Calcif Tissue Int (1991) 49:6--13

Calcified Tissue International 9 1991 Springer-Veflag New York Inc.

Comparative Solubility Study of Human Dental Enamel, Dentin, and Hydroxyapatite E. C. Moreno and T. Aoba Physical Chemistry Department, Forsyth Dental Center, 140 Fenway, Boston, MA 02115, USA

Summary. The solubility properties of hydroxyapatite (HA) are compared with those of human dental enamel and dentin. The apatites used in this study were equilibrated with dilute phosphoric acid solutions in CO2-containing atmospheres. The experimental results are interpreted in terms of solubility models which consider the biological materials as either H A or carbonatoapatites. Both in the H A and the dental mineral systems, the results are consistent with the precipitation of another carbonate-containing apatitic phase during equilibration. However, although the chemical behavior of the H A systems is in very good agreement with predictions based on the solubility models, the results with the bioapatites are not; this inconsistency is more marked for dentin than for enamel but in both cases the results clearly indicate the inadequacy of assuming for these dental apatites the stoichiometry of HA. The models and the experimental results show that, in principle, it is possible to define the two dental minerals in terms of respective solubility product constants, if independent information is attained on the stoichiometry of these bioapatites.

Key words: Dental enamel - - Dentin - - Hydroxyapatite - Solubility - - Carbonate.

The physicochemical properties of dental enamel determine the stability of the tooth in the oral environment. Among these properties, the solubility of the enamel is of paramount importance with reference to the initiation of caries, remineralization processes, and the use of laboratory models to d e v e l o p c a r i e s - l i k e l e s i o n s in vitro. The few efforts to d e f i n e t h e s o l u b i l i t y o f e n a m e l , on t e r m s t h a t approach thermodynamic validity, have been made [1-3] on the assumption that the enamel mineral has a stoichiometry corresponding to hydroxyapatite, Ca5OH(PO4)3, HA. A similar assumption has been used when introducing models for incipient caries formation [4] or defining the degree of saturation of demineralizing buffers [5] with respect to dental enamel; in those works the assumption has been that enamel corresponds to an H A having a higher solubility product constant than that of the pure compound. Although such an approximation facilitates the development of demineralization models with a reasonable degree of predictability [5, 6], it introduces inconsistencies, particularly when comparing the chemical properties of different biominerals, such as enamel and dentin. Other investigators [1, 7] have opted for models based on mixtures of apatitic and nonapatitic minerals in ad hoc proportions to yield compositions in agreement with those of enamel or dentin; this approach, however, has not been successful in defining quantitatively these properties, like solubility, that are vital to the integrity of the tooth. The presence of carbonate in enamel and dentin has been

acknowledged [8-11] for a long time but completely ignored in the attempts to define the solubility of the enamel mineral. Most probably, the reluctance to consider carbonate in the definition of enamel solubility stems from difficulties related in part to ascertaining the stoichiometry of the mineral and in part to the actual experimentation required to obtain numerical values for this important property. Since enamel and dentin have relatively large specific surface areas, there is always the possibility that a significant fraction of the carbonate be present adsorbed onto the surface of the dental apatite crystallites. The adsorbed carbonate should not be considered in the equilibrium between the constituent ions in the liquid phase and the bulk of the dental apatite crystals, i.e., in the equilibrium used to define a solubility product constant for each of the minerals. Consequently, the correct stoichiometry to be used in the definition of solubility product constants can not be determined by a total analysis of the minerals. However, at least part of the carbonate in the bioapatites is present as a constituent of the crystalline lattice [8-10]; this means that the determination of their solubilities has to be done under controlled partial pressures of CO2 (otherwise, solubility measurements become a reflection of the experimental procedure rather than of the properties of the mineral studied). No such determinations have been made until now. The present work is an attempt to bridge this gap in our present knowledge. Enamel and dentin are considered here to be carbonatoapatites having a definite solubility product constant, the value of which, in principle, can be derived from experimental results, through valid thermodynamic considerations. Parallel experimental work using synthetic HA illustrates the difference in the chemical nature of this calcium phosphate and the crystalline phases of enamel and dentin.

Materials and Methods Dental Enamel Human permanent premolars and molars, extracted for orthodontic or by periodontal reasons, were used. The caries-free teeth were stored in deionized water containing 0.5% (v/v) chloroform at 4~ Prior to sample preparation, the enamel surface was thoroughly cleaned with pumice and a rotary rubber cup and cut transversally to separate the crowns from the roots. A slow-rotating dental burr was then used, under water, to grind out the dentin; the grinding was advanced well beyond the enamel-dentin junction. The hollow crowns were then placed in a sonicator with water (to remove fine debris), crushed, dried at room temperature, and ground with a mortar and pestle; the resulting powder was passed through a 270 mesh sieve and stored in a freezer until used. Table 1 shows the composition of the enamel used. Dentin Sound roots of molars and premolars were separated by the use of

E. C. Moreno and T. Aoba:

Solubility of Enamel, Dentin, and Hydroxyapatite

Table 1. Chemical composition of dental enamel, dentin, and hydroxyapatite (weight percent • SE) Sample

Ca

P

CO3

Mg

Na

K

F

Enamel Dentin HA

35.6 • 0.5 26.4 • 0.7 38.3 • 0.2

17.2 - 0.6 12.7 --- 0.3 18.9 • 0.7

3.6 --- 0.5 6.6 --- 0.6 .

0.28 • 0.01 0.84 -4- 0.01 .

0.72 • 0.03 0.50 • 0.01 .

0.05 -+ 0.01 0.03 • 0.01

0.008 --- 0.001 0.020 --- 0.003

.

a circular saw under cooling by running water. Enough exterior surface was removed, using a dental burr under water, to insure the removal of dental cementum. A similar procedure was used to remove all the predentin from the pulp space. The roots thus prepared were dried, ground, and sieved, as in the case of enamel. The mineral composition of the dentin used is shown in Table 1.

Synthetic HA The synthesis procedure has been described in detail [12]. The preparation appeared as elongated crystals of pure hydroxyapatite having an hexagonal cross section, a specific surface area of 6.39 m2/g, and a Ca/P molar ratio of 1.65 • 0.02.

Reagents The phosphoric acid solutions used in the equilibrations were prepared using reagent grade H3PO 4 (Fisher Scientific, ACS) in 0.1 M KNO 3 solution (the presence of background electrolyte facilitates the potentiometric measurements, i.e., determinations of pH values and Ca ionic activity). Six acid solutions with concentrations varying from 0.066 mM to 1.54 mM were used for HA equilibrations; the upper concentration limit for enamel and dentin equilibrations was 1.10 mM. Six N2-CO2 gas mixtures (ultra-pure quality, Granite State Oxygen, Nashua, NH) were used in HA and enamel equilibrations, covering a range of partial pressures of C O 2 from 5 x 10 -5 to 5 x 10 2 atm (0.005 to 5%; 5.06 to 5060 pascals). The gas mixtures (four) used in dentin equilibrations covered the range from 1.08% to 3.33%.

Equilibrations The physical setup is shown schematically in Fig. 1. The crystals (220 mg) of HA, enamel, or dentin were equilibrated with the phosphoric acid solutions (100 ml) in wide-mouth glass bottles partially immersed in water thermostated at 25~ --- 0.1~ The bottles had rubber stoppers with orifices for specific ion (calcium and glass) and reference electrodes, and glass tubing for the inlet and outlet of the gas mixture. The latter went from the steel cylinder into two saturation towers, in series, containing 0.1 M KNO3 solution and 0.5% (v/v) chloroform to minimize bacterial growth; in this fashion, the water vapor pressure of the gas was essentially the same as that within the equilibration bottles, thus minimizing liquid losses by evaporation. The gas went then into a manifold with 30 outlets connected to three ten-channel peristaltic pumps with Tygon tubes. Each channel was then connected to the glass inlet of one of the bottles and its outlet was connected to a common outlet manifold attached to a manostat. The latter was calibrated to operate with pressure differences of less than 1/2 mm Hg with respect to atmospheric pressure. The use of the peristaltic pumps insures that all the systems receive a continuous stream of gas, and, consequently, that the CO2 partial pressure is the same in all the systems. The total number of systems were 64 for HA, 85 for enamel, and 59 for dentin. The number of equilibrations with each acid and CO2 level is shown in Table 2. The bottles rested on submersible magnetic stirrers and their contents were maintained in suspension by a rotating magnetic bar. At intervals of 3-4 days, the pH value of the solution was determined and 1 mL of the suspension was withdrawn and filtered through a cellulose membrane (Millipore, 0.45 p.m) in a device coupled to a disposable syringe; the filtrate was chemically analyzed. Equilibrium conditions were assumed when the solution composi-

.

tion did not change significantly for a period of 3-4 days which took from 15 to 21 days.

Chemical Analyses Calcium was determined by atomic absorption spectrophotometry (AA). Standards were prepared (0.25, 0.50, 1.00, 1.50, and 2.00 mmols Ca per liter) in a 100 mM solution of KNO3; degassed, deionized water was used for all the dilutions and preparation of reagents. Samples and standards were diluted 1:40 with a solution containing 0.1% lanthanum (chloride form) and 0.09 M HC1 (to avoid any precipitation in the experimental samples). Magnesium was also determined by AA using a Mg lamp. Its contribution to the ionic strength, although small, was calculated [13] considering ion-pair formation with phosphate and bicarbonate ions. Sodium and potassium were determined by AA in the emission mode. Phosphorus was determined colorimetrically by the Gee-Deitz procedure [14] using fresh solutions of ammonium molybdate and vanadate for each set of samples. The uncertainties associated with the foregoing analytical determinations were estimated to be: Ca, 3%; P, 1.5%; Mg, K, and Na, 4%. For the determination of the calcium ionic activity, standards of CaC12 were used; the ionic strength of the standard solutions was calculated by the use of pertinent programs (although its numerical value was always very close to the concentration of the background electrolyte, 0.1 M KNO 3) and used in conjunction with a version of the extended Debye-Huckel limiting law [13, 15, 16] to calculate the calcium ionic activity coefficient. The latter, multiplied by the Ca concentration, yielded the ionic activity in that solution to be used for the standard curve [mVolts vs log(Ca2§ A specific calcium-ion electrode (Orion, no. 932001) and a reference electrode were used to determine the EMF in the standard solutions. These electrodes were then positioned in the appropriate orifices through the stoppers of the bottles holding the experimental systems, and, after stabilization (3 min), the EMF was recorded, from which the corresponding Ca 2+ activity was obtained via the standard curve. The Ca 2+ activity in the experimental solutions was also calculated using a generalized program, previously reported [13], that takes into account the formation of calcium ion pairs with phosphate and bicarbonate ions. The pH value of the experimental solutions was determined using a glass-reference combination electrode and a pH-meter (Orion, model 901) that had been calibrated with NBS buffers (7.415, 6.863, and 4.006, at 25~ The electrode was placed through the stopper of the bottles containing the experimental systems. The filling hole of the reference electrode did clear the stopper so that the salt bridge was exposed uniformly to the very small back pressure (less than 1 mm Hg) in the bottle. Stable readings were attained after 3 min of contact of the electrode with the solution. The uncertainty in the pH values recorded was estimated as 0.01 pH units.

Solubility Models The majority of the results reported in the present publication are consistent with equilibria involving two solid phases and the liquid phase. The second solid phase is formed in the presence of atmospheres containing significant amounts of CO2 (at and higher than 1%). For the sake of simplicity, it is assumed here that those systems can be defined in terms of the components H3PO 4 - Ca(OH)z - CO2 - H20, notwithstanding the presence of other constituents in dental enamel such as sodium and magnesium (a justification of this assumption is given in Results and Discussion). Therefore, the equilibrium of the liquid with two solid phases has one degree of

E. C. Moreno and T. Aoba: Solubility of Enamel, Dentin, and Hydroxyapatite

Plde~iri:::tdicPure0

//~

(~ (~

@~

Electrodes Magnetic Stirrers

Q Manostat

Fig. 1. Equilibrations set-up. Gas mixture passed through two saturating towers in series (not shown in diagram) connected to the manifold (1). Tubings from this manifold went to the head of the peristaltic pump (2) and from there (individually) to the equilibrating systems on top of stirrers (4). Electrodes (3) are inserted through rubber stoppers for determination of Ca 2+ activity or the pH value in the solution. Gas from every equilibrating system goes to another manifold that is connected to a manostat which, in turn, is connected to a barometer (not shown in diagram). All systems and manifolds were placed in a water bath thermostated at 25~ See text for details.

Table 2. Equilibration conditions for hydroxyapatite, human enamel, and dentin (with number of replicates indicated in parentheses) HaPO 4 concentration (number of equilibrations) mmol/L Sample

CO 2 %

HA

5.00 3.33 2.48 1.86 0.10 0.02 0.005 0.00 (N2)

Enamel

Dentin

5.00 3.33 2.48 1.86 1.08 O.lO 0.02 0.005

0.066

0.11

0.33

(2)* (2) (1)

(1) (2) (2) (2) (1)

(4)

(4)

(1) (2) (2) (2) (1) (1) (1) (2)

(2) (4) (3) (2) (4) (1) (1) (1)

(2) (4) (3) (I) (2) (2) (2) (2)

(1) (2) (3) (2) (2)

(3) (3) (2) (2)

(3) (2) (2) (2)

(3) (2) (2) (3)

(3) (3) (1) (2)

3.33 2.48 1.86 1.08

(3) (2) (2) (3)

freedom, i.e., specification of one of the variables determines the values of the rest of them. In this sense, these systems are similar to those in which the equilibrium involves a single solid phase such as Cas(OH)(PO4)3, HA, in the ternary system defined by the constituents enumerated before except for the CO2. In such systems the single degree of freedom is associated with the solubility isotherm of HA [3, 4, 17]; in fact, this is the case of equilibrations of HA, in a nitrogen atmosphere, equilibrated with dilute solutions of phosphoric acid, as reported here. The equilibrium condition in these systems can be described by the expression. (Ca2+)5(OH-)(PO43-) 3 = KHA

(1)

in which parentheses indicate activities of the species enclosed and KaA is the solubility product constant of HA. Through simple algebraic manipulations (introducing the ionization constant of water Kw), Eq. (1) may be written (Ca 2+ )5( O H ) and taking logarithms,

10

( H )+( P9 O 43 - ) 3 = KHAKw 9

(2)

1.54

Total number

(2)

3 9 12 11 4 3 3 19

0.55

0.66

1.10

(1) (2) (2)

(1) (2) (2) (1) (1) (1) (2)

(1) (1) (2) (2) (1) (1) (1) (3)

(1) (3) (1) (1) (2) (2) (2)

(2) (2) (3) (2) (2) (2) (2) (2)

7 16 18 9 13 7 8 7

(3) (2) (2) (3)

(3) (2) (2) (3)

18 13 12 16

(2)

(1)

log[(Ca2+)(OH )2] = 1/5 log KI_IAKw9 -- 3/5 log[(H+)3(PO43-)].

(3) The quantities within brackets in the left-hand and right-hand side of the equation are proportional to the chemical potentials (partial molar free energies) of calcium hydroxide and phosphoric acid, respectively. For this reason, Eq. (3) is referred to as the representation of a "potential plot." Indeed, if the condition of equilibrium is fulfilled, a plot of the values of the left-hand term versus the values of the bracket in the right-hand term should result in a straight line with a slope equal to the P/Ca molar ratio of the HA, i.e., with a value of -0.6. In systems containing H A and equilibrated with atmospheres containing CO2 at partial pressures higher than a given value, a carbonate-containing phase precipitates. For reasons given later (Results and Discussion), the stoichiometry adopted in the present work for the precipitating phase is indicated by the formulation C a s _ p ( O H ) 1 _ p ( P O 4 ) 3 p ( f O 3 ) p ; this formulation implies that the carbonate may be occupying lattice positions filled by hydroxyl and phosphate ions in HA. Consequently, these systems, at equilibrium,

E. C. Moreno and T. Aoba: Solubility of Enamel, Dentin, and Hydroxyapatite -17.0

should satisfy Eq. (1), i.e., saturation with respect to HA, and the condition of equilibrium (saturation) with respect to the precipitated phase; this latter condition is expressed here as (Ca2+)5-p(PO43-) 3 P(CO32-)P(OH-) I - p = KCA

(4)

in which KCA is the solubility product constant of the precipitated carbonatoapatite, CA. Dividing Eq. (1) by Eq. (4), making KHA/KcA = K, introducing the ionization constant of water Kw, and through a simple algebraic manipulation, one obtains, (Ca 2+)(OH-)E(H +)3(PO43-) (H +)2(CO32_ ) = KI/PKw.

-18.1] O

(5)

\

Calling Kg the equilibrium constant for the reaction HzO + CO2 = 2H + + CO3z-

(6)

in dilute systems so that the activity of water is not significantly different from unity (Kg = 7.07 • 10-19 was used in the calculations [18]), Eq. (5) can he written (Ca2+)(OH-)2(H+)a(PO43) - KI/PKgKw. Pco2

(7)

-20.0 -32.0

j -31.0

j -30.0

j -29.0

i~ -28.0

-27.0

log [(H ~)3(PO4~)]

Fig. 2. Results of HA equilibrations in nitrogen and CO2-containing atmospheres plotted according to Eq. (8). Nitrogen, open circles; 0.005% CO2, triangles; 0.02% CO2, squares; 0.13% CO2, filled circles. Regression line on the N2 treatments has a slope of -0.59.

Taking logarithms and transposing terms, log[(Ca2§

)2] = log KI/PKgKw + {log Pco2 - log[(H+)3(PO43 )]}.

(8)

Therefore, if the model adopted is correct, a plot of the left-hand term versus the quantity within brackets in the right-hand side should yield a straight line with a slope equal to unity. It is seen that the slope of such a line is in no way related to the stoichiometry of either of the two phases in equilibrium with the solution. The position of the line in the plot described by Eq. (3) is determined by the solubility product constant of HA whereas, in the case of Eq. (8), it is determined by the two solubility product constants corresponding to the equilibrated solid phases. Similar solubility models were adopted to study the solubility of human dental enamel and dentin. However, since it is known [9, 19] that both bioapatites contain significant amounts of acid phosphate in their crystalline structures, the adopted model [20] for both enamel and dentin assumes a stoichiometry corresponding to the formulation Ca5_x_y (HPO4)v (CO3)w (PO4)3-x (OH)I x 2y, with the restrictions that 0 ~< x ~< 2, y ~< 1 - x/2, a n d v + w = x. Experimentally, there were indications of precipitation of a carbonate-containing apatite during equilibration in the presence of CO2containing atmospheres, and there was no apparent reason to think that the precipitating phase was different from that formed during equilibration of HA under similar conditions. Consequently, the conditions for equilibrium are now given by Eq. (4) and (9) (Ca2+)5- x - Y(HP042 )v(CO32-) w (PO43-) 3 x ( O H - ) l - x - 2 y = KBA

(9)

in which KBA is the solubility product constant of the bioapatite. Combination of these two equations (and the stoichiometric condition w = x - v) yields [(Ca2+)(OH-)2]p x y[(H+)3(PO43-)]p = KBAKwP-V-WK3VKg p

W[Pco2]W-p W/KcA = I

(10)

in which K3 is the third ionization constant of phosphoric acid; this constant enters in the derivation because the activity of HPO42(see Eq. (9)) is expressed here in terms of the activity of PO4 3- (and the proton) and its numerical value was taken as 4.52 • 10-13 [17]. Taking logarithms and rearranging terms log[(Ca2+)(OH_)2] _

log I p-x-y p-w + p - x - y {log Pco2 -

log[(H+)3(po43-)]}.

(11)

Consequently, a plot of the left-hand term versus the term within brackets in the right-hand side of Eq. (11) should result in a straight

line the slope of which will be determined by the stoichiometry of the two phases in equilibrium with the solution. It is seen that Eq. (8) is a particular case of the more general Eq. (11) when w = x = y = 0, i.e., when the equilibrating phases are hydroxyapatite and a carbonatoapatite of the general stoichiometry assumed here for the precipitating phase. In applying Eq. (11) to the bioapatites, the more the slope of the linear plot departs from unity, the more the stoichiometry of the biomineral differs from that of HA. The position of the line in the plot, i.e., the value of the intercept, will depend on the solubility product constants of the bioapatite and the precipitating carbonatoapatite, as well as on the stoichiometry of these two phases.

Results and Discussion

The potential plot constructed from the experimental results of H A equilibrations in a nitrogen a t m o s p h e r e is shown in Fig. 2. The results appear to be in v e r y good a g r e e m e n t with the solubility m o d e l r e p r e s e n t e d by Eq. (3), i.e., by a congruent dissolution of H A . The Ca 2§ activity m e a s u r e d with the specific ion electrode was used to calculate the abscissa values in the graph; h o w e v e r , there was a good a g r e e m e n t (10% m a x i m u m discrepancy in H A , enamel, and dentin systems) b e t w e e n these ionic activities and those obtained by the speciation program m e n t i o n e d in Materials and Methods. The slope of the regression line for the points corresponding to the equilibrations under a N 2 a t m o s p h e r e has a slope of - 0 . 5 9 which is in v e r y good a g r e e m e n t with the value of - 0 . 6 predicted by Eq. (3). According to Eq. (3), the intercept of the regression line contains, as a factor, the solubility p r o d u c t constant, KHA, of the H A used in the equilibrations. The value of the intercept is - 36.41; therefore, using a value of 1.008 x 10-14 for the ionization constant of w a t e r [17], a solubility product constant of 8.5 (-+3.2) x l 0 - 5 7 is obtained for the experimental apatite. The uncertainty in the value of KHA was calculated from the error in the intercept, assuming that the error in Kw is negligibly small; this p r o c e d u r e o v e r e s t i m a t e s the uncertainty but it was adopted b e c a u s e the K H A calculated from the linear regression is the best value consistent with all the experimental data. Other p r o c e d u r e s [17] aimed at maximizing the internal c o n s i s t e n c y of experimental data and derived parameters therein involve the statistical adjustment of the f o r m e r within experimental errors. Such proce-

10

E. C. Moreno and T. Aoba: Solubility of Enamel, Dentin, and Hydroxyapatite

-17.0

O

~

9

"-" -18.s -I-

0

s f

O -18.0

-19.0 ~ ! 2 ~

~ -19.0

27.0

281.0

29.0 30.0 log I(H+)~(PO,~)I Fig. 3. Results of HA equilibrations in N 2 atmospheres containing log Pc,,~

-

various concentrations of CO2: 1.86%, open circles; 2.46%, triangles; 3.33%, filled circles. Regression line has a slope of 0.95; unitary slope predicted by Eq. (8).

dures are more involved and not necessarily better than the approach used in the present investigation, although they may yield more statistical information on the set of experimental data. The actual value obtained here for KI~A is within the range of values reported [21-23] for HA precipitated from aqueous solutions. In Fig. 2 are also plotted points the coordinates of which were calculated from the solution compositions of HA equilibrated with dilute solutions of phosphoric acid under very low partial pressures of CO2 (0.005% to 0.13%). The position of these points is consistent with a simple dissolution process of H A without formation of another solid phase. In fact, including these points in the linear regression yields a value of - 0 . 6 8 for the slope of the line; such a value is not statistically different from the value of - 0 . 5 9 reported in the previous paragraph or the value of - 0 . 6 anticipated by the solubility model (Eq. (3)). Evidently, at the very low partial pressures o f CO 2 used in these experiments, some effect is to be expected on the solution composition, but the activity of the carbonate ion was not sufficiently high to create a state of supersaturation with respect to any carbonated solid phase; for this reason, the points lie very close to the regression line in a plot that does not have the partial pressure of CO2 as a component of either coordinate. The results obtained in atmospheres more concentrated in CO2 display quite a different behavior, as indicated in the next paragraph. The potential plot derived from the equilibrations of H A under atmospheres containing COz from 1.86% to 3.33% is shown in Fig. 3. The coordinates used in this plot are those defined in Eq. (8) and imply equilibrium with respect to both H A and a carbonatoapatite formed during equilibration. The points lie reasonably close to the regression line shown in the figure, regardless of the partial pressure of CO2. This reduced scattering is consistent with the formation of the same carbonatoapatite in all of these experimental systems. In fact, as shown in Materials and Methods (Eq. (8)), the potential plot in this case should have a slope of unity; the slope of the regression line in Fig. 3 is 0.95 which was found not to be significantly different (P < 0.01) from unity. Points corresponding to a partial pressure of 5% CO2 were not used in this plot because the solution compositions were close to the saturation value for calcite and exhibited some inconsistencies suggesting precipitation of such a mineral. The corresponding potential plot for the systems equili-

27.0

.0 29.0 log P(',,2 - log I(H~)~(PO,~)l

30.0

Fig. 4. Results of enamel equilibrations in N2-CO2 mixtures plotted according to Eq. (8). Symbols as in Fig. 3. Regression line has a slope of 0.81. Squares, 1.08% of CO 2.

brated with powdered enamel is shown in Fig. 4. The experimental points describe a straight line, as it was the case in the equilibrations with HA, for systems equilibrated in atmospheres having partial pressures of CO2 equal to or greater than 1.86%. However, the regression slope of such a line in Fig. 4 is 0.81 which, for this set of points, is significantly different (P < 0.01) from the unitary value predicted by the model described by Eq. (8). Since there is no reason to think that the precipitating carbonated phase in these systems is different from the phase precipitating in those systems containing HA (Fig. 2), the departure of the slope from the unitary value must be related to differences in the chemical nature of enamel with respect to HA. The formation of another apatitic phase was also observed directly by examining the enamel crystals after equilibration using transmission electron microscopy. Figure 5 is an electron micrograph of enamel crystals that had been equilibrated with a 0.6 mM H3PO 4 and a partial pressure of CO2 of 1.86%. It is possible to see new crystalline projections stemming from the C-planes of the prismatic crystals. A similar mode of crystal growth has been reported [24] for dental enamel; the projections from the C-planes thicken with time and eventually fuse together, thus increasing the length of the original crystal. This kind of growth appears to be faster [12] than on the faces parallel to the C-axis. The enamel systems equilibrated at CO2 pressures of 1.08% seem to define a line not far from parallel (slope 0.95) to that already described in Fig. 4 but displaced upwards in the diagram. This observation alone (with a limited number of points) might not have been significant were it not for a similar behavior observed with the equilibrations using powdered dentin, as shown in Fig. 6. The lines described by the composition of the solutions at equilibrium with the biominerals are another evidence of the chemical difference of these materials and HA. Most probably this difference is due to the formation of a metastable, more soluble carbonatoapatite in the equilibrations with enamel and dentin at 1.08% C O 2 than that formed at higher CO 2 partial pressures; presumably, the levels of Ca and phosphate in solution were sufficiently high to form the metastable phase(s). As in the case of enamel, the regression line for the results obtained with the dentin systems equilibrated with CO2 partial pressures of 1.86% or higher (Fig. 6) has a slope (0.75) which is significantly different from the unitary slope predicted by Eq. (8).

E. C. Moreno and T. Aoba: Solubility of Enamel, Dentin, and Hydroxyapatite

11

Fig. 5. Electron micrograph of HA seed crystals after equilibration with 0.6 mM phosphoric acid and a nitrogen atmosphere containing 1.86% CO2. The projections from the C-plates are clearly seen. Horizontal bar = 0.1 Ixm.

The agreement between the solubility models and the experimental results is shown in Table 3, in terms of the slopes predicted by the models and those of the regression lines. It is apparent that, while the agreement between predicted and experimental slopes is excellent for the H A systems (in the absence and presence of CO2), it is poor for the bioapatite systems. Furthermore, the agreement is worse for dentin than for enamel. Clearly, the present results indicate that the solubility model described by Eq. (8) does fit the experimental results obtained with H A but it does not fit those obtained with the biominerals; consequently, to assimilate the chemistry of enamel and dentin minerals to that of H A is not consistent with the properties reported here. The alternative solubility model described by Eq. (11) cannot be assessed at present from the linear regression because there are more than two variables in the quantities defining the slope and the intercept. It seems that if the carbonate and acid phosphate contents (i.e., w and v, respectively) in the crystalline lattice of the bioapatites were determined, valuable information could be derived to ascertain the validity of the proposed model. Under those conditions, the value of KBA (the solubility product constant of the bioapatite) could be calculated directly for each and all of the equilibrated systems; the constancy in these values would be a measure of the soundness of the model. Furthermore, since x = v + w, the parameter y could be determined from the electroneutrality condition for the stoichiometry of the solid, and the carbonate content,

-19.0

27.0

2~.0

J 29.0

30.0

log P,:oz - log [(H+)~(PO,~)I

Fig. 6. Results of dentin equilibrations in N2-CO2 mixtures plotted according to Eq. (8). Symbols as in Fig. 3. Regression line has a slope of 0.75. Squares, 1.08% of CO 2.

p, of the precipitating phase could be calculated from the value of the regression slope. The value of KCA could then be calculated from the value of the regression intercept. The reasonableness (or lack of it) of all the parameters calculated in the outlined fashion would provide a basis to judge the adequacy of the selected model or to adopt other alterna-

E. C. Moreno and T. Aoba: Solubility of Enamel, Dentin, and Hydroxyapatite

12 Table 3. Comparison of slopes in potential plots

Slope System

Atmosphere

Predicted

Experimental

Hydroxyapatite Enamel Dentin

Nz N 2 -{-

- 0.6 1.0 1.0 1.0

- 0.59 0.95 0.81 0.75

CO 2 N 2 + CO 2

N2 + CO2

tives. Work in this direction is being conducted in our laboratories. In the present work, necessary approximations were made in the solubility models adopted to show the differences in the chemical behavior of synthetic HA and the biological apatites. Probably the most questionable of the approximations made was to ignore other lattice constituents different from Ca 2+, O H - , PO43-, and CO32 for the biomaterials; the analysis of the sodium content in the enamel and dentin used was considerable (see Table 1). Nevertheless, it would be very different to ascertain whether the precipitating apatite contains sodium (from the partial dissolution of the original sample used in the equilibration) and the extent to which this N a occupies lattice positions. It appears, however, that the contribution of the sodium to the solubility properties of the apatite is rather minor by comparison with that associated with carbonate. Using thermodynamic data from the same source [25] for the sake of consistency, it is possible to calculate that the standard free energy of solution of H A is 357.26 kJ which, in absolute value, is only 5.6% of the free energy of formation ( - 6338.5 kJ) of HA. In other words, the free energy of HA originates almost totally from the presence of the various ions rather than from their relative position in the crystalline lattice. It seems reasonable, then, to assume that the contribution of each ion to the H A free energy of formation is proportional to its own standard free energy of formation (the proportionality constant was calculated as 1.06), since the latter quantity presumably reflects differences due to charge and size which also affect their contribution to the free energy of the lattice. If we now consider the two hypothetical compounds Ca4OH(PO4) 2- COaNa and Ca4OH(PO4)2CO3H, it can be calculated that their standard free energies of solution would be 309.01 kJ and 294.63 kJ, respectively. The difference between these two values is related only to the sodium since, by convention, the free energy of formation of the proton is taken to be zero. Consequently, the contribution of the Na ion to the significant change in the free energy of solution when the carbonate and sodium are incorporated into the H A lattice amounts to only 4% [(309.01 - 294.63) • 100/357.26], whereas 96% of the change is associated with the carbonate (and the required changes in the stoichiometry to keep electrical neutrality). Since the solubility properties of the apatites are directly related to their standard free energies of solution, it seems justifiable, as a first approximation, to ignore the sodium (and other possible minor constituents) in the present solubility models. An i m p o r t a n t c o n s i d e r a t i o n , brought a b o u t by the p r e s e n t results, pertains to the stability of carbonatecontaining apatite versus HA. The predominant view [26-31] is that introduction of carbonate into the crystal lattice increases the instability of apatite; this may be the case with reference to environments deprived of CO2. However, in the presence of CO2, the H A actually dissolves in the aqueous

medium and carbonatoapatite precipitates. In other words, the carbonated phase is more stable than HA. Since in biological systems, the presence of carbonate is the rule rather than the exception, it is not surprising that in most species a carbonate-containing apatite be the tooth mineral [8-11, 19, 32, 33]. F o r example, it was recently reported [34, 35] that the fluid from which porcine enamel precipitates contains about 10 mM total carbonate (a concentration higher than those of calcium and phosphate in the same fluid) which, it was calculated, would correspond to a partial pressure of 1.8%; the carbonate content of mature porcine enamel was 3.6%, the same as in the human enamel used in the present investigation (see Table 1). It is very interesting that the use of atmospheres containing more than 1.8% in CO 2 yielded results compatible with the formation (during equilibration) of the same carbonatoapatite although its actual stoichiometry is unknown at present. It is not possible to ascertain the actual stoichiometry of the dentin mineral on the basis of the present results. However, since the specific surface area of dentin is considerably higher than that of enamel, it is possible that a significant part of the carbonate content (6.6%) in dentin be present as adsorbed on the crystallite surfaces. The disagreement between the slope for the plot for dentin (Fig. 6) and the unitary slope predicted by Eq. (8) is greater than for the enamel plot (Fig. 4). These relative differences seem to indicate that the minerals in the two dental apatites have different solubility properties. Such a result has important implications for the planning of comparative in vitro studies of the kinetics of enamel and dentin demineralization. Such studies should be conducted under equal driving force for dissolution, i.e., in solutions having the same degree of undersaturation with respect to the mineral. Clearly, if the two minerals are different, using the same buffer solution to demineralize does not equalize the driving force for dissolution. Consequently, a faster development of caries-like lesions in tooth roots could be ascribed either to a more soluble mineral or to the greater porosity of dentin. A definitive clarification of this point requires a better definition of the mineral phases than that provided by the present investigation. The results of this investigation show that the solubility properties of human enamel and dentin are different from those of HA. However, a better characterization of the biominerals, e.g., by defining a solubility product constant, is not as yet possible. To such an end, additional work on the stoichiometry of the dental apatites is necessary and it is being conducted in our laboratories.

Acknowledgments. The authors are indebted to Ms. Sharon Norton for valuable technical assistance. This investigation was supported by grants DE-7009, DE-3187 and DE-8670 from the National Institute of Dental Research and a grant from the Colgate-Palmolive Company. References

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