1 3 0 1

Clhow. LC, Eanes, ED (eds): Octacalcium Phosplrate.

Monog l Ora l Sc i . Base l . Karger , 2001, vo l l13 . pp 94-11I

Solubility of Calcium Phosphates

L.C. Chow

Amcrican Dcntal Associat ion Heal th Foundal ion. Paf fenbargel Rcscarch Cenlcr .

Nat ional Insl i tute o[ Standards and Tcchnology, Gai thersburg. Md.. USA

Solubil ity is one of the most important properties of calcium phosphate

salts. It is the solubil ity that determines the direction of many reactions that

involve calcium phosphates such as dissolution, precipitation, hydrolysis,

and phase transformation. Calcium phosphate solubil ity also plays a maior

role in biological processes that involve formation and resorption ol' hard

tissues as well as pathological calcif ications. This chapter wil l focus on con-

cepts that would aid in gaining a better understanding of the solubil ity beha-

vior of calcium phosphzrtes, rather than provide a survey of the l iterature,which has been g iven e lsewhere [El l io t . 1994] . Solubi l i ty is convent ional ly

descr ibcd ns the nmount of a sol id that can d isst> lve in to a uni t vo lume of so-

lution. Fclr calcium phosphates, this quantity often changes by several orders

of magnitucle with changes in the pH and concentrations of acids and bases,

such as HCI and NaOH. Thus, on the surface. the solubil ity may appear to

be a complex function of these solution parameters. However, a clearer pic-

ture o1 the solubil ity properties for calcium phosphates can be gainecl by un-

derstanding the basic principles governing the solid-solution equil ibrium.

Gibbs' Components

The composition of a solution may be described in terms ol the quanti-

t ies of inclependent components defined in Gibbs'phase rule [Gibbs, 1876].

The components may be understood as the minimum number of compounds

that are neecled to form all of the phases that may be present in a system.

In the simplest case, a solution that contains calciurn and phosphate ions is

comprised of three such components, e.g., Ca(OH)2-H3PO1-H2O [Morenoet al., 1966]. Because the components in a given phase must be homoge-

ncously distributed, the Ca(OH)2 and H3POa components here refer to ma-

terials dissolved in water, which is also a component. The selection of com-

ponents is quite arbitrary and is usually based on the ease of expressing the

concentrations and chemical potentials of the components. For example.

CaO-P2O.5-H2O is another set of components that have been used in many

studies [Brown arnd Lehr, 19-59; Brown, 1992]. While considerable freedom

exists in choosing components, these components must be independent in

that zr combination of any ol the components does not form another compo-

nen t .It is important to distinguish between the concept of a 'component' and

that of a 'species'. The Ca(OH)2 and HjPO4 species refer to the undisso-

c iated Ca(OH)2 and H3PO4 present in the solut ion. An acid ic solut ion wi th

a pH ol 'approximately 4.4 can be prepared by combin ing 0.01 moles of thecompound Ca(OH)2, 0.02 moles of the compound HjPO4, and a suf f ic ientamount of water to make I l i ter of solution. While the concentration of the

Ca(OH)2 component in the solut ion is 0.01 mol /1, the concentrat ion of thc

Ca(OH)2 species is negl ig ib le at th is pH because the bulk of the solut ion

calcium is in the form of free Ca2* ions ancl a small amount is in the fortr cll 'ion pai rs wi th phosphate. A s imi lar analys is can be made o[ a basic solut ionconta in ing a s igni f icant anlount of thc H3PO1 component , but a ncgl ig ib lysmal l amount of the H3PO4 species bccause in a lka l ine solut ions the solu-t ion phosphatc arc prcscnt pr imar i ly in the forms t l l 'HPOar arrc l PO1' ' ior rs .It can be seen l 'rom the above example that the concentrations of theCa(OH)2 ancl H.1POa components are the same as the to la l ca lc iurn concen-t rat ion, ICa] , ancl to ta l phosphate concentrat ion, IP] , respect ive ly , o l ' thc so-lut ion. As a resul t , these terms are equivalent and can be usecl in terchangc-

ably. For practical purposes, [Ca]. IP], and pH are the three most commonlyused parameters I 'or describing the solution composition because all threeare directly measurzrble quantit ies. The reason for expressing the solt-tt ioncomposi t ion in terns of Gibbs 'components instead of ICa] , IP] and pH inth is chapter is because of the ease of def in ing the sol id-solut ion equi l ibr ium

described next.

Solubility - Theoretical Considerations

The clissolution reaction of a calcium phosphate solid, such as hydroxy-

apatite (OHAp), may be expressed in two equivalent ways in terms of the

ionic species (eq 1) and the components (eq.2) .

So luh i l i t v r r l ( r r l c i u r r r Ph t r sph : r t es

Cas(PO+):OH (sol id) <+ 5 Ca' t + 3 POa' + OH ( 1)

Cas(PO+):OH (sol ic l ) <= -5 Ca(OH). + 3 H3PO. ' 9 H2O. (2)

The terms on the right hand side of the equations refer to the spccics orcomponents in the aqueous solution phase. In a saturated solution in whichthe sol id and solut ion are in equi l ibr ium, eq.2 leads to the chemical poten-tial expression,

p"OHAp - 5lCa(OH): + 3 prHjPOa - c) pH2O. (3)

where p'OHAp is the chemical potential of OHAp at a standard state andis constant at a given temperature and pressure. The terms on the right handside of the equation are the chemical potentials of the components in theaqueous solution. These quantit ies, which would vary with the compositionof the solution, may be further described by the equations.

pCa(OH)2 = p 'Ca(OH)2 + RT ln (Ca2*)(OH )2. G)

pH:POr - proH3POa + RT In (H*)r (POr ' ) . (5)

tH.O = p 'H2O + R' r ln (H*)(OH ) . (6)

where p' is the chemical potential of the designated component at a stan-dard state zrnd quantit ies in the parenthescs are the activit ies. Substitutingcq.4-6 in to eq. 3 g ives

tr r 'OHAp - ( .5 p 'Ca(OH)2 + 3 g 'H3pOa - 9p"H2O) = RT ln (Cta2*)s(pO13 )3(OH) ( j )

The lef t hand s ide of eq.7, which c<lns is ts only of constant terms, is knownas the standard f ree energy of d issolut ion fbr OHAp, AG"OHAp, as cx-p ressed i n eq .8 .

AO 'OHAp=p"OHAp- (5p "Ca(OH)2+3proH lPOa-9p"H :O) . ( l J )

I t is seen that AG"OHAp is the d i f ference between the standard chemicalpotent ia l o f the sol id , OHAp, and the sum of the standarc l chemical poten-t ia ls of the components in the solut ion mul t ip l ied by thei r respect ive coef f i -cients that appear in the equil ibrium equation (eq. 2). The variable part ofthe r ight han<l s ide of eq.7, 1ca2*;s1PO.t ) t (OH), is known as the ion act iv-ity product for OHAp or IAP(OHAp). It follows from eq.7 that for any so-lution that is saturated with respect to OHAp, IAP(OHAp) is related onlyto AG"OHAp and therefore is a constant. Thus, for saturaled solutions,

Ksp(OHAp) = IAP(OHAp)= (Ca2. )5 (po1t ) t (Ou) . (9 )

where Ksp(OHAp) is known as the solubility product constant for OHAp.The Ksp value can be calculated from solubility measurement data, a knowl-edge of the dissociation constants of phosphoric acid and calcium hydroxide.

('horv

the various ion-pair formation constants, and an appropriate model for calcu-lating the activity coefTicients for the various species involved [McDowell elal.. 1L)111. Ksp, a thermodynamic property of the solid. is probably the mostfundamental way of defining the solubil ity properties of a calcium phosphate.Although the Ksp value does not directly reveal the amount of the solid thatcan dissolve under a particular solution condition. it can be used to calculatesolubil ity isotherms in a phase diagram to provide complete information onthe solubil ity as a function of pH and other solution parameters as describednext. Table 1 l ists the Ksp values of the various calcium phosphate com-pounds that herve been determined by clifferent ir.rvcstigators.

Solubil ity Phase Diagrams

Cibbs 'phase ru le [Gibbs. 1876] d ic tates that under a f ixec l temperatureand pressurc. a three-component system, such as Ca(OH)2-H3PO4-H2O.with a single phase, e.9., a solution, has two degrees of freeclorn. It fbllowsthat thc composition of any solution in this system is defincd [-ry fixing thcvalues o[ two composi t ion parameters. i .e . . pH and [Ca] , pH and [P] , or

[Ca] ancl [P] . F igure I shows a sur face known as thc 'c lect ro-neutra l i ty 'sur-l 'ace [Brown, I()731 in a three-climensional space with the coorclinates beinglog [Ca] , log IP] , and pH of the solut ions. Of a l l the solut ion composi t ionsrepresented by the three-din-rensional phase d iagram. only thosc conrposi -t ions that l 'a l l on the e lect ro-ncutra l i ty sur face sat is fy the c lect ro-neutra l i tyconcl i t ior l , i . e . , the sum of the charges carr ied by the anions ancl cat ions inthe solut ion equals to zero, as g iven by the ec luat i< ln.

I ; t r ;Cr - ( ; ( r 0 )where u and C are the charge and conccntration. respectively, of' species i.Because they are e lect r ica l ly neutra l , these are the only solut ions that canexist physically. Thus, this surface defines the compositions o1' all solutionsir.r the systcm without giving regarcls to the degree of saturation with respectto any sol ic l . Shown on the sur face are constant pH and [P] l ines ( l ig . l ) . I tis seen in th is d iagram that the [Cal of a solut ion is f ixed by select ing thevalues of the other two composi t ion parameters, pH and [P] .

The Ca(OH)2-H3PO4-H2O system with two phases (a solution and a so-l id) in equi l ibr ium has a s ingle degree of f reedom, and the composi t ion o1 ' thesaturated solution is completely defined by fixing the valuc of any one corl-posi t ion parameter , e.g. , pH, ICa] , or [P l . Thus a l ine. known as a solubi l i tyisotherm in the phase diagram defines the compositions of a series of solu-

tions. all of which are saturated with respect to the same solid. e. g., OHAp.

and for which eq.7 and 9 apply. The solubil ity isotherm of a calcium phos-

Solubi l i tv o l Calc ium Phosphatcs

Table 1. Calcium (ortho) phosphatc compounds and their solubi l i ty product constanls

Compound Formula Ca/P - log (Ksp) at 2-5'C

Monocalc ium phosphate monohydratc

Monocalc ium phosphatc anhydrous

Dicalc ium phosphatc anhydrous

Dictr lc ium phosphatc c l ihycl ratc

Octacalc ium phosphatc

cr-'Iiicalci un-r phosphatc

B-Tr icalc i unr phosphatc

Hvclroxyapat i te

Fluolapat i tc

Tctracalc iur .n phosphatc

Ca(H2POa)2 .H2O 0 . .5Ca(H2POa)2 0.5CaHPOa 1.0C a H P O I ' 2 H 2 O 1 . 0CasH2(PO1)6 . .5HrO 1 .33u-Cas(POa)2 1.5p-Ca.r(PO+)z 1..5Ca.s(PO+).rOH 1.67Cas(PO+)rF l .6lCaa(POa)2O 2.0

h igh ly so lub leh igh ly so lub lc6.90 [McDowell et al. . l96i i ]6.59 [Grcgory ct al. . 1970]

96.6 [Tung ct al. . l9tt t l l25.5 fFowler and Kuroda, l9[ i6]28.9 [Grcgorl ' ct al. . 19741-5t. l .4 [McDowcll ct al. . 1977]60 .5 [Moreno e t a l . . 1977]3t3.0 [Malsuya ct al. . 1996]

phate salt can be determinecl experimentally from solubil ity clata. Altcrna-Lively. experimentally obtained solubil ity data can be usecl to calculatc thcKsp of the sol id which is then usecl to calcula le the solubi l i ty isothcrm. A cal -culated isotherm is useful for estimating solution compositions over a wiclerranse than that covered by experimentally measured compositions. Figure 2is a stereo pair of solubil ity phase diagrams showing the cetlculatecl isothcrms(25 "C) of seven sal ts : d ica lc ium phosphate d ihydrate (DCPD), d ica lc iumphosphate anhydrous (DCPA), octacalc ium phosphate (OCP), cr - t r ica lc iunrphosphatc (cr-TCP), B- t r ica lc ium phosphate (B TCP), OHAp and tet racal -cium phosphate (TTCP). Isotherms were calculated with the use ol commer-c ia l ly avai lable sof tware (Chemist , Micromarh, Sal t Lake Ci ty , Utah, USA).Al though the e lect roneutra l i ty sur face is not shown in f igure 2, a l l isothermsdo l ie on th is sur l 'ace because a l l so lut ions must sat is fy the e lect roneutra l i tyrequirement. Figures 3 a-c show the phase diagram projected in two-climen-s ional spaces as v iewed a long the log [P] , log [Ca] , and pH axes, respect ive ly .I t can be seen in f igure 3 a that the isotherms have negat ive s lopes in the neu-t ra l and acid ic regions, i . e . , pH below about 7, of the phase d iagrams. This re-l ' lects the fact that all calcium phosphate compounds are rlore soluble as thepH decreases. The slope of the isotherm is an indication of how rapidly thesolubil ity of the salt increases with decreasing pH. Since, for a given drop inpH. the solubil ity of a basic salt woulcl increase more than would an aciclicsalt, the slope oi the isotherm is related to the alkalinity of the salt. Conse-qucntly, the more acidic salts, DCPD and DCPA, have smaller negativeslopes than clo the more basic salts, TTCP, OHAp and the two TCPs.

In the alkaline regions of the phase diagram, the [Ca] increases with in-creasing pH (fig. 3 a). In contrast, with the exceptions of DCPA and DCPD.

C'how

' i .\. , , \

\-4 1

-8

o

o)

Fig. 1. Solubi l i ty phasc cl iagram lbr the tcrnary syslcm, C'a(OH)2-H3POa-H2O. at

25 "C showing thc clcctroncutral i ty surlace.

the IPl clecreases with increasing pH (fig. 3 b). The reasons for the different

shapes of the log [P] vs. pH isotherms are also related to the basicity ol ' the

compouncl as has been descr ibed previously [Chow et a l . , 1991] . I t may bc

concluc led that the solubi l i ty behavic l r o f a calc ium phosphate sal t is pr inc i -

pally determinecl by two factors: the Ksp and the basicity of the compouncl.

The solubil ity phase cliagrams shown in figures 2 and 3 are quite usel'ul

because they reveal the relative stabil ity of the salts at various pHs. At a

given pH. a sal t whose isotherm l ies below that of another sal t is less soluble(rnore stable) t l ran the other . Thus, i t is readi ly seen f rom the phasc d ia-

grarns that OHAp is the least so luble among al l sa l ts unt i l t l - re pH fa l ls be-

lcrw approximately 4.2 where DCPA becomes the least soluble. Similarly,

TTCP is the most soluble salt for pH below t3.-5; erbove that DCPD is the

most soluble. Many phase transformation reactions reported in the l iterature

can be understood through the use of these phase diagrams. For example.

an acidic (pH2. 1) solution saturated with respect to DCPD was used as a

pretreatment in a topical f luoridation procedure [Chow and Brown, 197-5].

When the solution was applied to tooth enamel, the OHAp in enamel would

dissolve. making the solution superszlturated with respect to DCPD, and

DCPD would precipitate. At the same time, the pH of the solution would

Solubi l i ty o l C'a lc iunr Phosphatcs

t o

- DCPD

- p-TcP- oHAp

Fig, 2, A stereo pair of solubility phase diagrams for the ternary system, Ca(OH)2-H?PO4-H2O, ̂t25oC showing solubiliry isorherms of DCPA, DCPD, OCp, s-TCp, p-TCp,OHAp, and TTCP

increase from the initial value of 2.1 to a higher value, e. g., 3.5. The increasein pH is a result of dissolution of a more basic salt, OHAp, followed by pre-cipitation of a more acidic salt, DCPD. Because the [Ca] and [P] are lowerin the pH3.5 solution than those in the pH2.1 solution (fig.3a, b), onewould expect that this treatment should produce a net increase in mineralcontent in the enamel surface.

Multicomponent Systems

The phase diagrams shown in figures 2 and 3 apply only to the ternarysystem, Ca(OH)2-H3PO4-H2O. This means that the compositions describedin these phase diagrams can be obtained by equilibrating a calcium phos-phate salt in water or aqueous solutions containing H3POa and Ca(OH)2only and not in solutions that contain components other than those in theternary system, e. g., HCI or NaOH. However, diagrams similar to figures 2and 3 can be constructed for a quaternary system in which the quantity of

100

1

0

-1

6 - 2g

-5

-6

2

0

c;

-8

- 1 0

-12

1

0

- 1

6' .2

slJ - J

-o

r DCPA_ DCPD

- u-TCP* p-TCP- OHAp_ TTCP

8

P H

.12 -10 -8

Log [P]

pH

Fig. 3. The solubility phase diagrams shown in figure 2 projected on log [Ca] vs. pH

plane (a); log [P] vs. pH plane (6), and log [Ca] vs. log [P] plane (c).

Solubilitv of Calcium Phosohates

the fourth component is held constant. Figure 4 is a stereo pair of solubil ityphase diagrams showing solubil ity isotherms for OHAp in the four-compo-nent system, Ca(OH)2-H3PO1-U(+)-H2O. where U(+) is NaOH or U(-) isHCl. Each OHAp isotherm is for a fixed concentration of U(+) or U( ) at0mol . l0 4, 10 r , 10 2 or 10 lmol / | . F igure-5a-c show the same diagram pro-jected in a two-dimensional space viewed along the log [P]. log [Ca], and pHaxes. respectivcly. It can be seen in figure 5 c that thc primary effects ofNaOH or HCl, which cloes not form significant amounts of stable ion-pairsor insoluble salts with calcium or phosphate ions. arc to shift the loci of thcisotherms. The IP] of a l l po ints on the isotherms for the NaOH-conta in ingsystems are increersecl from the corresponcling values in the tcrnary system.simply to balance the positive charges carried by the Na* ions. Similarly, the

ICa] are higher in proportion to the HCI content of the solutions in order tobalance thc negative charges of the Cl ions. Additionally, the increase in

[Ca| causcs a recluctiorr in thc [PJ needed to satisfy thc Ksp such that theisotherms plottccl in the form of log [Pl vs. pH are significantly shiftcd to-warc l lower P concentrat ions ( f ig .4b) . Diagrams s imi lar to l igures4 and -5rray be constructecl for other calcium phosphate salls. In the cascs where anacicl is partially dissociatecl or fbrms stablc complexes with calcium or phos-phatc iorrs , knowledge of ' the ac id or complex d issociat ion constants is re-quirecl to procluce the phasc diagram.

Chemical Potential Diagrams

Figures 2-5 show the relat ionships of direct ly measurecl quant i l " ies, ICa]. Iel .ancl pH, o1'solut ions that are saturatcd with respect to the var ious sol ids.Another type of solubi l i ty phase diagram, known as a potent ial diagram,provides a cliflerent wzry to unclerstancling the solubility properties o1 cal-cium phosphates. Rearrangement of eq. 3, which is val id lbr al l solut ions sa-turatccl with OHAp, yielc ls the lol lowing equarion.

ptC'a(OH): = -3 l ,5 f tH.rPO+ + l / -5 (p 'OI- lAp + 9gH1). ( l l )

For dilute solutions, prH2O can be considered constant and the second tcrmon the r ight hancl s idc of the equat ion becomes a constant . I t fo l lows thatI 'or all solutions saturated with respect to OHAp, there cxists a l inear rela-t ionship between pCa(OH)2 and pHsPOa. The s lope of th is s t ra ight- l ine re-lationship. -3l-5, is equal to the negativc reciprocal of the molar Ca/P ratioof the sol ic l . When eq. 4-6 are subst i tu ted in to eq. 11, one obta i r rs

In (Car*)(OH )r - -3l5 ln (H*)r(POr3 ) + K.

Chow

( t2)

'.(' .i'\ 'IC

:\ ,)'

'

,Vl--*- -.,-,--Log

I

J

i 'i

- ':B----.--_r'.O* _ 1

-oo rpi

' - ---- -------ltl

I ul u

'-'--*--T-- ---o--l oLog [Pj

Fig, 4. A ste rco pair of solubi l i ty phasc cl iagrams for thc quatcrnary systcm,Ca(OH)2-H:PO4-LJ(t)-HrO, at 25"C showing OHAp isothcrms al l ixcd pLJ(+) valucs ina thrcc-cl imcnsional spacc.

where K is a constant comprising of the standard chemical potentials ofOHAp and the components Ca(OH)2 and H3POa, and the chemical poten-tial of H2O. This shows that the logarithms of the activit ies of the two com-ponents. Ca(OH)z ancl HjPOa, are also l inearly related. Similar l inear rela-tionships can be derived for other calcium phosphates, and figure 6 showsthe straight-l ine relationships for the seven calcium phosphate salts whoseisotherms are given in figures 2 and 3. It can be shown that in this diagramsolutions located to the right of the straight-l ine are under-saturated zrndthose to the left of the straight-l ine are supersaturated with respect to thesol id .

It should be noted that eq. 11 and l2 hold true for all solutions that aresaturated with OHAp regardless of whether or not any other components,such as HCI or NaOH, are also present. As a result, the potential diagram

Solub i l i t l , o f Ca lc iu rn Phosphates

0

-1

-2

6

-6

.7

0

7

pH

6'J

* P(u_/ _ |

*- p(u-) = 2- p(u-) :2* p(u") - 4r p ( u ) = 0- p(u+) : 4- p(u+) = 3- p(u+) - 2- p(u+) . 1

. 1 0

0

-1

-2

6 - 3eo

-7

7

pH

9 p H E p H 7 p H a p H s

\ \ \ \ \

\ \ \ \ \

\ \ \ \L \ \

Flg. 5. The solubility phase diagrams shown in figure 4 projected on log [Ca] vs. pHplane (a); log [P] vs. pH plane (D), and log [Ca] vs. log [P] plane (c).

Chow 104

(f ig. 6) is quite useful in multicomponent systems because a single l ine re-presents all the solubil ity isotherms with different U(t) values for OHApshown in figure 4. Because the activit ies, (Ca2*XOH )2 and (H*)3(pO13 ), ofa solution can be calculatecl from directly measurable quantit ies, i. e., pH,

[Ca]. [e], [Na], and [Cl], a solution can be represented as a point in the po-tential diagram, ancl the degrees of saturation with respect to the varioussolids wil l be revealed. The potential diagrams have proven uselul in a num-ber of studies in zrttempting to identify the phase(s) with which the solutionmay be in equil ibrium at ditferent t imes of the reaction process. The poten-tial diagram is especially useful fbr studies dealing with complex biologicalsamples. For example, based on potential plots of solubil ity data, MacGre-gor and Brown [1965] concluded that equil ibration of child ancl calf bonemineral with serum followed ocP solubil itv. whereas adult bone rnineralfollowed apatite solubil ity.

Solubil ity of Solid Solutions

An apat i t ic mineral that conta ins both F and OH- ions may be consic l -erecl as a solid solution of FAp and OHAp with the general forrnulaCas(PO+):(OH) ' "F^, where 0<x< l . Othcr apat i t ic composi t ions resul r inglrom similar substitutions may also be considered solicl scllutions, forexample. subst i tu t ion < l f CO.,2 for PO*r- wi th a general I 'ormula ofCzt l1; , * , , (PO+)o-*(CO:)- (OH)z ^*uu and 0< x <2 and 0< u ( 0. -5x [Labartheet a l . . 1973j . The solubi l i ty prc lper t ies of these sol id solut ions are r rore com-plcx bccause as the sol id- l iqu id equi l ibr ium is being approached, a chtrngein the sol id composi t ion (change in the x or u value) may occur on the sur-face of the crystall ine particles such that the surface phase has the least solu-b le (most s table) composi t ion for the par t icu lar aqueous solut ion composi-tion IDriessens, 1979]. Consequently, the solid phase that woulcl reach trueequi l ibr ium wi th the aql leous solut ion may have a d i f fercnt x value f romthat of the bulk sol ic l . Despi te the potent ia l d i f f icu l t ies in obta in ing re l iab leKsp(x) va lues as a funct ion of x , Dr iessens [1982] analyzed the solubi l i tydatir reported in the l iterature [Narasaraju, 1974; Moreno et al., 1L)]7;Yer-beeck et al., 1980] and concluded that the presence of F- ions in the apatit iccrystal structure reduces the solubil ity (in terms of the amount soluble) ofOHAp considerably, especially at low pH: a reduction of solubil ity of U0%can be expected at pH 4 for a Ca,5(POq):(OH)r *F*, solid solution with an xvalue of 0. 1.

In an attempt to understand the solubil ity behavior of the solid solu-tions as a function of the aqueous solution composition, Chow and Marko-

Solubi l i ty o l Cla lc iunr Phosphates

p(H)3(PO4)l

Fig. 6' Potcntial phasc cliagram at 25'C showing solubil i ly isothcrms ol' various cnl-cium phosphate salts.

vic [199[3] conclucted a theoreticnl analysis to determine which factors arethe major determinants of the x value of the least soluble (most stable) solictfor a particular aqueous solution composition. They concluded that the sta-bil i ty of the solid solutions depends entirely on how Ksp(x) varies with x. Itwas shown that OHAp is less soluble (more stable) than fluorapatite (FAp)and any of the sol id solut ions in aqueous solut ions that have re lat ive ly h ighpH ancl low [F], while FAp is less soluble than OHAp and any of the solidsolutions in aqueous solutions that have relatively low pH and high [F]. Thesolubil ity properties of the solids in aqueous solutions between these two ex-tremes would depend on how Ksp(x) varies with x. When Ksp(x) is a l inearfunction of x, all of the solid solutions are more soluble than OHAp or FApexcept in one series of aqueous solutions in which OHAp and FAp as wellas all of the solid solutions are equally soluble. Since the solid solutions curnexist only under this extremely confined condition, they play no significantroles in the dissolution behaviors of OHAp and FAp. In the case where theKsp(x) value falls below that predicted by the linear function, there will bea region in the aqueous compositions where a solid solution with a specific xvalue is less soluble than OHAp, FAp, or other solid solutions. In thesecases, there are no stable aqueous solutions that are simultaneously satu-rated with respect to both OHAp and FAp, the two end members of the so-

Clrow

l id solution series, but an aqueous solution can be simultaneously saturated

with respect to two adjacent members of the series. A solid solution with a

smaller x value tends to be more stable in solutions with higher pH and low-

er [F]; those with a larger x values are more stable in solutions with lowerpH and higher [F]. While it is possible to analyze the solubil ity properties ofsimple solid solutions, such as Cas(POa):(OH)r *F*. in a rigorous way, mostbiologically and geologically formed apatit ic minerals contain a large num-ber of different impurity ions. Their solubil ity behavior has been studiedwith a more empirical approach as described below.

Variable Solubility of Biominerals

A solid with a fixed composition and crystall inity has a well-clefinedstandard chemical potential (p'). A constant Ksp value woulcl be expectedfrom such a solid based on theoretical considerations, i. e., eq.3-9, given ear-l ier. Several calcium phosphate salts, such as DCPA [McDowell et al., 197 l]and DCPD [Gregory, 19681, appear to fall into this category, and constanrKsp values have been obtained from solubil ity measurernents conductecl un-der a wide range of experimental conditions. In contrast, OHAp, OCP, and

B-TCP. are able to include significant amounts of structurally incorporatedforeign ions [LeGeros, 1991] such as H*, Na*, Mg2*, Cl-, F-, and COr2-, anclto tolerate structural irnperfections. For these solids, the ;Lo would be ex-pected to have a range of values, and variations in the Ksp value are inevit-able. In some cases, the impurity content can vary continuously, making itcl iff icult to cletermine the Ksp experimentally, as in the case with solid solu-t ions descr ibed ear l ier .

Solubi l i ty propert ies of human denta l enamel and bone mineral havebeen a subject of great interest because of their roles in hard tissue forma-tion and disease processes. Dissolution properties of carbonate-containingapat i t ic minerals have a lso been invest igated in numerous studies as syn-thetic analogues of biological apatites. In earlier studies [Patel and Brown,197-5], OHAp was assumed to be the phase that would be in equil ibriumwith the solution, and the solubil ity of the mineral was expressed in termsof IAP(OHAp), i .e., with the use of eq. 9. In later studies, a formula thatincluded some of the impurity ions, such as Ca5_^_r(HPO+),(PO+): "-(CO1)*(OH)r , y, was used [Moreno and Aoba, 1990] as the entity that gov-erned the equil ibrium. Several studies also included different levels of CO2partial pressure to help establish equil ibrium between the carbonate in thesolid and solution phases [Moreno and Aoba, 1990; Larsen et al., 1997]. Re-gardless of the IAP formula or the experimental conditions used. many

Solub i l i t y o1 ' Ca lc ium Phosphatcs

1 . 0

o)

oaa

o(g

o.cE o.s

coo(g

Laa(U

0 . 0

MES, pK

) / / ' c

Frg. 7. Schematic drawing of rhrce MES profi les.

studies reported that the incorporated foreign ions, e. g., Na*, Mg2*, Cl andCO:t-, were pref'erentiatly liberated [Larsen et al., 1997], and nearly all ofthe studies found that the experimentally determined Ksp varied signili-cantly with the experimental conditions. While there is a large body of lit-erature demonstrating the effects of structural and compositional variationsin biologically formed minerals on Ksp, a clear understanding of the me-chanisms is lacking.

More recently, a new approach was used [Fox et al., 199-5] to gain a bet-ter understanding of the variable solubility phenomenon of synthetic carbo-nated apatites, biological apatites, and perhaps apatitic mineral in general.The model employs two new concepts to describe the solid-solution equili-br ium:(1) Metastable equilibrium solubility (MES): The MES behavior occurs

when a crystalline material dissolves relatively rapidly, leading to a solu-tion compositicln such that no further dissolution occurs, even thoughthe degree of saturation is significantly below that required for crystalgrowth. The investigators found that a given mineral sample does notexhibit a single MES value but a MES profile (a range of MES values).

(2) Dissolution-governing surface complex: The surface complex is visual-ized as an entity forming at the crystal surface in contact with the ionsin solution. and it determines the functional form of the dissolutiondriving force. The formula of the complex, which is often different from

the composition of the bulk mineral, can be experimentally determinedfrom solubil ity data.To help understand the concept of MES distribution, f igure 7 shows

3 hypothetical MES profi les for minerals with a surface complex ofCa5(POa)IOH and the metastable equil ibrium solubil ity product defined asMES Ksp = (Ca2*)5(POot )t(OH ). A MES profi le is the MES Ksp that themineral sample exhibits as a function of the fraction of the mineral that haclbeen dissolved. Profi le A has a lower mean MES pKsp value than does pro-fi le B. indicating that mineral A is on average more soluble than mineral B.Profi le A also has a wider MES distribution, indicating that its solubil itycovers a wider range. When the MES distribution converges to a step func-tion (profi le C). it exhibits a single value, approaching the corrventional solu-bil i ty product constant.

A number of interesting findings have been reported from studies thatused this approach. Carbonated apatite dissolution kinetics were found tobe governed by an OHAp surface complex, and not a carbonate-containingcomplex [Hsu et al., 1994]. When the MES of a large number of carbonatedapatite samples prepared at different temperatures and with different carbo-nate contents were examined, the mean MES was not directly related to thecarbonate content, but rather to the crystall inity of the mineral as measuredby the ((X)2) x-ray diffraction peak width. When crystall inity was taken intoaccount. the carbonate contcnt did not have any l 'urthcr cffccts on MES

IBaig et al., 1996]. With the use of the Rietveld method of whole x-ray dif-fraction pattern structure refinement, the effects of carbonate on two differ-ent crystall inity perrameters, crystal size and microstrain were cletermined

IBaig et a l . . 1999] . The resul ts showed that i t was microstra in, rather thancrystal size. that predominantly determined the MES of carbonated apatitesand dental enamel. These studies have advanced significantly our under-standing of the mechanisms through which the compositional and crystalstructural modifications brought about by the impurity ions affect the disso-It-tt ion behavior of apatites. Further studies wil l be able to determinewhether the MES model is applicable over a wide range of aqueous colrrpo-s i t ions that inc luc le the fu l l range of impur i ty ions. e. g. . Na*. Mg2*, Cl - , F ,and CO.:2 , that are present in the minerals.

Concluding Remarks

The discussions of calcium phosphate solubil ity behavior given in thischapter are focused on understanding the basic principles that govern thesolid-solution equil ibrium and on the use of solubil ity phase diagrams to de-

Solubi l i ty of Calc ium Phosphates

scribe the solubil ity over a wide range of concentrations and in the presenceof additional components. In reality, the dissolution process is often mademore complex by additional concomitant processes such as the solution-so-lid surface equil ibriums described by Tung and Skrtic [2001, this volume]. Aclear understanding of the solubil ity behavior offers a good starting pointfor gaining insight into more complex processes such as hycrrolysis [Tung etal.. 19851, phase transformation [Radin and Ducheyne, r993], incongruenrdissolution [Kaufman and Kleinberg.19791, calcium phosphate cement ser-ting reactions [chow et al., 1991] and demineralization of enamel in the car-ies process [Vogel et al., 198t3].

Acknowledgements

This investigation was supported. in part, by TJSPHS Research Grant DEllTgg to thcAntcrican Dcntal Association Health Foundation from the National Insti lules ol Hcalth -National Insti lute clf Dental and Craniofzrcial Rcsearch and is part of t lrc dental lcsearcl.rprogrant concluclcc l by thc Nat ional Inst i tutc o l 'Standalds and Tcchnology in coopcrat ionwith thc Amcr ican Dcnlal Associat ior-r Hcal th Foundat ion.

References

Ba igAA . FoxJL , I I su . l . WangZ . O tsukaM. H iguch i W I . l - e ( i c rosRZ : E l l c c t o l s i l r bon i t t c con rcn tancl crystal l in i ty on the mctastablc cclu i l i t r r iunr solubi l i lv bchavior o l carborratccl apat i tcs. . l ( i ) l -Io ic l Intcr lacc Sci 1996:179:f f ) f i 617.

I la ig AA. Fox. lL, Y<runq RA. Wang Z. Hsu. l . Higuchi Wl. Chhct t r l ,A. Zhuang H. Otsuka M: Rclar ion-s l t ip antOng carbonatccl apat i tc solubi l i tv . crystal s izc. ancl nr icrostra in parantctcrs. ( 'a lc i l icc l ' l ' issucInt l9t)9:64:437-449.

I l rowtt PW: Plrasc-tc lat ionships in thc tcnrrry-svstonr ( 'aO-l ' :C)s H3O at 2.5-dcgrccs-( ' . .1 Anr ( 'cr i rnr icSoc 1992:75:l'7-22.

Brou,n WE: Solubi l i t ics o l phosphatcs ancl ot l rcr spar ingly solublc compouncls: in Envinrnnrcntal Phos-phorus Hanclbook. Ncw York, Wilcv. 1973. pp 203-239.

[ ] rowrr WE, Lchr ' . l l l : Applrcat ion ol phase ru lc to thc chcnr ical bchavio l o l nrorrocalc iunr phosphatcnron()hv( l ratc in soi ls . Soi l Sci Soc Anr Proc 1959:23:7-12.

( 'how LC. Btown WE: Fotnrat ion oi CaHPOr.2 H2O in tooth enantel as an interrrcc l iz l te procluct intopical l luor ic lc t rcatr 'ncnts. J Dcn( Res 197.51.54:(15 76.

( 'how I-C. Markovic M: Physicochcmical propcrt ies o l l luorapal i tc : in Anr jacl Z (cc l ) : Calc iunr [ 'hos-phatcs in Bio logical ancl Inc lustr ia l Systenls. Boston. Kluwcr. 19913. pp 67-f i3.

( 'horv L( ' . T)rkagi S. Costant ino PD. Fr ieclman CD: Sel l -set t ing calc ium phosphi l tc ccnrcnts. Matcr RcsSvm p Proc 199 | J7 L):3-24.

I ) r icssens FCM: ' fherrr roclynamics

of thc solubi l i ty [ rchavior o1 t ' luolhych'oxyapat i tc sol i r l solut ions. BcrBunscnscs Phys Clhcn 1979:83:5ti3-5tt6.

Dt'icsscns FCM: ll4incrul AspeLts o.f l)utislr'r,. B'rscl. Kargcr. l9li2. pp ll3-l2fi.El l io t . lC: Structufc and chcmistry o l thc apat i tcs ancl ot l . rcr calc iunr or thoplrosphatcs. Arnsle lc lanr. Elsc-

vicr'. | 9921.Forvlcr BC), Kurocla S: Changes in heated and in laser-irradiated hunran toolh cnancl ancl their prob-

able e l lects on solubi l i ty . Calc i f T issue Int l9 l t6 l3t t :197 201J.

(-how

Fox JL. Wang Z, Hsu J. Baig S. Colby S. Rrwel l GL. Otsuka M. Higuchi WI: Metastablc cqui l ibr ium sc>lubi l i ty d ist r ibut ion and c l issolut ion k inct ics of carbonate apal i te; in Arnjacl Z (cc l ) : Mincral ScaleFornat ion ancl Inhib i t ion. New York, Plcnum Press. 1995. pp23l-250.

GibbsJW: On thc cquilibrium ol hetcrogeneous sutrslances. Trans Conn Acad Ill 1876:10fi-2.11i.1u78r3213--524.

GregorvTM. MorenoEC-' , Patel JM, BrownWE: Solubi l i ty of p-Ca3(POa)2 in the Systenr Ca(OH)3-H1POr-H:O at 5. 15.25 and 37'C. J Rcs NBS 1974:18A:667 674

Ci lcgory ' l 'M. Moreno EC, Brown WE: Solubi l i ty of CaHPO..2HzO in the systcm Ca(OH)2-HjpO.-HlO at -5. 15. 25 ancl 37.-5'C. J Rcs Natl Bur Stand lt)70'.74(A):461-475.

Crcgory TM. Morcno EC, Patc l JM. Brown WE: Solubi l i ty of B-Ca3(PO1)2 in the svsrem Ca(OH):-HrPOr-HrO at .5, 15.25. and 37'C. J Res Nat l BurStand 1974:7,5(A):667 674.

Hsu. l . FoxJL. Rrwel l GL, OtsukaM. Higuchi WI. YuD. WongJ. LecerosRZ: Quanl i tat ive re lat ion-ship betwecn carbonatecl apat i te metastable equi l ibr iurr solutr i l i ty and dissolut ion k inct ics. J Collo id lntcr face Sci 1994:168:3-56 372.

Kaul lnan HW. Klc inbcrg I : Stuc{ ics on thc incongruent solubib i ty ot hydroxyapat i te. Calc i f T iss IntIt)79l.27:l 13-15 | .

Labarthe JC. Bonel G. Montc l C: Sur la st ructure ct lcs propr i6t6s dcs apal i les carbonat6cs . lc type Bphospho-calc ic lues. Ann Chim 1973; l l :21J9,301.

Larscn MJ. Pcarsc EIF. Ravnhol t G: Dissolut ion of powcrcd human enamcl suspencled in acid solut ionsat a high solicl/sttltttion ratio undcr 5",1' CO2 atnrosphcre at 20 dccrccs Cl. Archivcs Oral tsiology1997l.42$57 663.

Lc( icros RZ: ( la lc iunt Phosphatcs in Oral Bioolouy ancl Mccl ic ine. Bascl . Karger. 1991.McDowcl l H. Brown WE. Suttcr . lR: Solubi l i ty stucly o l calc iurr hydrouen phosphatc: Ion pai l l i r rnra-

t i on . I no rg Chcm l 9T l : 10 : l 63 l l - 1643 .Mcl)orvcl l H, c i rcgoryTM. l l rownwE: Solubi l i ty ot ca5(PO1)3ol l in rhc sysrenr c ia(oH)3-H3poq-

HlO at 5, 1.5. 25 ancl 37"C. . l Rcs Nat l Bul Starrc l (Phvs Clhem) 1977; i i lA 273-281.MttcGrcsorJ. Brown WE: Bloocl-bone eclu i l ibr ium in calc iuur honreostasis. Naturc 196.5;205:359.Miltsuva S.

'lhkagi S. Clrow LO: I-{yclrolysis ol' tctracalcium phosphate in IljPOa ancl I(H2PO1. .l Matcr

Sci 1996:3 I :11263-32(19.Morcno EC. Aoba T: Solubi l i ty of humun cnamcl nr ineral . J Dc Biologic Buccalc l t )90: l l l :19.5-201Morcno E( ' . ( i lcgory ' l 'M. Brown WE,: Solubi l i ty o l CaHPOl .2 H3() ancl lbrnral ion ol ion pairs in the

svstcnr ( 'a(OH). , -HrPOr-H,O ar 37. .5"C. J Res Nat l Bur Stand (phys Chcnr) 1966:70A:545.Mtxcno EC. Klcsak M, Zahlacln ik RT: Physicocherr ical aspccts o l l luor idc-apat i tc systctns rc lcvant 1tr

t hc s t u ( l y o l c l cn ta l ca r i c s . Ca r i cs Rcs 1977 : l l ( supp l I ) : 142 -171 .Narasara. iu l 'SI l . Rao VLN: A ncw intefprctat ion ol thc solubi l i tv cc lu i l ibr ia o l 'hvcl roxyapat i tc . Z Phys

(-hcnr I t)74:255:65.s-otr0

Patc l PR. I l rown WE: ' l 'hcr t t toc lynamic

solubi l i ty procluct o l human toot l t cnantc l : Powclcrcd santplc. . lDcnt Rcs 1975:54:728-736.

Racl in SR. Duchcync P: l 'hc cf lcc(s o l calc ium phosphatc ccramic cornposi t ion ancl st ructurc on in v i t robehavior . I I . Plcc ip i tat ion. . l I l ionccl Mater Rcs l9t)3:27:35-45.

' l lng MS. Chow LC. Brown WE: Hyclro lys is o l c l icalc iunr phosphate dihych'atc in t l rc prcsencc ol ab-scnce ol calc iunr I luor ic lc . J Dent Res l9 l i5:64:2--5.

- l lng MS. Eic le lnran N. Sicck B. Brown WE: Octacalc iurr phosphatc solubi l i t l ' product l }om zl to 37'C.. l Rcs Nat l IJul Stancl l9t i f i r93:613-624.

' fung MS. Skrt ic D: Inter lacia l pfopert ies o l ' hydroxyapat i te. f luoroapat i te and octacalc ium phosphatc.Monogl Oral Sci . Bascl . Karger.2(X)1, vol l t l , pp l12-129.

Vclbccck RMH. Thun HP, Dr icsscns FCM: Solubi l i ty behavior of c lefect ive l ' luoroapat i tc ancl l ' luolhy-droxyapat i tcs. Bcr Bunsengcs Phys Cl iem l9 i i0:134: I59-I ( r3.

Vrsel ( iL. Crt 'e1, ( iM. Clrow LC, GregorvTM, Brown WE: Micro-analvsis of nr ineral saturat ion wi th inenanrcl c lur ing lact ic acid c lcmineral izat ion. J Dcnt Res l9 l l l l :67: l 172 I l l t0.

L. C. Chow. ADAHF Paffenbargcr Rcscarch Center. N:rtionill Institutc of Standarcls anclTi:chnology. l(X) Burcau Drivc Stop 1J546. Caithcrsburg. MD 20fi99-ti.516 (LISA)

Solubi l i ty of Calc ium Phosphatcs l l l