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Effect of Carbonate Content and Crystallinity on the Metastable Equilibrium Solubility Behavior of Carbonated Apatites
JOURNAL OF COLLOID AND INTERFACE SCIENCE ARTICLE NO.
179, 608–617 (1996)
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Effect of Carbonate Content and Crystallinity on the Metastable Equilibrium Solubility Behavior of Carbonated Apatites 1 ARIF A. BAIG, JEFFREY L. FOX, 2 JER HSU, ZEREN WANG, MAKOTO OTSUK A,* WILLIAM I. HIGUCHI, AND RACQUEL Z. LEGEROS† Department of Pharmaceutics and Pharmaceutical Chemistry, University of Utah, Salt Lake City, Utah 84112; *Kobe Pharmaceutical University, Kobe, Japan; and †D. B. Kriser Dental Center, College of Dentistry, New York University, New York, New York 10010 Received August 22, 1995; accepted October 31, 1995
The purpose of this investigation was to assess the applicability of the metastable equilibrium solubility (MES) concept, previously developed in our laboratory, over wide ranges of two independent variables, carbonate content and crystallinity, and also to examine the influences of these variables on the MES behavior of carbonated apatites (CAPs). The CAP samples were prepared by dicalcium phosphate dihydrate (DCPD) hydrolysis for 48 h in NaHCO3-containing media at 95, 70, and 507C. This method of preparation gave CAP samples with varying carbonate contents and crystallinities. A previously developed technique with slight modification was used to determine the MES distribution for each of the CAP samples. The equilibration solutions were prepared both with and without extraction of fluoride with hydroxyapatite (HAP). From X-ray diffraction, the full width at half-maximum (FWHM) of the 002 reflection was used as a measure of crystallinity. The findings of this study showed that each of these preparations possessed an MES distribution and therefore provided further support that the MES distribution is a common phenomenon describing the dissolution behavior of CAPs, regardless of their carbonate content and crystallinities. The crystallinities of the CAPs decreased and the MES values increased with increasing carbonate content and decreasing temperature of synthesis. A plot of the mean MES value against CAP crystallinity revealed that the mean MES was a single-valued function of crystallinity; i.e., when crystallinity was taken into account, there was no additional effect of carbonate on the MES. When fluoride was not extracted from the equilibration solutions, the MES shifted to lower values. The concept of MES distribution and its dependence on the crystallinity of CAP may provide insight into the mechanism of dissolution of biological apatites, which may be considered imperfect crystalline substances. q 1996 Academic Press, Inc. Key Words: apatites; crystallinity; X-ray diffraction; solubility. INTRODUCTION
Carbonated apatite (CAP), a prototype of the mineral component of human dental enamel, has been studied exten1 This study was supported by NIDR Research Grants DE-06569 and DE-07223. 2 To whom correspondence should be addressed.
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0021-9797/96 $18.00 Copyright q 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.
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sively because of the likely importance of the incorporated carbonate ion in the dental caries process. The carbonate content of human dental enamel is in the range of 2 to 4% by weight (1). The presence of carbonate as the major impurity anion has been found to decrease the stability of the apatite structure, increase its solubility, and thereby render it more susceptible to acid attack (2–7). The effects of carbonate substitution in apatites are manifested as changes in the lattice parameters, decreases in crystal size, increases in crystal strain and disorder, and changes in crystal morphologies (2, 5, 6, 8–12). The properties of carbonated apatites are also influenced by the conditions under which the synthesis is carried out. Numerous studies (5, 6, 10) have shown that carbonated apatites synthesized at different temperatures and pH exhibit different physicochemical properties, such as degree of crystallinity and dissolution characteristics. The variability in the properties of CAP due to either the incorporation of impurity ions during synthesis or the conditions of synthesis itself may be related to the imperfections in the crystalline structure of the material. These imperfections may result in a metastable substance with variable solubility properties. Recent studies by Hsu et al. (13) have shown that CAPs synthesized by the hydrolysis of anhydrous dicalcium phosphate (DCP) and human dental enamel exhibit metastable equilibrium solubility (MES) behavior. Although the MES phenomenon had previously been noted by Brown (14) in dissolution studies involving human dental enamel, there had been no attempts until recently (13) to quantitatively describe the MES concept. The results of the experiments reported by Hsu et al. (13) clearly show that the apparent solubility behavior of CAP is consistent with the MES phenomenon, and that the MES shifts to higher solubility values with an increase in the carbonate content. The purpose of this study was to assess the applicability of the MES concept over wide ranges of two of the independent variables. The previous work of Hsu et al. (13) involved CAP preparations synthesized at a single temperature (957C) and at two carbonate levels. In the present research CAPs
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FIG. 1. X-ray diffraction patterns of CAP synthesized at 957C (A), 707C (B), and 507C (C), with three different carbonate contents at each temperature. The values on the left-hand side correspond to the weight percentage carbonate.
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TABLE 1 Chemical Compositon and FWHM of Carbonated Apatite Samples Synthesized at 95, 70, and 507C with Different Carbonate Contents Temperature (7C)
CO3a (wt%)
Cab (wt%)
PO4b (wt%)
Ca/P (M)
002 Peak position
95 95 95 70 70 70 50 50 50
1.0 3.9 6.2 1.8 4.2 6.5 1.3 3.5 5.5
36.1 35.9 35.4 35.0 34.0 33.6 33.6 33.9 32.5
54.9 51.4 49.6 54.4 50.6 48.0 53.3 51.2 47.2
1.56 1.66 1.69 1.52 1.59 1.66 1.49 1.57 1.63
25.90 25.86 25.83 25.97 25.86 25.86 26.05 25.92 25.87
FWHM (72 theta) 0.3601 0.4052 0.4325 0.4251 0.4589 0.4838 0.4470 0.4877 0.5147
(0.0017)c (0.0010) (0.0004) (0.0025) (0.0007) (0.0039) (0.0076) (0.0059) (0.0100)
a
Experimental uncertainty was of the order of {3% of the estimated values. Experimental uncertainty was of the order of {1% of the estimated values. c The values within parentheses are standard deviations of duplicate runs. b
were prepared at three carbonate levels at each of three synthesis temperatures. The data obtained were expected to provide a comprehensive understanding of the relationships among CAP MES, carbonate content, temperature of CAP synthesis, and crystallinity. MATERIALS AND METHODS
Carbonated Apatite Synthesis Carbonated apatites with a range of carbonate contents and crystallinities were synthesized by the method of LeGeros
et al. (15) with some modifications. Dicalcium phosphate dihydrate (DCPD) was hydrolyzed for 48 h in sodium bicarbonate-containing media at temperatures of 95, 70, and 507C. A total of nine CAP samples were synthesized (at three carbonate levels at three temperatures of synthesis). Ten grams of DCPD was suspended in 4 liters of doubly deionized water containing a predetermined level of NaHCO3 . The mixture was then brought to predefined temperatures and maintained for 48 h with stirring. The residue was obtained by filtering the mixture and washing three times with
FIG. 2. Full width at half-maximum (FWHM) of CAP synthesized at 957C ( s ), 707C ( h ), and 507C ( n ) as a function of carbonate content. FWHM is inversely related to crystallinity.
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on a Siemens D5000 X-ray diffractrometer with a copper target at 40 kV and 20 mA. A step size of 0.057 held for 0.3 s/step was used for the range of 207 to 407 2 theta. The full width at half-maximum (FWHM) of the 002 reflection was taken as a measure of crystallinity (crystal size/disorder). A detailed scan of this reflection, from 24.57 to 277 2 theta was also carried out with a step size of 0.017 and held for 5 s/step. Infrared absorption analysis was carried out with a Fourier transform infrared (FTIR) spectrophotometer (Mattson Galaxy 3020); the samples were mixed with KBr to give a concentration of 1 mg/400 mg KBr and pressed into pellets of 13-mm diameter. Phosphate was determined by the method of Gee et al. (16). The absorbance of the color obtained by the reduction of phosphoammonium molybdate complex by stannous chloride was determined at l Å 720 nm in a Perkin–Elmer Lambda 7 spectrophotometer. Calcium concentrations were determined by the method of Ray Sarkar and Chauhan (17). Calcium was complexed with o-cresolphthalein complexone (dye) in ammonia/ammonium buffer. The absorbance of the resulting color from the calcium–dye complex was determined at l Å 565 nm in a Perkin–Elmer Lambda 7 spectrophotometer. Carbonate contents of the samples were determined by the microdiffusion method of Conway (18). Fluoride concentrations were determined by a modification of the method of Taves (19). Determination of MES Distribution
FIG. 3. Effect of carbonate on the cumulative solubility distribution for CAP synthesized at 957C (A), 707C (B), and 507C (C) at 307C. The numbers indicate the weight percentage carbonate. The abscissa represents the solution ion activity product of hydroxyapatite (HAP). The curves are the result of data fitting using the assumption of a normal distribution with respect to pKHAP .
doubly deionized water. The final residue was then dried at 607C for 24 h. Physical and Chemical Analysis X-ray powder diffraction and infrared spectroscopy were employed for the physical characterization of the carbonated apatite samples. X-ray diffraction measurements were made
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MES distributions were determined by a slight modification of the method recently developed by Hsu et al. (13). A series of 0.1 M acetate buffer solutions were prepared by mixing calculated amounts of AR-grade CaCl2 (Mallinckrodt) and NaH2PO4 (Fisher Scientific) stock solutions. The pH and ionic strengths were adjusted to their calculated values by NaOH and NaCl. These solutions mimic the conditions when specified amounts of CAP are dissolved in a standard dissolution medium (pH 4.5, 0.1 M acetate buffer, ionic strength 0.5 M) and therefore correspond to various levels of solution ion activity product [KHAP Å (aCa ) 10 (aPO4 ) 6 (aOH ) 2 ]. The calculations for the driving force function KHAP were done with the computer program EQUIL (MicroMath Scientific Software, Salt Lake City, UT), the details of which have been reported previously (13). The buffer solutions were prepared both with and without fluoride extraction. Commercially available hydroxyapatite (Bio-Rad Laboratories) was used for extracting the fluoride from the reagent stock solutions by equilibrating 2 g of hydroxyapatite with 1 liter of reagent solution for 24 h and then filtering. The extraction step was then repeated except that the equilibration was carried out for only 2 h. The reagent stock solutions were then used for the preparation of MES solutions (0.1 M acetate buffers with varying solution pKHAP ), which were subsequently employed in MES deter-
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FIG. 4. Effect of equilibration time on the dissolution of 3.5% CAP ( n ), synthesized at 507C, and 3.9% CAP ( s ), synthesized at 957C. The numbers on the right are the pKHAP . The error bars represent the deviation from the average of duplicate runs.
minations. Accurately weighed CAP powders of about 10 mg were suspended in 250 ml of each solution and allowed to equilibrate at 307C with strring. After 48 h of equilibration, the suspensions were filtered, washed once with the same buffer solution, and then rinsed three times with doubledeionized water. The residue was dissolved into 0.1 M perchloric acid and was then analyzed for calcium and phosphate. With the original sample as the control, the results of calcium and phosphate analysis were converted into the amount of undissolved CAP residue. The fraction of dissolved CAP was then obtained from the amount of undissolved residue and the initial CAP. The fraction of CAP dissolved in each solution was then plotted to construct the distribution of the cumulative apparent solubility versus solution ion activity product. RESULTS AND DISCUSSION
X-ray Diffraction Data and Chemical Analysis The X-ray diffraction patterns of the nine samples used in this study were characteristic of apatite, and solid phases other than apatite were not found. Figure 1 presents the Xray diffraction patterns of the CAP samples synthesized at 95, 70, and 507C, with three levels of carbonate at each temperature. The peaks become broadened with increasing
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carbonate content and decreasing temperature of synthesis; these results support the view that the crystallinity of CAPs decreases both with an increase in carbonate content and with a decrease in the temperature of synthesis. Chemical composition, FWHM values, and peak position of 002 reflection of the CAP are listed in Table 1. The calcium-tophosphate molar ratio increased with increasing carbonate content at each temperature. This increase correlated more with a decrease in phosphate than with a change in calcium content. The peak position of the 002 reflection, which represents the direction along the c axis, shifted to lower angles with increasing carbonate content, indicating an expansion of the c axis of the crystals. This trend is similar to results reported by LeGeros et al. (15). The position of the peak representing the a axis (300) could not be obtained because of the overlapping of the adjacent peaks and also because of the relatively low crystallinity. These results are consistent with carbonate being structurally incorporated into the lattice by substitution for phosphate. Carbonate Content, Crystallinity, and MES Behavior of CAP Figure 2 shows the effect of carbonate content and the temperature of synthesis on the FWHM of the CAPs. FWHM of the 002 reflection has been used as an indicator of the
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FIG. 5. Cumulative solubility distribution in solutions with (open symbols) and without (closed symbols) extraction of fluoride for 1% CAP ( s, l ) and 6.2% CAP ( n, m ), synthesized at 957C. The abscissa represents the solution ion activity product based on the stoichiometry of HAP.
crystallinity (crystal size/disorder) of CAP (5, 6), with increasing width of the peaks corresponding to decreasing crystallinity. By use of this parameter, a consistent trend can be noted in the data presented in Fig. 2: that the crystallinity of CAPs decreased both with increasing carbonate content and with decreasing temperature of synthesis. The solubility distributions of the CAPs are shown in Fig. 3. The fraction of CAP dissolved is plotted against the negative logarithm of the solution ion activity product (pKHAP ). The buffer solutions used in these studies were treated with hydroxyapatite prior to the MES determination to remove trace amounts of fluoride present. Typical reproducibility in these experiments estimated from select duplicate runs (see closed circles in Fig. 3A) was of the order of 0.05 in the fraction of powder dissolved. The curves in these figures are ‘‘best-fit’’ curves with the assumption of a normal distribution. For all of the CAP samples shown in Fig. 3, the results follow the idea that the CAP preparations behave as a mixture of polymorphs with a continuous distribution of apparent solubilities. This is consistent with the previous findings by Hsu et al. (13), who demonstrated that a metastable equilibrium solubility rather than a steady-state condition likely determines the apparent solubility of CAP. Figure 4 presents the results of a time-dependent study for
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two CAP preparations equilibrated in two partially saturated solutions, pKHAP 116 and pKHAP 113. It shows that the data obtained after 48 h of equilibration are a good approximation of the metastable plateau; this is in agreement with the previous studies of Hsu et al. (13). The effects on the MES of trace levels of fluoride ( Ç0.015 ppm) in the buffer solutions arising from trace fluoride levels in the reagents are shown in Fig. 5. The data compare the MES distributions of 1 and 6.2% CAP determined in buffer solutions prepared both with and without hydroxyapatite extraction of fluoride, resulting in solution fluoride concentrations of less than 1 ppb in the former case. A significant shift of the distributions toward lower solubility occurred when fluoride was not removed from the solutions. Figure 6A is a three-dimensional plot of the mean pKHAP (obtained from curve fitting of the MES data in Fig. 3 using the normal distribution assumption) as a function of the carbonate content and that of the FWHM of the nine CAPs. The best-fit planar surface of the same data is shown in Fig. 6B, and the relationship between the observed and calculated mean pKHAP , using the simple planar equation (pKHAP Å a / b*CO3 / c*FWHM), is plotted in Fig. 7. A surprisingly good correlation was obtained between calculated and observed mean pKHAP values. The important point apparent
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FIG. 6. Three-dimensional plot of mean pKHAP as a function of carbonate content and FWHM (inverse crystallinity). (A) Actual data. (B) Bestfit plane of the data.
from Fig. 6B is that the slope of the curve along the axis representing the carbonate content is close to zero, implying that there is no significant effect of carbonate content on the apparent solubility when the crystallinity is fixed. Figure 8 shows the relationship between FWHM and mean pKHAP : The open symbols are the mean pKHAP values obtained from buffer solutions that have been extracted with hydroxyapatite for fluoride removal, whereas the closed symbols are the MES distribution results in buffer solutions without extraction. The straight lines represent the respective best fits to the data. All the CAPs in this study with varying amounts
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of carbonate fall on the same line, indicating that crystallinity alone may account for the MES behavior of the CAPs. The crystallinity of carbonated apatites has been related to disorder/defects in the crystal structure and crystal size as deduced from X-ray diffraction and infrared studies on CAP samples (2, 3, 5–7, 10, 20–23). The quantities most often used as an indicator of crystallinity are parameters such as FWHM and integral area of the X-ray diffraction peaks. The shape and breadth of the diffraction peaks are influenced by microstructural imperfections such as microstrain and crystallite size and also by instrumental factors (24). Numerous reports are available on the separation of crystallite size and microstrain from the observed broadened diffraction peaks (25–29). However, the nature of the samples and the underlying assumptions limit the applicability of such techniques to apatite. For example, the Warren– Averbach method (30) provides a procedure for estimating the crystallite size and microstrain from specimen broadened profiles, but at least two orders of reflection along the same direction are needed for the analysis; this is not possible for apatites with very low crystallinities unless the crystals are oriented in some particular direction (31). Analyses based on single peaks have also been reported in which mixed Gaussian and Lorenztian profile functions are used to separate the crystallite size and microstrain effects with the assumption of a Lorenztian crystallite size contribution and Gaussian microstrain contribution to peak broadening (29, 32–34). These assumptions may not be realistic since crystallite size and microstrain may both contain the Lorenztian and the Gaussian components (35). To get an accurate estimate of the crystallite size and microstrain in a given sample, the contributions of both Lorenztian and Gaussian components to crystallite size, microstrain, and instrumental broadening must be taken into account. The extraction of crystallite size and microstrain from broadened diffraction profiles of the carbonated apatites with a range of carbonate contents would be a significant contribution to the understanding of the factors controlling the chemical stability of CAP; studies in this direction are underway. Considering the aforementioned limitations associated with an accurate estimation of microstrain in low-crystallinity apatites, the changes in crystallinity (crystallite size and/ or microstrain) may therefore be justifiably represented by the broadening of the diffraction peaks, especially when the broadening parameter is related to a range of some independent variable such as carbonate content and temperature of synthesis. Therefore, the raw FWHM values (instrumental broadening not accounted for) of the 002 reflection peak were used in this study to describe the changes in the crystallinity of CAP as a function of both carbonate content and temperature of synthesis (Fig. 2). The FWHM values (inversely related to crystallinity) of the diffraction peaks in other directions such as 300 (23) and 211 (7) have also
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FIG. 7. Relationship between the observed and the calculated mean p KHAP from the data in Fig. 6.
been shown to vary with the temperature of synthesis and changes in the composition of apatites. The variation in crystallinity so obtained has been related to the dissolution ten-
dency of apatites, where apatites synthesized at lower temperature and containing high carbonate levels were found to have higher initial dissolution rates (7) and apparent solubil-
FIG. 8. Mean value of the MES distribution in solutions with (open symbols) and without (closed symbols) extraction of fluoride. The values correspond to the amount of carbonate in wt percentage units. The curves are the best-fit straight lines.
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ities (6, 23). Okazaki et al. (6) have reported that the amount of CAP dissolved increased with increase in the carbonate content and decrease in the temperature of synthesis. High slurry densities were used in the latter studies, and therefore, the solubilities estimated based on sampling at 1 month represent only those from the readily dissolved fractions. Such experiments cannot then represent the real solubility characteristics of a nonhomogenous material like CAP. Nevertheless, such data have provided support for the view that the amount dissolved is somehow related to the crystallinity of the CAP. The role of carbonate in the enhanced dissolution tendency of carbonated apatites may then be explained on the basis of its destabilizing effect on apatites by the formation of defects in the crystals (2, 7). This interpretation is consistent with the results in Figs. 6 and 8, where the mean of the MES distribution is directly related to the crystallinity parameter of the CAPs. This surprisingly good correlation reflects the importance of the MES distribution concept in describing the solubility properties of CAPs. Based on the MES distribution concept, CAPs and human dental enamel may be regarded as polymorphic mixtures with a distribution of apparent solubilities. A probable cause of the solubility distribution resides in the nature and distribution of imperfections within the apatite crystals. The conditions under which the apatites are synthesized either in vivo or in vitro may determine the final states of the crystals, and in most circumstances the crystals may be far from perfect. It seems reasonable that a given CAP sample may be composed of domains with different degrees of imperfection. During equilibration, CAP domains having greater imperfection and therefore lower crystallinity will dissolve in a solution with a relatively high ion activity product. In a series of solutions with different but constant ion activity product used to equilibrate the CAP, a distribution of fractions with various MESs can be obtained (Fig. 3). The distribution of MESs would then correspond to a distribution of apatite crystal domains with various degrees of crystallinity, and the mean value of the MES distribution would be related to the average crystallinity of the particular apatite preparation. The MES distribution appeared to be a common phenomenon among the carbonated apatites studied previously (13). This study involving a range of CAPs with different carbonate contents and crystallinities generalizes the MES distribution concept. The carbonate contents of the CAPs investigated in this study correspond to levels found in human dental enamel, dentine, and also bone (36). The variations in carbonate content and crystallinity and the absence of true thermodynamic equilibrium confound and preclude an accurate assessment of the solubility properties of these biological apatites using the traditional approach based on thermodynamic principles. The MES concept, therefore, provides a reasonable explanation for the behavior of synthetic as well as biological apatites in terms of the structural and
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compositional properties. Carbonate, always present in biological apatites, is related to the MES via its destabilizing effect on the apatite crystals. CONCLUSIONS
Carbonated apatites synthesized by the hydrolysis of DCPD, at three different temperatures, in sodium bicarbonate-containing media exhibited the MES distribution phenomenon. The presence of fluoride at trace levels in the commercially available AR-grade reagents can have a significant effect on the observed MES behavior of the CAPs. For accurate determination of the MES distributions, the reagent stock solutions were extracted with hydroxyapatite. This procedure reduces fluoride levels from approximately 0.015 ppm to about 1 ppb in the dissolution media. A comparison between the MES results obtained in buffer solutions both with and without extraction reveals that the apparent solubility distributions shift to lower values in the former case. The magnitude of the CAP dissolution driving force (i.e., the MES) was found to increase with increases in carbonate content and/or with decreases in crystallinity (employing the FWHM of the 002 reflection as a measure of CAP crystallinity). The crystallinity, on the other hand, was found to be determined by both the temperature of synthesis and the carbonate content, the latter being related to the incorporation of the carbonate ion into the apatite structure. The present investigation has importantly shown that, when crystallinity is taken into account for these CAP preparations, there is no additional effect of carbonate on the MES; i.e., the MES behavior may be entirely ascribed to CAP crystallinity. REFERENCES 1. Young, R. A., in ‘‘Physico-Chimie et Cristallograpie des Apatites D’interet Biologique,’’ p. 21. Centre National de la Recherche Scientifique, Paris, 1975. 2. Nelson, D. G. A., J. Dent. Res. 60, 1621 (1981). 3. Nelson, D. G. A., Featherstone, J. D. B., Duncan, J. F., and Cutress, T. W., Caries Res. 17, 200 (1983). 4. LeGeros, R. Z., and Tung, M. S., Caries Res. 17, 419 (1983). 5. Nelson, D. G. A., Barry, J. C., Shields, C. P., Glena, R., and Featherstone, J. D. B., J. Colloid Interface Sci. 130, 467 (1989). 6. Okazaki, M., Noriwaki, Y., Aoba, T., Doi, Y., and Takahashi, J., Caries Res. 15, 477 (1981). 7. Featherstone, J. D. B., Shields, C. P., Khaderazad, B., and Oldershaw, M. D., J. Dent. Res. 62, 1049 (1983). 8. Blumenthal, N. C., Betts, F., and Posner, A. S., Calcif. Tissue Res. 18, 81 (1975). 9. LeGeros, R. Z., Nature (London) 206, 403 (1965). 10. LeGeros, R. Z., Ph.D. thesis, New York University, 1967. 11. LeGeros, R. Z., Trautz, O. R., LeGeros, J. P., Klein, E., and Shirra, W. P., Science 155, 1409 (1967). 12. LeGeros, R. Z., LeGeros, J. P., Trautz, O. R., and Klein, E., in ‘‘Developments in Applied Spectroscopy’’ (E. L. Grove, Ed.), p. 3. Plenum, New York, 1970.
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METASTABLE EQUILIBRIUM SOLUBILITY OF CARBONATED APATITES 13. Hsu, J., Fox, J. L., Higuchi, W. I., Powell, G. L., Otsuka, M., Baig, A., and LeGeros, R. Z., J. Colloid Interface Sci. 167, 414 (1994). 14. Brown, W. E., in ‘‘Environmental Phosphorus Handbook’’ (E. L. Griffith, A. Beeton, J. M. Spencer, and D. T. Mitchell, Eds.), p. 203. Wiley, New York, 1973. 15. LeGeros, R. Z., LeGeros, J. P., Trautz, O. R., and Shirra, W. P., in ‘‘Advances in X-ray Analysis’’ (C. S. Barrett, J. B. Newkirk, and C. O. Ruud, Eds.), p. 57. Plenum, New York, 1971. 16. Gee, A., Domingues, L., and Dietz, V., Anal. Chem. 26, 1487 (1954). 17. Sarkar, B. C. R., and Chauhan, U. P. S., Anal. Biochem. 20, 155 (1967). 18. Conway, E. J., ‘‘Microdiffusion Analysis and Volumetric Error.’’ Crosby Lockwood & Sons, London, 1962. 19. Taves, D. R., Talanta 15, 969 (1968). 20. Pleshko, N., Boskey, A., and Mendelsohn, R., Biophys. J. 60, 786 (1991). 21. Nelson, D. G. A., Featherstone, J. D. B., Duncan, J. F., and Cutress, T. W., J. Dent. Res. 61, 1274 (1982). 22. Okazaki, M., Noriwaki, Y., Aoba, T., Doi, Y., Takahashi, J., and Kimura, H., Caries Res. 16, 308 (1982).
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23. Okazaki, M., Takahashi, J., and Kimura, H., J. Osaka Univ. Dent. School 24, 13 (1984). 24. Klug, H. P., and Alexander, L. E., ‘‘X-ray Diffraction Procedures for Polycrystalline and Amorphous Materials.’’ Wiley, New York, 1974. 25. Langford, J. I., Boultif, A., Auffredic, J. P., and Louer, D., J. Appl. Crystallogr. 26, 22 (1993). 26. Schoeing, F. R. L., Acta Crystallogr. 18, 975 (1965). 27. Warren, B. E., ‘‘X-ray Diffraction.’’ Addison–Wesley, Reading, MA, 1969. 28. Keijser, T. H. D., Mittemeijer, E. J., and Rozendaal, H. C. F., J. Appl. Crystallogr. 16, 309 (1983). 29. Nandi, R. K., and Gupta, S. P., J. Appl. Crystallogr. 11, 6 (1978). 30. Warren, B. E., and Averbach, B. L., J. Appl. Phys. 21, 595 (1950). 31. Glas, J. E., and Omnell, K. A., J. Ultrastruct. Res. 3, 334 (1960). 32. Keijser, T. H. D., Langford, J. I., Mittemeijer, E. J., and Vgels, A. B. P., J. Appl. Crystallogr. 15, 308 (1982). 33. Langford, J. I., J. Appl. Crystallogr. 11, 10 (1978). 34. Nandi, R. K., and Gupta, S. P., J. Phys. D 8, 731 (1975). 35. Young, R. A., and Desai, P., Arch. Nauk Mater. 10, 71 (1989). 36. LeGeros, R. Z., ‘‘Calcium Phosphates in Oral Biology and Medicine.’’ S. Karger, Basel, 1991.
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Effect of Carbonate Content and Crystallinity on the Metastable Equilibrium Solubility Behavior of Carbonated Apatites 1 ARIF A. BAIG, JEFFREY L. FOX, 2 JER HSU, ZEREN WANG, MAKOTO OTSUK A,* WILLIAM I. HIGUCHI, AND RACQUEL Z. LEGEROS† Department of Pharmaceutics and Pharmaceutical Chemistry, University of Utah, Salt Lake City, Utah 84112; *Kobe Pharmaceutical University, Kobe, Japan; and †D. B. Kriser Dental Center, College of Dentistry, New York University, New York, New York 10010 Received August 22, 1995; accepted October 31, 1995
The purpose of this investigation was to assess the applicability of the metastable equilibrium solubility (MES) concept, previously developed in our laboratory, over wide ranges of two independent variables, carbonate content and crystallinity, and also to examine the influences of these variables on the MES behavior of carbonated apatites (CAPs). The CAP samples were prepared by dicalcium phosphate dihydrate (DCPD) hydrolysis for 48 h in NaHCO3-containing media at 95, 70, and 507C. This method of preparation gave CAP samples with varying carbonate contents and crystallinities. A previously developed technique with slight modification was used to determine the MES distribution for each of the CAP samples. The equilibration solutions were prepared both with and without extraction of fluoride with hydroxyapatite (HAP). From X-ray diffraction, the full width at half-maximum (FWHM) of the 002 reflection was used as a measure of crystallinity. The findings of this study showed that each of these preparations possessed an MES distribution and therefore provided further support that the MES distribution is a common phenomenon describing the dissolution behavior of CAPs, regardless of their carbonate content and crystallinities. The crystallinities of the CAPs decreased and the MES values increased with increasing carbonate content and decreasing temperature of synthesis. A plot of the mean MES value against CAP crystallinity revealed that the mean MES was a single-valued function of crystallinity; i.e., when crystallinity was taken into account, there was no additional effect of carbonate on the MES. When fluoride was not extracted from the equilibration solutions, the MES shifted to lower values. The concept of MES distribution and its dependence on the crystallinity of CAP may provide insight into the mechanism of dissolution of biological apatites, which may be considered imperfect crystalline substances. q 1996 Academic Press, Inc. Key Words: apatites; crystallinity; X-ray diffraction; solubility. INTRODUCTION
Carbonated apatite (CAP), a prototype of the mineral component of human dental enamel, has been studied exten1 This study was supported by NIDR Research Grants DE-06569 and DE-07223. 2 To whom correspondence should be addressed.
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sively because of the likely importance of the incorporated carbonate ion in the dental caries process. The carbonate content of human dental enamel is in the range of 2 to 4% by weight (1). The presence of carbonate as the major impurity anion has been found to decrease the stability of the apatite structure, increase its solubility, and thereby render it more susceptible to acid attack (2–7). The effects of carbonate substitution in apatites are manifested as changes in the lattice parameters, decreases in crystal size, increases in crystal strain and disorder, and changes in crystal morphologies (2, 5, 6, 8–12). The properties of carbonated apatites are also influenced by the conditions under which the synthesis is carried out. Numerous studies (5, 6, 10) have shown that carbonated apatites synthesized at different temperatures and pH exhibit different physicochemical properties, such as degree of crystallinity and dissolution characteristics. The variability in the properties of CAP due to either the incorporation of impurity ions during synthesis or the conditions of synthesis itself may be related to the imperfections in the crystalline structure of the material. These imperfections may result in a metastable substance with variable solubility properties. Recent studies by Hsu et al. (13) have shown that CAPs synthesized by the hydrolysis of anhydrous dicalcium phosphate (DCP) and human dental enamel exhibit metastable equilibrium solubility (MES) behavior. Although the MES phenomenon had previously been noted by Brown (14) in dissolution studies involving human dental enamel, there had been no attempts until recently (13) to quantitatively describe the MES concept. The results of the experiments reported by Hsu et al. (13) clearly show that the apparent solubility behavior of CAP is consistent with the MES phenomenon, and that the MES shifts to higher solubility values with an increase in the carbonate content. The purpose of this study was to assess the applicability of the MES concept over wide ranges of two of the independent variables. The previous work of Hsu et al. (13) involved CAP preparations synthesized at a single temperature (957C) and at two carbonate levels. In the present research CAPs
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FIG. 1. X-ray diffraction patterns of CAP synthesized at 957C (A), 707C (B), and 507C (C), with three different carbonate contents at each temperature. The values on the left-hand side correspond to the weight percentage carbonate.
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TABLE 1 Chemical Compositon and FWHM of Carbonated Apatite Samples Synthesized at 95, 70, and 507C with Different Carbonate Contents Temperature (7C)
CO3a (wt%)
Cab (wt%)
PO4b (wt%)
Ca/P (M)
002 Peak position
95 95 95 70 70 70 50 50 50
1.0 3.9 6.2 1.8 4.2 6.5 1.3 3.5 5.5
36.1 35.9 35.4 35.0 34.0 33.6 33.6 33.9 32.5
54.9 51.4 49.6 54.4 50.6 48.0 53.3 51.2 47.2
1.56 1.66 1.69 1.52 1.59 1.66 1.49 1.57 1.63
25.90 25.86 25.83 25.97 25.86 25.86 26.05 25.92 25.87
FWHM (72 theta) 0.3601 0.4052 0.4325 0.4251 0.4589 0.4838 0.4470 0.4877 0.5147
(0.0017)c (0.0010) (0.0004) (0.0025) (0.0007) (0.0039) (0.0076) (0.0059) (0.0100)
a
Experimental uncertainty was of the order of {3% of the estimated values. Experimental uncertainty was of the order of {1% of the estimated values. c The values within parentheses are standard deviations of duplicate runs. b
were prepared at three carbonate levels at each of three synthesis temperatures. The data obtained were expected to provide a comprehensive understanding of the relationships among CAP MES, carbonate content, temperature of CAP synthesis, and crystallinity. MATERIALS AND METHODS
Carbonated Apatite Synthesis Carbonated apatites with a range of carbonate contents and crystallinities were synthesized by the method of LeGeros
et al. (15) with some modifications. Dicalcium phosphate dihydrate (DCPD) was hydrolyzed for 48 h in sodium bicarbonate-containing media at temperatures of 95, 70, and 507C. A total of nine CAP samples were synthesized (at three carbonate levels at three temperatures of synthesis). Ten grams of DCPD was suspended in 4 liters of doubly deionized water containing a predetermined level of NaHCO3 . The mixture was then brought to predefined temperatures and maintained for 48 h with stirring. The residue was obtained by filtering the mixture and washing three times with
FIG. 2. Full width at half-maximum (FWHM) of CAP synthesized at 957C ( s ), 707C ( h ), and 507C ( n ) as a function of carbonate content. FWHM is inversely related to crystallinity.
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on a Siemens D5000 X-ray diffractrometer with a copper target at 40 kV and 20 mA. A step size of 0.057 held for 0.3 s/step was used for the range of 207 to 407 2 theta. The full width at half-maximum (FWHM) of the 002 reflection was taken as a measure of crystallinity (crystal size/disorder). A detailed scan of this reflection, from 24.57 to 277 2 theta was also carried out with a step size of 0.017 and held for 5 s/step. Infrared absorption analysis was carried out with a Fourier transform infrared (FTIR) spectrophotometer (Mattson Galaxy 3020); the samples were mixed with KBr to give a concentration of 1 mg/400 mg KBr and pressed into pellets of 13-mm diameter. Phosphate was determined by the method of Gee et al. (16). The absorbance of the color obtained by the reduction of phosphoammonium molybdate complex by stannous chloride was determined at l Å 720 nm in a Perkin–Elmer Lambda 7 spectrophotometer. Calcium concentrations were determined by the method of Ray Sarkar and Chauhan (17). Calcium was complexed with o-cresolphthalein complexone (dye) in ammonia/ammonium buffer. The absorbance of the resulting color from the calcium–dye complex was determined at l Å 565 nm in a Perkin–Elmer Lambda 7 spectrophotometer. Carbonate contents of the samples were determined by the microdiffusion method of Conway (18). Fluoride concentrations were determined by a modification of the method of Taves (19). Determination of MES Distribution
FIG. 3. Effect of carbonate on the cumulative solubility distribution for CAP synthesized at 957C (A), 707C (B), and 507C (C) at 307C. The numbers indicate the weight percentage carbonate. The abscissa represents the solution ion activity product of hydroxyapatite (HAP). The curves are the result of data fitting using the assumption of a normal distribution with respect to pKHAP .
doubly deionized water. The final residue was then dried at 607C for 24 h. Physical and Chemical Analysis X-ray powder diffraction and infrared spectroscopy were employed for the physical characterization of the carbonated apatite samples. X-ray diffraction measurements were made
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MES distributions were determined by a slight modification of the method recently developed by Hsu et al. (13). A series of 0.1 M acetate buffer solutions were prepared by mixing calculated amounts of AR-grade CaCl2 (Mallinckrodt) and NaH2PO4 (Fisher Scientific) stock solutions. The pH and ionic strengths were adjusted to their calculated values by NaOH and NaCl. These solutions mimic the conditions when specified amounts of CAP are dissolved in a standard dissolution medium (pH 4.5, 0.1 M acetate buffer, ionic strength 0.5 M) and therefore correspond to various levels of solution ion activity product [KHAP Å (aCa ) 10 (aPO4 ) 6 (aOH ) 2 ]. The calculations for the driving force function KHAP were done with the computer program EQUIL (MicroMath Scientific Software, Salt Lake City, UT), the details of which have been reported previously (13). The buffer solutions were prepared both with and without fluoride extraction. Commercially available hydroxyapatite (Bio-Rad Laboratories) was used for extracting the fluoride from the reagent stock solutions by equilibrating 2 g of hydroxyapatite with 1 liter of reagent solution for 24 h and then filtering. The extraction step was then repeated except that the equilibration was carried out for only 2 h. The reagent stock solutions were then used for the preparation of MES solutions (0.1 M acetate buffers with varying solution pKHAP ), which were subsequently employed in MES deter-
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FIG. 4. Effect of equilibration time on the dissolution of 3.5% CAP ( n ), synthesized at 507C, and 3.9% CAP ( s ), synthesized at 957C. The numbers on the right are the pKHAP . The error bars represent the deviation from the average of duplicate runs.
minations. Accurately weighed CAP powders of about 10 mg were suspended in 250 ml of each solution and allowed to equilibrate at 307C with strring. After 48 h of equilibration, the suspensions were filtered, washed once with the same buffer solution, and then rinsed three times with doubledeionized water. The residue was dissolved into 0.1 M perchloric acid and was then analyzed for calcium and phosphate. With the original sample as the control, the results of calcium and phosphate analysis were converted into the amount of undissolved CAP residue. The fraction of dissolved CAP was then obtained from the amount of undissolved residue and the initial CAP. The fraction of CAP dissolved in each solution was then plotted to construct the distribution of the cumulative apparent solubility versus solution ion activity product. RESULTS AND DISCUSSION
X-ray Diffraction Data and Chemical Analysis The X-ray diffraction patterns of the nine samples used in this study were characteristic of apatite, and solid phases other than apatite were not found. Figure 1 presents the Xray diffraction patterns of the CAP samples synthesized at 95, 70, and 507C, with three levels of carbonate at each temperature. The peaks become broadened with increasing
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carbonate content and decreasing temperature of synthesis; these results support the view that the crystallinity of CAPs decreases both with an increase in carbonate content and with a decrease in the temperature of synthesis. Chemical composition, FWHM values, and peak position of 002 reflection of the CAP are listed in Table 1. The calcium-tophosphate molar ratio increased with increasing carbonate content at each temperature. This increase correlated more with a decrease in phosphate than with a change in calcium content. The peak position of the 002 reflection, which represents the direction along the c axis, shifted to lower angles with increasing carbonate content, indicating an expansion of the c axis of the crystals. This trend is similar to results reported by LeGeros et al. (15). The position of the peak representing the a axis (300) could not be obtained because of the overlapping of the adjacent peaks and also because of the relatively low crystallinity. These results are consistent with carbonate being structurally incorporated into the lattice by substitution for phosphate. Carbonate Content, Crystallinity, and MES Behavior of CAP Figure 2 shows the effect of carbonate content and the temperature of synthesis on the FWHM of the CAPs. FWHM of the 002 reflection has been used as an indicator of the
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FIG. 5. Cumulative solubility distribution in solutions with (open symbols) and without (closed symbols) extraction of fluoride for 1% CAP ( s, l ) and 6.2% CAP ( n, m ), synthesized at 957C. The abscissa represents the solution ion activity product based on the stoichiometry of HAP.
crystallinity (crystal size/disorder) of CAP (5, 6), with increasing width of the peaks corresponding to decreasing crystallinity. By use of this parameter, a consistent trend can be noted in the data presented in Fig. 2: that the crystallinity of CAPs decreased both with increasing carbonate content and with decreasing temperature of synthesis. The solubility distributions of the CAPs are shown in Fig. 3. The fraction of CAP dissolved is plotted against the negative logarithm of the solution ion activity product (pKHAP ). The buffer solutions used in these studies were treated with hydroxyapatite prior to the MES determination to remove trace amounts of fluoride present. Typical reproducibility in these experiments estimated from select duplicate runs (see closed circles in Fig. 3A) was of the order of 0.05 in the fraction of powder dissolved. The curves in these figures are ‘‘best-fit’’ curves with the assumption of a normal distribution. For all of the CAP samples shown in Fig. 3, the results follow the idea that the CAP preparations behave as a mixture of polymorphs with a continuous distribution of apparent solubilities. This is consistent with the previous findings by Hsu et al. (13), who demonstrated that a metastable equilibrium solubility rather than a steady-state condition likely determines the apparent solubility of CAP. Figure 4 presents the results of a time-dependent study for
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two CAP preparations equilibrated in two partially saturated solutions, pKHAP 116 and pKHAP 113. It shows that the data obtained after 48 h of equilibration are a good approximation of the metastable plateau; this is in agreement with the previous studies of Hsu et al. (13). The effects on the MES of trace levels of fluoride ( Ç0.015 ppm) in the buffer solutions arising from trace fluoride levels in the reagents are shown in Fig. 5. The data compare the MES distributions of 1 and 6.2% CAP determined in buffer solutions prepared both with and without hydroxyapatite extraction of fluoride, resulting in solution fluoride concentrations of less than 1 ppb in the former case. A significant shift of the distributions toward lower solubility occurred when fluoride was not removed from the solutions. Figure 6A is a three-dimensional plot of the mean pKHAP (obtained from curve fitting of the MES data in Fig. 3 using the normal distribution assumption) as a function of the carbonate content and that of the FWHM of the nine CAPs. The best-fit planar surface of the same data is shown in Fig. 6B, and the relationship between the observed and calculated mean pKHAP , using the simple planar equation (pKHAP Å a / b*CO3 / c*FWHM), is plotted in Fig. 7. A surprisingly good correlation was obtained between calculated and observed mean pKHAP values. The important point apparent
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FIG. 6. Three-dimensional plot of mean pKHAP as a function of carbonate content and FWHM (inverse crystallinity). (A) Actual data. (B) Bestfit plane of the data.
from Fig. 6B is that the slope of the curve along the axis representing the carbonate content is close to zero, implying that there is no significant effect of carbonate content on the apparent solubility when the crystallinity is fixed. Figure 8 shows the relationship between FWHM and mean pKHAP : The open symbols are the mean pKHAP values obtained from buffer solutions that have been extracted with hydroxyapatite for fluoride removal, whereas the closed symbols are the MES distribution results in buffer solutions without extraction. The straight lines represent the respective best fits to the data. All the CAPs in this study with varying amounts
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of carbonate fall on the same line, indicating that crystallinity alone may account for the MES behavior of the CAPs. The crystallinity of carbonated apatites has been related to disorder/defects in the crystal structure and crystal size as deduced from X-ray diffraction and infrared studies on CAP samples (2, 3, 5–7, 10, 20–23). The quantities most often used as an indicator of crystallinity are parameters such as FWHM and integral area of the X-ray diffraction peaks. The shape and breadth of the diffraction peaks are influenced by microstructural imperfections such as microstrain and crystallite size and also by instrumental factors (24). Numerous reports are available on the separation of crystallite size and microstrain from the observed broadened diffraction peaks (25–29). However, the nature of the samples and the underlying assumptions limit the applicability of such techniques to apatite. For example, the Warren– Averbach method (30) provides a procedure for estimating the crystallite size and microstrain from specimen broadened profiles, but at least two orders of reflection along the same direction are needed for the analysis; this is not possible for apatites with very low crystallinities unless the crystals are oriented in some particular direction (31). Analyses based on single peaks have also been reported in which mixed Gaussian and Lorenztian profile functions are used to separate the crystallite size and microstrain effects with the assumption of a Lorenztian crystallite size contribution and Gaussian microstrain contribution to peak broadening (29, 32–34). These assumptions may not be realistic since crystallite size and microstrain may both contain the Lorenztian and the Gaussian components (35). To get an accurate estimate of the crystallite size and microstrain in a given sample, the contributions of both Lorenztian and Gaussian components to crystallite size, microstrain, and instrumental broadening must be taken into account. The extraction of crystallite size and microstrain from broadened diffraction profiles of the carbonated apatites with a range of carbonate contents would be a significant contribution to the understanding of the factors controlling the chemical stability of CAP; studies in this direction are underway. Considering the aforementioned limitations associated with an accurate estimation of microstrain in low-crystallinity apatites, the changes in crystallinity (crystallite size and/ or microstrain) may therefore be justifiably represented by the broadening of the diffraction peaks, especially when the broadening parameter is related to a range of some independent variable such as carbonate content and temperature of synthesis. Therefore, the raw FWHM values (instrumental broadening not accounted for) of the 002 reflection peak were used in this study to describe the changes in the crystallinity of CAP as a function of both carbonate content and temperature of synthesis (Fig. 2). The FWHM values (inversely related to crystallinity) of the diffraction peaks in other directions such as 300 (23) and 211 (7) have also
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FIG. 7. Relationship between the observed and the calculated mean p KHAP from the data in Fig. 6.
been shown to vary with the temperature of synthesis and changes in the composition of apatites. The variation in crystallinity so obtained has been related to the dissolution ten-
dency of apatites, where apatites synthesized at lower temperature and containing high carbonate levels were found to have higher initial dissolution rates (7) and apparent solubil-
FIG. 8. Mean value of the MES distribution in solutions with (open symbols) and without (closed symbols) extraction of fluoride. The values correspond to the amount of carbonate in wt percentage units. The curves are the best-fit straight lines.
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ities (6, 23). Okazaki et al. (6) have reported that the amount of CAP dissolved increased with increase in the carbonate content and decrease in the temperature of synthesis. High slurry densities were used in the latter studies, and therefore, the solubilities estimated based on sampling at 1 month represent only those from the readily dissolved fractions. Such experiments cannot then represent the real solubility characteristics of a nonhomogenous material like CAP. Nevertheless, such data have provided support for the view that the amount dissolved is somehow related to the crystallinity of the CAP. The role of carbonate in the enhanced dissolution tendency of carbonated apatites may then be explained on the basis of its destabilizing effect on apatites by the formation of defects in the crystals (2, 7). This interpretation is consistent with the results in Figs. 6 and 8, where the mean of the MES distribution is directly related to the crystallinity parameter of the CAPs. This surprisingly good correlation reflects the importance of the MES distribution concept in describing the solubility properties of CAPs. Based on the MES distribution concept, CAPs and human dental enamel may be regarded as polymorphic mixtures with a distribution of apparent solubilities. A probable cause of the solubility distribution resides in the nature and distribution of imperfections within the apatite crystals. The conditions under which the apatites are synthesized either in vivo or in vitro may determine the final states of the crystals, and in most circumstances the crystals may be far from perfect. It seems reasonable that a given CAP sample may be composed of domains with different degrees of imperfection. During equilibration, CAP domains having greater imperfection and therefore lower crystallinity will dissolve in a solution with a relatively high ion activity product. In a series of solutions with different but constant ion activity product used to equilibrate the CAP, a distribution of fractions with various MESs can be obtained (Fig. 3). The distribution of MESs would then correspond to a distribution of apatite crystal domains with various degrees of crystallinity, and the mean value of the MES distribution would be related to the average crystallinity of the particular apatite preparation. The MES distribution appeared to be a common phenomenon among the carbonated apatites studied previously (13). This study involving a range of CAPs with different carbonate contents and crystallinities generalizes the MES distribution concept. The carbonate contents of the CAPs investigated in this study correspond to levels found in human dental enamel, dentine, and also bone (36). The variations in carbonate content and crystallinity and the absence of true thermodynamic equilibrium confound and preclude an accurate assessment of the solubility properties of these biological apatites using the traditional approach based on thermodynamic principles. The MES concept, therefore, provides a reasonable explanation for the behavior of synthetic as well as biological apatites in terms of the structural and
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compositional properties. Carbonate, always present in biological apatites, is related to the MES via its destabilizing effect on the apatite crystals. CONCLUSIONS
Carbonated apatites synthesized by the hydrolysis of DCPD, at three different temperatures, in sodium bicarbonate-containing media exhibited the MES distribution phenomenon. The presence of fluoride at trace levels in the commercially available AR-grade reagents can have a significant effect on the observed MES behavior of the CAPs. For accurate determination of the MES distributions, the reagent stock solutions were extracted with hydroxyapatite. This procedure reduces fluoride levels from approximately 0.015 ppm to about 1 ppb in the dissolution media. A comparison between the MES results obtained in buffer solutions both with and without extraction reveals that the apparent solubility distributions shift to lower values in the former case. The magnitude of the CAP dissolution driving force (i.e., the MES) was found to increase with increases in carbonate content and/or with decreases in crystallinity (employing the FWHM of the 002 reflection as a measure of CAP crystallinity). The crystallinity, on the other hand, was found to be determined by both the temperature of synthesis and the carbonate content, the latter being related to the incorporation of the carbonate ion into the apatite structure. The present investigation has importantly shown that, when crystallinity is taken into account for these CAP preparations, there is no additional effect of carbonate on the MES; i.e., the MES behavior may be entirely ascribed to CAP crystallinity. REFERENCES 1. Young, R. A., in ‘‘Physico-Chimie et Cristallograpie des Apatites D’interet Biologique,’’ p. 21. Centre National de la Recherche Scientifique, Paris, 1975. 2. Nelson, D. G. A., J. Dent. Res. 60, 1621 (1981). 3. Nelson, D. G. A., Featherstone, J. D. B., Duncan, J. F., and Cutress, T. W., Caries Res. 17, 200 (1983). 4. LeGeros, R. Z., and Tung, M. S., Caries Res. 17, 419 (1983). 5. Nelson, D. G. A., Barry, J. C., Shields, C. P., Glena, R., and Featherstone, J. D. B., J. Colloid Interface Sci. 130, 467 (1989). 6. Okazaki, M., Noriwaki, Y., Aoba, T., Doi, Y., and Takahashi, J., Caries Res. 15, 477 (1981). 7. Featherstone, J. D. B., Shields, C. P., Khaderazad, B., and Oldershaw, M. D., J. Dent. Res. 62, 1049 (1983). 8. Blumenthal, N. C., Betts, F., and Posner, A. S., Calcif. Tissue Res. 18, 81 (1975). 9. LeGeros, R. Z., Nature (London) 206, 403 (1965). 10. LeGeros, R. Z., Ph.D. thesis, New York University, 1967. 11. LeGeros, R. Z., Trautz, O. R., LeGeros, J. P., Klein, E., and Shirra, W. P., Science 155, 1409 (1967). 12. LeGeros, R. Z., LeGeros, J. P., Trautz, O. R., and Klein, E., in ‘‘Developments in Applied Spectroscopy’’ (E. L. Grove, Ed.), p. 3. Plenum, New York, 1970.
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METASTABLE EQUILIBRIUM SOLUBILITY OF CARBONATED APATITES 13. Hsu, J., Fox, J. L., Higuchi, W. I., Powell, G. L., Otsuka, M., Baig, A., and LeGeros, R. Z., J. Colloid Interface Sci. 167, 414 (1994). 14. Brown, W. E., in ‘‘Environmental Phosphorus Handbook’’ (E. L. Griffith, A. Beeton, J. M. Spencer, and D. T. Mitchell, Eds.), p. 203. Wiley, New York, 1973. 15. LeGeros, R. Z., LeGeros, J. P., Trautz, O. R., and Shirra, W. P., in ‘‘Advances in X-ray Analysis’’ (C. S. Barrett, J. B. Newkirk, and C. O. Ruud, Eds.), p. 57. Plenum, New York, 1971. 16. Gee, A., Domingues, L., and Dietz, V., Anal. Chem. 26, 1487 (1954). 17. Sarkar, B. C. R., and Chauhan, U. P. S., Anal. Biochem. 20, 155 (1967). 18. Conway, E. J., ‘‘Microdiffusion Analysis and Volumetric Error.’’ Crosby Lockwood & Sons, London, 1962. 19. Taves, D. R., Talanta 15, 969 (1968). 20. Pleshko, N., Boskey, A., and Mendelsohn, R., Biophys. J. 60, 786 (1991). 21. Nelson, D. G. A., Featherstone, J. D. B., Duncan, J. F., and Cutress, T. W., J. Dent. Res. 61, 1274 (1982). 22. Okazaki, M., Noriwaki, Y., Aoba, T., Doi, Y., Takahashi, J., and Kimura, H., Caries Res. 16, 308 (1982).
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23. Okazaki, M., Takahashi, J., and Kimura, H., J. Osaka Univ. Dent. School 24, 13 (1984). 24. Klug, H. P., and Alexander, L. E., ‘‘X-ray Diffraction Procedures for Polycrystalline and Amorphous Materials.’’ Wiley, New York, 1974. 25. Langford, J. I., Boultif, A., Auffredic, J. P., and Louer, D., J. Appl. Crystallogr. 26, 22 (1993). 26. Schoeing, F. R. L., Acta Crystallogr. 18, 975 (1965). 27. Warren, B. E., ‘‘X-ray Diffraction.’’ Addison–Wesley, Reading, MA, 1969. 28. Keijser, T. H. D., Mittemeijer, E. J., and Rozendaal, H. C. F., J. Appl. Crystallogr. 16, 309 (1983). 29. Nandi, R. K., and Gupta, S. P., J. Appl. Crystallogr. 11, 6 (1978). 30. Warren, B. E., and Averbach, B. L., J. Appl. Phys. 21, 595 (1950). 31. Glas, J. E., and Omnell, K. A., J. Ultrastruct. Res. 3, 334 (1960). 32. Keijser, T. H. D., Langford, J. I., Mittemeijer, E. J., and Vgels, A. B. P., J. Appl. Crystallogr. 15, 308 (1982). 33. Langford, J. I., J. Appl. Crystallogr. 11, 10 (1978). 34. Nandi, R. K., and Gupta, S. P., J. Phys. D 8, 731 (1975). 35. Young, R. A., and Desai, P., Arch. Nauk Mater. 10, 71 (1989). 36. LeGeros, R. Z., ‘‘Calcium Phosphates in Oral Biology and Medicine.’’ S. Karger, Basel, 1991.
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