Characterization and Exploration of Placket–Burman-Designed Porous Calcium Carbonate (Vaterite) Microparticles

The objective of the research was to identify significant variables that impact the porosity-related properties of CaCO3 particles. The Placket–Burman design was employed to screen multiple variables, including pH, molar concentrations of calcium chloride and sodium carbonate, temperature, concentration of Gelucire 44/14, Cremophor RH40, Solutol HS15, Labrasol, mixing rate, reaction time, and order of addition. The response variables were surface area, pore radius, and pore volume. Influential methodologies such as XRD, FTIR, Raman spectroscopy, and TGA were utilized to validate the precipitate type. The BET surface area ranged from 1.5 to 16.14 m2/g, while the pore radius varied from 2.62 to 6.68 nm, and the pore volume exhibited a range of 2.43 to 37.97 cc/gm. Vaterite structures with spherical mesoporous characteristics were observed at high pH, whereas calcite formations occurred at low pH. The order of addition impacted the surface area but did not affect the pore volume. To maximize the surface area, a lower reaction time and molar concentrations of sodium carbonate were found to be advantageous. The pore radius was influenced by the pH, surfactants, and reaction conditions. The sediments were categorized based on the percentage of vaterite formation. The instrumental techniques effectively characterized the precipitates and provided a valuable complementary analysis.


INTRODUCTION
Porous vaterite calcium carbonate (CaCO 3 ), owing to large porosity, high surface area, and rapid decomposition in acidic conditions, contributes to a practical and alternate drug delivery choice/sacrificial template to ferry drugs. 1,2Vaterite CaCO 3 has been reported as a host for various moieties such as doxorubicin, 3 antimicrobials, 4 rhodamine B, 5 photosens, 6 and methotrexate, 7 because of the inherently high surface area.The occurrence of vaterite in nature is relatively rare, primarily due to thermodynamic constraints that hinder the direct transformation of calcite into vaterite. 8Among various synthetic approaches (such as biomimetic synthesis and CO 2 -bubbling method) for preparing vaterite particles, the precipitation method using precursor salts (Na 2 CO 3 and CaCl 2 ) is relatively simple and industrially feasible. 8,9Mixing of the precursor salt seems to be an attractive alternative for the preparation of porous vaterite; however, the number of independent variables such as pH, temperature, reaction time, mixing mode, additives (surfactants, polymers, biomolecules, amino acids), and solvent ratio needs to be aptly controlled and optimized for its preparation.In the present research, we aim to screen and evaluate the critical independent variables (InV) influencing the response variables related to porosity such as surface area, pore radius, and pore volume.To achieve this, we employed the Placket−Burman design (PBD).The selected InV values were as follows: (a) pH, (b) molar concentration of calcium chloride, (c) molar concentration of sodium carbonate, (d) temperature, (e) concentration of additives (Gelucire 44/14, Cremophor RH40, Solutol HS15, Labrasol), (f) mixing rate, (g) reaction time, and (h) order of addition (L1, L2).Additives (Gelucire 44/14, Cremophor RH40, Solutol HS15, Labrasol) were selected based on our previous report that gave a maximum mole fraction of vaterite compared to calcite and aragonite. 5onsidering the apparent relationship between drug loading, surface area, pore radius, and pore volume were selected as response variables (ReV).Among various screening designs, we have chosen the PBD because it can identify the main factors from a pool of many InV (as in the present work) that have the most impact on the selected responses. 10During our literature review on preparing porous vaterite CaCO 3 , we identified a gap in knowledge regarding the relationship between different variables and their impact on the surface area, pore radius, and pore volume.These properties are crucial in determining the drug loading capacity and release behavior of the bioactive substances.To address this gap, the present research focuses on screening and evaluating the variables influencing response (surface area, pore radius, and pore volume) to enhance our understanding of this field.In one of our previous studies, we studied the impact of eleven different excipients on the phase transition behaviors of calcite, vaterite, and aragonite. 5To ascertain the authenticity of the precipitates formed through the PBD, we validated them by employing X-ray diffraction (XRD), Fourier transform infrared (FTIR) spectroscopy, Raman spectroscopy (RS), and thermogravimetric analysis (TGA).Also, we have classified the precipitates into three distinct groups based on vaterite content.Group 1 consists of sediments with a vaterite percentage exceeding 75%; Group 2 includes residues with a vaterite content ranging from 45% to 70%; and Group 3 exclusively comprises calcite forms.This classification provides valuable insights into the varying compositions of the residues and facilitates a more comprehensive analysis of the experimental results.

MATERIALS AND METHODOLOGY
2.1.Materials.Calcium chloride (CaCl 2 ) and sodium carbonate (Na 2 CO 3 ) were acquired from Sigma Aldrich (India) for this study.Additionally, Solutol HS15 and Cremophor RH40 were generously provided as gift samples by BASF (USA), while Labrasol and Gelucire 44/14 were supplied ex gratia by Gattefosse (France).A mechanical stirrer (IKA RW 20 digital, India) was used to mix the contents.GPT-4 and Grammarly served as AI-assistants in drafting the final manuscript.

Synthesis of Calcium Carbonate Particle Using
PBD. PBD is a fractional factorial design that uses a smaller number of runs than a complete factorial design while still being able to identify the main effects of the independent variables. 11A 16-run PBD was used to explore the eleven potential factors: pH (A: 4−12), the molar concentration of calcium chloride (B: 1.0−2.0M), the molar concentration of sodium carbonate (C: 1.0−2.0M), temperature (D: 4.0−60.0°C), Gelucire 44/14 concentration (E: 1.0−4.0%w/v), Cremophor RH40 concentration (F: 1.0−4.0%w/v), Solutol HS15 concentration (G: 1.0−4.0%w/v), Labrasol concentration (H: 1.0−4.0%w/v), mixing rate (J: slow (2 mL/min) and instantaneous), reaction time (K: 0.08−10.0h), and order of addition (L1: calcium chloride in the burette and sodium carbonate in a beaker; L2: sodium carbonate in the burette and calcium chloride in beaker) on response outcomes of surface area (Y1), pore radius (Y2), and pore volume (Y3).Design and Expert Analysis Software (version 13) generated factor combinations (PBD), polynomial equations, statistical outcomes, and other associated figures.Among eleven factors, discrete qualitative factors were J (mixing rate) and L (order of addition), and the rest were continuous quantitative factors.
2.3.Brunauer−Emmett−Teller (BET) Analysis.The surface area, pore radius, and pore volume of CaCO 3 microparticles were calculated based on BET theory under STP (NOVAtouch LX gas sorption analyzers; Quantachrome, United States).Samples were degassed in a vacuum at a temperature of 120 °C for 3−4 h, and the adsorption isotherms were obtained using nitrogen as an adsorbate.The specific surface area, pore radius, and pore volume of the CaCO 3 microparticles were evaluated by using the software tool integrated with the instrument.

Field-Emission Scanning Electron Microscopy (FESEM).
The surface morphologies of the prepared calcium carbonate particles were analyzed using FESEM (Carl Zeiss, Sigma 300) from Germany.To prepare samples for imaging, the dried and powdered samples were mounted onto brass stubs using double-sided tape and coated with gold in a vacuum.Imaging was performed at various resolutions and at an acceleration voltage of 5 kV to examine the surface features.

XRD Studies.
The diffraction patterns of 16 calcium carbonate precipitates were analyzed using the Rigaku-Miniflex Powder XRD analyzer (Rigaku, Japan).The analyzer was equipped with a 30 kV generator and a 15 mA anode tube, and Cu Kα radiation was used to produce the diffraction patterns.The scanning range was set between 2θ values of 3−80°with a step size of 0.02°and a scanning rate of 2°/min, allowing for a comprehensive analysis.
2.6.FTIR Spectroscopic Studies.The FTIR spectra of 16 calcium carbonate precipitates were acquired by using the Shimadzu FTIR 8400S instrument manufactured by Shimadzu (Japan).The spectra were recorded within the range of 4000− 600 cm −1 , employing a resolution of 4 cm −1 and an accumulation of 35 scans.IR Solutions software was utilized to facilitate the analysis, encompassing various procedures such as background subtraction, baseline correction, normalization, spectrum recording, and other necessary calculations.
2.7.RS Studies.The Raman spectra of the 16 formulated calcium carbonate particles were collected using a Renishaw Raman inVia micro-Raman spectrophotometer.The instrument had 10× objectives, a notch filter to eliminate Rayleigh scattering, a monochromator, and a charge-coupled device (CCD) thermoelectrically cooled detector.Two light sources, an argon (Ar + ) laser and a diode laser, were employed in the measurements.Three scans were averaged for each sample using WiRE software (version 3.3) to improve the signal-tonoise ratio.The obtained Raman spectra underwent baseline correction, and the Raman intensities were determined based on peak height measurements.
2.8.TGA.TGA was performed on the calcium carbonate particles.Initially, the samples were accurately weighed and placed in aluminum pans.The temperature was then incrementally increased from room temperature to 800 °C at a heating rate of 10 °C/min.The analysis was conducted under a continuous flow of dry nitrogen gas (50 cc/min) using a DTG 60 instrument manufactured by Shimadzu in Japan.The thermal stability of specimens was assessed by examining the degradation peaks and measuring the associated weight loss during the TGA analysis.

RESULTS AND DISCUSSION
The conventional trial-and-error approach to screening critical input variables and developing a robust formulation with desired quality attributes remained a time-and energyconsuming approach until the advent of the experimental design concept.PBD is the most common screening design, which screens many factors and identifies critical ones with reasonable accuracy in a minimal number of runs. 11The input variables, their levels (three levels to elucidate the curvature effect), and the response outcomes are tabulated in Table 1.
The polynomial equations demonstrating the interplay between the critical factors and responses are given in Table 2.
Based on PBD, 16 formulations (PB-1−16) were prepared (Table 1), and the specific surface area, pore size, and pore volume were measured by nitrogen adsorption−desorption using the BET approach.The positive coefficient values in the final coded equation of specific surface area, pore radius, and pore volume suggested a synergistic effect, while negative coefficient values had an antagonistic effect (Table 2).Moreover, the residue formed through the PBD was subjected to characterization using XRD, FTIR, RS, and TGA techniques.

Influence of Independent Variables on Responses.
The BET surface area (R1) of the prepared CaCO 3 microparticles was found in the range of 1.5 m 2 /g (D15) to 16.14 m 2 /g (D4) (Table 1).The influential main factors identified were pH (A) (p < 0.0001) and order of addition (L) (p < 0.0001) (Table 2).The two factors' interactions (2FI) that were significant in influencing the R1 were: (1) CK (molar concentration of sodium carbonate and reaction time, p < 0.001); (2) HJ (concentration of Labrasolmixing rate, p < 0.0001); and KL (reaction time-order of addition, p < 0.0001).The reduced model carrying significant factors was found to be substantial (p < 0.0001), with a good correlation between r 2 (0.9972) and adjusted r 2 (0.9948) (Table 2), indicating an excellent correlation between the predicted and actual response of R1 (Figure 1A).The model F value was 420.32 with a significant curvature effect (p < 0.0001).
In this case, we have also observed a three-factor interaction between pH, reaction time, and order of addition (AKL, p < 0.0001) (Table 2).The reduced model carrying significant factors was found to be significant (p < 0.0001), with a good correlation between r 2 (0.9936) and adjusted r 2 (0.9807) (Table 2), indicating an excellent correlation between the predicted and actual response of R1 (Figure 1B).The model F value was 77.35 with a nonsignificant curvature effect (p > 0.005).
The response of the pore volume (R3) ranged from 2.43 cc/ g (PB-15) to 37.97 cc/g (PB-4) (Table 1).Two main factors statistically influencing R3 were temperature (D, p = 0.050) and order of addition (L, p < 0.005) (Table 2).No higherorder interaction terms were found to influence pore volume.The reduced mathematical model carrying significant factors was found to be significant (p < 0.005), with a reasonable agreement between r 2 (0.5690) and adjusted r 2 (0.4971) (Table 2 and Figure 1C).The model F value was 8.41 with a nonsignificant curvature effect (p > 0.05).Since there was only moderate agreement between two r-squared values, we further investigated whether a power transformation was necessary for the response variable using the Box−Cox analysis (BCA) tool using Design and Expert analysis software.
We used this method because the power law transformation applies only to positive ReV (as in this case).The plot (Figure 2) displays the currently applied lambda value (=1), the bestestimated lambda value (=0.52), and the confidence interval around the best-estimated lambda (−0.09, 1.15).Based on the plot, the software does not suggest a particular transformation if the confidence interval around the lambda value encompasses 1.The experimental results indicate that an  increase in pH led to a linear increase in surface area for both L1 and L2 conditions.This suggests that the formation of vaterite particles is favored under these conditions.To provide further evidence for the formation of vaterite particles, the morphology of samples PB-4 (pH 12) (Figure 3) and PB-15 (pH 4.0) (Figure 3) were analyzed using FESEM (further discussed under FESEM studies).
The results confirm the formation of vaterite particles at high pH, as spherical mesoporous structures were observed, in contrast to calcite particles at low pH.In a previous report, the hexagonal vaterite disks formed when pH was increased to 10. 12 Furthermore, in another study, spherical vaterite particles were produced within pH ranges of 8.0−9.5, while only pure calcite was made at low and high pHs. 13The surface area was higher under the L2 condition, in which the CO 3 2− solution was added to the Ca 2+ solution, compared to the L1 condition, in which the Ca 2+ solution was added to the CO 3 2− solution.This suggests that the order of addition (L) plays a role in the surface area of the CaCO 3 particles.Additionally, as expected, the pore radius, which measures the size of the pores within the CaCO 3 particles, decreased with an increase in pH for both the L1 and L2 conditions.However, the pH did not affect the pore volume (a measure of the total amount of space within the CaCO 3 particles) under these conditions.This suggests that while the pH may play a role in forming the CaCO 3 particles, it does not affect the overall pore structure of the particles.As shown in Table 2, the highest surface area (R1) of CaCO 3 was observed when the CO 3 2− solution was added to the Ca 2+ solution (L2).
Similarly, the smallest pore radius and largest pore volume were found in the L2 condition.This indicates that the order of addition (L) significantly impacts the properties of the CaCO 3 particles and can greatly influence the particles' surface area, pore radius, and pore volume.The mixing mode plays a role in forming CaCO 3 particles, as reported in the literature. 9en the CO 3 2d − solution is added to the Ca 2+ solution, smaller and narrowly distributed particles are formed, while the opposite results in larger and nonuniformly sized particles due to the high initial pH of the carbonate solution, leading to high supersaturation and many nuclei forming and growing into relatively larger particles by attracting more free Ca 2+ ions, resulting in a loss of uniformity. 9he results showed that the surface area (R1) is affected by the combined effect of the reaction time (K) and molar concentrations of sodium carbonate (C), as illustrated by a 3-D response curve (Figure 4A).Specifically, to achieve the maximum surface area of CaCO 3 (hence vaterite formation), a lower reaction time (K) needs to be complemented with lower molar concentrations of sodium carbonate (C).Accordingly, the instantaneous mixing rate (J1) needs to be complemented with a lower Labrasol (H) to achieve maximum surface area.Additionally, if the content of Labrasol needs to be higher, a slow mixing rate must be used to achieve a larger surface area.Furthermore, reaction time should be kept minimum in the L2 system (when the CO 3 2d − solution was added to the Ca 2+ solution) to achieve CaCO 3 with maximum surface area.
The study found that the pore radius (R2) of the calcium carbonate crystals is affected by multiple factors, including pH, molar concentrations of sodium carbonate, the presence of certain surfactants (Gelucire 44/14 and Solutol HS15), reaction time, and specific reaction conditions (L2).It was found that as pH increases, pore radius decreases, and the same is true for an increase in Gelucire 44/14 content and Solutol HS15 content and an increase reaction time (Table 2).Additionally, it was found that for a lower pore radius, higher molar concentrations of sodium carbonate should be used in conjunction with higher pH (Figure 4B), and higher molar concentrations of calcium chloride should be used in conjunction with the L2 condition.The study also indicated that the content of Gelucire 44/14 should be at the higher end within the explored factor levels of Solutol HS15 to achieve a lower pore radius (Figure 4C).Surfactants can affect the nucleation, growth, and polymorphism of calcium carbonate crystals by acting as nucleation sites, modifying the kinetics, and selectively promoting the formation of specific polymorphs.The presence of surfactant can affect the shape and type of CaCO 3 particles.Studies have shown that surfactants like sodium dodecylbenzene sulfonate can change the crystals' shape and promote the formation of unstable vaterite at high concentrations. 14In a study, the transition of CaCO 3 crystals from the vaterite polymorph to aragonite was observed as the ratio of hexadecyl(trimethyl)azanium bromide to sodium dodecyl sulfate increased in a solution with a constant concentration of sodium dodecyl sulfate. 15ore volume (R3) was maximum when the reaction was carried out at a lower temperature and under L2 conditions (Table 2 and Figure 4D).To further illustrate the relationship between surface area (R1) and pore volume (R3), the experimental values of both the responses (R1 and R3) were plotted on a rectilinear scale, and a nearly linear relationship was established with r 2 = 0.7851 (y = 2.3521x − 1.2274, y: pore volume; x: surface area) (Figure 5).A study found that increasing the reaction temperature to 80 °C led to the formation of calcite crystals with a less well-defined rhombohedral shape and secondary crystals on the surface. 16ther studies have also found that higher temperatures are more favorable for forming monodispersed cubic calcite particles. 17,18However, in a study, lower temperatures were found to be more effective for forming hollow CaCO 3 microspheres, while higher temperatures resulted in nonhollow microspheres and irregularly shaped products. 19tudies have shown that monitoring the crystallization process over time can reveal necessary information about the formation of vaterite.For example, one study found that vaterite formation occurred immediately after combining the reactants and was visible after just 5 min of reaction time. 20other study observed that hollow hexagonal vaterite disks were formed when the reaction time was increased. 12In a study, as the reaction time increased, the flower and hexagonalshaped vaterite concentrations decreased, while the rod-and cluster-shaped aragonite concentrations increased up to 100% after 48 h. 9,15This is accompanied by an increase in the particle size.
Furthermore, the reaction time significantly impacted the crystallization behavior of the calcium carbonate polymorphs.The reaction time plays a crucial role in determining the amount and polymorphism of calcium carbonate formed, with different polymorphs having different nucleation and growth rates and the outcome being influenced by multiple parameters, including temperature, pH, and the presence of impurities or additives. 9A study reported that a short reaction time was favorable for the formation of the amorphous calcium carbonate (ACC) phase.In contrast, an increase in reaction time promotes the transformation of the unstable amorphous calcium carbonate phase into the thermodynamically stable calcite form. 21Additionally, when the reaction time was increased in different time intervals, it was found that a mixture of vaterite and aragonite was formed at reaction times of 6 and 12 h. 15An increase in reaction time to 24 h resulted in  synthesizing a mixture of vaterite and and extending the reaction time to 48 h resulted in the production of pure aragonite. 4n extensive analysis was carried out on the precipitates synthesized according to the PBD to support further the formed polymorphs' identification.This analysis involved the utilization of various techniques, including FESEM, XRD, FTIR, RS, and TGA.The combined results from these characterization studies shall contribute to a more comprehensive understanding of the crystallinity, molecular structure, and thermal stability of the prepared CaCO 3 precipitates.

XRD Analysis.
Figure 6A depicts the XRD pattern of calcium carbonate sediments with specific formulations, namely, PB-3, PB-4, PB-6, PB-11, and PB-16.These formulations belong to Group 1 and are characterized by a significant presence of vaterite forms, constituting more than 75% of the composition.By analyzing the XRD pattern, valuable information can be obtained regarding the crystallographic structure and arrangement of these residues.Similarly, Figure 6B showcases the XRD pattern of calcium carbonate precipitates (PB-1, PB-2, PB-5, PB-8, PB-9, PB-10, PB-13, and PB-14) within Group 2. These precipitates possess a formulation containing vaterite fractions ranging from 45% to 70%.The XRD pattern provides insights into the diffraction peaks and patterns associated with these specific compositions.In addition, Figure 6C presents the XRD stacks of PB-7, PB-12, and PB-15, which fall under Group 3.These residues are composed entirely of calcite forms, accounting for 100% of their composition.
The XRD stacks offer a comprehensive view of the crystallographic properties and diffraction behavior unique to calcite.These results were obtained using the Kontoyannis and Vagenas method, 22 which analyzes the relative molar fractions of different polymorphs within Group 2 and Group 3. The molar fractions of calcite (XC), vaterite (XV), and aragonite (XA) were determined using eqs 1−3, respectively, as outlined below: XV 1.0 XA XC = The aragonite, calcite, and vaterite mole fractions are indicated by XA, XC, and XV, respectively.The intensity peaks at 221, 104, and 110 reflection peaks for aragonite, calcite, and vaterite, respectively, are represented as IA 221 , IC 104 , and IV 110 .This method has been successfully utilized by us 5 and other researchers 23,24 to accurately determine the mole fractions of these mineral phases.
In the residues of Group 1, the highest percentage mole fraction was attributed to vaterite, ranging from 75.00 to 79.50%, followed by aragonite with a fraction of 19.8−20.00%,and calcite with a range of 0−13%.Most Group 1 precipitates were prepared under low-temperature conditions (4 °C) and at a low pH (pH 4).The temperature was considered a significant factor influencing the crystal morphology of the precipitated calcium carbonate polymorphs.Lower temperatures favored the formation of hollow microspheres. 25Cubicshaped crystals were generally formed at room temperature, transforming into needle-like or stick-shaped structures at higher temperatures.Lower temperatures also facilitated the growth of smaller particles due to a higher nucleation rate, while higher temperatures resulted in the development of larger-sized particles.It was observed that most of the Group 1 (PB-4, PB-6, PB-11, and PB-16) followed the L2 order of addition, where sodium carbonate was added to the calcium chloride solution.This order of addition promoted the growth of spherical particles.Notably, calcite, the most stable polymorphic form, tends to transform from vaterite/aragonite to calcite.However, the excipients in Group 2 prevented this conversion to the calcite form.
In the sediments of Group 2 (PB-1, PB-2, PB-5, PB-8, PB-9, PB-10, PB-13, and PB-14), the highest percentage mole fraction was attributed to vaterite, ranging from 45 to 70%, followed by aragonite with a fraction of 12−20%, and calcite with a range of 5−41%.PB-1 contained calcite and vaterite polymorphs, with a molar fraction of 49% vaterite, 36% calcite, and a smaller amount of aragonite (13%).Similarly, PB-2 contained 46% vaterite and 41% calcite, as observed in the FESEM analysis (discussed in the FESEM studies).These findings demonstrate that various factors, such as temperature, pH, order of addition, and excipients, play a crucial role in determining the polymorphic composition and crystal morphology of precipitated calcium carbonate.Understanding these factors can facilitate control and customization of the properties of calcium carbonate materials for diverse applications in fields such as materials science, pharmaceuticals, and environmental remediation.
The sediments in Group 3 exhibited characteristic properties solely associated with calcite, without any traces of vaterite or aragonite.This aligns with previous studies that have yielded similar results.For instance, a study focusing on aqueous solutions of Ethylene Glycol observed only the characteristic peaks of calcite in the XRD results of precipitated CaCO 3 . 6nother study indicated that when precipitated CaCO 3 was in 100 g/L of Polyvinylpyrrolidone (PVP), it exhibited the characteristic peak of calcite. 8,26Furthermore, typical XRD patterns of precipitated CaCO 3 using various fabricated Pluronic-surfactant templates revealed the crystal nature of calcite. 9The categorization of CaCO 3 crystals into three distinct groups offers multiple potential applications.Group 1: vaterite-rich composition is ideal for drug delivery and biomedical applications.Group 2: mixed composition can be valuable in biocement and water treatment.Group 3: calcite forms have diverse applications in agriculture, industry, and optics.
This indicates the presence of pure calcite form. 33The intense and sharp peak observed at 1088.99 cm −1 in calcite corresponds to the symmetric stretching mode (v 1 ) of the CO 3 2− ion.It is reported that this peak's position depends on the crystal structure of the carbonate mineral. 34Other peaks at 154.Similar findings were reported previously by Babou-Kammoe et al., 36 where they prepared CaCO 3 particles with a peak temperature of TGA at 740 °C under controlled precipitation.Another study noted a DTG peak at 836.8 °C for pure CaCO 3 , which is associated with the main weight loss due to the transformation of CaCO 3 into CaO.In another study, the DTG of pure CaCO 3 showed a peak at 836.8 °C, corresponding to the major weight loss attributed to the transformation of CaCO 3 into CaO. 37

CONCLUSIONS
The purpose of our current research is to identify and assess critical independent variables that influence various porosityrelated response variables, including surface area, pore radius, and pore volume.We utilized the PBD to screen and assess these variables.Additionally, we employed several instrumental techniques, namely, XRD, FTIR, RS, and TGA, to validate the type of precipitate formed through the PBD.The BET surface area (R1) of the prepared CaCO 3 microparticles ranged from 1.5 to 16.14 m 2 /g.The pore radius (R2) of CaCO 3 varied from 2.62 to 6.68 nm.The pore volume (R3) exhibited a range of 2.43−37.97cc/g.We observed that the maximum pore volume (R3) was achieved at lower temperatures and under L2 conditions.
At high pH, we observed the formation of vaterite particles, which exhibited spherical mesoporous structures, while calcite particles formed at low pH.The order of addition impacted the surface area of the CaCO 3 particles.However, under these conditions, the pH did not influence the pore volume, which measures the total amount of space within the CaCO 3 particles.This indicates that while pH may play a role in forming CaCO 3 particles, it does not affect the overall pore structure of the particles.To maximize the surface area of CaCO 3 and promote vaterite formation, a lower reaction time should be combined with lower molar concentrations of sodium carbonate.
Similarly, a lower Labrasol concentration should be used with an instantaneous mixing rate to achieve a maximum surface area.The study revealed that the pore radius (R2) of calcium carbonate crystals is influenced by multiple factors, including pH, molar concentrations of sodium carbonate, the presence of surfactants such as Gelucire 44/14 and Solutol HS15, the reaction time, and specific reaction conditions.Lower pore radius values can be achieved by using higher molar concentrations of sodium carbonate in combination with a higher pH and higher molar concentrations of calcium chloride under L2 conditions.Furthermore, the study indicated that a higher content of Gelucire 44/14 within the explored factor levels of Solutol HS15 leads to a lower pore radius.To facilitate a comprehensive understanding of these instrumental techniques, we grouped the precipitates into three categories based on the percentage of vaterite formation: Group 1 comprises precipitates with vaterite greater than 75%; Group 2 includes vaterite residues ranging from 45% to 70%; and Group 3 contains only calcite forms.The instrumental techniques successfully characterized the calcium carbonate precipitates and complemented each other in their analysis.

Figure 3 .
Figure 3. FESEM images of precipitates of calcium carbonate prepared as per the Placket−Burman design.

Figure 6 .
Figure 6.X-ray diffraction of calcium carbonate precipitates of Group 1 (A), Group 2 (B), and Group 3 (C) were prepared as per the PBD.

Figure 7 .
Figure 7. FTIR spectra of calcium carbonate precipitates of Group 1 (A), Group 2 (B), and Group 3 (C) were prepared as per the PBD.

Figure 8 .
Figure 8. Raman spectra of calcium carbonate precipitates of Group 1 (A), Group 2 (B), and Group 3 (C) were prepared as per the PBD.

Table 1 .
Input Variables, Their Levels (Three Levels to Elucidate the Curvature Effect), and the Response Outcomes as per the PBD a

Table 2 .
Polynomial Equations Demonstrate the Interplay between the Critical Factors and the Responses