freundlich equation is an empirical relation based on the sorption onto a heterogeneous surface.It is commonly represented as [25] where K F ((mg•g −1 )•(mg•L −1 ) n ) and n are the Freundlich parameters related to adsorption capacity and adsorption intensity, respectively.e maximum capacity, q m (mg•g −1 ), can be calculated from the following equation [26]: where C 0 is the initial concentration.
Redlich-Peterson isotherm: Redlich-Peterson isotherm [27] contains three parameters and involves the features of both Langmuir and Freundlich isotherms.It can be described as follows: where K R (L•g −1 ) and a R (L•mg −1 ) are the Redlich-Peterson isotherm constants and b R is the exponent which lies between 0 and 1.When b R approaches 1, (12) becomes the Langmuir equation.
en, the maximum adsorption capacity, q m (mg•g −1 ), can be determined by the following equation: Sips isotherm: Sips isotherm is a combination of the Langmuir and Freundlich isotherms and expected to describe heterogeneous surfaces much better [24].e model can be written as [28] where K s and a s are the Sips constants related to the energy of adsorption.e maximum monolayer adsorption capacity could is given by K a /a s .
Toth isotherm: Toth isotherm is the Langmuir-based isotherm and considers a continuous distribution of site affinities.It is expressed as [29] where K T 0 is the Toth model constant and n is the Toth model exponent (0 < n ≤ 1).It is obvious that, for n � 1, this isotherm reduces to the Langmuir equation.

Piecewise Linear Regression and Model
Comparison. e application of Weber's model often suffers from uncertainties caused by the multilinear nature of its plots.Malash and El-Khaiary [30] proposed the piecewise linear regression for the analysis of multilinearity in intraparticle diffusion and film diffusion.In this method, the experimental data could be fixed for one-, two-, three-, or fourlinear-segment lines: one-linear-segment line: where the values of A, B, C, D, E, F, G, and H are estimated by nonlinear regression.D, F, and H, called breakpoints, are the boundaries between the segments.e Microsoft Excel "SIGN" function is defined as follows: e example for the three-linear-segment equation is expressed as follows: e linear equation of the second segment is e model's parameters are determined using the least squares method.is is calculated by minimizing the sum of squared errors, SSE S , by numerical optimization techniques using the Solver function in Microsoft Excel.e function for minimization is where y exp is experimental datum and y est is the value estimated from the model.e determination coefficient, R 2 , is obtained by the following expression: where SSE T is the total sum of squares equal to  N 1 (y exp − y mean ) 2 (y mean is the mean value of y).
We know that increasing the number of linear segments increases the number of regression parameters that almost universally led to the decrease of SSEs or the increase of R 2 .
erefore, the model compatibility cannot be based only on SSE or R 2 but must also include the number of regression parameters as well as the experimental points.Akaike's information criterion (AIC) is one of the well-known statistical methods used in this case.
where N p is the parameter of the model.e other parameters are described above.

4
Journal of Chemistry e AIC C is applied as N is small compared with N p .AIC C is only computed as N is at least two units greater than N p .e value of AIC C could be positive or negative, and the lower the AIC C value, the better it is.Another way of comparing AIC C is using the evidence ratio (ER) which is expressed as follows [17]: where Δ is the absolute value of the di erence between AIC C and AIC S scores.ER means that the model with lower AIC is 1/e −0.5Δ times more likely to be correct than the alternative model.
In the present study, the comparison of the model will use R 2 or SSE if the models possess the same experimental points (N) and parameter numbers of models (N p ). Otherwise, AIC will be employed.

Characterization of MIL-101 Samples.
Figure 1 shows the XRD patterns of MIL-101 synthesized with the HF/H 2 BDC molar ratios of 0.00, 0.25, and 0.75.e characteristic di ractions of the samples matched well with the published XRD patterns of MIL-101 [18]. is means that the obtained materials are MIL-101.However, the peak intensity of the samples synthesized with HF is signi cantly higher than that of the sample synthesized without HF (MHF0). is could be due to uorine that acts as a mineralizing agent in the hydrothermal synthesis for the formation of well crystalline microporous materials [31].
e morphology of the obtained material consists of octahedron-shaped crystals with smooth facets (Figure 2).e particle size of MIL-101 increases with the increase in the HF/H 2 BDC ratio.
e textural properties of the MIL-101 samples were investigated by using nitrogen adsorption/desorption isotherms.e isotherm curves belong to type IV according to IUPAC classi cation (Figure 3).e BET speci c surface area for MHF0.25 is the highest (Table 1), and thus, MIL-101 synthesized with HF/H 2 BDC 0.25 was chosen for adsorption experiments.

RDB Adsorption on MIL-101 3.2.1. E ect of Initial Concentrations.
e RDB kinetics of adsorption on MIL-101 at di erent initial concentrations in the range of 25-600 ppm is illustrated in Figure 4(a).It is obvious that the adsorption capacity of RDB on MIL-101 increases when RDB initial concentration increases from 25 to 400 ppm. is might be due to the fact that, initially, the sites on the adsorbent surface are less occupied by the dye molecules, and increasing the concentration increases the interaction between the dye molecules and the adsorbent; V pore (cm  thus, more dye molecules adsorb on the surface [10,32,33]. In addition, the mass transfer driving force becomes larger as the initial concentration increases, and this results in higher adsorption capacity [21].At higher concentrations (>400 ppm), the adsorption takes place very fast during the rst 15 minutes, and then, it slows down and reaches equilibrium at about 150 minutes.Meanwhile, for concentration at 25 ppm, the adsorption reaches equilibrium practically immediately, just after about 10 minutes. is might be because at low dye concentration, the driving force is very small and the adsorption takes place only on the surface of MIL-101, whereas when the dye concentration is high with large driving force, the adsorption also occurs in the pore of the adsorbent, and due to high resistance in the pores, the adsorption becomes slower and reaches equilibrium after a longer period.Furthermore, adsorption might take place in several stages.At a very high dye concentration (600 ppm), the RDB adsorption on MIL-101 does not follow the same pattern as at lower initial dye concentration (Figure 4). is might be the result of forming a colloidal solution at a high concentration of RDB [20,34].
erefore, the RDB initial concentration from 50 to 400 ppm is suitable for the kinetic study of adsorption on MIL-101.In this kinetic study, Weber's intraparticle di usion model [19] was applied to study the adsorption mechanism.e values of q t at di erent times were analysed using piecewise linear regressions based on the assumption of one, two, three, and four linear segments.e AIC C value was the criterion for determining which one is the goodness of t (Table 2).
e data indicate that the three-linear-segment model has the lowest AIC C , and therefore, this Weber's model is the most accurate because for this criterion the lower the value, the more suitable the model.ree distinct steps can be seen on the kinetic curves: (i) instantaneous adsorption of RDB molecules within the rst 7-21 minutes, (ii) a gradual attainment of the equilibrium due to the utilization of the all active sites on the adsorbent surface, and (iii) an equilibrium attainment of RDB molecules onto MIL-101 (Figure 4(b)).At the initial concentration of 50 mg•L −1 , for example, the intercept of the rst linear segment is 0.05, and its 99% con dence interval is (−3.14;3.23), indicating that the intercept is not signi cantly di erent from zero. is strongly suggests that intraparticle di usion is the rate-controlling mechanism during the rst 15 minutes of adsorption.e next two linear segments do not pass through the origin because the 99% con dence intervals of their intersects do not contain zero, indicating that the intraparticle di usion is not the only rate-limiting step and lm di usion or chemical  Journal of Chemistry reaction might take place during these periods of adsorption [20,33]. is behavior is found for all concentrations.e intraparticle parameters are illustrated in Table 3. e data indicate that the lm thickness (intercept 2 and intercept 3) increases with the increase in initial RDB concentration. is suggests that lm di usion controls the adsorption process in the last two steps.In the rst step, the intraparticle di usion parameter, k p1 , increases as initial RDB concentration increases.
ese results suggest that intraparticle di usion controls the rate in the initial step of the adsorption process.
In addition, the nature of the rate-limiting step is also con rmed by plotting the intraparticle di usion constant, k p1 , versus the rst power of the initial concentration.If k p1 is proportional to the initial dye concentration, the adsorption process is controlled by lm di usion, whereas, if intraparticle di usion limits the adsorption process, the relationship between dye concentrations and k p1 will not be linear [20,35].For the adsorption of RDB onto MIL-101, the plot of k p1 versus the initial concentration (C 0 ) is not linear (R 2 0.875; p 0.02 > 0.01), con rming that the intraparticle di usion mechanism controlled the adsorption in the initial step.
To study the formal kinetics of the RDB adsorption on MIL-101, the experimental data were subjected to pseudorst-order and pseudo-second-order kinetics in the nonlinear form.e results are shown in Figure 5(a) and Table 4.
e experimental points in Figure 5(a) are very far from the rst-order model curves, whereas they practically coincide with the second-order kinetic curves.From Table 4, we can see that the pseudo-second-order kinetic model has lower AIC values than the pseudo-rst-order kinetic model.
is means that the pseudo-second-order kinetic model explains the experimental data more appropriately.ese results are consistent with those of other reports [30,36,37].e rate constant k 2 calculated from the pseudo-secondorder kinetic model decreases as the initial RDB concentration increases.is indicates that chemisorption is signi cant in the rate-limiting step, involving valence forces through sharing or exchange of electrons between RDB and MIL-101.However, as mentioned earlier, in the present study, the adsorption process took place in three steps.Although the pseudo-second-order kinetic model accounts for the chemisorption nature well, it does not support the multisegment adsorption process.Al-Ghouti et al. [20] mentioned this problem and tried to analyse the adsorption as a threestep process with three linear segments on the kinetic plots by using the graphical approach method.erefore, in this study, we analyse the adsorption process in the same way; that is, the kinetic plot is also divided into three segments each of which follows the pseudo-first-order adsorption kinetics.
e three-step kinetic rate equation was expressed as follows: where q 1 , q 2 , and q 3 are the amount of dye adsorbed at time t after the subsequent kinetic steps (mg•g −1 ); q 0 is the amount of dye adsorbed at time t � 0; and k 1 , k 2 , and k 3 are the kinetic rate constants associated with each kinetic step.At t � ∞, when the adsorption reaches equilibrium, q t � q e , and q e � q 0 + q 1 + q 2 + q 3 .erefore, ( 22) can be written as e values of q 1 , q 2 , and q 3 and k 1 , k 2 , and k 3 can be obtained using nonlinear regression by means of the Statistical Package for Scientific Social 20 (SPSS 20).e three-nonlinear-segment regressions using the pseudo-first-order kinetic model for the RDB adsorption on MIL-101 are shown in Figure 5(b) and Table 5. High determination coefficients (0.91-0.99) indicate the appropriateness of the model.In addition, the AIC C values for the pseudo-first-order kinetics with three segments are also the lowest of the three kinetic models (Table 6). is further confirms the best fit of the pseudo-first-order kinetics with three segments with the experimental data.e finding is also consistent with the analysis of the three-step adsorption process using Weber's intraparticle diffusion model.

Effect of Particle Size and Agitation.
To study diffusion kinetics of the RDB adsorption on MIL-101 in terms of particle size, the three-linear-segment regression for the intraparticle diffusion model was applied to analyse the experimental data (Figure 6(a)).e results were the same as those of the effect of initial concentration.Intraparticle diffusion limited the adsorption rate at the initial step, and film diffusion controlled the process in the next two steps.
e values of k p1 are 14.04, 29.94, and 13.55 mg•g −1 •min −0.5 for MHF0, MHF0.25, and MHF0.75, respectively.eoretically, the intraparticle diffusion constant, k p1 , versus the inverse particle diameter, d −1 , did not give a straight line, and the conclusion for this is that the intraparticle diffusion was not the only operative mechanism [20].In fact, in our study, this line was not linear (R 2 � 0.008, p � 0.943) although MIL-101 is a porous material; hence, we cannot rely on the particle size (external surface area) to confirm the adsorption mechanism.erefore, the intraparticle diffusion Table 4: Kinetic parameters for pseudo-first-order and pseudo-second-order kinetic models of RDB adsorption on MIL-101.
Pseudo-first-order kinetics Pseudo-second-order kinetics q e,cal (mg•g −1 )  As can be seen from Figure 6(a), the adsorption capacity depends on the speci c area rather than the particle size. is is because, for porous materials, the external surface contributes very little to the total surface area.In terms of particle size, only external surface area is concerned.
Stirring speed a ects not only the distribution of the dye molecules in the bulk solution but also the formation of the external boundary lm.Increasing stirring speed decreases the lm thickness and thus the resistance to mass transfer around the adsorbent particle and increases the mobility of the whole system [38].e e ect of the stirring speed on RDB adsorption on MIL-101 was carried out with three values: 200, 300, and 400 rpm (Figure 6(b)).It is evident that the adsorption capacity increased when the stirring speed increases from 200 rpm to 300 rpm and remained practically stable at 400 rpm.As the stirring speed increases the diffusion rate, the resistance of the solution becomes small.After a certain stirring rate, the external resistance no longer a ects the sorption process.

3.2.3.
ermodynamic Studies.Temperature signi cantly a ected the RDB adsorption over MIL-101.When the temperature increased from 301 K to 333 K, the adsorption capacity increased rapidly from 120 mg•g −1 to 190 mg•g −1 (Figure 7(a)).
is indicates that the RDB adsorption on MIL-101 is an endothermic process.Similar results were Journal of Chemistry observed in the adsorption of uranine [9] and methyl orange [32] on MIL-101.
It is obvious that high temperature increased the diffusion rate of the dye molecules across the external boundary layer and in the internal pores of the adsorbent particle.is was the result of the decrease in the viscosity of the solution.In addition, the increase in adsorption capacity could also be ascribed to the increase in the number of active sites on the MIL-101 surface due to the decrease in the hydrogen bonding between adsorbed water and the adsorbent making more sites available for RDB molecules.
e pseudo-second-order kinetic model was more consistent with the kinetic data than the pseudo-first-order kinetic model in the temperature range of 301 K to 333 K. Hence, the rate constant k 2 was used to calculate the thermodynamic parameters.e E a value obtained from the slope of the linear plot of ln k 2 versus T −1 (F(3) � 59.15; R 2 � 0.98, p < 0.01) (Figure 7(b)) was 50.39 kJ•mol −1 . is large activation energy (over 42 kJ•mol −1 ) implies that chemisorption controlled the adsorption of RDB on MIL-101.
e thermodynamic parameters of the system, namely, ΔH 0 , ΔS 0 , and ΔG 0 were evaluated using the van't Hoff equation to determine the spontaneity of the adsorption process.e positive value of ΔH 0 (Table 7) suggested an endothermic adsorption process.e positive value of ΔS 0 indicated the increase in the randomness at the solid-liquid interface during the adsorption of RDB molecules on the adsorbent [39].e large negative values of ΔG 0 strongly recommended the spontaneous RDB adsorption on MIL-101.e more negative value at higher temperatures suggested that the spontaneity increased with temperature.As the change of Gibbs free energy was negative and accompanied by the positive standard entropy change, the adsorption reaction was spontaneous with high affinity.

Effect of pH.
e pH of the solution affects the dye adsorption process because it can alternate both dye ionization and the ionic state of the surface of the adsorbent.Figure 8(a) presents the effect of pH on RDB adsorption from aqueous solutions.e RDB adsorption capacity of MIL-101 increased slightly with pH from 3 to 5, followed by a significant increase with pH from 5 to 9. e pH pzc (the point of zero charge) of MIL-101 determined by the pH drift method [40] is around 5 (Figure 8(b)). is pH pzc implies that the surface of the MIL-101 is positively charged when pH of the solution is below 5, whereas the surface of adsorbent becomes negatively charged at pH above 5.
Increasing pH led to an increase in adsorption capacity, suggesting that the adsorption could follow a mechanism other than electrostatic interaction.
e π-π stacking interaction between the aromatic rings of the RDB and the aromatic rings of terephthalate in the MIL-101 framework was also thought to contribute to the RDB adsorption capacity.In addition, the coordination of the oxygen of the carboxyl group in the RDB molecules with the unsaturated Cr(III) ions in the MIL-101 framework is also responsible for more efficient adsorption.A possible mechanism of RDB adsorption on MIL-101 is illustrated in Scheme 2.

Adsorption Isotherms of RDB on MIL-101.
To describe the adsorption isotherms, Langmuir, Freundlich, Redlich-Peterson, Sips, and Toth equations were selected for use in this study.
e determination of parameters of isotherm models is often based on the linear regression.However, linear regression requires the transformation of the original equation into a linear form that induces a problem related to abuse R 2 .For example, the popular linear form of the Langmuir model is C e /q e � C e /q m + 1/(K L • q m ), in which C e is present in both independent and dependent variables [41].Some papers [42,43] reported that the linear form is less accurate than the nonlinear form in some cases of isotherm sorption as well as sorption kinetics.For these reasons, the isotherm equations in the nonlinear form are used in this study.Figure 9 shows the graphs that plot q e versus C e using the Langmuir, Freundlich, Redlich-Peterson, Sips, and Toth models.ese models displayed lines around the experimental data, indicating that they all could describe the experimental data well.
e parameters of the isotherm models calculated using nonlinear regression are listed in Table 8.Except q m derived from the Sips model (290.15mg•g −1 ), the values of q m from the Redlich-Peterson and Toth models are fairly similar to that of q m obtained from the Langmuir model due to the parameter of n being close to 1.
Based on the values of SSE as well as the coefficient of determination, we can see that the Langmuir, Redlich-Peterson, and Toth models provide a higher goodness of fit than the Sips and Freundlich models (Table 8).
To compare models with the same parameters and experimental points, SSE or R 2 are frequently utilized to estimate the goodness of fit.As a result, it is obvious that the experimental data fit the Langmuir model better than the Freundlich model.However, for models with a different degree of freedom, Akaike's information criterion [44] is used instead.
Table 9 shows the comparison of the Langmuir model with other models in the study.e value of ER (15.1, 15.8, 28.6, 1875.1)indicates that the Langmuir model is more appropriate than the Toth, Redlich-Peterson, and Freundlich models, implying that the monomolecular-layer nature is prevalent for the adsorption of RDB onto MIL-101.
It is obvious that the piecewise linear regression is a useful approach to analyse the multilinearity.In order to find out the parameters in regression equations, the initial variables should be provided.If the initial variable is as far ree generations were performed, and the RDB adsorption capacity decreases slightly (96.5%) and remained at around 120 mg•g −1 (Figure 10(a)).Furthermore, MIL-101 seems to be stable under adsorption conditions since the

Conclusions
MIL-101 was synthesized using the hydrothermal process.e particle size of MIL-101 could be controlled by adjusting the molar ratio of HF/H 2 BDA.MIL-101 can serve as a useful adsorbent for RDB under batch conditions.e synthesized MIL-101 material displays high adsorption capacity and can be reused.Piecewise linear regression allows to objectively analyse the experimental data using Weber's intraparticle di usion and pseudo-kinetic adsorption models during the sorption process.e results of kinetic analysis suggested that the mechanism of the sorption of RDB on MIL-101 might take place throughout the three steps: (i) lm di usion that dominates at the beginning of the process, (ii) chemisorption that monitors the subsequent period of the process, and (iii) intraparticle di usion, where the adsorption signi cantly slowed down.e best t of the pseudo-rstorder kinetics with three segments with the experimental data is consistent with the analysis of the three-step adsorption process using Weber's intraparticle di usion model.Akaike's information criterion was employed to compare di erent isotherm models with a di erent degree of freedom.e equilibrium data of RDB onto MIL-101 tted well to the Langmuir model rather than the Freundlich, Sips,   12 Journal of Chemistry Toth, and Redlich-Peterson models.As the change of Gibbs free energy was negative and accompanied by the positive standard entropy change, the adsorption process was spontaneous with high affinity.

Figure 2 :
Figure 2: TEM images of MIL-101 synthesized with di erent molar ratios of HF/H 2 BDC.

1 )Figure 6 :Figure 7 :
Figure 6: (a) Plots of the three-linear-segment regression of intraparticle di usion model; (b) e ect of stirring speed on the adsorption capacity of RDB on MIL-101.

Figure 8 :Scheme 2 :
Figure 8: (a) E ect of pH on adsorption capacity; (b) the point of zero charge determined using the pH drift method.

Figure 9 :
Figure 9: Plot of adsorption isotherms of RDB on MIL-101 using di erent models.

Table 2 :
Comparison of piecewise models of one, two, three, and four linear segments using AIC for Weber's model.

Table 3 :
Parameters of Weber's three-linear-segment model (the values in parentheses are 99% con dence intervals).

Table 5 :
Kinetic parameters of three-nonlinear-segment regression for pseudo-first-order kinetic model of RDB adsorption on MIL-101.

Table 6 :
AIC C values of the different kinetic models.
go wrong due to nding the local minimum.is problem needs to study further.In this study, using AIC is proved to be e ective for evaluating the goodness of t for models which have a di erent number of parameters and experimental points.However, the application of AIC in adsorption led is limited.Clari cation of the meaning behind the AIC should be clari ed.

Table 8 :
Parameters of isotherm models.K L , K F , K T , K R , or K S

Table 9 :
Comparison of the Langmuir model with others using evidence ratio (ER).