Investigation of Dealumination in Phosphate-Based Geopolymer Formation Process: Factor Screening and Optimization

Abstract

In this study, phosphate-based geopolymers obtained from two aluminosilicate precursors with different mineralogical compositions were investigated. The used experimental methods were X-ray fluorescence, X-ray diffraction, atomic absorption measurements and experimental designs. Nine factors influencing the dealumination process during geopolymer formation were screened based on a Plackett–Burman design. The results show that the control factors are the P/Al molar ratio, curing temperature and curing time. These significant parameters were selected for further optimization using a central composite design. It was found that regardless of the used P/Al molar ratio, curing temperature and curing time increases generate an increase in the response. However, the P/Al molar ratio variation strongly affects Al removal only at low curing temperatures (between 22 and 50 °C) and with short curing times (between 0.2 and 3 h). The curing time parameter is the most significant factor. In addition, the same percentage of liberated Al can be achieved either by increasing the curing temperature in the earliest steps of geopolymer formation or by prolonging the curing time, even at low curing temperatures. Finally, the optimal conditions allowing maximum aluminum release are P/Al molar ratio = 2.0, curing temperature ≈ 70 °C and curing time = 4.76 h.

1. Introduction

In the last several decades, Earth’s resources have become more and more limited. In fact, their excessive exploitation and the corresponding extraction processes have led to environmental degradation and a climate emergency. In 2019, Pierrehumbert [1] declared that “With regard to the climate crisis, yes, it’s time to panic”. Thus, resource efficiency issues inevitably require solutions in order to decouple resource use from environmental degradation and improve economic development. One of the proposed crucial alternatives is the use of geopolymers. This new type of material allows the efficient valorization of several aluminosilicate resources, such as clays [2,3], or industrial by-products such as fly ash [4,5,6], mining residues [7], concrete waste [8] and blast furnace slag [9]. In addition, geopolymers present an ecological character and improve green production. This character is manifested in the absence of CO₂ and harmful gas emissions during its fabrication [10,11,12]. This advantage has increased the demand for the use of this material, especially in the industrial field, due to increased global pollution problems. Moreover, the possibility of synthesizing a material with high performance and ecological character at atmospheric pressure and at a temperature below 100 °C [12] gives it an economic character. Thus, the investigation of geopolymers has attracted the attention of researchers and scientists in the last several decades. One of the related topics that are fundamental to investigate is the comprehension of the geopolymeric reaction, especially the dealumination process, which represents the first and one of the more monitored steps in all geopolymerization processes [13]. It is premised on the release of aluminum from the aluminosilicate precursor until its reaction with phosphoric acid [12,13]. The investigation of factors that it influences represents an interesting issue to study due to its importance and its effects on the structure, properties and formation mechanism of phosphate-based geopolymers.

In fact, the Al released from aluminosilicate precursors reacts with the phosphate ions liberated from the dissolved phosphoric acid [14,15,16]. As a result, different phosphate-based phases are formed, mainly aluminum phosphate phases [16,17,18]. These new phases play the role of reinforcement in the obtained blended composite geopolymer and consequently ensure its favorable properties [16,19]. Therefore, factors influencing dealumination systematically affect the structure of reinforced phosphate-based geopolymers and their properties. In addition, the dealumination process generally constitutes a monitoring step in the mechanism and formation kinetics of geopolymers [13,19,20]. Therefore, any factor that influences this process will strongly affect these two material properties.

In relation to phosphate-based geopolymer composite materials, many factors can be investigated, as presented in the literature [21]: The first one is the P/Al molar ratio (with Al = number of aluminum moles derived from the alumina-silicate precursor, and P = number of phosphorus moles derived from phosphoric acid). Several works have revealed the dependence of phosphate-based geopolymers on this factor [18,22,23]. The second proposed factor is the curing temperature. The noteworthy effect of this factor on geopolymer properties has been confirmed in different works that studied similar varieties of materials, such as fly-ash-based geopolymers [24]. The third factor that can be investigated is the curing time. The literature demonstrates few works that proved the effect of this factor on alkali-based geopolymers [25]. In addition to these factors, the aluminosilicate particle size can represent a substantial factor in this research work. Many studies have proved the dependence of different material properties on this factor [14,26,27]. According to preliminary tests, the conditions of the mold used during heating (opened or closed) can represent another factor to be studied in this work. In addition, the acidic solution, which can be prepared immediately or 24 h before the reaction with the aluminosilicate precursor, can have an effect on dealumination owing to the energy released during the mixing of acid with water and the endothermic character of the studied process. Another factor that can be considered in this work is the chemical composition of the aluminosilicate precursor. The used precursor can have a mineralogical composition rich in different oxides, such as Tunisian local clays [28], or it can be free of them [29], such as pure kaolin. Researchers have also investigated the effect of adding other different chemical elements to the starting aluminosilicate precursor composition, such as calcium [30], to achieve better material properties. The calcination of the aluminosilicate precursor also represents one of the main factors to be studied. Generally, the used aluminosilicate precursor should be calcinated to ameliorate its reactivity [31]. In addition, the pH of the starting mixture can perhaps be a significant factor in any chemical synthesis. For the elaboration of phosphate-based geopolymers, this factor has not yet been studied, owing to the difficulty of its control.

Thus, this work has two objectives: the first one is the screening of the above-mentioned different factors that can influence the dealumination process in phosphate-based geopolymer formation. The second one is the optimization of the significant factors to determine the optimum values of each factor. It is worth noting that whereas researchers in the civil engineering field focus on maximum dealumination to obtain the maximum reinforcement and better compressive strength in the long term, researchers in the medical field focus on the minimum free aluminum in the obtained geopolymers. In fact, it can present a real danger to the human body after material implantation.

2. Materials and Methods

2.1. Raw Material Characterization and Geopolymer Preparation

Two different aluminosilicate precursors were used in this study: natural Tunisian clay and kaolin provided by Imerys, France.

These two used aluminosilicate precursors differ in their chemical composition, as proved by X-ray fluorescence element analysis and X-ray diffraction. According to X-ray fluorescence element analysis, illustrated in

Table 1. Chemical composition of the used aluminosilicate precursors.

Type of Aluminosilicate Precursor	Kaolin	Natural Tunisian Clay
Oxides	%mass	%mass
Al2O3	47	31.12
SiO2	51.91	49.03
CuO	0.01	3.94
Fe2O3	0.56	6.72
K2O	0.03	4.57
MgO	0.0.4	2.38
Cao	0.01	2.15
P2O5	0.04	0.09

, kaolin has a mineralogical composition free of impurities. It is essentially composed of silicon and aluminum oxides. However, natural Tunisian clay is characterized by a mineralogical composition rich in different oxides. First, the significant percentage of iron (Fe₂O₃ = 6.72%), which is responsible for the clay’s red color, proves the probable presence of hematite in its composition. In addition, we can note that the alkali content (K₂O = 4.57%) in this clay is relatively high, which reflects the presence of illite. Finally, the existence of oxides of magnesium (MgO = 2.38%) and calcium (CaO = 2.15%) can indicate the presence of dolomite.

The analysis of the Tunisian clay XRD diffractogram (Figure 1a) shows that this precursor is composed of two clay minerals, namely, kaolinite (Al₂O₃ 2SiO₂ 2H₂O) and illite (k (Al₄Si₂O₉ (OH)₃). In addition, it proves the propositions deduced fromthe X-ray fluorescence analyses, which suggest the presence of quartz (SiO₂), gypsum (CaSO₄.2H₂O), muscovite ((K, Na) (Al, Mg, Fe)₂) (Si_3.1, Al_0.9) O₁₀ (OH)₂, hematite (Fe₂O₃) and dolomite (Ca Mg (CO₃)₂).

However, the XRD diffractogram of kaolin (Figure 1b) proves the presence of kaolinite mineral (Al₂O₃ 2SiO₂ 2H₂O) only. This result again confirms the purity of this clay and the absence of associated minerals in its chemical composition.

The presence of different minerals in the starting geopolymeric mixture can represent a potential factor that influences the geopolymeric process and properties, hence the justification for using the two aluminosilicate precursors in this study.

In addition, a commercial phosphoric acid (H₃PO₄, 85%) provided by the Scharlau-chémie (SA) Society was used.

In accordance with each assembly, the corresponding aluminosilicate precursor was mixed with the corresponding phosphoric acid solution concentration. The obtained mixture was kept at the curing temperature throughout the heating time chosen for the studied assembly. The calcination of aluminosilicate precursors was carried out at 750 °C for 3 h in a static bed oven.

2.2. Methods

2.2.1. Chemical Experimental Methods

To characterize the used aluminosilicate precursors’ chemical compositions, X-ray fluorescence spectrometry (ARL 8400, Malvern Panalitycal, Gabes cement plant, Gabes, Tunisia) was used. In addition, X-ray diffraction (XRD) (the National School of Engineers of Sfax, Laboratory of advanced materials, Sfax, Tunisia) with a BRUKER-AXS-D8-Advance powder diffractometer using Cu Ka radiation (λka = 1.5418 Å) was carried out on the two corresponding specimens. The analytical range was between 5° and 70° (2θ) at a rate of 1°/min. Crystallographic phases were identified with High Score Plus software.

The atomic absorption technique was used in order to quantify the concentration of the released aluminum percentage. The protocol adopted is as follows: For each experiment, the corresponding geopolymeric mixture was filtered under vacuum, and then the solid residue obtained was rinsed with distilled water in order to extract all of the aluminum atoms. Finally, the Al concentration of the filtrate was measured using an Analytik Jena AG-ZEEnit 700 atomic absorption spectrometer, taking into account the effect of dilution.

2.2.2. Experimental Designs

• Plackett–Burman design

To ensure the screening of the main factors, a Plackett–Burman design was used. This design allows the study of k factors through N experiments (N ≥ k + 1), where N must be a multiple of 4. The different factors tested in this study are summarized in

Table 2. Considered factors for the Plackett–Burman design and their high and low levels.

Factors Levels	Coded Variable	Lower Level (−1)	Higher Level (+1)
P/Al molar ratio	X1	0.5	2
Curing temperature	X2	25 °C	85 °C
Curing time	X3	1 day	7 days
Aluminosilicate particle size	X4	≥63 µm	≤63 µm
Mold’s condition	X5	Opened	Closed
Acidic solution	X6	A *	B **
Nature of aluminosilicate precursor	X7	Kaolin	Natural Tunisian clay
Calcination of aluminosilicate precursor	X8	With	Without
pH of starting mixture	X9	Low (between 1 and 3)	High (between 4 and 5)

* Prepared immediately. ** Prepared 24 h before mixing with aluminosilicate precursor.

with their high and low levels. In view of the fact that the number of factors used in this work was fixed at 9, a design consisting of 12 experiments (N = 12) was used, as illustrated in

Table 3. Experimental matrix.

N° Exp	X1	X2	X3	X4	X5	X6	X7	X8	X9
1	1	1	−1	1	1	1	−1	−1	−1
2	−1	1	1	−1	1	1	1	−1	−1
3	1	−1	1	1	−1	1	1	1	−1
4	−1	1	−1	1	1	−1	1	1	1
5	−1	−1	1	−1	1	1	−1	1	1
6	−1	−1	−1	1	−1	1	1	−1	1
7	1	−1	−1	−1	1	−1	1	1	−1
8	1	1	−1	−1	−1	1	−1	1	1
9	1	1	1	−1	−1	−1	1	−1	1
10	−1	1	1	1	−1	−1	−1	1	−1
11	1	−1	1	1	1	−1	−1	−1	1
12	−1	−1	−1	−1	−1	−1	−1	−1	−1

.

In this design, each experiment contained only either a + 1 or −1 value foreach variable corresponding to the high and low levels of natural variables, respectively. According to the Plackett–Burman design rules, none of the twelve experiments was similar to the other [32]. For each experiment, the measured response was recorded.

The corresponding mathematical model is a first-degree polynomial described by Equation (1):

ŷ = b₀ + ∑_j=1b_jX_j

(1)

Where b₀ is the average value of the responses.

Coefficient b_j represents the effect of factor X_j.

The model coefficients were estimated by the least squares method to fit the model to the experimental results obtained in the design points.

• Central composite designs

The central composite design (CCD) with independent variables was followed to optimize the potential factors and to check the response patterns. The ranges of the studied parameters, which had been determined in preliminary tests, are presented in

Table 4. Experimental range and level of independent variables.

Independent Variables	Variable Symbol	Domain Center	Variation Step
P/Al molar ratio	X1	2	0.8
Curing temperature (°C)	X2	50	15.5
Curing time (h)	X3	3	1.6

.

The central composite design leads to the optimization of the experiment number in addition to the consideration of possible interactions between the studied factors and their effects on the measured response [33]. In light of the results of the Plackett–Burman design and preliminary tests, the factors and their levels were selected for the central composite design. Three significant factors were chosen for further study and are identified as X₁, X₂ and X₃, respectively. The corresponding experimental matrix is presented in

Table 5. Experimental matrix.

N° Exp	X1	X2	X3
1	−1	−1	−1
2	1	−1	−1
3	−1	1	−1
4	1	1	−1
5	−1	−1	1
6	1	−1	1
7	−1	1	1
8	1	1	1
9	−1.6818	0	0
10	1.6818	0	0
11	0	−1.6818	0
12	0	1.6818	0
13	0	0	−1.6818
14	0	0	1.6818
15	0	0	0
16	0	0	0
17	0	0	0
18	0	0	0
19	0	0	0
20	0	0	0

with corresponding ranges and levels of independent variables. Figure 2 presents the geometry of the central composite design with these three design factors.

For the central composite design (CCD), the selected experimental points are based on:

• A 2³ complete factorial design (N_F = 8 experiments carried out at the corners of the cube);
• Six axial points at a distance of ±α from the center. The distance a is calculated so as to obtain rotatability. A three-variable central composite design is rotatable if:

  A = ±(N_F)^1/4 = ±1.6818
• Six replicates at the center point in order to estimate pure error.

This experimental design permits the modeling of a second-order equation (Equation (2)):

ŷ = b₀ +∑_jb_jX_j + ∑_j,kb_jkX_jX_k + ∑_jb_jj X_j²

(2)

where y is the measured response, b₀ represents the constant, b_j, b_jk and b_jj are the regression coefficients, and X_j and X_k are coded values of the independent factors.

A total of 20 experiments were necessary to determine the different coefficients of the previous model. For the estimation of the central composite model errors, the central design point was repeated six times. The validity and reliability of the model were verified by a statistical test called analysis of variance (ANOVA). The regression analysis of the experimental design and the quadratic polynomial model were obtained using Nemrod W software [34,35,36,37].

It is worth noting that the other six factors (other than the control factors) are used in this plan at the levels that improve dealumination, according to the Plackett–Burman design.

3. Results and Discussion

3.1. Screening of Factors Influencing Phosphate-Based Dealumination Process Based on Plackett-Burman Design

Table 6. Plackett–Burman experimental plan.

N° Exp	P/Al Molar Ratio	Curing Temperature	Time of Heating	Particle Size	Mold’s Condition	Acidic Solution	Nature of Aluminosilicate	Calcination	pH	% of Released Al
1	2	85	1 day	≤63	Closed	B	Kaolin	With	Low	11
2	0.5	85	7 days	≥63	Closed	B	Natural Tunisian clay	With	Low	10
3	2	25	7 days	≤63	Opened	B	Natural Tunisian clay	Without	Low	13
4	0.5	85	1 day	≤63	Closed	A	Natural Tunisian clay	Without	High	5
5	0.5	25	7 days	≥63	Closed	B	Kaolin	Without	High	5
6	0.5	25	1 day	≤63	Opened	B	Natural Tunisian clay	With	High	2
7	2	25	1 day	≥63	Closed	A	Natural Tunisian clay	Without	Low	9
8	2	85	1 day	≥63	Opened	B	Kaolin	Without	High	7
9	2	85	7 days	≥63	Opened	A	Natural Tunisian clay	With	High	16
10	0.5	85	7 days	≤63	Opened	A	Kaolin	Without	Low	13
11	2	25	7 days	≤63	Closed	A	Kaolin	With	High	13
12	0.5	25	1 day	≥63	Opened	A	Kaolin	With	Low	2.5

presents the experimental plan for the screening design. Each line of these tables presents a specific experiment. In addition, each of the 12 experiments is different from the others. The first column shows the experiment number, and the last column shows the recorded response. Each of the other columns (from column 2 to column 10) is reserved for a specific factor.

The model coefficients were obtained by applying the least squares method. The statistical mathematical model, which represents the response (% of released aluminum), is presented in Equation (3):

ŷ = 8.87 + 2.63X₁ + 1.46X₂ + 2.79X₃ + 0.63X₄ − 0.04X₅ − 0.88X₆ + 0.29X₇ − 0.21X₈ − 0.88X₉

(3)

The influence of the studied factors on the percentage of the released Al is presented in the bar graph of the effects, illustrated in Figure 3.

In this graph, the area of each bar is proportional to the effect of the corresponding factor. The design results show that the most significant effects correspond to the P/Al molar ratio (X1), curing temperature (X2) and reaction time (X3) factors. In addition, the effects of these three factors are characterized by their positive contributions, which implies that passage from the negative level (−1) to the positive one (+1) generates an increase in the % of released Al. Thus, in order to maximize this %, it is recommended to use these factors in their positive states (+1), and to minimize this %, it is recommended to use these factors in their negative (−1) states. In addition to the significant factors, there are other factors that have a more modest effect. For example, we can cite aluminosilicate particle size (X4), the preparation of the acidic solution (X6) and the pH of the starting mixture (X9). Concerning the aluminosilicate particle size, the smaller the particle size, the more favorable the dealumination. In fact, the clay reactivity increases considerably with the decrease in its particle size due to the increase in its grain specific surface [14]. The preparation of the acidic solution and the pH of the starting mixture present negative effects on the measured response. Thus, using them at their low levels promotes dealumination. Indeed, the dissolution of phosphoric acid presents an exothermic reaction, which releases energy. This energy is able to favor dealumination (endothermic reaction, which requires heating to be favored and accelerated) [13]. In addition, the decrease in the pH of the starting mixture allows its increase in the medium. As a result, the attack of Al-based bonds will easily take place.

According to the Pareto diagram shown in Figure 4, we can conclude that:

• The curing time factor predominates, and the relatively high sensitivity of the response to this factor (41.32%) shows that the % of the released Al is highly dependent on this factor. This is well expected and justified. Indeed, when the reaction time is prolonged, the probability of protonating the bonds increases, and dealumination becomes more favored [13,38]. Subsequently, the different stages of geopolymerization will have the necessary time to take place successively.
• The P/Al molar ratio factor contributes 36.53% to the sensitivity of the response. Indeed, the increase in this factor means, firstly, the increase in the concentration of phosphoric acid as an activating solution and, secondly, the decrease in the pH of the reaction medium. These two conditions favor the dealumination process as well as the other stages of geopolymerization.
• The curing temperature factor contributes 11.27% to the sensitivity of the response. Indeed, dealumination, like any breakage of chemical bonds, requires energy [39]. Thus, by providing heat, the % of released Al increases systematically.

Besides these factors, the acidic aluminosilicate precursor solution preparation (X6), the pH of the starting mixture (X9) and the aluminosilicate precursor particle size (X4) influence the % of the released Al, but modestly. Finally, other factors do not have a significant effect on the considered response. Therefore, the effects of the studied factors can be classified as follows: X3 > X1 > X2 >>> X6 > X9 > X4 >>> X7 > X8 > X5.

Finally, based on this screening design, the curing time, the P/Al molar ratio and the curing temperature represent the major factors that control the dealumination process. Thus, these three factors were studied in the central composite design for their optimization.

3.2. Optimization of Selected Variables by Using Central Composite Design

The experimental plan of the central composite experiment design, based on three independent factors with a five-level structure and the % of released Al as the measured response, is presented in

Table 7. Central composite experimental plan.

N° Exp	P/Al Molar Ratio	Curing Temperature (°C)	Curing Time (h)	Released Al (%)
1	1.20	34.50	1.40	2
2	2.80	34.50	1.40	3
3	1.20	65.50	1.40	6
4	2.80	65.50	1.40	5
5	1.20	34.50	4.60	5
6	2.80	34.50	4.60	3
7	1.20	65.50	4.60	16
8	2.80	65.50	4.60	19
9	0.65	50.00	3.00	5
10	3.35	50.00	3.00	0
11	2.00	23.93	3.00	1
12	2.00	76.07	3.00	12
13	2.00	50.00	0.30	2
14	2.00	50.00	5.69	9
15	2.00	50.00	3.00	5
16	2.00	50.00	3.00	5
17	2.00	50.00	3.00	4
18	2.00	50.00	3.00	6
19	2.00	50.00	3.0	7
20	2.00	50.00	3.000	8

.

The broad range of the aluminum percentage removal (from 0 to 19%) demonstrates the need to optimize the liberation conditions. The quadratic polynomial equation (presented in Equation (4)) obtained from the experimental results, which is expressed in coded units, defines the relationship between the independent variables (P/Al molar ratio, curing temperature and curing time) and the studied response (percentage of released Al).

ŷ = 5.75 − 0.54X₁ + 3.77X₂ + 2.84X₃ − 0.63X₁² + 0.78X₂² + 0.43X₃² + 0.38X₁X₂ + 0.12X₁X₃ + 2.62X₂X₃

(4)

Evaluation of Model Adequacy and Validation

The adequacy and validation of the model were carried out by an appropriate analysis of variance (ANOVA), as presented in

Table 8. Analysis of variance.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F0	Test F
Regression	383.3893	9	42.5988	7.7227	**
Residuals	55.1607	10	5.5161
Lack of fit	44.3273	5	8.8655	4.0918	(NS)
Pure error	10.8333	5	2.1667
Total	438.5500	19

** Significant at the level of 99%. NS: non-significant at the level of 95%.

.

• Model Adequacy

The total sum of squares SS_T (with 19 degrees of freedom) is divided into the sum of squares due to regression SS_Reg (with 9 degrees of freedom) and the residual sum of squares SS_Res (with 10 degrees of freedom) (Equation (5)). The method is based on the comparison of variance due to residuals with that of regression, which is addressed by calculating F_Reg (Equation (6)). To obtain a valid model, this value should be higher than the Fisher critical value for a particular confidence level. The principle of this method is widely detailed in similar works [35,40].

SS_T = SS_Reg + SS_Res

(5)

$$F_{Reg}=\frac{\raisebox{1ex}{$S{S}_{Reg}$}\!\left/ \!\raisebox{-1ex}{$d.o.f_{(Reg)}$}\right.}{\raisebox{1ex}{$S{S}_{Res}$}\!\left/ \!\raisebox{-1ex}{$d.o.f_{(Res)}$}\right.}$$

(6)

F_Reg = 7.72 is higher than the Fisher critical value for a confidence level of 99% (F_0.01 (9,10) = 4.94), which means that the regression is good.

• Validation of the Model

The residual sum of squares (SS_Res) can be divided into two parts (Equation (7)).

The first one is due to “pure” experimental error (SS_E), which is calculated as the sum of squared deviations in the center point experiments with 6 − 1 = 5 degrees of freedom. The second part (SS_L.o.f), which relates to the “lack of fit”, can be used to assess the significance of the model. SS_L.o.f is determined with 10 − 5 = 5 degrees of freedom.

SS_Res = SS_E + SS_L.o.f

(7)

The model validation is based on the comparison of variance due to the lack of fit with that of the error, which is addressed by calculating F_L.o.f (Equation (8)). To obtain a valid model, this value should be lower than the Fisher critical value for a 95% confidence level.

$$F_{L.o.f}=\frac{\raisebox{1ex}{$S{S}_{L.o.f}$}\!\left/ \!\raisebox{-1ex}{$d.o.f_{L.o.f}$}\right.}{{\raisebox{1ex}{$S{S}_E$}\!\left/ \!\raisebox{-1ex}{$d.o.f$}\right.}_E}=4.09$$

(8)

The F_L.o.f value is lower than the Fisher critical value for a confidence level of 95% (F_0.01 (5,5) = 5.19). Thus, the variance due to the lack of fit is not significantly different from the pure error variance. Consequently, the model is considered valid.

• Exploitation of the Model

After validation of the model, it is possible to exploit the isoresponse curves (2D) and response surfaces (3D), which are presented in Figure 5, Figure 6 and Figure 7. In each plot, two factors are variable, while the third one is maintained at a constant value of the zero coded level. The shape of these plots permits the comprehension of the interactions of the independent factor level and quality.

Figure 5 presents the trend of Al removal against the coinciding variation in the P/Al molar ratio and curing temperature at a constant curing time equal to 3 h. The corresponding 2D contour plot (Figure 5a) shows that, regardless of the used P/Al molar ratio, the curing temperature increase generates an increase in the liberated Al percentage. In fact, this process involves a bond-breaking reaction, which requires heating to be favored [13,39].

However, the P/Al molar ratio variation affects Al removal in a more modest way, mainly in the high curing temperature range (higher than 50 °C). Generally, increasing this ratio results in an increase in the response until a value of P/Al equal to1.5 is obtained. In fact, the increase in this ratio yields an increase in the reaction medium acidity, which is a measure of all of the aluminum bonds’protonation and breakage. When the optimal molar ratio is achieved, the maximum accessible Al is liberated. Later, the phosphate anions will react with the liberated Al to form new geopolymeric phases. Thus, the percentage of free Al³⁺ decreases.

Figure 5a shows again that the optimal conditions allowing maximum aluminum release are:

• P/Al molar ratio close to 2;
• Curing temperature ≈ 70 °C.

The 3D surface plot, presented in Figure 5, again confirms the important effect of the curing temperature factor variation on the studied response. In addition, it is worth noting that, in the studied conditions, the liberated Al percentage varies between 2 and 14%. This observation coincides with the literature [14,41]. In fact, the dissolution of Al present in the starting aluminosilicate precursor is limited and depends strongly on the Al coordination-type phases [13,19,22]. It essentially concerns the tetra-coordinated phase.

The combined effect of the curing time and P/Al molar ratio on Al removal efficiency at a fixed curing temperature of 50 °C is presented in Figure 6. Here, it can be seen that the efficiency of Al removal depends strongly on the curing time factor, which has a positive effect. In fact, dealumination isa progressive process that requires a considerable period to be achieved. This period is strongly affected by the geopolymer synthesis conditions. Thus, it differs from one research work to another. In this research work, it required more than 5h to complete. In addition, the P/Al molar ratio variation effect is more significant with a low curing time range (between 0.2 and 3 h). As seen in Figure 5a, an increase in this ratio results in an increase in the response until a P/Al molar ratio equal to 1.5 is reached. Later, the increase in this factor negatively affects the measured response. The explanation is the same as that proposed in the previous discussion.

Figure 6a shows that the optimal conditions allowing maximum aluminum release are:

• P/Al molar ratio between 1.5 and 2.5;
• Curing time close to 5 h.

The 3D surface plot, presented in Figure 6b, again confirms the important effect of the curing time factor variation compared to the P/Al molar ratio factor variation on the studied response. This result is in agreement with the results observed with the Plackett–Burman design. In addition, it is worth noting that, in the studied conditions, the liberated Al percentage varies between 2 and 13%. Thus, we are always in the same range of liberation.

The combined effect of curing time and curing temperature on Al removal efficiency, at a fixed P/Al molar ratio equal to 2, is presented in Figure 7. Here, it can be observed that the efficiency of Al removal depends on the curing time and curing temperature factors at the same time. The increase in curing time presents a positive effect on Al removal. This effect becomes more and more considerable at the highest curing temperature values. In fact, at low curing temperatures (lower than 30 °C), there is a kinetic block even after a considerable curing time. Thus, the increase in curing temperature presents a positive effect on Al removal. It is worth noting that we can achieve the same high percentage of liberated Al either by increasing the curing temperature in the earliest steps of geopolymer formation or by prolonging the curing time, even at low curing temperatures.

The 3D surface plot, presented in Figure 7b, again confirms the important effect of the two studied factors’ variation on the studied response. In addition, it is worth noting that, in the studied conditions, the liberated Al percentage can reach 19%. Thus, dealumination is improved.

3.3. Study of the Optimal Path

The analysis of the optimal path makes it possible to determine, for any hypersphere of radius R, centered at the origin of the domain of study, the point where the studied response is optimal: the set of points obtained constitutes the optimal path.

Nemrod software presents the results in the form of graphs (Figure 8) indicating, at each distance from the center of the domain, the optimal value of the response studied, as well as the optimum levels to be attributed to the factors.

For example, if we intend to maximize the % of released Al, the radius of the circle should be 1.68, which corresponds to a maximum response = 19.5 (Figure 8).

Then, we projected the distance 1.68 on curve 1 to obtain the value of the coded variable X₁ = 0, on curve 2 to obtain the coded variable X₂ = 1.3 and on curve 3to obtain the variable corresponding to X₃ = 1.1 (Figure 9). In conclusion, the optimal conditions allowing maximum aluminum release are:

• P/Al molar ratio = 2.0;
• Curing temperature ≈ 70 °C;
• Curing time = 4.76 h.

This result is in accordance with that obtained from the interpretation of the isoresponse curves.

4. Conclusions

This work presents two main objectives: The first one concerns the screening of nine factors influencing the dealumination process during phosphate-based geopolymer formation using a Plackett–Burman design. The second one is to optimize the three significant factors using a central composite design. Based on the above experimental results, the P/Al molar ratio, curing temperature and curing time were defined as the control factors influencing the dealumination process. Moreover, these significant parameters were selected for further optimization. It was found that regardless of the used P/Al molar ratio, curing temperature and curing time increases generated an increase in the response. However, the P/Al molar ratio variation strongly affected Al removal only at low curing temperatures (between 22 and 50 °C) and with short curing times (between 0.2 and 3 h). The curing time factor represented the most significant factor. Additionally, the same percentage of liberated Al can be achieved either by increasing the curing temperature in the earliest steps of the geopolymer formation or by prolonging the curing time, even at low curing temperatures. To end with the determination of the optimal conditions that allowed maximum aluminum release, they were defined as follows: P/Al molar ratio = 2.0, curing temperature ≈ 70 °C and curing time = 4.76 h. Thus, this work allows the dealumination process to be mastered for phosphate-based geopolymers. The aim of future works will be to study the different possible applications of this new kind of material after choosing suitable factor values for each application.