Optimization of mineral trioxide aggregate formulation using Taguchi design and impedance analysis

Introduction

Since its introduction in 1993 under the brand name ProRoot^® MTA (Dentsply Tulsa Dental, Johnson City, TN, USA), mineral trioxide aggregate (MTA) has become an widely used material in endodontic and restorative dentistry. Its clinical applications include root canal sealing, pulp capping, pulpotomy, apexification, perforation repair, and apical sealing (1, 2). MTA is favored for its excellent biocompatibility, non-toxicity, reliable sealing ability even under moist conditions, and dentin bridge formation (3). It is primarily composed of Portland cement and bismuth oxide (as a radiopacifier), typically mixed at a 4:1 ratio (4). The major functional components of MTA, tricalcium silicate (C3S) and dicalcium silicate (C2S), react with water to form calcium silicate hydrate (C-S-H) and calcium hydroxide (CH). The C-S-H contributes to mechanical strength and dimensional stability, while CH provides high alkalinity (pH ~12.5), promoting antibacterial effects and hard tissue formation (5).

Gray MTA (GMTA), the original formulation, contains aluminoferrite, which contributes to discoloration. In 2002, white MTA (WMTA) was developed by removing this component to enhance aesthetics (6, 7). WMTA exhibits a significantly shorter setting time (~15 min) compared to the 2-4 h required for conventional GMTA (8). However, due to its smaller and narrower particle size distribution (eight times smaller than GMTA), some studies have reported that WMTA is more challenging to work with than GMTA (9).

Numerous commercial MTA products have been introduced over the years. Despite these advancements, MTA continues to face limitations such as high cost, handling difficulty, and long setting time, restricting its widespread application (10). To address these issues, various approaches have been explored, including the use of additives such as calcium chloride, sodium lactate, and propylene glycol, and the development of improved delivery systems (11, 12). However, many of these efforts have relied on empirical, trial-and-error approaches, lacking a systematic investigation of how individual component ratios affect performance.

The Taguchi L9 (3⁴) orthogonal array design provides a statistically robust and efficient method to evaluate the effects of multiple variables with a limited number of experiments. This method has been widely used in materials research to identify key compositional factors influencing physical properties (13). Applying this approach to MTA enables a structured optimization of formulation by examining the influence of C3S, C2S, tricalcium aluminate (C3A), and the water-to-cement (W/C) ratio on setting behavior. Furthermore, electrochemical impedance spectroscopy (EIS) was used to monitor the hydration process and determine setting time with precision. EIS is a non-destructive, real-time analytical technique that captures the evolution of electrical resistance during hydration, making it well suited for evaluating the dynamic setting behavior of cementitious systems.

In this study, the major components of C3S, C2S, and tricalcium aluminate (C3A) were individually synthesized using a solid-state method. Their structural and physicochemical characteristics were characterized using XRD, SEM, and DSC. Impedance analysis was performed to monitor the hydration process, and additional characterization was conducted after halting hydration with acetone. Using the Taguchi L9 design, this study systematically evaluated the influence of key compositional factors and W/C ratio on setting time. This study provides a systematic and efficient approach for controlling the setting time of MTA, providing foundational insights for the development of high-performance dental materials.

Materials and Methods

Reagent-grade raw materials were used to synthesize the cement components, including CaO (99.95%), SiO₂ (99.9%), Al₂O₃ (99%), MgO (99+%), Na₂CO₃ (99.5%), CaF₂ (99.5%), Bi₂O₃ (99.9%), and CaSO₄·2H₂O (99%), all of which were purchased from Alfa Aesar. The compositions for synthesizing tricalcium silicate (C3S), dicalcium silicate (C2S), and tricalcium aluminate (C3A) are listed in Table 1. The raw materials were weighed accordingly, mixed with isopropyl alcohol (IPA), and homogenized using a ball mill for over 24 h. The resulting slurry was dried at 80 °C for 24 h, followed by calcination in a platinum crucible at designated temperatures: 1150 ℃ for C2S, 1450 ℃ for C3S, and 1400 ℃ for C3A, each for 5 h. The samples were then rapidly cooled.

Table 1.

Composition of starting materials for synthesizing C3S, C2S, and C3A

The synthesized powders were characterized using X-ray diffractometry (XRD; D/Max Ultima III, Rigaku, Japan) and scanning electron microscopy (SEM; JSM-7900F, JEOL, Japan). The heat evolution during hydration was evaluated by differential scanning calorimetry (DSC; DSC3, Mettler Toledo, Switzerland). Setting behavior was analyzed using electrochemical impedance spectroscopy (EIS) with a frequency response analyzer (SI-1260, Solatron, UK). Impedance spectra were acquired using Z60 software, over a frequency range from 10⁶ Hz to 0.1 Hz, with 10 points per decade on a logarithmic scale.

To systematically evaluate the influence of C3S, C2S, C3A content, and the water-to-cement (W/C) ratio on MTA setting time, a Taguchi L9 (3⁴) orthogonal array design was employed (13). The factors and their corresponding levels are listed in Table 2.

Table 2.

Experimental factors and levels using Taguchi L9 (34) orthogonal array

Results

1. X-ray diffraction and microstructure of the synthesized MTA components

X-ray diffraction (XRD) analysis was performed to verify the phase purity of the synthesized MTA components-C3S, C2S, and C3A. The diffraction patterns shown in Figures 1(a), 1(b), and 1(c) correspond to monoclinic C3S (JCPDS # 860402), β-C2S (JCPDS # 860398), and cubic C3A (ICDD # 38-1429), respectively, confirming the successful synthesis of single-phase structures (14). Minor secondary peaks were observed in the C3S and C2S patterns at 2θ = 32.1° and 34.4°, indicating trace coexistence of C2S and C3S (denoted by* and ▼). In the C3A pattern, additional peaks suggest the coexistence of approximately 11% CaO impurities (ICDD card #37-1497). These impurities may affect the initial and intermediate setting behavior of the cement (15). Therefore, optimizing the synthesis conditions is essential to minimize the formation of such secondary phases.

Figure 1.

XRD patterns of synthesized C3S, C2S, and C3A powders.

The microstructures of C3S, C2S, and C3A were examined using scanning electron microscopy (SEM), as shown in Figure 2. All synthesized powders exhibited irregular, plate-like morphologies, and the particle sizes were found to be approximately below 30 µm.

Figure 2.

SEM images of synthesized C3S, C2S, and C3A powders.

2. Differential scanning calorimetric analysis

Differential scanning calorimetry (DSC) was conducted to evaluate the hydration behavior of the synthesized powders over a 120-min period, as shown in Figure 3. The initial peak in the heat flow curve corresponds to the dissolution of cement particles upon mixing with water (16). The induction period of cement hydration of C3S is slower compared to C2S and C3A. The cumulative heat curves of C3S and C2S exhibit a rapid exothermic reaction within the first 10 min, reflecting the formation of calcium silicate hydrate (C-S-H) and calcium hydroxide (CH), with continued heat release up to 80 min, suggesting sustained hydration and strength development (17). In contrast, C3A reacted rapidly, completing its exothermic reaction within approximately 20 min due to the formation of calcium aluminate hydrate (C–A–H), which contributes to early-stage strength development of the cement (18). These results highlight the functional distinction among the components: C3A plays a critical role in initiating early setting and strength gain, while C3S and C2S contribute to the prolonged hydration process essential for long-term structural stability. This thermal behavior also supports the compositional optimization results derived from the Taguchi analysis, where higher C3A content was associated with faster setting times.

Figure 3.

Heat flow (blue line) and cumulative heat (red line) of synthesized C3S, C2S, and C3A powders.

3. Electrochemical impedance spectroscopy

Electrochemical impedance spectroscopy (EIS) was employed to monitor the hydration behavior of C3S, C2S, and C3A over time. Figures 4(a)–4(c) display the Nyquist plots of impedance spectra for each component at various hydration times, while Figures 4(d)–(f) present the corresponding resistance values extracted from the high-frequency intercepts. All samples exhibited a characteristic semicircular arc, indicating typical ionic conduction behavior in cement pastes (19, 20).

Figure 4.

Impedance measurement results (a-c) and inferred resistance values (d-f) at different curing ages for C3S, C2S, and C3A.

For C3S, the resistance initially decreased and then increased after approximately 60 min. This trend suggests that ionic mobility for dissolved species (e.g., Ca²⁺, SiO₄⁴⁻, OH⁻) was initially high due to rapid dissolution, but progressively declined as hydration products, such as calcium silicate hydrate (C–S–H), accumulated and hindered ion transport (21, 22). C2S showed a continuous decrease in resistance throughout the hydration period, indicating a slower but sustained reaction, consistent with its known long-term contribution to strength development. In contrast, C3A exhibited a rapid increase in resistance within the first 20 min, quickly reaching a plateau, reflecting its fast reactivity and early formation of calcium aluminate hydrate (C–A–H). These results clearly demonstrate that electrical resistance is closely correlated with the hydration kinetics of each cement component. The impedance trends also reinforce the findings from DSC analysis, confirming the distinct roles of each phase in controlling the setting behavior of MTA.

Figure 5.

XRD patterns (a, b) and SEM image analysis (c, d) of C3S and C2S after 2 h of hydration.

5. Impedance analysis

To quantify the setting behavior of cement, impedance spectra were further analyzed by converting the data into conductance (S) values across a range of frequencies. As shown in Figure 6(a), raw impedance data were transformed into frequency-dependent conductance curves (Figure 6(b)), allowing for clearer identification of hydration stages. From these data, conductance values at a fixed frequency of 100,000 Hz-where frequency dependence is minimal-were extracted and plotted over time, as shown in Figure 6(c).

Figure 6.

(a) Analysis of the cement hydration process through impedance measurements, (b) conductance changes with frequency, and (c) setting process over time.

The conductance-time profile (Figure 6(c)) revealed three distinct stages in the hydration process: an initial increase phase corresponding to ionic dissolution, a rapid decrease indicating the setting point due to the formation of hydration products, and a final plateau phase representing the completion of hydration. This approach enabled precise determination of the setting time for each sample. The analysis demonstrated that impedance-derived conductance is a reliable indicator of the progression of cement hydration, offering a non-destructive, time-resolved method for evaluating material performance.

Discussion

To identify the optimal combination of factors influencing MTA setting behavior, a Taguchi L9 (3⁴) orthogonal array was employed using four variables-C2S (A), C3S (B), C3A (C), and water-to-cement (W/C) ratio (D)-each at three levels. The experimental matrix and the corresponding setting times derived from impedance analysis are summarized in Figure 7. Conductance values were tracked over time for each of the nine experimental conditions. The conductance-time curves revealed clear differences in setting behavior depending on the combination of components. Samples containing a higher level of C3A generally exhibited a more rapid decrease in conductance, indicating faster setting due to accelerated hydration. Conversely, higher levels of C2S tended to delay the decrease in conductance, reflecting slower hydration kinetics. The W/C ratio also played a significant role, with lower ratios associated with faster setting due to denser microstructures and limited water availability.

Figure 7.

(Experimental results using L9 (34) orthogonal array and impedance measurements.

This systematic analysis enabled the identification of an optimal formulation-C3S: level 2, C2S: level 1, C3A: level 3, W/C: level 1-that resulted in the shortest setting time. These results confirm the effectiveness of impedance-based evaluation combined with Taguchi design in optimizing cement formulations.

Figure 8 presents the effect of each experimental factor-C3S, C2S, C3A, and W/C ratio-on the hydration completion time, as determined through Taguchi analysis. Each factor was tested at three levels, and the mean setting time at each level was calculated based on impedance measurements. The shortest setting time was observed at level 2 for C3S, indicating that a moderate proportion of C3S facilitates balanced hydration and efficient formation of calcium silicate hydrate (C–S–H). For C2S, level 1 resulted in the fastest setting, consistent with its known slower hydration behavior at higher concentrations. In the case of C3A, level 3 exhibited the shortest setting time, confirming that higher C3A content promotes rapid formation of calcium aluminate hydrate (C–A–H) and accelerates the initial setting. Similarly, the W/C ratio showed an optimal value at level 1, where a lower water content likely limited ion mobility but enhanced particle packing, leading to faster setting. Collectively, these results suggest that the optimal formulation for minimizing the hydration setting time comprises C3S at level 2, C2S at level 1, C3A at level 3, and W/C at level 1. This combination yields the fastest setting, as confirmed by both impedance-derived conductance trends and statistical Taguchi analysis, and is consistent with thermochemical behavior observed in previous DSC results.

Figure 8.

Hydration completion time based on levels of each factor.

To further assess the effect of physical properties on cement performance, the optimized MTA composition (C3S: 2, C2S: 1, C3A: 3, W/C: 0.3) was sieved into three distinct particle size ranges: ≤38 µm, 38–75 µm, and >75 µm. Figure 9 shows the setting behavior of each group, monitored using impedance-based conductance analysis. The finest particle group (≤38 µm) exhibited the fastest setting time, completing hydration in approximately 41 min. In comparison, the 38–75 µm group set in about 59 min, while the >75 µm group required approximately 74 min to complete hydration. This trend clearly demonstrates that smaller particle sizes significantly accelerate the setting process, likely due to their increased surface area and reactivity, which enhance water penetration and ion exchange during hydration (24, 25).

Figure 9.

Comparison of MTA setting times based on particle size.

These findings are consistent with cement chemistry principles and prior thermal and impedance analyses, further validating the role of particle size in optimizing MTA performance. The results suggest that controlling particle size distribution is an effective strategy for tuning setting characteristics in clinical applications. The particle size classification in this study was based on the practical limitations of ball milling and sieving techniques. In future studies, additional work with smaller particles obtained by jet milling and particle size selector should be employed to further optimize MTA properties.

These findings underscore the effectiveness of combining the Taguchi method with impedance analysis as a systematic approach to optimize MTA formulation. In particular, the integration of compositional design and particle size control provides a practical strategy to enhance setting performance. Future studies should aim to validate the clinical applicability of the optimized MTA and explore further functional modifications to expand its utility in dental materials.

Conclusion

This study successfully optimized the setting time of mineral trioxide aggregate (MTA) using the Taguchi method, focusing on the key components tricalcium silicate (C3S), dicalcium silicate (C2S), and tricalcium aluminate (C3A). The synthesized compounds were systematically characterized using XRD, SEM, and DSC analyses. XRD analysis confirmed the single phases of the synthesized compounds, while SEM images showed irregular plate-like structures with particle sizes below 30 µm. DSC analysis demonstrated prolonged exothermic behavior for C3S and C2S, whereas C3A exhibited a rapid thermal response within the first 20 min. Impedance analysis further elucidated the hydration behavior of each component: C3S showed an initial resistance drop followed by an increase, C2S exhibited a gradual resistance decrease, and C3A displayed a rapid resistance rise, reflecting their respective hydration kinetics. The optimized cement composition (C3S:2, C2S:1, C3A:3, and W/C:0.3) was evaluated across three particle size ranges (≤38 µm, 38–75 µm, >75 µm), confirming that smaller particles significantly accelerated the setting process. The final optimized formulation achieved a setting time of approximately 41 min. These results offer an effective approach for tailoring MTA formulations and provide foundational data for the development of high-performance dental cements with improved clinical usability.

Acknowledgments

This research was supported by the National Research Foundation of Korea (NRF) funded by the Korea government (MSIT) (RS-2019-NR040056) and by Chonnam National University (Grant No. 2025-0397-01).

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