Title: Using response surface methodology to optimize the operating parameters on the sorption of cadmium and surface area of the adsorbent
S.Meski1,2✉Emailsamira.meski@univ-bejaia.dz
H.Khireddine2Emailhafit.khireddine@univ-bejaia.dz
1
A
Faculté des Sciences de la nature et de la vie, Département de biotechnologieUniversité de Bejaia06000BejaiaAlgérie2Faculté de Technologie, Département de Génie des Procédés, Laboratoire de Génie de l’EnvironnementUniversité de Bejaia06000BejaiaAlgérie
S. Meski1,2*, H. Khireddine2
1.Faculté des Sciences de la nature et de la vie, Département de biotechnologie, Université de Bejaia,06000, Bejaia, Algérie.
2. Faculté de Technologie, Département de Génie des Procédés, Laboratoire de Génie de l'Environnement, Université de Bejaia,06000, Bejaia, Algérie.
Corresponding author : samira.meski@univ-bejaia.dz
2 hafit.khireddine@univ-bejaia.dz
Abstract
In this study, the adsorption of cadmium ions from aqueous solution onto hydroxyapatite was investigated. A series of apatite powders were synthesized under varying conditions of reaction time, reaction temperature and calcination temperature. In addition, the surface area (SBET) of each synthetized powders were measured. To model and optimize both the cadmium adsorption efficiency and the surface area of the prepared apatite, response surface methodology (RSM) was employed.
three variables were considered such as: reaction time (time: 1–96 h), reaction temperature (TSol: 20–70°C) and calcination temperature (TCal: 45–655°C). The pH reaction was fixed at 9. The regression models developed showed good agreement with the experimental data, as indicated by high R2 values, confirming the adequacy of the fitted models.
The optimal conditions for achieving the maximum surface area (SBET) of 98 m2/g were found be: calcination temperature (TCal) of 354.26°C, reaction temperature (TSol) of 41.036°C and maturation time of 48h. For cadmium adsorption, the maximum adsorption yield was obtained for TCal = 235°C, TSol = 17.5°C and time = 48h.
In the second step, anew parameter such as reaction pH was introduced to study its effect on cadmium removal. The results indicated that when the pH exceeded 9, cadmium removal efficiency decreased, while the maximum adsorption was observed at pH = 8.5.
Keywords:
cadmium
Doehlert matrix
hydroxyapatite
statistical modeling
Sorption
1. Introduction
A
Industrials wastes and fertilizers can introduce excessive amounts of heavy metals into the environment. Even at very low concentrations, heavy metals are highly toxic and pose a serious menace to the environment and human health (Prodipto Bishnu Angon et al, 2024). Among these, cadmium is considered one of the most harmful to human health. It can enter the human body through food (65%), water (20%) and air (15%). Continuous exposure to cadmium may lead to severe health effects such as encephalopathy, kidney damage, and other systemic disorders (Agniezka Ruczai et al, 2023). Several methods have been proposed and tested for the removal of toxic metals from wastewater, including chemical precipitation, ion exchange, membrane filtration, and electrochemical treatment (M, Benalya, 2022, L. Hao-Jie et al, 2025, C. Fostop et al, 2025, R. Yang et al, 2025). However, due to techno-economic considerations, many of these methods have limited large –scale applicability. Biosorption has emerged as a promising alternative for the removal of heavy metal ions, offering a cost-effective and eco-friendly solution (A. Othman et al, 2022, K.F.Lam et al, 2007d Bailey et al, 1999).
Hydroxyapatite (HAP), which is represented by the formula Ca10(PO4)6(OH)2, has received much attention recently due to its potential for use as bioactive bone substitute (S. Mondal, 2023 and J. J. Yoo, 2014). It is one of the most studied calcium phosphate compounds because of its excellent biocompatibility and bioactivity, making it widely used as a bone substitute in biomedical applications. It also is used industrially in sensors (P.Kanchana et al, 2014), fluorescence materials (P. Li et al, 2013), chromatography (Y. Murrakami et al, 2013), phosphorus recovery; and drug delivery systems (N. Safitri et al, 2023). However, due to its crystal structure and chemical composition, hydroxyapatite exhibits a high ion exchange capacity for heavy metals ions (A. Corami et al, 2008), making it suitable for environmental remediation.
In the present work, hydroxyapatite synthesized from the calcium carbonate was used for the sorption of cadmium ions from aqueous solutions. Many factors may influence the adsorption capacity and the surface area of the synthesized apatite, including reaction time, reaction temperature, calcination temperature and pH. These parameters were studied and optimized using Doehlert experimental design, a powerful tool of response surface methodology (RSM).
2. Materials and methods
2.1. Powder synthesis
A series of apatite powders were prepared by the precipitation method by following the steps below:
A solution of the calcium carbonate was obtained by the dissolution of 25.0225 g of CaCO3 (98% purity) in 350 mL of distilled water.
In the second step, the solution of the phosphate was prepared by the dissolution of 19.809 g of (NH4)2HPO4 (98% purity) in 150 mL of distilled water.
Subsequently, a solution of (NH4)2HPO4 was slowly added to the solution of CaCO3.The reaction processed following the equation:
In all experiments, the reaction time, reaction temperature and the calcination temperature are fixed at the values presented in Table 1. The pH of the reaction medium is kept constant (pH = 9) by addition of NH4OH ammonia solution. The stirring is set at a speed of 300 rpm by means of a magnetic stirrer. The white solids collected by filtration were open dried, crushed (0.335 mm) and calcined at a desired temperature. The calcination was performed in the following heating schedule: 10 ◦C/min up to the desired temperature and a plateau with a residence time at this temperature of 3 h. Then, it was cooled down at 10 ◦C/min to room temperature.
Table 1
2.2. Characterization of the adsorbent
To study the crystallinity of the prepared samples, powder X-ray diffraction (XRD model PHILIPS X pert prof, analytical, system MPD) patterns were recorded using CuK_ radiation at 50 kV and 100 mA.
Fourier transform infrared spectrophotometry (SHIMADZU-8300 IR-TF) analysis was performed to identify the presence of functional groups in the samples.
Surface morphologies of the powders synthesized were observed by employing a scanning electron microscope (FTI QUANTA 200) with an accelerating voltage of 5 kV.
The specific surface area (SBET) was evaluated from the N2 adsorption isotherms by applying the Brunauer and al. equation in the relative pressure (p/p0) range and taking am (i.e., the average area occupied by a molecule of N2 in the completed monolayer) to be equal to 16.2 A°2.
The results were plotted using the ORIGIN-6 software.
2.3. Batch mode studies
Batch equilibrium experiments were carried out at room temperature using a standard procedure. Cadmium ions solutions were prepared by dissolving cadmium nitrate tetra hydrate (Cd(NO3)2,4H2O) in distilled water. A volume of 250 mL of cadmium solution with an initial concentration of 100 mg/L was placed in 500 mL reaction bottles. The initial pH of the solution was adjusted to 5 using either 0.1 N nitric acid or a dilute potassium hydroxide solution.
A known amount of sorbent (1 g/ 250 mL) was added to each bottle. The mixtures were agitated on a mechanical shaker at 250 rpm for two hours to ensure equilibrium. The adsorbents were separated by filtration and the cadmium concentration in the filtrate was determined using an atomic absorption spectrophotometer (Shimadzu AA 6500 with air/ acetylene (C2H5) flame).
The adsorption yield of cadmium Y(%) was defined by:
Where C0 and Ct represent, respectively, the cadmium concentrations before and after adsorption (mg/L).
2.4. Statistical method
Response surface methodology and the Doehlert’s experimental design (Doehlert, 1970) was used in this work to study the synthesis parameters influencing the properties of apatite. This method allows for the fitting of a quadratic polynomial surface and it helps to optimize the effective parameters with a minimum number of experiments, while also enabling the analysis of interactions between variables (B. Bjaoui Kefi et al, 2023). The total experimental domain can be explored efficiently, as the number of required experiments depends on the number of independent variables (k), following the relation:
N = k2 + k + 1
In order to compare the effects of the different factors across the experimental domain, coded variable (xi) were used as the independent variables in the regression analysis. These coded values were then transformed into their natural values using the relations follow (S. MESKI et al 2011).
Where Ui is the value of natural variable (or real value), U0i is the central value of natural variable i, 𝛥U is the increment that can be calculated from Eq. (4), max denotes maximum value.
Different factors can influence the adsorption of cadmium (YCd (%)) and the surface area (SBET (m2/g)) of the synthesized apatite. Preliminary works realized in our laboratory using a factorial design allowed us to identify the most influential experimental variables and determine the appropriate levels for each factor. Three factors were chosen (Table 1): reaction time (X1), reaction temperature (x2) and calcination temperature (X3). Fifteen experiments, including three repetitions at the center point, were carried out as shown in Table 2.
Variables (Xi) | Experimental levels | ||
|---|---|---|---|
Low (-1) | Centre (0) | High (+ 1) | |
x1 : maturation time (h) | 1 | 48.5 | 96 |
x2 : Synthesis temperature (TSyn) (°C) | 20 | 45 | 70 |
x3 : Calcination Temperature (TCal) (°C) | 45 | 350 | 655 |
Coded matrix | Real matrix | Responses | |||||||
|---|---|---|---|---|---|---|---|---|---|
Exp N° | Time (x1) | Tsol (x2) | Tcal (x3) | time (h) U1 | Tsol (°C) U2 | Tcal (°C) U3 | SBET (m2/g) | YCd (%) | |
1 | 0 | 0 | 0 | 48.5 | 45 | 350 | 94 | 97.278 | |
2 | 1 | 0 | 0 | 96 | 45 | 350 | 78 | 93.81 | |
3 | 0.5 | 0.866 | 0 | 72.5 | 66.65 | 350 | 43.077 | 86.626 | |
4 | -0.5 | 0.866 | 0 | 24.75 | 66.65 | 350 | 44.053 | 87 | |
5 | -1 | 0 | 0 | 1 | 45 | 350 | 42 | 94 | |
6 | -0.5 | -0.866 | 0 | 24.75 | 23.35 | 350 | 65.519 | 97.772 | |
7 | 0.5 | -0.866 | 0 | 72.25 | 23.35 | 350 | 67.378 | 97.03 | |
8 | 0 | 0 | 0 | 48.5 | 45 | 350 | 98 | 95.55 | |
9 | 0.5 | 0.289 | 0.816 | 72.75 | 52.225 | 598.88 | 12.79 | 72 | |
10 | -0.5 | 0.289 | 0.816 | 24.75 | 52.225 | 598.88 | 14.08 | 87.132 | |
11 | 0 | -0.577 | 0.816 | 48.5 | 30.575 | 598.88 | 48.5 | 88 | |
12 | 0.5 | -0.289 | -0.816 | 72.25 | 37.775 | 101.12 | 36 | 97.03 | |
13 | -0.5 | -0.289 | -0.816 | 24.75 | 37.775 | 101.12 | 45.674 | 92.803 | |
14 | 0 | 0.577 | -0.816 | 48.5 | 59.425 | 101.12 | 62.56 | 75 | |
15 | 0 | 0 | 0 | 48.5 | 45 | 350 | 95 | 97.3 | |
| Doehlert experimental matrix and experimental results. | |||||||||
Table 1
Table 2
The correlations between the independent variables and the responses were estimated by using a second- order polynomial Eq. 6, based on the least-squares method, as shown below:
3. Results and discussion
3.1. XRD analysis of the simples
The X-ray crystallography analysis for the 13 hydroxyapatites sample prepared in this study is presented in Figure.1.
Figure.1
The X-ray diffraction patterns of the thirteen powders are similar, and all samples are identified as hydroxyapatite (S. Meski et al, 2011). However, the presence of minor impurities such as bruchite (CaHPO4, 2H2O), vaterite (CaCO3), and lime (CaO) was also detected in all samples.
At a fixed pH (pH = 9), the increase of the maturation time, synthesis temperature and calcination temperature leads to the appearance of a new of hydroxyapatite peaks. Furthermore, the diffraction lines corresponding to the (002), (211), (112) and (300) planes become more intense and resolute, indicating an improvement in the crystallinity of the apatite structures.
3.2. FT-IR analysis of the simples
The FT-IR spectra obtained (Figure.2) show that all the powders exhibit identical spectral features, confirming the presence of the characteristic functional groups of hydroxyapatite, (a) Bands of H2O molecules: The broad band at 3748 cm–1 corresponds to the ν3 and ν1 stretching modes of hydrogen-bonded H2O molecules. Additionally, the band at 1630 cm–1 is attributed to the bending vibration of water molecules and the OH group within the hydroxyapatite structure.
a.
b) The bands et 1064 cm–1 and approximately 1037cm–1 are assigned to the ν3 asymmetric stretching modes of PO43−. The band at 614 cm–1 corresponds to the ν4 bending mode, and the band at 474 cm-1 is associated with the bending ʋ2 vibration of the PO3 − 4 group (S. MESKI, 2023). A Band in the 1423–1440 cm− 1 region is attributed to components of the ν3 asymmetric stretching mode of CO32–, indicating the partial substitution of phosphate groups by carbonate ions.
b.
(c) The group of weak bands observed between 870 cm–1 and 876 cm–1 is attributed to the ν2 bending mode of CO32−.
Figure .2
3.4. Morphology of the samples
The SEM images of hydroxyapatite powders prepared at different experimental conditions are presented in Fig. 3.
Figure. 3
The scanning Electron Micrograph (Figure.3) shows phosphatic particles with irregular forms at different sizes. The powders exhibit a highly porous structure with a mixed morphology consisting of both plate-like and rounded particles.
3.5. Response models and validation
The experimental results obtained from the cadmium adsorption tests and specific surface area measurements are summarized in Table 2. The coefficients of the response surface models were estimated using the following second-order polynomial equation, based on the least-squares method (S. MESKI et al, 2011):
Where:
ß: denotes the column matrix of the regression coefficients;
X: is the matrix of coded variables;
Y: is the column matrix of experimental values of response.
: was the dispersion matrix;
Xt : was the transpose matrix.
The coefficients values of the studied model are grouped in the Table 3, 4. In order to verify the significance of each coefficient, the student’s t- test was applied using the following equation (A. Nilchi, 2006):
Factor | Coefficients | Sbj | tj | Signifiance |
|---|---|---|---|---|
b0 | 96.186 | 0.321 | 298.974 | S |
b1 | -1.825 | 0.278 | 6.552 | S |
b2 | -7.244 | 0.278 | 26.002 | S |
b3 | -2.027 | 0.278 | 7.280 | S |
b12 | -1.538 | 0.643 | 2.391 | NS |
b13 | -8.396 | 0.71 | 11.678 | S |
b23 | 10.638 | 0.718 | 14.799 | S |
b11 | -4.605 | 0.508 | 9.053 | S |
b22 | -2.218 | 0.508 | 4.360 | S |
b33 | -15.620 | 0.481 | 32.410 | S |
Factor | Coefficients | Sbj | tj | Signifiance |
|---|---|---|---|---|
b0 | 95,666 | 2,501 | 38,238 | S |
b1 | 2,739 | 2,166 | 1,264 | NS |
b2 | -11,834 | 2,166 | 5,462 | S |
b3 | -14,043 | 2,165 | 6,485 | S |
b12 | -1,636 | 5,004 | 0,327 | NS |
b13 | 5,709 | 5,591 | 1,021 | NS |
b23 | -37,740 | 5,590 | 6,751 | S |
b11 | -45,666 | 3,955 | 11,544 | S |
b22 | -38,993 | 3,956 | 9,856 | S |
b33 | -67,336 | 3,748 | 17,965 | S |
Where:
bj : Is the coefficient
Sbj: The standard deviation of each coefficient. It is calculated by the following relation (K. Yetilmezso, 2009):
Cjj: Was the diagonal term of
matrix
S2rep : the error mean square.
Where:
Y0i: Observed value of response at the central point;
: is the average value of Y0i;
m: The number of experiments in the central point (reproctubility).
The results of Sbj and tj values for the two responses are presented on the Table 3 and Table 4.
Table 3
Table 4
At a 95% confidence level and with 2 degrees of freedom (f = m − 1), the tabulated t-value tTab was found to 4.32. All effects values (Tables 3 and 4) presenting t-values lower than 4.32 were considered statically non-significant and were then eliminated from the model.
The correlation between the cadmium adsorption yield and the specific area SBET with respect to the synthesis parameters of the adsorbent is expressed by the following equations:
3.6. Validation of the models
The significance of the regression models was evaluated using the Fischer test (F-test), calculating according to the following equation(K. Yeltimezsoy, 2009):
Where
: The average of the experimental values.
Yi: Experimental value of the response;
i: Predicted value of the response;
N: Number of experiment;
λ: Number of the significance parameters.
The F-ratio obtained for both regression models are presented in Table 5.
Response | YCd (%) | SBET (m2/g) |
|---|---|---|
FExperimental | 4.875 | 45.24 |
f1 = λ-1 | 8 | 6 |
F2 = N-λ | 6 | 8 |
Ftab(f1, f2) | 4.15 | 3.58 |
Table 5
..
The Fisher values obtained for both regression models are higher than the corresponding tabulated F-value, indicating that the mathematical models provide a good fit to the experimental data.
Another equation of the Fischer test can be used to evaluate the model’s adequacy. This test allows us to determine whether the reproducibility variance and the residual variance can be considered as statistically equivalent. The latter is calculated using the following equation (K. Yetilmezsoy, 2009):
Where:
Sres2 : The residual mean square;
f1 and f2: Degree of freedom
The results obtained were presented in Table 6.
Response | YCd (%) | SBET (m2/g) |
|---|---|---|
FExp | 16.19 | 6,03623 |
f1 = N-λ | 6 | 8 |
f2 = m-1 | 2 | 2 |
Ftab(f1, f2)(p = 0.05) | 19.33 | 19.37 |
| Fischer values obtained for the two responses | ||
Table 6
According to the results obtained, the F-ratio is lower than the tabulated value in both cases, the fitness can be considered satisfactory.
3.7. Correlation coefficient
The values of the correlation coefficient R2 and the adjusted R2, calculated using the equations (16) [(S. Ait ali 2023), are presented in Table 7.
Responses | YCd (%) | SBET (m2/g) |
|---|---|---|
R2 | 0.931 | 0.978 |
Adjusted R2 | 0.921 | 0.981 |
| R2 and adjusted R2 values for the two responses. | ||
Exp N° | X1 | X2 | X3 | X4 | YCd (%) |
|---|---|---|---|---|---|
1 | + | 0 | 0 | 0 | 97,278 |
2 | + 1 | 0 | 0 | 0 | 93,81 |
3 | + 0.5 | + 0.816 | 0 | 0 | 86,626 |
4 | -0.5 | + 0.816 | 0 | 0 | 87 |
5 | -1 | 0 | 0 | 0 | 94 |
6 | -0.5 | -0.816 | 0 | 0 | 97,772 |
7 | + 0.5 | -0.816 | 0 | 0 | 97,03 |
8 | + 0.5 | + 0.289 | + 0.816 | 0 | 95,55 |
9 | -0.5 | + 0.289 | + 0.816 | 0 | 72 |
10 | 0 | -0.577 | + 0.816 | 0 | 87,132 |
11 | + 0.5 | -0.289 | -0.816 | 0 | 88 |
12 | -0.5 | -0.289 | -0.816 | 0 | 97,03 |
13 | 0 | + 0.577 | -0.816 | 0 | 92,803 |
14 | 0.5 | + 0.289 | + 0.204 | + 0.791 | 75 |
15 | -0.5 | + 0.289 | + 0.204 | + 0.791 | 74,76 |
16 | 0 | -0.577 | + 0.204 | + 0.791 | 97,3 |
17 | 0 | 0 | -0.612 | + 0.791 | 88 |
18 | 0.5 | -0.289 | -0.204 | -0.791 | 78,8 |
19 | -0.5 | -0.289 | -0.204 | -0.791 | 90,596 |
20 | 0 | 0.577 | -0.204 | -0.791 | 96,535 |
21 | 0 | 0 | + 0.612 | -0.791 | 97,03 |
Table 7
All coefficient values obtained for the two responses are close to one, indicating that both models provide a good fit to the experimental data.
3.8. Graphical analysis of the model
Different types of graphs can be used to interpret the equation of the empirical model. In the context of experimental design, this representation typically takes two main forms: the response surface and iso-response curves. However, before proceeding with these graphical representations, it is essential to assess the descriptive quality of the empirical model. The construction adequacy graph serves this purpose.
3.8. a. Model adequacy graph:
The model adequacy graph is constructed using a scatter plot, where the X-axis presents the variation of the measured response (experimental), and represents the y-axis the variation of the response calculated (predicted) from the model obtained. The resulting plot (Figure. 4) shows that the closely aligned along the first bisector, which confirs the model’s ability to accurately predict the response. This alignment indicates that the statistical model provides a reliable fit to the experimental data.
Figure.4
3.8. b. The response surface
The response surface and contour plots illustrating the relationship between the experimental variables and the efficiency of cadmium removal (YCd), as well as the evolution of surface area (SBET), are presented in Figure.5 and 6.
Figure.5 represent the iso response curve corresponding to SBET as a function of calcination temperature (TCal) and solution temperature (TSol). On this plot, the contour lines represent constant response values and indicate the predicted surface area (SBET) for each combination of the design variables. It is clear from the plot that increasing temperature leads to a decrease in surface area, while lower calcination temperature favor larger SBET values. These findings are consistent with those reported by (C. Verwilghen, 2007).
A response surface can be used to determine optimal factor settings that maximize or minimize the response, or to define a range of factors levels produce similar response values.
From the obtained equation, it was possible to deduce the coordinates of the maximum point of the surface, which corresponds to the point where the SBET achieves a more elevated value. So that, solving the equation, indicate that the maximum surface area (SBET) occurs when the synthesized temperature (TSol) is 41.036°C and the calcination temperature (TCal) is 354.26°.
Figure.5
The Fig. 6.a. shows the interaction effect between variables X1 and X3 on cadmium sorption yield. The removal efficiency of cadmium increases with the calcination temperature up to approximately 300°C. However, beyond 450°C, the adsorption yield decreases as the calcination temperature continues to rise. In this domain of calcinations temperature (300–450°C), no significant effect of contact time on cadmium sorption was observed.
The increase of adsorption yield with increase of calcination temperature TCal from 100 to 350°C can be attributed to the removal of moisture and the increase in the number of available active sites on the prepared apatite surface.
Figure 6.b shows the combined effect of reaction temperature and calcination temperature on the cadmium adsorption yield on the powder prepared with a reaction time of 48.5 hours.
An increase in reaction temperature results in a decrease in the cadmium removal capacity of the prepared powders. It is clear from the figure that the maximum response lies outside the experimental design space. Therefore, it would be necessary to shift the initial experimental design, if possible, in order to reach the optimum conditions.
Figure.6
3.9. Effect of reaction pH on the sorption yield of cadmium
Boehlert’s method represents a different approach compared to other experimental designs. The experimental points uniformly fill the experimental space, forming a hexagon in two dimensions (when two factors are studied) or a "hyper-hexagon" when more than two factors are involved. This method allows for an optimal organization of experiments, improved efficiency and the flexibility to expand the experimental domain or add new factors without having to repeat previously conducted experiments (Sergio Ferreira, 2003).
The only precaution is to maintain the levels of unstudied factors constant while analyzing the effects of other factors. This feature makes the Doehlert design sequential and open facilitating the progressive acquisition of experimental information. To further explore the influence of operating parameters, we introduced a new variable- the pH of the reaction- to study its effect on cadmium adsorption yield within the range (7 ≤ pH ≤ 11). The mathematical model used for of the response surface design is a second-order polynomial. For four variables, the model is given by the following equation:
The new matrix and the results obtained are presented in the Table. 8
Table.8
After validating the model using the same method as in the first part of the study, the following equation was obtained:
The comparison between the experimental adsorption yields obtained and those predicted by Eq. 21 is presented in Fig. 7. The coefficient of determination (R2 = 0.826 indicates that approximately 18% of the total variation is not adequately explained by the model.
Figure.7
The iso-response curves generated from the model are presented in Fig. 8. (a, b and c).
Figure 8.a shows the effect of maturation time and reaction pH on cadmium removal (with Tcal=350°C and Tsol = 45°C) whereas Fig. 8.b shows the combined effect of reaction temperature and pH on cadmium removal yield (with time = 48.5 h and Tcal = 350°C).
The cadmium removal was observed to increase with pH in the range of 7 to 9.5, followed by a slight decrease at higher pH levels.
Figure 8.c indicates that cadmium removal increased significantly with both pH and a second variable (likely temperature or time, depending on context) within the range of 250 to 500 value.
It is possible to calculate the coordinates of the maximum point by taking the first derivative of the mathematical function that describes the response surface and setting it equal to zero. The quadratic function obtained for two variables (Tcal and pH) is described below:
Thus, to calculate the coordinates of the critical point, it is necessary to solve the first order system formed by Eqs. (22) and (23) to determine the values of X3 and X4 values. the maximum adsorption yield is obtained when the calcinations temperature (TCal) is 365°C and the pH is 8.36.
Figure.8
Conclusions
The experimental design used in this study proved to be an effective mathematical tool for optimizing the experimental results. It allowed for the validation of the model and the rapid determination of the optimal values for the process variables. The present work demonstrated the applicability of this approach in determining the optimal conditions for enhancing cadmium removal and increasing the surface of the synthesized apatite. A second-order polynomial equation was found to be suitable for predicting the responses studied specific surface area (SBET) and cadmium adsorption yield (YCd). This was confirmed by the high values of the coefficient of determination (R2) and the adjusted R2, indicating a strong fit between the model and the experimental data.
The analysis revealed that reaction temperature and calcinations temperature had significant effects on both SBET and YCd, whereas reaction time showed no notable influence. Furthermore, the interactions between the process parameters were found to significantly affect both the cadmium adsorption yield and the surface area of the synthesized apatite.
Finally, by use of response surface methodology enabled the determination of optimized conditions under which both SBET and YCd reached their maximum values
A
A
Author Contribution
Samira MESKI conceived and designed the study and conducted the experiments and collected data. Hafit khireddine, erformed data analysis and prepared Figures
References
A
Agnieszka Ruczaj, Małgorzata Michalina Brzóska (2023) Environmental exposure of the general population to cadmium as a risk factor of the damage to the nervous system: A critical review of current data. J Appl Toxicol 43:66–88AitAli S, Ziani S, Yahiaoui I, Brahmi A, Boudrahem F, Aissani-Benissad F (2023) Application of central composite design and response surface methodology for the study of extraction of gentian violet dye in aqueous solution by polystyrene membrane modified with oleic acid. Environ Prog Sustainable Energy 42:e14200
Bejaoui Kefi B, Nefzi Kh, Koumba S, M’Hamdi N, Martin P (2023) Application of Doehlert Experimental Design for Optimization of a New-Based Hydrophilic Interaction Solid-Phase Extraction of Phenolic Acids from Olive Oils. Molecules 28:1073
Benalia MC, Youcef L, Ghrissi Bouaziz M, Achour S, Menasra H (2022) Removal of Heavy Metals from Industrial Wastewater by Chemical Precipitation: Mechanisms and Sludge Characterization. Chem Eng 47:587–599
A
Charern tanyarak L (1999) Heavy metals removal by chemical coagulation and precipitation. Water Sci Technol 39:135–138Corami A, Mignardi S, Ferrini V (2008) Cadmium removal from single- and multi-metal (Cd + Pb + Zn + Cu) solutions by sorption on hydroxyapatite. J Coll Inter Sci 317:402–408
A
Cyrille Ghislain F, Lieb A, Scheffler F (2025) Tailoring the water vapor adsorption properties by thermal performance analysis of post-synthetically ion-exchanged LTA zeolite derived from Cameroonian kaolin. J Ind Eng Chem. https://doi.org/10.1016/j.jiec.2025.08.017A
Ferreira Sérgio LC, Bezerra MA, Dos Santos WNL, Benıcio BN (2003) Application of Doehlert designs for optimisation of an on-line preconcentration system for copper determination by flame atomic absorption spectrometry. Talanta 61:295–303Hao-Jie Q, Ming Zh S, Ji R, Wu, Yuki Y, Yu Qin Y-Y, Li (2025) Fouling dynamics varied by filtration cycles in high-solid anaerobic membrane bioreactors for sewage sludge treatment. J Environ Manag 392:126659
Kanchana P, Lavanya N, Sekar C (2014) Development of amperometric l-tyrosine sensor based on Fe-doped hydroxyapatite nanoparticles. Mater Sci Eng C 35:85–91
Lam KF, Yeung KL, McKay G (2007) Efficient Approach for Cd2+ and Ni2+ removal and recovery using mesoporous adsorbent with tunable selectivity. Environ Sci Technol 41:3329–3334
Li P, Yao A, Zhou Ti WD (2013) Fabrication of N-acetyl-l-cysteine-capped Cd Se-polyelectrolytes and Hydroxyapatite Composite Microspheres for Fluorescence Detection of Cu. Ions J Mater Sci Techno 29:1104–1110
Meski S, Ziani S, Khireddine H, Yataghane F, Ferguene N (2011) Elaboration of the hydroxyapatite with different precursors and application for the retention of the lead. Water Sci Techno 63:2087–2096
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Meski S, Bibba Ou, Khireddine H, Boudjouan F, Djermoune A, Yala S, Ziani S (2025) Removal of methylene blue and brilliant yellow from aqueous solutions using sodium metasilicate modified hydroxyapatite derived from Algerian phosphate rocks. J Disper Sci Technol 46:861–874A
Murakami Y, Sugo K, Yoshitake T, Hirano M, Okuyama T (2013) Large-scale preparation and characterization of zinc-substituted hydroxyapatite for metal affinity chromatography. Sep Purif Techno 103:161–166A
Nilchi A, Maalek B, Khanchi A, Ghanadi MM, Bagheri A, Savoji K (2006) Ion exchangers in radioactive waste management: natural Iranian zeolites. Appl Radiat Isot 64:138–1433Othmani A, Magdouli S, Senthil Kumar P, Kapoor As Padmanaban Velayudhaperumal Che, Gökkuş O (2022) Agricultural waste materials for adsorptive removal of phenols, chromium (VI) and cadmium (II) from wastewater: A review. Environ Res 204:111916
Prodipto Bishnu A, Md SI, Shreejana KC, Arpan Das, Nafisa A, Amrit P, Shaharia Akter Su (2024) Sources, effects and present perspectives of heavy metals contamination: Soil, plants and human food chain. Heliyon 10:e28357
A
Ruirui Y, Haifang W, Xu Zhu, Zhumei S (2025) Review on electrochemical processes for the treatment of heavy metal complexes in wastewater: Performance, mechanism, application and improvement. Int J Electrochem Sci 20:100971Safitri N, Nurlaela R, Dahlang T (2023) Enhancing drug loading and release with hydroxyapatite nanoparticles for efficient drug delivery: A review synthesis methods, surface ion effects, and clinical prospects. J Drug Deliv Sci Technol 90:105092
A
Sudip M, Sumin P, Jaeyeop C, Vu TTH, Vu Hoang MD Truong Tien Vo, Byeongil Lee, Junghwan Oh (2023), Hydroxyapatite: A journey from biomaterials to advanced functional materials. Adv Colloid Interface Sci 321: 103013A
Verwilghen C, Rio S, Nzihou A, Gauthier D, Flamant G, Sharrock P (2007) Preparation of high specific surface area hydroxyapatite for environmental applications. Mater Sci 42:6062–6066A
Yetilmezsoy K, Demirel S, Vanderbei RJ (2009) Response surface modeling of Pb(II) removal from aqueous solution by Pistacia vera L.: Box–Behnken experimental design. J Hazard Mater 171:551–562A
Yoo JJ, Hee J, Kim Seo SM, Sik, Oh K (2014) Preparation of a hemi porous hydroxyapatite scaffold and evaluation as a cell-mediated bone substitute. Ceram Inter 40:3079–3087A
Funding
The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.
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Data Availability
All data generated or analyzed during this study are included in this published article.
Competing interests
The authors declare no competing interests.
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Fig. 1
X-ray diffraction patterns of the powders synthesized.
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Fig. 2
FTR spectra of the powders synthesized
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Fig. 3
SEM image for the powders prepared.
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Fig. 3
SEM image of the powders synthesized
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Fig. 4
Correlation between predicted and experimental responses (a) :YCd (%) and (b): SBET (m2/g)
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Fig. 5
Combined effects of synthesized and calcination temperature on the surface area value (SBET).
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Fig. 6
Contour plot for the effect of different variables on cadmium removal
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Fig. 7
Correlation between predicted and experimental responses (YCd (%)).
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Fig. 8
Contour plot for the effect of different interaction between pH and other variables
