SEM. The pH values of the reaction mixture at different times are summarized in Table 1

Results and Analyses

A. SEM. The pH values of the reaction mixture at different times are summarized in Table 1

Referring to the SEM images of our sample series shown in Figure 1, the crystals of the 1.5-h sample are poorly faceted rectangular plates. The blade-like crystals of the 3-h sample is the characteristic morphology of OCP. As the pH value of the reaction mixture rose to 5.01 at which the 4-h sample was collected, notches become found on the rectangular OCP crystals. Formation of slits along the c axis is also observed in previous study.^14,29 The 12-h sample was collected at pH of 6.69 and the crystals are mainly hexagonal rod-shaped.

B. TEM and ED. The 3-h, 6-h and 12-h samples were characterized by TEM and ED. The long edge of the blade-like OCP crystal is found to be along the c axis. The selected-area electron diffraction (SAED) patterns of the 3-h and 12-h samples can be assigned to the reflections along the [110] zone axis of OCP and the [210] zone axis of HAp, respectively. Consequently, the SAED patterns of the two samples can be served as a reference for the analysis of the SAED pattern of the 6-hr sample. Figure 2(a) shows the TEM image of the 6-h sample. Consistent with what has been observed in the SEM image, the blade-like crystal splits along its long edge.

Referring to Figure 2(b), the SAED pattern of the notch area can be indexed to the [210] zone axis of HAp as well as the [110] zone axis of OCP. Both the c axes of HAp and OCP in the 6-hr sample are parallel or anti-parallel with respect to the slits along the elongated side of the blade-like crystal. This alignment of the crystallographic c axes of OCP and HAp is an important structural constraint for the OCP to HAp transformation (vide infra).

C. XRD. As an independent approach to identify the crystalline phases of our samples, the XRD patterns were measured (Figure 3). Any reflections at 2θ = 4.9°, 10.8° and 13.1° can be considered as the characteristic peaks of OCP (JCPDS 44-0778), HAp (JCPDS 24-0033) and monetite (JCPDS 09-0080), respectively. For the 1.5-h sample, the absence of the reflections at 2θ = 10.8° and 13.1° indicates that the sample is pure OCP. For the 3-h sample, trace amount of monetite is present in addition to OCP. The crystalline phase of HAp becomes observable for the 4-h sample. For the samples with longer reaction time, the HAp crystalline phase becomes more prominent at the expense of OCP and monetite. Eventually, the 12-h sample is pure HAp. Note that the two characteristic reflections of brushite (CaHPO4⋅2H2O) at 2θ = 11.6° and 23.4° are not found in our samples (JCPDS 11-0293). The variation in the lattice parameters was analyzed by Rietvald analysis. As summarized in Table 2, the lattice parameters of the 3-h and 5-h samples are approximately the same but both the a and b axes of the OCP lattice have significant increase in the 4-h sample.

D. Solid-State NMR. Figure 4 shows the ³¹P MAS spectra measured for our sample series, together with the spectral assignment we made earlier.³² It is quite clear that the samples of reaction times from 1.5 h to 5 h contain mainly the OCP species. The crystallinity is rather poor for the 1.5-h sample because the corresponding signals have larger line widths than the 3-h sample. This observation is consistent with our SEM data, in which the crystals of the 1.5-h sample are found to be poorly faceted. Presumably, there are a lot of excess water molecules in the 1.5-h sample which cannot be accommodated in the OCP lattice. Judging from the NMR spectrum, the molecular structure of the 3-h sample is closest to that of pure OCP, in spite of the fact that trace amount of monetite is present in it. The ³¹P chemical shift data and the assignment of the 3-h sample are summarized in Table 3. As the reaction time proceeds to 6 h, a significant change in the signal pattern is observed, showing that the system has undergone a considerable change in the phosphorus environments. Note that the 6-h spectrum is not a superposition of the 3-h (OCP) and the 12-h (HAp) spectra. Therefore, re-precipitation is unlikely the predominant transformation mechanism. The structural transition is essentially completed after 12 h because the spectra of the 12-h and 96-h samples are identical. The spectrum of the 12-h sample shows a single peak positioned at 3.2 ppm and is readily assigned to the PO43- group of HAp.⁴⁹ This series of spectra demonstrate that the transformation of OCP to HAp can be effectively monitored by taking ³¹P as the probe nucleus.

31P{¹H} Heteronuclear Correlation (HETCOR). To obtain a better spectral resolution we measured the ³¹P{¹H} HETCOR spectra for the sample series. Figure 5 shows the HETCOR spectra of the 1.5-h, 3-h and 5-h samples. Consider the spectrum of the 1.5-h sample, the ³¹P peak at -0.2 ppm (P5 and P6) is correlated to the ¹H signals at 5.5 and 13.3 ppm, which have been assigned to the structural water and the acidic proton of the HPO42- ions.⁵⁰ Note that a relatively weak correlation peak can also be identified for the ¹H signal at 0.2 ppm and the P2 signal (3.3 ppm). This correlation peak is a well-known marker for apatite-like structures.34,35,40,50 For the spectrum of the 3-h sample, an additional set of cross peaks denoted by a rectangle is observed, which is due to the HPO42- group of monetite.^30,32,50 As the reaction time proceeds further, the corresponding HETCOR spectra show that the intensity of the apatite component increases at the

expense of the monetite and the OCP signals (see Figure S 1 of the Supporting Information).

Overall, our HETCOR data is in complete agreement with the XRD results.

31P{¹H} Lee-Goldburg Cross Polarization. Recently, it has been shown that the LG homonuclear decoupling technique can be combined with CP to achieve polarization transfer with efficient suppression of ¹H-¹H spin diffusion.^41,42 Therefore, it is possible to investigate the hydration state of the individual phosphorus species by measuring the LG-CPMAS spectra with variable contact times. The intensities of the four resolved ³¹P signals (P1, P2/P4, P3, P5/P6) were fitted by the following equation as a function of contact time (τ_CP) and relaxation time (T₁^H_ρ ):

( )

t I

{ (

t CP

) } (

t T^H

)

I = ₀ 1−exp − τ exp− ₁_ρ

Typical fitting of the raw data was shown in Figure S 2 of the Supporting Information. The parameters τ_CP and T₁^H_ρ obtained for our sample series were shown in Figure 6, which do not show any strong correlation in the non-linear least-squares fittings. Consider the data of the 1.5-h sample, the relative τ_CP and T₁^H_ρ values are consistent with the facts that (i) P5 and P6 are HPO42- species; (ii) P3 is hydrogen bonded to one of the HPO42- groups; (iii) the distance between P2 and its closest neighboring water molecule is 3.5 Å; (iv) P1 is rather isolated from all the water molecules (distance > 4.6 Å).²⁵ For the 3-h sample, the τ_CP and T₁^H_ρ values of the PO43- species increase considerably. Together with the fact that the ³¹P signal line widths are narrower for the 3-h sample, it can be surmised that the crystallinity of the 3-h sample improves when those excess water molecules are expelled from the structure. For the 4-h and 5-h samples, the τ_CP values of all the PO43- species decrease significantly and then increase again. An opposite trend was observed for the T₁^H_ρ data. This interesting variation of the τ_CP and T₁^H_ρ values of the PO43- species is possibly due to a change in the hydration level of the phosphate ions. As the pH of the reaction mixture increases continuously due to the decomposition of urea, the equilibrium of the following reaction shifts to the right:

HPO42- + OH^- = PO43- + H2O.

When the pH value reaches 5.01 at which we collect the 4-h sample, more water molecules will enter the hydration layer of the OCP structure, resulting in the formation of straight notches along the c-axis for the 4-h sample (Figure 1). Indeed, the Rietvald analysis of the XRD patterns show that both the a and b axes of the OCP unit cells increase considerably for the 4-h sample. Our interpretation is also in line with the ³¹P MAS spectrum of the 4-h sample, where the line widths of the P1 and P2/P4 signals are somewhat broadened due to an increase in structural disorder.

Consequently, the water molecules in the 4-h sample will cause a decrease in the τ_CP value because we have more water molecules surrounding the PO43- species. On the other hand, T₁^H_ρ is sensitive to molecular motions in the frequency range around the effective LG irradiation field (c.a. 61 kHz).⁵¹ Therefore, as more water molecules enter the OCP hydration layer, the more

frequent collision among the water molecules, which should be much faster than the inverse of 61 kHz, will cause an increase in T₁^H_ρ . As the pH of the reaction mixture increases further, the excessive water molecules in the hydration layer start to diffuse out of the OCP structure, resulting in an increase in τ_CP and a decrease in T₁^H_ρ for the 5-h sample. Accordingly, the cell dimensions of the 5-h sample become comparable to those of the 3-h sample (Table 2). Note that the variation in the CP dynamics of P3 is not as dramatic as those of P1, P2 and P4 because P3 is hydrogen bonded to the acidic proton of P6.²⁵

31P-³¹P Double Quantum NMR. When two or more nuclear spins are in close proximity, they become coupled through the homonuclear dipole-dipole interaction. The magnitude of such interaction is inversely proportional to the third power of the internuclear distance. The so-called DQ coherence is a concerted evolution of coupled spins. The two-dimensional ³¹P DQ spectrum of the 1.5-h sample is shown in Figure 7(a), where there are eight sets of auto- and cross-correlation peaks assigned to the OCP signals. Surprisingly, in the DQ spectra measured for the 3-h, 4-h and 5-h samples we do not observe any correlation peaks due to monetite (see Figure S 3 of the Supporting Information). Referring to Figure 7(a), by varying the DQ excitation and reconversion periods systematically, one can fit the intensities of the correlation peaks as a function of the excitation time based on the following equation⁴⁰

( )

{

}

I τ_exe = τ_exe² exp −τ_exe²

In the above equation the build up of the DQ signals is described by a parabolic function^52,53 and the decay of the DQ signals is approximated by a Gaussian function.⁵⁴ Figure 7(b) illustrates such a fit for the P3-P6 DQ signals of the 1.5-h sample, in which the signal intensities had been normalized with respect to the MAS signals measured under identical conditions (spinning frequency, saturation comb and relaxation delay).³³ In principle, the parameter A can be used to determine the van Vleck’s second moment of the coupled spins, whose magnitude depends on both the number of interacting spins and the internuclear distances.⁵⁵ However, the quantification of the second moment in the present study is not warranted due to the different efficacy of proton decoupling for different phosphorus species. Nevertheless, the variation of the parameter A should reflect the same variation in the second moment for a particular DQ signal, provided that the efficacy of the proton decoupling remains approximately the same. On the other hand, since the values of the parameter B are affected by both the ³¹P spin-spin relaxation times and the spatial arrangement of the interacting phosphorus species, it is difficult to interpret the data trend unequivocally.

Figure 8 summarizes the values of the parameter A extracted for the cross-correlation peaks of our sample series. As expected, the A values for the 1.5-h sample are attenuated significantly due to insufficient proton decoupling. For the 3-h sample, the following data trend is parallel to what we expected from the calculated van Vleck’s second moment:

3 2 P

AP ₋ > A_P₃₋_P₅_/_P₆ > A_P₂₋_P₅_/_P₆ > A_P₁₋_P₅_/_P₆ > A_P_{1 P}₋ ₃

(3.19) (1.84) (1.08) (0.46) (0.35)

where the bracketed data denote the corresponding second moments (× 10⁶ rad²/s²) calculated based on the X-ray structural data. As revealed in Figure 6, the efficacy of proton decoupling

should be very similar for the 3-h and the 5-h samples. Therefore it is legitimate to calculate the percentage change of their A values corresponding to the same DQ coherence and compare the results with what we expected from our model for the OCP transformation (vide infra).

E. Computer Assisted Lattice Matching. It has been well established that the apatitic layer of OCP is structurally very similar to HAp. Indeed, our TEM/ED results are consistent with the scenarios that the c axes of the OCP and HAp unit cells are parallel or anti-parallel to one another during the phase transformation. For the OCP to HAp transformation, we assume that the phosphorus sites of OCP will take the shortest pathways to migrate to the nearest phosphorus sites of HAp. We generate two unit-cell models, viz. the guest and the host. The guest model contains the Cartesian coordinates of 24 phosphorus atoms in four unit cells of HAp while the host model contains the coordinates of 96 phosphorus atoms in 2 × 2 × 2 unit cells of OCP.

Initially, the crystallographic c axes of both models are aligned in the same direction. The coordinates of the guest lattice are then mapped onto the host lattice rotationally and translationally. The rotation is about the c axis at steps of one degree and the translations are along three orthogonal axes at steps of 0.5 Å. The mean-square deviations (χ²) between the OCP phosphorus sites of the apatite layer and the corresponding nearest HAp sites are calculated for each matching step. For the best matching with minimum χ², the shortest distances between selected OCP sites are calculated after they have been mapped onto the corresponding HAp sites.

In other words, we label all the phosphorous atoms in the HAp lattice by the name tags of the six non-equivalent phosphorus sites in OCP and then calculate the corresponding distances of, say, P2-P3. Based on the distance information the van Vleck’s second moments arising from P2-P3 are calculated using the following formula:⁵⁵

(

⁺

) ∑

The ratio of the P2-P3 M2 values calculated for the matched HAP lattice and the OCP lattice are thus obtained. Similarly we obtained the ratios corresponding to the M2 values of P1-P3, P1-P5/P6 and so on. All the calculations were then repeated for opposite alignment of the crystallographic c axes of the guest and host models (see Table S1 of the Supporting Information).

Provided that the phosphorus sites of OCP will take the shortest pathways to migrate to the nearest phosphorus sites of HAp, the ratios of the experimental A values of P2-P3 measured for the 3-h and 5-h samples should be very similar to that calculated in our lattice matching model.

Figure 9 plots the calculated ratios versus the ratios of the experimental A values. Note that a perfect agreement between the calculated and experimental ratios is not expected because the OCP to HAp transformation is not yet completed for the 5-h sample. Overall, our DQ experimental data are more consistent with the scenario that the crystallographic c axes of OCP and HAp are in opposite direction during the transformation. In addition, the lattice matching results for the anti-parallel alignment of the c-axes show that during the structural transformation the b axis of OCP is parallel to the a or b axis of HAP, where the a and b axes of HAP are equivalent because of the hexagonal symmetry of the unit cells.

Discussion

Double-Quantum NMR in Multiple-Spin Systems. DQ NMR spectroscopy under magic angle spinning has been the major research area in the solid-state NMR community for many years. Since the pioneering work of Tycko,⁵⁶ numerous pulse sequences designed for DQ NMR have been reported in the literature.^57-60 Our previous work illustrates that the excitation of DQ coherence is inherently difficult in multiple-spin system due to the dephasing effect of other passive spins.³³ It has also been shown that distance measurement by DQ NMR spectroscopy in homonuclear spin system is practical only if the two-spin approximation holds.⁶¹ Nevertheless, here we have demonstrated that it remains possible to employ DQ NMR spectroscopy to monitor the change of the spatial arrangement of interacting spins, provided that an adequate structural model is constructed to interpret the variation of the DQ signal intensities. In this work, our computer assisted lattice matching provides such a model in which the structural constraint obtained by SAED measurements is incorporated. We note in passing that Levitt and co-workers have successfully employed solid-state ²⁹Si DQ dipolar recoupling NMR to help elucidate the crystal structures of siliceous zeolite model compounds by measuring distance-dependent dipolar interactions between naturally abundant ²⁹Si nuclei in the zeolite frameworks, where the two-spin approximation clearly holds for two interacting ²⁹Si nuclei.^62,63

OCP to HAp transition. In an early study by Eanes and Meyer, the nature of the phase changes occurring in spontaneously precipitated amorphous calcium phosphate (ACP) was studied under physiological condition.⁹ Based on the measured ion concentrations and Ca/P ratio, it was concluded that the ACP precipitate would first transform into an OCP-like phase which subsequently hydrolyzed into apatite. This result is consistent with the Ostwald-Lussac law of stages, which states that under conditions of sequential precipitation the initial phase formed is the one with the highest solubility followed by other crystalline phases in order of decreasing solubility.¹ For our in-vitro system, we also observe the co-precipitation of monetite at 100ºC. In the thermodynamic aspect, the co-precipitation of monetite is not unexpected because the solubility product of brushite, the hydrated form of monetite, is very similar to that of OCP at pH around 4.71 to 5.12.⁶⁴ The detection of co-precipitation of monetite by the HETCOR NMR technique is of great interest in the study of biomineralization because diffraction techniques are unlikely to distinguish between HAp, OCP or monetite when the crystallites are thinner than 10 nm as reported for bone.⁶⁵ Based on the similarity of the calcium phosphate chains present in both the OCP and monetite structures, it has been speculated the formation of intracrystalline mixture of OCP and monetite by direct precipitation or by hydrolysis of OCP.⁶⁵ From our NMR data, however, we have no direct evidence for the existence of such intracrystalline mixture. The absence of the monetite ³¹P signals in the DQ spectra of our 3-h, 4-h and 5-h samples could be explained by the argument that the amount of the monetite phase is too low to give any appreciable DQ signals.

Some years ago, Nelson and co-workers described the OCP to HAp transformation as a simple dehydration process.¹² Here, we could refine this description further for our in-vitro system as follows. The OCP crystals obtained at 1.5 h contain a lot of structural waters, rendering the crystallinity rather poor. The amorphous character of the crystals reveals that the formation of OCP crystals is preceded by the precipitation of ACP. When the pH of the reaction mixture is

lower than 4.71, those water molecules in excess will be eventually driven out of the lattice, resulting in an improvement of the crystallinity. As the pH increases to around 5, water molecules will reenter the OCP lattice, presumably through the hydration layer of the OCP structure. This reversal in water flow direction is accompanied by a significant lengthening of the crystallographic a and b axes, causing an expansion of the OCP lattice. The “crowded” water molecules in the hydration layer then provide a collisional mechanism for the relocation of the HPO42- groups (P5 and P6) as shown in Figure 10. In spite of the 2.1 % mismatch between the (100) crystal planes of OCP and HAp, the structural stress induced by the movement of P5 and P6 will cause the apatite layers in the blade-like OCP crystals splitted across the b axis. The HPO42- ions are subsequently deprotonated and the water molecules of the hydration layers are released to stabilize the structure. Those apatite layers serve as nucleation centers for further

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