Introduction

The construction industry is responsible for a large portion of global carbon dioxide emissions, mainly due to the production of Portland cement. Therefore, alternative binders, such as geopolymers, have gained attention due to their lower environmental impact. Geopolymers are inorganic materials synthesized through the alkaline activation of aluminosilicate sources rich in SiO₂ and Al₂O₃, undergoing a reaction mechanism analogous to polymerization. The resulting structure consists of a three-dimensional Si–O–Al (sialate) network, where SiO₄ and AlO₄ tetrahedra are alternately linked by shared oxygen atoms1. A great advantage of geopolymers, when compared to the use of Portland cement, is the possibility of using industrial waste or by-products2. Examples include glass, melt-tempered aluminosilicates, and natural materials, such as kaolinite and zeolites, volcanic ash, clays from deterrents countries and composites woods3,4 and industrial by-products, such as mining waste, ceramic waste5 or even mixtures of all these materials6.

Another viable option is the use of fly ash, generated as a byproduct of thermoelectric plants. Reports in the literature show that only part of the ash is reused, and that the majority is discarded in inappropriate areas and without environmental protection measures7,8. In other words, although there is a use of ash as pozzolanic materials, there is still a significant amount of this material discarded irregularly9,10.

Fly ash is a hazardous byproduct primarily generated from coal-fired power plants. During coal combustion in boilers, fine ash particles are carried with the flue gases and subsequently captured by particulate control devices, such as electrostatic precipitators or fabric filters, located in the plant’s exhaust system7,11. Generally, it is disposed of by mixing the ash with water and storing it underground to reduce the risk to human health11. This byproduct has already been used by the cement industry as a supplementary cementitious pozzolanic material12. It has been identified as a potential source of aluminosilicate in geopolymer, thus presenting an opportunity to eliminate health and environmental risks associated with storing the material. Due to large stocks of fly ash around the world, researchers are looking for ways to utilize these reserves10,13.

Geopolymer based on fly ash is generally more durable, stronger and represents an opportunity due to low cost along with significant global production and reserves, according to the different studies14,15. It has different applications, such as the production of geopolymeric concrete and application for the treatment of contaminated water16. Furthermore, fly ash is an industrial byproduct, different from other precursors such as metakaolin, widely used in geopolymers. However, metakaolin requires thermal processing that must also be considered problematic for the environment, in addition to being a material with heterogeneous characteristics, damaging the material’s geopolymerization process17.

It is known that the geopolymerization of fly ash is influenced by multiple factors, including the molar concentration of the activating solution, the kinetics of thermal curing, and the availability of reactive silica—represented by the silica modulus of the activator. Although the literature provides recommended ranges for parameters such as molarity and silica modulus, a standardized and well-defined mix design methodology for fly ash-based geopolymers is still lacking, unlike the well-established practices available for conventional cementitious materials18,19. Unlike mortars and concretes containing Portland cement, which, for example, have a clear relationship between the water/cement factor established by Abrams’ Law, in the case of geopolymers based on fly ash, it is not a rule that the higher the water content used, the lower will be the compressive strength20. This happens because the water used in the geopolymer reaction is generally rich in alkaline compounds necessary for geopolymerization to occur. The need for studies on defining clearer parameters for the dosage of geopolymeric materials is clear.

There is some research on the dosage of geopolymers obtained from municipal solid waste incineration fly ash and construction and demolition waste21. However, the authors’ study does not provide equations or a clear methodology that would facilitate the replication of the approach in future research, making it challenging to apply this methodology in other studies. Another study presents the effect of silicate modulus and alkali dosage on the performance of geopolymers containing electric furnace nickel slag22 but the proposed methodology is not easily replicated in other studies. Other studies have carried out studies to optimize the compressive strength of geopolymers using the central composite design method23,24; or analysis of geopolymer pastes using different precursors and simplex-centric experimental design24. Nevertheless, these methodologies are not easy to replicate because they involve the study of computational tools and/or statistical and mathematical analyses. This is a distinguishing feature of this article, which presents a methodology that is easily applicable to similar research.

In this context, the need for studies of geopolymer materials from fly ash becomes evident, due to the advantages presented by this binder when compared to Portland cement or other pozzolans, such as metakaolin25. However, there is a lack of clear methodologies for dosing these materials. Some authors highlight that for geopolymers, and other alkali activated materials, several factors affect the properties, such as: solution/binder ratio, aggregate content, molarity, silica modulus, type of alkaline activator and type of curing used. However, there are still few studies that establish methodologies for dosing this type of material. This article presents as its objective and main novelty the evaluation of key parameters in the dosage of geopolymers, applied to fly ash. Parameters such as solution/binder ratio, aggregate/binder, molarity, and silica modulus will be evaluated to investigate the possibility of using the material.

Materials and methods

The materials used in this study included fly ash supplied by the Tractebel Energia thermoelectric plant, located in Santa Catarina, Brazil; quartz sand (DMAX = 2.4 mm) used as fine aggregate; commercial alkaline activators (sodium hydroxide and sodium silicate); and water. The chemical composition of the fly ash, presented in Table 1, indicates a high content of aluminosilicates (approximately 80%), which is a key requirement for effective alkaline activation in geopolymer synthesis26. Figure 1 shows the granulometric curve of the materials used in the production of geopolymers.

Table 1 Chemical composition of fly ash.
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Fig. 1
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Granulometry of materials used for geopolymer production.

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Regarding the choice of activators, it is worth highlighting sodium hydroxide (NaOH) in spherical format 99% purity produced by Dinamica was used as an alkaline activator due to commercial availability and high use in another research27. Sodium silicate (Na2SiO3.nH2O) with 63% SiO2 and 18% Na2O produced by Dinamica was chosen because it causes an increase in silica and an acceleration in the geopolymerization process, as silica reacts with free alumina in the mixture, improving mechanical strength28.

Dosage setting

After selecting the binder to be evaluated and the activators to be used in the study, the proposed dosing methodology is divided into distinct steps, as outlined below. Given the interactive nature of the geopolymer dosage parameters, it is essential to fix certain parameters to allow for the variation of others. Additionally, the optimal composition was determined through compressive strength testing, as it is a critical performance indicator for geopolymeric materials. Five specimens per composition were prepared, each in a cylindrical shape measuring approximately 18 × 36 mm. Compressive strength tests were conducted using an INSTRON universal testing machine at a loading rate of 0.5 mm/min. Figure 2 illustrates the flowchart of the experimental steps used to define the dosage of fly ash-based geopolymers.

Fig. 2
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Flowchart of the steps for dosage of geopolymers.

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Step 01: solution/binder radio

In this step, the molarity and silica modulus of the activating solution are set at 5 M and Ms = 0.25; and the binder: aggregate ratio is set at 1:1, to eliminate the influence of this parameter on the study. These initial parameters were established after evaluating other similar publications29,30. The solution/binder ratio is varied by at least three values. In this research we chose to evaluate the relationships 0.40, 0.45 and 0.50, based on previous research29,31. The compositions evaluated at this stage are presented in Table 2.

Table 2 Compositions for evaluating the solution/binder ratio and binder: aggregate ratio (Steps 01, 02 and 03).
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Step 02: binder: aggregate ratio

At this stage, the molarity and silica modulus of the activating solution are set at 5 M and Ms = 0.25. The solution/binder relationship is defined through the best results found in Step 01. The varied parameter is the ligand: aggregate ratio, in the proportions 1:0.50, 1:1 and 1:1.50, through the analysis of previous research29,32. The compositions evaluated at this stage are highlighted in Table 2.

Step 03: type of cure used

The compositions defined in Steps 01 and 02, through Table 2, are evaluated in two curing procedures: (i) at an ambient temperature of 25 ± 2ºC (normal curing); (ii) and at a temperature of 60 ± 2ºC (thermal curing)32. It is known that the geopolymer reaction has greater kinetics at elevated temperatures. However, if the binder is very reactive, thermal curing can cause cracks and cracks, weakening the material33. Therefore, it is important to establish the best type of cure for each geopolymer produced with different binders.

Step 04: molarity

After defining the ideal proportion of binding material: aggregate: solution and defining the most suitable type of curing, it is possible to make variations in the solution parameters. One of the essential parameters is molarity, due to the amount of moles of alkali metal used in the solution (in this case Na2O) per volume of water. The molarity, until then fixed at 5 M, was varied from 3 M to 7 M (Table 3), based on other articles with geopolymeric materials30,34.

Table 3 Compositions for molarity assessment (Step 04).
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Step 05: silica module

Once the appropriate molarity has been established in Step 04, it is possible to vary the silica modulus (Ms), defined as the molar ratio between SiO2 and Na2O present in the activating solution. In this research, Ms varied in intervals from 0.20 to 0.35 (Table 4), based on another similar research22,33.

Table 4 Compositions for evaluating the silica modulus (Step 05).
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Statistical analysis

To verify the relationship between the factors studied in the previous steps and the compressive strength of the geopolymers, a linear and quadratic regression analysis was performed using Ordinary Least Squares (OLS). To validate the efficiency of the regression, the coefficient of determination (R²) was used.

Complementary analysis

At this stage, the characterization of the geopolymer that obtained the best strength parameters defined using following techniques was carried out. This was necessary to prove that the geopolymerization process took place, validating the proposed dosing methodology. First, a calorimetry test was performed using I-CAL 2000 HPC isothermal calorimeter to compare to the typical heat peaks of geopolymerization. XRD tests were then performed using Proto benchtop AXRD equipment with 2q scanning from 5 to 60º to detect the presence of minerals typical of geopolymerization. Finally, Scanning Electron Microscopy (SEM) technique was applied to analyze the morphology of the geopolymer produced using Shimadzu microscope, model SSX-550. To perform these analyses, the samples obtained in the compressive strength test after the rupture process were used. The samples were sanded and sieved through a 200 mesh sieve before performing the XRD and SEM tests.

Results and discussion

Step 01: solution/binder radio

Figure 3 presents the results of the geopolymer compositions as a function of varying the solution/binder ratio (w/b). It is possible to observe that increasing the solution/binder ratio (w/b) promotes an increase in the compressive strength of geopolymers, in the range of 0.40 to 0.50. This happens by two mechanisms: due to the greater alkalinity of the solution, which increases the kinetics of alkaline reactions; and due to greater workability, which allows for better packaging35,36. It is important to note that in the case of geopolymers, Abrams’ Law, established for cementitious materials, is not valid, due to differences in chemical reaction mechanisms and differences in rheological properties between these materials20,31. It is important to highlight that, within the experimental limit established in this research, the optimal w/b value is 0.50.

Fig. 3
figure 3

Compressive strength of geopolymers as a function of the solution/binder ratio.

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Step 02: binder: aggregate ratio

Figure 4 presents the results of the geopolymer compositions depending on the variation in the binder: aggregate ratio. It is observed that there is an optimum point in the aggregate ratio, which is related to the packaging of the material. It is known that the aggregate does not have a chemical function, but it promotes shrinkage control and fills the voids arising from the geopolymerization process37,38. However, as it does not have a chemical function, the use of excess aggregate can negatively affect the strength of the material. In the case of the present research and based on experimental results, the best ratio was 1:1, like what was defined in other research with alkali activated materials29,39.

Fig. 4
figure 4

Compressive strength of geopolymers as a function of the binder: aggregate ratio.

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Step 03: type of cure used

Through the results obtained in Figs. 3 and 4, it is easy to define that the best strength values were obtained for thermal curing. Although this is a common standard, not all geopolymers have better strength values in thermal curing, as this depends on the reactivity of the binder used33,40. With these results it is possible to define that the ideal composition for this research, up to Step 03, is 1:1:0.50 (binder: aggregate: solution) performing thermal curing. All other tests were carried out considering this composition.

Using this information and considering the thermal curing results, it is possible to identify a correlation equation between compressive strength (s), solution/binder ratio (w/b) and between the binder: aggregate ratio (m). Equation (1) presents the relationship between s and w/b performed linearly, with R² = 0.9952, indicating high correlation. Thinking physically, the parameter s cannot acquire negative values, therefore the smallest w/b value that can be used in the equation is 0.30. As a result, the value was limited to 0.30 ≤ w/b ≤ 0.60, to keep the interval regular and homogeneous. Theoretically, the compressive strength obtained for the geopolymers studied in this research varies from 0.43 ≤ s ≤ 46.04 MPa.

$$\:\sigma\:=151.94*\frac{w}{b}-45.15\:{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:R}^{2}=0.9952$$
(1)
$$\:\sigma\:=-27.25*{m}^{2}+54.12*m+1.65{\:\:\:\:\:\:\:\:\:R}^{2}=0.9927$$
(2)

Equation (2) presents the correlation between compressive strength (s) and the binder: aggregate ratio (m). In the case of these parameters, the best correction was quadratic with R² = 0.9927. It is important to limit the value of m = 0 since it is impossible for aggregate in the composition to be negative. In the case of m = 0, it is a geopolymeric paste. In this case, the minimum strength value is s = 1.65 MPa. The maximum value of m can be obtained considering that the strength cannot be negative. In this case, it is necessary to solve the 2nd degree equation proposed by Eq. (2), obtaining the value of approximately m = 2.02. It is also possible to obtain the maximum strength value and the value of m corresponds. This information occurs when m = 0.99, providing s = 28.52 MPa. Based on this, it is possible to establish limit values for the ligand ratio: aggregate of 0.00 ≤ m ≤ 2.02.

Figure 5 shows the ternary dosage diagram, taking into account the percentages of binder, aggregate and solution. The diagram was developed considering a solution with 5 M and Ms = 0.25 and through Eq. (1) and Eq. (2) developed for the relationship between compressive strength and w/b and m, respectively. It is observed that, unlike cementitious materials, in which there is a direct relationship between the w/c factor and compressive strength20, in the case of geopolymers this parameter is not fully established, since the aqueous part of the geopolymer is where the alkaline products necessary for the reaction to occur are located. It is noteworthy that compositions with good mixtures of binder, aggregate and solution present better strength parameters, highlighting the importance of this research.

Fig. 5
figure 5

Ternary diagram of binder, aggregate and solution for compressive strength of geopolymers.

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Step 04: molarity

Figure 6 presents the results of the geopolymer compositions as a function of the molarity of the activating solution. It is observed that the increase in molarity is beneficial in the compressive strength of the material, which has already been highlighted in another research. This happens because molarity directly interferes with the kinetics of the alkaline reaction and strengthens the geopolymer networks formed41,42. However, it is important to highlight that the increase in molarity also impairs the workability properties and may compromise the moldability of the material43.

Fig. 6
figure 6

Compressive strength of geopolymers as a function of molarity.

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Equation (3) presents the correlation between compressive strength (s and molarity (M) carried out in a linear manner, considering that the curve presents a growing trend. The value of R² = 0.9009 indicates a good correlation with this model. Knowing that the strength cannot be negative, the value of s = 0 MPa is limited, obtaining the minimum value of M of approximately 2.65. Limiting the linear model of Eq. (3) to equal deviations around the central value used in the experimental M = 5, there is a variation range of 5.00–2.65 = 2.35. This way it is possible to obtain the upper limit of the equation as 5.00 + 2.35 = 7.35. Using the information from 2.35 ≤ M ≤ 7.35, it is possible to obtain the variation range 0.22 ≤ s ≤ 41.34 MPa.

$$\:\sigma\:=\text{8,75}*M-22.97\:{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:R}^{2}=0.9009$$
(3)

Step 05: silica module

Figure 7 presents the results of the geopolymer compositions as a function of the silica modulus of the activating solution. It is observed that this parameter interacts with the strength of the geopolymer in a non-linear way. It is known that the silica module (Ms) establishes the ionic balance between the alkali metal and the silica that will participate in the geopolymerization reaction44,45. However, as can be seen in Table 1, the binder contains 55.44% SiO2 and 7.52% Na2O in its composition. Therefore, it is important to analyze the correlation between compressive strength (s and silica modulus (Ms), established by Eq. (4), since the interaction between these components depends on other chemical factors. Knowing that strength can be at least s = 0.0 MPa, it is possible to find the minimum and maximum values of Ms as being approximately 0.135 and 0.390. For geopolymer production reasons, the minimum Ms was limited to 0.05. This generates a variation range 0.135 ≤ Ms ≤ 0.390. The highest strength value is obtained when Ms = 0.263, corresponding to s = 46.99 MPa. This information establishes the values of 1.37 ≤ s ≤ 46.99 MPa.

$$\:\sigma\:=-2783*{{M}_{s}}^{2}+1464.8*{M}_{s}-145.62{\:\:\:\:\:\:\:\:\:\:\:\:\:R}^{2}=0.8956$$
(4)
Fig. 7
figure 7

Compressive strength of geopolymers as a function of silica modulus.

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Some authors have obtained similar results for compressive strength of geopolymers: for example, Cakmak et al., who obtained maximum values ​​of 41.7 MPa for compressive strength of geopolymers produced with vitreous materials and cured for 7 days46. Other studies have obtained similar results for geopolymers produced with obsidian and silica fume47,48. Therefore, the compressive strength results obtained in this study are consistent.

Table 5 presents a summary of the results obtained in the previous steps, individualizing the mean, average and experimental standard deviation values ​​for each composition involved in the study.

Table 5 Individual results obtained for each composition studied.
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Additional analysis

Figure 8 presents the calorimetry results for the composition 1:1:0.50 (binder: aggregate: solution), with molarity 7 M and Ms = 0.25, whose compressive strength values ​​were 50.19 MPa. This composition was chosen based on the best compressive strength parameters obtained in the previous stages. In Fig. 8, the following characteristic peaks can be observed: (i) the peak with approximately 4.5 mW/g, related to the initial dissolution of aluminosilicates in the activating solution; and (ii) the peak of approximately 3.0 mW/g, related to the geopolymerization process and formation of resistant phases. The heat flow values ​​obtained, and the corresponding peaks are similar to other studies with geopolymers, such as Ling et al.49 and Hou et al.50, and are characterized as clear evidence of the geopolymerization of the composition 1:1:0.50 (binder: aggregate: solution), 7 M and Ms = 0.25.

Fig. 8
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Calorimetry results for the composition 1:1:0.50, 7 M and Ms = 0.25.

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Figure 9 illustrate the results of X-ray diffraction by XRD and scanning electron microscopy by SEM for the composition 1:1:0.50 (binder: aggregate: solution), with molarity 7 M and Ms = 0.25, whose compressive strength values were 50.19 MPa. The XRD results show the presence of two phases: quartz (SiO2) and sodalite (Na2[Al2Si1,85O7,7].5H2O). The quartz particles are attributed to the use of sand in the production of geopolymers, but the presence of sodalite indicates that the geopolymerization process occurred for this composition, justifying the compressive strength results obtained. The formation of sodalite is the main phase in the geopolymerization process for precursors rich in aluminosilicates, such as fly ash51,52. Therefore, the information obtained is coherent. The SEM results show an irregular particle with rough topography, which represents the presence of quartz in the material. This particle is covered by agglutinated lamellar particles formed by small roughness or imperfections due to incomplete growth or interaction with other matrix compounds, stuck and adhered to the quartz particle. In other words, this is the formation of sodalite being experimental evidence of the geopolymerization process.

Figure 10 presents a schematic representation of sodalite, where it is possible to observe the formation of a lamellar and needle-like phase, typically the morphology of this material. Sodalite or hydroxysodalite is a compound that forms only when geopolymerization reaches an intense degree of reactivity, generally in thermal curing and when the dosage of the geopolymer is well carried out. This happens because this is a cage-shaped crystal, forming a well-ordered and highly strength crystalline network32 illustrated in Fig. 10. The objective of this section is to prove that fly ash geopolymerization occurred efficiently and that the proposed dosage methodology is suitable for defining the best proportion of fly ash-based geopolymers and similar precursors32,51,52.

Fig. 9
figure 9

(a) X-ray diffraction (XRD) and (b) – Scanning electron microscopy (SEM) of the geopolymer 1:1:0.50 (binder: aggregate: solution) 7 M and Ms = 0.25. Caption: Q = quartz; S = sodalite.

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Fig. 10
figure 10

Source: Crystallography Open Database (1010998).

Crystal structure of Sodalite.

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Conclusions

This study proposed a parameter optimization for fly ash geopolymers activated with sodium hydroxide and sodium silicate, considering key parameters such as solution-to-binder ratio (w/b), binder-to-aggregate ratio (m), molarity (M), and silica modulus (Ms). The results showed linear and quadratic correlations between these parameters and compressive strength, with optimal ranges identified: 0.30 ≤ w/b ≤ 0.60, 0.00 ≤ m ≤ 2.02, 2.35 ≤ M ≤ 7.35, and 0.135 ≤ Ms ≤ 0.390.

The best-performing composition—1:1:0.50 (binder: aggregate: solution), 7 M molarity, and Ms = 0.25—achieved a compressive strength of 50.19 MPa, closely matching the predicted value of 46.99 MPa (6.3% deviation). Complementary characterization (calorimetry, XRD, and SEM) confirmed the formation of sodalite and validated the occurrence of geopolymerization, reinforcing the reliability of the proposed mix design methodology.

The proposed methodology proved effective in predicting the compressive strength of fly ash-based geopolymers, supported by high R² values and low prediction error. The study offers a practical contribution through a simplified flowchart for mixture design, enabling more accurate and efficient development of sustainable geopolymeric materials for construction applications.

As a suggestion for future work, it is recommended: (i) to evaluate the applicability of the methodology for studies with geopolymers produced with metakaolin, blast furnace slag and agro-industrial ash; (ii) to evaluate the viability of the optimization methodology for fly ash geopolymer produced with other activators, such as potassium hydroxide and silicate; and (iii) to produce geopolymers in the proportion that indicates the best compressive strength results, that is, 30 ≤ w/b ≤ 0.60, 0.00 ≤ m ≤ 2.02, 2.35 ≤ M ≤ 7.35, and 0.135 ≤ Ms ≤ 0.390.