Structural effects of phosphate groups on apatite formation in a copolymer modified with Ca²⁺ in a simulated body fluid

Abstract

Organic–inorganic composites are novel bone substitutes that can ameliorate the mismatch of Young's moduli between natural bone and implanted ceramics. Phosphate groups contribute to the formation of apatite in a simulated body fluid (SBF) and the adhesion of osteoblast-like cells. Therefore, modification of a polymer with these functional groups is expected to enhance the ability of the organic–inorganic composite to bond with bone. Two phosphate groups have been used, phosphonic acid (–C–PO₃H₂) and phosphoric acid (–O–PO₃H₂). However, the effects of structural differences between these phosphate groups have not been clarified. In this study, the apatite formation of copolymers modified with Ca²⁺ and either –C–PO₃H₂ or –O–PO₃H₂ was examined. The mechanism of apatite formation is discussed based on analytical and computational approaches. The copolymers containing –O–PO₃H₂, but not those containing –C–PO₃H₂, formed apatite in the SBF, although both released similar amounts of Ca²⁺ into the SBF. Adsorption of HPO₄²⁻ from –O–PO₃H₂ in the SBF following Ca²⁺ adsorption was confirmed by zeta-potential measurement and X-ray photoelectron spectroscopy. The measurement of the complex formation constant revealed that the –O–PO₃²⁻⋯Ca²⁺ complex was thermodynamically unstable enough to convert into CaHPO₄, which was not the case with –C–PO₃²⁻⋯Ca²⁺. The formation of CaHPO₄-based clusters was found to be a key factor for apatite nucleation. In conclusion, this study revealed that modification with –O–PO₃H₂ was more effective for enhancing apatite formation compared with –C–PO₃H₂.

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1. Introduction

The ability to bond to existing bone is one of the essential properties for permanent implanted bone substitutes used to repair defects. Bioactive ceramics, such as Bioglass,¹ the glass-ceramic A-W,² and sintered hydroxyapatite³ can bond to living bone without encapsulation by fibrous tissue. They are able to form bone-like apatite with low levels of crystallinity on their surfaces in physiological environments. Although these materials are used clinically as bone substitutes, implantation may cause stress-shielding and subsequent bone absorption due to their higher Young's moduli compared with natural bone. Natural bone is an organic–inorganic composite consisting of collagen fibers and apatite. Here, the fabrication of artificial bioactive organic–inorganic composites is used to solve this mismatch problem. However, specific functional groups, such as Si–OH,⁴ Ti–OH,⁵ carboxyl (–COOH),⁶ and sulfonate (–SO₃H)⁷ can contribute to the formation of a bone-like apatite layer in simulated body fluid (SBF). SBF has inorganic ion concentrations similar to human blood plasma.^8,9 These groups interact with Ca²⁺ ions in the SBF, and induce heterogeneous nucleation of apatite. Thus, modifications to these functional groups is an important method for preparing composites possessing bone-bonding ability.

Phosphate groups (–PO₃H₂) have also attracted a great deal of attention for improving the biocompatibility of implants, and their ability to bond to bone. Tanahashi et al. found that phosphate groups immobilized on gold in self-assembled monolayers exhibited better apatite-forming ability compared with carboxyl groups as a result of stronger interactions with Ca²⁺.⁶ Datta et al. prepared nanofibers and films of poly(vinyl alcohol) modified with phosphate groups via phosphorylation with phosphoric acid.⁷ They reported that such modification led to the formation of calcium phosphate in SBF, and the enhancement of the proliferation of osteoblast-like MG63 cells.¹⁰ Moreover, López-Pérez et al. showed that the number of SaOs-2 osteoblast-like cells attached on a poly(ε-polycaprolactone) scaffold increased after surface modification using poly(vinylphosphonic acid).¹¹

We previously examined the effect of phosphate group content on the apatite-forming ability of copolymers based on vinylphosphonic acid treated with a CaCl₂ solution.¹² As a result, an increase in the phosphate group content actually inhibited apatite formation in SBF, despite the fact that the copolymer released Ca²⁺ into the SBF. These results indicate that the incorporation of phosphate groups using vinylphosphonic acid has an adverse effect on apatite formation in SBF.

To clarify these different phenomena, we focused on the molecular structures of the phosphate groups. They have two types of structure, phosphonic acid (–C–PO₃H₂) and phosphoric acid (–O–PO₃H₂). Tanahashi et al. and Datta et al. used –O–PO₃H₂, while we used –C–PO₃H₂. These structural differences are expected to affect the interactions with Ca²⁺ ions, and subsequent apatite formation, because the stability of the ionized phosphate groups is dependent on element substitution as a result of the inductive effect.¹³ However, this hypothesis has not been previously examined.

In this study, we prepared copolymers containing Ca²⁺ and either –C–PO₃H₂ or –O–PO₃H₂ under identical synthetic conditions and examined the apatite formation on their surfaces in SBF. The mechanism of apatite formation on the copolymers is discussed using chemical analytical and computational approaches.

2. Materials and methods

2.1 Preparation of copolymers modified with Ca²⁺ and different phosphate groups

Vinylphosphonic acid (VPA, 95%, Tokyo Chemical Industry Co., Ltd, Tokyo, Japan) and methacryloyloxyethyl phosphate (MOEP, 90%, Phosmer™ M, Yuni Chemical Co., Ltd, Nara, Japan) were used to incorporate the –C–PO₃H₂ and –O–PO₃H₂ phosphate groups, respectively, in the copolymers. 2-Hydroxyethyl methacrylate (HEMA, 95%, Wako Pure Chemical Industries, Ltd, Osaka, Japan) and triethylene glycol dimethacrylate (TEGDMA, 90%, Wako Pure Chemical Industries, Ltd) were mixed with VPA or MOEP. The molar ratio of the phosphate monomers, HEMA and TEGDMA was VPA : HEMA : TEGDMA = 10 : 85 : 5 or MOEP : HEMA : TEGDMA = 7 : 88 : 5, and the total weight of the monomers was 10 g. Then, 0.5 wt% sodium p-toluene sulfinate (p-TSS, 98%, Tokyo Chemical Industry Co., Ltd) and 2 wt% of N,N′-dimethyl-p-toluidine (97%, Wako Pure Chemical Industries, Ltd) were added to the monomers. Then, 1 mol% of (±)-camphorquinone (97%, Wako Pure Chemical Industries, Ltd) was added, and the mixture was stirred for 1 hour with light shielding.

Then, the mixture was polymerized for 1 hour using irradiation with blue light (λ = 460 nm) and the obtained copolymers were dried at 60 °C for 1 day. The copolymers were cut into rectangles and polished with #1000 SiC waterproof abrasive paper. To remove the unreacted regents, the copolymers were soaked in ultra-pure water for one day at room temperature, and dried at 60 °C for 1 day. The final size of the copolymers was 10 × 10 × 1 mm (weight = 0.1 g). The copolymers were soaked in 30 cm³ of 0, 0.1, or 1 kmol m⁻³ CaCl₂ solution at 36.5 °C for 1 day. The specimens prepared from VPA and MOEP were denoted VPA(C)xCa and MOEP(O)xCa, respectively, and x gives the molarity of the CaCl₂ solution used.

2.2 Soaking specimens in SBF, 1.5CaSBF, or Tris–NaCl buffer

The SBF (Na⁺ 142.0, K⁺ 5.0, Mg²⁺ 1.5, Ca²⁺ 2.5, Cl⁻ 147.8, HCO₃⁻ 4.2, HPO₄²⁻ 1.0, SO₄²⁻ 0.5 mol m⁻³) at pH 7.40 was prepared as follows: NaCl, NaHCO₃, KCl, K₂HPO₄·3H₂O, MgCl₂·6H₂O, CaCl₂, and Na₂SO₄ (Nacalai Tesque, Inc., Kyoto, Japan) were dissolved in ultrapure water, and the pH was adjusted with the addition of 1 kmol m⁻³ HCl and tris(hydroxymethyl) aminomethane (Nacalai Tesque, Inc.). In addition, a solution with a Ca²⁺ concentration 1.5 times that of the final SBF (1.5CaSBF) with a pH 7.25 was also prepared by the same method as the SBF.¹⁴ The specimens were soaked in 30 cm³ of SBF or 1.5CaSBF at 36.5 °C for various time intervals.

The Tris–NaCl buffer (NaCl 142, tris(hydroxymethyl) aminomethane 50 mol m⁻³) at pH 7.40 was prepared by dissolving NaCl and tris(hydroxymethyl) aminomethane in ultrapure water. Then, the pH of the resulting solution was adjusted with the addition of 1 kmol m⁻³ HCl. The specimens were soaked in 30 cm³ of Tris–NaCl buffer at 36.5 °C for various time intervals to measure the amount of released Ca²⁺.

2.3 Characterization of the specimens

To measure the phosphate group content and acid dissociation constant (pK_a) of the specimens, 30 cm³ of a 0.16 kmol m⁻³ NaCl solution, after soaking a VPA(C)0Ca or MOEP(O)0Ca sample in it, was titrated using 0.01 kmol m⁻³ NaOH solution at 36.5 °C. During the titration, the pH value of the solution was measured with a pH meter (F-23IIC, Horiba Ltd, Kyoto, Japan).

The Ca content of the specimens before soaking in the SBF was measured by an energy-dispersive X-ray (EDX) analysis system (EMAX Energy, Horiba Ltd). The surfaces of the specimens after soaking in SBF or 1.5CaSBF were analyzed by thin-film X-ray diffraction (TF-XRD; MXP3V, Mac Science, Co., Yokohama, Japan), X-ray photoelectron spectroscopy (XPS; KRATOS Nova, KRATOS Analytical Ltd, Manchester, UK), and scanning electron microscopy (SEM; S-3500N, Hitachi Co., Tokyo, Japan). For the TF-XRD analysis, the angle of the incident X-rays (CuKα) was fixed at 1° with respect to the surface of the specimens. In the XPS analysis, AlKα (hν = 1486.6 eV) was used as the X-ray source, and the spectra were measured with a high-resolution scan at 20 eV of pass energy. The binding energies of these elemental spectra were calibrated with the binding energy of a methylene group (284.6 eV). The observed spectra was subjected to peak fitting using a blend function consisting of 70% Gaussian and 30% Lorentzian curves.

The zeta-potentials of the surfaces of the specimens were measured with a zeta-potential analyzer (Otsuka Electronics Co., Osaka, Japan) connected to a box-like quartz cell. After being soaked in SBF for various periods, the specimens were washed with ultrapure water, and then placed in a quartz cell. Fresh SBF mixed with polyethylene latex particles (Otsuka Electronics Co.) was introduced into the cell, and the electrophoretic mobilities of the particles were measured using the laser Doppler method to find the zeta-potentials.

The Ca and P concentrations, along with the pH of the SBF and Tris–NaCl buffers after soaking the copolymer specimens with Ca²⁺, were measured with an inductively coupled plasma atomic emission spectrometer (ICP-AES; ICPE-9820, SHIMADZU Co., Kyoto, Japan) and pH meter, respectively.

2.4 Evaluation of the complex formation constant

The stability constant of the polymer–Ca²⁺ complex was determined in accordance with the method reported by Szabadka et al.¹⁵ A 0.1 g sample of a VPA(C)0Ca or MOEP(O)0Ca copolymer was soaked in 30 cm³ of a 10 mol m⁻³ CaCl₂ solution for 5 days at 36.5 °C. Then, they were soaked in 30 cm³ of the Tris–NaCl buffer, simulating physiological conditions (ion strength: I = 0.16, pH 7.40, 36.5 °C), for 5 days. The common logarithm of the stability constant (log β) of the complex in the buffer was calculated using eqn (1):where [–P_ion⋯Ca²⁺], [*Ca²⁺], and [*–P_ion] are the molar concentrations of the complex of the ionized phosphate groups immobilized in the copolymer, the free calcium ions, and the unbound ionized phosphate groups, respectively, in the Tris–NaCl buffer. These concentration values were calculated using the content of phosphate groups in the copolymer, the pK_a of the groups at I = 0.16, and the concentrations of Ca²⁺ in the CaCl₂ solution and buffer.

2.5 Simulation of the dipole moments and molecular orbitals

The structure with the lowest energy using each of the two phosphate groups was found using the restricted local density approximation and the Perdew–Wang correlational (LDA/PWC) method® with double-numerical basis sets, as implemented in the DMol³ software package®.^16,17 The ground-state geometries were calculated with the phosphate groups bound to Ca as structural models to evaluate their electron density states by DMOl³. The dipole moments of the species were determined using the Hirshefeld approach.

3. Results

Table 1 shows the phosphate group content in the copolymers prepared from different monomers, along with their acid dissociation constants at 36.5 °C measured via neutralizing titration. The VPA(C) and MOEP(O) copolymers contained nearly equivalent amounts of the phosphate groups. The first and second proton dissociation constants for MOEP(O) were lower than those of VPA(C).

Table 1 Phosphate group content (n = 3) and acid dissociation constant at 36.5 °C of different copolymers measured by neutralizing titration

	VPA(C)	MOEP(O)
Phosphate group/mmol g^−1	0.24 ± 0.02	0.24 ± 0.002
pKa1	3.63	3.48
pKa2	6.11	5.96

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Fig. 1(A) and (B) show the Ca/P molar ratios of the specimens after treatment with different concentrations of the CaCl₂ solution, and the Ca concentration in the Tris–NaCl buffer after soaking the specimens. The ratios for the VPA(C) and MOEP(O) samples were very similar with regard to CaCl₂ concentration. The Ca concentration in the Tris–NaCl buffer increased and became almost constant after 7 days for all the specimens. The Ca concentrations after 14 days satisfied MOEP(O)1Ca > VPA(C)1Ca ≈ MOEP(O)01Ca > VPA(C)01Ca.

Fig. 1 Ca/P molar ratio of the specimens after soaking in 0.1 or 1 kmol m⁻³ of CaCl₂ solution (A) and Ca concentration in Tris–NaCl buffer following soaking of the different specimens (n = 3) (B).

Fig. 2 shows the TF-XRD results of the specimens after soaking in SBF for various time intervals. The two broad peaks at 2θ = 26° and 32° corresponding to apatite (JCPDS #09-0432) were observed in MOEP(O)01Ca and MOEP(O)1Ca after 7 days and 1 day, respectively. Conversely, these peaks were not observed in VPA(C)01Ca or VPA(C)1Ca even after 14 days.

Fig. 2 TF-XRD patterns of the specimens following soaking in SBF for various periods.

Fig. 3 shows surface SEM images of different specimens that were soaked in SBF for various time intervals. Deposition was observed on the MOEP(O)01Ca and MOEP(O)1Ca samples after 7 days and 1 day, respectively, but not on the VPA(C)01Ca or VPA(C)1Ca surfaces. The scale-like morphology of the primary particles was similar to the apatite formed in the SBF.⁷

Fig. 3 SEM images of the surfaces of the specimens following soaking in SBF for various periods.

Fig. 4(A) shows the XPS spectra of the surfaces of VPA(C)1Ca and MOEP(O)01Ca after soaking in SBF for various time intervals. Peaks attributed to –C–PO₃H₂ and –C–PO₃Ca were observed in VPA(C)1Ca at 133.2 and 132.7 eV, respectively.¹⁸ The peak position did not shift regardless of the soaking time. In contrast, the peaks attributed to –O–PO₃H₂ and –O–PO₃Ca were observed in MOEP(O)01Ca at 134.5 and 133.8 eV, respectively.¹⁹ These peaks decreased after 3 hours, while those corresponding to CaHPO₄²⁰ and octacalcium phosphate (OCP)²¹ became visible at 133.4 and 133.2 eV, respectively. Then, the peak corresponding to apatite was observed at 133.0 eV after 1 day.²²Fig. 4(B) shows the change in the rate for each component of calcium phosphate formed on the MOEP(O)01Ca surface calculated from the area of the fitted peaks in the P_2p spectra. The ratio of CaHPO₄ to OCP initially increased during the first 3 hours, and then decreased with soaking time. Conversely, the signal from apatite monotonically increased, and the calcium phosphate phase was almost entirely apatite after 7 days.

Fig. 4 P_2p XPS spectra of VPA(C)1Ca and MOEP(O)01Ca (A) and change in rate of component of calcium phosphate formed on the MOEP(O)01Ca (B) following soaking in SBF for various periods.

Fig. 5 shows the changes in the surface zeta-potential of the VPA(C)1Ca and MOEP(O)01Ca samples after soaking in the SBF. The potential of both specimens changed from negative to positive after 5 days. Afterwards, the potential of VPA(C)1Ca was almost constant, while that of MOEP(O)01Ca decreased and became negative after 7 days.

Fig. 5 Change in surface zeta potential of VPA(C)1Ca and MOEP(O)01Ca following soaking in SBF for various periods (n = 3).

Fig. 6 shows the changes in the Ca and P concentrations, along with the pH value after soaking the specimens in SBF for various time periods. The Ca concentration after 1 day decreased according to VPA(C)1Ca > MOEP(O)1Ca ≈ MOEP(O)01Ca > VPA(C)01Ca. Then, the Ca concentration gradually decreased in all specimens. The P concentration significantly decreased in MOEP(O)01Ca and MOEP(O)1Ca, while it was almost constant in VPA(C)01Ca and VPA(C)1Ca. The pH value of the SBF following soaking for all the specimens increased after 1 day, and then gradually decreased.

Fig. 6 Change in Ca and P concentrations and pH in SBF following soaking of different specimens (n = 3).

Fig. 7 shows the P_2p XPS spectra of the VPA(C)0Ca and MOEP(O)0Ca samples after being soaked in 1.5CaSBF for various time periods. The peaks attributed to –C–PO₃H₂ and –C–PO₃Ca were observed in VPA(C)0Ca, and remained constant regardless of the soaking time. On the other hand, the peaks attributed to CaHPO₄ and OCP, as well as those from –O–PO₃H₂ and –O–PO₃Ca, were observed in MOEP(O)0Ca after 3 hours. The peaks from CaHPO₄ and OCP were almost replaced by those of apatite after 1 day. This indicates that the initial processes of calcium phosphate formation were similar, irrespective of previous Ca²⁺ incorporation (see Fig. 4).

Fig. 7 P_2p XPS spectra of VPA(C)0Ca and MOEP(O)0Ca following soaking in 1.5CaSBF for various periods.

Table 2 shows the stability constants of the polymer–Ca²⁺ and CaHPO₄ (aq.) complex under physiological conditions. The constant for the CaHPO₄ (aq.) complex under these conditions was calculated using the ion strength I = 0.02 at 37 °C reported by Chughtai et al.²³ The constant increased according to MOEP(O) < HPO₄²⁻ < VPA(C).

Table 2 Stability constants of ionized phosphate group-Ca²⁺ complexes on the different polymers (n = 4) in comparison with that of CaHPO₄ complexes under physiological conditions

	VPA(C)	CaHPO4(aq.)	MOEP(O)
log β	4.44 ± 0.07	3.41	3.08 ± 0.13

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Fig. 8 shows the structures with the lowest energy from the molecular models of CH₃–CH₂–PO₃Ca and CH₃–O–PO₃Ca with –C–PO₃H₂ and –O–PO₃H₂, respectively. The O atom forms a double bond with P close to the Ca atom in the CH₃–CH₂–PO₃Ca. On the other hand, this was located in the reverse direction from Ca in CH₃–O–PO₃Ca. The calculated highest occupied molecular orbital (HOMO) was distributed around the O atoms, while the lowest unoccupied molecular orbital (LUMO) was widely distributed around the Ca atom in both of the phosphate groups. The energy levels of the HOMO and LUMO for CH₃–CH₂–PO₃Ca were −0.156 and −0.118, and for CH₃–O–PO₃Ca they were −0.186 and −0.146 eV, respectively. The value of the dipole moment of CH₃–CH₂–PO₃Ca was 9.35 Debye, and for CH₃–O–PO₃Ca it was 15.71 Debye. This suggests that the structural differences between –C–PO₃Ca and –O–PO₃Ca were not at the molecular orbital level, but rather a result of the most stable structures and polarizability.

Fig. 8 The structure of the molecular model of (A) CH₃–CH₂–PO₃Ca and (B) CH₃–O–PO₃Ca with the lowest energy for each type of phosphate group (white: H, gray: C, red: O, purple: P, green: Ca atom).

4. Discussion

Copolymers containing equivalent amounts of the phosphate group and Ca²⁺ were prepared by radical polymerization (see Table 1 and Fig. 1(A)). It was found that the copolymers modified with –O–PO₃H₂ had much higher apatite-forming ability in SBF than those modified with –C–PO₃H₂ when treated with the CaCl₂ solution (see Fig. 2 and 3). This means that modification with –O–PO₃H₂ was more effective for apatite formation on the copolymers modified with Ca²⁺, when compared with –C–PO₃H₂.

The formation of embryos, which are pre-nucleation clusters, larger than the critical size r* is important for the spontaneous nucleation of apatite on the substrate. The activation free energy (ΔG*) for heterogeneous nucleation is given by eqn (2):²⁴

where γ and V_β, are the interface energies between the nucleus and solution and the molecular volume of the crystalline phase, respectively. On the other hand, f(θ) is a function of contact angle between the nucleus and the substrate surface, and σ is the supersaturation degree with respect to apatite. σ can be expressed using eqn (3):where IP_HAp and K_sp HAp are the ion activity and solubility product with respect to apatite, respectively. Moreover, IP_HAp can be calculated from the pH and concentrations of Ca and P using eqn (4):where the values of a_Ca²⁺, a_PO4³⁻ and a_OH⁻ are assumed to be 0.36, 0.06, and 0.72 at physiological ionic strength (I = 0.16), respectively, and K_sp HAp is the solubility product for hydroxyapatite (5.5 × 10⁻¹¹⁸).^25,26 Therefore, the heterogeneous apatite nucleation in this study was governed by the supersaturation degree and the surface condition of the specimens.

The supersaturation degree with respect to apatite in the SBF can be increased by the release of Ca²⁺ from the substrate.²⁷Fig. 9 shows the changes in the logarithm of σ in the SBF after soaking the specimens for various time periods. The supersaturation degree decreased as VPA(C)1Ca ≈ MOEP(O)01Ca > VPA(C)01Ca > MOEP(O)1Ca. Although the largest amount of Ca²⁺ was released from MOEP(O)1Ca in the Tris–NaCl buffer (see Fig. 1(B)), the supersaturation degree was low for all specimens. It was speculated that apatite formation on MOEP(O)1Ca occurred rapidly, within 1 day (see Fig. 2 and 3), and that the supersaturation degree rapidly decreased due to ion consumption in the SBF after that time. Although the supersaturation degree values in MOEP(O)01Ca and VPA(C)1Ca were similar, the former formed apatite, but not the latter. These results indicate that structural differences in the phosphate groups affected the surface conditions related to the heterogeneous nucleation of apatite.

Fig. 9 Change in supersaturation degree with respect to the apatite in SBF following soaking of different specimens (n = 3).

It was confirmed by XPS that the surface reaction process was significantly different in –C–PO₃H₂ and –O–PO₃H₂ (see Fig. 4(A)). VPA(C)1Ca only adsorbs Ca²⁺ to form the –C–PO₃²⁻⋯Ca²⁺ complex, but not HPO₄²⁻ in SBF. This is supported by the fact that the P concentration in SBF was almost constant (see Fig. 6). On the other hand, MOEP(O)01Ca formed CaHPO₄ and OCP at the initial stage, and subsequently the OCP that formed was transformed into apatite (see Fig. 4(B)). A similar transformation from OCP to apatite on a plasma-treated polymer in SBF was discussed by Oyane et al.²⁸ These results indicate that only MOEP(O)01Ca adsorbs HPO₄²⁻ following Ca²⁺ adsorption to form calcium phosphate as the precursor of apatite. In addition, MOEP(O)0Ca formed calcium phosphate in 1.5CaSBF even without a release of Ca²⁺ (see Fig. 7). Thus, these results suggest that the specific structures of the phosphate groups provide the surface conditions favorable for apatite nucleation via the adsorption of HPO₄²⁻ in SBF.

It has been reported that the surface zeta-potential is one of the parameters that governs apatite formation on bioactive materials in SBF.^29,30 In the case of titanium metal bound to bone prepared by treatment with an alkaline solution, the negatively charged surfaces becomes positive due to Ca²⁺ adsorption in SBF, then becomes negative again via the subsequent adsorption of phosphate, ultimately forming apatite.²⁹ In contrast, VPA(C)1Ca did not demonstrate such behavior, even though the zeta-potential of both specimens changed from negative to positive (see Fig. 5). Based on the results of XPS and the zeta-potential measurement, differences in apatite formation cannot be explained in terms of surface charge alone.

With regard to the initial reaction process for each phosphate group on the surface of specimens with Ca²⁺ and HPO₄²⁻ in the SBF, we consider two viewpoints: (1) the interaction energies between the reactive chemical species in the transition state, and (2) the thermodynamic stability of the products.

With viewpoint (1), it is assumed that a transition state –PO₃Ca⋯HPO₄²⁻ is formed for all the specimens. The interaction energy is obtained as the sum of the frontier orbital interaction and the Coulomb interaction.^31,32 The LUMO around the Ca atom in the both models (see Fig. 8) was expected to accept the HOMO electron of HPO₄²⁻. When comparing the energy levels of the orbitals, a significant difference is observed for the LUMO in both models (−0.146 and −0.118 eV) and the HOMO level of O atoms in HPO₄²⁻ (−8.9 eV) estimated from the vertical ionization energy.³³ This means that the Coulomb interaction contributes more to the formation of the transition state than the frontier orbital. A computational simulation of the polarizability indicated that the Coulomb interaction of the –O–PO₃²⁻⋯Ca²⁺ complex with HPO₄²⁻ was stronger than with –C–PO₃²⁻⋯Ca²⁺. Therefore, the transition state in MOEP(O) was predicted to be more stable than VPA(C), leading to a decrease in activation energy for the formation of CaHPO₄ in the former.

Using viewpoint (2), the thermodynamic stability values between CaHPO₄ (aq.) and the complex composed of Ca²⁺ and one of the phosphate groups were evaluated. The magnitude of the complex formation constants in Table 2 indicates that Ca²⁺ bound with MOEP(O) has a higher ability to bond to HPO₄²⁻via a ion–dipole interaction, and subsequently become converted into CaHPO₄, because the stability of the –O–PO₃²⁻⋯Ca²⁺ complex was lowest.

The Ca²⁺⋯HPO₄²⁻ interaction on the surface of the MOEP(O) sample had an important role for apatite deposition. It was recently reported that heterogeneous apatite nucleation on a titanium substrate treated with H₂O₂ in SBF progresses via the formation of a pre-embryo consisting of Ca²⁺, HPO₄²⁻, and OH⁻.^34,35 Moreover, self-assembled monolayers containing carboxyl groups formed clusters by accumulation of pre-nucleation complexes of [Ca(HPO₄)₃]⁴⁻.^36,37

Summarizing the mechanism described above, apatite formation on the surface of MOEP(O) is assumed to progress as follows: an increase in [Ca(HPO₄)₃]⁴⁻ concentration results in the formation of many clusters larger than r*. Subsequently, the clusters transformed into OCP, the apatite precursor, via ion adsorption in the SBF. In fact, Habraken et al. demonstrated that amorphous calcium phosphate with the formula [Ca₂(HPO₄)₃]²⁻ grew into Ca-deficient OCP via the aggregation of the pre-nucleation complex and ions in a solution supersaturated with respect to the apatite.³⁷

Finally, the results of this study reveal that differences in the molecular structures of the phosphate groups govern the apatite-forming ability of the copolymers modified with Ca²⁺, because the low thermodynamic stability of the phosphate⋯Ca²⁺ complex on the specimen enhances calcium phosphate cluster formation that is favorable for apatite nucleation. It is also expected that such structural differences affect the ability of the composites to bond with bone. Recently, Huang et al. reported that modification of –O–PO₃H₂ promoted the differentiation of mesenchymal stem cells to provide mineralization on the polymer.³⁸ However, it has never been revealed whether structural differences affect the behavior of calcification induced by the cells. To clarify this point in detail, the adsorption behavior of proteins, and the response of the cells, should be investigated in future work.

5. Conclusion

The structural effects of phosphate groups on apatite formation on the surface of a copolymer modified with Ca²⁺ in SBF were examined. The copolymers modified with phosphoric acid (–O–PO₃H₂) induced heterogeneous nucleation of apatite, but not those modified with phosphonic acid (–C–PO₃H₂), because the amount of adsorbed HPO₄²⁻ in the SBF was insufficient for apatite nucleation. The reason for this phenomenon was that the thermodynamic stability of the ionized –O–PO₃²⁻⋯Ca²⁺ complex was lower than that of –C–PO₃²⁻⋯Ca²⁺. It was found that the reaction with HPO₄²⁻ that allowed the calcium phosphate clusters to become precursors of apatite was a key issue that significantly affected apatite formation on the copolymer.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This study was supported by Grant-in-Aid for JSPS Research Fellow Grant Number 17J02000. We thank Louis R. Nemzer, PhD, from Edanz Group for editing a draft of this manuscript.

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