1 Introduction

The uses of dyes in industrial fields are one of the most important causes of environmental pollution. These dyes cause toxicity and an effect on living organisms (Yagub et al. 2014; Safa et al. 2014). Eriochrome Black T (EBT) is an azo dye that utilizes in the textile industry, but the presence of this dye in drinking water can lethal to human health caused to its poisonous and carcinogenic nature, due to its chemically stable structure (Vaiano et al. 2017; Ajitha et al. 2018). The removal of EBT from water is extremely difficult because of its chemical stability and high water solubility (Boudouaia et al. 2019). Many techniques used to get rid of the dye such as photocatalytic (Sharma et al. 2010), oxidation and Fenton process (Bedoui et al. 2009), membrane technology (Hassanzadeh et al. 2017) and ultrasonic-assisted degradation (Sisi et al. 2020). Compared to other technologies, adsorption technology is easy, environmentally friendly (Chiban et al. 2011), effective and less expensive (Dave et al. 2011).

The continuous development of nanotechnology and its use in removing environmental pollution has increased the interest in using metal oxides nanoparticles as effective surfaces in adsorption technology (Dhawale et al. 2018). Aluminum oxide nanoparticles is an inexpensive surface that has many properties that make it an effective surface in dye removal since it has a high surface area, surface reaction, good absorption capacity, surface acidification and many hydroxide groups (Banerjee et al. 2019).

The study of all adsorption parameters needs to do many experiments and this takes time so we used a central composite designed to reduce the number of practical experiments method and find the interacting influences between the operating factors. Usually, the central composite design (CCD) is used with surface response methodology (RSM) to find optimal conditions and improve the adsorption process (Boudrahem et al. 2019; Garba et al. 2016). Langmuir and Freundlich isotherm conducted to reach the best understanding of potential adsorbent for removal colored dye (Hassani et al. 2015a, b).

The most important points mentioned by the research are:

  1. (a)

    The CCD used to verify the impact of adsorbent dosage, temperature and pH on the adsorption of BET on Al2O3 nanoparticles

  2. (b)

    The appropriate isotherm selected based on the error function values

  3. (c)

    Comparing the results with the previous studies

2 Materials and Methods

2.1 Apparatus

UV–visible spectrophotometer (Cary 100, VARIAN company, USA), pH meter (pH 211, Hanna, USA), XRD (6000, SHIMADZU, Japan) and a shaking water bath (BS-11, lab companion, Korea) were used in this study.

2.2 Chemicals

As an adsorbate, Al2O3 nanoparticles (Hongwu International Group, China) of 99.5% purity and 10–30 nm diameter (shown in Fig. 1) were used. Eriochrome Black T dye has been supplied by BDH. For pH adjustments, 0.01 N HCl (BDH, England) and 0.01 N NaOH (Merck, Germany) were used.

Fig. 1
figure 1

XRD of standard Al2O3 nanoparticles

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2.3 The Experimental Design and Data Analysis

The removal percentage (R%) of experimental values and predicted values were obtained by using a central composite design (CCD) to find the optimum conditions for removal of EBT onto Al2O3 nanoparticles (Table 1) (Pucarevic et al. 2017).

Table 1 CCD matrix used in the present study
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Table 2shows the levels and range of three important parameters, namely weight of Al2O3 nanoparticles surface (X1), pH (X2) and temperature (X3) chosen for this study as optimized factors.

Table 2 Variables and levels considered for removal EBT
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Twenty experiments (N = 20) were conducted by applying CCD design for three parameters as the following equation:

$$N = 2^{3} + \left( {2 \times 3} \right) + 6 = 20$$
(1)

where (2 × 3) is axial points, 23 is factorial points and 6 is central points (Haffad et al. 2019; Ali and Ahmed 2017).

The coded variables are expressed as (± 1) for the factor points, (± α) for the axial points and (0) for the center points. The test factors are coded as the following (Sivarajasekar et al. 2018):

$$\chi_{i} = \frac{{\alpha \left[ {2X_{i} - \left( {X_{\hbox{max} } - X_{\hbox{min} } } \right)} \right]}}{{X_{\hbox{max} } - X_{\hbox{min} } }}$$
(2)

where i is the ith variable, \(X_{\hbox{max} }\) is the highest limits, \(X_{\hbox{min} }\) is the lowest limits, \(X_{i}\) is the natural value and finally, χi is the dimensionless coded value (Table 2) (Khataee et al. 2010).

2.4 Adsorption Studies

Adsorption processes using EBT dye have been estimated according to various adsorption factors, such as weight of Al2O3 nanoparticles, pH and temperature. For this purpose, A weighed of Al2O3 nanoparticles (0.25 g) were mixed with a 10 mL of (25 mg/L) dye solution in 10mL volumetric flask. Flasks containing the EBT solution and the surface of Al2O3 nanoparticles were agitated at a constant time 20 min by using a shaking water bath, which was more than enough to achieve equilibrium.

The experiments of isotherm studies were done with four different initial concentrations of dye (25, 35, 45 and 55 mg/L) at different temperatures (35, 45, 55 °C). The final concentration of dye after an adsorption process was determined by using a UV–visible spectrophotometer at 530 nm.

Defined the amount of EBT adsorbed at equilibrium (qe) and its removal percentage (R %) as shown in Eqs. (3) and (4) (Abbas et al. 2019; Hami et al. 2019):

$$q_{\text{e}} = \frac{{\left( {C_{o} - C_{e} } \right)V}}{m}$$
(3)
$$R\% = \frac{{\left( {C_{o} - C_{e} } \right)}}{{C_{o} }} \times 100$$
(4)

where V (ml) = volume of EBT, Co (mg/L) = initial concentration of EBT, m (gm) = weight of Al2O3 nanoparticles surface, Ce (mg/L) = final concentration of EBT after an adsorption process.

To describe adsorption process properties, Langmuir and Freundlich isotherm models were suggested for this study (Table 3).

Table 3 Langmuir and Freundlich isotherm equations
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2.5 Error Function

Five mathematically error functions used in this study are listed in Table 4. The aim to use error functions to measure the goodness-of-fit of isotherm models. In error functions equations, n (4) = number of experimental data points,\(q_{cal.}\) = calculated EBT dye concentration obtained from isotherm model, \(q_{exp.}\) = experiment dye concentration and p (2) = number of parameters in each Langmuir and Freundlich isotherm model.

Table 4 Error functions list
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3 Results and Discussion

3.1 XRD Analysis

The crystalline size of the standard gamma Al2O3 nanoparticles was checked and determined by X-ray meter (Ebrahimia et al. 2019). The conditions of X-ray Diffraction analysis are: scan range = 10–120°, λCu = 1.5405Å, tube voltage = 40 (kV), and finally, tube current = 30 (mA).

Debye–Sherrer equation was used to find the means size of Al2O3 nanoparticles (Hassani et al. 2015a, b):

$$D = \frac{0.9\lambda }{\beta \cos \theta }$$
(5)

where λ = 1.5406 (X-ray wavelength), β = FWHM (the line broadening at half of maximum intensity), θ = the Bragg angle.

The mean crystalline size of the standard Al2O3 nanoparticles was obtained 30 nm (Fig. 1).

3.2 Development of Model and Effect of Factors on EBT Removal

Table 1 shows the design matrix containing the factors which effected on the removal of EBT dye on Al2O3 nanoparticles surface. The optimum conditions to achieve a maximum percentage of dye removal of 98.8 were obtained under the optimum wt of Al2O3 nanoparticles 0.25, pH of 7 and temperature 45 °C (Fig. 2). The results obtained from Table 1 are evaluated with CCD coupled with RSM for the development of the regression equation for the suggested model’s (Agarwal et al. 2016).

Fig. 2
figure 2

UV–Vis absorption spectrum for removal of 25 mg/L EBT by using Al2O3 nanoparticles at wt of surface 0.25, pH of 7 and temperature 45 °C. The inset shows the photographies taken for (25, 35, 45 and 55 mg/L) EBT before and after adsorption process

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The final CCD obtained for percentage removal (R %) of EBT dye by using Al2O3 nanoparticles surface was suggested by Minitab software and is given as (Dehghani et al. 2018):

$$\begin{aligned} R\% & = - 21.0 + 74.6x_{1} + 8.71x_{2} + 3.20x_{3} - 54.5x_{1}^{2} - 0.7241x_{2}^{2} \\ & \quad - \;0.0373x_{3}^{2} - 4.12x_{1} \times x_{2} - 0.19x_{1} \times x_{3} + 0.0424x_{2} \times x_{3} . \\ \end{aligned}$$
(6)

From above equation, the individual factors increased EBT dye removal by Al2O3 nanoparticles surface (positive coefficient values), while the double factors (except \(x_{2}\) × \(x_{3}\)) decreased dye removal (negative coefficient values) (Garba et al. 2016).

Figure 3shows the experimental value plotted versus predicted value. In this figure, there are tendencies in the linear regression fit and the fitted regression equation showed a good fit of the CCD model (Gengec et al. 2013).

Fig. 3
figure 3

Comparisons of the removal% of experimental value plotted versus the predicted values

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The ANOVA of EBT removal is listed in Table 5, the F value of the model is 9.18 and the p value of the model is 0.001 (less than 0.05) indicating that the CCD model is significant. In this case, the p values of the \((x_{1} )\), \((x_{2}\) × \(x_{2}\)) and \((x_{3}\) × \(x_{3} )\) are less than 0.05 on the removal of dye; this means that the EBT removal capacity increases with the increase in these factors and most significant effect, followed by individual factors (pH and temperature). The “F value of the lack-of-fit” of 1.57 refers to that the lack-of-fit is not significant relative to the pure error. There is 89.21% chance that “F value of the lack-of-fit” is significant. This large value of F could be caused by noise. So, it can be concluded that wt of Al2O3 nanoparticles \((x_{1} )\) play an important role in dye removal (Asfaram et al. 2015; Nekouei et al. 2017).

Table 5 ANOVA for the removal of EBT dye by CCD model
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The high value of regression coefficient R2 (0.8921 for EBT removal) indicated that 89.21% of the total variation on EBT removal data can be described by the CCD model.

The 3D surface plots easy the determination of the main factors influencing the removal of EBT (Khataee et al. 2010). For the weight of Al2O3 nanoparticles between (0.15 and 0.35 g) and pH 6 (the temperature is kept constant at 45 °C), 3D-RSM (Fig. 4a) shows the highest dye removal (over 90%).

Fig. 4
figure 4

3D surface plots for EBT removal (R%) onto Al2O3 nanoparticles surface: a effect weight of Al2O3 nanoparticles surface/pH (temperature 45 °C); b effect weight of Al2O3 nanoparticles surface/temperature (pH 7); c effect pH/temperature (weight of Al2O3 nanoparticles surface 0.15 g)

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The adsorption process for removal of EBT onto Al2O3 nanoparticles was endothermic in nature because of EBT removal capacity increased with increasing temperature from 35 to 55 °C when the weight of surface 0.25 and pH of 7, as shown in 3D-RSM plots (Fig. 4b, c).

3.3 Isotherm Study and Error Functions

Langmuir and Freundlich models were employed for describing the relationship between EBT and Al2O3 nanoparticles surface at equilibrium (Table 6). The monolayer adsorption of EBT onto the surface of the nanoparticles homogeneous Al2O3 is called Langmuir isotherm (Ali et al. 2017), while multilayer formation of EBT onto the heterogeneous solid Al2O3 nanoparticles surface is called Freundlich isotherm. In the Freundlich isotherm model, adsorption capacity (n and k) are Freundlich constants. The weak adsorptive forces are effective on the surface of Al2O3 nanoparticles when Freundlich constants have the lower fractional value of 1/n [0 < (1/n) < 1] (Khalid and Zubair 2018). The values of five mathematically error functions and regression coefficient (R2) are listed in Table 6. Based on the values of Table 6, it seems that the high value of (R2) for the Langmuir model makes it more adequate to adjusting the adsorption isotherms of EBT dye onto Al2O3 nanoparticles. A similar result may be observed from the values used in this study for the five error functions. The error functions show that all values are minimum for Langmuir rather than Freundlich, indicating that Langmuir is the best model for this study. The monolayer adsorption capacity (qm) of treated Al2O3 nanoparticles is found to be 3.831 mg/g. This means that commercially available and inexpensive Al2O3 nanoparticles can be used as an adsorbent for the removal of EBT dye from its aqueous solution (Fig. 5).

Table 6 Linear isotherm constants for adsorption of EBT onto Al2O3 nanoparticles at 45 °C (wt of surface 0.25 and pH of 7)
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Fig. 5
figure 5

Linear isotherm for adsorption of EBT onto Al2O3 nanoparticles at 45 °C (wt of surface 0.25 and pH of 7) a Langmuir and b Freundlich

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3.4 Comparison with Other Studies

The comparison of the removal percentage (R %) of EBT onto different adsorbents surfaces is listed in Table 7. It shows that this work has larger R % than those mentioned in previous studies.

Table 7 Comparison of removal percentage (R%) with other adsorbents in the literature
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4 Conclusions

In this study, removal of EBT was achieved by using Al2O3 nanoparticles as a cheap and commercially available surface. The effect of the weight of Al2O3 nanoparticles, pH and temperature were investigated by using CCD coupled with RSM. The Minitab software showed that the optimum removal of 89.21% was obtained at wt of Al2O3 nanoparticles, pH and temperature of 0.25 g, 7 and 45 °C, respectively. The results of R2 and error functions showed that the Langmuir isotherm was the best-fitted isotherm model.