Refining Oxide Ratios in N-A-S-H Geopolymers for Optimal Resistance to Sulphuric Acid Attack

Abstract

As an alternative to Portland cement systems, geopolymers have been found to display superior acid resistance. However, at present, there exists no strategy to regulate the suitable design of mixtures. Particularly, the mechanisms underlying the effect of principal oxide ratios on the performance of N-A-S-H geopolymers in acid-rich environments are missing. Nor is any information available on the optimal range for SiO₂/Al₂O₃, Na₂O/Al₂O₃, and H₂O/Na₂O ratios under acid attack. This study investigates N-A-S-H geopolymers incorporating varying compositional oxide ratios to assess their resistance to sulphuric acid attack. The results show that the optimal range for acid-resistant durability is a narrow band within the optimal range for workability and strength. A SiO₂/Al₂O₃ ratio of 3.4 balanced the enhanced degree of geopolymerization with an increase in the amount of permeable voids. At the same time, the Na₂O/Al₂O₃ and H₂O/Na₂O ratios should be maintained within 0.8~0.9 and 8~10, respectively. Quantitatively, for the mixture designed within these optimal oxide ranges, the associated strength loss after 84 weeks of acid exposure was only about 10~20%, whereas other mix proportions may lead to a maximum strength loss of up to ~58%. Anything higher will offset the polycondensation and instead raise the volume of permeable voids. A sensitivity analysis suggests that the acid resistance depends chiefly on the Na₂O/Al₂O₃ and H₂O/Na₂O ratios. The proposed multi-factor models predict the acid-induced neutralization efficiently, and the associated output displays a correlation with the loss in compressive strength.

1. Introduction

Portland cement and its composites are, on their own, responsible for 5~8% of global carbon emissions [1,2]. Manufacturing one tonne of Portland cement generates about 0.8 tonnes of CO₂ [3]. On the other hand, this value drops to 0.15~0.2 tonne/tonne in the case of geopolymers [4]. The family of geopolymers, resulting from the alkali activation of aluminosilicate precursors, has emerged as an attractive alternative to Portland cement composites [5]. In direct comparison, geopolymers display matching engineering properties, including suitable workability, quick set, equal strength, and excellent chemical resistance [6,7]. Together, these attributes encourage a widespread adoption of geopolymers across a multitude of applications. In turn, this will offset the current dependence on Portland cement and lead to alleviating climate change.

In its basic format, a geopolymer requires a precursor and an activator. The precursor refers to the aluminosilicate source that contains adequate amorphous silica and alumina. So far, a variety of materials have been identified as eligible precursors. Often, these are either combustion waste from agro-forestry and industrial sources, by-products, or just natural deposits. Thus, metakaolin [8,9], slag [10,11], fly ash [12,13], red mud [14], zeolite [15], and sugarcane bagasse ash [16] have all been variously used as a precursor. The activator is either sodium hydroxide or potassium hydroxide in combination with their respective silicate in an aqueous solution [17]. Upon blending with the alkali activator, the amorphous silica and alumina preferentially exist in the form of tetrahedral SiO₄ and AlO₄ units, which are subsequently transformed into aluminosilicate oligomers by sharing their bridging oxygen atoms. Subsequently, these oligomers self-condense and develop into a more complex and rigid network [17,18], which may be expressed as M_n[-(Si-O₂)_z–Al–O]_n· wH₂O [19]. The principal oxide ratios, namely, SiO₂/Al₂O₃, Na₂O/Al₂O₃, and H₂O/Na₂O, have been extensively examined for impact on the strength of the resulting geopolymer [20,21,22,23,24,25]. So, an increase in the SiO₂/Al₂O₃ ratio increases strength but delays the setting time [22]. Each oligomeric aluminosilicate chain carries a negative charge due to the tetrahedral AlO₄ unit, and the molarity of the alkaline metal ion should be equivalent to that of the aluminum species that comprises the polymerized network [23]. Thus, alkali cations (M⁺) in excess will hinder geopolymerization and deter strength development [24]. Further, a lower than optimal H₂O/M₂O ratio will destabilize the already formed aluminosilicate framework [24], while an excessively high value depresses the activation efficiency [25]. So, both an excess and a deficit in the H₂O/M₂O ratio are detrimental to the strength development in geopolymers.

As a potential alternative to Portland cement, geopolymers must register superior strength and, at the same time, display durability against adverse environments. Here, acid resistance is an important concern. In the case of Portland cement systems, an acid attack causes irreversible loss in strength, stiffness, and integrity [26,27]. Numerous applications demand adequate acid resistance, and geopolymers must meet this demand [28]. And the results so far are promising. Vafaei et al. report that when subjected to a sulphuric acid environment with a pH of 3 for 12 months, the compressive strength of Portland cement systems dropped from 45 MPa to 5 MPa, which was a 90% reduction. The associated loss in geopolymer systems was only 48% strength [29]. Similarly, Qu et al. reported that even those geopolymers that were preloaded with sulphuric acid performed better than their Portland cement counterparts [30]. Yet, chemically induced deteriorations were observed, and the damage was seen to worsen with exposure time [29]. Applications including sewer systems, industrial estates, mines, geothermal wells, and backfill regions are susceptible to sulphuric acid attack [31,32,33,34,35,36]. Prior studies show that in geopolymers, a sulphuric acid attack starts with the replacement of exchangeable alkali metal ions, i.e., Na⁺ or K⁺, by hydrogen ions (H⁺) [37,38,39]. Next, the sulphuric acid solution breaks the principal Si-O-Al bonds and then forms two separate groups, namely, Si-OH and Al-OH. This process is also called dealumination. As a result, the aluminosilicate network converts to silicic acid ions and dimers in solution. Eventually, at a macroscopic scale, this breach manifests in mass and strength loss [39]. In recent publications, variables such as the precursor type, activator type, and alkali content have been examined for their effect on the sulphuric acid resistance of geopolymers [27,40,41,42,43,44]. Thokchom et al. stated that an increase in the alkali dosage led to a rise in the mass loss for geopolymers subjected to sulphuric acid attack. However, the residual compressive strength was higher [40]. Aiken et al. examined the acid resistance of binary slag/fly ash geopolymers [27]. They found that an increase in the slag fraction led to pore size refinement. However, the resulting products became more susceptible to sulphuric acid attacks. This finding was supported elsewhere [41]. Vogt et al. noted that replacing metakaolin with 7.5~9% silica fume contributed to the formation of a silicate-rich geopolymerized structure and, in turn, improved the resistance to sulphuric acid [42]. Bouguermouh et al. compared the acid resistance of metakaolin-based (N-A-S-H) geopolymers that were variously activated by potassium-based and sodium-based activators [43]. The lowest mass loss was witnessed for formulations based on potassium, attributed to the presence of secondary minerals such as quartz and muscovite. These crystals serve physically as pore fillers and, accordingly, hinder exchange between the alkali cations and hydrogen ions. Recently, geopolymers made with other types of precursors/blends and precursors were also examined for their acid resistance [45,46,47,48,49,50,51,52,53,54]. For instance, Teshnizi et al. reported that the molar ratios of alkaline activators dominated the durability of geopolymer mortar, and a slag-based system produced with an 8 M KOH performed best [45]. On the other hand, Yang et al. revealed that the optimal concentration for a sodium-based activator was found as 12 M for high-calcium fly ash-based geopolymers by examining the neutralization depth of specimens subjected to acid attack [46]. In a study conducted by Zhao et al., an alkali-activated fly ash/slag (AFS) system was noted to display much superior acid resistance in comparison to OPC systems, and the calcium content was found to play a part in this regard [47]. In another dependent study, adding 20% soda residue to a low-calcium fly ash-based geopolymer was reported to improve the resistance against the joint deterioration led by HCl and Na₂SO₄ environments, and the associated performance was even better than cement mortar [48]. As summarized, an appropriate mix design could enable us to produce durable geopolymers [49], regardless of the choice of precursor and activator.

The authors find that there exists little information to optimize the mixture design toward acid resistance in N-A-S-H-based geopolymers. Further, the mechanisms governing the effect of compositional ratios on such acid-induced deterioration of geopolymers are not clear. This hinders their regulation of optimal acid resistance. This study was carried out to close this scientific gap. Accordingly, three series of specimens were prepared by varying the SiO₂/Al₂O₃, Na₂O/Al₂O₃, and H₂O/Na₂O ratios one at a time. A combination of macroscopic, morphological, chemical, and microscopic characterizations was carried out, followed by a sensitivity analysis. Based on the experimental results, here, multi-factor models were proposed to predict the deterioration led by sulphuric acid attack on geopolymers with a given mixture formulation. These outcomes will help optimize the mixture design of N-A-S-H geopolymers and, in turn, promote their practical application in an acidic environment.

2. Experimental Program

2.1. Materials

A commercially sourced metakaolin was used as previously described [54] to serve as the aluminosilicate precursor, and its chemical composition is listed in

Table 1. Chemical composition of metakaolin.

SiO2	Al2O3	TiO2	Fe2O3	P2O5	Na2O	K2O	CaO
53.8%	43.8%	0.9%	0.5%	0.4%	0.3%	0.2%	0.1%

. X-ray Diffraction (XRD) revealed a broad and clear hump, centered at 2θ = 22.5°, illustrating its amorphicity, as shown in Figure 1a. Minor crystals identified as anatase and quartz were detected as well. The principal chemical bands were evaluated from Fourier Transform Infrared spectroscopy (FTIR). The FTIR spectrum, shown in Figure 1b, reveals three prominent peaks, identified as the Si–O bond in amorphous SiO₂ at 1060 cm⁻¹, the tetrahedral AlO₄ at 792 cm⁻¹, and the T-O-T band (T: tetrahedral Si or Al) at 434 cm⁻¹.

The alkali activator was a combination of sodium hydroxide and sodium silicate. The former was sourced as solid pellets with a purity of 99%. The sodium silicate solution comprised a 40% sodium silicate compound and 60% deionized water, and together with the sodium hydroxide, the overall SiO₂/Na₂O modulus was 3.2.

The fine aggregates had an oven-dried bulk density of 1570 kg/m³, while the moisture content reached surface saturated dry (SSD) and, further, the water absorption was 0.11% and 1.54%, respectively. A laboratory reagent-grade sulphuric acid, containing 95~98% H₂SO₄, was blended with deionized water at 1% (mass fraction) to produce the acid-rich environment for the subsequent immersion test. The pH value of the resultant solution was determined using a digital pH meter and was recorded at 0.7.

2.2. Mix Proportions and Specimens

In order to satisfy the proposed objectives, three batches of mixtures were designed. They were conceived by varying the following three molar ratios of the constituent oxides, namely, SiO₂/Al₂O₃, Na₂O/Al₂O₃, and H₂O/Na₂O. The mixtures are listed in

Table 2. Mix proportions of N-A-S-H geopolymers.

SiO2/Al2O3	Na2O/Al2O3	H2O/Na2O	Metakaolin (g)	Sodium Silicate (g)	NaOH (g)	Water (g)	Sand (g)	Liquid/Solid
								Paste	Mortar
2.2	0.9	11	500	51.5	148.7	350.6	1000	1.102	0.367
2.8	0.9	11	500	321.0	117.8	182.2	1000	1.242	0.414
3.1	0.9	11	500	455.7	102.3	98	1000	1.312	0.437
3.4	0.9	11	500	590.4	86.9	13.8	1000	1.382	0.461
3.7	0.9	11	500	702.7	74.0	−56.4	1000	1.441	0.480
3.1	0.8	11	500	455.7	85.1	55.4	1000	1.193	0.398
3.1	0.9	11	500	455.7	102.3	98.0	1000	1.312	0.437
3.1	1.1	11	500	455.7	136.7	183.0	1000	1.551	0.517
3.1	1.3	11	500	455.7	171.1	268.1	1000	1.790	0.597
3.1	1.0	8	500	455.7	119.5	24.5	1000	1.199	0.400
3.1	1.0	10	500	455.7	119.5	101.8	1000	1.354	0.451
3.1	1.0	12	500	455.7	119.5	179.2	1000	1.509	0.503
3.1	1.0	14	500	455.7	119.5	256.5	1000	1.663	0.554

. Note that for each combination of oxides, specimens were prepared first as paste and then as mortar. The paste samples were taken for microscopic characterization using X-ray Diffraction (XRD), Thermo-Gravimetric Analysis (TGA), Fourier Transform Infrared (FTIR) spectroscopy, and Scanning Electron Microscopy (SEM) equipped with Energy-Dispersive X-ray Spectroscopy (EDS). The mortar specimens were examined to measure the compressive strength, any loss in mass or dimension, the neutralized depth, and the apparent volume of permeable voids.

About 24 h prior to casting, the sodium hydroxide pellets were blended with the sodium silicate solution along with extra deionized water to prepare the alkali activator. This mixture was left for 24 h to cool under a fume-hood. On the following day, this alkali activator in solution was first stirred in a mixing drum for 60 s to achieve a homogeneous solution. Next, the solid aluminosilicate precursor was added to blend well with the activator until a homogeneous paste mixture was observed. At this point, fine aggregate was added to the paste mixture to produce the mortar series. The mortar mixture was cast into cylindrical moulds of Φ50 mm × 100 mm dimension and then transferred onto a vibrating table for 30 s of compaction. These specimens were demoulded 24 h later and cured in air-tight plastic bags under ambient conditions for up to 28 days.

2.3. Test Protocols and Sample Collections

After reaching 28 days of maturity, the specimens sourced from each mix were divided into two series. The first group was tested immediately to measure their macroscopic properties to serve as the reference. The second group was immersed in a sulphuric acid solution (prepared at 1% mass fraction) for up to 3 months of exposure. Note here that the sulphuric acid solution was periodically refreshed every 7 days to maintain its pH, and the ratio between the solution volume and the specimen’s surface area was consistently fixed at 10 [29]. The exposure protocol was decided at 4 weeks, 8 weeks, and 12 weeks. After each duration, the mortar specimens were retrieved from the bath of sulphuric acid to measure changes in mass, diameter, and compressive strength. The effect of acid exposure on the above macroscopic properties was examined further through powder samples that were collected from the respective paste specimens. The powder samples were tested for chemical composition, microstructure, and morphology. A flowchart is presented in Figure 2 to show the workflow of the experimental investigations.

The powder samples were obtained as follows. After each duration of exposure, a representative specimen was sawn into 6 pieces, as shown schematically in Figure 3. First, the 2 endpieces were discarded in order to account for any disturbance brought upon by the multi-dimensional penetration. Note here that upon visual inspection, the later visual inspection upon neutralization also confirmed that the degraded depth along one certain direction was significantly smaller than the thickness of 2 endpieces (~20 mm). The remaining 4 slices, close to the plane at mid-height, were used for subsequent powder collection. In order to characterize the region that had deteriorated severely, the first layer of powder samples was collected at the region near the exterior edge with a thickness of about 2 mm. Note here that during this powder collection process, 2 slices from the same specimen were placed in a crafted mould. This allowed us to constrain the drilled slices, on the one hand, and avoid unexpected cracking due to the stress concentration during the drilling process, on the other hand. The second layer of powder samples was collected at a relatively deep location (approximately 4 mm), wherein much less deterioration was expected. The drilling protocol alongside the actual operation is shown in Figure 4.

2.4. Testing Program

The pH value of the external sulphuric acid solution was monitored daily. The mass and diameter were measured, and the exposed specimens were tested in compression as per ASTM C39/C39M-18 [55]. The degree of penetration was assessed with a phenolphthalein solution [56,57]. Loss in alkalinity for the geopolymer matrix was estimated by mixing powder samples with deionized distilled water [57,58]. A suspension with a solid-to-liquid ratio of 1 was produced and then tested by a calibrated pH probe. In addition, the apparent volume of permeable voids (AVPV) was evaluated, referring to ASTM C642-13 [59]. In Equation (1), W_s refers to the mass of the surface-dried sample in air after immersion and boiling, while W_a indicates the apparent weight of the sample in water after immersion and boiling. W_d is the weight of the sample after oven-drying at 100 °C for 24 h.

$$AVPV={\displaystyle \frac{W_s-W_d}{W_s-W_a}}\times 100\%$$

(1)

In addition, the samples were subject to X-ray Diffraction (XRD) using a Bruker D8 instrument, that uses Copper-Kα radiation beam (operated at 40kV and 44mA), with a step size of 5°/min, from a diffraction angle (2θ) of 10° to 60°. A Thermo-Gravimetric Analysis (TGA) was conducted using the Leco TGA 701 instrument that functions in a temperature range of 20~1000 °C and at a heating rate of 10 °C/min. The chemical bonds of geopolymers were examined by iS50 Fourier Transform Infrared spectroscopy (FTIR), using a Nicolet iS50R model. Then, the obtained FTIR spectra were deconvoluted for the range of 800~1250 cm⁻¹. Representative paste samples from each mixture were placed in a Field Emission Scanning Electron Microscope (FE-SEM) that was coupled with an Oxford Energy-Dispersive X-ray Spectroscope (EDS). This was a Zeiss Sigma 300 VP-FESEM. A 15 kV accelerating voltage resulted in a magnification scale ranging from 300× to 5000×. The generated images were binarized to show the voids or cracks as the black region and the solid geopolymer gel as the white region.

3. Experimental Results and Analyses

3.1. pH Evolution of Sulphuric Acid Solution

Figure 5 presents the pH evolution of the sulphuric acid solution during the immersion of the geopolymers made with varying compositional oxide ratios. For all mixtures, the pH values of the acid solution increased up to 3.5~4.0 after the first attack cycle. In other words, over 99% of the hydrogen ions in the sulphuric acid solution had been consumed by this point. As time elapsed, the maximum pH value at the end of each cycle decreased consecutively throughout the entire 12 weeks of acid exposure. This implies the following: (i) the sulphuric acid attack and the attendant leaching behaviour in the geopolymers decelerated over time, and (ii) for a certain area, the associated capacity to consume penetrating hydrogen ions had a threshold, and the excess of those ions could only diffuse toward the deeper location while much more time was needed. Note that a similar finding was also observed elsewhere [27,57]. It is noted that as compared to the H₂O/Na₂O ratio, varying the SiO₂/Al₂O₃ and Na₂O/Al₂O₃ ratios generate a stronger influence on the neutralization rate of the acid solution. As for the SiO₂/Al₂O₃ ratio, an increase from 2.2 to 3.4 is found to alleviate the neutralization of the acid solution. As evident, the neutralization potential decreased from 95.1% (pH = 2.01) to 82.6% (pH = 1.46) after the 12th attack cycle, as per Equation (2). However, any further increase in this ratio from 3.4 to 3.7 did not slow down the neutralization rate significantly; see Figure 5a. The possible underlying reason is likely that the continuous rise in this ratio also increases the liquid content in the geopolymer, which may plant a hidden danger to form permeable pores and, in turn, facilitate the transport of hydrogen ions. This part will be introduced later in Section 3.4. Regarding the Na₂O/Al₂O₃ ratio, the mixture made with the higher value consumed more hydrogen ions within a single attack cycle. After 12 weeks of exposure, the neutralization potential dropped from 94.6% (pH = 1.97) to 81.4% (pH = 1.43) as the Na₂O/Al₂O₃ ratio decreased from 1.3 to 0.8. This means that increasing the net amount of alkali cations does not correspond to an absolute improvement in the acid resistance of geopolymers. Decreasing the H₂O/Na₂O ratio from 14 to 8 was observed to favour the resistance to the sulphuric acid attack, manifesting as a reduction in the neutralization potential from 89.5% (pH = 1.68) to 86.5% (pH = 1.57) after 84 days of exposure. Notice that the lower end of this ratio essentially corresponds to a stronger alkalinity, on the one hand, and much less liquid content, on the other hand. As a result, the ability of the geopolymer to retain its alkalinity and also resist the penetration of hydrogen ions was concurrently improved.

$$P_n=(1-{10}^{c_1-c_2})\times 100\%$$

(2)

where P_n represents the neutralization potential, c₁ denotes the initial pH value of the sulphuric acid solution, and c₂ is the instant pH value of the sulphuric acid solution as the attack progresses.

3.2. Loss in Alkalinity

Strong alkalinity is an important characteristic of cementitious materials, as it maintains the chemical stability of reaction products, on the one hand, and avoids the corrosion of embedded reinforcement by forming a passivation film, on the other hand [60]. In this study, the alkalinity of the geopolymer paste was approximated using the powder suspension method. With all mixtures, the initial alkalinity of the hardened specimen was found to be 12.3 ± 0.2, and this value agrees well with prior studies [57]. After the sulphuric acid attack, the remaining alkalinity was evaluated at varying depths inside the geopolymer mixtures, as presented in Figure 6. It is clear that the alkalinity of all examined mixtures decreases substantially over time. Indeed, the corresponding pH may drop to 7 or even shift lower toward the acidic range. For a given depth, increasing the SiO₂/Al₂O₃ ratio from 2.2 to 3.4 was found to mitigate the loss in alkalinity of the geopolymer matrix, whereas any increase beyond this value caused an unexpected rise in pH. It is widely reported that higher SiO₂/Al₂O₃ ratios boost the degree of geopolymerization by extending the length of the aluminosilicate oligomer chains [22]. However, a continuous increase in this ratio will also introduce more liquid fractions into the mixture, which only degrades the evolving microstructure. Hence, there exists an optimal SiO₂/Al₂O₃ value to achieve superior acid resistance. A decrease in both the Na₂O/Al₂O₃ and H₂O/Na₂O ratios was noted to relieve the loss in alkalinity, as evident in Figure 6b,c. In prior studies, a smaller Na₂O/Al₂O₃ ratio was reported to impart a higher degree of geopolymerization [24]. Note that lowering the H₂O/Na₂O ratio essentially corresponds to the enhanced alkalinity of the activator. Alongside this, the lower this ratio, the smaller the liquid-to-solid ratio and, likely, the denser the geopolymer network. Given the above, it is not surprising to observe that the loss in alkalinity is tempered when both these ratios decrease.

Phenolphthalein was used as the indicator to conduct the visual inspection of the geopolymers subjected to the sulphuric acid attack. The representative images are presented in Figure 7. By computing the ratio of the neutralization depth to the original diameter, the authors defined the so-called penetration degree. It was measured against each oxide ratio, as shown in Figure 8. As seen therein, regardless of exposure duration, the smallest penetration degree was seen at a SiO₂/Al₂O₃ ratio of 3.4, a Na₂O/Al₂O₃ ratio of 0.8, and a H₂O/Na₂O ratio of 8.

3.3. Changes in Mass, Diameter, and Compressive Strength

A sulphuric acid attack occurring in geopolymers will replace the exchangeable metal cations and trigger the dealumination of polymerized aluminosilicate frameworks. The above process macroscopically reflects noticeable losses in the mass, size, and mechanical strength of the geopolymers. Figure 9 presents the mass and diameter changes in each mix when subjected to the sulphuric acid attack for up to 12 weeks. As seen therein, raising the SiO₂/Al₂O₃ ratio from 2.2 to 3.4 mitigates the mass loss and reduction in diameter. Any further increase beyond 3.4 is, however, not beneficial. Once again, this optimum may be explained through the antagonism between the enhanced geopolymerization degree and the enlarged liquid-to-solid ratio. When the SiO₂/Al₂O₃ ratio is smaller than the optimal value (here 3.4), the benefits are led by the improved geopolymerization degree govern. If any higher, the higher liquid content adversely impacts the microstructure. Nevertheless, it is interesting to note in Figure 10a that the mixture made with the SiO₂/Al₂O₃ ratio of 3.7 registers the maximum compressive strength even after 84 days of exposure. Note that this mixture possessed the highest compressive strength prior to sulphuric acid exposure. However, this mixture also registered the highest percentage loss in compressive strength.

As expected, an increase in the Na₂O/Al₂O₃ ratio and in the H₂O/Na₂O ratio both caused further deterioration from the sulphuric acid attack. This is evident from the greater mass and diameter losses shown in Figure 9 and the lower residual compressive strength, together with a larger loss, as illustrated in Figure 10. Further, it is clear to see that when the Na₂O/Al₂O₃ ratio reaches 1.1, or the H₂O/Na₂O ratio goes up to 14, the associated mixtures register significantly large percentages of loss in compressive strength. This may suggest that when subjected to an acidic environment, the Na₂O/Al₂O₃ and H₂O/Na₂O ratios must be kept within a narrow range for N-A-S-H geopolymers.

And so, the optimal combination of compositional ratios against the sulphuric acid attack may be summarized as follows: SiO₂/Al₂O₃ = 3.1~3.4, Na₂O/Al₂O₃ = 0.8~0.9 and H₂O/Na₂O = 8~10. Note here that some prior studies that optimized the oxide ratios or other mix-design parameters for superior properties are compared in

Table 3. Comparisons of optimal proportions constituting geopolymers according to some independent studies.

Precursors	Properties	Optimal Value/Range	Source
Metakaolin	Acid resistance	SiO2/Al2O3 = 3.1~3.4 Na2O/Al2O3 = 0.8~0.9 H2O/Na2O = 8~10	Present study
Slag	Acid resistance	KOH = 8 M	[45]
Fly ash	Acid resistance	NaOH = 12 M	[46]
Metakaolin	Compressive strength	SiO2/Al2O3 = 3.6~3.8 Na2O/Al2O3 = 1.0~1.2 H2O/Na2O = 10~11	[21]
Metakaolin	Workability, setting, and compressive strength	SiO2/Al2O3 = 2.8~3.6 Na2O/Al2O3 = 0.75~1.0 H2O/Na2O = 9~10	[54]
Metakaolin	Compressive strength	Si/Al = 1.65 Na/Al = 0.83	[61]
Fly ash	Compressive strength	SiO2/Al2O3 = 3.37	[62]
Metakaolin and Sugarcane bagasse ash	Compressive and flexural strength	SiO2/Al2O3 = 3.1~3.4 Na2O/Al2O3 = 0.8~0.9 H2O/Na2O = 8~10	[63]

. Clearly, the optimal mixing proportions noted in the different studies vary. This may be due to changes in precursor, target properties, selected parameters, and even the testing conditions. The present study tailors the mixture design further for an acid-rich environment.

3.4. Apparent Volume of Permeable Voids

The porous character of cementitious systems determines that the associated structural members are detrimental to aggressive ions in external environments. As stated earlier, an external sulphuric acid attack involves both physical diffusion and chemical reaction. The apparent volume of permeable voids (AVPV) indicates the capacity of cementitious materials to resist the penetration of aggressive ions from the exterior [64]. As seen in Figure 11, as the SiO₂/Al₂O₃ ratio increases from 2.2 to 3.7, the AVPV of the geopolymers experiences a noticeable drop and reaches an optimal trough at the SiO₂/Al₂O₃ ratio of 3.4, followed by a rise due to an increase in this ratio to 3.7. Note here that this trend is consistent with results in terms of the losses in alkalinity, mass, diameter, and compressive strength presented in Figure 8, Figure 9 and Figure 10. It is well established that a higher SiO₂/Al₂O₃ ratio usually corresponds to a higher polycondensation degree of the N-A-S-H framework and, thus, a greater initial strength [22]. However, the results obtained here also suggest that the acid-induced deterioration of geopolymers depends not only on the degree of geopolymerization but also on the evolution of its pore structure. In the case of the Na₂O/Al₂O₃ ratio, the lowest AVPV is found for the mixture made with a value of 0.8~0.9. The mixtures incorporating a Na₂O/Al₂O₃ ratio beyond 1 experience a considerable increase in the AVPA. As well, a monotonic rise in the AVPA is observed when increasing the H₂O/Na₂O ratio from 8 to 14. The above phenomena are likely attributed to the rise in both the liquid-to-solid ratio and the water content when the Na₂O/Al₂O₃ and H₂O/Na₂O ratios increase, as evident from Table 2. Again, the higher liquid content will degrade the pore structure in the geopolymer system [65].

3.5. X-Ray Diffraction (XRD)

The XRD diffractograms of representative geopolymers taken right before and just after the sulphuric acid attack are presented in Figure 12. As seen in Figure 12a, the aluminosilicate precursor activated with a low SiO₂/Al₂O₃ ratio, here 2.2, displays an insufficient amorphocity. This is evident firstly from numerous crystals, including Faujasite (F), anatase (A), Na-Chabazite (C), Hydroxysodalite (S), and quartz (Q), and secondly, from the irregular shape of the diffuse hump centered at about 28.5° of 2θ. As the SiO₂/Al₂O₃ ratio increases through 2.8 and to 3.7, the clear diffuse hump ascribed to the N-A-S-H framework evolves alongside the obvious disappearance of the above crystalline impurities. This may be attributed to the increase in amorphous silica, which boosts the formation of aluminosilicate oligomers. Figure 12b,c present the XRD spectra for the respective samples post-exposure that were each collected at different layers. Interestingly, the diffuse hump of samples located at layer 1 shifts toward the lower end, and this includes the mix incorporating a SiO₂/Al₂O₃ ratio of 2.2. More importantly, no visually detectable difference is witnessed. Taken together, it may indicate the following: (i) the geopolymer matrix suffering from the acidic environment will experience a reduction in the amorphicity due to the dealumination of N-A-S-H networks as the attack progresses; (ii) once the aluminosilicate frameworks are depolymerized completely, any further acid exposure will not affect the amorphicity any longer; and (iii) zeolitic crystals formed in the case of low geopolymerization may also be susceptible to sulphuric acid attack. With regard to layer 2, the associated XRD spectra are mutually comparable. One sees in Figure 12c that the diffuse hump for the mixture made with the higher SiO₂/Al₂O₃ ratio shifts toward the smaller end of 2θ. This implies that the associated mixture registered a higher residual amorphocity. As seen in Figure 12d, increasing the Na₂O/Al₂O₃ ratio of the geopolymers from 0.8 to 1.3 reflects a prominent shift in the diffuse hump from 28.7° to 27.4° in 2θ. This suggests a depressed amorphocity and also explains the lower compressive strength of the geopolymers in their mature states without any sulphuric acid immersion (see Figure 10b). As for those samples examined post-exposure, once again, no obvious difference is detected for the series of layer 1, whereas the XRD patterns captured at the deeper location are mutually comparable; see Figure 12f. In this regard, as the Na₂O/Al₂O₃ ratio rises from 0.8 to 1.3, the center of the corresponding diffuse hump moves from 27.4° to 25.7° in 2θ. More importantly, the change in 2θ right before and after the acid attack is determined as 1.3° for the mixture of Na₂O/Al₂O₃ = 0.8 and 1.7° for the mixture of Na₂O/Al₂O₃ = 1.3. This may illustrate that the loss in amorphocity is less than in the latter within the same exposure durations. Also, the above XRD results agree with trends found in various macro-properties (Figure 8, Figure 9 and Figure 10). In Figure 12g, a minor difference can be found between the un-exposed samples incorporating varying H₂O/Na₂O ratios. Connecting to the initial compressive strength shown in Figure 10c, this may suggest that varying this ratio may generate a stronger influence on other characteristics such as the pore structure in comparison to the amorphocity. As the sulphuric acid attack progressed, the region suffering from the acid attack lost more amorphocity when the larger H₂O/Na₂O ratio was designed, as evident in Figure 12i.

3.6. Thermo-Gravimetric Analysis (TGA)

The TGA curves of the examined geopolymers right before and after the sulphuric acid attack are plotted in Figure 13. As widely reported, the principal weight loss is usually witnessed as heating from room temperature (~22 °C) to 300 °C due to the evaporation of free water and the chemically bound water constituting N-A-S-H frameworks [66,67]. Prior to the sulphuric acid immersion, a relatively minor difference was noted among the thermo-gravimetric curves of various geopolymers. As the acid attack progressed, their mutual differences appeared to evolve, as evident in Figure 13. According to the principal chemical equation of polycondensation to form N-A-S-H geopolymers [19] (plotted in Figure 14), the side functional groups in the aluminosilicate oligomer chain are silanes that register more hydroxyls compared to the intermediate tetrahedral Si and Al groups. However, as the sulphuric acid attack dealuminates the aluminosilicate frameworks and releases out the connected Al-OH groups, the relative proportion of hydroxyls carried in the side silanol groups increases accordingly. In addition, a part of water will be formed during the formation of the silicious framework as the sulphuric acid attack progresses. These may together explain the intensified DTG peak witnessed between 20 and 300 °C after the sulphuric acid immersion. By computing this thermo-gravimetric variation, the degree of acid-induced deterioration may be compared between various geopolymers, as presented in Figure 15. Clearly, the mixture made with a SiO₂/Al₂O₃ ratio of 3.4 once again displays the minimal variation in that respective series. This is mutually supported by the XRD traces. As for the Na₂O/Al₂O₃ and H₂O/Na₂O ratios, reducing both their values is noted to alleviate the thermo-gravimetric variation related to the N-A-S-H framework.

3.7. Fourier Transform Infrared Spectroscopy (FTIR)

The XRD traces suggest that the region near the exterior surface is likely deteriorated completely over the duration of exposure. Thus, no obvious difference was detected among the different samples variously exposed to acid attack. Hence, apart from the un-exposed samples, only those powder samples collected at layer 2 from the exposed specimens were examined in the FTIR characterization. As seen in Figure 16, the minor band detected at 560~570 cm⁻¹ is ascribed to the external linkage vibrations of the TO₄ in the double rings of zeolite [68]. The most prominent peak is noted between 800 and 1300 cm⁻¹, attributed to the asymmetric stretching vibrations of the polymerized band ‘Si-O-T’, [69,70]. Here, ‘T’ indicates the four coordinated silicon or aluminum atoms. Note that the degree of geopolymerization is widely recognized to be associated with the shift in this band under FTIR evaluations [70]. Further, other minor bands positioned at ~1645 cm⁻¹ and ~3370 cm⁻¹ are attributed to the vibrations of H–O–H and –O–H, both implying the presence of chemically bound water in the reaction products [68]. Figure 16a–c illustrate the FTIR spectra for the geopolymers prior to sulphuric acid immersion, while Figure 16d–f show the respective case after the sulphuric acid attack. Whether the SiO₂/Al₂O₃ ratio rises or whether it drops, the Na₂O/Al₂O₃ ratio is seen to decide the degree of geopolymerization for the un-exposed specimens. This is evident from the noticeable increase in the wavenumber of the principal Si-O-T band. By contrast, varying the H₂O/Na₂O ratio causes a very minor difference in this regard. Evidently, the H₂O/Na₂O ratio governs the microstructure and pore structure but not the reaction products.

Sulphuric acid attack on geopolymers is seen to trigger dealumination in polymerized aluminosilicate frameworks, and, afterwards, the aluminum atoms are mostly leached out to the exterior [71]. Also, the peak of the S-O bond is located within the range of the Si-O-T band in the FTIR spectrum. But the center of the former is about 1070 cm⁻¹ [30], which is slightly higher than the latter (~960–1000 cm⁻¹ noted here). Given the above, the overall peak assigned to the Si-O-T band was widely found to shift toward the higher end of the wavenumber after sulphuric acid immersion [31,71]. This phenomenon was also witnessed in the present study; see Figure 16. The difference in the wavenumber for the principal Si-O-T band just before and after the sulphuric acid attack is computed in Figure 17. As expected, the mixture made with SiO₂/Al₂O₃ = 3.4 displays the smallest shift in terms of the Si-O-T band after sulphuric acid immersion. This is mutually supported by the corresponding XRD results (in Figure 12). Further, it is interesting to note that the mixture incorporating a SiO₂/Al₂O₃ of 2.2 experienced the second-lowest shift across the five examined specimens, ranking only behind the optimal case of 3.4. Recall, as stated earlier, the mixture made with the lowest SiO₂/Al₂O₃ ratio was found to contain numerous crystals and also displayed low amorphicity in the previous XRD evaluation. This may imply that its polymerized aluminosilicate amount was considerably less than that for the other four mixes. As a result, the corresponding Si-O-T band in the FTIR spectrum is likely to show a relatively small shift after sulphuric acid immersion. With regard to the two Na₂O-involved ratios, one sees in Figure 17 that increasing either of them boosts the acid-induced shift in terms of the principal Si-O-T band. This justifies that the geopolymer system made with the larger Na₂O/Al₂O₃ or/and H₂O/Na₂O ratios will deteriorate more substantially when subjected to sulphuric acid attack. In the former, this may be due to the depressed degree of geopolymerization alongside the degraded pore structure. While in the latter, the evolving deterioration is mainly attributed to the increase in permeable voids.

In order to interpret the structural changes referred to above, the FTIR spectra were deconvoluted for the range of 800~1250 cm⁻¹, which corresponds to the polymerized Si-O-T band [68]. The associated fitting procedure was performed according to the related literature [68,72]. In this manner, the following peaks were considered: Peak I (~850–860 cm⁻¹) to Si-OH bending; Peak II (~930 cm⁻¹) to Si-O-T in Q²; Peak III (~960 cm⁻¹) to asymmetric stretching vibrations of nonbridging oxygen (NBO) sites; Peak IV (~1000 cm⁻¹) to Si-O-T in a three-dimensional N-A-S-H network; Peak V (~1070–1080 cm⁻¹) to Si-O-Si of silica gels (also the S-O bond after sulphuric acid immersion [30]); and Peak VI (~1150–1160 cm⁻¹) to Si-O-T of unreacted metakaolin. The FTIR deconvolution peaks for representative mixtures right before and after the sulphuric acid attack are now presented in Figure 18 and Figure 19, respectively, with a regression coefficient R² of 0.99. Also, the relative area proportions for the aforementioned sub-peaks are quantified, as illustrated in Figure 20.

For the geopolymers prior to the sulphuric acid attack, increasing the SiO₂/Al₂O₃ ratio leads to a significant rise in the area proportion of Peak V, alongside a reduction in the area fraction of Peak III; see Figure 20a. Since amorphous silica is now abundantly available to promote the aluminosilicate oligomer formation as well as the chain length, a greater degree of geopolymerization ensues [70]. Moreover, it is once again confirmed here that mixtures made with the larger Na₂O/Al₂O₃ or H₂O/Na₂O ratios register a lower polycondensation degree, as particularly evident from the smaller proportion of N-A-S-H networks (Peak IV) and the greater percentage for NBO (Peak III). Comparing Figure 20a,b, the sulphuric acid attack on the geopolymers causes a significant rise in the relative proportion of Peak V and a considerable reduction in the relative fraction of NBO (Peak III). The increased Peak V is led by the penetrated ${\mathrm{S}\mathrm{O}}_4^{2-}$ and the released silicic acid during the sulphuric acid attack. The reduced Peak III area may be attributed to the fact that the dealuminated N-A-S-H frameworks release numerous Al-OH groups to the exterior, accompanied by the leaching of nonbridging oxygens. Although a part of silicon species may also be leached out, the corresponding amount is significantly lower than aluminum species [57]. From the prospect of chemistry, the tetrahedral ${\mathrm{A}\mathrm{l}\mathrm{O}}_4^{-}$ could only attain stability under a strong alkaline condition, whereas the progressive acid attack reduces the alkalinity inside the geopolymer significantly, which in turn transforms ${\mathrm{A}\mathrm{l}\mathrm{O}}_4^{-}$ into general Al³⁺ [19]. These Al³⁺ ions are no longer able to form aluminosilicate oligomers. Instead, the depolymerized SiO₄ groups are still tetrahedral due to the nature of tetravalence and may possibly re-link to the local geopolymer as time elapses. Furthermore, one can note in Figure 20c that in each of the independent series, the respective optimal case, i.e., SiO₂/Al₂O₃ = 3.4, Na₂O/Al₂O₃ = 0.8, and H₂O/Na₂O = 8, displays the minimal increase in the relative proportion of Si-O-Si (Peak V) as well as the smallest reduction in the relative fraction of NBO (Peak III). In other words, they were the most chemically durable against the sulphuric acid attack across their respective series.

3.8. Scanning Electron Microscope and Energy Dispersive X-Ray Spectroscopy (SEM-EDS)

Prior to the sulphuric acid attack, the microstructure of various N-A-S-H geopolymer mixtures was evaluated under SEM at 300X and 5000X magnifications. The raw images, alongside the associated binarized images, are now presented in Figure 21 and Figure 22. The images taken under the lower magnification visibly showed the microcracks, while the other set captured under the higher magnification yielded a clear view of the voids and compactness of the examined samples. As seen in Figure 21a–c, an increase in the SiO₂/Al₂O₃ ratio from 2.1 to 3.4 led to a considerable refinement of the microstructure of the geopolymers. This manifested in an approximate reduction in the width of microcracks from 8 μm to 1 μm. However, the further increase in this ratio from 3.4 to 3.7 appeared to increase the size of microcracks up to about 2 μm, likely attributed to the increased liquid content and the resultant high liquid-to-solid ratio. Under the higher magnification (5000X), the mixture made with a SiO₂/Al₂O₃ ratio of 3.4 also displayed the densest texture across the three examined samples shown in Figure 22a–c. This is then supported by the quantification of the area of voids and microcracks based on the associated binarized images; see Figure 23. With regard to the Na₂O/Al₂O₃ ratio, increasing the value from 0.8 to 1.3 boosted the evolution of microcracks appearing in the N-A-S-H geopolymers and loosened the associated texture. This is evident in Figure 21d–f and Figure 22d–f, alongside the quantified area of voids and cracks shown in Figure 23. In the case of the H₂O/Na₂O ratio, lowering this ratio effectively alleviated the appearance of cracks and large pores in the hardened geopolymers; see Figure 21g–i. However, in comparison with Figure 22g,h, the excessively low H₂O/Na₂O ratio degrades the texture of the formed N-A-S-H networks. This may be explained through polycondensation. Recall that in Figure 14, the polycondensation of aluminosilicate oligomers is a regeneration process of Na⁺ and OH^-. The low H₂O/Na₂O ratio essentially corresponds to the high alkali concentration. Thus, once this ratio exceeds a certain threshold, the polycondensation may be depressed instead, and hence, the texture of the polymerized N-A-S-H framework is so loosened.

For various post-exposed specimens, SEM images were captured at the transition zone, as highlighted in Figure 24, namely, the position between the severely degraded and visually intact regions. As seen in Figure 25, regardless of the mixture compositions, varying crack growths could be noted in comparison to the respective un-exposed sample (at 300×). Nevertheless, the mixtures respectively made with a SiO₂/Al₂O₃ ratio of 3.4 (Figure 25b), a Na₂O/Al₂O₃ ratio of 0.8 (Figure 25d), and a H₂O/Na₂O ratio of 8 (Figure 25g) displayed the smallest acid-induced microcracks in the respective series. This phenomenon also supports their physical and mechanical performances after the sulphuric acid attack. Further, the EDS results sourced from the cross section at 300X magnifications are summarized in

Table 4. Relative mass proportion of various elements constituting N-A-S-H geopolymers.

Mixture Designations		O (%)	Na (%)	Al (%)	Si (%)	S (%)
SiO2/Al2O3 = 2.2	un-exposed (exposed)	49.42 (43.23)	13.98 (2.72)	17.12 (26.83)	19.48 (21.81)	0 (5.21)
SiO2/Al2O3 = 3.4	un-exposed (exposed)	46.96 (44.54)	11.51 (11.30)	14.81 (15.49)	26.71 (28.62)	0 (0.044)
SiO2/Al2O3 = 3.7	un-exposed (exposed)	48.39 (40.56)	12.45 (11.24)	13.06 (16.07)	26.10 (31.99)	0 (0.14)
Na2O/Al2O3 = 0.8	un-exposed (exposed)	47.22 (40.19)	12.28 (12.44)	15.40 (16.71)	25.09 (30.28)	0 (0.39)
Na2O/Al2O3 = 0.9	un-exposed (exposed)	50.00 (48.40)	10.31 (10.03)	14.44 (14.43)	25.24 (26.45)	0 (0.69)
Na2O/Al2O3 = 1.3	un-exposed (exposed)	49.62 (39.22)	18.38 (13.31)	11.88 (16.48)	20.11 (27.88)	0 (3.11)
H2O/Na2O = 8	un-exposed (exposed)	45.68 (42.54)	14.28 (12.53)	14.47 (16.89)	25.57 (27.91)	0 (0.13)
H2O/Na2O = 10	un-exposed (exposed)	49.20 (45.61)	13.47 (11.72)	13.07 (15.53)	24.25 (26.72)	0 (0.42)
H2O/Na2O = 14	un-exposed (exposed)	47.81 (42.61)	12.51 (8.70)	14.75 (17.90)	24.93 (30.15)	0 (0.63)

. As widely reported, the acid-induced degradation of geopolymers is commonly stated to start with the replacement of exchangeable alkali metal ions by hydrogen ions (H⁺) [36,37,38]. This was also confirmed in the present study. One sees that most of the mixtures experienced a noticeable reduction in the relative mass proportion of Na. On the other hand, only minor amounts of sulphur (S) could be detected in various specimens after exposure. This is likely due to the acid-induced degradation of N-A-S-H networks, which is led by hydrogen ions (H⁺). However, the attendant sulphur could not form any corrosion products due to the extremely low Ca²⁺ content in aluminosilicates and, therefore, displayed a relatively low content. This phenomenon was confirmed elsewhere by Qu et al. [30]. Their EDS results indicated that even after 18 months of exposure to sulphuric acid, the region identified as the N-A-S-H network only registered 0.06~0.56% S, whereas this value in the area contained gypsum and AFt increased up to 5.69~11.99% [30]. Nevertheless, the Na content in the mixture with a SiO₂/Al₂O₃ ratio of 2.2 reduced drastically after 12 weeks of acid exposure, from 13.98% to 2.72%. In addition, it registered the highest increase in the S content (5.21%), progressively followed by 0.14% for SiO₂/Al₂O₃ = 3.7 and 0.044 for SiO₂/Al₂O₃ = 3.4. The N-A-S-H geopolymer made with a very low SiO₂/Al₂O₃ ratio was extremely susceptible to the sulphuric acid environment, which is likely due to the low polycondensation degree and the loose microstructure. On the other hand, due to the higher liquid content, a continuous increase in the SiO₂/Al₂O₃ ratio will not enhance the acid resistance monotonically. In the case of the Na₂O/Al₂O₃ ratio, increasing its value from 0.8 to 1.3 appeared to boost the replacement of Na⁺ in the N-A-S-H framework by H⁺. This is evident from the highest S content (3.11%) alongside the greatest reduction rate in the Na⁺ content (5.07%), as noted for the mixture of Na₂O/Al₂O₃ = 1.3. Similarly, the higher H₂O/Na₂O ratio corresponds to greater deterioration, manifesting chemically as a higher reduction in Na⁺ along with the higher S content after the sulphuric acid attack.

3.9. Sensitivity Analysis

An effective variance-based sensitivity analysis [73] was conducted, as per Equations (3) and (4), to quantify the influence of compositional oxide ratios on the performances of the geopolymers. Here, x indicates the respective compositional oxide ratio and y is the evaluated performance. As well, n denotes the size of the dataset and m represents the median value of each factor. The data in terms of the acid penetration degree and the compressive strength loss at 84 days of exposure were analyzed. The sensitivity index, S_i, for each factor is defined as the proportion of the effective partial variance, V_ei, in the total effective variance, V_te. An increment coefficient, α_ij, is introduced to eliminate the disturbance and to normalize the traditional variance.

$$V_{ei}={\displaystyle \frac{1}{n-1}}{\displaystyle \sum _{j=1}^n\frac{{\left(y_{ij}-y_{im}\right)}^2}{{\alpha }_{ij}}} \mathrm{with} {\alpha }_{ij}={\displaystyle \frac{x_{ij}-x_{im}}{x_{im}}}$$

(3)

$$S_i={\displaystyle \frac{V_{ei}}{V_{te}}}={\displaystyle \frac{V_{ei}}{{\sum }_{i=1}^l{V}_{ei}}} \in [0,1]$$

(4)

The computed sensitivity indices are now illustrated in Figure 26. As seen therein, the sulphuric acid-induced deteriorations are more dependent on the other two Na₂O-involved ratios. Particularly, the H₂O/Na₂O ratio is noted to dominate the resistance of the geopolymers to the penetration of acid ions, as evident from the highest sensitivity index, i.e., 77.6%. This is likely due to the following: (i) While a continuous increase in the SiO₂/Al₂O₃ ratio favours the degree of geopolymerization, an excess, i.e., a value beyond 3.4, may also degrade the associated microstructure. Accordingly, there exists an offset between these two attendant effects. (ii) On the other hand, raising the Na₂O/Al₂O₃ and H₂O/Na₂O ratios depresses the geopolymerization and threatens the microstructure of geopolymers in parallel. This, in turn, intensifies the eventual acid-induced deterioration.

4. Multi-Factor Modelling

Multi-factor modelling allows us to establish the explicit model and determine the coefficients empirically when adequate data points are obtained [74,75]. This study aims to propose a guideline for designing durable N-A-S-H geopolymers based on principal compositional ratios, namely, SiO₂/Al₂O₃, Na₂O/Al₂O₃, and H₂O/Na₂O so that they are considered as three explanatory variables in the model establishment. In addition, as varying any one of the above ratios will automatically alter the liquid-to-solid ratio (L/S), it is taken here as the fourth explanatory variable. Further, the penetration of deleterious chemicals in cementitious materials is also a time-dependent behaviour [76]. Therefore, the exposure duration (t) is treated as the fifth explanatory variable. Here, the correlation between the acid-induced penetration degree (D_n/R or D_cn/R) and t is illustrated in Figure 27. A linear approximation was assumed in this study, as supported by experimental evidence here. The dataset used to establish the multi-factor models is now summarized in

Table 5. Dataset for establishing the multi-factor models and the predicted outcomes.

SiO2/Al2O3	Na2O/Al2O3	H2O/Na2O	L/S	Exposure Time (yrs)	Tested Depth (mm)	Predicted Depth, Dn (mm)	Predicted Depth, Dcn (mm)
2.2	0.9	11	1.102	0.077	2.80	2.47	2.38
2.8	0.9	11	1.242	0.077	2.10	2.09	2.45
3.1	0.9	11	1.312	0.077	1.99	2.08	2.06
3.4	0.9	11	1.382	0.077	1.67	2.20	1.79
3.7	0.9	11	1.441	0.077	2.32	2.43	1.99
3.1	0.8	11	1.193	0.077	2.16	1.97	1.93
3.1	1.1	11	1.551	0.077	2.44	2.31	2.38
3.1	1.3	11	1.790	0.077	2.48	2.53	2.78
3.1	1.0	8	1.199	0.077	1.38	1.47	1.29
3.1	1.0	10	1.354	0.077	2.11	1.95	1.89
3.1	1.0	12	1.509	0.077	2.54	2.44	2.54
3.1	1.0	14	1.663	0.077	3.24	2.92	3.23
2.2	0.9	11	1.102	0.153	4.65	4.91	4.73
2.8	0.9	11	1.242	0.153	4.37	4.14	4.88
3.1	0.9	11	1.312	0.153	4.08	4.14	4.09
3.4	0.9	11	1.382	0.153	3.60	4.38	3.57
3.7	0.9	11	1.441	0.153	4.12	4.83	3.95
3.1	0.8	11	1.193	0.153	3.73	3.92	3.83
3.1	1.1	11	1.551	0.153	4.42	4.58	4.72
3.1	1.3	11	1.790	0.153	4.97	5.03	5.52
3.1	1.0	8	1.199	0.153	3.41	2.91	2.56
3.1	1.0	10	1.354	0.153	3.87	3.88	3.75
3.1	1.0	12	1.509	0.153	5.32	4.84	5.04
3.1	1.0	14	1.663	0.153	7.03	5.80	6.43
2.2	0.9	11	1.102	0.230	7.17	7.39	7.11
2.8	0.9	11	1.242	0.230	6.91	6.23	7.33
3.1	0.9	11	1.312	0.230	5.76	6.22	6.15
3.4	0.9	11	1.382	0.230	4.85	6.59	5.36
3.7	0.9	11	1.441	0.230	5.64	7.26	5.94
3.1	0.8	11	1.193	0.230	5.17	5.89	5.76
3.1	1.1	11	1.551	0.230	6.50	6.89	7.10
3.1	1.3	11	1.790	0.230	8.15	7.56	8.30
3.1	1.0	8	1.199	0.230	4.99	4.38	3.84
3.1	1.0	10	1.354	0.230	5.19	5.83	5.64
3.1	1.0	12	1.509	0.230	8.15	7.28	7.58
3.1	1.0	14	1.663	0.230	10.76	8.72	9.66

.

In Figure 8, it is seen that the penetration degree of acid ions grows with an increase in the Na₂O/Al₂O₃ and H₂O/Na₂O ratios, whereas there exists an optimal value for the SiO₂/Al₂O₃ ratio (here, 3.4) to achieve the smallest neutralized depth. Once again, linear correlations are adopted for the first two ratios, while a parabolic correlation is assumed for the third ratio. Further, the neutralization degree is assumed to vary linearly with the liquid-to-solid ratio, L/S. Thus, a preliminary mathematical expression for the neutralized depth is described as Equation (5). However, this model does not account for any coupling between the four selected variables. So, an updated model was obtained using the product of these four explanatory variables, and the coupled multi-factor model is presented as Equation (6).

$$D_n=\left[a_1{(x_1-3.4)}^2+a_2{x}_2+a_3{x}_3+a_4{x}_4\right]x_5$$

(5)

$$D_{cn}=\left[c_1{(x_1-3.4)}^2+c_2{x}_2+c_3{x}_3+c_4{x}_4+c_5{(x_1-3.4)}^2{x}_2{x}_3{x}_4\right]x_5$$

(6)

where x_i denotes the individual explanatory variable: SiO₂/Al₂O₃, Na₂O/Al₂O₃, H₂O/Na₂O, L/S ratios, and t when the sub-index i increases from 1 to 5 continuously. D_n and D_cn mean the neutralized depth, as predicted by the uncoupled and coupled models, respectively.

Each unknown coefficient is linearly expanded with a couple of regression coefficients, b_i. The size of the coefficient vector, b, is dependent on the number of items after variable separation, z. The expanded model may be updated as a matrix form to include all n sets of data, as given in Equation (7). The residual error, ε, between the predicted and the actual values is computed by a n × 1 vector; see Equation (8). The optimal solution to Equation (7) will be determined when the estimator in terms of the residuals (Equation (9)) achieves the minimum. Therefore, the derivative of S(ε) is set to zero, and this yields the equation for solving the coefficient vector, as shown in Equation (10). The error is quantified here by calculating the corresponding coefficient of determination, R², as per Equation (11), where l and l’ are the unit vector and the respective inverse and I represents the identity matrix.

$$Y=Xb , Y=\left(\begin{array}{c}{Y}_1\\ Y_2\\ ⋮\\ Y_n\end{array}\right),X=\left(\begin{array}{cccc}{X}_{11}& \cdots & X_{1z}& 1\\ X_{21}& \cdots & X_{2z}& 1\\ ⋮& ⋮& ⋮& ⋮\\ X_{n1}& \cdots & X_{nz}& 1\end{array}\right),b=\left(\begin{array}{c}{b}_1\\ b_2\\ ⋮\\ b_n\end{array}\right)$$

(7)

$$\epsilon =y-Xb$$

(8)

$$S(\epsilon )={\displaystyle \sum {\epsilon }_i}={\epsilon }^{’}\epsilon ={(y-Xb)}^{’}(y-Xb)$$

(9)

$$b={(X^{’}X)}^{-1}{X}^{’}y$$

(10)

$$R^2=1-{\displaystyle \frac{{\epsilon }^{’}\epsilon }{y^{’}Ny}}={\displaystyle \frac{b^{’}{X}^{’}(I-\frac{1}{n}l{l}^{’})Xb}{y^{’}(I-\frac{1}{n}l{l}^{’})y}}$$

(11)

The optimal estimate of coefficient vectors for each proposed multi-factor model is solved using the experimental dataset so that the uncoupled model and the coupled multi-factor model are now determined as Equation (12) and Equation (13), respectively. Figure 28 compares the outcome from the proposed multi-factor models and the actual experimental observations. One can see that even without the coupling between explanatory variables, the data points distribute uniformly around the linearly fitted line (Y = X), with a promising determination coefficient equaling 0.92. This suggests that the employed linear approximation is capable of describing well the relationship between the output and the considered inputs. Moreover, the considered coupling term is found to increase the R² slightly from 0.92 to 0.94.

$$D_n=\left[9.2{(R_{S/A}-3.4)}^2-27.2R_{N/A}+0.44R_{H/N}+34.9R_{L/S}\right]t$$

(12)

$$D_{cn}=\left[-118.4{(R_{S/A}-3.4)}^2+11.9R_{N/A}+3.23R_{H/A}-16.6R_{L/S}+11.05{(R_{S/A}-3.4)}^2{R}_{N/A}{R}_{H/N}{R}_{L/S}\right] t$$

(13)

where R_S/A, R_N/A, R_H/N, and R_L/S represent the SiO₂/Al₂O₃, Na₂O/Al₂O₃, H₂O/Na₂O, and L/S ratios, respectively.

5. Correlation Between D_cn/R and Losses in Compressive Strength

The previously proposed multi-factor model defines the neutralized degree as the fraction of D_cn over the initial diameter of the specimen (R). The neutralized degree (D_cn/R) may now be correlated with the loss in compressive strength (CSL). Once the degree of acid-induced neutralization is determined based on the multi-factor models, its impact on the mechanical strength of geopolymers may therefore be estimated. In this manner, the potential acid-induced damage to both the geopolymer matrix and the embedded reinforcements may be evaluated over time. Connecting back to the compressive strength results shown in Figure 10, all the geopolymers displayed a loss in compressive strength at and after 8 weeks of sulphuric acid immersion. So, the strength data collected at 8 and 12 weeks are accordingly plotted against the respective D_cn/R in Figure 29. As seen therein, an approximate polynomial correlation is used, and the corresponding result displays an adequate fitting efficiency and accuracy, as evident from an R² of 0.833. Note that the expression with the higher degree of the polynomial has also been examined during the fitting process. However, the quadratic equation is found to be the optimal one and, therefore, was eventually adopted in this study.

The current investigation focuses on the performance of metakaolin-based geopolymers exposed to sulphuric acid attack. Future work should examine other types of precursors, and certain combinations of these alumina–silica precursors deserve special attention. In addition to acid attack, those compositional ratios should be optimized further for other durability concerns, including chlorides, carbonates, dry–wet cycling, and also their mutual couplings.

6. Conclusions

This study examines the effect of sulphuric acid attack on N-A-S-H geopolymers, with a particular focus on the constituent oxides. Metakaolin served as the aluminosilicate precursor. The geopolymer was cast both as paste and as mortar. The specimens were immersed in sulphuric acid for periods of up to 12 weeks. The mortar specimens were examined for macroscopic properties, while the paste mixtures were examined for microstructure, morphology, and chemical composition. Based on the findings, the principal conclusions are as follows:

(1) In metakaolin-based geopolymers, exposure to sulphuric acid leads to depolymerization in the N-A-S-H network. As well, the crystalline zeolites transform into their respective amorphous phase. However, the amorphicity of the geopolymer, on the whole, is diminished with the progressive duration of exposure, as evident from XRD traces, wherein the diffuse hump shifts toward the lower end of 2θ. The structure of N-A-S-H geopolymers witnesses a loss in nonbridging oxygen atoms, as evident from a forward shift for the principal Si-O-T band in the FTIR spectrum. Simultaneously, under thermo-gravimetric analysis, the DTG peak related to the N-A-S-H framework was higher after the sulphuric acid attack. This illustrates the acid-induced dealumination, which leaches Al-OH groups out to the exterior. Concurrently, the associated Si-OH groups may re-link to the intact aluminosilicate network.

(2) When exposed to sulphuric acid, resistance to acid-induced deterioration is best obtained at a SiO₂/Al₂O₃ ratio of 3.1–3.4. Although an increase in this ratio promotes the formation and length of aluminosilicate oligomers, it also increases the amount of permeable voids. Similarly, the optimal Na₂O/Al₂O₃ ratio was observed at 0.8~0.9, which is slightly lower than the theoretical value of 1.0 for the equilibrium of chemical valency states. An increase beyond this range led to depressed geopolymerization and higher liquid content. The optimal H₂O/Na₂O ratio was 8–10.

(3) The sensitivity analysis illustrates that the performance of N-A-S-H geopolymers after sulphuric acid attack is more sensitive to Na₂O and its relative proportions. In particular, decreasing the Na₂O/Al₂O₃ is most beneficial to retain compressive strength. On the other hand, a decrease in the H₂O/Na₂O ratio will slow the rate of loss in alkalinity of the geopolymer matrix, which ultimately is favourable to resist acid-induced corrosion.

(4) The proposed multi-factor models capture the effect of each oxide ratio on the performance of geopolymers against the penetration of acid ions. Even without coupling, the proposed multi-factor model successfully predicts the neutralization depth, as evident from the coefficient of determination, R² > 0.90. Also, upon using the quadratic polynomial expression, the predicted neutralization depth agrees with the actual loss in compressive strength.