#### Abstract

In the present paper, the adsorption of Astrazon Black AFDL dye onto Vietnamese diatomite has been demonstrated. The diatomite was characterized by XRD, SEM, TEM, EDS, and nitrogen adsorption/desorption isotherms. The results show that diatomite mainly constituted centric type frustules characterized by pores as discs or as cylindrical shapes. The adsorption kinetics and isotherms of dye onto Vietnam diatomite were investigated. The experimental data were fitted well to both Freundlich and Langmuir in the initial concentration range of 400–1400 mg L^{−1}. The average value of maximum adsorption capacity, , calculated from Freundlich equation is statistically similar to the average value of maximum monolayer adsorption capacity calculated from Langmuir equation. The thermodynamic parameters evaluated from the temperature dependent on adsorption isotherms in the range of 303–343 K show that the adsorption process was spontaneous and endothermic. The Webber and pseudo-first/second-order kinetic models were used to analyze the mechanism of adsorption. The piecewise linear regression and Akaike’s Information Criterion were used to analyze experimental data. The results show that the dye adsorption onto diatomite was film diffusion controlled and the goodness of fit of experimental data for kinetics modes was dependent on the initial concentration.

#### 1. Introduction

Dyes are a kind of organic compounds with complex aromatic molecular structures that can cause bright and firm color to other materials. However, the complex aromatic molecular structures of dyes make them more stable and more difficult to be biodegraded [1, 2]. Waste water from the textile industry is often strongly colored even for low dye concentrations. In addition, these molecules lead to high chemical oxygen demand, and they exhibit low biodegradability. An important class of molecules is the azo-dyes, which contain nitrogen atoms as azo functional groups [–N=N–] in their chemical structure. They represent half of the dyes used nowadays in the textile industry [2]. Many treatment systems have been proposed for the removal of synthetic dyes from aqueous solution. Methods based on adsorption [3, 4], biological treatments [5], coagulation, electrochemical techniques [6], membrane processes [7, 8], oxidation/ozonation [9, 10], and photochemical oxidation [11, 12] are known to be effective in the removal of this type of dyes from polluted water. Adsorption is considered to be competitive and economically cost effective and efficient process for removal of dyes and heavy metals. Activated carbon is the most employed adsorbent for toxic species removal from aqueous solution because of well-developed pore structures and a high internal surface area that leads to its excellent adsorption properties [13]. However, the high cost of activated carbon and recycle ability sometimes restrict its applicability for dye removal. Therefore, in recent years, a considerable number of studies have investigated into low cost and efficient alternative materials such as clay [14], diatomite [15], and zeolite [16].

Diatomite, a siliceous lightweight sedimentary rock, has received attention for its unique properties including high porosity, small particle size, large surface area, and chemical inertness and as low cost material for the removal of pollutants from waste water. Several studies have been studied on using diatomite as an adsorbent for removing some contaminants such as heavy metals [17], volatile organic compounds (*o*-xylene) [18], basic dyes (methylene blue) [19], and some textile dyes (Red 3BS, Int Yellow 5GF) [20].

In the present paper, the adsorption of AB dye onto Vietnam diatomite has been demonstrated. The adsorption isotherms and kinetics of AB onto diatomite were studied. The thermodynamic data (, , and ) are calculated from temperature dependent sorption isotherms and are used to evaluate the sorption properties of dye on raw diatomite. Webber’s intraparticle-diffusion model and* pseudo*-first/second-order kinetic models were used to analyze the mechanism of adsorption. AIC and the piecewise linear regression method were used to analyze kinetics data for Webber’s intraparticle diffusion model.

#### 2. Experimental

##### 2.1. Materials

Diatomite sample was supplied as a natural resource from Phu Yen province, Vietnam. After removing organic stuff by repeated sedimentation and desiccation at 100°C, the sample was stored in a desiccator for further usage. Sodium hydroxide (NaOH) and hydrochloric acid (HCl, 39%) were purchased from Sigma-Aldrich. Astrazon Black AFDL (C_{28}H_{28}N_{5}O g mol^{−1}) (denoted as AB) was provided kindly from Thuyduong Textural Company (Vietnam). AB is a cationic dye that belongs to azo-dye group. Its structure is shown in Scheme 1.

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

The point of zero charge () of diatomite was determined by the solid addition method [21]. 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 () of the solution was adjusted from 2.3 to 7.7 by adding either 0.1 M NaOH or 0.1 M HCl. Total volume of solution in each flask was made exactly to 50 mL by adding distilled water. The 0.01 M NaCl solution with different pH value was obtained. Then, 0.1 grams of diatomite was added to each flask and mixtures were stirred for 24 hours; the final pH () of solution was measured. The difference between the initial solution and final solution () was plotted against the . The point of intersection of curve with abscissa, at which ΔpH = 0, provided .

##### 2.3. Isothermal and Thermal Dynamic Studies

For the adsorption isotherm study, add in turn 50, 100, 150, 200, 250, and 300 mg diatomite into 6 stopper 250 mL Erlenmeyer flasks containing 100 mL of AB solution with known concentration (400–1400 mg L^{−1}) and then place them into the shaker bath at °C for 24 hours. Since initial experiments show that the AB dye/diatomite system reached equilibrium around 120 minutes, the adsorption time was prolonged for 24 hours to ensure saturation. Thereafter supernatant liquid was separated by centrifugation and the final dye concentrations were determined by visible spectrophotometry. A series of isothermal experiments were repeated three times.

The amount of the dye adsorbed by the adsorbents was calculated by the equation:where is the amount of dye adsorbed per unit of amount absorbent (mg g^{−1}), is the initial AB concentration (mg L^{−1}), is the dye concentration (mg L^{−1}) after the batch adsorption procedure, is the volume of dye solution (L), and is the mass (g) of the adsorbent.

To describe the adsorption isotherms, the Langmuir and Freundlich models were selected for using in this study.

Langmuir isotherm: the Langmuir equation is valid for monolayer sorption onto the surface. Its linear form could be expressed as follows [17, 22]:where is the maximum monolayer capacity amount (mg g^{−1}), is Langmuir equilibrium constant, is the quantity of AB dye adsorbed per unit of amount absorbent (mg g^{−1}) at equilibrium time, and is the concentration present at equilibrium (mg L^{−1}). The linear plot of * versus * provides the value of and .

The essential characteristics of Langmuir isotherm can be expressed in terms of a dimensionless constant separation factor, , which is performed aswhere the value of indicates the type of isotherm: unfavorable (), linear (), favorable (), or irreversible () [23].

Freundlich isotherm: Freundlich equation is empirical relation based on the sorption onto the heterogeneous surface. Its linear form is commonly represented as [17, 24]where (mg g^{−1}) is the Freundlich constants, which is a measure of adsorption capacity, and is an empirical parameter related to the nature and strength of the adsorption process and the distribution of the active sites. The linear plot of * versus * provides the value of and . Low values of mean that the surface is heterogeneous. For values in the range , adsorption is favorable. Values of between 0.1 and 0.5 represent good adsorption processes, whereas indicates that adsorption capacity is only slightly suppressed at lower equilibrium concentrations [25].

In order to evaluate whether the adsorption process is spontaneous, the thermodynamic parameters of adsorption are studied. Experimental procedure was conducted as an adsorption isotherm study; however, the temperature of process was fixed at 303, 313, 323, 333, and 343 K. The Gibbs free energy of adsorption is given by the relation [17]where is given by Van’t Hoff’s equation:where is equilibrium constant equal to Langmuir equilibrium constant. The linear plot of * versus * gives the value of and .

##### 2.4. Adsorption Kinetics Study

Kinetic studies were carried out in a 3 L plastic beaker. The plastic beaker was equipped with a stainless steel flat blade impeller using an electric motor to stir the dye solution. Diatomite (0.50 g) was mixed thoroughly with 1000 mL of RDB solution in the beaker at room temperature. Ten-millilitre samples were drawn periodically through tap and diatomite was removed by centrifuging process. The final dye concentrations were determined by visible spectrophotometry. The experiments were conducted with various AB concentration in the range of 150–900 ppm. For each concentration, the experiments were repeated three times and the mean value was taken.

In the present paper, two kinetic models and Webber intraparticle-diffusion model were used. The* pseudo*-first-order kinetic model in nonlinear form is Lagergren equation [26, 27] and written as where and are the capacity amount of dye adsorbed at time (min) and at equilibrium time, respectively, and is rate constant of* pseudo*-first-order equation (min^{−1}). and were calculated by nonlinear regression method.

And the* pseudo*-second-order kinetic model in nonlinear form was expressed as follows [28, 29]:where is rate constant of* pseudo*-second-order kinetic equation (g mg^{−1} min^{−1}).

, , and were calculated by nonlinear regression method using Solver function in Microsoft®Excel*™*.

Webber’s intraparticle-diffusion model is described as the following equation [28, 30]:where is intraparticle-diffusion rate constant (mg g^{−1} min^{−0.5}) and is the intercept which represents the thickness of the boundary layer. If intraparticle-diffusion is the rate-limiting step, then a plot of * versus * will give a straight line with a slope that equals and an intercept equal to zero.

##### 2.5. Characterization of Materials

The powder X-ray diffraction (PXRD) patterns were recorded by a D8 Advance, Bruker, Germany, with CuK*α* radiation (*λ* = 1.5406 Å). The morphology and surface composition of diatomite were determined by scanning electron microscope (SEM) and energy dispersive spectroscopy (EDS), respectively, using SEM JMS-5300LV. The textural properties of diatomite were determined by nitrogen adsorption/desorption isotherms using a Micromeritics 2020 volumetric adsorption analyzer system. Fourier transform-infrared (FTIR) measurements were carried out by the KBr method using Shimadzu FTIR 8010M. Visible spectrophotometry was measured by Lambda 25 Spectrophotometer (Perkinelmer, Singapore) at of AB dye (610 nm).

#### 3. Results and Discussion

##### 3.1. Characterization of Diatomite

Figure 1(a) shows the SEM observation and PXRD patterns of diatomite in this study. As observed in Figure 1, the sample of diatomite was mainly formed by centric type frustules which were characterized by notable pores as discs or as cylindrical shapes indicating that there is a good possibility for dyes to be adsorbed into these pores. The chemical analysis by EDS (Table 1) showed that silica represents the major composition (68% wt) and metallic oxides contribute to the rest. PXRD analysis presented in Figure 1(b) indicating that silica occurs under amorphous phase due to very low intensity of PXRD diffraction. The amorphous silica phase is found to be characteristic of the frustule composition as reported in previous studies [30, 31].

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FTIR analyses were performed in the range 400–4000 cm^{−1} as shown in Figure 2. The main absorption bands for diatomite were observed at 3695, 3622, 3421, 2858, 1639, 1153, 1022, 914, 798, 690, 528, and 443 cm^{−1}. The bands at 3695, 3622, and 2858 are attributed to the free silanol group (Si–O–H) and the band at 1639 cm^{−1} corresponds to H–O–H bending vibration of water. The bands at 1153 and 1022 are assigned to the siloxane (–Si–O–Si–) group stretching and the 914 cm^{−1} band represents Si–O stretching of silanol group. The 798 and 690 cm^{−1} bands represent SiO–H vibration. The absorption peaks around 528 and 443 cm^{−1} are attributed to the Si–O–Si bending vibration [32–34].

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Figure 2(b) shows the nitrogen adsorption/desorption isotherm of diatomite. Diatomite sample exhibited type IV isotherm and a H4-type hysteresis loop indicating the presence of the slit-like pore structure [35]. The diatomite with BET surface area around 51 m^{2} g^{−1} and pore volume of 0.0952 cm^{3} g^{−1} is rather higher than those of reported diatomite [34, 36]. The present diatomite, which is composed of amorphous silica, has properties such as high porosity and high surface area indicating a potential absorbent for adsorption.

##### 3.2. pH Effect of Solution on AB Dye Adsorption

Solution pH has a significant influence on the adsorption process because it can influence both the ionisation of pollutants and the ionic state of the functional groups on the surface of adsorbent. As seen in Figure 3, the adsorption capacity of AB onto diatomite increased with the increase in pH. The equilibrium adsorption capacity, , increased from 80.08 to 98.1 mg g^{−1} as pH of the dye solution increased from 4 to 11. The p of diatomite determined by solid addition method is around 5.4 (the inset in Figure 3) which was similar to that of a kind of diatomite as [37]. Thus, it is obvious that the ionisable charge sites on the diatomite surface increased when pH increased from 4 to 11. When the solution pH was below , the diatomite surface had a positive charge, while at high pH (pH > 5.4) it has a negative charge. Hence, when the pH of AB solution increased, the adsorption of AB molecules with positive charge was enhanced as described in

##### 3.3. The Study of Adsorption Isotherm and Thermodynamics

Isotherm studies were conducted to provide information on the capacity of the adsorbents under different concentrations of AB. The equilibrium data were analysed using the Langmuir and Freundlich model. The Langmuir and Freundlich isotherm parameters for AB adsorption onto the diatomite were calculated by plotting of * versus * and * versus *, respectively, and the results are presented in Table 2. The Freundlich equation describes an equilibrium between and and value of increases with an increase in . The maximum adsorption capacity amount is not obtained in Freundlich equation. In the present work, the equilibrium experiments were controlled as if the initial concentration () was kept constant and the diatomite absorbent was varied from 50; 100; 150; 200; 250; and 300 mg L^{−1}. Halsey [38] supposed that the maximum adsorption capacity, , by Freundlich equation could be expressedwhere calculated based on Freundlich equation are also shown in Table 2.

As can be seen in Table 2 both models are very close to coefficients of determination () and favorable characteristic parameters (i.e., for Langmuir isotherm and for Freundlich isotherm). The value () and the value of in the range 0.1–0.5 indicate both isotherms are favorable. In the statistical view the linear regression between * versus * and * versus *, respectively, does have statistical significance because the value of is much smaller than the usually accepted 0.05 significance level ( in all cases) [39]. These results confirmed that the equilibrium data of AB adsorption onto the diatomite could be well fitted by the two adsorption isotherm models. The high correlation to both Langmuir and Freundlich isotherms implies a monolayer adsorption and the existence of heterogeneous surface in the adsorbents, respectively.

For Langmuir model, was known as equilibrium constant which should be constant at specified temperature. is the maximum monolayer adsorption capacity which is thought to be specified for each absorbent. However, the data in Table 2 show that and are not constant at specified temperature but tend to increase as the initial concentration increases. In similar manner, the parameters of Freundlich model were also varied monotonically with the increase in initial concentration in the range of 400–900 mg L^{−1}. As the initial concentration is too high, the large AB aggregates could block the pores of diatomite that result in low adsorption capacity amount. Then, the parameters of models calculated in case of high initial concentration may be uncorrected. In the range of initial concentration from 400 to 900 mg L^{−1}, and are as a function of initial concentration. Pair sample -test was conducted to compare the difference of and . Since value is larger than 0.05 significant level the difference between the average value of ( mg g^{−1}) and the average value of ( mg g^{−1}) is not statistically significant (, ) [38]. It means the value calculated from both isotherm models is statistically similar. The data of maximum adsorption capacity shows that diatomite possesses very high capacity of dye adsorption compared to other minerals as adsorbents [2].

The thermodynamics were studied at 303, 313, 323, 333, and 343 K. At each temperature, were determined through (2) by linear plot of and . The thermodynamic parameters, , , and , of the system were determined using the Van’t Hoff equation to evaluate the spontaneity of the adsorption process. The graph of plotting * versus * provided the linear line in statistical view (, ) (see Figure 5).

The thermodynamic parameters are presented in Table 3. The large and positive value of indicates that adsorption is endothermic process and chemical sorption by nature. The positive value of indicates the increasing randomness at the solid-liquid interface during the adsorption of AB molecules on the diatomite [40]. The higher the temperature the more the negative values of Gibbs free energy, , for AB adsorption on diatomite, which implies that the spontaneity increases with the increase in the temperature. As the Gibbs free energy change is negative accompanied by the positive standard entropy change, the adsorption reaction is spontaneous with high affinity. Based on the values of [41], it is suggested that the AB adsorption using diatomite probably involved a chemical mechanism.

##### 3.4. Kinetic Studies

The effect of contact time on the AB adsorption over diatomite at the initial concentrations in the range of 150–900 ppm was presented in Figure 6. It was observed that the amount of AB adsorbed increased from 71 to 140 mg g^{−1} with an increase in the initial AB concentration from 150 to 400 mg L^{−1}. When the initial AB concentration increased from 150 to 400 mg L^{−1}, the adsorption capacity also rose rapidly, thereafter increasing slightly as reaching 400 mg L^{−1}. The reason for this observation might be the increase in initial dye concentration that enhanced the interaction between AB and diatomite. Moreover, the higher initial concentration provides the higher driving force to overcome all the mass transfer resistance of AB between the aqueous solution and the diatomite surface. As a result, high initial AB concentration will enhance the adsorption process [42]. The low adsorption rate at high AB concentration can be explained by the fact that the active sites are sufficient in diatomite surface at low AB/diatomite ratios. However, as AB/diatomite ratio increases, active sites are saturated, leading to a decline in the adsorption efficiency. The equilibrium time was obtained less than 120 minutes at dye concentration from 150 to 900 mg L^{−1}.

In the present paper, the diffusion kinetics was studied by using Webber’s model. Because the plots of this model often have a multilinear nature, in general, the graphical method is employed to analyze the data in which the linear segments are determined visually [43]. This method is prone to objectivity. Malash and El-Khaiary [43] suggested a statistical method of piecewise linear regression for the analysis of experimental adsorption data to avoid objective estimation. In this process, the experimental data could be fixed for one, two, or three linear segments’ line by Webber’s equation: One linear segment line: (two parameters), Two linear segments’ line: (4 parameters), Three linear segments’ line: (6 parameters),where the values of , , , , , and are estimated by nonlinear regression. and called breakpoints are the boundaries between the segments. The Microsoft Excel “SIGN” function determines the sign of a number and then returns 1 if the number is positive, zero if the number is 0, and −1 if the number is negative. Nonlinear regression estimates the model’s parameters by the method of least squares. This is done by minimizing the sum of squared deviations, SSE, by numerical optimization techniques. The function for minimization is where is experimental datum and is the valued estimated by model.

It can be clear that the number of parameters, , estimated by nonlinear regression is double the number of linear segments. Increasing the number of regression parameters in model almost universally decreases the sum of squared deviations (SSE) or the coefficient of determination (). Therefore, the goodness of fit cannot be based solely on SSE or [43]. In other words, SSE or could not be used to estimate the goodness of fit for two models which have different parameters. In this case, the well-known statistical method used in the comparison of models is based on Akaike’s Information Criterion (AIC) [38]. 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:The values of AICs calculated by (14) are listed in Table 4. Figure 7, for example, illustrates Webber’s plot analyzed by one, two, and three segments’ linear regression models for AB adsorption onto diatomite at initial AB concentration of 200 mg L^{−1}. The linear regression for one segment showed poor compatibility with experimental data. The experimental points are distributed very closely to three or segments’ linear regression model. Table 4 shows that Webber’s model analyzed three segments’ linear regression provides the lowest AICc in comparison with one or two segment models. In conclusion, the experimental data were best fit with the three segments linear regression model.

Results of piecewise linear regression for different initial concentration were obtained from Table 5. For example, for 200 mg L^{−1} concentration it was found that the intercept of the first, second, and third linear segment lines in the Webber plot was 55.26 with 95% confidence limits of 42.42 to 68.10; 78.44 with 95% confidence limits of 76.76–80.10; 89.05 with 95% confidence limits of 88.02–90.08, respectively. 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. Moreover the intraparticle parameters illustrated in Table 3 show that value is irregular as initial AB concentration increases. These results strongly suggest that the AB adsorption on diatomite is controlled by film diffusion or chemical reaction controls the adsorption rate (e.g., surface adsorption and liquid film diffusion) instead of intraparticle diffusion [19, 43]. From Figure 7 the breakpoints for first and second period time are 2.6 and 8.9 min, respectively. They are corresponding to the time where the transition of adsorption stage could occur. It is clear that the curves in Figure 6 presented three distinct stages: (i) immediate adsorption of AB molecules within 2.6 min of the contact times, (ii) gradual attainment of the equilibrium where only about 5–10% of the adsorption is encountered; this is due to the utilization of the all active sites on the adsorbent surface, and (iii) an equilibrium attainment of AB molecules onto diatomite. The same behaviors for other concentration were also observed. It is emphasized that analysis of experimental adsorption data by using piecewise linear regression for Webber’s intraparticle-diffusion models is useful for providing the exact time periods for each diffusion.

In order to determine the rate-limiting step, kinetic models such as* pseudo*-first-order and* pseudo*-second-order equation were employed to evaluate the experimental data. The parameters of kinetics equations (7) and (8) obtained by nonlinear regression method were listed in Table 6. could be used to compare* pseudo*-first-order and* pseudo*-second-order models for the goodness of fit because both models have the same parameters and experimental points. For initial concentration from 200 to 400 the experimental points of the* pseudo*-second-order kinetic model reflected high correlation coefficients () and values agreed with the value indicating that the adsorption may be governed by a* pseudo*-second-order mechanism. This suggests that the rate-limiting step is a chemical adsorption which might be involved in the formation of covalent bonds between AB molecules and diatomite through enabled sharing or exchange of electrons. A chemisorption mechanism only allows for a monolayer adsorption, which is in good agreement with Langmuir model that describes well the equilibrium adsorption data [44]. The* pseudo*-second-order kinetic rate coefficient decreases from 0.040 to 0.009 mg g^{−1} min^{−1} when the initial AB concentration increases from 150 to 600 mg L^{−1}. This behavior was observed by various authors [37, 44]. This could be attributed to the fact that increasing the dye concentration might reduce the diffusion of dye molecules in the boundary layer and enhance the diffusion in the solid [37]. Conversely, high correlation () with the* pseudo* first order was observed at higher initial concentration in the range of 600–900 mg L^{−1} indicating that the AB adsorption process obeys the* pseudo*-first-order kinetic model. At high concentration possible desorption might be occurring where the AB adsorption capacity appears to fluctuate or even reduce as little as shown in Figure 4. This behavior could be attributed to either a reversible adsorption or a back diffusion controlling mechanism [28, 45] indicating that rate-limiting step in this case involved a physical-chemical mechanism and not purely physical or chemical.

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#### 4. Conclusions

The Vietnamese diatomite, which is composed of amorphous silica, has high porosity and surface area. It was studied as an adsorbent for the removal of AB dye from aqueous solution. Solution pH has a significant influence in the adsorption of AB, where the capacity of the adsorbents increases with increasing pH from 4.0 to 11.0. Experimental isothermal data were fitted well to both Langmuir and Freundlich model in the large range of 400–1400 mg L^{−1}. The maximum adsorption capacity, mg g^{−1}, calculated from Freundlich equation and mg·g^{−1} calculated from Langmuir equation, is statistically similar. However, parameters of these equations had an effect remarkably on the initial AB concentrations. Both values of and increase with the increasing initial AB concentration. The free energy of AB adsorption on diatomite is more negative at higher temperature, which demonstrates that the spontaneity increases with the rise of temperature. Piecewise linear regression as a statistical method for the analysis of experimental adsorption data by Webber’s intraparticle-diffusion models provides the time periods for each diffusion and results show that the AB adsorption onto diatomite was film diffusion controlled. The rate-limiting step has effect on the initial AB concentration. The adsorption processes obey the* pseudo*-second-order process in the range of 150–400 mg L^{−1} and the* pseudo*-first-order one in range of 400–900 mg L^{−1}.

#### Competing Interests

The authors declare that they have no competing interests.