Precursor Decomposition and Nucleation Kinetics during Platelike

College of Science, Technology and EnVironment, UniVersity of Western Sydney, Locked Bag 1797,. Penrith South DC 1797, Australia. ReceiVed: February 1...
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J. Phys. Chem. B 2005, 109, 17304-17310

Precursor Decomposition and Nucleation Kinetics during Platelike Apatite Synthesis Adriyan S. Milev,* Alan McCutcheon, G. S. Kamali Kannangara, Michael A. Wilson, and Thilanga. Y. Bandara College of Science, Technology and EnVironment, UniVersity of Western Sydney, Locked Bag 1797, Penrith South DC 1797, Australia ReceiVed: February 11, 2005; In Final Form: August 1, 2005

Self-organization of calcium and phosphorus precursors in solution containing acetic acid and ethylene glycol produces a nanosized lamellar acetate-phosphonate hybrid containing two acetate and one phosphonate components. The lamellar morphology of the hybrid precursor is responsible the formation of platelike apatite product after thermal treatment at or above 400 °C. However a preliminary preheating stage (300 °C, 24 h) is crucial in determining the morphology of the apatite. Activation energy measurements by nonisothermal thermogravimetric analysis show that decomposition of the hybrid precursor involves at least two steps. Among the three components, it appears that the calcium acetate bidentate chelate component is stable below or at 300 °C. However, the calcium phosphonate and calcium acetate monodentate components are decomposed at this temperature. Above 360 °C, nuclear magnetic resonance and infrared spectroscopic data reveal the decomposition of more stable calcium acetate bidentate chelate. It is evident that the bond rupture of the bidentate calcium acetate species in the precursor results in the start of crystalline apatite formation but the other components must be decomposed by heating prior to this critical step in order to produce platelike apatite.

1. Introduction Chemical and structural similarities between synthetic apatite [Ca10(PO4)6(OH)2] and biogenic bone material has led to its use as a biomaterial.1,2 To produce highly bioactive synthetic bonelike material it is essential to mimic all properties of the biogenic bone material. New bone forming processes by bone osteoblast cells are dependent not only on the chemical composition but also on the physical characteristics of the material. Thus, crystallite size, particle morphology, lattice substitutions, and lattice defects all contribute to the effective and efficient new bone formation (osteogenic) process.3,4 Recently, our research in this area has demonstrated a new method for production of synthetic bone material that mimics the platelike morphology, carbonate content, crystallite sizes, and microstrain of the bone mineral tissue.5-8 The method involves self-organization in solution containing acetic acid and ethylene glycol of a nanosized lamellar acetate-phosphonate hybrid.6,7 Evaporation of the solution at 130 °C for 48 h produces a white powder. This dried precursor has platelike morphology similar to that of biogenic apatite. Existing data show that platelike apatite is produced after heating of the dried precursor at temperatures above 500 °C for 2 h. During the process, it is necessary that the precursor is first subjected to heating at 300 °C for 24 h.5 If, however, the heating at 300 °C is omitted, the apatite can still be produced at higher temperatures of 600 °C and above but is produced with poor morphology. In this paper we have employed kinetics methods to investigate why the two-step heating process is necessary to preserve the precursor morphology en route to apatite. * Corresponding author. College of Science, Technology and Environment, University of Western Sydney, Building LZ, Parramatta Campus, Locked Bag 1797, Penrith South DC 1797, Australia, tel.: +61 2 9685 9936; fax: +61 2 9685 9915, E-mail: [email protected].

Decomposition reactions of solids are usually monitored under nonisothermal conditions in which a sample is heated at a constant heating rate. The apparent reaction kinetic parameters (activation energy, Arrhenius factor, and conversion function) can be evaluated from the mass loss or reaction heat obtained by thermogravimetry (TG) or differential scanning calorimetry (DSC) measurements. In the simplest case, the degree of decomposition is given by the conversion (1 - R), where R is the fraction of unreacted solid that can be calculated from a TG curve. The rate of single-step decomposition reactions is then expressed by eq 1.

β

dR ∆E ) A exp f(R) dT RT

(

)

(1)

where β ) dT/dt is the heating rate, dR/dT is the temperature dependence of the conversion R, T is temperature (K), A is Arrhenius factor (s-1), ∆E is apparent activation energy (J/mol), f(R) is empirical differential conversion function, and R is the gas constant (J/molK). The f(R) functions are derived on the basis of various models of the reaction interface movement, and the corresponding mathematical expressions are well-known in the literature.9 The kinetic analysis involves curve fitting based on ∆E, A values and selection of the f(R) function that gives best approximation of experimental data. However, under nonisothermal conditions both T and R change simultaneously, and the curve fitting to data obtained from one heating-run experiment usually fails to achieve clean separation between the kinetic parameters.10 Another more successful method of analysis of the decomposition of solids is the multivariate (multicurve) nonlinear regression (NLR) method.11-13 The determination of the kinetic parameters relies on iterative calculations of minimum sum of

10.1021/jp0507445 CCC: $30.25 © 2005 American Chemical Society Published on Web 08/20/2005

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least squares (LSQ) between the measured data points (Yexp) by DSC or TG runs and curve fitting based on computed data points (Ycalc) (eq 2). n

LSQ )

s

∑ ∑(Yexp,j,i - Ycalc,j,i)2 ) min j)1 i)1

(2)

where n is the number of heating runs, s is the number of data points of the respective run, Ycalc is calculated by numerical solution of a system of differential equations. Because the determination of the regression value Ycalc is an iterative procedure, the NLR method requires initial estimates of the activation energy and the Arrhenius factor produced by other methods.14 Such initial values can be obtained by isoconversion methods, which are based on eq 1 but combine at least three nonisothermal measurements to derive ∆E and A estimates.15-18 Multivariate nonlinear regression kinetic analysis methods based on four thermogravimetric measurements have been used here to study the decomposition kinetics of the acetate and phosphonate components of the hybrid precursor to platelike apatite. Chemical transformations in the apatite precursor have been followed by spectroscopic (IR, Raman, NMR) methods, and support for the proposed reaction mechanisms is obtained by X-ray diffraction. 2. Experimental Details Sample Preparation. The method differs slightly from that published elsewhere.6 Calcium acetate half-hydrate, Ca(CH3COO)2 0.5H2O (Aldrich > 99% purity), and dimethyl hydrogen phosphonate, H(O)P(CH3O)2 (Aldrich, > 98% purity), were used as reactants. The dried calcium acetate half-hydrate (5.9 × 10-3 mol) was dissolved in a mixed solvent containing 5.00 g ethylene glycol (Fluka, > 99.5% purity) and 4.80 g acetic acid (Sigma, > 99.7% purity) in 1:1 molar ratio. The mixture was stirred for 1-2 h at ambient temperature in order to dissolve the calcium acetate. Then a stoichiometric amount (3.4 × 10-3 mol) of dimethyl hydrogen phosphonate was added so the Ca/P ratio in the product would be close to 1.67. The mixture containing all the components was stirred for 30 min, and then heated at 70 °C for 48 h in a closed vial. Powders were prepared from the solution after drying at 130 °C for 48 h in air in a Petri dish. The powder produced at 130 °C was further isothermally heated at 200, 250, 300, and 400 °C for 24 h in air to produce samples for spectroscopic characterization. Only samples produced after drying at 130 °C for 48 h and then heated at 300 °C for 24 h were used for the kinetic study. Infrared (IR) and Nuclear Magnetic Resonance (NMR) Spectroscopy. The IR spectra were recorded on a PerkinElmer Spectrum One spectrometer (≈1 mg sample in 150-200 mg KBr, 128 scans, 2 cm-1 resolution). The powders were also analyzed by solid-state magic angle spinning (MAS) cross polarization (CP) 13C and 31P NMR spectroscopy. The spectra were acquired on Bruker DRX200 solid-state spectrometer using 4 mm zirconia rotor. The rotor was spun at 5 kHz spinning rate, 64 scans with recycle delay 2 s for phosphorus and at 5 kHz, 4096 scans with 2 s recycle delay for carbon. The high power pulse widths and contact times were 3.0 µs, 1.5 ms for carbon and 2.9 µs, 0.3 ms for phosphorus. The phosphorus chemical shifts were referenced to external 85% phosphoric acid while carbon chemical shifts were relative to tetramethylsilane (TMS) using adamantane as an external reference (the CH2 peak of adamantane was calibrated to be 38.3 ppm downfield from the 0.00 ppm TMS peak).

Imaging and Phase Characterization. A Philips Biofilter 120 operating at 120 kV transmission electron microscope (TEM) was used for imaging. The specimens were sonicated in ethanol in order to separate aggregates. A drop of the suspension was transferred onto lacey carbon foils supported on copper grids for examination. Diffraction patterns were collected on a Philips PW1825/20 diffractometer (CuKR, 40 kV, 30 mA, 2θ 20-50 deg, 4 s, 0.02° step). Kinetic Analysis by TG-DTA. The kinetic analysis involved the following steps: (i) mass-loss (TG) data collection under four different heating rates, (ii) computation of (∆E) and Arrhenius factor (logA) parameters according to the OzawaFlynn-Wall (OFW)17,19 isoconversion method in the temperature interval 300-600 °C, (iii) differential conversion function f(R) determination by NLR using starting values of ∆E and logA calculated according to OFW, (iv) determining of mechanism from the above data. Step (i). The thermal behavior of the powders obtained at 130 and 300 °C was monitored by simultaneous DTA/TG measurements at four different heating rates by a STD 2960 simultaneous thermal analyzer (TA Instruments). Samples weighing between 10 and 14 mg were placed in open platinum pans and heated in a flowing atmosphere (40 mL/min) of purified dry air. The instrument was programmed to heat the sample from room temperature at constant heating rates of 1.2, 2.5, 5.0, and 10.0 deg/min. After an initial period of nonlinear heating ( Fcrit, the reaction model was improved by adding an extra step. 3. Results and Discussion Isothermal Decomposition. Spectroscopic Analysis. Most of the metal phosphonate and some carboxylic acid salts form twodimensional sheets of metal ions joined to the phosphonate or carboxylate groups in such a way that the organic moieties are arranged above and below the plane of the inorganic layer (Figure 1 A).25-27 The inorganic layers stack in the third dimension so that the organic moieties from the adjacent layers are weakly bonded to each other and can relatively easily be separated into nanometer thin sheets. In our current research, the ability of the phosphonate and the carboxylate salts to form layered compounds (Figure 1 B) has been exploited in order to produce platelike apatite with morphology similar to that of biogenic apatite.7,8 The principal challenge was the preparation of a mixed carboxylate-phosphonate precursor since there is no reported single-phase calcium phosphonate salt with the apatite Ca/P ratio of 1.67. Thus, the precursor was constituted by a Ca-phosphonate component with Ca/P ratio of 1:1 and two Ca-acetate components that provide additional calcium so that the overall Ca/P ratio is near 1.67, characteristic for the apatite (structure 1 A-C).7

Figure 1. (A) Schematic representation of the layered structure typical for metal phosphonate salts. Adapted from ref. 27. (B) TEM image of several layers of mixed acetate-phosphonate apatite precursor produced at 130 °C.

SCHEME 1: (A) Acetyl 2-Hydroxyethyl Phosphonate Calcium Salt, (B) Monodentate Acetate, (C) Bidentate Acetate Complexes

The thermal decomposition that is required to produce apatite from such a hybrid precursor would be rather complex because the acetate and phosphonate components may have different decomposition pathways upon heating. Thus, variations in the composition of material produced at 130 °C and subsequent isothermal heating of the individual samples at 200, 250, 300, and 400 °C for 24 h in air have been analyzed by NMR and FTIR and the spectral data are shown in Figures 2 and 3. The 31P CP/MAS NMR spectrum of powders prepared at 200 °C showed two distinct peaks at 8.6, 7.0 typical for the phosphonates and two weaker peaks at 1.0 and -1.9 ppm that were assigned to phosphate impurities (Figure 2 A). Upon heating

Figure 2. Solid-state CP/MAS NMR spectra of apatite precursor heated for 24 h at the respective temperature. (A) Phosphorus-31. The spectra of samples prepared at 300 and 400 °C are magnified three times compared with these at lower temperatures. Asterisks mark the sidebands. (B) Carbon-13 CP/MAS spectra. The 13C spectrum of the sample produced at 400 °C was obtained after the accumulation of 25 000 scans.

Apatite Precursor Decomposition

Figure 3. Infrared spectra of hydroxyapatite precursor isothermally heated at (A) 200 °C, (B) 250 °C, (C) 300 °C, and (D) 400 °C for 24 h.

to 250 °C the single resonance at 7.0 ppm became split into two peaks at 7.0 and 6.5 ppm, and a new shoulder at about 2.7 ppm appeared. The samples heated at 300 °C and 400 °C produced only one peak at 3.0 ppm with about three times lower intensity compared with the samples prepared at lower temperatures. The decreased intensity was because of the reduced number of protonated species, so fewer protons were available to transfer polarization to the 31P nuclei during cross polarization. The peak position and the peak line broadening of more than 500 Hz were indicative of an amorphous calcium phosphate with chemical shift quite close to the chemical shift of stoichiometric apatite (2.81 ( 0.2 ppm) was produced.28,29 Carbon-13 CP/MAS NMR spectra of powders heated at 200 and 250 °C indicated the presence of acetyl methyl (23-29 ppm), methylene (60-66 ppm), and carbonyl (175-186 ppm) chemical shifts (Figure 2 B). Previous work showed that the two methylene carbon chemical shifts can be attributed to the P-O-CH2-CH2- moiety, whereas the methyl and carbonyl carbons can be attributed to acetate moieties.6,7 The existence of three carbonyl chemical shifts indicated three different modes of carbonyl oxygen-calcium coordination. Sample heated at 300 °C had no methylene carbons, whereas the acetyl methyl and carbonyl chemical shifts were weakened. A new faint resonance upfield the carbonyl chemical shift at about 168.9 ppm emerged. At 400 °C no organic carbons were present, whereas the new resonance was stronger. This resonance was assigned to carbonate ions incorporated in amorphous phosphate.30 The IR spectra did not reveal significant differences between samples heated at 200 and 250 °C in the P-O-C (1200-900 cm-1) and the P-H (2460-2360 cm-1) phosphonate stretching vibration regions (Figure 3 A and B).7 However, the intensity of the stretches of the phosphonate phosphoryl group coordinated to calcium in the wavenumbers region 1240-1220 cm-1 decreased after heating at 250 °C. At 300 and 400 °C, the absence of P-O-C, phosphonate PdO and P-H stretching

J. Phys. Chem. B, Vol. 109, No. 36, 2005 17307 vibrations indicated that all the phosphonate groups have been ionized. The two strong vibrations at 1605 and 1564 cm-1 and the shoulder at about 1573 cm-1 were assigned to antisymmetric calcium-carboxylic group stretches (Figure 3 A and B). Respective symmetric stretches were assigned to the bands at 1475, 1426, cm-1 and at 1356 cm-1. The assignment of the symmetric stretches at 1356 cm-1 was also supported by FTRaman spectra (not shown here). Upon heating to 300 °C the resonances at 1570 and 1561 cm-1 (Figure 3 B) merged in a less intense singlet at 1568 cm-1 (Figure 3 C). A new band at 1653 cm-1 was assigned to deformation mode of water molecules produced probably by the oxidation of the organic moieties of the precursor. After heating at 400 °C, the resonance at 1568 cm-1 further weakened and a new resonance at 1491 cm-1 appeared (Figure 3 D). The bands at 1491 and 1426 cm-1 were previously attributed to carbonate groups structured in amorphous calcium phosphate phase.31 It seems that the stretches at 1426 cm-1 below 250 °C and above 300 °C correspond to different chemical species. At lower temperatures those stretches most probably originated from the symmetric vibrations of acetate groups, whereas at and above 300 °C from oxidized acetate group incorporated in the amorphous phosphate phase as carbonate. This corresponds well with the appearance of 168.9 ppm peak in the 13C CP/MAS NMR spectral data at 300 °C. Coordination of a metal ion to a carboxylic group causes red frequency shifts (from > 1700 cm-1 to about 1610-1300 cm-1) and band splitting into antisymmetric (νaCOO-) and symmetric (νsCOO-) stretches because of the lowering of group symmetry.32,33 Based on the frequency shifts and the splitting between the antisymmetrical and symmetrical carboxylate stretches (∆ ) νaCOO- - νsCOO-), three coordination modes have been recognized: (i) monodentate where one of the carboxylic group oxygen atoms is bonded to a metal ion, (ii) bidentate where both oxygen atoms are boded to a same metal ion, and (iii) bridging mode where each of the oxygen atoms is bonded to a different metal ion. Recent molecular orbital studies and experimental data have shown the following trend for the band splitting exists: ∆νa-s monodentate, (200-300 cm-1) > ∆νa-s bridging (140 - 160 cm-1) > ∆νa-s bidentate (80-120 cm-1).32-34 Here the carboxylate stretches in the wavenumber region of 1610-1300 cm-1 were used to monitor the effect of the isothermal heating on the calcium coordination modes.7 At 200 and 250 °C the resonances 1607 and 1356 cm-1 (∆νa-s of 261 cm-1) indicated that some quantity of the mixed precursor was monodentate type given by structure 1B. The other two coordination modes were most probably bidentate type (structures 1A and 1C),7 but definitive assignment of the symmetric stretches was difficult since deformational and scissoring vibration modes of the acetate methyl groups (C-H3) could be present in the same spectral region (1480-1350 cm-1). At 300 °C the broad 13C NMR chemical shift at 182.4 ppm and the antisymmetric and symmetric carboxylate stretches at 1568 and at 1453 cm-1 (∆νa-s of 115 cm-1) suggested that only one bidentate calcium-acetate structure was present (structure 1C). In summary, the spectroscopic data of the samples decomposed under isothermal conditions showed that the apatite precursor consisted of three components at temperatures below 250 °C; a calcium phosphonate, and two calcium acetate complexes. The calcium phosphonate and monodentate calcium acetate components were decomposed to form amorphous calcium phosphate in the temperature interval 250-300 °C, whereas the bidentate calcium acetate was more stable. Nonisothermal Decomposition. Figure 4 shows simultaneous TG-DTA traces of samples produced at 130 and 300 °C

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Milev et al.

Figure 4. DTA-TG traces (heating rate 1.2 deg/min) showing the thermal effects of apatite precursor. (A) thermo-oxidative degradation of HAp precursor dried at 130 °C. (B) Precursor that was heated at 300 °C prior to the thermal analysis.

Figure 5. Ozawa-Flynn-Wall isoconversion kinetic analysis of apatite precursor isothermally heated at 300 °C for 24 h in air. (A) Dependence of logarithm heating rate vs the reciprocal temperature. (B) Estimation of the activation energy and Arrhenius factor vs the fractional mass loss.

measured with a heating rate of 1.2 °C/min. The application of higher heating rates displayed strong overlapping of the exothermic peaks, in particular, at 5.0 and 10.0 deg/min. Neither sample showed thermal effects below 200 °C, except for insignificant weight loss related to evaporation of absorbed moisture. The sample produced at 130 °C in the temperature interval 200-600 °C demonstrated three partly overlapped exothermic peaks at 310, 378, and 396 °C, with total mass loss of about 28 wt %. The correlation between the thermal and the spectroscopic data revealed that the preliminary heating at 300 °C for 24 h, decomposed the structures A and B shown in Scheme 1. The sample that was isothermally decomposed at 300 °C for 24 h upon subsequent heating produced a single exothermic peak at 362 °C that was associated with 6% mass loss (Figure 4 B). The mass loss continued at a much lower rate above 400 °C, so the total weight loss was 7.5 wt % at 500 °C. At this stage, the crystallization of apatite containing carbonate begins. OFW Analysis. Estimation of the ActiVation Energy and the Arrhenius Factor. The mass-loss pattern of the precursor produced at 130 °C showed that decomposition of structure 1 happened in a relatively narrow temperature interval and separation of the individual mass-loss effects could not be achieved. For that reason, kinetic analysis to the precursor produced at 130 °C has not been carried out. Only samples that were preheated at 300 °C for 24 h were characterized by the isoconversion and nonliner regression methods. The thermal measurements according to OFW method are to be transformed to degree of conversion (R), which in the case of thermogravimetric (TG) data has the meaning of fractional mass-loss. The fractional mass-loss variable (Ri) was calculated according eq 3 and assumed value of 0 at 300 °C and 1 at 600 °C. According

to the DTA-TG and the spectroscopic measurements, in those temperature limits the decomposition temperature of structure 1C and the apatite formation took place for all heating rates. Figure 5 A shows a plot of the logarithm of the heating rate (logβi) vs the reciprocal temperature (1000/T) for a series of fixed values of Ri with a step of 0.01, which produced a respective series of straight (isoconversion) lines. For clarity, only several isoconversion lines are presented. It can be seen that the slope of the isoconversion lines varies with the reciprocal temperature, which indicates that the apparent activation energy is not constant. The dependence of the activation energy calculated from the slopes of the isoconversion lines as a function of the fractional mass loss (i.e., ∆E ) ∆E(Ri)) is plotted in Figure 5B. Two distinct regions of ∆E ) ∆E(Ri) can be observed. In the first region (0.02 < Ri < 0.7), the apparent activation energy (∼160 kJ/mol) does not significantly depend on the fractional mass loss. Above fractional mass loss of 0.7 the value of the activation energy rapidly increases, and near the end of the reaction process (Ri ∼ 0.9) it is about 270 kJ/ mol. This dependence of the activation energy is an indication that the overall reaction contains at least two steps. The logA estimates follow similar dependence on the fractional mass loss (Figure 5 B). Determination of the Conversion Functions [f (r1), f(r2)]. As noted above, the kinetic modeling by multivariate NLR was carried out using software NETZSCH Thermokinetics-2. Because it is an iterative procedure, NLR method requires initial estimates of the activation energy and Arrhenius factors as input data, which were obtained from OFW method. The following values were selected; for R1 ) 0.2, ∆E1 ) 157.6 kJ/mol, and logA1 ) 9.5 s-1) and for R2 ) 0.9, ∆E2 ) 267.7 kJ/mol and logA2 ) 15.2 s-1). Initially, regression analysis was employed

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TABLE 2: Kinetic Parameters Best Describing the Thermal Behavior of the Apatite Precursor Preheated at 300 °C for 24 h upon Heating parameter

value

description

Cn

Cn

Step 1: A f B 0.02 < R < 0.7561 log (A1) (s-1) ∆E1 (kJ/mol) n1 log (Kcat)

9.5 ( 0.08 155.9 ( 0.8 2.32 ( 0.08 0.61

Arrhenius factor Activation energy reaction order Autocatalysis parameter

An

log (A2) (s-1) ∆E2 (kJ/mol) n2 Foll. React.1

Step 2: Bf C 0.7561 < R < 0.98 16.8 ( 0.97 284.9 ( 7.5 n)0.42 ( 0.02 0.7561

step (codes Fn, Bn, R3) were also tested but they gave poorer fits and were excluded by the F-test (Table 1). Therefore the thermal effects of the precursor preheated at 300 °C for 24 h in the temperature interval 300-600 °C could be best modeled

Arrhenius factor Activation energy reaction order share of the step 1 in the total mass-loss

mass difference of the heating scans (j) for the temperature interval 300-600 °C (wt %) mass diff. scan j ) 1 (wt %) -7.4407 at 1.2 deg/min mass diff. scan j ) 2 (wt %) -7.5281 at 2.5 deg/min mass diff. scan j ) 3 (wt %) -7.5582 at 5.0 deg/min mass diff. scan j ) 4 (wt %) -7.1738 at 10.0 deg/min

to model the one-step reaction mechanism by fitting to the four TG curves various differential conversion functions f(R) and the kinetic parameters corresponding to R1 ) 0.2. The fitting showed that nth order autocatalytically activated reaction (code Cn) produced best statistical fit to all TG curves (corr. coeff. 0.9971). For comparison, a list of differential conversion functions f(R) that produced satisfactory fits is listed in Table 1. Modeling of a reaction mechanism consisting of two consecutive steps described by the two sets of kinetic parameters given above, and with f (R1) of autocatalysis (Cn) and with f (R2) of nth order nucleation (code An) further improved the fit quality (corr. coeff. > 0.9998) and significantly decreased the F-test value Fexp < Fcrit. A hypothesis that the first and the second steps might be parallel was tested, but Fexp > Fcrit, though the fit quality was satisfactory. Combinations of two consecutive elementary steps described by other f(R2) functions in the second

An

by two successive steps AfBfC (Table 2). Differential eq 5 illustrates the proposed two-consecutive-step reaction scheme for the formation of component C.

( ) ( )

∆E1 dA ) - A1 exp C dt RTj,i n

∆E2 dB dA )) - A2 exp An dt dt RTj,i C)1-A-B

(5)

,where dA/dt and dB/dt are rate of formation of the components B and C as function of time, logA1, logA2, ∆E1, ∆E2 are the Arrhenius factors and activation energies for the decomposition and nucleation steps, Cn and An are the mathematical expressions of the respective differential conversion functions (Table 2). The reaction model (Ycalcj,i eq 2) is then the solution for a system of the differential calculations 5, taking into account the balance equation for mass-loss data (eq 6).

Ycalcj,i ) Ycalcj,0 + MassDiffj[FollReact1(1 - A) + (1 - FollReact1)C] (6) where FollReact1 is the share of the first step in the total mass loss, the share of the second step is then (1 - FollReact1), MassDiffj is the total mass loss of scan j (Table 2). The measured TG curves (Yexpj,i) and the calculated (Ycalc2 NLR fits are shown in Figure 6 A. It can be seen that two consecutive step reaction mechanism provided very good fit to the experimental data. The remaining residual deviations between the experimental and the calculation curves were less than 0.2% within the range of the experimental errors. Optimization of decomposition conditions and apatite formation. Based on the two-step kinetic model given by eqs

Figure 6. (A) Fits (solid lines) by NLR to the four TG measurements (symbols), simulated with reaction type Cn followed by type An for the heating rates 1, 2.5, 5, and 10 K/min. (B-D) Rate of the structure 1C decomposition and apatite formation based on the two-step model given by eqs 5 and 6, at 360 °C, 400 °C, and 450 °C.

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Figure 7. XRD patterns of apatite produced from heated at 300 °C material followed by heating at 360 °C for 4 h and firing at (A) 450 °C for 12 h, (B) Same as A but fired at 400 °C for 14 days instead of 450 °C for 12 h. (C) 130 °C followed by firing at 450 °C 12 h without the intermediate heating at 300 and 360 °C. Y-axis is equal for all XRD traces.

5 and 6 and the refined kinetic parameters by NLR analysis (Table 2), the decomposition of component A (assigned to structure 1C) and rate of component C development (apatite product) could be predicted under isothermal conditions at different temperatures. The calculations by Thermokinetics-2 software indicated that after 4 h at 360 °C, structure 1C should be almost decomposed (Figure 6B). However, the rate of apatite phase development would be very low. Similarly, at 400 °C the predictions showed that apatite could be produced, but it was not practical because more than 10 days heating was required (Figure 6C) whereas at 450 °C heating time of 10 h would be sufficient (Figure 6 D). The kinetic model also indicated that regardless of the temperature when the amount of the intermediate component B reaches about 80% it would begin to be incorporated into the apatite product (C). We consider that the intermediate component B is CaO, though there is no evidence for separate phase formation. That phase might be nanocrystalline being completely incorporated into the apatite structure during apatite phase development. Testing of the Reaction Model. The predictions of the kinetic model were verified by X-ray analysis (Figure 7 A and B). Precursor samples were heated at 360 °C for 4 h followed by firing at either 400 °C for 14 days or 450 °C for 12 h. Although relatively broad, all the peaks corresponded to typical apatite XRD pattern (JCPDS standard, File Card No. 9-432). Therefore, the kinetic model given by eqs 5 and 6 proved to be valid at least for the tested temperatures and times. For comparison, X-ray pattern of material produced from precursor dried at 130 °C then heated at 450 °C for 12 h without the intermediate heating at 300 and 360 °C is shown in Figure 7C. Clearly the product is not crystalline apatite. This is strong evidence that the apatite nucleation is kinetically controlled by the bond rupture of the structure 1C. It is possible that that the stepwise heating at 300 and 360 °C, where the thermo-oxidation of structures 1A-C take place at relatively slower rate prevents fast oxidation of the organics of the precursor. If all three structures are decomposed simultaneously as result of fast heating to any temperature above 360 °C, the strong exothermic decomposition reactions can destroy the desirable platelike morphology of the precursor. 4. Conclusions 1. Reaction kinetic parameters determined by nonisothermal thermogravimetric analysis show that the decomposition of a

Milev et al. nanosized lamellar acetate-phosphonate hybrid, which can produce platelike apatite, involves least two steps. The activation energy of apatite nucleation calculated by the isoconversion and regression analysis is 268 and 285 kJ/mol respectively. 2. The calcium acetate bidentate chelate component of the nanosized lamellar acetate-phosphonate hybrid is stable below or at 300 °C, but the calcium phosphonate and calcium acetate monodentate components are decomposed at this temperature. Above 360 °C the decomposition of more stable calcium acetate bidentate chelate takes place. Bond rupture of the bidentate calcium acetate species in the hybrid results in the start of crystalline apatite formation but the other components of the hybrid must be decomposed by heating prior to this critical step for particle morphology to be preserved in the apatite. Acknowledgment. This work was produced as part of the activities of the ARC Centre for Functional Nanomaterials funded by the Australian Research Council under the ARC Centres of Excellence Program and UWS internal grant # 80548. The authors would like to thank to NETZSCH-Gera¨tebau, which kindly provided the NLR Thermikinetics-2 software. References and Notes (1) Brown, W. Clin. Orthop. 1966, 44, 205. (2) Brown, W.; Schroeder, L.; Ferris, J. J. Phys. Chem. 1979, 83, 1385. (3) Elliott, J. Structure and chemistry of the apatites and other calcium orthophosphates; Elsevier: London, 1994. (4) Shwartz, Z.; Lohmann, C.; Oefinger, J.; Bonewald, L.; Dean, D.; Boyan B. AdV. Dent. Res. 1999, 13, 38. (5) Milev, A.; Kannangara, G. S. K.; Ben-Nissan, B. Mater. Lett. 2003, 57, 1960. (6) Milev, A.; Kannangara, G. S. K.; Ben-Nissan, B.; Wilson, M. J. Phys. Chem. B 2004, 108, 5516. (7) Milev, A.; Kannangara, G. S. K.; Wilson, M. Langmuir 2004, 20, 1888. (8) Milev, A.; Kannangara, G. S. K.; Wilson, M. J. Phys. Chem. B 2004, 108, 13015. (9) Chemical Kinetics of Solids; Schmalzried, H., Ed.; VCH: Weinheim, 1995. (10) Vyazovkin, S. Thermochim. Acta 2000, 355, 155. (11) Opfermann, J. J. Therm. Anal. Calorim. 2000, 60, 641. (12) Opfermann, J.; Kaisersberger, E.; Flammersheim, H. Thermochim. Acta 2002, 391, 119. (13) Vyazovkin, S.; Wight, C. A. J. Phys. Chem. A 1997, 101, 8279. (14) Flammersheim, H.-J.; Opfermann, J. R. Thermochim. Acta 2002, 388, 389. (15) Ozawa, T. Thermochim. Acta 1986, 100, 109. (16) Ozawa, T. Thermochim. Acta 1992, 203, 159. (17) Flynn J.; Wall A. J. Res. Nat. Bur. Stand. 1966, 70A, 487. (18) Flynn J.; Wall L. Polym. Lett. 1966, 4, 232. (19) Ozawa, T. Bull. Chem. Soc. Jpn. 1965, 38, 1881. (20) Doyle, C. J. Appl. Polymer Sci. 1962, 16, 639. (21) Doyle, C. Nature 1965, 207, 290. (22) Galwey, A.; Brown, M. Handbook of Thermal Analysis and Calorimetry; Elsevier: York-Oxford-Shannon-Singapore-Tokyo, 1998. (23) NETZSCH-Gera¨tebau, G. NETZSCH Thermokinetics-2; 2004.05 ed. Selb, Germany, 2004. (24) Roduit, B.; Maciejewski, M.; Baiker, A. Thermochim. Acta 1996, 282-283, 101. (25) Clearfield, A. Prog. Inorg. Chem. 1998, 47, 371. (26) Mao, J.; Clearfield, A. Inorg. Chem. 2002, 41, 2319. (27) Seip, C.; Granroth, G.; Meisel, M.; Talham, D. J. Am. Chem. Soc. 1997, 119, 7084. (28) Rothwell, W.; Waugh, J.; Yesinowski, J. J. Am. Chem. Soc. 1980, 102, 2637. (29) Belton, P.; Harris, R.; Wilkes, P. J. Phys. Chem. Solids 1988, 49, 21. (30) Beshah, K.; Rey, C.; Glimcher, M.; Schimizu, M.; Griffin, R. J. Solid State Chem. 1990, 84, 71. (31) Termine, J.; Lundy, D. Calcif. Tissue Res. 1973, 13, 73. (32) Deacon, G.; Philips, R. Coord. Chem. ReV. 1980, 33, 227. (33) Tackett, J. Appl. Spectroscopy 1989, 43, 483. (34) Nara, M.; Tori, H.; Tasumi, M. J. Phys. Chem. 1996, 100, 19812.