Calcium Ion Deposition with Precipitated Calcium Carbonate: Influencing Factors and Mechanism Exploration

: In order to apply precipitated calcium carbonate (PCC) in the detergent industry, its ability to deposit calcium ions in hard water is an important process. In this work, the calcium ion deposition in the presence of PCC from different sources is investigated to reveal the influencing factors and mechanism of nucleation and crystal growth of CaCO 3 . SEM, XRD, Malvern particle size analysis, and calcium electrodes are used to evaluate the effects of PCC morphology, saturation of Ca 2+ , and PCC additive amount on the deposition behavior of CaCO 3 . Through SEM and Malvern particle size analysis, it is found that the precipitation of calcium ions is obviously accelerated by PCC acting as seeds. Moreover, calcium ions are effectively adsorbed on (211) crystal facets, thus prismatic and scalenohedral PCC crystals exhibit better adsorption performance than irregular cubic PCC ones. In addition, XRD demonstrates that PCC reduces or even eliminates the formation of crystals such as vaterite, displaying high deposition capacity under complex water conditions (slightly acidic or highly alkaline pH, low magnesium ion concentration (<0.01 M), and temperatures of 0–60 ◦ C), forming thermodynamically stable calcite in water, which significantly controls the instability of the washing process.


Introduction
Glidants occupy approximately 20% to 55% of the laundry detergent composition [1].Their presence enables to not only significantly improve the flowability of laundry detergents, but also ensure water softening.The performance of laundry detergents is categorized as 'primary' (removing stains) and 'secondary' (preventing redeposition) [2].Sodium carbonate (Na 2 CO 3 ) is a common non-phosphorus detergent aid with excellent calcium removal and stain removal properties [3,4].Meanwhile, it poses difficulties in hard water conditions due to the formation of insoluble calcium carbonate deposits on the fabric surface [5].There may be challenges between optimizing detergent fluidity and overcoming problems related to 'secondary' performance in hard water.
Common methods for softening hard water or preventing scale include ion exchanger [6], boiling hard water, additives [7], membrane separation [8], adsorption [9], and seedinduced route.However, applying these methods in detergents remains significant challenges.To overcome challenges and simultaneously enhance the flow property, zeolite has been introduced because of its ability to acts as an ion exchanger to removal metal ions in water and as a surfactant carrier to improve powder flowability [10,11].However, the non-biodegradability and cost of zeolite have been considered the major problems encountered so far [12].Seed-induced route emerges as a more effective, environmentally sustainable, and cost-efficient approach.In turn, we propose the addition of precipitated calcium carbonate (PCC) to detergents as a means to achieve water softening.The solubility product of calcite is 10 −8.48 [13], compared to hard water (>60 mg•L −1 CaCO 3 ) [14], its dissolution has a minor impact on water quality.PCC is also characterized by high purity, controllable properties and good chemical absorption performance, which make it as a promising glidant.Industrial waste gas (CO 2 ) is increasingly utilized as a raw material for PCC production, contributing significantly to the circular economy of PCC [15].However, in spite of great potential, the application mechanisms and impact patterns of PCC in the detergent industry are scarcely reported.
The nucleation and growth kinetics of calcium carbonate, as well as the morphology and polymorphism of the obtained precipitate are affected by various parameters [16], for example, temperature [17], pH [18], additives [19][20][21], saturation, stirring conditions [22], solvents [23], etc.In this respect, special attention has been paid to the role of solution parameters (pH, temperature, supersaturation, additives and impurity ions, etc.) in these processes, owing to their ability to impact the formation of the calcium carbonate crystal phase in the solution.For instance, high pH increases the lifetime of amorphous ACC and makes it directly convert into calcite [24].Aragonite is preferentially crystallized at the temperatures higher than 75 • C [25].Among the foreign elements, iron is more conducive to the formation of vaterite [16], while magnesium ions promote the emergence of aragonite.
Furthermore, seeds also play an important role in the regulation of solution crystallization.They provide growth sites for molecules on the seed surface, reducing the difficulty of achieving the phase transition from the solution to a solid during the crystallization [26].In particular, PCC crystals act as 'crystal seeds' in hard water, inducing surface nucleation and growth of CaCO 3 crystals in water.Ming-Qi Cui et al. [27] have found that adding seeds to the feed solution induces CaCO 3 precipitation, which can promote the forward osmosis performance, allowing magnesium ions to be deposited under certain conditions [28].The presence of calcite seeds also affects microbial-induced carbonate precipitation processes [29].As is known, the surface properties of seeds, such as morphology, roughness and exposed crystal facets, are directly related to their behavior in different condition solutions [30].Therefore, based on the concept of 'seeds', PCC can replace zeolite as a powder glidant, as it can induce the deposition of substances on its surface while softening water.Moreover, PCC with an appropriate particle size exhibits lower fabric adsorption and is effectively washed away with the washing water, thus, achieving an improvement in fabric surface 'fouling'.Meanwhile, there are still few reports on the laws and mechanisms of CaCO 3 deposition on PCC in water, leaving open the questions concerning the interaction between seeds and solution parameters.
Taking into account the above, this study presents the results of a study on the deposition of CaCO 3 in the presence of PCC.Six PCC samples from different regions and different surface properties were chosen to evaluate their calcium ion deposition capabilities.Secondary nucleation is the important assessment index in the addition of seeds, thus, particle sizes distribution (PSD) analysis was employed to estimate secondary nucleation and efficiency of the CaCO 3 deposition.Experiments involving the response surface method (RSM) were conducted to elucidate the effect of water quality parameters, including pH, temperature and magnesium ion concentration, on the CaCO 3 crystallization in the presence of PCC.Finally, based on the experimental results, the impacts of exposed PCC crystal faces on the surface nucleation and the growth mechanism of CaCO 3 crystals were discussed.The findings of this study provide theoretical guidance for expanding the application range of PCC in the detergent industry.

Experiment
Step 1-High Calcium Hard Water: Hard water (0.01 M) was prepared by mixing CaCl 2 •6H 2 O with pure water.It was, then passed through a membrane filter (0.22 µm) to eliminate impurities.
Step 3-Simulated Washing Environment: A suspension (20 mL) obtained during step 2 was added to a jacketed crystallizer, using a stirring paddle to mix the solid uniformly.Then, high-calcium hard water (80 mL) from step 1 was rapidly added and stirred at 200 rpm for 30 min.(The pH of the solution was afterward adjusted using HCl and ammonia solution.)

Scanning Electron Microscope (SEM)
Morphology of CaCO 3 was characterized by a scanning electron microscope (Apreo S, FEI, Brno, Czech Republic) at an accelerating voltage of 20 kV.The purpose is to analyze the influence of different variables on the deposition morphology of PCC.Prior to SEM characterization, a thin layer of gold was sputter-coated onto CaCO 3 particles through a Quorum SC7640 high-resolution sputter coater to provide a conductive path and limit the charge accumulation on the particle surfaces.The size and shape of CaCO 3 particles were analyzed using ImageJ 1.54f software.

Particle Size Distribution (PSD)
The PSD of the samples was conducted using the Mastersizer 3000 particle size analyzer (Worcestershire, UK).The operating principle of this instrument is based on laser diffraction, whereby a series of photosensitive detectors measure the intensity of diffracted light from particles at different angles.Subsequently, a diffraction model is employed for mathematical inversion to obtain the particle size distribution of the sample.Considering that samples tend to aggregate under dry conditions, wet testing was chosen to mitigate significant errors associated with dry measurements.Water was selected as the dispersant due to the very low solubility of calcium carbonate in water.The refractive index of the sample was set to 1.660, and the absorbance was set to 0.01.The amount of sample added depended on whether the shading ratio range was reached, typically with a shading ratio setting of 5-10% for particles smaller than 10 µm.Volume density was used as the ordinate when outputting results, and the D (4,3) was recorded.
In this study, PSD tests were divided into two testing schemes: 1. Dynamic PSD Testing: Suitable for particle size processes that vary over time.
Into a certain concentration of clarified Na 2 CO 3 solution (250 mL) was the testing probe first immersed.The solution, to prevent bubble interference during the experiment, should cover the pores of the probe.Upon addition of PCC, the initial PSD of PCC was determined (corresponding to the PSD curve at 0 min on the figures).Subsequently, a calcium ion solution (80 mL) was rapidly introduced to initiate deposition, and the change process of PSD with time was recorded (corresponding to the PSD curve at 1-7 min on the figures).(All experiments were repeated three times.)

2.
Static PSD Testing: Suitable for the calculation process of effective deposition.
After deposition, the samples were filtered using a 0.22 µm filter membrane then dried, followed by dispersion in water for PSD testing, three sets of measurements were taken, and the average of the last set of values was used.

X-ray Powder Diffractometer (XRD)
The XRD pattern from the CaCO 3 powder (20-70 • ) was collected using a smartlab X-ray diffractometer (Rigaku, Japan) with Cu Kα radiation (λ = 1.54 Å) at a scan rate of 8 • /min.The XRD spectra were analyzed using MDI Jade 6.To prepare the XRD test samples, the reaction solution was filtered using a vacuum filtration flask, then a quick rinse was performed with acetone at the same temperature as the reaction conditions to inhibit the transformation of the unstable crystalline form.

The Perfect Combination Calcium Electrode
The Perfect Combination Calcium electrode (Mettler Toledo, Greifensee, Switzerland) was used in conjunction with an ions meter (SevenCompact, S220-k, Mettler Toledo, Greifensee, Switzerland).The calcium ion selective electrode was calibrated using calcium ion standard solutions (0.1, 1.0, 10.0, 100.0, and 1000.0 mg•L −1 ) at room temperature.Measurement of c(Ca 2+ ).To enhance the ionic strength of the solution and shield the impact of impurity ions on the results, an ion strength adjuster was added to the sample or standard solution at a ratio of 50:1.

Effective Deposition Capacity
When seeds are introduced into a supersaturated solution, the solute undergoes consumption through two distinct mechanisms.On the one hand, the solute adsorbs and grows on the surface of the seeds; on the other hand, a secondary nucleation phenomenon occurs, leading to the generation of smaller particles [31].This leads to the double-peak PSD spectrum of the product.For evaluating the secondary nucleation and effective deposition ability, PSD is combined with the total calcium deposition D Tot , as follows: The percentages of secondary nucleation and effective deposition are determined using the formulae below: where D represents calcium deposition percentage; the subscript Tot denotes the total deposition; C i is the calcium concentration in the initial solution; C f is the calcium concentration in the filtrate solution; subscript Sec and Eff stand for the secondary nucleation and effective deposition, respectively; V s is the volume of secondary nucleation particles; V d is the volume of particles after deposition, and V i is the volume of initial PCC particles.
The respective results are shown in Figure 1.

Experimental Design
The relationships between independent variables, such as temperature, pH and magnesium ion concentration, were discussed through the RSM analysis based on Box Behnken design (BBD).and effective deposition, respectively; Vs is the volume of secondary nucleation particles; Vd is the volume of particles after deposition, and Vi is the volume of initial PCC particles.
The respective results are shown in Figure 1.

Experimental Design
The relationships between independent variables, such as temperature, pH and magnesium ion concentration, were discussed through the RSM analysis based on Box Behnken design (BBD).

Materials
Calcium carbonate exists in three anhydrous crystalline forms, which include calcite, aragonite, and vaterite.Calcite is the most stable form, followed by vaterite, and then aragonite [32].In this study, all the types of PCC we used were in the form of calcite, exhibiting sharp and standard XRD peaks, which indicated high crystallinity (Figure S1).
Crystal morphology, a crucial technical aspect ensuring successful practical application of CaCO3, varies due to different processing methods and crystallization conditions, resulting in diverse effects in use.It can be seen that VI exhibits a prismatic morphology with an aspect ratio of approximately 2 (Figure 2a), SC has a cubic morphology (Figure 2b), while SO, HI, PC and IB all possess a scalenohedral morphology with an aspect ratio of 4-5 and differences in their specific face areas (Figure 2c-f).As shown in Figure 2g,h, the scalenohedral PCC has the (211) crystal faces [33].The flat square surface in an irregular cubic particle is characterized by the (104) crystal plane, and the rough plane is represented by the (211) one [34].Additionally, in the irregular prismatic PCC, the crystal faces on the larger-area flanks are identified as (211), while the smaller faces at the two ends have the indices of (101) [33].
The specific surface areas of six PCC types are characterized by concave adsorption isotherms without inflection points (Figure 3a).According to the IUPAC classification, they indicate the typical Type III isotherms, suggesting the nonporous or macroporous solid materials [35].Except for the SC sample, the other samples exhibit an upward adsorption volume trend when P/P0 approaches 1, meaning a small amount of accumulated pores.The PSD spectra of PCC, displaying a unimodal distribution, are illustrated in Fig- ure 3b.

Materials
Calcium carbonate exists in three anhydrous crystalline forms, which include calcite, aragonite, and vaterite.Calcite is the most stable form, followed by vaterite, and then aragonite [32].In this study, all the types of PCC we used were in the form of calcite, exhibiting sharp and standard XRD peaks, which indicated high crystallinity (Figure S1).
Crystal morphology, a crucial technical aspect ensuring successful practical application of CaCO 3 , varies due to different processing methods and crystallization conditions, resulting in diverse effects in use.It can be seen that VI exhibits a prismatic morphology with an aspect ratio of approximately 2 (Figure 2a), SC has a cubic morphology (Figure 2b), while SO, HI, PC and IB all possess a scalenohedral morphology with an aspect ratio of 4-5 and differences in their specific face areas (Figure 2c-f).As shown in Figure 2g,h, the scalenohedral PCC has the (211) crystal faces [33].The flat square surface in an irregular cubic particle is characterized by the (104) crystal plane, and the rough plane is represented by the (211) one [34].Additionally, in the irregular prismatic PCC, the crystal faces on the larger-area flanks are identified as (211), while the smaller faces at the two ends have the indices of (101) [33].The specific surface areas of six PCC types are characterized by concave adsorption isotherms without inflection points (Figure 3a).According to the IUPAC classification, they indicate the typical Type III isotherms, suggesting the nonporous or macroporous solid materials [35].Except for the SC sample, the other samples exhibit an upward adsorption volume trend when P/P0 approaches 1, meaning a small amount of accumulated pores.The PSD spectra of PCC, displaying a unimodal distribution, are illustrated in Figure 3b.

Morphology
To a certain extent, the morphology determines whether the adsorption can occur and to what degree.The epitaxial morphology of various CaCO3 forms generally relies

Morphology
To a certain extent, the morphology determines whether the adsorption can occur and to what degree.The epitaxial morphology of various CaCO 3 forms generally relies on the original morphology of PCC used as seeds.In this study, the SEM analysis reveals the presence of two deposition morphologies flaky and cubic.Flakes are caused by SO and SC phases, and cubic particles are attributed to VI (Figure 4a-c), being the typical structural characteristics of calcite [36].It is discerned that crystals tend to continuously aggregate at rough and defective sites.The presence of abundant vacancies at rough interfaces is conducive to a firmer binding of deposited atoms with surface atoms in different directions.As a result, the surface energy at this particular location becomes higher, contributing to the effective adsorption and growth of atoms.
The PSD curves of the three PCC types display a double-peak structure during the adsorption process (Figure 4d-f), indicating the occurrence of secondary nucleation.This observation confirms that differences in morphology contribute to the variations in adsorption.During the deposition, the SO and VI particle sizes exhibited the up shift, indicating that the main deposition occurs on the surface of PCC, while those of SC first displaced toward the smaller sizes and then to the larger values, which indicated the formation of new particles.The variation trends of the volume-average diameters D (4,3) are summarized in Figure 4g.The growth rate (D (4,3)/t) of VI slightly exceeds that of SO, and much greater than that of SC.This is because the VI phase has a faster adsorption rate, contributing to crystal defects, whereas the adsorption of SO phase is more uniform owing to its integrity and even crystal surface, ensuring the high surface energy of the crystal faces.In turn, the adsorption characteristics of SC are limited due to the thermodynamic stability of its (104) crystal faces exposed in water, yielding the low surface energy [37].This results in slow ion consumption and high saturation, leading to the formation of numerous nuclei.
The larger specific surface area of the crystals indicates that, there are more active sites to adsorb, ensuring.the greater adsorption capacity.The equal-mass adsorption analysis was further conducted on four scalenohedral PCC types.As shown in Figure 4h, within the specific surface area range of 1.736 to 7.4451 m 2 •g −1 , the effective deposition rate increases from 72.201% to 76.618%.The linear correlation, reaching the value of 0.99 (Figure 4i), demonstrates a strong association between specific surface area and effective deposition.

Supersaturation and PCC addition
SO was selected for subsequent experiments because of the best adsorption uniformity and the largest specific surface area.Seed can be introduced via two ways: full seeding or partial seeding.Full seeding consists in crystal growth, while partial seeding aims to induce crystal nucleation to avoid explosive nucleation during crystallization.To maximize adsorption efficiency, it is important to achieve 'full seeding' so as to suppress secondary nucleation.Supersaturation and seed concentration are considered to be the critical parameters influencing this process.Once supersaturation increases, the deposition behavior gradually shifts from growth-dominated to nucleation-dominated, resulting in the transition of the deposition mechanism from lattice binding to the generation of new atomic nuclei [38].When a small amount of seed is introduced into a supersaturated solution or the saturation is insufficient for the reaction, the secondary nucleation cannot be suppressed.
In this work, the dissolution of PCC was not considered in the calculation of supersaturation level (S), and only the corresponding ions introduced with Na2CO3 and Ca-CO3 into the solution were taken into account.The relative supersaturation σ for calcite is defined as follows [39]:

Supersaturation and PCC Addition
SO was selected for subsequent experiments because of the best adsorption uniformity and the largest specific surface area.Seed can be introduced via two ways: full seeding or partial seeding.Full seeding consists in crystal growth, while partial seeding aims to induce crystal nucleation to avoid explosive nucleation during crystallization.To maximize adsorption efficiency, it is important to achieve 'full seeding' so as to suppress secondary nucleation.Supersaturation and seed concentration are considered to be the critical parameters influencing this process.Once supersaturation increases, the deposition behavior gradually shifts from growth-dominated to nucleation-dominated, resulting in the transition of the deposition mechanism from lattice binding to the generation of new atomic nuclei [38].When a small amount of seed is introduced into a supersaturated solution or the saturation is insufficient for the reaction, the secondary nucleation cannot be suppressed.
In this work, the dissolution of PCC was not considered in the calculation of supersaturation level (S), and only the corresponding ions introduced with Na 2 CO 3 and CaCO 3 into the solution were taken into account.The relative supersaturation σ for calcite is defined as follows [39]: where Ksp is the thermodynamic solubility product of calcite (Ksp = 10 −8.48 (mol•L −1 ) 2 ) [13], and a represents the ion activity.The activity coefficients of anions and cations are determined using the Debye-Huckel formula below [40]: where I is the ionic strength, and A is the Debye-Huckel constant (0.509 (kg•mol −1 ) 1/2 at room temperature).
The PSD spectra in Figure 5a reveal that the crystal size remains constant as σ increases from (90-210).This is particularly pronounced at the lower PCC concentration (Figure S2), possibly due to the presence of impurities in the material [41].Small amounts of impurities adsorbed on the crystal face can completely prevent step growth at low supersaturation levels, creating a 'dead zone' upon the crystal growth even if there is sufficient supersaturation.Secondary nucleation is almost absent at a relatively low σ of 50 (Figure 5b).However, with the increase of σ, the PSD spectra show a double-peak structure, indicating that secondary nucleation has occurred, and the mass of secondary nucleation increases almost linearly.This is due to the transition of deposition behavior from crystal growth to nucleation with increasing supersaturation caused by the increase of solute concentration, influencing the deposition mechanism.The increase in supersaturation accelerates the deposition rate of CaCO 3 on the PCC surface and improves the effective deposition mass.where I is the ionic strength, and A is the Debye-Huckel constant (0.509 (kg•mol −1 ) 1/2 at room temperature).
The PSD spectra in Figure 5a reveal that the crystal size remains constant as σ increases from (90-210).This is particularly pronounced at the lower PCC concentration (Figure S2), possibly due to the presence of impurities in the material [41].Small amounts of impurities adsorbed on the crystal face can completely prevent step growth at low supersaturation levels, creating a 'dead zone' upon the crystal growth even if there is sufficient supersaturation.Secondary nucleation is almost absent at a relatively low σ of 50 (Figure 5b).However, with the increase of σ, the PSD spectra show a doublepeak structure, indicating that secondary nucleation has occurred, and the mass of secondary nucleation increases almost linearly.This is due to the transition of deposition behavior from crystal growth to nucleation with increasing supersaturation caused by the increase of solute concentration, influencing the deposition mechanism.The increase in supersaturation accelerates the deposition rate of CaCO3 on the PCC surface and improves the effective deposition mass.PCC concentration is a crucial parameter that directly affects the content c(Ca 2+ ) in the solution, thereby influencing nucleation and crystal growth.With a higher PCC concentration, more active sites for adsorption become available.At σ = 170, as the amount of PCC increases, the PSD peak gradually narrows and downshifts (Figure 5c), indicating the thinning of the adsorption layer (from 0.594-18.664μm to 0.767-14.458μm).In Processes 2024, 12, 629 9 of 16 PCC concentration is a crucial parameter that directly affects the content c(Ca 2+ ) in the solution, thereby influencing nucleation and crystal growth.With a higher PCC concentration, more active sites for adsorption become available.At σ = 170, as the amount of PCC increases, the PSD peak gradually narrows and downshifts (Figure 5c), indicating the thinning of the adsorption layer (from 0.594-18.664µm to 0.767-14.458µm).In Figure 5d, the mass of secondary nucleation decreases linearly as the PCC concentration increases (from 0.4 to 1.2 g•L −1 ).This decrease is due to the rapid adsorption of CaCO 3 on the surface of PCC in the solution, which causes a rapid decrease in saturation and consequently reduces the occurrence of secondary nucleation.Meanwhile, effective deposition exhibits an increase followed by a subsequent decrease.This is because the rise of initially low PCC concentrations within a certain limit leads to an increase in active sites, resulting in effective deposition.However, at higher concentrations, free Ca 2+ is introduced by the dissolution of PCC, which reduces the effective deposition performance.

Impacts of pH, Temperature and c(Mg 2+ )
Temperature, pH value and Mg 2+ impurity content are the common influencing factors in water deposition, which can significantly affect the stability of CaCO 3 crystal forms and indirectly affect the ability of PCC to deposit Ca 2+ .The transformation of calcium carbonate crystal morphology follows the Ostwald maturation law [42].In turn, vaterite is highly prone to the solution-mediated dissolution and the reprecipitation of calcite, making the deposition unstable and increasing the risk of reprecipitation during laundry processes.

RSM Results
Based on BBD, the effects of c(Mg 2+ ), temperature and pH on the ability of PCC to deposit calcium ions were investigated.Table S1 provides the experimental results for each combination of factors along with the corresponding predicted responses Y (Effective deposition percentage) for each run.The empirical relationship between the response and the independent variables can be represented through a polynomial below: where A, B and C respectively represent pH, temperature and magnesium ion.Y represents D Eff .It revealed that the calcium effective deposition is mostly affected by c(Mg 2+ ) and pH, which was evident from their larger coefficients compared to temperature.ANOVA experiments were further conducted to analyze the linear relationship between factors and response values.A statistically significant regression equation was obtained, in which a smaller p-value indicated a higher significance of the corresponding variable [43].Table 1 shows the F-value of 44.5625 and the p-value smaller than 0.0001, as well as high goodnessof-fit parameters (R 2 = 0.9828 and R Adj 2 = 0.9608 with a coefficient of variation of 1.47%), indicating the model significance.The missing fit p-value above 0.05 confirmed the ability of the model to well fit the actual data.Therefore, the model can be used to analyze and predict the effects of water quality conditions on sedimentation.According to the p-value, the contribution degree of each factor on the effective deposition is as follows: pH > c(Mg 2+ ) > temperature.
The three-dimensional response surface under optimized conditions illustrates the relationship between experimental variables and responses (Figure 6).Based on the results, some conclusions can be drawn, as follows: (i) with an increase in pH from 5 to 9, the effective deposition exhibits an initial descent followed by a subsequent ascent, taking 0.00 M Mg 2+ and 30 • C as an example, the corresponding D Eff of pH: pH = 5 (86.44%)-pH = 7 (68.98%)-pH= 9 (74.72%);(ii) as the c(Mg 2+ ) increases from 0.00 to 0.04 M, the D Eff decreases; (iii) when the temperature and various factors interact simultaneously, the impact is relatively low, and the interactions are primarily influenced by pH and Mg 2+ .The three-dimensional response surface under optimized conditions illustrates the relationship between experimental variables and responses (Figure 6).Based on the results, some conclusions can be drawn, as follows: (i) with an increase in pH from 5 to 9, the effective deposition exhibits an initial descent followed by a subsequent ascent, taking 0.00 M Mg 2+ and 30 °C as an example, the corresponding DEff of pH: pH = 5 (86.44%)-pH = 7 (68.98%)-pH= 9 (74.72%);(ii) as the c(Mg 2+ ) increases from 0.00 to 0.04 M, the DEff decreases; (iii) when the temperature and various factors interact simultaneously, the impact is relatively low, and the interactions are primarily influenced by pH and Mg 2+ .

The Effect of pH
Being one of the most crucial indicators of water quality, the pH level exerts a significant influence on the phase properties and morphology of CaCO3 [44].The XRD patterns at different pH conditions (T = 30 °C) reveal the effect of PCC on the crystal structure of CaCO3 (Figure 7a,b).The partial individual peaks could be assigned to the corresponding crystal faces of vaterite, namely (110), (112), ( 114) and (118), while the rest of peaks were indexed to (104), (110), and (113) crystal faces of calcite.Based on the analysis, at pH = 5, the solution reaction leads to the formation of vaterite (Figure 7a), while the addition of PCC results in the emergence of calcite (Figure 7b).Furthermore, under acidic pH conditions, there is a higher effective deposition, potentially due to the increase in PCC dissolution rate, thereby elevating the solution saturation and finally accelerating the deposition rate onto the existing PCC structure.The increase in the effective deposition amount is attributed to the higher OH -concentration associated with the higher PH, enhancing the water exchange frequency around the calcium ions, which is beneficial for the incorporation of calcium ions into the calcite structure and improves the crystallinity (Figure S3).

The Impact of Temperature
Besides the pH, temperature significantly influences the crystalline structure of Ca-CO3 in solutions.Without the addition of PCC at the pH of 11, only the calcite characteristic XRD peaks are observed within the temperature range of 0-30 °C (Figure 7c).However, the temperature of 60 °C promotes the transformation of calcium carbonate into vaterite (Figure 7c).The respective peaks become broader than the calcite-related bands, indicating the smaller particle size, likely due to a slower particle growth at lower temperatures.The increase in temperature results in the higher removal rate of calcium ions and the local supersaturation of Ca 2+ , which promotes the formation of vaterite.In turn, the addition of PCC inhibits the formation of vaterite and promotes the formation of calcite in the range of 0-60 °C (Figure 7d).

The Effect of pH
Being one of the most crucial indicators of water quality, the pH level exerts a significant influence on the phase properties and morphology of CaCO 3 [44].The XRD patterns at different pH conditions (T = 30 • C) reveal the effect of PCC on the crystal structure of CaCO 3 (Figure 7a,b).The partial individual peaks could be assigned to the corresponding crystal faces of vaterite, namely (110), (112), ( 114) and (118), while the rest of peaks were indexed to (104), (110), and (113) crystal faces of calcite.Based on the analysis, at pH = 5, the solution reaction leads to the formation of vaterite (Figure 7a), while the addition of PCC results in the emergence of calcite (Figure 7b).Furthermore, under acidic pH conditions, there is a higher effective deposition, potentially due to the increase in PCC dissolution rate, thereby elevating the solution saturation and finally accelerating the deposition rate onto the existing PCC structure.The increase in the effective deposition amount is attributed to the higher OH − concentration associated with the higher PH, enhancing the water exchange frequency around the calcium ions, which is beneficial for the incorporation of calcium ions into the calcite structure and improves the crystallinity (Figure S3).

The Impact of Temperature
Besides the pH, temperature significantly influences the crystalline structure of CaCO 3 in solutions.Without the addition of PCC at the pH of 11, only the calcite characteristic XRD peaks are observed within the temperature range of 0-30 • C (Figure 7c).However, the temperature of 60 • C promotes the transformation of calcium carbonate into vaterite (Figure 7c).The respective peaks become broader than the calcite-related bands, indicating the smaller particle size, likely due to a slower particle growth at lower temperatures.The increase in temperature results in the higher removal rate of calcium ions and the local supersaturation of Ca 2+ , which promotes the formation of vaterite.In turn, the addition of PCC inhibits the formation of vaterite and promotes the formation of calcite in the range of 0-60 • C (Figure 7d).The Effect of Mg 2+ Concentration Hard water contains Ca 2+ and Mg 2+ [14], and Figure 8a reveals that as the Mg 2+ concentration increases from 0-0.04 M in solution, the DEff decreases from 70.6% to 67.913% due to the Mg 2+ substitution for Ca 2+ in the calcite lattice formed in a supersaturated solution with magnesium ions.In addition, as shown in Figure 6b, the influence of temperature reverses the effective deposition trend with the increasing Mg 2+ content, which changes from 70.04-73.54%at 0.00 M Mg 2+ to 68.46-62.15%at 0.04 M Mg 2+ .
The XRD data indicate the formation of magnesian calcite, characterized by a gradual decrease in peak intensity and an upward peak position shift (Figure 8b).Taking the characteristic peak corresponding to the (104) crystal face of calcite as the example, it can be seen that its position shifts toward the larger angles (29.400° (control group) → 29.439° → 29.480° → 29.520° → 29.578°) (Figure 8c), which is in agreement with the results reported by Wang [45].The smaller radius of Mg 2+ compared to Ca 2+ results in a decrease in the cell parameters and an increase in the distance from the crystal lattice.Furthermore, the XRD peaks has a tendency to split (Figure 8c: taking the peak corresponding to the (104) crystal face as an example), it is presumed that the increase of c(Mg 2+ ) makes the crystallinity of magnesium calcite crystal increase, and the initially unclear double peak becomes distinct, in which the lower-angle component corresponds to the crystal face of PCC seeds and the higher-angle components is ascribed to the aftergrowth magnesium calcite.When [Mg 2+ ]aq > [Ca 2+ ]aq, there is usually the formation of aragonite rather than calcite [46], whereas PCC changes this conversion pathway of calcium carbonate and generates more stable calcite moieties.
With the increase in c(Mg 2+ ), the distinctive rhombohedral-shaped morphology of calcite is replaced by spherical particles, and their average sizes are reduced from 130 μm to 25 μm (Figure 8d).Based on classical nucleation theory, the key to CaCO3 nuclea-

The Effect of Mg 2+ Concentration
Hard water contains Ca 2+ and Mg 2+ [14], and Figure 8a reveals that as the Mg 2+ concentration increases from 0-0.04 M in solution, the D Eff decreases from 70.6% to 67.913% due to the Mg 2+ substitution for Ca 2+ in the calcite lattice formed in a supersaturated solution with magnesium ions.In addition, as shown in Figure 6b, the influence of temperature reverses the effective deposition trend with the increasing Mg 2+ content, which changes from 70.04-73.54%at 0.00 M Mg 2+ to 68.46-62.15%at 0.04 M Mg 2+ .
The XRD data indicate the formation of magnesian calcite, characterized by a gradual decrease in peak intensity and an upward peak position shift (Figure 8b).Taking the characteristic peak corresponding to the (104) crystal face of calcite as the example, it can be seen that its position shifts toward the larger angles (29.400 • (control group) → 29.439 • → 29.480 • → 29.520 • → 29.578 • ) (Figure 8c), which is in agreement with the results reported by Wang [45].The smaller radius of Mg 2+ compared to Ca 2+ results in a decrease in the cell parameters and an increase in the distance from the crystal lattice.Furthermore, the XRD peaks has a tendency to split (Figure 8c: taking the peak corresponding to the (104) crystal face as an example), it is presumed that the increase of c(Mg 2+ ) makes the crystallinity of magnesium calcite crystal increase, and the initially unclear double peak becomes distinct, in which the lower-angle component corresponds to the crystal face of PCC seeds and the higher-angle components is ascribed to the aftergrowth magnesium calcite.When [Mg 2+ ]aq > [Ca 2+ ]aq, there is usually the formation of aragonite rather than calcite [46], whereas PCC changes this conversion pathway of calcium carbonate and generates more stable calcite moieties.the increase in c(Mg 2+ ), the distinctive rhombohedral-shaped morphology of calcite is replaced by spherical particles, and their average sizes are reduced from 130 µm to 25 µm (Figure 8d).Based on classical nucleation theory, the key to CaCO 3 nucleation is the initial binding and growth of CO 3 2− and Ca 2+ ions in solution until reaching the critical radius to form stable nuclei.In the presence of Mg 2+ in solution, due to its similar ionic nature to Ca 2+ , it tends to adsorb at specific sites such as kink sites on the surface of calcite.The adsorption of Mg 2+ inhibits the binding of CO 3 2− , thereby suppressing CaCO 3 nucleation and reducing calcite deposition [47].Furthermore, the SEM-EDX analysis reveals an increasing proportion of magnesium ions and a decreasing proportion of calcium ions as the amount of Mg 2+ dopant rises (Figure S4).calcite.The adsorption of Mg 2+ inhibits the binding of CO3 2− , thereby suppressing CaCO3 nucleation and reducing calcite deposition [47].Furthermore, the SEM-EDX analysis reveals an increasing proportion of magnesium ions and a decreasing proportion of calcium ions as the amount of Mg 2+ dopant rises (Figure S4).

Deposition Mechanism Discussion
Based on the experimental results, the CaCO3 deposition mechanism following the addition of PCC was investigated.The pH variations with and without the addition of PCC are shown in Figure 9.The hydrolysis of Na2CO3 generates OH − , which leads to a rapid increase in pH from 8.3 to 10 at the beginning of both reaction pathways (R1).

Deposition Mechanism Discussion
Based on the experimental results, the CaCO 3 deposition mechanism following the addition of PCC was investigated.The pH variations with and without the addition of PCC are shown in Figure 9.The hydrolysis of Na 2 CO 3 generates OH − , which leads to a rapid increase in pH from 8.3 to 10 at the beginning of both reaction pathways (R1).
In the absence of PCC, during the initial stage, HCO 3 − is consumed by the formation of vaterite (R4), and the release of H + leads to a decrease in pH, followed by the rapid dissolution of vaterite, releasing CO 3 2− (R3).Since the hydrolysis of CO 3 2− contributes to the recovery of pH, the overall downward trend of pH is slow (from 10-9.6 only).The rapid decrease in pH from 9.6 to 8.4 in the second stage is due to the reaction between Ca 2+ released from vaterite and CO 3 2− , forming the thermodynamically stable calcite phase (R5) and releasing H + .During the third stage, the pH level achieves its stability (pH = 8.4), suggesting that the precipitation is over.Similar findings have been reported by Kogo et al. [48].

Deposition Discussion
Based on the experimental results, the CaCO3 deposition mechanism following the addition of PCC was investigated.The pH variations with and without the addition of PCC are shown in Figure 9.The hydrolysis of Na2CO3 generates OH − , which leads to a rapid increase in pH from 8.3 to 10 at the beginning of both reaction pathways (R1).In the presence of PCC, the pH rapidly decreases from 10 to 8.1 in the first stage.Moreover, the ions that constitute PCC are the same as those in the solution.In this respect, the surface defects of the material as well as the specific charge distribution, such as vacancies, provide adsorption sites and promote adsorption.Following the arrangement of the PCC lattice, a stable structure similar to the original calcite lattice is formed through epitaxy.In the second stage, adsorption is essentially concluded and pH is almost unchanged.The above results prove that under the experimental conditions, the PCC addition leads to the reduction or even loss of vaterite in the process, forming a stable calcite.Besides, the difference in pH slope before and after the introduction of PCC indicates that the presence of PCC shortens the deposition time and accelerates the deposition rate.
In Section 3.2.1,distinct adsorption behaviors were observed for PCC with different morphologies, suggesting their correlation with exposed crystal faces.Because of the 'steric effect' of the molecular structure, the outer surfaces of calcium carbonate particles are mostly composed of negatively charged carbonate ions, easily attracting the positively charged calcium ions in the solution.Single-slice (101), (104), and (211) crystal faces with similar areas were further cleaved using Material Studio (Figure 10), these crystal faces are the exposed crystal faces of PCC with different morphologies (VI, SO and SC (Figure 2g-i)).It can be observed that the cation ratios vary on the surface layers of different crystal faces, potentially resulting in differences in their ability to bind calcium ions during the adsorption process.The (104) crystal face represents the best stability for calcite; however, due to its high surface cation density, it exhibits the poor adsorption performance.In turn, the (211) crystal face may possess the better adsorption performance owing to its lower surface cation density, while the performance of the (101) crystal face is between those of (211) and (104) faces.Therefore, the superior adsorption performance of prismatic PCC is likely attributed to the presence of numerous defects on the (101) crystal face, making it more effective in adsorption compared to scalenohedral PCC.

Figure 3 .
Figure 3. (a) Specific surface area isothermal adsorption line and (b) PSD spectra of PCC.

Figure 3 .
Figure 3. (a) Specific surface area isothermal adsorption line and (b) PSD spectra of PCC.

Figure 5 .
Figure 5. (a) PSD spectra and (b) secondary nucleation mass and effective deposition mass at different values of σ (here, the PCC concentration is 0.4 g•L −1 ).(c) PSD spectra and (d) secondary nucleation mass and effective deposition mass at different PCC concentrations (here, σ = 170).

Figure 5 .
Figure 5. (a) PSD spectra and (b) secondary nucleation mass and effective deposition mass at different values of σ (here, the PCC concentration is 0.4 g•L −1 ).(c) PSD spectra and (d) secondary nucleation mass and effective deposition mass at different PCC concentrations (here, σ = 170).

Figure 9 .
Figure9.The mechanism of calcium carbonate deposition on PCC (see also the corresponding SEM image in FigureS5).

Figure 9 .
Figure 9.The mechanism of calcium carbonate deposition on PCC (see also the corresponding SEM image in Figure S5).

Figure 9 .
Figure 9.The mechanism of calcium carbonate deposition on PCC (see also the corresponding SEM image in Figure S5).

Table 1 .
Effective deposition percentage: Variance Analysis based on BBD model.