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An X-ray diffraction and solubility study of equilibration of human enamel-powder suspensions in fluoride-containing buffer
Archs oral Biol. Vol. 30, NC’. 6, pp. 471-475, 1985 Printed in Great Britain. All rights reserved
Copyright 0
0003-9969/85 $3.00 + 0.00 1985 Pergamon Press Ltd
AN X-‘RAY DIFFRACTION AND SOLUBILITY STUDY OF EQUILIBRATION OF HUMAN ENAMEL-POWDER SUSPE
Institute
of Der.tal
Pathology
J.
LARSEN
and S. J.
and Operative Dentistry Dental College, DK-8000
JENSEN
and Institute of Technology Aarhus, Denmark
and Physics,
Royal
Summary-Various amounts of enamel-apatite powder were suspended in an acetate buffer (pH 4.5) containing sufficient fluoride to give molar ratios of fluoride/apatite from zero to unity. The suspensions were equilibrate:d at 20°C for periods between 4 h and 1 year, with continuous gentle stirring. Solubility studies showed dissolution of hydroxyapatite, formation and re-dissolution of calcium fluoride and formation of fluorapatite. The amount of mineral dissolved was low during the fluorapatite formation and increased by a factor of approx. 10 as equilibrium was approached. The fluoride content of the solid apatite, which ranged from 0. I to 70 mol’% fluorapatite, only influenced the solubility slightly, whereas the fluoride content of the bathing solution had a large effect. X-ray diffraction showed a linear correlation between the fluoride content and the a-axis of the apatite.
INTRODUCTION
Chemical reaction between dental enamel and fluoride ions in aqueous solution causes calcium fluoride to be formed when the fluoride concentration is high (> 50 parts/106), and fluoride-containing apatite to be formed when the concentration is low (Leach, 1959). Larsen, Jensen and Thorsen (1977) exposed crowns of human premolar teeth to a pH 4 buffer containing 150 parts/lo6 F- and found that the reaction period could be divided into three parts. Initially, the solution became supersaturated with respect to CaF, causing this salt to precipitate; in the second stage, the solution became supersaturated with respect to fluorapatite; in the final stage, the liquid became undersaturated with respect to CaF, and this salt dissolved. X-ray diffraction of the outer layers of the teeth showed that CaF, was formed during the first stage and had disappeared after the third stage. The a-axis dimension of the unit cell of different apatites varies with the composition of the apatite, whereas the c-axis dimension is almost constant. McConnell (1970) proposed that atomic substitutions produce a proportional dimensional change of the apatite unit cell (Vegard’s law). Moreno, Kresak and Zahradnik (1977) fi3und the a-parameter to be a linear function of the degree of fluoridation of synthetic fluorhydroxyapatites. The a-parameter of human enamel is 0.9442 +_0.0005 nm (Glas, 1962) compared with 0.,9421 f 0.0001 nm in synthetic hydroxyapatite (Carlstriim, 1955). The difference is probably due to partial substitutions of OH- by H,O or H30+ (McConnell, 1970). The corresponding a-axis dimension of synthetic fluorapatite is 0.9370 * 0.0001 nm (Carlstriim, 1955). Moreno et al. (1!)77), using X-ray diffraction of controlled fluorhydroxyapatites, found a solubilitydepressing effect of fluoride after an equilibration period as long as one month. The effect was of particular significance when the nFAp/nApranged from 0.2 to 0.8. 471
Our present aim was to equilibrate suspensions of enamel in fluoride buffers for an adequate period of time in order (a) to describe the possible reactions leading to equilibrium, (b) to investigate by X-ray diffraction the fluorhydroxyapatite obtained and (c) to study the solubility of the fluorhydroxyapatite solid solution. MATERIALS AND METHODS
Various amounts of powdered human dental enamel were suspended in 9 ml of a pH 4.50 buffer made from 50mM acetic acid-potassium acetate containing 6.4 mM fluoride. Control experiments used the same buffer without fluoride. pH was readjusted with perchloric acid. The enamel powder was prepared from caries-free enamel, freed from dentine with a bur. The enamel was crushed and ground in steel and agate mortars and sieved through a 170-mesh sieve to obtain a powder with a particle size less than 90pm. Dentine remnants and lowdensity enamel were removed by the flotation procedure of Manly and Hodge (1939). The various amounts of enamel used ensured that the molar ratio (R) between available fluoride and X-ion sites in the apatite (Table 1) ranged from 1 to 0.12. The equilibration was continued for 4 h, 24 h, 30 days or 365 days at 20°C with constant stirring. The solution calcium concentration was determined by the method of Willis (1961); phosphate was measured by that of Chen, Toribara and Warner (1956). The hydrogen and fluoride-ion activities were determined electrometrically by glass electrode (Radiometer@)), and ion-selective electrode (Orion@). For calculation of ion-activity products and degrees of saturation, the following constants were used: dissociation constants: phosphate, pK 7.21 (Bates and Acree, 1943); phosphate, pK 12.34 (Vanderzee and Quist, 1961). Stability constants for ion pair formation: CaH,PO:, K 3.67 (Gregory, Moreno and Brown, 1970); CaHPO,, K 264 (Gregory et al., 1970);
472
M. J. LARSEN and S. J. JENSEN 1. Concentrations,
Table
activities and negative logarithms in apatite suspensions Composition
of solution
C.-. (mti)
C, (mti)
a, (mM)
4.66 4.65 4.65 4.66
1.82 2.01 2.04 2.32
2.69 2.80 2.73 2.88
0.899 0.847 0.826 0.753
1.49 1.59 1.81 1.94 7.62
2.51 2.53 2.62 2.58 5.21
Sample
of ion-activity
products
after termination PI,,,
PI”,
Pk.4
9.1 9.1 9.1 9.2
63.1 62.9 62.9 62.5
56.8 56.6 56.6 56.3
0.758 0.784 0.758 0.673 -
9.3 9.3 9.3 9.3 -
64.1 64.0 63.9 63.7 59.8
57.8 57.6 57.6 57.4
4 h treatment: 0.97 0.68 0.47 0.25
Ah Bh ch
D,
24 h treatment:
1.15
Ad h D,
0.81 0.59 0.30
Od
0
4.58 4.58 4.54 4.56 4.58
0.85 0.59 0.47 0.22 0
4.54 4.47 4.52 4.51 4.52
2.06 2.49 2.70 10.41 23.10
2.27 2.23 2.09 6.47 13.99
0.579 0.469 0.294 0.001 -
9.4 9.5 9.9 14.3 -
63.8 63.9 63.4 59.5 57.1
57.6 57.7 57.5 56.0 -
1.00
4.53 4.51 4.56 4.51 4.48 4.52 4.49 4.49
2.49 2.63 13.80 18.12 23.10 22.95 24.60 31.23
3.36 2.60 11.48 11.24 13.99 13.45 15.08 18.69
0.395 0.226
9.7 10.1
-
-
-
-
63.0 63.3 58.0 57.8 57.4 57.1 57.1 56.5
56.9 57.5 -
Cd
I m treatment: ‘%I
B, C, % 0, 1 y treatment:
4 BY
0.68 0.50 0.25 0.16 0.12 0 0
CY D, E, FY 0, 0”
CaPO,,
K 2.9 x lo6 (Chughtai,
Marshall
and
Nan-
(pK = -log K): CaF,, pK 10.5 (McCann, 1968); CaS(PO,)jOH, pK 56.8 (Lindsay and Moreno, 1960); CaS(P04),F, pK 59.6 (McCann, 1968). The ion-activity products were calculated after 5 iterations of a series of subroutines to calculate the ratio between the concentrations of phosphate species, the concentration of calcium-phosphate ion-pairs, the ion strength and the activity coefficients. The amount of alkali-soluble fluoride formed on the enamel powder was determined by the method of Caslawska, Moreno and Brudevold (1975) using 1 M KOH. As most of this fluoride is assumed to be calcium fluoride, it is hereafter referred to as CaF,. After removal of CaF, by the KOH treatment, the ratio nFApI%, 2the molar fraction of OH- in hydroxyapatite substituted by F-, was determined by analysis of dissolved powder samples using the expression: denotes number of nFAp InAp = 5 x CF-/CCa>+ (n moles, FAp fluorapatite, HAp hydroxyapatite, Ap fluorhydroxyapatite and C molar concentration). X-ray diffraction analysis was made by means of a Nonius@ Guinier camera (FeKol, 30 kV, 15 h). Lattice constants of apatite were determined from the (002), (300), (310) and (004) reflections. CaF, was used as internal standard (a = 0.54634 nm). Densitometer curves were produced from a double-beam JoyceLoebl@ densitometer. collas,
1968).
Solubility
products
RESULTS At
the
initial
of the
equilibration
buffer, the liquids were undersaturated with respect to any salt. Due to the high soiubility of apatite at this low pH, the dental enamel started to dissolve and, after 4 h, the liquid phase became supersaturated with respect to calcium fluoride (Table l), which caused this salt to precipitate. Chemical analysis showed that most of the fluoride had reacted to form calcium fluoride, which in sample A amounted to about 6 per cent w/w of the total (Table 2). The amount was, however, not sufficient for an X-ray diffraction verification. Almost all samples equilibrated for 24 h and for one month were saturated with respect to calcium fluoride, supersaturated with respect to fluorapatite and undersaturated with respect to hydroxyapatite (Table l), which indicates a continuous formation of fluorapatite and a dissolution of hydroxyapatite, whereas calcium fluoride maintained the fluoride level by its dissolution. In experiment D, , the final dissolution of calcium fluoride is indicated by undersaturation with respect to calcium fluoride and the low fluoride-ion activity.
Table
A, &I ch
in the
pH 4.5
D,
2. Calcium
fluoride formed during equilibration
Weight of Ap + CaF, (mg)
Weight of CaF, (mg)
26.6 41.3 56.9 116.7
1.71 1.74 1.62 1.59
the first 4 h of
CaF, AP 0.064 0.042 0.028 0.014
473
Equilibration of enamel powder with buffer and fluoride Table 3. Lattice parameters and fluoride content of enamel after one year equilibration as determined by X-ray diffraction and chemical analysis X-ray diffraction a-axis (4
Before start A, BY CY DY EY FY 0, 0,
9.442 9.384 9.383 9.396 9.421 9.433 9.437 9.445 9.441
c-axis (‘Q
nFAp %
6.881 6.877 6.880 6.879 6.879 6.881 6.879 6.878 6.881
The composition of the liquid phases after 1 year of equilibration showed, for the experiments with the highest concentrations of fluoride, that the liquid was still saturated with respect to calcium fluoride, supersaturated with respect to fluorapatite and undersaturated with respeci to hydroxyapatite, indicating that equilibrium had still not been attained (Table 1 A,, By). When less fluoride was available, the fluoride activity ended below lower limit of detection, i.e. 10m6M. Consequently, no ion product for the fluoride containing salts could be calculated. The liquid in these samples had become almost saturated with respect to hydroxyapatite. Only small changes of the solubility of the salts (measured as l/5 x Cc,,+) in the samples C, through 0, were observed, despite the finding that the fluorapatite fraction of the apatite ranged from 0.001 to 0.73. Chemical analysis of the salts after 1 year of equilibration showed that, in most cases, all calcium fluoride was replaced by fluorapatite (Table 3). Completion of this change was accompanied by a drop in the fluoride-ion activity of the supernatant below the lower limit of electrode detection. Apparently, it was difficult to obtain an apatite with a fluori’de content higher than 33,000 parts/106, although the fluoride content of pure fluorapatite is 37,700 parts/106. The fraction of 01% substituted with fluoride in the enamel during the l-year treatment is given in Table 3 as nFAp/nAp. This ratio was determined both by chemical analysis and by means of the aparameter of the apatite unit cell by a linear interpolation between a = 0.9442 nm (enamel) and a = 0.9370 nm (fluorapatite). The results are in good agreement and indicate that fluoride was taken up during hydroxyapatite replacement by fluorapatite. Further, the low ncaF,/nAp ratio shows that almost all CaF, has been used in the formation of fluorapatite. Comparison of the initial F-/Ap ratios with nFAp/nAp in the solids after the treatment shows some variation. Figure 1 shows parts of the X-ray diffraction patterns of the enamel powder; the peaks in the F-containing enamel (A,) are displaced to higher angles compared with apatites without F (0,). The (300) reflection, and to a lesser extent the (211) reflection, of the apatites with a high F-content was not symmetic as was the case of F-free apatites; these reflections of the F-rich apatites terminate sharply on the high-angle side and fall off gradually in intensity on the low angle side.
Chemical analysis
0 0.80 0.82 0.63 0.28 0.17 0.06 0 0
%aFz __
*FAp %
%
0.060 0.020 0.0055 0.0035 0.0025 0.0017 -
0.76 0.89 0.73 0.36 0.17 0.14 0.003 0.003
DISCUSSION
The enamel powder passed through drastic chemical treatment, namely dissolution of apatite with calcium-fluoride formation, followed by a dissolution of calcium fluoride and of hydroxyapatite with fluorapatite formation. We used a rather low pH to speed up both processes; a low pH creates high calcium activity in the aqueous phase, which facilitates calcium-fluoride precipitation. A low pH further increases the solubility ratio between the hydroxyapatite and fluorapatite, which again favours the formation of fluorapatite (Larsen, 1974). The particle size was less than 90 pm with no lower limit. It may be assumed that the smallest particles were entirely dissolved at the initial dissolution, and that the larger particles were responsible for inhomogeneity of the fluoride distribution in the solid after the experiments (see below). The nFAp/nApin the final apatite differed from what was intended at the initiation (cf. Tables 1 and 3). Probably this change is due partly to the high solubility of the solid (which increases the +/n,, ratio by decreasing the actual amount of solid) and partly to the inevitable sampling of liquid for analysis during the year. Equilibrium was obviously not attained in the fluoridelapatite suspensions after one month of equilibration as indicated by the supersaturation, with respect to fluorapatite, and undersaturation, with respect to hydroxyapatite. After one year, equilibrium between the aqueous and the solid phase can be assumed in samples C,-O,. Table 1 shows that the amount of apatite in solution was low as long as the fluoride activity was measurable. The degrees of saturation indicate continuous formation of fluorapatite during hydroxyapatite dissolution. As soon as a shortage of dissolved fluoride stops the fluorapatite formation, the calcium and phosphate concentrations increase and the hydroxyapatite-ion product approaches the hydroxyapatite solubility-product. Apparently a final ratio of 0.7 (cf. sample C, Table 3) which nFAp corresponds to a fluoride content of enamel of 25,000 parts/106, does not decrease the amount of enamel apatite in solution by more than a factor of 2 (cf. C, and 0, Table 1). The results are in good agreement with the solid solution solubility calculations, as suggested by Berndt and Stearns (1973). According to the solid
in,,
M. J. LARSENand S. J.
JENSEN
6%
210
20.6
20.4
20.6
20.2
20 0 -e
(B)
21.0
20.8
20.6
20.4
20.2
20.0
: -0
Fig. 1. X-ray diffraction patterns of enamel powder. (A) Represents a fluor-free apatite (0,). Represents a F-rich apatite (A,,).
solution theory, the solubility products of hydroxyapatite and fluorapatite respectively are nHAp
a&+ x a&- x aoH_ = -
x KHAp
nap
and a&+ x a&
nFAp
x aF- = -
x KFAp
nap
which by division
give aOH~~_--_--aF-
nHAp nFAp
K HAP K FAP
(1)
Two aspects of the above may be of importance: the dOS nHAp/nAp and nrAp/nAr Will alWayS be less than unity, except for pure salts, the aqueous phase in a fluorhydroxyapatite suspension at equilibrium would theoretically be undersaturated, with respect to pure hydroxyapatite and fluorapatite. Secondly, if the above condition is not found in an apatite suspension, equilibrium seems unlikely. Inserting the solubility products, pH and nHAP/nFAp ratios from the experimental series C,-F, into equation 1 gives a fluoride activity of 10-‘2-10-‘3, which is far below the lower limit of detection. The equation indicates that studies on the solubility of fluorhydroxyapatite, including control of the fluoride ion, require a high pH of the solution. firstas
Comparison solid solution shows that the of the solid
(B)
of the ion products (C,-0,) and the solubility products, nHAp/nAp x K,,,, observed effects of the fluoride content is in excess of that calculated by nHAp/(nHAp + nFAp). This slightly increased effect of fluoride may be due to inhomogeneous distribution of fluoride in the solid. The lack of symmetry of the (300) reflection in the X-ray diffraction pattern of the F-rich apatites (AY and B, , Fig. 1) could be explained by supposing that the F-content in the powder was not evenly distributed, with a high content in the outer parts of the powder particles and a smaller amount in the central parts. This would be consistent with the existence of small amounts of solid CaF, (Table 2), indicating that the systems with the highest F-/Ap ratios have not reached a complete chemical equilibrium even after one year. improved crystalhnity could be expected in the F-rich apatites compared to the F-free apatites (Posner et al., 1963; LeGeros and Suga, 1980). Figure 1 does not show any sharpening of the peaks as a consequence of the higher F content; this could be explained either by the above-mentioned lack of symmetry of the reflections or on the basis that crystal growth or perfection demands a longer period of time. Our findings lead to two conclusions: equilibrium
Equilibration
of enamel
powder
in an enamel
(fluorhydroxyapatite) suspension is only attained slowly and yields, even in a fluoride-rich suspension, a fluoride activity in the aqueous phase of less than IO-” M. 7Nhen fluoride-ion activity is more than 10m6 M and I;he pH is below 7, an ongoing formation of fluorapati.te suppresses the enamel solubility until equilibrium is attained. The second conclusion to be drawn is of significance to dental caries. The solubility of enamel is little influenced by the fluoride content of the crystals once equilibrium is attained (exp. C,-O,), whereas fluoride present in the aqueous phase causes a marked reduction. The data indicate that the most important cariostatic action of fluoride results from its presence in the aqueous phase or as calcium fluoride in the enamel pores (Fejerskov, Thylstrup and Larsen, 1981; ten Cate, 1984). REFERENCES
Bates R. G. and Acree S. F. (1943) H values of certain phosphate-chloride mixtures, and the second dissociation constant of phosphoric acid from 0” to 60°C. J. Rex nam. Bur. Stand. 30, 129-155. Bemdt A. F. and Stearns R. I. (1973) The equilibrium between a solid solution and an aqueous solution of its ions. J. &em. Educ. 50, 415417. Carlstriim D. (1955) X-ray crystallographic studies on apatites and calcified structures. Acta radiol. 121, l-59. Caslawska N., Moreno E. C. and Brudevold F. (1975) Determination of the calcium fluoride formed from inairro exposure of human enamel to fluoride solutions. Archs oral Biol. 20, 3’3-339. Cate J. M. ten (1984) The effect of fluoride on enamel de and remineralization in &r-o and in uiuo. In: Cariofogy Today (Edited by Guggenheim B.) pp. 231-236. Karg&, Basei. Chen P. S., Toribara T. Y. and Warner H. (19561 Microdetermination of plosphorus. Analyt.‘ Ch;m. 28, 375&1758. Chughtai A., Marshall R. and Nancollas G. H. (1968) Complexes in calcium phosphate solutions. J. phys. Chem. 72, 208-2 11.
with buffer and fluoride
415
Fejerskov O., Thylstrup A. and Larsen M. J. (1981) Rational use of fluorides in caries prevention, a concept based on possible cariostatic mechanisms. Acta odont. stand. 39, 241-249. Glas J.-E. (1962) Studies on the ultrastructure of dental enamel. VI. Crystal chemistry of shark’s teeth. Odont. Revy 13, 315-326. Gregory T. M., Moreno E. C. and Brown W. E. (1970) Solubility of CaHP0,2H,O in the system Ca(OH),-H,PO,-H,O at 5, 15, 25, and 37S”C. J. Res. natn. Bar. Stand. 74A, 461-475. Larsen M. J. (1974) In uiwo studies of fluoride uptake in human enamel. &and. J. denl. Res. 82, 448-154. Larsen M. J., Jensen S. J. and Thorsen A. (1977) Calcium fluoride formation on enamel and its influence on uptake of fluoride in the apatitic lattice. Stand. J. dent. Res. 85, 327-333. Leach S. A. (1959) Reaction of fluoride with powdered enamel and dentine. Br. dent. J. 106, 133-142. LeGeros R. Z. and Suga S. (1980) Crystallographic nature of fluoride in enameloids of fish. Calc. Tissue Res. 32, 169-l 74. Lindsay W. L. and Moreno E. C. (1960) Phosphate phase equilibria in soils. Soil Sci. Sot. Am. Proc. 24, 177-182.
Manly R. S. and Hodge H. C. (1939) Density and refractive index studies of dental hard tissues. J. dent. Res. 18, 133-141. McCann H. G. (1968) The solubility of Auorapatite and its relationship to that of calcium fluoride. Archs oral Biol. 13, 987-1001. McConnell D. (1970) Crystal chemistry of bone mineral: hydrated carbonate apatites. Am. Miner. 55, 1659-1669. Moreno E. C., Kresak M. and Zahradnik R. T. (1977) Physiochemical aspects of fluoride-apatite systems relevant to the study ofdental caries. Caries Res. 11,142-171. Posner A. S., Eanes E. D., Harper R. A. and Zipkin I. (1963) X-ray diffraction analvsis of the effect of fluoride &I himan bone apatite. A&s oral Biol. 8, 549-570. Vanderzee C. E. and Quist A. S. (1961) The third dissociation constant of orthophosphoric acid. J. phys. Chem. 65, 118-123. Willis J. B. (1961) Determination of calcium and magnesium in urine by atomic absorption spectroscopy. Analyf. Chem. 33, 556559.
Copyright 0
0003-9969/85 $3.00 + 0.00 1985 Pergamon Press Ltd
AN X-‘RAY DIFFRACTION AND SOLUBILITY STUDY OF EQUILIBRATION OF HUMAN ENAMEL-POWDER SUSPE
Institute
of Der.tal
Pathology
J.
LARSEN
and S. J.
and Operative Dentistry Dental College, DK-8000
JENSEN
and Institute of Technology Aarhus, Denmark
and Physics,
Royal
Summary-Various amounts of enamel-apatite powder were suspended in an acetate buffer (pH 4.5) containing sufficient fluoride to give molar ratios of fluoride/apatite from zero to unity. The suspensions were equilibrate:d at 20°C for periods between 4 h and 1 year, with continuous gentle stirring. Solubility studies showed dissolution of hydroxyapatite, formation and re-dissolution of calcium fluoride and formation of fluorapatite. The amount of mineral dissolved was low during the fluorapatite formation and increased by a factor of approx. 10 as equilibrium was approached. The fluoride content of the solid apatite, which ranged from 0. I to 70 mol’% fluorapatite, only influenced the solubility slightly, whereas the fluoride content of the bathing solution had a large effect. X-ray diffraction showed a linear correlation between the fluoride content and the a-axis of the apatite.
INTRODUCTION
Chemical reaction between dental enamel and fluoride ions in aqueous solution causes calcium fluoride to be formed when the fluoride concentration is high (> 50 parts/106), and fluoride-containing apatite to be formed when the concentration is low (Leach, 1959). Larsen, Jensen and Thorsen (1977) exposed crowns of human premolar teeth to a pH 4 buffer containing 150 parts/lo6 F- and found that the reaction period could be divided into three parts. Initially, the solution became supersaturated with respect to CaF, causing this salt to precipitate; in the second stage, the solution became supersaturated with respect to fluorapatite; in the final stage, the liquid became undersaturated with respect to CaF, and this salt dissolved. X-ray diffraction of the outer layers of the teeth showed that CaF, was formed during the first stage and had disappeared after the third stage. The a-axis dimension of the unit cell of different apatites varies with the composition of the apatite, whereas the c-axis dimension is almost constant. McConnell (1970) proposed that atomic substitutions produce a proportional dimensional change of the apatite unit cell (Vegard’s law). Moreno, Kresak and Zahradnik (1977) fi3und the a-parameter to be a linear function of the degree of fluoridation of synthetic fluorhydroxyapatites. The a-parameter of human enamel is 0.9442 +_0.0005 nm (Glas, 1962) compared with 0.,9421 f 0.0001 nm in synthetic hydroxyapatite (Carlstriim, 1955). The difference is probably due to partial substitutions of OH- by H,O or H30+ (McConnell, 1970). The corresponding a-axis dimension of synthetic fluorapatite is 0.9370 * 0.0001 nm (Carlstriim, 1955). Moreno et al. (1!)77), using X-ray diffraction of controlled fluorhydroxyapatites, found a solubilitydepressing effect of fluoride after an equilibration period as long as one month. The effect was of particular significance when the nFAp/nApranged from 0.2 to 0.8. 471
Our present aim was to equilibrate suspensions of enamel in fluoride buffers for an adequate period of time in order (a) to describe the possible reactions leading to equilibrium, (b) to investigate by X-ray diffraction the fluorhydroxyapatite obtained and (c) to study the solubility of the fluorhydroxyapatite solid solution. MATERIALS AND METHODS
Various amounts of powdered human dental enamel were suspended in 9 ml of a pH 4.50 buffer made from 50mM acetic acid-potassium acetate containing 6.4 mM fluoride. Control experiments used the same buffer without fluoride. pH was readjusted with perchloric acid. The enamel powder was prepared from caries-free enamel, freed from dentine with a bur. The enamel was crushed and ground in steel and agate mortars and sieved through a 170-mesh sieve to obtain a powder with a particle size less than 90pm. Dentine remnants and lowdensity enamel were removed by the flotation procedure of Manly and Hodge (1939). The various amounts of enamel used ensured that the molar ratio (R) between available fluoride and X-ion sites in the apatite (Table 1) ranged from 1 to 0.12. The equilibration was continued for 4 h, 24 h, 30 days or 365 days at 20°C with constant stirring. The solution calcium concentration was determined by the method of Willis (1961); phosphate was measured by that of Chen, Toribara and Warner (1956). The hydrogen and fluoride-ion activities were determined electrometrically by glass electrode (Radiometer@)), and ion-selective electrode (Orion@). For calculation of ion-activity products and degrees of saturation, the following constants were used: dissociation constants: phosphate, pK 7.21 (Bates and Acree, 1943); phosphate, pK 12.34 (Vanderzee and Quist, 1961). Stability constants for ion pair formation: CaH,PO:, K 3.67 (Gregory, Moreno and Brown, 1970); CaHPO,, K 264 (Gregory et al., 1970);
472
M. J. LARSEN and S. J. JENSEN 1. Concentrations,
Table
activities and negative logarithms in apatite suspensions Composition
of solution
C.-. (mti)
C, (mti)
a, (mM)
4.66 4.65 4.65 4.66
1.82 2.01 2.04 2.32
2.69 2.80 2.73 2.88
0.899 0.847 0.826 0.753
1.49 1.59 1.81 1.94 7.62
2.51 2.53 2.62 2.58 5.21
Sample
of ion-activity
products
after termination PI,,,
PI”,
Pk.4
9.1 9.1 9.1 9.2
63.1 62.9 62.9 62.5
56.8 56.6 56.6 56.3
0.758 0.784 0.758 0.673 -
9.3 9.3 9.3 9.3 -
64.1 64.0 63.9 63.7 59.8
57.8 57.6 57.6 57.4
4 h treatment: 0.97 0.68 0.47 0.25
Ah Bh ch
D,
24 h treatment:
1.15
Ad h D,
0.81 0.59 0.30
Od
0
4.58 4.58 4.54 4.56 4.58
0.85 0.59 0.47 0.22 0
4.54 4.47 4.52 4.51 4.52
2.06 2.49 2.70 10.41 23.10
2.27 2.23 2.09 6.47 13.99
0.579 0.469 0.294 0.001 -
9.4 9.5 9.9 14.3 -
63.8 63.9 63.4 59.5 57.1
57.6 57.7 57.5 56.0 -
1.00
4.53 4.51 4.56 4.51 4.48 4.52 4.49 4.49
2.49 2.63 13.80 18.12 23.10 22.95 24.60 31.23
3.36 2.60 11.48 11.24 13.99 13.45 15.08 18.69
0.395 0.226
9.7 10.1
-
-
-
-
63.0 63.3 58.0 57.8 57.4 57.1 57.1 56.5
56.9 57.5 -
Cd
I m treatment: ‘%I
B, C, % 0, 1 y treatment:
4 BY
0.68 0.50 0.25 0.16 0.12 0 0
CY D, E, FY 0, 0”
CaPO,,
K 2.9 x lo6 (Chughtai,
Marshall
and
Nan-
(pK = -log K): CaF,, pK 10.5 (McCann, 1968); CaS(PO,)jOH, pK 56.8 (Lindsay and Moreno, 1960); CaS(P04),F, pK 59.6 (McCann, 1968). The ion-activity products were calculated after 5 iterations of a series of subroutines to calculate the ratio between the concentrations of phosphate species, the concentration of calcium-phosphate ion-pairs, the ion strength and the activity coefficients. The amount of alkali-soluble fluoride formed on the enamel powder was determined by the method of Caslawska, Moreno and Brudevold (1975) using 1 M KOH. As most of this fluoride is assumed to be calcium fluoride, it is hereafter referred to as CaF,. After removal of CaF, by the KOH treatment, the ratio nFApI%, 2the molar fraction of OH- in hydroxyapatite substituted by F-, was determined by analysis of dissolved powder samples using the expression: denotes number of nFAp InAp = 5 x CF-/CCa>+ (n moles, FAp fluorapatite, HAp hydroxyapatite, Ap fluorhydroxyapatite and C molar concentration). X-ray diffraction analysis was made by means of a Nonius@ Guinier camera (FeKol, 30 kV, 15 h). Lattice constants of apatite were determined from the (002), (300), (310) and (004) reflections. CaF, was used as internal standard (a = 0.54634 nm). Densitometer curves were produced from a double-beam JoyceLoebl@ densitometer. collas,
1968).
Solubility
products
RESULTS At
the
initial
of the
equilibration
buffer, the liquids were undersaturated with respect to any salt. Due to the high soiubility of apatite at this low pH, the dental enamel started to dissolve and, after 4 h, the liquid phase became supersaturated with respect to calcium fluoride (Table l), which caused this salt to precipitate. Chemical analysis showed that most of the fluoride had reacted to form calcium fluoride, which in sample A amounted to about 6 per cent w/w of the total (Table 2). The amount was, however, not sufficient for an X-ray diffraction verification. Almost all samples equilibrated for 24 h and for one month were saturated with respect to calcium fluoride, supersaturated with respect to fluorapatite and undersaturated with respect to hydroxyapatite (Table l), which indicates a continuous formation of fluorapatite and a dissolution of hydroxyapatite, whereas calcium fluoride maintained the fluoride level by its dissolution. In experiment D, , the final dissolution of calcium fluoride is indicated by undersaturation with respect to calcium fluoride and the low fluoride-ion activity.
Table
A, &I ch
in the
pH 4.5
D,
2. Calcium
fluoride formed during equilibration
Weight of Ap + CaF, (mg)
Weight of CaF, (mg)
26.6 41.3 56.9 116.7
1.71 1.74 1.62 1.59
the first 4 h of
CaF, AP 0.064 0.042 0.028 0.014
473
Equilibration of enamel powder with buffer and fluoride Table 3. Lattice parameters and fluoride content of enamel after one year equilibration as determined by X-ray diffraction and chemical analysis X-ray diffraction a-axis (4
Before start A, BY CY DY EY FY 0, 0,
9.442 9.384 9.383 9.396 9.421 9.433 9.437 9.445 9.441
c-axis (‘Q
nFAp %
6.881 6.877 6.880 6.879 6.879 6.881 6.879 6.878 6.881
The composition of the liquid phases after 1 year of equilibration showed, for the experiments with the highest concentrations of fluoride, that the liquid was still saturated with respect to calcium fluoride, supersaturated with respect to fluorapatite and undersaturated with respeci to hydroxyapatite, indicating that equilibrium had still not been attained (Table 1 A,, By). When less fluoride was available, the fluoride activity ended below lower limit of detection, i.e. 10m6M. Consequently, no ion product for the fluoride containing salts could be calculated. The liquid in these samples had become almost saturated with respect to hydroxyapatite. Only small changes of the solubility of the salts (measured as l/5 x Cc,,+) in the samples C, through 0, were observed, despite the finding that the fluorapatite fraction of the apatite ranged from 0.001 to 0.73. Chemical analysis of the salts after 1 year of equilibration showed that, in most cases, all calcium fluoride was replaced by fluorapatite (Table 3). Completion of this change was accompanied by a drop in the fluoride-ion activity of the supernatant below the lower limit of electrode detection. Apparently, it was difficult to obtain an apatite with a fluori’de content higher than 33,000 parts/106, although the fluoride content of pure fluorapatite is 37,700 parts/106. The fraction of 01% substituted with fluoride in the enamel during the l-year treatment is given in Table 3 as nFAp/nAp. This ratio was determined both by chemical analysis and by means of the aparameter of the apatite unit cell by a linear interpolation between a = 0.9442 nm (enamel) and a = 0.9370 nm (fluorapatite). The results are in good agreement and indicate that fluoride was taken up during hydroxyapatite replacement by fluorapatite. Further, the low ncaF,/nAp ratio shows that almost all CaF, has been used in the formation of fluorapatite. Comparison of the initial F-/Ap ratios with nFAp/nAp in the solids after the treatment shows some variation. Figure 1 shows parts of the X-ray diffraction patterns of the enamel powder; the peaks in the F-containing enamel (A,) are displaced to higher angles compared with apatites without F (0,). The (300) reflection, and to a lesser extent the (211) reflection, of the apatites with a high F-content was not symmetic as was the case of F-free apatites; these reflections of the F-rich apatites terminate sharply on the high-angle side and fall off gradually in intensity on the low angle side.
Chemical analysis
0 0.80 0.82 0.63 0.28 0.17 0.06 0 0
%aFz __
*FAp %
%
0.060 0.020 0.0055 0.0035 0.0025 0.0017 -
0.76 0.89 0.73 0.36 0.17 0.14 0.003 0.003
DISCUSSION
The enamel powder passed through drastic chemical treatment, namely dissolution of apatite with calcium-fluoride formation, followed by a dissolution of calcium fluoride and of hydroxyapatite with fluorapatite formation. We used a rather low pH to speed up both processes; a low pH creates high calcium activity in the aqueous phase, which facilitates calcium-fluoride precipitation. A low pH further increases the solubility ratio between the hydroxyapatite and fluorapatite, which again favours the formation of fluorapatite (Larsen, 1974). The particle size was less than 90 pm with no lower limit. It may be assumed that the smallest particles were entirely dissolved at the initial dissolution, and that the larger particles were responsible for inhomogeneity of the fluoride distribution in the solid after the experiments (see below). The nFAp/nApin the final apatite differed from what was intended at the initiation (cf. Tables 1 and 3). Probably this change is due partly to the high solubility of the solid (which increases the +/n,, ratio by decreasing the actual amount of solid) and partly to the inevitable sampling of liquid for analysis during the year. Equilibrium was obviously not attained in the fluoridelapatite suspensions after one month of equilibration as indicated by the supersaturation, with respect to fluorapatite, and undersaturation, with respect to hydroxyapatite. After one year, equilibrium between the aqueous and the solid phase can be assumed in samples C,-O,. Table 1 shows that the amount of apatite in solution was low as long as the fluoride activity was measurable. The degrees of saturation indicate continuous formation of fluorapatite during hydroxyapatite dissolution. As soon as a shortage of dissolved fluoride stops the fluorapatite formation, the calcium and phosphate concentrations increase and the hydroxyapatite-ion product approaches the hydroxyapatite solubility-product. Apparently a final ratio of 0.7 (cf. sample C, Table 3) which nFAp corresponds to a fluoride content of enamel of 25,000 parts/106, does not decrease the amount of enamel apatite in solution by more than a factor of 2 (cf. C, and 0, Table 1). The results are in good agreement with the solid solution solubility calculations, as suggested by Berndt and Stearns (1973). According to the solid
in,,
M. J. LARSENand S. J.
JENSEN
6%
210
20.6
20.4
20.6
20.2
20 0 -e
(B)
21.0
20.8
20.6
20.4
20.2
20.0
: -0
Fig. 1. X-ray diffraction patterns of enamel powder. (A) Represents a fluor-free apatite (0,). Represents a F-rich apatite (A,,).
solution theory, the solubility products of hydroxyapatite and fluorapatite respectively are nHAp
a&+ x a&- x aoH_ = -
x KHAp
nap
and a&+ x a&
nFAp
x aF- = -
x KFAp
nap
which by division
give aOH~~_--_--aF-
nHAp nFAp
K HAP K FAP
(1)
Two aspects of the above may be of importance: the dOS nHAp/nAp and nrAp/nAr Will alWayS be less than unity, except for pure salts, the aqueous phase in a fluorhydroxyapatite suspension at equilibrium would theoretically be undersaturated, with respect to pure hydroxyapatite and fluorapatite. Secondly, if the above condition is not found in an apatite suspension, equilibrium seems unlikely. Inserting the solubility products, pH and nHAP/nFAp ratios from the experimental series C,-F, into equation 1 gives a fluoride activity of 10-‘2-10-‘3, which is far below the lower limit of detection. The equation indicates that studies on the solubility of fluorhydroxyapatite, including control of the fluoride ion, require a high pH of the solution. firstas
Comparison solid solution shows that the of the solid
(B)
of the ion products (C,-0,) and the solubility products, nHAp/nAp x K,,,, observed effects of the fluoride content is in excess of that calculated by nHAp/(nHAp + nFAp). This slightly increased effect of fluoride may be due to inhomogeneous distribution of fluoride in the solid. The lack of symmetry of the (300) reflection in the X-ray diffraction pattern of the F-rich apatites (AY and B, , Fig. 1) could be explained by supposing that the F-content in the powder was not evenly distributed, with a high content in the outer parts of the powder particles and a smaller amount in the central parts. This would be consistent with the existence of small amounts of solid CaF, (Table 2), indicating that the systems with the highest F-/Ap ratios have not reached a complete chemical equilibrium even after one year. improved crystalhnity could be expected in the F-rich apatites compared to the F-free apatites (Posner et al., 1963; LeGeros and Suga, 1980). Figure 1 does not show any sharpening of the peaks as a consequence of the higher F content; this could be explained either by the above-mentioned lack of symmetry of the reflections or on the basis that crystal growth or perfection demands a longer period of time. Our findings lead to two conclusions: equilibrium
Equilibration
of enamel
powder
in an enamel
(fluorhydroxyapatite) suspension is only attained slowly and yields, even in a fluoride-rich suspension, a fluoride activity in the aqueous phase of less than IO-” M. 7Nhen fluoride-ion activity is more than 10m6 M and I;he pH is below 7, an ongoing formation of fluorapati.te suppresses the enamel solubility until equilibrium is attained. The second conclusion to be drawn is of significance to dental caries. The solubility of enamel is little influenced by the fluoride content of the crystals once equilibrium is attained (exp. C,-O,), whereas fluoride present in the aqueous phase causes a marked reduction. The data indicate that the most important cariostatic action of fluoride results from its presence in the aqueous phase or as calcium fluoride in the enamel pores (Fejerskov, Thylstrup and Larsen, 1981; ten Cate, 1984). REFERENCES
Bates R. G. and Acree S. F. (1943) H values of certain phosphate-chloride mixtures, and the second dissociation constant of phosphoric acid from 0” to 60°C. J. Rex nam. Bur. Stand. 30, 129-155. Bemdt A. F. and Stearns R. I. (1973) The equilibrium between a solid solution and an aqueous solution of its ions. J. &em. Educ. 50, 415417. Carlstriim D. (1955) X-ray crystallographic studies on apatites and calcified structures. Acta radiol. 121, l-59. Caslawska N., Moreno E. C. and Brudevold F. (1975) Determination of the calcium fluoride formed from inairro exposure of human enamel to fluoride solutions. Archs oral Biol. 20, 3’3-339. Cate J. M. ten (1984) The effect of fluoride on enamel de and remineralization in &r-o and in uiuo. In: Cariofogy Today (Edited by Guggenheim B.) pp. 231-236. Karg&, Basei. Chen P. S., Toribara T. Y. and Warner H. (19561 Microdetermination of plosphorus. Analyt.‘ Ch;m. 28, 375&1758. Chughtai A., Marshall R. and Nancollas G. H. (1968) Complexes in calcium phosphate solutions. J. phys. Chem. 72, 208-2 11.
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415
Fejerskov O., Thylstrup A. and Larsen M. J. (1981) Rational use of fluorides in caries prevention, a concept based on possible cariostatic mechanisms. Acta odont. stand. 39, 241-249. Glas J.-E. (1962) Studies on the ultrastructure of dental enamel. VI. Crystal chemistry of shark’s teeth. Odont. Revy 13, 315-326. Gregory T. M., Moreno E. C. and Brown W. E. (1970) Solubility of CaHP0,2H,O in the system Ca(OH),-H,PO,-H,O at 5, 15, 25, and 37S”C. J. Res. natn. Bar. Stand. 74A, 461-475. Larsen M. J. (1974) In uiwo studies of fluoride uptake in human enamel. &and. J. denl. Res. 82, 448-154. Larsen M. J., Jensen S. J. and Thorsen A. (1977) Calcium fluoride formation on enamel and its influence on uptake of fluoride in the apatitic lattice. Stand. J. dent. Res. 85, 327-333. Leach S. A. (1959) Reaction of fluoride with powdered enamel and dentine. Br. dent. J. 106, 133-142. LeGeros R. Z. and Suga S. (1980) Crystallographic nature of fluoride in enameloids of fish. Calc. Tissue Res. 32, 169-l 74. Lindsay W. L. and Moreno E. C. (1960) Phosphate phase equilibria in soils. Soil Sci. Sot. Am. Proc. 24, 177-182.
Manly R. S. and Hodge H. C. (1939) Density and refractive index studies of dental hard tissues. J. dent. Res. 18, 133-141. McCann H. G. (1968) The solubility of Auorapatite and its relationship to that of calcium fluoride. Archs oral Biol. 13, 987-1001. McConnell D. (1970) Crystal chemistry of bone mineral: hydrated carbonate apatites. Am. Miner. 55, 1659-1669. Moreno E. C., Kresak M. and Zahradnik R. T. (1977) Physiochemical aspects of fluoride-apatite systems relevant to the study ofdental caries. Caries Res. 11,142-171. Posner A. S., Eanes E. D., Harper R. A. and Zipkin I. (1963) X-ray diffraction analvsis of the effect of fluoride &I himan bone apatite. A&s oral Biol. 8, 549-570. Vanderzee C. E. and Quist A. S. (1961) The third dissociation constant of orthophosphoric acid. J. phys. Chem. 65, 118-123. Willis J. B. (1961) Determination of calcium and magnesium in urine by atomic absorption spectroscopy. Analyf. Chem. 33, 556559.