Prediction of Sodium Substitution Sites in Octacalcium Phosphate: The Relationships of Ionic Pair Ratios in Reacting Solutions

: Octacalcium phosphate (OCP) is widely used in biomaterial fabrication by virtue of its unique crystal structure and low environmental loading. Although various ion and molecule substitution methods into the OCP unit lattice have been introduced, it remains unclear which factors and mechanisms dominate the substitution process. Experimental studies have indicated that Na alkali metal ions are substituted at the P 3 PO 4 conjugated site in acidic to weakly acidic conditions and the P 5 PO 4 conjugated site in neutral to weak basic conditions. Ionic species calculation methods have indicated that the pair ratios of Na and HPO 42 − (NaHPO 4 − ) are small in acidic reacting solutions but large under weakly basic conditions. Consequently, the roles played by NaHPO 4 − and ionic pair formation processes are thought to dominate ion and molecule substitution into the OCP unit lattice. Such ionic pair formation strongly inhibits dicarboxylic acid substitution into the OCP unit lattice due to the replacement of the Ca ion, which conjugates P 5 PO4 as an anchor of dicarboxylic acid.


Introduction
Calcium phosphates constitute a diverse group of minerals that play important roles in geology and biology [1][2][3]. Among these minerals, some are constituent of bones and teeth and are thus closely related to hard tissue health and diseases [4,5]. They are also essential components in fertilizer, food additives, and other engineering aspects while constituting an important part of the phosphate cycle at the Earth's surface [1,6]. Octacalcium phosphate (OCP: Ca 8 H 2 (PO 4 ) 6 ·5H 2 O), a major inorganic component of immature bone, has received much attention for its excellent biocompatibility and the ability to substitute various ions and molecules whose properties could be applied to green and low-toxicity drug delivery systems (DDS) and combination medical products [7][8][9]. In addition, the substitute ions and molecules in the OCP unit lattice could be controlled by radiation processes [10]. Therefore, OCP has been attracting attention from radiation medicine as novel DDS devices.
OCP are mainly synthesized via hydrolysis in solution [11][12][13][14]. During this process, coexisting ions and molecules present in the ambient fluid are substituted into the OCP unit lattice. Previous studies have indicated that metal ions [7,[15][16][17], cationic molecules [18], ammonium ions [19] and dicarboxylic molecules [20][21][22][23] could substitute within the interlayer of the OCP unit lattice. Although the sizes of substituted ions and molecules have been extensively investigated, it remains unclear which factors, such as pH and co-existing ions, control their substitution.
For OCP synthesis, three processes have been identified based on the initial pH conditions: an acidic solution with a pH increasing process, a weak acidic solution with a titrate pH process, and a weak basic solution with a pH decreasing process [12,[14][15][16].

Fabrication Methods of Na-Substituted OCP
All reagents were purchased from FUJI Film Wako Pure Chemical Inc., Japan. H 3 PO 4 , NaCl, and Na 2 HPO 4 were diluted to 2 mol/L using distilled water. Thus, experimental solutions consisted of a 1.0 mol/L PO 4 and a 2.0 mol/L Na mixture of either Na 2 HPO 4 or H 3 PO 4 -NaCl.
In an acidic solution with increasing pH, 5.0 g of CaCO 3 was immersed into 20 mL of H 3 PO 4 -NaCl solution. Following the elimination of initially formed CO 2 , the samples were packed and incubated at 60 • C for 1 day.
In weak basic solutions with decreasing pH, 2.39 g of dicalcium hydrogen phosphate hydrate (DCPD: CaHPO 4 ·2H 2 O) was immersed into 20 mL of Na 2 HPO 4 solution and incubated at 60 • C for 1 day.
The initial and final pH values of the solutions were measured using a pH electrode (LAQUA ToupH 9615S-10D) connected to a pH meter (Horiba Co. D-72, Kyoto, Japan). These treated samples were washed several times using distilled water and 99.5% ethanol to eliminate the residual immersion solution and were subsequently dried in an oven at 40 • C overnight.

Characterization
Crystallographic characterization of the samples was obtained via X-ray diffraction (XRD, MiniFlex600, Rigaku Co., Tokyo, Japan) at an accelerating voltage of 40 kV and an amplitude of 15 mA. The diffraction angle was continuously scanned over the 3−70 • 2θ range at a scanning rate of 2 • /min for characterization and over the 2−12 • 2θ range at a scanning rate of 0.8 • /min for crystallographic parameter analysis.
The chemical bonding structures of the samples were determined using Fouriertransform infrared spectroscopy (FT-IR, Nicolet NEXUS670, Thermo Fisher Scientific Co., Waltham, MA, USA) with a triglycine sulfate detector using the KBr method (32 scans, 2 cm −1 resolution) and using a ZnSe attenuate total reflection (ATR) prism (64 scans, 2 cm −1 resolution). Measurements were obtained in the air.
The Ca, P(PO 4 ), and Na ion concentrations of the samples were measured using inductively coupled plasma-atomic emission spectroscopy (ICP-ES, 5110VDV, Agilent Technology Co., Tokyo, Japan) following the dissolution of the samples in 2% HNO 3 .

Calculation of Ionic Species in Solutions
The ionic complexes present in the reaction solutions were simulated as data inputs for speciation modeling using the PhreeqC software [24,25]. The input thermodynamic data for each ionic species and the reaction code are listed in Table 1. Briefly, each ionic species in solution was calculated at 333 K (60 • C), and 0.1 MPa with O 2 contents assumed to be in equilibrium with the atmosphere. The phase diagrams of each ionic species were drawn using Microsoft Excel (Microsoft Office 365 MSO, Microsoft Co., Redmond, WA, USA).

Results
As described in Scheme 1, the OCP unit lattice used in these experiments consisted of eight Ca ions, four PO 4 ions, two HPO 4 ions, and five H 2 O molecules [11,28,29]. Some Ca, and PO 4 ions exhibited conjugated relationships. Detecting ionic replacement of Ca ions used the vibration alternations in conjugated PO 4 and HPO 4 ions afforded by spectroscopic methods [28,29].

Results
As described in Scheme 1, the OCP unit lattice used in these experiments consisted of eight Ca ions, four PO4 ions, two HPO4 ions, and five H2O molecules [11,28,29]. Some Ca, and PO4 ions exhibited conjugated relationships. Detecting ionic replacement of Ca ions used the vibration alternations in conjugated PO4 and HPO4 ions afforded by spectroscopic methods [28,29]. Scheme 1. Schematic illustration of the OCP unit lattice oriented toward the c-axis, with phosphates labeled as P1 to P4 in their PO4 form (black labels) and P5, P6 in their HPO4 form (green labels) drown by VESTA3 program and ref [28,30]. The black dashed circle and red dotted circle indicate Ca ions corresponding to the conjugated sites of P3 and P5 PO4, respectively.
We then evaluated whether synthesis methods dominated Na substitution mode and controlled the site of the OCP unit lattice into which it substituted. We chose two methods for OCP synthesis: an acidic solution with an increasing pH and a basic solution with a decreasing pH. Both solutions contained 1 mol/L PO4 and 2 mol/L Na. Figure 1 shows the XRD patterns of the treated materials. In both methods of synthesis, the treated materials were monophasic OCP. Table 2 shows the initial and final pH values of the reacting solutions. For convenience, we denote the OCP synthesized acidic solution with increasing pH as OCP(Na) and that OCP basic solution with decreasing pH as OCP-Na. The Na contents of OCP(Na) and OCP-Na were 6.68 ± 0.21 at % and 6.83 ± 0.74 at %, respectively. There was no significance between Na contents of OCP(Na) and of OCP-Na (p = 0.39). Scheme 1. Schematic illustration of the OCP unit lattice oriented toward the c-axis, with phosphates labeled as P1 to P4 in their PO 4 form (black labels) and P5, P6 in their HPO 4 form (green labels) drown by VESTA3 program and ref [28,30]. The black dashed circle and red dotted circle indicate Ca ions corresponding to the conjugated sites of P3 and P5 PO 4 , respectively.
We then evaluated whether synthesis methods dominated Na substitution mode and controlled the site of the OCP unit lattice into which it substituted. We chose two methods for OCP synthesis: an acidic solution with an increasing pH and a basic solution with a decreasing pH. Both solutions contained 1 mol/L PO 4 and 2 mol/L Na. Figure 1 shows the XRD patterns of the treated materials. In both methods of synthesis, the treated materials were monophasic OCP. Table 2 shows the initial and final pH values of the reacting solutions. For convenience, we denote the OCP synthesized acidic solution with increasing pH as OCP(Na) and that OCP basic solution with decreasing pH as OCP-Na. The Na contents of OCP(Na) and OCP-Na were 6.68 ± 0.21 at % and 6.83 ± 0.74 at %, respectively. There was no significance between Na contents of OCP(Na) and of OCP-Na (p = 0.39).  [28] and the VESTA3 program [30]. Spectroscopic analysis indicated Na-substituted sites as features exhibiting alternation of vibration in conjugated sites of PO4 and/or HPO4. Figure 2 and Figure S1 showed the transmitting FT-IR (KBr method) spectra, and ATR-FT-IR spectra of each OCP studied with conventional OCP provided for comparison. In OCP-Na, the P3 PO4 band of PO4 revealed v3′ PO4 mode rather than v3′ HPO4. It was indicated that the cations substituted in the conjugated site of P3 PO4 were likely to conjugate PO4 rather than HPO4. Considering the charge of cations, Ca 2+ is likely to be placed into the conjugated site of P3 PO4 rather than Na + . On the other hand, in OCP(Na), the v3′ PO4 mode of the P3 PO4 band was significantly attenuated. Then, in OCP-Na, the P5 PO4 band was significantly altered relative to conventional OCP and OCP(Na). Furthermore, in ATR-FT-IR observation, unlike in the OCP and OCP(Na) cases, clearly γOH HPO4 band corresponded to hydrous layer structure around 633 cm −1 was observed. This strongly suggests that Na could be substituted into the conjugated site of P5 PO4 for OCP-Na, and into P3 PO4 for OCP(Na).  [28] and the VESTA3 program [30]. Spectroscopic analysis indicated Na-substituted sites as features exhibiting alternation of vibration in conjugated sites of PO 4 and/or HPO 4 . Figure 2 and Figure S1 showed the transmitting FT-IR (KBr method) spectra, and ATR-FT-IR spectra of each OCP studied with conventional OCP provided for comparison. In OCP-Na, the P3 PO 4 band of PO 4 revealed v 3 PO 4 mode rather than v 3 HPO 4 . It was indicated that the cations substituted in the conjugated site of P3 PO 4 were likely to conjugate PO 4 rather than HPO 4 . Considering the charge of cations, Ca 2+ is likely to be placed into the conjugated site of P3 PO 4 rather than Na + . On the other hand, in OCP(Na), the v 3 PO 4 mode of the P3 PO 4 band was significantly attenuated. Then, in OCP-Na, the P5 PO 4 band was significantly altered relative to conventional OCP and OCP(Na). Furthermore, in ATR-FT-IR observation, unlike in the OCP and OCP(Na) cases, clearly γ OH HPO 4 band corresponded to hydrous layer structure around 633 cm −1 was observed. This strongly suggests that Na could be substituted into the conjugated site of P5 PO 4 for OCP-Na, and into P3 PO 4 for OCP(Na).
Ionic species calculation methods were used to determine the key factor for different Na substitution modes in the OCP unit lattice. The K sp values of ions and each ionic pair are summarized in Table 1. Herein, we focused on the pH dependence of the ionic pair consisting of Na and HPO 4 2− as NaHPO 4 − . NaHPO 4 − in the OCP unit lattice is described as having the form of Na substitution in a conjugated P5 PO 4 site. Figure 3 shows the calculation results of the amount and ratio of NaHPO 4 − versus total Na ions as a function of pH and Na concentration. Note that, in this calculation, we used NaCl instead of Na + due to the inherent limitations of the calculation. In addition, the pH values of each pH series were slightly altered by, at most, 0.3 between Na-0 mol/L and Na-2 mol/L ( Figure S2). The concentration of NaHPO 4 − in solutions increased with increasing Na concentration between pH 5 and pH 10. On the other hand, below pH 5 and above pH 10, limited NaHPO 4 − was formed, irrespective of the Na concentration used. Other ionic species in this system exhibited the same tendency as NaHPO 4 − ( Figure S3). s 2021, 4 244 Ionic species calculation methods were used to determine the key factor for different Na substitution modes in the OCP unit lattice. The Ksp values of ions and each ionic pair are summarized in Table 1. Herein, we focused on the pH dependence of the ionic pair consisting of Na and HPO4 2− as NaHPO4 − . NaHPO4 − in the OCP unit lattice is described as having the form of Na substitution in a conjugated P5 PO4 site. Figure 3 shows the calculation results of the amount and ratio of NaHPO4 − versus total Na ions as a function of pH and Na concentration. Note that, in this calculation, we used NaCl instead of Na + due to the inherent limitations of the calculation. In addition, the pH values of each pH series were slightly altered by, at most, 0.3 between Na-0 mol/L and Na-2 mol/L ( Figure S2). The concentration of NaHPO4 − in solutions increased with increasing Na concentration between pH 5 and pH 10. On the other hand, below pH 5 and above pH 10, limited NaHPO4 − was formed, irrespective of the Na concentration used. Other ionic species in this system exhibited the same tendency as NaHPO4 − ( Figure S3). During OCP synthesis, the Ca ion is initially released into reacting solution as dissolving Ca salts. Therefore, the Ca ion effect toward NaHPO4 − ratios in solution should be evaluated. Figure 4 shows the concentration and ratio of NaHPO4 − as a function of Ca concentration and pH. The concentrations and ratios of NaHPO4 − and other ionic pairs were almost constant with pH regardless of Ca ion concentration (Figures S4 and S5).  Ionic species calculation methods were used to determine the key factor for different Na substitution modes in the OCP unit lattice. The Ksp values of ions and each ionic pair are summarized in Table 1. Herein, we focused on the pH dependence of the ionic pair consisting of Na and HPO4 2− as NaHPO4 − . NaHPO4 − in the OCP unit lattice is described as having the form of Na substitution in a conjugated P5 PO4 site. Figure 3 shows the calculation results of the amount and ratio of NaHPO4 − versus total Na ions as a function of pH and Na concentration. Note that, in this calculation, we used NaCl instead of Na + due to the inherent limitations of the calculation. In addition, the pH values of each pH series were slightly altered by, at most, 0.3 between Na-0 mol/L and Na-2 mol/L ( Figure S2). The concentration of NaHPO4 − in solutions increased with increasing Na concentration between pH 5 and pH 10. On the other hand, below pH 5 and above pH 10, limited NaHPO4 − was formed, irrespective of the Na concentration used. Other ionic species in this system exhibited the same tendency as NaHPO4 − ( Figure S3). During OCP synthesis, the Ca ion is initially released into reacting solution as dissolving Ca salts. Therefore, the Ca ion effect toward NaHPO4 − ratios in solution should be evaluated. Figure 4 shows the concentration and ratio of NaHPO4 − as a function of Ca concentration and pH. The concentrations and ratios of NaHPO4 − and other ionic pairs were almost constant with pH regardless of Ca ion concentration (Figures S4 and S5). During OCP synthesis, the Ca ion is initially released into reacting solution as dissolving Ca salts. Therefore, the Ca ion effect toward NaHPO 4 − ratios in solution should be evaluated. Figure 4 shows the concentration and ratio of NaHPO 4 − as a function of Ca concentration and pH. The concentrations and ratios of NaHPO 4 − and other ionic pairs were almost constant with pH regardless of Ca ion concentration (Figures S4 and S5).  The pH dependence of the ratio of NaHPO4 − in the Na-Ca system suggested that this ionic pair was significantly affected by the mode of Na substitution into the OCP unit lattice. Our previous studies also indicated that the ionic radii of substituted cations were an important parameter in OCP substitution. Excluding ionic radii, we evaluated how The pH dependence of the ratio of NaHPO 4 − in the Na-Ca system suggested that this ionic pair was significantly affected by the mode of Na substitution into the OCP unit lattice. Our previous studies also indicated that the ionic radii of substituted cations were an important parameter in OCP substitution. Excluding ionic radii, we evaluated how ionic pair formation was influenced by OCP unit lattice substitution. In that study, we also considered K ion, i.e., an alkali metal ion with a larger ionic radius (1.38 Å) than Na + (1.02 Å) and Ca 2+ (1.00 Å) [31]. Figure 5 shows the calculated results of KHPO 4 − concentration and ratio as a function of pH and K concentration in solution. Both the concentration and ratio of KHPO 4 − were the same as those of NaHPO 4 − . For alkali metal substitution into the OCP P5 PO 4 conjugated site, the ionic radius of the cation was found to be a more important factor than the mode of ionic pair formation. The pH dependence of the ratio of NaHPO4 − in the Na-Ca system suggested that this ionic pair was significantly affected by the mode of Na substitution into the OCP unit lattice. Our previous studies also indicated that the ionic radii of substituted cations were an important parameter in OCP substitution. Excluding ionic radii, we evaluated how ionic pair formation was influenced by OCP unit lattice substitution. In that study, we also considered K ion, i.e., an alkali metal ion with a larger ionic radius (1.38 Å) than Na + (1.02 Å) and Ca 2+ (1.00 Å) [31]. Figure 5 shows the calculated results of KHPO4 − concentration and ratio as a function of pH and K concentration in solution. Both the concentration and ratio of KHPO4 − were the same as those of NaHPO4 − . For alkali metal substitution into the OCP P5 PO4 conjugated site, the ionic radius of the cation was found to be a more important factor than the mode of ionic pair formation. These experimental and simulation results clearly indicate that the formation ratio of ionic pairs of Na + and HPO4 2− is influenced by the site of Na substitution into the OCP unit lattice. When NaHPO4 − forms in solution, Na is likely to substitute into the conjugated site of P5 PO4, whereas bare Na + was likely to substitute into the conjugated site of P3 PO4. These results support previous studies concerning the ionic potential and molecular orbital analysis of OCP crystals [32] and other trivalent cation substitution processes into OCP unit lattice [33,34]. Considering the unit lattice of OCP and FT-IR results, the cations were substituted at the conjugated site of P5 PO4. Nevertheless, pH and related ionic pair formation are the key factors influencing molecule and ion substitution into the OCP unit lattice.
Based on the analytical results presented, we considered how such cations strongly inhibited dicarboxylic intercalation into the OCP unit lattice under neutral to weak basic These experimental and simulation results clearly indicate that the formation ratio of ionic pairs of Na + and HPO 4 2− is influenced by the site of Na substitution into the OCP unit lattice. When NaHPO 4 − forms in solution, Na is likely to substitute into the conjugated site of P5 PO 4, whereas bare Na + was likely to substitute into the conjugated site of P3 PO 4 . These results support previous studies concerning the ionic potential and molecular orbital analysis of OCP crystals [32] and other trivalent cation substitution processes into OCP unit lattice [33,34]. Considering the unit lattice of OCP and FT-IR results, the cations were substituted at the conjugated site of P5 PO 4 . Nevertheless, pH and related ionic pair formation are the key factors influencing molecule and ion substitution into the OCP unit lattice.
Based on the analytical results presented, we considered how such cations strongly inhibited dicarboxylic intercalation into the OCP unit lattice under neutral to weak basic conditions [35]. When dicarboxylic acid was intercalated into the OCP interlayer termed the hydrous layer, the a-axis of the OCP unit lattice expanded; this phenomenon was detected via a peak shift in OCP d(100) from 4.7 • to~4.2 • [19][20][21][22][23]35,36]. As shown in Figure 6 and Table S1, when OCP fabricated in dicarboxylic ions (thiomalate: HOOC(SH)(CH 2 ) 2 COOH) and Na-containing weak basic solutions, a small number of dicarboxylic ions are intercalated into the OCP unit lattice, whereas significant intercalation is observed under acidic to weak acidic solutions. The Na + substitution process at conjugated sites of P5 PO 4 inhibited the Ca fulfilling process, which is the process as an anchor for such dicarboxylic molecules.
For calcium phosphate, including OCP so on formation process, Ca and PO 4 ionic pair formation has mostly been discussed. During forming crystalline calcium phosphates from amorphous calcium phosphate, Ca-PO 4 ionic pairs and clusters (such as Posner's cluster) play essential roles [37][38][39][40][41][42][43]. Although the cluster structures of Ca-PO 4 have been extensively investigated, the formation of Ca-PO 4 with third and fourth molecules remains unclear, although molecular dynamics studies suggest that Posner-like clusters of Ca-Na-PO 4 are important [44]. For in vivo and physiological conditions, residual ions and molecules with Ca and PO 4 have not previously been considered. In this study, we demonstrate that Na also plays an important role in calcium phosphate formation processes.
conditions [35]. When dicarboxylic acid was intercalated into the OCP interlayer termed the hydrous layer, the a-axis of the OCP unit lattice expanded; this phenomenon was detected via a peak shift in OCP d(100) from 4.7° to ~4.2° [19][20][21][22][23]35,36]. As shown in Figure  6 and Table S1, when OCP fabricated in dicarboxylic ions (thiomalate: HOOC(SH)(CH2)2COOH) and Na-containing weak basic solutions, a small number of dicarboxylic ions are intercalated into the OCP unit lattice, whereas significant intercalation is observed under acidic to weak acidic solutions. The Na + substitution process at conjugated sites of P5 PO4 inhibited the Ca fulfilling process, which is the process as an anchor for such dicarboxylic molecules.  [28] and the VESTA3 program [30].
For calcium phosphate, including OCP so on formation process, Ca and PO4 ionic pair formation has mostly been discussed. During forming crystalline calcium phosphates from amorphous calcium phosphate, Ca-PO4 ionic pairs and clusters (such as Posner's cluster) play essential roles [37][38][39][40][41][42][43]. Although the cluster structures of Ca-PO4 have been extensively investigated, the formation of Ca-PO4 with third and fourth molecules remains unclear, although molecular dynamics studies suggest that Posner-like clusters of Ca-Na-PO4 are important [44]. For in vivo and physiological conditions, residual ions and molecules with Ca and PO4 have not previously been considered. In this study, we demonstrate that Na also plays an important role in calcium phosphate formation processes.

Conclusions
In conclusion, using Na as a model cation, we investigated the role played by the cation substitution site in the OCP unit lattice on synthesis processes under acidic conditions with increasing pH and weak basic conditions with decreasing pH. Ionic species calculations indicated that the concentration of ionic pairs of Na + and HPO4 2− were the key factors determining the Na substitution site. Under NaHPO4-poor conditions (i.e., pH < 5), Na was more likely to substitute in the conjugated site of P3 PO4. On the other hand, under NaHPO4-rich conditions (pH 5 to 10), Na was more likely to substitute in the conjugated site of P5 PO4.

Supplementary Materials:
The following are available online at www.mdpi.com/2571-6131/4/2/18/s1. The details of the experimental setting in the systems of SH-malate containing. Table  S1: initial and final pH values of the SH-malate-containing systems. Figure S1: ATR-FT-IR spectra of the samples. Figures S2 and S3: calculation results of pH and other ionic species in the system of pH-Na, Figures S4 and S5: calculation results of pH and other ionic species in the system of pH-Ca containing 1 mol/L Na + .

Conclusions
In conclusion, using Na as a model cation, we investigated the role played by the cation substitution site in the OCP unit lattice on synthesis processes under acidic conditions with increasing pH and weak basic conditions with decreasing pH. Ionic species calculations indicated that the concentration of ionic pairs of Na + and HPO 4 2− were the key factors determining the Na substitution site. Under NaHPO 4 -poor conditions (i.e., pH < 5), Na was more likely to substitute in the conjugated site of P3 PO 4 . On the other hand, under NaHPO 4 -rich conditions (pH 5 to 10), Na was more likely to substitute in the conjugated site of P5 PO 4 .