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JOURNAL O F RESEARC H of the National Bureau of Standards - A. Ph ys ics a nd Chemistry Vol. 72A, No. 6, N ovember- December 1968

Preparation and Solubility of

E. C. Moreno,* T. M. Gregory,* and W. E. Brown*

Institute for Basic Standards, National Bureau of Standards, Washington, D.C. 20234

(August 2, 1968)

Two portions of a syntheti c hydroxyapatite (HA), Ca" OH(PO'}J, full y characterized by x-ray, infrared, petrographi c, and chemi cal anal yses, were heated at 1,000 °C in air and steam atmospheres, respectively. Solubility isotherms for these two samples in the syste m Ca(OH}2 -H3PO,-H20 were determined in the pH range 5 to 7 by equilibrating the solids with dilute H3 PO. solutions. Both sam­ ples of HA disso lved stoichiometrically. The activity products (Ca + +)'( OH - ) (pO~f' and their standard errors-obtained by a least squares adjustment of the measurements (Ca and P concentrations and pH of the saturated solutions) subject to the conditions of electroneutralit y, constancy of the activity product, and stoichiometric dissolution - were 3.73 ± 0.5 x 10- 58 for the steam-h eated HA and 2_5, ± 0.4 x 10- 55 for the air-heated HA. Allowance was made in the calculations for the presence of the pairs [CaHPO. lo and [CaH2P04 1+ The hi gher solubility product for the air-heated HA is as­ cribed either to a change in the heat of formation brought about by partial dehydration or to a state of fine subdivision resulting from a disproportionation reacti on_ The solubility product constant s were used to cal culate the points of intersection (i.e_, sin gular points) of the two HA solubility isot herms with the isotherms of CaHPO. ·2H20 and CaHPO.; it was found that the pH's of the sin gul ar points for the air-heated HA were a full unit hi gher than those of the steam-heated preparation_ Conditions are described for the precipitation of HA suitabl e for solubility measuremen ts_

Key Words: ; hydroxyapatite; ; solubili ty; olubility isotherms; solubility product.

1. Introduction based on the stoi chi ometry of the salt. Among the models th at have been advanced to explain the

Hydroxyapatite (HA), CasOH(P0 4 h, has wide apparent anomalous behavior of HA in aqueous solu­ biological and industrial importance. Its physico­ tions, those advocating formation of complexes on the chemical properties, in particular solubility and de­ surface of the solid [5 , 8J have received considerable tailed crystallographic structure, are directly related attention. These models implicitly assume that to the mineralization processes in biological systems. equilibrium between the solid and the liquid phases The various reports in the literature on solubility of is not achieved with the crystalline portion of the HA, HA are contradictory. Clark [l J, Ion the basis of but instead with surface layers having quite different precipitation and dissolution experiments, concluded chemical composition from that of the bulk of the that HA has a definite solubility product. Thermody­ solid. Furthermore, the compositi on of such layers namic functions for HA (from whi ch a solubility prod­ has been assumed to be co nstant over a wid e range of uct constant can be calculated) have also been reported calcium, phos phorus, and hydrogen concentrations [2 , 3, 4]. Other reports [5- 8], however, claim that in th e liquid phase. systems saturated with respect to HA do not con­ At least part 01 th e proble m in the interpretation form to the principle of a solubility product constant of data on solubility of HA is related to the difficulty in preparing pure samples of this compound. So *Research Associates from the A me ri can Dent al Associati on of the Nati onal Bu rea u far, the best crystals have been obtained by hydro­ of Stand ards, Washington, D.C. 20234. This investi gat ion was support ed in part by Research Grant s DE- OJ8J9 and DE-02659 thermal methods, but the yields are smail, the equip­ to th e Ameri can Dental Associati on fr om th e National In stitute of Dental Research and is part of th e de nt al research program condu cted by the Nati onal Bureau of Stand ards, in ment is relatively expensive and the product may cooperation with th e Council on De ntal Research of th e Am erican De nt al Associati on­ contain extraneous phases such as ,B-calcium pyro­ th e National Instit ute of Dent al Researc h; th e Arr..y De ntal Corps; th e Aerospace Medicai Division, USAF School of Aerospace Medi cin e; and the Veterans Administration. and/or ,B-. Direct I Figures in brackets ind icate th e literature references at th e end of thi s pape r. precipitation methods usually yield very fin ely divided

773 products, often without the stoichiometric composition the reaction vessel for petrographic examination of of HA. A particularly serious difficulty is contamination the solid and pH determination of the liquid. by precipitation of the more acid calcium phos­ Initially, 9 1 of N ammonium acetate solution were phates, among which octacalcium phosphate (OCP), boiled in the reaction vessel for about 12 hr to remove CaSH 2(P04}6 • 5H20 and its decomposition products CO2 ; then ammonia gas was passed in until the pH are the most difficult to eliminate. reached a value between 8.5 and 9, and the pumping T he purposes of thi s work were (a) to devise a sim­ of the phosphate and calcium solutions was started, ple method for preparation of HA that would yield maintaining vigorous boiling. The pH was maintained sufficiently large and pure crystals so that an un­ between 8.5 and 9.5 (measured at room temperature) ambigious characterization would be possible, (b) by an adequate flow of NH3 until the total volume of I to learn whether this compound behaves as a normal the solutions was pumped into the reaction vessel; chemical compound with unique thermodynamic then the flow of NH3 was discontinued but boiling properties when equilibrated with aqueous solutions, was continued for about 3 hr. The solid was allowed and (c) to establish its solubility isotherm and solu­ to settle, the supernatant liquid was withdrawn, bility product constant at 25°C. about 9 1 of boiled distilled water were introduced and the mixture was boiled for about 2 hr. This 2. Experimental Methods and washing operation was repeated as was deemed nec­ Procedures essary to remove the soluble salts (usually five times). Further washing was done by decantation, using boiled distilled water and short settling periods so In the method of preparation outlined here, the as to discard as much as possible the finest fraction possibility of OCP precipitation is minimized by the of the precipitate. Precautions to avoid contami­ use of relatively high temperature and pH. However, nation by atmospheric CO2 were taken during all pH values higher than 10 are avoided because they these operations. The suspension was then filtered seem to favor the formation of very finely divided and the solid was dried at 150 °C for 48 hr. As ex­ precipitates. Other conditions are (a) slow addition plained in section 3, a portion of this sample was of reagents to reduce continuous nucleation, (b) heated at 1,000 °C in air and another portion was heated high ionic strength and the presence of acetate at the same temperature in steam at one atmosphere. (a Ca complexing agent) to increase the solubility of HA, and thus to favor formation of larger crystals, (c) use of a large reaction vessel to perform the pre­ 2.2. Equilibrations cipitation without sacrificing yields, and (d) special Equilibrations were made in glass-stoppered bot­ precautions to avoid contamination with carbonate tles, each of which contained 5g of HA and 120 ml from the atmosphere or reagents (ammonia was used of a solution, by slowly rotating end­ to control the pH instead of NaOH or KOH because over-end in a water bath at 25 ± 0.1 0C. After two the alkali are difficult to obtain free of weeks, the suspension was transferred to a thermo­ carbonate contamination). stated saturator, described in an earlier publication [9], in which the pH of the clear filtered solution was 2.1. Prepara tion of HA measured. Samples of this solution were taken for calcium and phosphorous analyses. Standardization Freshly boiled distilled water and chemically of the pH-meter (with claimed relative accuracy pure salts were used to prepare 2.5 liter of 7.25 X 10- 2 of ± 0.0037 pH units) was made with certified NBS M (NH4}zHP04 solution and 2.5 liter of 13.33 X 10- 2 M buffer standards [10]. Ca(N0 ·4H20 solution; their pH's were adjusted 3h Phosphoric acid solutions used in the equilibra­ with ammonia gas to 8.5-9. These solutions were tions were prepared from doubly crystallized stored in borosilicate glass bottles vented through 2~P04 . H2 0 and freshly boiled conductance water. ascarite tubes. The molarities of the final solutions were determined The reaction vessel was a 22-1, 3-neck, borosili­ by chemical analyses. cate glass flask. A 4-ft condenser was attached to one neck; transfer of reagents and materials was done through the other two necks. The top of the condenser 2.3. Calcium and Determinations was connected by a glass tube to a 6-1, 3-neck flask containing 3 liters of 10 N NaOH solution; a check Calcium was determined colorimetrically by the valve permitting outward flow of gases was con­ indirect technique described by Banerjee et al. [llJ. nected to one neck and a tube, extending into the N aOH Phosphorus was determined using the vanadomolyb­ solution and acting as a relief valve, entered through date reagent of Brabson et al. [12]. In both analyses, the third neck. The reactant solutions were introduced samples were compared directly with blanks and into the large vessel by a peristaltic pump at a rate standards in a double-beam spectrophotometer. of 100 ml/hr. Ammonia gas was passed through an The analytical errors estimated for the measure­ ascarite tower and then bubbled through water be­ ments reported here were: pH, ± 0.009 units; calcium fore entering the reaction vessel. Samples were with­ ± 2.5 percent; and phosphorus, ± 1.5 percent of the drawn through a tube that extended to the bottom of amounts analyzed.

774 3. Characterization of the Solid The infrared spectra of the heated samples were very similar, both corresponding to pure HA [14J but The HA was characterized by petrographic, gas­ the height of the peak at 3,570 cm- I was considerably greater for the steam-heated sample, indicatin g either , chemical, infrared and x-ray methods_ Under the petrographic microscope, the crystals a more uniform environment for the OH- group in appeared as masses of birefringent, irregularly shaped this sample or actually a higher content of OH- in equant particles up to 5 fJ-m in diameter- Present, also, the crystals. was a minor fraction of thin needles up to 10 fJ-m in Another sample of HA, referred to here as "as length_ The mean index of refraction (white radiation, prepared" was synthesized according to the method 25°C) was 1-636 with a standard error of±0_002. The described above, but it was not subjected to high material was petrographically homogeneous, both the temperature treatment. equant particles up to 5 fJ-m in diameter. Present, also, HA. The mean index is lower than the indexes usually given for HA prepared hydrothermally, N. = 1.644 and 4. Calculation of Solubility Product Nw = 1.651 [37J, but this appears to be a character­ Constants istic of precip:itated HA. The treatments at 1,000 °C did not change the mean indexes significantly. The solubility product constants, The surface area determined by the BET procedure,2 using nitrogen as the adsorbate, yielded a surface area of 6 m2 / g. Although this area is 5 to 10 times larger than that expected from microscopic examination, the where parentheses denote ionic activities, were cal­ agreement is reasonable considering the uncer­ culated by a procedure very similar to the one de­ tainties inherent to the two methods. scribed elsewhere [9]. The values are listed in tables 1, Chemical analyses yielded 18.22 ± .27 percent P 2, and 5. However, it was recognized that the best and 39.63 ± 0_ 99 percent Ca, the indicated errors values to be derived from such data must take into being calculated on the basis of the estimated standard account more completely the propagation of errors errors of the analytical procedures employed_ These and the proper weight of the measurements. A more values compare with the theoretical values 18.50 refined method was devised, therefore, for these percent P and 39.89 percent Ca for HA. calculations which entails the simultaneous ad­ The infrared spectrum displayed all the bands justment of the weighted observables-i.e., calcium characteristic of well-crystallized HA [14] _ Small and phosphorus concentrations and pH's in the various bands in the regions of 1410 and 1640 cm- I indicated equilibrated solutions plus the initial concentration slight contamination with carbonate and moisture, of H3P04-and the determination of a parameter respectively. Analysis by the Warburg method yielded which yields best estimates of Ksp. The main features 0.04 percent CO2 • of the method follow the general least-squares adjust­ The x-ray diffraction pattern was sharp and charac­ ment discussed by Deming [15] and they are similar teristic of that for pure HA [13] _ No extraneous peaks to those recently presented by Wentworth et a1. were found. [16] for the calculation of complexing constants Although the above methods to characterize the HA using spectrophotometric data. However, for the pres­ did not reveal the presence of extraneous phases, when ent work, two or three condition functions were used a sample of the HA was heated to 1,000 °C for 24 hr, instead of one. A detailed account of the method the infrared spectrum showed small peaks in the will be given elsewhere [17]. It suffices here to give region 920 to 1,200 cm- I . These peaks indicate the the three condition functions used in this investiga­ presence of ,B-Ca3(P04h [14], which presumably tion, based on electroneutrality, the ~olubility prod­ formed on heating from a contaminant, an acid cal­ uct for HA, and congruency in the dissolution of the cium phosphate. solid, respectively, A portion of the HA, therefore, was heated at 1,000 °C for 6 days in room atmosphere to anneal the (H+) Kw crystals, to drive off carbon dioxide and moisture, 2[M-TJ+-J, +RT-(H+){ o (1) and to convert the less basic into H+ VOH - ,B-CaAP04h . Following the heat treatment, the sample 3 was extracted with 2 X 10- M H3P04 to remove the (2) ,B-Caa(P04h. Approximately 10 percent of the sample was dissolved by this treatment. Another portion of the HA was subjected to the same heat treatment but in the presence of one at­ mosphere of water vapor, and then extracted with the (3) H3P04 solution. in which M and P are the total molar concentrations of Ca and P in solution, respectively; (H+) is the ac­ tivity of the hydrogen ion; f is the molar activity

2 Measurement made by Dr. W. V. Loebenstein, NBS. coefficient of the subscripted species; Kw and Ka

775 are the dissociation constants of water and the third ionization constant of H3 P04 , respectively; Po is the initial molar concentration of H3 P04 ; S is the parameter to be calculated , its value being the best (11) estimate of Ksp; the fraction ' 5/3 is the theoretical Ca/P ratio in HA; 7 is the total molar concentration in which of Ca or P present as the ion pairs [CaHP04 ]O and [CaH2 P04]+ [9] and it is defin ed , as 'are the quanti­ ties L , QI , Q2, and R , by the expressions, Q:l = (H+) +_4_ + 9K:l (12) KdH 2PO~ IHPO; (H + )/po~ 7= 0/2 M+l/2 P+L) The values for the ionic activity coefficients were ca~c ulated .by the use of the Debye-Hiickel theory - V (1/2 M + 1/2 P+L)2- MP (4) usmg the dIstances of the closet approach given in the appendix. The iterative procedure, starting with uni­ tar~ activity coefficients, reported in previous publi­ (5) catIOns [9, 18] was used for these calculations. The activity coefficients Ix and IH po were taken to be +y3 = unity, and it was assumed that J! 4j,H2PO, _.

= (H+) +_2_+ 3Kl 5. Results Q (6) I KJ + - (H+)+ _ "lJ H2PO 4 J HPO ~ J PO ;f S.l . Solubility of HA The experimental results for the steam-heated and air-heated preparations are given in tables 1 and 2 (7) respectively, along with the values of KSfJ calculated from these results using the activity product that ap­ pears as the leading term in eq (2). The spread in Ksp (8) in each table is acceptably low even though the aver­ age Ksp for the steam-heated material, table 1, is three orders of magnitude less than that for the air-heated material, table 2. The other tests that can be applied In eqs (4--8), KI and K2 are the fir st and second ioniza­ to these data - apparent electroneutrality unbalance, . tion constants of H: I PO~ , respectively, and Kx and Ky stoi chiometry of the dissolution reaction, and smooth­ are the association constants for the ion-pairs ness of the plots of Ca or P versus pH - also show [CaHPO~] O and [CaH2PO.I] +. A list of the numerical deviations which are within the anticipated experi­ values for the various constants used in this investi­ mental errors, thus vouching for the validity of the gation is ~iv e n in the appendix. results. In tables 3 and 4 are given the adjusted values The three condition functions, eqs (1-3), were fo~ the three observables, Ca, P, and pH, and the used to obtain the best estimates of Ksp for the pre­ adjusted values of Ksp , electroneutrality and the heated (in air and steam). Condi­ ratio Ca/P of the dissolution reactions. It is clear tion (3), defining stoichiometric dissolution, was that the adjustments in the Ca, P , and pH values are excluded for the calculations with HA " as prepared" within their anticipated experimental errors. The fact because phosphate was adsorbed in some of these that these adjustments are small is further confirmation equilibrations, as explained in section 5.1. of the internal consistency of the data. We believe that Equation (4) was obtained from the simultaneous the best estimate of the two K SfJ's obtained by the solution of eqs (9) and (10) which describe the equi­ adjustment procedure (tables 3 and 4), which weights libria involved in the formation of ion pairs. Calling the experimental measurements according to their errors, constitute better values for the solubility prod­ X the concentration of [CaHP04 ]O and Y that of ~cts than the simple unweighted mean values, given [CaH2 PO.I ] +, m tables 1 and 2. X=Kx[M -7] [P-7 ]/ca++ (9) TABLE 1. Solubility of steam-heated HA , unadjusted quantities QJx Initial Co mposition of saturated solution [H, PO,) Ca/p K.px 1 ~8 y=Ky[M -7] [P-7 ]/ca++(H +) M X IQ3 pH [P) rCa) Di ssol. Reac. (10) M X ]Q3 M x 1

The ionic strength, j.L, was defin ed in these calcu­ Avg. 1.57 ± 0.02' 5.3$ ± 2.62,a lations by a Standard errors," the means. 776 TABLE 2. Solubility of air·heated HA , unadjusted quantities than HA; evidence for this type of contamination is presented in section 3. The data also suggest the Initial Composition of saturated solu ,ion pres e nce of an anion foreign to th e sys t e m [ H"PO ,) eaIP K ~ p X IO:'!') Mx 10' pll [P) [Ca) Di ssol. Reae. Ca(OH)z-H3P 0 4-H2 0 as evidenced by an apparent M x 10 ' M X IO' positive electroneutrality unbalance which is far be­ 2.04 5.76, 3.02 1.62 1.65 2.5, yond experimental error for the three treatments 1.98 5.790 3.00 1.57 1.53 3. 1" 0.99 6. 11 , 1.39 0.76 1.90 2.3u with pH's above 6. This may have been caused by 1.01 6. 12, 1.46 .83 1.85 4.1 :\ carbonate since the infrared spectrum showed small 1.01 6. 13u 1.51 .84 1.70 5.6, 0.50 6.400 0.75 .49 1.95 3.8, CO:l peaks. .10 7.07, .19 .15 1.60 3.60 .05 7.36, .1 1 .09 1.62 2.27

Avg. 1.72±0.02' 3.41±O. 1 11 TABLE 5. So lubility of "as prepared " HA, una.djusted quantities a Standard errors in the means. Final solution compos ition Initial [I LoPO,] K.11x 10·-,11 Mx 10" pI! 11'1 rCal TABLE 3. Solubility of steam·heated HA , adjusted quantities AI X 10" M X HP

7.82 4.74, 10.17 5.11 0.8, Compositiun of saturated Apparent ealp 3.05 5.26, 3.43 1.67 1. 5, Initial solution Ionic charge K,p 0.49 6.60, 0.23 0.16 11.9, [ l brO ,) Dissol. r il strength im balance X 10·" Reae. .20 7.05, .06 . 10 10.9, M X 1O:1 pH [P) [ea) J.LX 10:\ At X 106 .05 7.45" .03 . 11 25 1. 2 M x 10' Mx 10 ,\

4.28 5.05, 6. 13 '3.10 1.68 0.03, 9. 10 0.0 3.7:1 2.00 5.38" 2.89 1."47 1.67 .02, 4.40 -.1 3.9, 1.02 5.69, 1.48 0.77 1.67 .01, 2.32 .0 3.9, 1.00 S.72() 1.45 .75 1.67 .01. 2.28 -.3 5.3, 0.31 6.23,; 0.46 .25 1.68 .01, 0.80 .0 3.8, Interpretation of the data in table 5 is further complicated by sorption phenomena; for example the S=3.7:,±O.4/!h phosphorus concentrations in the solutions for the a Frac tion of ea present as ion pairs. last three entries of table 5 are less than the initial h S tandard e rror from least-squares adjustment. H ;jP04 concentrations. A systematic study of this type of surface phenomenon with finely divided HA has been reported elsewhere [20]. Although so me of

TABLE 4. Solubility of air-heated HA , adjusted quantities the K S/J values in table 5 are in th e range of those given in table 1 for the steam-heated HA, the three

Composit io n of saturated Apparent at the higher pH's are abnormally large. Furthermore, CaW Ini tial solution Ioni c c harge K .

777 318- 0920- 69- 15 10-,

<:J<: W ~ ::;

~ Q) a. 0... 0- Vl w -' -, 0 10 :E

pH

FIGURE 1. Solubility isotherms of steam-heated HA, full circles, and air-heated HA, open circles, at 25 °C.

The two li ghter curves are the isotherms of CaHP04 • 2H 20 [171. DePD, and CaHP04 [19] , DCPA. Compositions of the calculated singular points A , B. C. and 0 are given in table 6.

in which KDC represents the solubility product constant The chemical compositions of the solutions at the four for either DCPD or DCPA, as the case may be, and singular points, calculated in the foregoing fashion, K is defined by are given in table 6. Considerably higher concentra­ tions of Ca and P (and lower pH's) are found at the singular points of the preheated HA's with DCPD than K K= [ sp ]'/2 (14) at the corresponding singular points with DCPA; the K 3 K!V K~c same pattern is observed for the fractions of Ca present as ion pairs (r in the table). These results are a conse­ The value for (fI+) obtained from eq (13) was then quence of the higher solubility of DCPD [17, 18] used to obtain lhe numerical value of 7 since, for relative to the anhydrous salt at 25°C [19]. The most saturation with respect to either DCPD or DCPA, striking differences in the compositions at the singular points, however, are brought about by the solubility of the HA itself. Thus, a full pH unit difference exists (15) between the singular points of air-heated and steam­ heated HA with either of the two dicalcium phosphates; The concentrations of calcium and phosphorus are changes in calcium and phosphorus concentrations obtained from eqs (16) and (17), respectively. by factors of about 3.5 and 4, respectively, parallel this pH difference. If, as it is apparent from the present (H +)2K K results, the solubility of HA depends upon the previous M= DC +7 (16) history of the sample, it is nearly impossible to predict fca ++ the composition of singular points between a precipi­ tated HA and other calcium phosphates without fully characterizing the solubility properties of the HA (17) involved.

778 TABLE 6. SoLution co mpositions at singuLar points 6. Discussion

Solid phases pH [P] [Cal r' M x 10' M X IO ' 6.1. Solubility of HA The solubility data given in tables 1 and 2 for the DCPD + HA (a ;r) ... 5.31, 8.64 4.43 0.05. two pre heated HA samples are consistent with DCPD + HA (s.eam) ... 4.41, 30.21 15.09 .10. DCPA + HA (a; r) ... 5.70, 3.53 1.85 .03, stoi chiometric dissolution represented by the reacti on DCPA + HA (s.eam) .... 4.79, 11.54 5.80 .Os, Ca .>OH(p O . , h ~5Ca + + +OH - +3PO :i'- It is believed that saturation conditions were obtained in the two­ .3 Fraction of Ca present as ion pairs. week equilibrations as evidenced by the smooth curves obtained in the plots of calcium concentration versus pH (fi g. 1), calcium concentration versus phosphorus CO 'l centration (not shown in this paper), and a rea­ Although the weight loss in our sample was not so nable constancy in the ioni c activity product for measured, slight weight losses have been reported HA. The success of the adjustment procedure de­ [22] in the range 1,000 to 1,100 °C for synthetic HA scribed in section 4 is additional evidence that the samples heated gradually from 25 to 1,200 °C; these parameters 5, tables 3 and 4, are valid solubility losses occurred without alteration in the x-ray product co nstants for the preheated hydroxyapatites. patterns. Also, it has been reported [23] that at 1,200 °C The higher solubility product constant obtained for in air, dis proportionation of HA into tri calcium phos­ the HA heated in air, relative to the product obtained phate and tetracalcium phosphate occurs according for the sample heated in s team, is most probably due to the reaction, to structural changes induced by the thermal treat­ ment. Such c hanges might relate in part to the statis­ tically di sordered structure of HA described by Kay 2Ca"OH(P04):1 ~ 2 a-Ca;I(P04)2 et al. [21], originating from small displacements of the OH - groups from the mirror planes in the + Ca40(P04h + H20. (18) P63/m. If this were purely an entropy effect, such disorder would tend to stabilize the lattice; the steam­ The x-ray powder diffraction pattern of the air-heated heated sample, therefore, would have to be the dis­ sample was the same as that of HA, but it is impossible ordered one. However, it is difficult to see why heating to rule out a partial disproportionation. HA in air would induce more order in the OH - groups In view of the foregoing considerations, there are than would be obtained by heating in steam. A more two explanations for the higher solubility of the air­ likely explanation is that heating in air results in heated HA: (1) Reversal of the disproportionation loss of OH- groups by partial dehydration of the HA. reaction [18] when the sample is returned to an aqueous Indeed, the infrared spectra te nd to substantiate this system might yield very finely divided HA with an alternative. Whereas the half width of the peak at unu sually high solubility because of surface energy 3,570 cm - 1 corresponding to the OH - stretching contribution, or (2) loss of OH - ions by dehydration mode, was essentially the same for both preheated during heating of the solid, without destruction of the hydroxyapatites, its height for the steam-heated HA HA lattice, might yield crystals with higher free energy. was almost twice that of the air-heated HA. Evidently, the process responsible for the increased solubility is not readily reversible, since otherwise 6.2. Singular Points the values for the K S]J of the two preparations would A system of two solid phases in equilibrium with have been the same. Therefore, the equilibria attained an aqueous phase in the ternary system Ca(OH)z­ with the air-heated HA must have been metastable HaPOrHzO is characterized by zero degrees of relative to the more stable form of HA. This would freedom (under conditions of constant temperature require that the rate of dissolution of the air-heated and pressure). Such singular points are important HA was higher than the rate of precipitation of the in solubility diagrams because they correspond to more stable salt. points where there is a change in the relative s tability The K S]J values for the two kinds of preheated of the two solid phases. Thus, with reference to table correspond to a difference of about 16 kllmol 6, in saturated solutions with pH's below 4.33, DCPD (3.9 kcal/mol) in the standard free e nergies of forma­ is more stable than th e steam-heated HA; in solutions tion. If it were assumed that the standard heat of with pH's above 4.33, steam-heated HA is more formation is the same for both compounds, the ob­ stable than DCPD. The greater solubility of the served difference in free energy would correspond to air-heated HA has th e effect of increasing the pH of about 59 Jlmol K (14 cal/mol K) less entropy in the the singular points with the dicalcium phosphates air-heated apatite than in the steam-heated salt. by about one pH unit relative to those with steam­ This difference appears too large to be associated heated HA. If an apatite comparable to the air-heated with a c hange in entropy resulting from vacancies HA were formed in oral environments, its greater or ordering. For this reason It is believed that the solubility would extend the stability ranges of the difference in solubility is mostly related to a difference two dicalcium phosphates to conditions which occur in their heat contents. in saliva in vivo.

779 -I In the concentration ranges covered by the present and 1.68 with standard errors of 0.02 and 0.07, respec­ experiments, the degree of ion-pair formation varied tively. These ratios agree with the theoretical ratio from about 1.4 percent (at the highest pH) to about for HA, 1.67, and the ratio, 1.68 obtained by chemical 3_4 percent (at the lowest pH) of the total calcium analysis of the untreated solid. In view of these facts, concentration. In view of the uncertainty, both theo­ the relatively low value obtained for the Ca/P ratio retical and experimental in these calculations for in the dissolution reaction, 1.57, of the steam-heated nonsymmetrical electrolytes, the formation of ion­ preparation, table 1, must be ascribed to experimental pairs in the experimental segments of the solubility errors. It is to be noted that the CaIP ratio calculated isotherms for HA is not considered significant. How­ from dissolution involves a difference between two ever, in more acid solutions, such as those of the experimental measurements. calculated singular points, the ion-pair formation does become significant. 6.4. Comparison With Reported Data

6.3. Stoichiometry and Potential Diagrams Clark [1] reported a value of 57.75 as his best estimate of pKsp (the negative logarithm of Ksp) of The stoichiometry of a solid calcium phosphate HA at 25 °C. (The actual value he reported, 115.5, is equilibrated with aqueous solutions is easily revealed based on the formula Calo(OH h(PO~) 6 rather than the by the use of " potential diagrams" [24, 25, 26]. These formula CaoOH(P04 h used here.) His systems con­ are solubility diagrams in which the coordinates are sisted of HA precipitated by mixing dilute solutions functions of the chemical potentials of the components, of Ca(OHh and H 3 PO~ at 90 °C; he ke pt the resulting Ca(OHh and H:IPO~, in solution. For example, if the suspensions at that temperature for 120 hr and quantity -log (Ca ++ )(OH- )2 is plotted against -log reequilibrated them at 25 °C for 90 hr. The Ksp cor­ (H +yl(PO'l'), the saturation condition is defined by a responding to his pKsp value of 57.75 is 1.78 X 10- 58, straight line and the absolute value of its slope cor­ which is in good agreement with the value 3.73 X 10- 58 responds to the reciprocal of the CaIP ratio in the reported here for the steam-heated HA. The individual solid. This kind of diagram is illustrated in figure 2 values reported by Clark range from 0.53 X 10- 58 to with calculations based on the data for the two pre­ 7.59 X 10- 58. Even though Clark's data, as plotted in heated apatites (tables 1 and 2). Similar calculations the chemical potential diagram, figure 2, have some were made with data from other investigators and scatter, it is apparent that they approximate closely these are plotted in the same diagram. The slopes the same line as our data for the steam-heated HA. and their standard errors, of the regression lines l'or The same author observed that equilibrations made the air-heated and steam-heated apatites shown in at 25°C with HA precipitated at 40 °C resulted in figure 2 correspond to apparent CaIP ratios of 1.69 large apparent supersaturations with respect to the

.... ~~ 20 ~~ ~~ ...... ~ ~ ~ .. D I' ~~~ .... J: ~ 0 0 .... 19 .. ~ .... + D .... + ~~ D 0 ~ .. 10 Do u ~.. 0 ~~ ~ ctB Ol ...Q ...... ~~ ~~~ ~ 18 ~ ...... ~~ Q~ • ~~ • • • ~ .. •• • .. ,,~ • • ~~ 17 • • • • • • 27 28 29 30 31 32 -log (H+)3(po!)

FiGURE 2. Potential plot, calcium versus phosphoric acid. e. steam·healed HA; 0 , air-heated HA ; 0 , data from Clark [1]; & , data from Levinskas and Neuman [31] 0 0 data from Rootare et al. [5] at 25 'C; . , data from Rootare et al. [5] at 40 ' CO ' ,

78"0 values for K sp given above. In light of present knowl· define a single line, and cannot be used to derive a edge, one would expect that those precipitates con· reli able KS]J for a solid of any Ca/P ratio. tained some of the more acid calcium phosphate whi ch Rootare, Deitz, and Carpenter [5] reported results are more soluble than HA. Thus, the more reliable on solubility studies done with several commercial of Clark's res ults agree with those reported here for and laboratory-prepared samples. They observed wide steam-heated HA. We consider it significant that suc h variations in the calculated ion-activity products for good agreement was ob tained between materi als HA; these were explained by postulating formation prepared by precipitation from aqueous systems add of a surface complex according to the reactions, a ·material subjected to annealing at 1,000 °C in a steam atmosphere. This suggests th at the K S]J value CaiO(P0 4Jt;(OHh + 6H20 ?4Ca2(HP04 )(OH)2] obtained for the steam-heated material is characteristi c of any well-crystallized HA. + 2Ca++ + 2HP04' (19) A solubility product constant for HA was calcu­ lated from the following thermodynamic quantities: CaAHP04)(OHh ? 2Ca + + HP04' 20H - (20) IlH/=-13,439 kJ/mol (-3,212 kcal/mol) reported by + + Smirnova et al. [2] for HA which had also been heated at 1,000 °C in the presence of steam; 5°= 780.7 J/m ol K It is true, as they claim, that the ionic product cal­ (186.6 cal/mol K) reported by Egan and Wakefield culated according to eq (20) showe d less variability [4] for another HA treated in a similar way, and (PK values from 24.6 to 26.8) than those calculated for standard entropies of formation of the elements and HA on the basis of the formula unit CaIO(OHh(P04)6 standard free energies of formation of ions reported (P K from 108 to 120). However, the mechanis m postu­ in NBS Publications [27, 28]. The product thus ob­ lated by Rootare et al. is open to the following criti­ tained , based on the formula Ca5 0H(P04h, is of the cisms: (a) Although the composition of the HA surface order 10- 57• does not have to conform necessarily to the stoichi om­ This result, too, is considered to be in good agree­ etry of the bulk solid, there is no a priori reason to ment with the order of magnitude given here, 10- 58 , postulate that certain surface compositions will for the steam-heated apatite, considering the un­ prevent equilibrium with the crystalline HA lattice certainties in some of the thermodynamic quantities [30]; (b) It is hi ghly improbable that the surface of used and the great effect that small variations in these HA equilibrated in aqueous solutions has a defi nite quantities have on the K S]J calculated in this fashion. composition independent of the compositi on of the The foregoing results are not in agreement with aqueous medium [20] ; (c) If a definite co mposition those of Levinskas [29], Levinskas and Neuman [6], is ascribed to the "surface complex" and the solubility and Neuman and Neuman [7] who concluded that product principle is appli ed according to its stoichiom­ synthetic preparations of HA equilibrated in aqueous etry, it is mandatory that s uch species be considered solutions do not obey the solubility-product constant as another solid phase (i.e., has constant molar free principle. One of the hydroxy apatites (L-apatite) most energy and stoichi ometry [30]); then , in the li ght of extensively studied by these authors was a commercial eqs (19) and (2 0), the system would have zero degrees 2 preparation of fine particle size, 68 m /g. The large of freedom (in the system Ca(OH )2 -H3 P04 -H2 0) under surface areas of their materials could introduce dif­ fixed temperature and pressure [30] so that the solu­ ficulties in the interpretation of solubility studies. tion composition could not vary as observed by them; However neither theoretically [30] nor experimentally (d) It can be easily shown that the equilibrium con· [20] do sorption phenomena invalidate the application ditions [19] and [20], as given by Rootare et aI. , also of the solubility product constant to systems equili­ imply equilibrium with respect to the HA solid phase; brated with HA. It should be pointed out that the (e) Of the 12 samples used by Rootare et aI., only four sample of HA (L:apatite) used by Neuman and co­ were petrographically homogeneous [5] ; the rest were workers had a of 1.605 [5] which is contaminated with calcite varying from traces to about much too low for a well-crystallized HA; in addition, 1 percent, with sulfate varying from 0.006 to 0.29 their preparation was contaminated with calcite, percent and, with the exception of two, all the samples contained 0.28 percent sulfate and 0.8 percent CO2 contained carbonate in signifi cant amounts; only the [5]. No history is given for the synthesis of L-apatite, four samples prepared in the laboratory s howed a but the analytical results clearly show the heteroge­ refractive index approaching the one expected for neity of the sample. Under these circumstances, well-crystallized HA; one of the latter, P-20, probably reactions other than simple dissolution and precipita­ contained less basic calci um phosphates as evidenced tion of HA are to be expected, and their involved by a Ca/P ratio of 1.583 and the report by Gee [32] kinetics is a burden for sound interpretations of that was formed upon heating it at solubility s tudies. The adoption of the ion-activity 600 °C for 60 hr. product (Ca++)(HP04') to characterize HA systems, The results repuneo DY Rootare et a1. [5] form two as suggested by Neuman and co-workers [7, 29] distinct populations when plotted in figure 2. The cannot be justified on theoretical bases [30]. Our regression line for the points at 25°C (the point 30.20, recalculation of their data [31] plotted in figure 2 19.61 excluded) has a slope of - 0.778, which would shows that the points are widely scattered, do not correspond to a ratio of Ca/p= 1.28 in the solid phase.

781 The points from treatments at 40°C appear to define 8 . References two lines with slopes - 0.309 and - 0.211 which would correspond to Ca/P ratios of 3.24 and 4.74 in the solid. [1] Clark,1. S., Can. J. Chern. 33, 1696 (1955). If equilibrium with respect to Ca2 (HP04 ) (OH}z had [2] Smirnova, F. G. , Illarionov, V. V. , and Vol'fkovich, S. I., Rus· been established, as claimed by Rootare et al. [5], sian 1. Inorg. Chern. 7, 920 (1962). [3] Jacques, 1. K., 1. Chern. Soc. 3820 (1963). lines with slope of - 0.5 (CaIP = 2) s hould have been [4] Egan, E. P., Jr. , Wakefield, Z. T., and Elmore, K. L., 1. Am. defined by their data in the potential plot. The fact Chern. Soc. 73,5579 (1951). that their data defin e two or three Ca/P ratios, none of [5] Rootare, H. M., Deitz, V. R. , and Carpenter, F. G. , 1. Colloid which correspond to their postulated surface complex, Sci. 17, 179 (1962 ). [6] Levinskas, G. J., and Neuman, W. F., J. Phys. Chern. 59, along with the other criticisms listed above, argue very 164 (1955). strongly against the existence of the surface com­ [7] Neuman, W. F., and Neuman, M. W. , The Chemical Dynamics plex hypothesized by them. LaMer [8] reexamined the of , p. 30 (U niversity of Chicago Press, Chicago, data of Rootare et al. [5] and came to the conclusion Ill., 1958). [8] LaMer, V. K , 1. Phys. Chern. 66,973 (1962). that the product, (Ca++) (HPO:n showed the least [9] Moreno, E. c., Gregory, T. M. , and Brown, W. E., 1. Res. NBS variation. However, for the reasons given above, this 70A (phys. and Chern.) No.6, 545 (1966). is not an adequate basis for any conclusions regarding [10] Bates, R. G., 1. Res. NBS 66A (phys. and Chern.) No.2, the nature of the equilibrating solid phase. 179 (1962). [Il] Banerjee, D. K. , Budke, C. c., and Miller, F. D., Anal. Chern. In the light of the foregoing results and discussion 33, 418 (1961). we conclude that our samples of preheated HA did [12] Brabson, 1. A. , Dunn, R. L. , Epps, E. A., Jr., Hoffman, W. M., equilibrate according to the stoichiometry of HA and and Jacob, K. D. , J .A.O.A.C. 41, 517 (1958). according to the usual solubility product principles, [13] ASTM Powder diffraction file , Card No. 9-432. [14] Fowler, B. 0., Moreno, E. c., and Brown, W. E. , Arch. Oral that the steam-heated HA yielded a solubility constant BioI. 11,477 (1966). usable as a frame of reference for well-crystallized [15] Deming, W. E. , Statistical Adjustment of Data (John Wiley HA, and that most of the difficulties reported in the & Sons, Inc., New York, 1943). [16] Wentworth, W. E. , Hirsch, W., and Chen, E. , 1. Phys. Chern. literature on this matter relate to contamination of 71,218 (1967). the solid and lack of equilibrium between the solution [17] Gregory, T. M., Moreno, E. c., and Brown, W. E. (Abstract), and the solid. Internal. Assoc. Dental Res., 45th General Meeting, Wash· ington, D.C. (1967)_ [18] Moreno, E. c., Brown, W. E. , and Osborn, G., Sci. Soc. Amer. Proc. 24,94 (1960). [19] McDowell, H. , Ph. D. Thesis, Howard University, Washington, D.C. (1967). 7. Appendix [20] Avnimelech, Y. , Moreno, E. c., and Brown, W. E. (Abstract), Internal. Assoc. Dental Res. , 45th General Meeting, Wash· ington, D.C. (1967). Ionic activity coefficients were calculated from the [21J Kay, M. I., Young, R . A., and Posner, A. S. Nature 204, 1050 extension of the Debye-Hiickellimiting law, (1964). [22] Egan, E. P. , Jr. , Wakefield , Z. T., and Elmore, K. L., 1. Am . Chern. Soc. 72,2418 (1950). AZyVJ;, [23] Bredig, M. A., Franck , H. H., and Flildner, H. , Z. Elecktrochem. log.li = - --"----'---= (21) 39, 959 (1933). 1 + BaiVJ;, [24] Aslyng, H. c., Royal Vel. and Agric. CoIL Copenhagen, Den­ mark, Yearbook Reprint, pp. 1- 50 (1954). The values used [33] for the temperature-dependent [25] Moreno, E. c. , Lindsay, W. L. , and Osborn, G. , Soil Sci. 90, constants A and B were 0.5092 and 0.3286 X 108 , 59 (1960). respectively; those for the parameters ai [34] were [26J MacGregor, 1. , and Brown, W. E., Nature 205, 359 (1965). Ca++, 6 X 10- 8 cm; H2POi, HPO;, and PO ~, 4 X 10- 8 [27] National Bureau of Standards. Selected Values of Chemical Thermodynamic Properties, Circ. 500 (1952). cm; H+, 9 X 10- 8 cm; and OH-, 3.5 X 10- 8 cm. [28J National Bureau of Standards. Technical Note 270-1 (1965) The values used for the three ionization constants and Technical Note 270-2 (1966). of H3P04 were KJ, 7.108 X 10- 3 [35] ; K2 , 6.3ls X 10- 8 [29] Levinskas, G. 1. , Ph_ D. Thesis, University of Rochester, New York (1953). [36]; K , 4.73 X 10- 13 [37]; and for Kw, 1.012 X 10- 14 3 [30] Brown, W. E. , Moreno, E. c., and Gregory, T. M., Thermody- [38]. The association constants used in this paper namics of hydroxyapatite solubility. In preparation. are defined by [31] Table 2 of reference 6. [32] Gee, A. , Proc. Third T ech. Session on Bone Char. p. 337 (1953). (CaHzPOt) [33] Manov, G. G. , Bates, R. G., Hamer, W. 1., and Acree, S. F. , [CaHP04 r 1. Am. Chern. Soc. 65, 1765 (1943). Kx = (Ca++) (HPO;) Ky = (Ca++ ) (H2PO;;-) [34] Kielland, 1. , J. Am . C hern. Soc. 59, 1675 (1937). [35] Bates, R. G., J. Res. NBS 47, 127 (1951) RP2236. [36] Bates, R. G., and Acree, S. F., 1. Res. NBS 34, 373 (1945) with values [17] Kx, 244.0; and Ky , 8.20. RPl648. The points in the potential plot (fig. 2) corresponding [37] Tennessee Valley Authority. Chern. Eng. Report No.8 (1950). to the data of Rootare et al. [5], at 40 °C were cal­ [38] Harned, H. S., and Owen, B. B. , The physical chemistry of culated using the following constants: K\ , 5.996 X 10- 3 electrolytic solutions, p. 645 (equation 15- 3-7a), (Reinhold 8 13 Publishing Corporation, New York, 1958). [3 5]; K2 , 6.607 X 10- [36]; K3 , 7.586 X 10- [39]; [39] Bj errum, N., and Unmack, A., Kg!. Danske Vid enskab. Selskab., Kw, 2.936 X 10- 14 [38]; A, eq (21), 0.524\ [33] ; and Math-fys. Medd. 9, 5 (1929). B, 0.3318 X 108 [33]. (paper 72A6- 527)

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