Clustering of Calcium Phosphate in the System CaCl2−H3PO4−KCl

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J. Phys. Chem. B 1999, 103, 8230-8235

Clustering of Calcium Phosphate in the System CaCl2-H3PO4-KCl-H2O Ayako Oyane,† Kazuo Onuma,*,‡ Tadashi Kokubo,† and Atsuo Ito‡ Department of Material Chemistry, Graduate School of Engineering, Kyoto UniVersity, Yoshida, Kyoto, 606-8501, Japan, and National Institute for AdVanced Interdisciplinary Research, 1-1-4 Higashi, Tsukuba, Ibaraki, 305-8562, Japan ReceiVed: March 26, 1999; In Final Form: June 28, 1999

The stability of calcium phosphate clusters approximately 0.8 nm in diameter, which were found in a simulated body fluid in a previous work, was investigated in the system CaCl2-H3PO4-KCl-H2O using an intensityenhanced dynamic light-scattering technique at 25 °C. It was shown that tris(hydroxymethyl)aminomethane, which was used as a buffer in the previous study, had no effect on the formation of the clusters. The amount of clusters decreased with decreasing supersaturation of the solution with respect to hydroxyapatite. Under constant supersaturation with respect to hydroxyapatite, the amount of the clusters reached a maximum in solutions with Ca/P molar ratios ranging from 1 to 8.

Introduction An understanding of the mechanism involved in the formation of hydroxyapatite (Ca10(PO4)6(OH)2; HAP) in an aqueous solution is important from the standpoint of biological mineralization, biomimetic processes, and biomaterial performance.1-6 With the exception of a few studies,7-10 the growth mechanism of HAP has been analyzed on the basis of conventional theories in which the molecules or ions arrive at the growth sites as individual moieties, one by one.11-15 Recently, however, the presence of calcium phosphate clusters ranging from 0.7 to 1.0 nm in diameter was first demonstrated by using an intensityenhanced dynamic light-scattering (DLS) technique in a simulated body fluid supersaturated with respect to HAP.16 In addition, it was observed by in situ atomic force microscopy that HAP grew by step flow with a height of 0.8 or 1.6 nm, and that the probability of incorporation of the growth unit into the crystal was extremely low as seen in the growth of protein or virus crystals.17,18 Based on these findings, we proposed a cluster growth model in which HAP grew by selective hexagonal packing of left- and right-handed chiral Ca9(PO4)6 clusters of 0.8 nm diameter.16 The investigation of calcium phosphate clusters using the intensity-enhanced DLS technique, however, has only been conducted under limited ionic concentration and pH conditions. Typical concentrations of salts in the solution used for the observation of calcium phosphate clusters were NaCl 140 mM, K2HPO4‚3H2O 1.0 mM, and CaCl2 2.5 mM. The solution was buffered at pH 7.40 by adding tris(hydroxymethyl)aminomethane ((CH2OH)3CNH2) and HCl at 25 °C. The tris(hydroxymethyl)aminomethane molecule has, however, an amino group that interacts with phosphate groups. Therefore, it must be clarified whether the tris(hydroxymethyl)aminomethane is involved in the formation of calcium phosphate clusters. If the calcium phosphate cluster is a growth unit of * Author to whom correspondence should be addressed at National Institute for Advanced Interdisciplinary Research, 1-1-4 Higashi, Tsukuba, Ibaraki, 305-8562, Japan. Telephone: +81-298-54-2557. Fax: +81-29854-2565. E-mail: [email protected]. † Kyoto University. ‡ National Institute for Advanced Interdisciplinary Research.

HAP, the amount of clusters will be strongly dependent on the supersaturation (σ) of the solution with respect to HAP. On the other hand, if the chemical composition of the cluster is Ca9(PO4)6, as indicated in the cluster growth model, the amount of clusters will reach a maximum in a solution with a Ca/P molar ratio of approximately 1.5, under constant σ. In the present study, we thus investigated the change in the amount of calcium phosphate clusters in the system CaCl2-H3PO4-KCl-H2O by changing ionic concentration, pH, and the Ca/P molar ratio at a constant temperature of 25 °C using the intensity-enhanced DLS technique. Experimental Section 1. Preparation of Solutions. Four series of solutions were investigated (Table 1) at 25.0 °C. Solution 1-A corresponded to a simulated body fluid, containing 2.5 mM CaCl2 and 1.0 mM H3PO4. Solutions 2-A and 3-A were used to investigate the effects of σ on the amount of clusters by changing calcium and phosphate concentrations and pH values, respectively. Solution 4-A was used to investigate the effects of the Ca/P molar ratio of the solution on the amount of clusters under constant σ. All solutions were prepared using two stock solutions of CaCl2 and H3PO4, reagent-grade KCl (Wako Pure Chemical Industries, Ltd., Osaka, Japan), ultrapure water, and a reagentgrade solution of either KOH (Wako Pure Chemical Industries, Ltd., Osaka, Japan) or HCl (Wako Pure Chemical Industries, Ltd., Osaka, Japan). The stock solutions of CaCl2 and H3PO4 were prepared from reagent-grade CaCl2 (Nacalai Tesque, Inc., Tokyo, Japan) and H3PO4 (Nacalai Tesque, Inc., Tokyo, Japan), respectively. The concentrations of CaCl2 and H3PO4 in the stock solutions were determined respectively to be 45.7 mM and 19.0 mM by EDTA photometric back-titration (NN indicator)19 and the molybdenum-blue colorimetric method.20 Solutions excluding either H3PO4 or CaCl2 were prepared for use as references in each series of experiments, and designated as solution (1-4)-B or solution (1-4)-C, respectively. The accuracy of the pH values of the solutions was within (0.02. All the solutions were clear, and no spontaneous precipitation was observed during measurements of particle size.

10.1021/jp9910340 CCC: $18.00 © 1999 American Chemical Society Published on Web 09/15/1999

Calcium Phosphate Clustering in CaCl2-H3PO4-KCl-H2O

J. Phys. Chem. B, Vol. 103, No. 39, 1999 8231

TABLE 1: CaCl2, H3PO4, and KCl Concentrations, pH, Ca/P Molar Ratio, and σ of Solutions concentration/mM solution 1-A 1-B 1-C 2-A 2-B 2-C 3-A 3-B 3-C 4-A 4-B 4-C

CaCl2 2.50 2.50 1.25-3.75 1.25-3.75 2.50 2.50 0.72-12.5 0.72-12.5

H3PO4 1.0 1.0 0.50-1.50 0.50-1.50 1.0 1.0 0.08-10.0 0.08-10.0

KCl

pH (25.0 °C)

250 250 250 250 250 250 250 250 250 250 250 250

7.40 7.40 7.40 7.40 7.40 7.40 3.00-7.40 3.00-7.40 3.00-7.40 7.40 7.40 7.40

The supersaturation of the solution with respect to HAP, σ, was calculated according to

σ ) (C - Ce)/Ce ) (Ip/Ksp)1/18 - 1

(1)

where C, C e, Ip, and Ksp are the actual concentration, the equilibrium concentration, the ionic activity product of the solution, and the solubility product of HAP, respectively. Ip was calculated using equilibrium constants described elsewhere.21 The Ksp value used was 10-117(1.21-23 2. Measurement of Particle Size. The method of particle size measurement by DLS has been described elsewhere.24 Briefly, the fluctuation of light scattered by particles in a solution is analyzed by a photon correlation method based on the concept of Rayleigh scattering. The particle diameter, d, can be obtained from the attenuation constant, Γ, of the auto-correlation function for the photon count of scattered light, g1(τ), which is expressed as

g2(τ) ) 1 + a|g1(τ)|2

(2)

where a, τ, g1(τ) and g2(τ) are a constant, the correlation time, the first-order correlation function, and the second-order correlation function, respectively. Γ is related to

g1(τ) and the particle diameter, d, by g1(τ) ) exp(-Γτ)

(3)

d ) (1/Γ){kT/(3πη)}[4πn/{λ sin(θ/2)}]2

(4)

where k, T, η, Γ, n, λ, and θ are the Boltzmann constant, the absolute temperature, the viscosity of the solution, the attenuation constant, the refractive index of the solution, the wavelength of the laser, and the scattered angle, respectively. When particles with different sizes are mixed in the solution, g1(τ) is expressed as the weighted sum of each g1(τ) for the particles of each size, i.e., g1(τ) ) ∑Γi exp (-Γiτi). Each Γi was calculated using a nonlinear least-squares method by the Marquadt method in the present study. Solutions filtered through a filter of 100 nm pore size were put into a Pyrex-glass cylindrical cell of 30 mm diameter. The solutions were refiltered through a filter of 40 nm pore size using a peristaltic pump at a flow rate of 15 mL/min for 30 min under nitrogen atmosphere to prevent a change in the pH of the solutions. After filtration, the cell was inserted into a DLS-7000 dynamic light-scattering photometer (Ohtsuka Electric Co., Ltd., Osaka, Japan) remodeled with the use of a highpower Ar-ion laser (Spectra-Physics Lasers, Mountain View, USA; multiline 4 and 1.2 W max for 488 nm). A schematic of the DLS system used is shown in Figure 1. After waiting for

Ca/P 2.5

σ 13.7

2.5

7.1-19.7

2.5

-1.0-13.7

0.07-156

13.7

30 min to suppress convection in the solution, DLS measurements were carried out for each solution under the following conditions: a 7° scattered angle, 2-4 µs sampling times, 5121024 correlation channels, and 500-1000 times of accumulation of measured data at 25 °C. The accuracy of the DLS system used was checked by measuring the particle sizes of R-cyclodextrin, dehydrocholic acid sodium salt, and tris(hydroxymethyl)aminomethane. The observed values were 1.4 nm for R-cyclodextrin, 1.2 nm for dehydrocholic acid sodium salt, and 0.5 nm for tris(hydroxymethyl)aminomethane, which showed good agreement with the theoretical values of 1.46 nm × 0.8 nm,25 1.2 nm (Murata, Y., personal communication), and 0.49 nm × 0.62 nm,16 respectively. Therefore, this DLS system is sufficiently accurate to measure particle size ranging from 0.5 to 1.4 nm. Results 1. Size Measurement of Particles in the Solution Corresponding to a Simulated Body Fluid. Figure 2a,b show the raw data of the auto-correlation function, g2(τ), and the size distribution of particles in solution 1-A, respectively. Solution 1-A had a particle size distribution ranging from 0.4 to 1.5 nm with a peak at 0.8 nm. The fraction of particles whose size was larger than 0.7 nm was 52% of the total amount of particles in the distribution. The exclusion of either phosphate or calcium ions from solution 1-A (Figure 2c,d) resulted in a dramatic decrease in the fraction of particles whose size was larger than 0.7 nm, i.e., down to 12%-23%. Both solutions had a particle size distribution ranging from 0.3 to 1.1 nm with a peak at 0.5 nm. Particles of approximately 0.8 nm in size shown in Figure 2b were, therefore, found to be calcium phosphate clusters. Particles approximately 0.5 nm in size shown in Figure 2c,d were found to be KCl0, since particles of the same size were also detected in a solution containing only 250 mM KCl (Figure 2e), while not detected in either a 2.5 mM CaCl2 or a 1.0 mM H3PO4 solution. Moreover, the theoretical diameter of KCl0 was calculated to be 0.41 or 0.42 nm in accordance with the observed value. The former was calculated as the diameter of a sphere having a volume equal to the sum of the volumes of Cl- and K+ ions. The latter was the hydrodynamic diameter calculated according to the equation, D ) 2(a2 - b2)1/2/ln[{a + (a2 b2)1/2}/b],26 assuming that KCl0 is ellipsoidal with the lengths of major (a) and minor (b) axes corresponding to the sum and the average, respectively, of the ionic radii of Cl- and K+. Without KCl, the particle larger than 0.7 nm in size soon aggregated and formed a large particle as seen in Figure 3. Figure 3 indicates the relationship between the average size of particle in the solution and the concentration of KCl. The concentrations of Ca2+, PO43-, and pHs of the solutions are

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Figure 1. Schematic of the dynamic light-scattering system.

Figure 2. Raw data of the auto-correlation function for solution 1-A (a). Size distributions of particles in solutions 1-A (b), B (c), C (d), and a 250 mM KCl solution (e).

the same as that of solution 1-A. It can be seen when KCl is less than 100 mM, the particles in the solution immediately aggregate to large particles whose sizes are an order of micron,

and precipitation is observed within a few hours for the solution without KCl. This situation is apparently not suitable to follow the change of amount of the calcium phosphate cluster, 0.8 nm

Calcium Phosphate Clustering in CaCl2-H3PO4-KCl-H2O

Figure 3. The relationship between average size of particle in the solution and concentration of KCl. Calcium phosphate clusters aggregate and form large particles when the concentration of KCl is less than 100 mM.

Figure 4. Fraction of the particle larger than 0.7 nm in solution 1-A with time. It can be seen that the fraction is almost constant during 5 days.

diamter, depending on the experimental condition. We fixed the concentration of KCl as 250 mM in the following measurements. 2. Relationship between Particle Size and Time. Time evolution of the particle larger than 0.7 nm found in solution 1-A was investigated to confirm the stability of the clusters. Figure 4 shows the relationship between the fraction of the particle larger than 0.7 nm and time. It was found that the fraction was almost constant, at 44%-50%, from 1 h after preparing the solution to 5 days. Thus the present calcium phosphate clusters in solution 1-A is stable and never forms an aggregate at least during 5 days. Measurement before 1 h is impossible since the filtering of the solution requires 30 min and we should wait more 30 min to suppress the convection in the cell as described in the Experimental Section. 3. Relationship between Particle Size and σ. The size fraction ascribable to calcium phosphate clusters decreased with σ. For solutions 2-A, the fraction of particles whose size was larger than 0.7 nm within the total amount of particles in the distribution decreased from 60% to 11% with a decrease in the concentrations of calcium and phosphate ions (Figure 5a, solutions 2-A). The latter value of 11% was found to be the

J. Phys. Chem. B, Vol. 103, No. 39, 1999 8233 background level because the exclusion of either phosphate or calcium ions also resulted in the same value (Figure 5a, solutions 2-B, C). The fraction of particles whose size was larger than 0.7 nm correlated linearly with the change in σ (Figure 5b). A decrease in σ because of a pH change also decreased the size fraction of calcium phosphate clusters (Figure 6b). The fraction of particles whose size was larger than 0.7 nm decreased with a decrease in pH (Figure 6a). The relationship between the size fraction and σ, however, was different compared with the relationship involving the change in concentrations of calcium and phosphate ions. The fraction of particles whose size was larger than 0.7 nm decreased dramatically at approximately σ ) 0, showing an asymptotic relationship with an increase in σ. The ionic products of each solution with respect to amorphous calcium phosphate (Ca3(PO4)1.87(HPO4)0.2 or Ca(PO4)0.74H0.22; ACP) and octacalcium phosphate (Ca4H(PO4)3; OCP) were also calculated according to constants described elsewhere.21-23,27-30 All the solutions (1-4)-A were undersaturated with respect to ACP. Solutions (1,2,4)-A were saturated or nearly saturated with respect to OCP, though solutions 3-A with a pH below 6.0 were undersaturated with respect to OCP. It was noted that the calcium phosphate clusters existed in the solution 3-A with pH 6.0. This solution is supersaturated with respect to only HAP and undersaturated with respect to ACP and OCP. 4. Relationship between Particle Size and Ca/P Molar Ratio of Solution. Calcium phosphate clusters were detected in solutions 3-A with Ca/P molar ratios ranging from 0.2 to 50 under constant σ (Figure 7). When a Ca/P molar ratio is out of this range, the size fraction ascribable to calcium phosphate clusters is equal to the background level. The amount of calcium phosphate clusters reached a maximum and was nearly constant in solutions with Ca/P molar ratios ranging from 1 to 8. Discussion The presence of calcium phosphate clusters of approximately 0.8 nm in diameter was demonstrated in simple solutions containing only CaCl2, H3PO4, and KCl without tris(hydroxymethyl)aminomethane. Although the precise composition of calcium phosphate cluster needs to be clarified in future, the cluster should be the same as that proposed in a previous work, Ca9(PO4)6, judging from its average size, 0.8 nm. As discussed in the previous paper,16 the cluster is not necessary to be the single molecule of HAP since hexagonal closed packing of the Ca9(PO4)6 clusters automatically forms the frame of HAP. Ca and OH ions are then or simultaneously incorporated into the void of the clusters, and stoichiometric HAP is formed. It has been well-known that the precipitate from concentrated simulated body fluid had Ca/P ratio around 1.50-1.55, which was very close to that of the Ca9(PO4)6 cluster. We also confirmed using XPS in the previous work31 that the initial grown phase on HAP seed crystal was HAP with low crystallinity and its Ca/P ratio was about 1.50. Calcium phosphate clusters were detected only when the solutions were supersaturated or nearly saturated with respect to HAP. A decrease in σ resulted in a decrease in the amount of calcium phosphate clusters. These features are the same as those observed for calcium phosphate clusters detected in solutions containing tris(hydroxymethyl)aminomethane used in the previous study. It is thus concluded that tris(hydroxymethyl)aminomethane does not significantly contribute, physically and/ or chemically, to the formation of calcium phosphate clusters. Therefore, the probability for tris(hydroxymethyl)aminomethane to act as a heterogeneous nucleation center of the cluster is nullified.

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Figure 5. Variations in the fraction of particles whose size is larger than 0.7 nm within the total amount of particles in the distribution of the solutions 2-A, B, C with changing concentrations of H3PO4 and CaCl2 (a) and σ (b). The vertical error bar is a standard deviation (n g 3) and the horizontal error bar is derived from a Ksp value,10-117(1.

Figure 6. Variations in the fraction of particles whose size is larger than 0.7 nm within the total amount of particles in the distribution of the solutions 3-A, B, C with changing pH (a) and σ (b). The vertical error bar is a standard deviation (n g 3) and the horizontal error bar is derived from a Ksp value,10-117(1.

The amount of calcium phosphate clusters decreased with a decrease in σ. A change in pH, however, had a peculiar effect on the stability of calcium phosphate clusters in comparison with that caused by a change in the concentrations of CaCl2 and H3PO4. The change in pH of the solution affects the electrostatic interaction of each ion in the cluster. It is natural to assume that the thermodynamic driving force, σ, caused by the change in pH of the solution, has nonlinear effect on the amount of clusters, since the electrostatic force has a threshold below which the cluster cannot be stabilized. It was previously revealed by Nancollas et al. that the kinetics of HAP growth was pH-dependent and the growth rate changed at a pH above or below 6.5-7.0 using the constant composition method.32 This conclusion can be explained by assuming that clusters dissociate at around pH 6.5 and that the growth rate of HAP increases as a result of cluster dissociation, since the incorporation of the cluster into the crystal is the rate-determining step for HAP growth. This hypothesis is consistent with the present results

that the pH change has a peculiar effect on the stability of calcium phosphate clusters. The reason the relationship seen in Figure 5b does not pass through σ ) 0 is not yet clarified. However we may propose the following reasons. First, at low σ due to the decrease of Ca and PO4, the cluster may dissociate to ions and the growth proceeds by ionic unit. This hypothesis means that there are critical concentrations of Ca and PO4 below which the cluster cannot exist, and the growth kinetics under very low σ is different from that under high σ. We already performed the growth rate measurement of (0001) face of HAP in the simulated body fluid coupling with surface observation by AFM in the previous study.31,33 From AFM observation, it was confirmed that the growth took place at σ < 2. In this region, the growth rate vs supersaturation relationship does not coincide with that in the high supersaturation region although the growth rate was too slow to be measured. Second, the effect of solubility product of HAP, Ksp. The Ksp values used in this study to calculate

Calcium Phosphate Clustering in CaCl2-H3PO4-KCl-H2O

J. Phys. Chem. B, Vol. 103, No. 39, 1999 8235 molar ratios ranging from 1 to 8. All these results agree with the conclusion from a previous study that the growth unit of HAP is a Ca9(PO4)6 cluster. Acknowledgment. This study was supported by AIST (Agency of Industrial Science and Technology). References and Notes

Figure 7. Variations in the fraction of particles whose size is larger than 0.7 nm within the total amount of particles in the distribution of the solutions 4-A, B, C with changing Ca/P molar ratio. The error bar is a standard deviation (n g 3).

supersaturation are in the range between 10-116 to 10-118. These values are well accepted as being adequate, however, if we use the Ksp 10-103.5, which is close to the lowest among the Ksp values previously reported, the relationship seen in Figure 5b passes through σ ) 0. However, judging from the result of Figure 6 that the amount of the cluster goes downt to zero around σ ) 0 when σ is changed by the pH of the solution, the second reason is difficult to accept. Under constant σ, calcium phosphate clusters existed in solutions with Ca/P molar ratios ranging from 0.2 to 50. The cluster (Ca9(PO4)6) with a Ca/P molar ratio of 1.5 is assumed to be the growth unit of HAP, according to the cluster growth model for HAP. This model is consistent with the present result because the amount of calcium phosphate clusters reaches a maximum in solutions with Ca/P molar ratios ranging from 1 to 8. It should be noted that the Ca9(PO4)6 cluster exists not only in the HAP structure but also in the structures of ACP and OCP, both of which are the precursors of HAP,34,35 and that the Ca/P molar ratios of these three calcium phosphates (1.33-1.67) are all within the Ca/P molar ratio range in which the amount of calcium phosphate clusters reaches a maximum. Conclusion Calcium phosphate clusters approximately 0.8 nm in diameter were detected in simple solutions containing only CaCl2, H3PO4, and KCl. The formation of these clusters is not affected by the presence of tris(hydroxymethyl)aminomethane. The amount of clusters decreases with decreasing σ. Under constant σ, the amount of clusters reaches a maximum in solutions with Ca/P

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