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Interfacial properties and equilibria in the apatite-aqueous solution system
Interfacial Properties and Equilibria in the Apatite-Aqueous Solution System S. C H A N D E R ~ AND D. W. F U E R S T E N A U 2 Department of Materials Science and Mineral Engineering, University of California, Berkeley, California 94720 Received March 30, 1976; accepted January 18, 1979 Thermodynamic calculations of the solubility of hydroxyapatite have been carried out and the results are presented in different types of equilibrium diagrams in order to interpret observed interfacial behavior in this system. For predicting the electrical double-layer properties, especially the conditions for zero surface charge, diagram with activities of predominant calcium and phosphorous species as the axes and pH as the third independent variable have been found to be most useful. Conditions for zero charge at the surface are predicted based on the assumption that the affinity for the surface of all the lattice ions in solution is nearly equal. The different kinds of equilibrium diagrams have been found useful to explain some hitherto unexplained observations in the literature. Calculations have also been made to determine the effect of fluoride ions on the thermodynamic properties of the system. Experimental data are presented to support the calculations. INTRODUCTION
Apatites are of great importance to industrial chemistry as well as biological science. It is the most abundant of the phosphatic minerals and consequently it is essential in the technological development of such phosphorous-containing compounds as fertilizers, detergents, phosphors, dentifrices, insecticides, etc. Furthermore, hydroxyapatite is the prototype of the inorganic constituent found in tooth and bone. Thus, a knowledge of the properties of apatite is of great importance. The solubility of hydroxyapatite has been the subject of study in a number of recent theoretical and experimental investigations (1-4). After considerable experimental work, it is now established fairly well that pure hydroxyapatite has a well-defined solu1 Visiting Assistant Research Engineer. Permanent Address: Assistant Professor, Metallurgical Engineering, Indian Institute of Technology, Kanpur, India 208016. 2 Professor.
bility product (5), with p g s p [ C a l 0 ( P O 4 ) 6 (OHh] = 115. Most of the thermodynamic data for the C a - P - H ~ O system have been derived from experimental solubility data. In the past, the equilibria among various solids in the C a - P - H 2 0 system and the aqueous phase have been represented in a variety of diagrams, with either CaD, PzOs, and HzO or Ca(OH)z, HaPO4, and H20 being chosen as the independent variables (6). A knowledge of the properties of the apatite/aqueous solution interface is also important in both industry and biology. Apatite occurs in nature along with various undesirable materials and has to be purified by techniques often based on differential interfacial properties. In teeth and bones apatite is invariably present in the form of small crystallites which give rise to large interfacial areas, and thus interfacial phenomena must enter into processes involving the behavior of teeth and bones. The interfacial properties of solids in aqueous environment depend strongly upon the nature of the ionic species present in the aqueous phase
506
0021-9797/79/090506-11 $02.00/0 Copyright © 1979 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal o f Colloid and Interface Science, VoL 70, No. 3, July 1979
APATITE EQUILIBRIA
(7). Therefore, if the interfacial properties of apatites are to be understood, it is important to know more about the nature of charged and uncharged aqueous species that may be in contact with the solid phase. In discussing the mechanism of charge generation at the apatite surface, Somasundaran (8) and Bell et al. (9) listed several chemical reactions involving apatite and the aqueous solution. These authors suggested that the surface charge and surface potential are determined by the adsorption of charged aqueous species containing lattice ions. In this paper, the equilibrium relations for the apatite/aqueous solution system are presented in a graphical form to enable easy identification of the predominant charged species under a given set of solution conditions. The conditions for zero charge at the surface are calculated from the solubility data. The utility of different equilibrium diagrams has been established with the aid of suitable examples and by providing explanations for some previously unexplained observations. EQUILIBRIUM DIAGRAMS: THE C a - P - H z O SYSTEM
The selection of independent variables in the ternary system C a - P - H z O is arbitrary to some extent. Brown (6) chose to use Ca(OH)z, HaPO4, and H20 as the variables. This set of variables has the advantage that activities of components of the aqueous phase can be directly related to the activities of the chosen variables. In interfacial phenomena, charged species, especially the lattice ions common to the solid and the solution, play an important role (7). For a number of ionic solids such lattice ions determine the Galvani potential at solid/ solution interfaces and are known as potential-determining ions. Because of this, the activities of several different charged species, and combinations thereof, have been chosen as independent variables, leading to different kinds of diagrams. Myers (10) has also pointed out the need for know-
507
ing the role of individual ions, namely, Ca 2+ and OH-, in caries. It will be shown that each diagram constructed with a particular set of variables provides information not readily available when a different set of variables is used. The equilibrium diagram based on the activities of the predominant calcium and phosphorous species in solution and the pH as the independent variables is shown in Fig. 1. The diagram is drawn with calcium and phosphorous ion activities as the independent variables and the lines marked with a pH from 4 to I0 are the respective pH-invariant lines on the solubility surface. For a fixed pH, the area bound by the solid lines and the axes defines the stability region of hydroxyapatite. Outside this region, hydroxyapatite dissolves to form either simple ions such as Ca 2+, H2PO~, or HPO~- if the dissolution occurs along face A or B (on the solubility surface) or complex molecules or ions such as CaHPO4, CaPOn, or CaH2PO4+ if the dissolution occurs along other faces. The type of predominant soluble calcium or phosphorous species changes with solution conditions and their stability domains (separated by broken lines) are labeled in the diagram. The chemical reactions and the corresponding standard free energies are given in Table I. Each of the reactions in Table I is plotted in Fig. 1 and is marked by the respective letter. In the pH region 4-10, the diagram shows nine stability domains corresponding to Ca 2+, H2POi; Ca 2+, HPO~-; Ca 2+, CaH2PO4+; Ca z+, CaHPO4(aq); Ca 2+, CaPOn; CaPO4-, HPO~-; CaHPO4(aq), HPO]-; CaHPO4(aq), H2PO~; and CaH2PO~, H~PO~ as the principal solution species. The importance of these in interfacial processes is that the charge of the hydroxyapatite-aqueous solution interface is expected to be governed by the nature of the ionic species in solution. If hydroxyapatite is placed in an aqueous solution in the absence of any soluble salt of calcium or phosphorous, the system will equilibrate along the dotted Journal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
508
CHANDER AND FUERSTENAU
0 Q.
d CL
CL ° 0 13. "r
~o~ o. -r
A~ n
£ CL
0
I
2 pCo,
3 ptCoHP04)
4
5
, p(CoHzPO ~)
6 or
7
B
9
p(CaPO 4}
FIG. I. Equilibrium diagram for hydroxyapatite. Solid lines are the pH-invariant lines on the solubility surface. Broken lines separate the stability domain of various solution species. Heavy solid line is the calculated line of zero charge. The experimental results are: O, Bell e t al. (9); I , Saleeb and deBruyn (11); and &, Mishra et al. (26).
line ( Z - Z ' ) shown in Fig. 1, provided the adsorption of calcium or phosphorous species at the interface is negligible. The concentrations of various ionic species in equilibrium with hydroxyapatite at several different pH values are given in Table II. The last column in this table gives the net charge due to charged hydrogen (or hydroxyl), calcium, and phosphorous species in solution. The solution remains electrically neutral because of the presence of an equal amount of non-surface active anion (when the pH is adjusted with an acid) or non-surface active cation (when the pH is adjusted with an alkali). The net charge is Journal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
plotted in Fig. 2 from which the iso-ionic point, determined by extrapolation of the positive and negative branches, is at pH 8.7. At pH values greater than 8.7, the HA is expected to be negatively charged and it should be positively charged at lower pH values provided all the ionic species have equal affinity for the surface, ~ i.e., the conConditions for zero charge of a solid with three lattice ions. The charge at the surface of a solid containing a lattice cation and a lattice anion is zero when the surface concentrations (or adsorption densities) of the two ions are etiual. The solution conditions where this situation occurs is referred to as the point of zero charge (PZC). In dealing with solids containing
APATITE EQUILIBRIA c e n t r a t i o n o f a s p e c i e s at t h e s u r f a c e is d i r e c t l y p r o p o r t i o n a l t o its b u l k c o n c e n t r a tion. T h u s , this c o n c e p t s t a t e s t h a t t h e p o i n t o f z e r o c h a r g e ( P Z C ) o f H A o c c u r s at p H 8.7. S a l e e b a n d d e B r u y n (11) p o i n t e d o u t t h a t f o r a t ri -i o n i c s y s t e m like a p a t i t e o n e c a n l o c a t e a line o r a c u r v e o n t h e s o l u b i l i t y s u r f a c e c o n n e c t i n g , in p r i n c i p l e , an infinite n u m b e r o f P Z C s . U s i n g t h e d i a g r a m pres e n t e d in Fig. 1, it is p o s s i b l e t o d e t e r m i n e the locus of isoelectric points, which may be c a l l e d t h e line o f z e r o c h a r g e ( L Z C ) , o n the solubility surface of hydroxyapatite. T h e L Z C is s h o w n as a h e a v y line in t h e figure. T h e e x p e r i m e n t a l P Z C d a t a p o i n t s o f S a l e e b a n d d e B r u y n (11), Bell et al. (9), a n d M i s h r a et al. (26) a r e a l s o p l o t t e d in Fig. I. In p l o t t i n g t h e e x p e r i m e n t a l d a t a p o i n t s , it h as b e e n a s s u m e d t h a t t h e solut i o n is in t h e r m o d y n a m i c e q u i l i b r i u m w i t h t h e solid p h a s e . T h e h e a v y b r o k e n lines t h r o u g h t h e d a t a o f B e l l et al. a n d M i s h r a et al. m a y be r e f e r r e d to as t h e e x p e r i three lattice ions, the condition of zero charge may be obtained by changing the concentration of two of the ions independently. This leads to a set of points where the surface charge is zero, giving rise to a line of zero charge on the solubility surface (11). Characterization of the electrical double layer properties of apatites, therefore, requires determination of the line of zero charge (LZC). Attempts to calculate PZCs from thermodynamic properties have been partially successful. Parks carried out such calculations for oxides (12) and complex silicate minerals (13). For a number of oxidic solids the assumption that all hydroxo complexes adsorb onto the surface with about equal equilibrium constants gave fairly good agreement between experimental and calculated PZCs. For many ionic solids, such as Agl, AgBr, AgCI, CaF2, etc. the experimental point of zero charge considerably differs from the equivalence point (14) suggesting higher affinity of one of the ions compared to the other. Roman et al. (15) attributed the difference in affinity of the ions for the surface to the differences in the hydration characteristics of the ions. Miller and Hiskey (16) suggested that the surface anions and cations may have different energies at the surface which should also be taken into consideration. In this paper, the line of zero .charge for hydroxyapatite has been calculated with the assumption that the affinity for surface of all the lattice ions in solution can be considered essentially equal.
509 TABLE I
List of Chemical Reactions in the HydroxyapatiteAqueous Solution System A:
Calo(PO4)dOHh + 14H+ = 10 Ca2÷ + 6H~PO~ + 2H20; pCa + 0.6 p(H~PO.) pH -- -2.66 B: Calo(PO4h(OHh + 8H + = 10 Ca2+ + 6HPO4~+ 2H20; pCa + 0.6 p(HPO4) - 0.8 pH = 1.54 C: Calo(PO4)dOHh + 14H+ = 6CaH2PO~ + 4Ca2+ + 2H20; p(CaH2PO4) + 0.667 pCa - 2.333 pH = -5.51 D: Cal0(PO4)dOHh + 4H2PO~ + 14H+ = 10 CaI-I2PO+ + 2H~O; p(CaH2PO4) - 1.4 pH 0.4 p(H2PO4) = -3.74 E: Ca~o(PO4)~(OH)2+ 4H~PO~ + 4H ÷ = 10 CaHPO4(aq) + 2H20; p(CaI-IPO4) 0.4 p(H2PO,) - 0.4 pH = 1.64 F: Cal0(PO4)dOH)~ + 8H + = 6CaHPO4(aq) + 4Ca2+ + 2H~O; p(CaHPO4) + 0.667 pCa - 1.333 pH = -0.133 G: Cax0(PO4)6(OHh+ 8H + + 4HPO']- = 10 CaI-IPO4 + 2H20; p(CaHPO4) - 0.8 pH - 0.4 p(HPO4) = -1.16 H: Ca~0(PO4)e(OHh + 2H + = 4Ca2+ + 6CaPO~ + 2H20; p(CaPO4) + 0.667 pCa - 0.333 pH = 8.107 I: Cato(POJdOHh + 4 HPO|- = 10 CaPO~ + 2H + + 2H20; p(CaPO4) + 0.2 pH 0.4 p(HPO4) = 7.08 J: CaH2PO+ = Ca2+ + H2PO~ K: CaH2PO~ = CaHPO4(aq) + H + L: CaHPO4(aq) + H + = Ca2+ + H~PO~ M: CaHPO4(aq) = Caz+ + HPO~N: CaHPO4(aq) = CaPOn + H + O: CaPOn- + H + = Ca2+ + HP042P: H2PO~-= H + + HPO~41.4
-
-
-
mental LZC. Although the calculated and e x p e r i m e n t a l L Z C s d o n o t m a t c h , similarities b e t w e e n t h e t w o a r e r e m a r k a b l e . T h e g e n e r a l s h a p e o f t h e t w o L Z C c u r v e s is t h e same. Bell's L Z C and the calculated L Z C i n t e r s e c t at a b o u t p H 8.5, a n d P Z C o b t a i n e d without addition of any calcium or phosp h o r o u s c o n t a i n i n g salt t o t h e s y s t e m . It is t e m p t i n g to e x p l a i n t h e d e s c r e p a n c y b e tween calculated and experimental values e i t h e r in t e r m s o f specific a d s o r p t i o n ( h i g h e r affinity) o f o n e o r t h e o t h e r o f t h e l a t t i c e ions o r in t e r m s o f l a c k o f e q u i l i b r i u m c o n d i t i o n s in t h e e x p e r i m e n t s , b u t w e a r e g o i n g Journal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
510
CHANDER
AND FUERSTENAU TABLE
II
M o l a r C o n c e n t r a t i o n o f V a r i o u s S o l u t i o n S p e c i e s in E q u i l i b r i u m w i t h H y d r o x y a p a t i t e
pH
H+
4 5 6 7 8 9 I0 11
10 -4 10 -5 10 -6 10 -7 Very small Very small Very small Very small
1.92 2.51 3.45 6.03 1.45 4.43 1.41 4.59
Ca 2+
OH-
H=PO~
× × x × × × × ×
Very small Very small Very small 10 -7 10 -6 10 -5 10 -'1 10 -3
1.07 x 10 -2 1.47 x 10 -3 1.86 × 10 -4 1.58 × 10 -5 7 . 8 8 × 10 - r Very small Very small Very small
10 -2 10 -a 10 -4 10 -5 10 -5 10 -6 10 -6 10 -7
Net charge in solution ~
H P O 2-
1.05 1.47 1.86 1.58 7.88 2.64 8.63 6.22
x x × x × x x x
10 -5 10 -5 10 -5 10 -s 10 -6 10 -6 10 -T 10 -s
2 . 7 8 × 10 -2 3 . 5 7 × 10 -a 4 . 6 7 x 10 -4 7 . 3 2 × 10 - s 1.22 × 10 -5 - 6 . 4 1 x 10 -6 - 9 . 8 9 × 10 -5 - 1 0 -3
B a l a n c e d b y a n i o n of the a c i d o r c a t i o n of the a l k a l i .
to the adsorption of Ca 2+ ions whereas the negative charge results from the adsorption of OH- ions. Deviations from Z - Z ' line in Fig. 1 would occur when (a) the adsorption of calcium or phosphorous species is significant, or (b)
to refrain from making such explanations at the present. An important aspect to be noted here is that the predominant positively charged species at pHs less than about 8 is Ca 2+ whereas it is OH- at pHs greater than 9. Thus, the positive charge is probably due 16"
i
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i
i
LATTICE /ON CONTRIBUTION TO HARGE
i(~~
;
,, NEGATIVE POSITIVE ~ o
rr 7U I.-m Z
164
i(~5
I$O-iONIC
POINT
pH
FIG. 2. N e t l a t t i c e i o n c o n t r i b u t i o n t o c h a r g e in s o l u t i o n in e q u i i b r i u m w i t h h y d r o × y a p a t i t e as a function of solution pH. Journal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
APATITE EQUILIBRIA
511
point (see Fig. 2), the hydroxyapatite surface charge will first decrease and then become negative with increase in t h e salt concentration. Such behavior was observed experimentally by Saleeb and DeBruyn (11). The activity ratio product diagram for hydroxyapatite is presented in Fig. 3 by plotting log [Ca2+/(H+) 2] as a function of log [HPO~-. (H+)2]. The axes in these kinds of diagrams are chosen in such a w a y that the C a - P - H20 equilibria of different solids with the aqueous phase can be represented by straight lines (see Fig. 3). The diagram is, however, not quite adequate to obtain direct, more detailed information about the solution conditions. To obtain such information, a surface representing solution phase equilibria alone (equilibrium between solution species only without any consideration to the solid phase) is plotted on the diagram in the form of a grid. The intersection of this surface with the straight line for a solid then gives the conditions for equilibrium between the solid and the solution. In constructing the aqueous equilibria surface shown in Fig. 3, the total phosphorous (PT) and pH of the solution were chosen as the 28 i independent variables. The total calcium concentration in the solution (CAT) is a de24 -, ,~xx\\ CQ(OH)2 pendent variable and is determined by aqueous phase equilibrium relations. This 20 I ~ diagram was used to plot the subsequent diagrams between the variables CaT, PT, and pH, which are discussed in the paragraphs that follow. With the knowledge of equilibrium values for CaT, PT, and pH and e~ 12 ~ the equilibrium constants, the concentration of all other solution species in equilibrium with the solid under consideration can be readily calculated. In determining the grid 4i , pH6 ..6l/ representing solution phase equilibria, a | . PT-,o ,c strictly three-component system was con01. i I I sidered, namely, Ca 2+, HPO~-, H + ions and -32 -28 -24 -20 -16 -ll2 .: log [( HPO~)" 0"i+)2] their complexes. In such a case the pH of the solution can be altered only through Fla. 3. The activity ratio diagram showing the equilibria of solids as straight lines ancl the equilibria addition of HaPO4 o r Ca(OH)2 because the in solutionas the surface shown by a two-dimensional addition of a different acid or alkali introgrid. duces another component. some soluble calcium or phosphorous salt is added to the system. In both cases the calcium-to-phosphorous ratio in the solution will be different from 1.67. As an illustration of the use of Fig. i, consider hydroxyapatite in equilibrium with aqueous solution at pH 6. To this solution a soluble salt of calcium is added and the pH is kept constant. The equilibria in the system will shift in the direction shown by the arrow, X. As more and more Ca 2+ is added, the concentration of HsPO~ and HPO]- will decrease which, in turn, may give rise to posi?, tive charge at the interface. As the con'centration of Ca 2+ increases above 10-1'7, the solution species are Ca 2+ and CaHPO4(aq). Since the predominant negatively charged species is the indifferent anion, the charge at the interface may significantly increase, showing large adsorption of Ca 2+ ions. On the other hand, if a soluble phosphorous salt is added at constant pH, the equilibria in the system will shift in the direction shown by the arrow, Y. Since the solid is positively charged at the starting
Journal of Colloid and Interface Science,
Vol. 70, No. 3, July 1979
512
CHANDER AND F U E R S T E N A U
The Ca,r-Vs-pH, Pr-vs-pH, and Car-vs-Pr diagrams for hydroxyapatite (HA), octacalcium phosphate (OCP), and dicalcium phosphate dihydrate (DCPD) are presented in Figs. 4, 5, and 6. The solid lines are for the situation when the acid added to adjust pH is HAP04 and the alkali is Ca(OH)~. These diagrams are quite useful to estimate at any pH value the total amount of calcium or phosphorous in equilibrium with the solid. The diagrams also provide a quick comparison of the relative solubility of different solids as a function of solution conditions. Figure 4 clearly shows that the total calcium concentration in solution is minimum at pH 8.8 for HA, 9.8 for OCP, and is almost constant between pH 7 and 11 for DCPD. Also, the equilibrium total calcium concenI01
I
i
,6 z
1
I
~ ~
~ ~o.a
~ j64 ~.
~
§ j6~ O
~ ,66 o ,~ ~ =6r
I
DCPD
OCP
\\ N
\ \
\
\ ~ HA \
HA
i I~ 8
4
I 6
I 8
I I0
1 12
,,
14
pH
FIG. 5. Total phosphorous concentration in solution in equilibrium with dicalcium phosphate dihydrate (DCPD), octacalcium phosphate (OCP), and hydroxyapatite (HA). Solid lines are for pHs adjusted with H3PO4 or Ca(OH)2 and the broken line is for pH adjusted with HX or MOH (where X and M are indifferent ions.)
~,,.~
o.~.c,oM P . o s p . . . E
Z
(2_
..z, J6" t.)
),
Z
8
/
q ,d~ u _1
HYDROXYAPATITE \
i~',
I
e
t
8
pH
,'o
\
\
I
,z
,4
FIG. 4. Total calcium concentration in solution in equilibrium with dicalcium phosphate dihydrate, octacalcium phosphate, or hydroxyapatite. Solid lines are for pHs adjusted with HaPO4 or Ca(OH)= and the broken line is for pH adjusted with HX or MOH (where X and M are indifferent ions). Journal of Colloid and Interface Science, Vol. 70, N o . 3, J u l y 1979
tration increases in order for HA, OCP, and DCPD in the pH range shown in the diagram. The increase in calcium concentration in alkaline pHs is due to the fact that the solution pH must be increased through additions of Ca(OH)~. The broken line shows the curve for HA when pH is adjusted either with MOH where M ÷ is an indifferent (i.e., a non potential-determining) cation or with HX where X is an indifferent anion. The total phosphorous concentration in solution, presented in Fig. 5, continuously decreases with the increase in pH for each of the three solids and Px is the least for HA and the largest for DCPD in the pH range shown in the diagram. Thus, if one is interested in solubility of a
APATITE EQUILIBRIA i
i
i
i
i
i6 3 Z
_o Z
§
164
/
513
CSP values for these three solids does not have much significance since the number of moles of calcium and phosphorus on the basis of which the CSP*s are defined are different for each of the solids. The most important feature of this diagram is that CSP is relatively independent of pH in the range 7 to 11 for each of the three solids. At lower or higher pH values the solids are relatively more soluble.
q g i6 s
EQUILIBRIUMDIAGRAMS:THE Ca-P-F-H20 SYSTEM
_J ¢ I--
":////
/ I °"'
/
It is very well established that fluoride ions impart caries-resistant properties to I6 10-5 10-4 10-~, 10-2 tooth enamel. Attempts have been made TOTAL PHOSPHOROUS CONCENTRATION, to incorporate fluoride into enamel through mole/liter fluoride-rich diets (18), fluorides in dentiFro. 6. Total calcium and phosphorous concentrations in equilibriumwithdicalciumphosphate(DCPD), frices (19), mouthwashes or chewable octacalcium phosphate (OCP), and hydroxyapatite tablets (20), and through topical applications (21). Clinical studies have reiterated (HA). the beneficial effects of these methods of fluoride application. Laboratory investigasolid as a function of pH, at least two of tions, however, show that the mechanistic these three diagrams (Figs. 4, 5, and 6) role of fluoride in caries prevention is still must be used to adequately describe the far from understood. Several different salts system. To overcome this difficulty, condihave been tried as a source of fluoride tional solubility producP diagrams are ions, including NaF, acidulated phosphate drawn that better describe the pH defluoride (APF), monofluorophosphate pendence of the solubility behavior of these solids. The conditional solubility product (CSP) is defined as follows:
"YF
For HA:
CSP = (CaT)10(PT)6/(H+)S
For OCP:
CSP = (Ca,r)S(PT)6/(H+) 4
For DCPD:
XYAPATITE
i6 2
CSP = (Car)(PT)
CSP~*
A normalized conditional solubility product, CSP*, has been used such that one mole of calcium is involved in reactions for each of the three solids. (For hydroxyapatite, CSP* = (CSP)I/t°; for OCP, CSP* = ( C S p ) l l S ; and for DCPC, CSP* = CSP.) The CSP* vs pH curves for the three solids are presented in Fig. 7. The relative magnitude of the 4 The concept of conditional solubility product is used by Stummand Morgan(17) to describe equilibria in a varietyof systems.
OCTACALCIUM PHOSPHATE
PT" 10-3M I
I 4
DICALCIUM PHOSPHATEDIHYMG [ 6
I e pH
0 I
I 12
14
FIG. 7. Normalized conditionalsolubilityproduct, CSP* (see text for definitions) for hydroxyapatite octacalcium phosphate and dicalciumphosphate as a function of pH. Journal of Colloid and Interface Science,
V o l . 70, N o . 3, J u l y 1979
514
CHANDER AND FUERSTENAU I
co~ H2Po~
,,} ,]
i
p(HP042") ,2
'~ HYDROXYAPATITE CeHP04, HP042-
8
p(F)
FLUORITE k\ \X 5
4
5
6
7
8
p(Co} FIG. 8. Phase equilibria diagram showing stability domains of fluorite, fluorapatite, hydroxyapatite, and various solution species at a total phosphate concentration of l0 -2 M.
(MFP), SnF2, SnZrFe, Sn2ZrFs, TiF4, ZrF4, HfF4, etc. Many of the metal ions (except Na ÷ and K ÷) form complexes with fluoride and phosphate ions that make the chemistry of the system very complex. In the absence of complete thermodynamic data for these complexes, it is not possible to make a thermodynamic analysis of these systems. To simplify, only the system to which fuoride ions are added as the soluble salt of a monovalent nonactive cation has been considered. The thermodynamic analysis based on this is useful when the system contains NaF, KF, APF, etc. Hydroxyapatite, fluorapatite, and fluorite are the principal solids in the C a - P - F - H ~ O system. Apatites of the general formula Ca~0(PO4)6 × OHxF2-x may form, but they have been ignored for lack of thermodynamic data. 5 Graphical representation of stability rela5 Moreno et al. (22) have recently reported the stability constants of these apatites. Journal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
tions in a quaternary system such as this requires that activity of some of the variables be kept constant and a large number of diagrams can be drawn simply by choosing different variables to be constant. The diagrams presented in this paper are drawn with emphasis on the ability to understand the behavior of tooth materials when they are exposed to fluoride, or phosphate solutions of known concentrations. The choice of variables and presentation of the diagrams is somewhat arbitrary. The set of diagrams presented in Figs. 8 and 9, show the phase equilibria between hydroxyapatite, fluorapatite, and fluorite for l0 -2 and 10-3 M phosphorous in solution, respectively. The activities of various species in these diagrams refer to the activity of the predominant species. The diagrams are drawn with pF as the ordinate and pCa as the abscissa. The solid lines are the pH-invariant lines on the stability surface. The broken lines separate the
515
APATITE EQUILIBRIA
stability domains of different solution species. For example, in Fig. 8, there are two broken lines: the one on the left corresponds to the equilibrium between Ca 2+ and CaHPO4 in the solution, and the one on the right corresponds to the equilibrium between H2PO4 and HPO~-. A number of additional observations can be made from these two diagrams: (i) In acidic solutions, the H A - F A boundary moves with increase in phosphate activity in a direction so as to enlarge the stability domain of FA. Perhaps this is the reason behind use of phosphate solutions with fluoride for enamel treatments (23). (ii) In alkaline solution, the H A - F A boundary moves in a direction opposite to that in acidic solutions. The shift in the position of the boundary being significant only in acidic solutions. Off) The fluoride ion activity necessary
to convert HA to FA increases with increase in pH. If FA is the desired goal, low pH values are desirable at low F- concentrations. This is consistent with the observation of Spinelli et al. (14) that the uptake of fluoride, at low F - concentrations, increases with decrease in pH of the solution. (iv) At high fluoride concentrations, CaF2 is the product of reaction, and for effective topical applications this fluoride must be converted into FA at the enamel surface. Lin (25) recently studied the uptake of Fions on hydroxyapatite and her results show that below a certain fluoride concentration which depends on solution pH, the fluoride ions adsorb on the surface to form a layer of fluoroapatite; at high fluoride concentrations fluorite forms. The concentrations at which fluorite begins to form are plotted for the three pHs in Fig. 9 which shows that
14
i p(HPO2") ,, 3, Co::'+, H2PO
LIN (CoF2 FORMATIO HYDROXYAPATITE |
Co2+ HP024-
PCF) I
\o..5
\oH6' FLUORAPATITE
pH4
FLUORITE \
\
0 3
4
,5
6
7
8
p (Ca) FIG. 9. Phase equilibria diagram showing stability domains of fluorite, fluorapatite, hydroxyapatite, and various solution species at a total phosphate concentration of 10-~ M . The data points are for the formation of fluorite (25) in hydroxyapatite/fluoride ion system. Journal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
516
CHANDER AND FUERSTENAU
the observed values are in fair agreement with the calculated values. SUMMARY
The equilibrium diagrams presented in this paper can be used to determine the concentrations of various solution species in contact with the solid phases (principally hydroxyapatite) in the calcium-phosphatewater system. From the concentrations of the charged lattice species in solution (those species that can transfer across the interface), the iso-ionic point for the solution is predicted. The line of zero charge on the solubility surface for hydroxyapatite has been calculated from the solution isoionic points with the assumption that the affinity for surface of all the lattice ions in solution can be considered essentially equal. The predicted values show reasonable agreement with the published PZC data for HA. Total concentrations of calcium, phosphate, and hydrogen or hydroxyl ions in equilibrium with hydroxyapatite are interdependent and can be determined with the aid of Figs. 4, 5, and 6. These diagrams also show the effect of the acid or alkali that may be used to adjust the pH of hydroxyapatite suspensions. All the solids in the C a - P - H 2 0 system exhibit relatively low solubility in the pH range 7 to 11. Fluorite, ftuorapatite or hydroxyapatite may be the solids in equilibrium with the solution depending upon the fluoride ion concentration (Figs. 8 and 9). These diagrams show the thermodynamic conditions where one solid may transform into another. The diagrams correctly predict a number of observations reported in the literature. ACKNOWLEDGMENTS Discussions with Dr. S. Raghavan are gratefully acknowledged. This research was supported by the National Institute of Health, National Institute of Dental Research, Grant No. NIHR03DE 3708.
Journal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
REFERENCES 1. Moreno, E. C., Gregory, T. M., and Brown, W. E., J. Res. Natl. Bureau Stand. 72A, 773 (1968). 2. Avnimelech, Y., Moreno, E. C., and Brown, W. E., J. Res. Natl. Bureau Stand. 77A, 149 (1973). 3. Chuong, R., J. Dent. Res. Supplement No. 5 52, 911 (1973). 4. Smith, A. N., Posner, A. M., and Quirk, J. P., J. Colloid Interface Sci. 48, 442 (1974). 5. Kirby, C. L., and Hall, W. K., in "The Chemistry of Bio-Surfaces" (M. L. Hair, Ed.), chap. 15. Marcel Dekker, New York, 1972. 6. Brown, W. E., in "Environmental Phosphorous Handbook" (E. J. Griffith et al., Ed.), chap. 10. John Wiley, New York, 1973. 7. Fuerstenau, D. W., Pure Appl. Chem. 24, 135 (1970). 8. Somasundaran, P., J. Colloid Interface Sci. 27, 659 (1968). 9. Bell, L. C., Posner, A. M., and Quirk, J. P., J. Colloid Interface Sci. 42, 250 (1973). 10. Myers, H. M., Caries Res. ll(Suppl. 1), 141 (1977). 11. Saleeb, F. Z., and deBruyn, P. L., J. Electroanal. Chem. 37, 99 (1972). 12, Parks, G. A., Chem. Rev. 65, 177 (1965). 13. Parks, G. A., Adv, Chem. Series No. 67 ACS, 121 (1967). 14. Honig, E. P., and Hengst, J. H. Th., J. Colloid Interface Sci. 29, 510 (1969). 15. Roman, R. J., Fuerstenau, M. C., and Seidel, D. C., Trans. A I M E 56 (1968). 16. Miller, J. D., and Hiskey, J. B., J. Colloid Interface Sci. 41, 567 (1972). 17. Stumm, W., and Morgan, J. J., "Aquatic Chemistry," p. 197. Wiley (Interscience), New York, 1970. 18. Toth, K., J. Dent. Res. 52, 533 (1973). 19. Asenden, R., Arch. Oral Biol. 18, 133 (1973). 20. Parkins, F. M., J. Dent. Res. 51, 1346 (1972). 21. Wei, S. H. Y., J. Dent. Res. 53, 57 (1974). 22. Moreno, E. C., Kresale, M., and Zahradnik, R. T., Caries Res. ll(Supp. 1), 142 (1977). 23. Brudevold, F., Savory, A., Gardner, D. E., Spinelli, M., and Speirs, R., Arch. Oral Biol. 8, 167 (1963). 24. Spinelli, M. A., Brudevold, F., and Moreno, E., Arch. Oral Biol. 16, 187 (1971). 25. Lin, L. J., The Adsorption of Fluoride Ions by Hydroxyapatite from Aqueous Solutions, M.S. Thesis, University of California, Berkeley, 1978. 26. Mishra, R. K., Chander, S., and Fuerstenau, D. W. ,Appl. Colloids Surfaces, to be published.
Apatites are of great importance to industrial chemistry as well as biological science. It is the most abundant of the phosphatic minerals and consequently it is essential in the technological development of such phosphorous-containing compounds as fertilizers, detergents, phosphors, dentifrices, insecticides, etc. Furthermore, hydroxyapatite is the prototype of the inorganic constituent found in tooth and bone. Thus, a knowledge of the properties of apatite is of great importance. The solubility of hydroxyapatite has been the subject of study in a number of recent theoretical and experimental investigations (1-4). After considerable experimental work, it is now established fairly well that pure hydroxyapatite has a well-defined solu1 Visiting Assistant Research Engineer. Permanent Address: Assistant Professor, Metallurgical Engineering, Indian Institute of Technology, Kanpur, India 208016. 2 Professor.
bility product (5), with p g s p [ C a l 0 ( P O 4 ) 6 (OHh] = 115. Most of the thermodynamic data for the C a - P - H ~ O system have been derived from experimental solubility data. In the past, the equilibria among various solids in the C a - P - H 2 0 system and the aqueous phase have been represented in a variety of diagrams, with either CaD, PzOs, and HzO or Ca(OH)z, HaPO4, and H20 being chosen as the independent variables (6). A knowledge of the properties of the apatite/aqueous solution interface is also important in both industry and biology. Apatite occurs in nature along with various undesirable materials and has to be purified by techniques often based on differential interfacial properties. In teeth and bones apatite is invariably present in the form of small crystallites which give rise to large interfacial areas, and thus interfacial phenomena must enter into processes involving the behavior of teeth and bones. The interfacial properties of solids in aqueous environment depend strongly upon the nature of the ionic species present in the aqueous phase
506
0021-9797/79/090506-11 $02.00/0 Copyright © 1979 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal o f Colloid and Interface Science, VoL 70, No. 3, July 1979
APATITE EQUILIBRIA
(7). Therefore, if the interfacial properties of apatites are to be understood, it is important to know more about the nature of charged and uncharged aqueous species that may be in contact with the solid phase. In discussing the mechanism of charge generation at the apatite surface, Somasundaran (8) and Bell et al. (9) listed several chemical reactions involving apatite and the aqueous solution. These authors suggested that the surface charge and surface potential are determined by the adsorption of charged aqueous species containing lattice ions. In this paper, the equilibrium relations for the apatite/aqueous solution system are presented in a graphical form to enable easy identification of the predominant charged species under a given set of solution conditions. The conditions for zero charge at the surface are calculated from the solubility data. The utility of different equilibrium diagrams has been established with the aid of suitable examples and by providing explanations for some previously unexplained observations. EQUILIBRIUM DIAGRAMS: THE C a - P - H z O SYSTEM
The selection of independent variables in the ternary system C a - P - H z O is arbitrary to some extent. Brown (6) chose to use Ca(OH)z, HaPO4, and H20 as the variables. This set of variables has the advantage that activities of components of the aqueous phase can be directly related to the activities of the chosen variables. In interfacial phenomena, charged species, especially the lattice ions common to the solid and the solution, play an important role (7). For a number of ionic solids such lattice ions determine the Galvani potential at solid/ solution interfaces and are known as potential-determining ions. Because of this, the activities of several different charged species, and combinations thereof, have been chosen as independent variables, leading to different kinds of diagrams. Myers (10) has also pointed out the need for know-
507
ing the role of individual ions, namely, Ca 2+ and OH-, in caries. It will be shown that each diagram constructed with a particular set of variables provides information not readily available when a different set of variables is used. The equilibrium diagram based on the activities of the predominant calcium and phosphorous species in solution and the pH as the independent variables is shown in Fig. 1. The diagram is drawn with calcium and phosphorous ion activities as the independent variables and the lines marked with a pH from 4 to I0 are the respective pH-invariant lines on the solubility surface. For a fixed pH, the area bound by the solid lines and the axes defines the stability region of hydroxyapatite. Outside this region, hydroxyapatite dissolves to form either simple ions such as Ca 2+, H2PO~, or HPO~- if the dissolution occurs along face A or B (on the solubility surface) or complex molecules or ions such as CaHPO4, CaPOn, or CaH2PO4+ if the dissolution occurs along other faces. The type of predominant soluble calcium or phosphorous species changes with solution conditions and their stability domains (separated by broken lines) are labeled in the diagram. The chemical reactions and the corresponding standard free energies are given in Table I. Each of the reactions in Table I is plotted in Fig. 1 and is marked by the respective letter. In the pH region 4-10, the diagram shows nine stability domains corresponding to Ca 2+, H2POi; Ca 2+, HPO~-; Ca 2+, CaH2PO4+; Ca z+, CaHPO4(aq); Ca 2+, CaPOn; CaPO4-, HPO~-; CaHPO4(aq), HPO]-; CaHPO4(aq), H2PO~; and CaH2PO~, H~PO~ as the principal solution species. The importance of these in interfacial processes is that the charge of the hydroxyapatite-aqueous solution interface is expected to be governed by the nature of the ionic species in solution. If hydroxyapatite is placed in an aqueous solution in the absence of any soluble salt of calcium or phosphorous, the system will equilibrate along the dotted Journal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
508
CHANDER AND FUERSTENAU
0 Q.
d CL
CL ° 0 13. "r
~o~ o. -r
A~ n
£ CL
0
I
2 pCo,
3 ptCoHP04)
4
5
, p(CoHzPO ~)
6 or
7
B
9
p(CaPO 4}
FIG. I. Equilibrium diagram for hydroxyapatite. Solid lines are the pH-invariant lines on the solubility surface. Broken lines separate the stability domain of various solution species. Heavy solid line is the calculated line of zero charge. The experimental results are: O, Bell e t al. (9); I , Saleeb and deBruyn (11); and &, Mishra et al. (26).
line ( Z - Z ' ) shown in Fig. 1, provided the adsorption of calcium or phosphorous species at the interface is negligible. The concentrations of various ionic species in equilibrium with hydroxyapatite at several different pH values are given in Table II. The last column in this table gives the net charge due to charged hydrogen (or hydroxyl), calcium, and phosphorous species in solution. The solution remains electrically neutral because of the presence of an equal amount of non-surface active anion (when the pH is adjusted with an acid) or non-surface active cation (when the pH is adjusted with an alkali). The net charge is Journal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
plotted in Fig. 2 from which the iso-ionic point, determined by extrapolation of the positive and negative branches, is at pH 8.7. At pH values greater than 8.7, the HA is expected to be negatively charged and it should be positively charged at lower pH values provided all the ionic species have equal affinity for the surface, ~ i.e., the conConditions for zero charge of a solid with three lattice ions. The charge at the surface of a solid containing a lattice cation and a lattice anion is zero when the surface concentrations (or adsorption densities) of the two ions are etiual. The solution conditions where this situation occurs is referred to as the point of zero charge (PZC). In dealing with solids containing
APATITE EQUILIBRIA c e n t r a t i o n o f a s p e c i e s at t h e s u r f a c e is d i r e c t l y p r o p o r t i o n a l t o its b u l k c o n c e n t r a tion. T h u s , this c o n c e p t s t a t e s t h a t t h e p o i n t o f z e r o c h a r g e ( P Z C ) o f H A o c c u r s at p H 8.7. S a l e e b a n d d e B r u y n (11) p o i n t e d o u t t h a t f o r a t ri -i o n i c s y s t e m like a p a t i t e o n e c a n l o c a t e a line o r a c u r v e o n t h e s o l u b i l i t y s u r f a c e c o n n e c t i n g , in p r i n c i p l e , an infinite n u m b e r o f P Z C s . U s i n g t h e d i a g r a m pres e n t e d in Fig. 1, it is p o s s i b l e t o d e t e r m i n e the locus of isoelectric points, which may be c a l l e d t h e line o f z e r o c h a r g e ( L Z C ) , o n the solubility surface of hydroxyapatite. T h e L Z C is s h o w n as a h e a v y line in t h e figure. T h e e x p e r i m e n t a l P Z C d a t a p o i n t s o f S a l e e b a n d d e B r u y n (11), Bell et al. (9), a n d M i s h r a et al. (26) a r e a l s o p l o t t e d in Fig. I. In p l o t t i n g t h e e x p e r i m e n t a l d a t a p o i n t s , it h as b e e n a s s u m e d t h a t t h e solut i o n is in t h e r m o d y n a m i c e q u i l i b r i u m w i t h t h e solid p h a s e . T h e h e a v y b r o k e n lines t h r o u g h t h e d a t a o f B e l l et al. a n d M i s h r a et al. m a y be r e f e r r e d to as t h e e x p e r i three lattice ions, the condition of zero charge may be obtained by changing the concentration of two of the ions independently. This leads to a set of points where the surface charge is zero, giving rise to a line of zero charge on the solubility surface (11). Characterization of the electrical double layer properties of apatites, therefore, requires determination of the line of zero charge (LZC). Attempts to calculate PZCs from thermodynamic properties have been partially successful. Parks carried out such calculations for oxides (12) and complex silicate minerals (13). For a number of oxidic solids the assumption that all hydroxo complexes adsorb onto the surface with about equal equilibrium constants gave fairly good agreement between experimental and calculated PZCs. For many ionic solids, such as Agl, AgBr, AgCI, CaF2, etc. the experimental point of zero charge considerably differs from the equivalence point (14) suggesting higher affinity of one of the ions compared to the other. Roman et al. (15) attributed the difference in affinity of the ions for the surface to the differences in the hydration characteristics of the ions. Miller and Hiskey (16) suggested that the surface anions and cations may have different energies at the surface which should also be taken into consideration. In this paper, the line of zero .charge for hydroxyapatite has been calculated with the assumption that the affinity for surface of all the lattice ions in solution can be considered essentially equal.
509 TABLE I
List of Chemical Reactions in the HydroxyapatiteAqueous Solution System A:
Calo(PO4)dOHh + 14H+ = 10 Ca2÷ + 6H~PO~ + 2H20; pCa + 0.6 p(H~PO.) pH -- -2.66 B: Calo(PO4h(OHh + 8H + = 10 Ca2+ + 6HPO4~+ 2H20; pCa + 0.6 p(HPO4) - 0.8 pH = 1.54 C: Calo(PO4)dOHh + 14H+ = 6CaH2PO~ + 4Ca2+ + 2H20; p(CaH2PO4) + 0.667 pCa - 2.333 pH = -5.51 D: Cal0(PO4)dOHh + 4H2PO~ + 14H+ = 10 CaI-I2PO+ + 2H~O; p(CaH2PO4) - 1.4 pH 0.4 p(H2PO4) = -3.74 E: Ca~o(PO4)~(OH)2+ 4H~PO~ + 4H ÷ = 10 CaHPO4(aq) + 2H20; p(CaI-IPO4) 0.4 p(H2PO,) - 0.4 pH = 1.64 F: Cal0(PO4)dOH)~ + 8H + = 6CaHPO4(aq) + 4Ca2+ + 2H~O; p(CaHPO4) + 0.667 pCa - 1.333 pH = -0.133 G: Cax0(PO4)6(OHh+ 8H + + 4HPO']- = 10 CaI-IPO4 + 2H20; p(CaHPO4) - 0.8 pH - 0.4 p(HPO4) = -1.16 H: Ca~0(PO4)e(OHh + 2H + = 4Ca2+ + 6CaPO~ + 2H20; p(CaPO4) + 0.667 pCa - 0.333 pH = 8.107 I: Cato(POJdOHh + 4 HPO|- = 10 CaPO~ + 2H + + 2H20; p(CaPO4) + 0.2 pH 0.4 p(HPO4) = 7.08 J: CaH2PO+ = Ca2+ + H2PO~ K: CaH2PO~ = CaHPO4(aq) + H + L: CaHPO4(aq) + H + = Ca2+ + H~PO~ M: CaHPO4(aq) = Caz+ + HPO~N: CaHPO4(aq) = CaPOn + H + O: CaPOn- + H + = Ca2+ + HP042P: H2PO~-= H + + HPO~41.4
-
-
-
mental LZC. Although the calculated and e x p e r i m e n t a l L Z C s d o n o t m a t c h , similarities b e t w e e n t h e t w o a r e r e m a r k a b l e . T h e g e n e r a l s h a p e o f t h e t w o L Z C c u r v e s is t h e same. Bell's L Z C and the calculated L Z C i n t e r s e c t at a b o u t p H 8.5, a n d P Z C o b t a i n e d without addition of any calcium or phosp h o r o u s c o n t a i n i n g salt t o t h e s y s t e m . It is t e m p t i n g to e x p l a i n t h e d e s c r e p a n c y b e tween calculated and experimental values e i t h e r in t e r m s o f specific a d s o r p t i o n ( h i g h e r affinity) o f o n e o r t h e o t h e r o f t h e l a t t i c e ions o r in t e r m s o f l a c k o f e q u i l i b r i u m c o n d i t i o n s in t h e e x p e r i m e n t s , b u t w e a r e g o i n g Journal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
510
CHANDER
AND FUERSTENAU TABLE
II
M o l a r C o n c e n t r a t i o n o f V a r i o u s S o l u t i o n S p e c i e s in E q u i l i b r i u m w i t h H y d r o x y a p a t i t e
pH
H+
4 5 6 7 8 9 I0 11
10 -4 10 -5 10 -6 10 -7 Very small Very small Very small Very small
1.92 2.51 3.45 6.03 1.45 4.43 1.41 4.59
Ca 2+
OH-
H=PO~
× × x × × × × ×
Very small Very small Very small 10 -7 10 -6 10 -5 10 -'1 10 -3
1.07 x 10 -2 1.47 x 10 -3 1.86 × 10 -4 1.58 × 10 -5 7 . 8 8 × 10 - r Very small Very small Very small
10 -2 10 -a 10 -4 10 -5 10 -5 10 -6 10 -6 10 -7
Net charge in solution ~
H P O 2-
1.05 1.47 1.86 1.58 7.88 2.64 8.63 6.22
x x × x × x x x
10 -5 10 -5 10 -5 10 -s 10 -6 10 -6 10 -T 10 -s
2 . 7 8 × 10 -2 3 . 5 7 × 10 -a 4 . 6 7 x 10 -4 7 . 3 2 × 10 - s 1.22 × 10 -5 - 6 . 4 1 x 10 -6 - 9 . 8 9 × 10 -5 - 1 0 -3
B a l a n c e d b y a n i o n of the a c i d o r c a t i o n of the a l k a l i .
to the adsorption of Ca 2+ ions whereas the negative charge results from the adsorption of OH- ions. Deviations from Z - Z ' line in Fig. 1 would occur when (a) the adsorption of calcium or phosphorous species is significant, or (b)
to refrain from making such explanations at the present. An important aspect to be noted here is that the predominant positively charged species at pHs less than about 8 is Ca 2+ whereas it is OH- at pHs greater than 9. Thus, the positive charge is probably due 16"
i
i
i
i
i
i
LATTICE /ON CONTRIBUTION TO HARGE
i(~~
;
,, NEGATIVE POSITIVE ~ o
rr 7U I.-m Z
164
i(~5
I$O-iONIC
POINT
pH
FIG. 2. N e t l a t t i c e i o n c o n t r i b u t i o n t o c h a r g e in s o l u t i o n in e q u i i b r i u m w i t h h y d r o × y a p a t i t e as a function of solution pH. Journal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
APATITE EQUILIBRIA
511
point (see Fig. 2), the hydroxyapatite surface charge will first decrease and then become negative with increase in t h e salt concentration. Such behavior was observed experimentally by Saleeb and DeBruyn (11). The activity ratio product diagram for hydroxyapatite is presented in Fig. 3 by plotting log [Ca2+/(H+) 2] as a function of log [HPO~-. (H+)2]. The axes in these kinds of diagrams are chosen in such a w a y that the C a - P - H20 equilibria of different solids with the aqueous phase can be represented by straight lines (see Fig. 3). The diagram is, however, not quite adequate to obtain direct, more detailed information about the solution conditions. To obtain such information, a surface representing solution phase equilibria alone (equilibrium between solution species only without any consideration to the solid phase) is plotted on the diagram in the form of a grid. The intersection of this surface with the straight line for a solid then gives the conditions for equilibrium between the solid and the solution. In constructing the aqueous equilibria surface shown in Fig. 3, the total phosphorous (PT) and pH of the solution were chosen as the 28 i independent variables. The total calcium concentration in the solution (CAT) is a de24 -, ,~xx\\ CQ(OH)2 pendent variable and is determined by aqueous phase equilibrium relations. This 20 I ~ diagram was used to plot the subsequent diagrams between the variables CaT, PT, and pH, which are discussed in the paragraphs that follow. With the knowledge of equilibrium values for CaT, PT, and pH and e~ 12 ~ the equilibrium constants, the concentration of all other solution species in equilibrium with the solid under consideration can be readily calculated. In determining the grid 4i , pH6 ..6l/ representing solution phase equilibria, a | . PT-,o ,c strictly three-component system was con01. i I I sidered, namely, Ca 2+, HPO~-, H + ions and -32 -28 -24 -20 -16 -ll2 .: log [( HPO~)" 0"i+)2] their complexes. In such a case the pH of the solution can be altered only through Fla. 3. The activity ratio diagram showing the equilibria of solids as straight lines ancl the equilibria addition of HaPO4 o r Ca(OH)2 because the in solutionas the surface shown by a two-dimensional addition of a different acid or alkali introgrid. duces another component. some soluble calcium or phosphorous salt is added to the system. In both cases the calcium-to-phosphorous ratio in the solution will be different from 1.67. As an illustration of the use of Fig. i, consider hydroxyapatite in equilibrium with aqueous solution at pH 6. To this solution a soluble salt of calcium is added and the pH is kept constant. The equilibria in the system will shift in the direction shown by the arrow, X. As more and more Ca 2+ is added, the concentration of HsPO~ and HPO]- will decrease which, in turn, may give rise to posi?, tive charge at the interface. As the con'centration of Ca 2+ increases above 10-1'7, the solution species are Ca 2+ and CaHPO4(aq). Since the predominant negatively charged species is the indifferent anion, the charge at the interface may significantly increase, showing large adsorption of Ca 2+ ions. On the other hand, if a soluble phosphorous salt is added at constant pH, the equilibria in the system will shift in the direction shown by the arrow, Y. Since the solid is positively charged at the starting
Journal of Colloid and Interface Science,
Vol. 70, No. 3, July 1979
512
CHANDER AND F U E R S T E N A U
The Ca,r-Vs-pH, Pr-vs-pH, and Car-vs-Pr diagrams for hydroxyapatite (HA), octacalcium phosphate (OCP), and dicalcium phosphate dihydrate (DCPD) are presented in Figs. 4, 5, and 6. The solid lines are for the situation when the acid added to adjust pH is HAP04 and the alkali is Ca(OH)~. These diagrams are quite useful to estimate at any pH value the total amount of calcium or phosphorous in equilibrium with the solid. The diagrams also provide a quick comparison of the relative solubility of different solids as a function of solution conditions. Figure 4 clearly shows that the total calcium concentration in solution is minimum at pH 8.8 for HA, 9.8 for OCP, and is almost constant between pH 7 and 11 for DCPD. Also, the equilibrium total calcium concenI01
I
i
,6 z
1
I
~ ~
~ ~o.a
~ j64 ~.
~
§ j6~ O
~ ,66 o ,~ ~ =6r
I
DCPD
OCP
\\ N
\ \
\
\ ~ HA \
HA
i I~ 8
4
I 6
I 8
I I0
1 12
,,
14
pH
FIG. 5. Total phosphorous concentration in solution in equilibrium with dicalcium phosphate dihydrate (DCPD), octacalcium phosphate (OCP), and hydroxyapatite (HA). Solid lines are for pHs adjusted with H3PO4 or Ca(OH)2 and the broken line is for pH adjusted with HX or MOH (where X and M are indifferent ions.)
~,,.~
o.~.c,oM P . o s p . . . E
Z
(2_
..z, J6" t.)
),
Z
8
/
q ,d~ u _1
HYDROXYAPATITE \
i~',
I
e
t
8
pH
,'o
\
\
I
,z
,4
FIG. 4. Total calcium concentration in solution in equilibrium with dicalcium phosphate dihydrate, octacalcium phosphate, or hydroxyapatite. Solid lines are for pHs adjusted with HaPO4 or Ca(OH)= and the broken line is for pH adjusted with HX or MOH (where X and M are indifferent ions). Journal of Colloid and Interface Science, Vol. 70, N o . 3, J u l y 1979
tration increases in order for HA, OCP, and DCPD in the pH range shown in the diagram. The increase in calcium concentration in alkaline pHs is due to the fact that the solution pH must be increased through additions of Ca(OH)~. The broken line shows the curve for HA when pH is adjusted either with MOH where M ÷ is an indifferent (i.e., a non potential-determining) cation or with HX where X is an indifferent anion. The total phosphorous concentration in solution, presented in Fig. 5, continuously decreases with the increase in pH for each of the three solids and Px is the least for HA and the largest for DCPD in the pH range shown in the diagram. Thus, if one is interested in solubility of a
APATITE EQUILIBRIA i
i
i
i
i
i6 3 Z
_o Z
§
164
/
513
CSP values for these three solids does not have much significance since the number of moles of calcium and phosphorus on the basis of which the CSP*s are defined are different for each of the solids. The most important feature of this diagram is that CSP is relatively independent of pH in the range 7 to 11 for each of the three solids. At lower or higher pH values the solids are relatively more soluble.
q g i6 s
EQUILIBRIUMDIAGRAMS:THE Ca-P-F-H20 SYSTEM
_J ¢ I--
":////
/ I °"'
/
It is very well established that fluoride ions impart caries-resistant properties to I6 10-5 10-4 10-~, 10-2 tooth enamel. Attempts have been made TOTAL PHOSPHOROUS CONCENTRATION, to incorporate fluoride into enamel through mole/liter fluoride-rich diets (18), fluorides in dentiFro. 6. Total calcium and phosphorous concentrations in equilibriumwithdicalciumphosphate(DCPD), frices (19), mouthwashes or chewable octacalcium phosphate (OCP), and hydroxyapatite tablets (20), and through topical applications (21). Clinical studies have reiterated (HA). the beneficial effects of these methods of fluoride application. Laboratory investigasolid as a function of pH, at least two of tions, however, show that the mechanistic these three diagrams (Figs. 4, 5, and 6) role of fluoride in caries prevention is still must be used to adequately describe the far from understood. Several different salts system. To overcome this difficulty, condihave been tried as a source of fluoride tional solubility producP diagrams are ions, including NaF, acidulated phosphate drawn that better describe the pH defluoride (APF), monofluorophosphate pendence of the solubility behavior of these solids. The conditional solubility product (CSP) is defined as follows:
"YF
For HA:
CSP = (CaT)10(PT)6/(H+)S
For OCP:
CSP = (Ca,r)S(PT)6/(H+) 4
For DCPD:
XYAPATITE
i6 2
CSP = (Car)(PT)
CSP~*
A normalized conditional solubility product, CSP*, has been used such that one mole of calcium is involved in reactions for each of the three solids. (For hydroxyapatite, CSP* = (CSP)I/t°; for OCP, CSP* = ( C S p ) l l S ; and for DCPC, CSP* = CSP.) The CSP* vs pH curves for the three solids are presented in Fig. 7. The relative magnitude of the 4 The concept of conditional solubility product is used by Stummand Morgan(17) to describe equilibria in a varietyof systems.
OCTACALCIUM PHOSPHATE
PT" 10-3M I
I 4
DICALCIUM PHOSPHATEDIHYMG [ 6
I e pH
0 I
I 12
14
FIG. 7. Normalized conditionalsolubilityproduct, CSP* (see text for definitions) for hydroxyapatite octacalcium phosphate and dicalciumphosphate as a function of pH. Journal of Colloid and Interface Science,
V o l . 70, N o . 3, J u l y 1979
514
CHANDER AND FUERSTENAU I
co~ H2Po~
,,} ,]
i
p(HP042") ,2
'~ HYDROXYAPATITE CeHP04, HP042-
8
p(F)
FLUORITE k\ \X 5
4
5
6
7
8
p(Co} FIG. 8. Phase equilibria diagram showing stability domains of fluorite, fluorapatite, hydroxyapatite, and various solution species at a total phosphate concentration of l0 -2 M.
(MFP), SnF2, SnZrFe, Sn2ZrFs, TiF4, ZrF4, HfF4, etc. Many of the metal ions (except Na ÷ and K ÷) form complexes with fluoride and phosphate ions that make the chemistry of the system very complex. In the absence of complete thermodynamic data for these complexes, it is not possible to make a thermodynamic analysis of these systems. To simplify, only the system to which fuoride ions are added as the soluble salt of a monovalent nonactive cation has been considered. The thermodynamic analysis based on this is useful when the system contains NaF, KF, APF, etc. Hydroxyapatite, fluorapatite, and fluorite are the principal solids in the C a - P - F - H ~ O system. Apatites of the general formula Ca~0(PO4)6 × OHxF2-x may form, but they have been ignored for lack of thermodynamic data. 5 Graphical representation of stability rela5 Moreno et al. (22) have recently reported the stability constants of these apatites. Journal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
tions in a quaternary system such as this requires that activity of some of the variables be kept constant and a large number of diagrams can be drawn simply by choosing different variables to be constant. The diagrams presented in this paper are drawn with emphasis on the ability to understand the behavior of tooth materials when they are exposed to fluoride, or phosphate solutions of known concentrations. The choice of variables and presentation of the diagrams is somewhat arbitrary. The set of diagrams presented in Figs. 8 and 9, show the phase equilibria between hydroxyapatite, fluorapatite, and fluorite for l0 -2 and 10-3 M phosphorous in solution, respectively. The activities of various species in these diagrams refer to the activity of the predominant species. The diagrams are drawn with pF as the ordinate and pCa as the abscissa. The solid lines are the pH-invariant lines on the stability surface. The broken lines separate the
515
APATITE EQUILIBRIA
stability domains of different solution species. For example, in Fig. 8, there are two broken lines: the one on the left corresponds to the equilibrium between Ca 2+ and CaHPO4 in the solution, and the one on the right corresponds to the equilibrium between H2PO4 and HPO~-. A number of additional observations can be made from these two diagrams: (i) In acidic solutions, the H A - F A boundary moves with increase in phosphate activity in a direction so as to enlarge the stability domain of FA. Perhaps this is the reason behind use of phosphate solutions with fluoride for enamel treatments (23). (ii) In alkaline solution, the H A - F A boundary moves in a direction opposite to that in acidic solutions. The shift in the position of the boundary being significant only in acidic solutions. Off) The fluoride ion activity necessary
to convert HA to FA increases with increase in pH. If FA is the desired goal, low pH values are desirable at low F- concentrations. This is consistent with the observation of Spinelli et al. (14) that the uptake of fluoride, at low F - concentrations, increases with decrease in pH of the solution. (iv) At high fluoride concentrations, CaF2 is the product of reaction, and for effective topical applications this fluoride must be converted into FA at the enamel surface. Lin (25) recently studied the uptake of Fions on hydroxyapatite and her results show that below a certain fluoride concentration which depends on solution pH, the fluoride ions adsorb on the surface to form a layer of fluoroapatite; at high fluoride concentrations fluorite forms. The concentrations at which fluorite begins to form are plotted for the three pHs in Fig. 9 which shows that
14
i p(HPO2") ,, 3, Co::'+, H2PO
LIN (CoF2 FORMATIO HYDROXYAPATITE |
Co2+ HP024-
PCF) I
\o..5
\oH6' FLUORAPATITE
pH4
FLUORITE \
\
0 3
4
,5
6
7
8
p (Ca) FIG. 9. Phase equilibria diagram showing stability domains of fluorite, fluorapatite, hydroxyapatite, and various solution species at a total phosphate concentration of 10-~ M . The data points are for the formation of fluorite (25) in hydroxyapatite/fluoride ion system. Journal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
516
CHANDER AND FUERSTENAU
the observed values are in fair agreement with the calculated values. SUMMARY
The equilibrium diagrams presented in this paper can be used to determine the concentrations of various solution species in contact with the solid phases (principally hydroxyapatite) in the calcium-phosphatewater system. From the concentrations of the charged lattice species in solution (those species that can transfer across the interface), the iso-ionic point for the solution is predicted. The line of zero charge on the solubility surface for hydroxyapatite has been calculated from the solution isoionic points with the assumption that the affinity for surface of all the lattice ions in solution can be considered essentially equal. The predicted values show reasonable agreement with the published PZC data for HA. Total concentrations of calcium, phosphate, and hydrogen or hydroxyl ions in equilibrium with hydroxyapatite are interdependent and can be determined with the aid of Figs. 4, 5, and 6. These diagrams also show the effect of the acid or alkali that may be used to adjust the pH of hydroxyapatite suspensions. All the solids in the C a - P - H 2 0 system exhibit relatively low solubility in the pH range 7 to 11. Fluorite, ftuorapatite or hydroxyapatite may be the solids in equilibrium with the solution depending upon the fluoride ion concentration (Figs. 8 and 9). These diagrams show the thermodynamic conditions where one solid may transform into another. The diagrams correctly predict a number of observations reported in the literature. ACKNOWLEDGMENTS Discussions with Dr. S. Raghavan are gratefully acknowledged. This research was supported by the National Institute of Health, National Institute of Dental Research, Grant No. NIHR03DE 3708.
Journal of Colloid and Interface Science, Vol. 70, No. 3, July 1979
REFERENCES 1. Moreno, E. C., Gregory, T. M., and Brown, W. E., J. Res. Natl. Bureau Stand. 72A, 773 (1968). 2. Avnimelech, Y., Moreno, E. C., and Brown, W. E., J. Res. Natl. Bureau Stand. 77A, 149 (1973). 3. Chuong, R., J. Dent. Res. Supplement No. 5 52, 911 (1973). 4. Smith, A. N., Posner, A. M., and Quirk, J. P., J. Colloid Interface Sci. 48, 442 (1974). 5. Kirby, C. L., and Hall, W. K., in "The Chemistry of Bio-Surfaces" (M. L. Hair, Ed.), chap. 15. Marcel Dekker, New York, 1972. 6. Brown, W. E., in "Environmental Phosphorous Handbook" (E. J. Griffith et al., Ed.), chap. 10. John Wiley, New York, 1973. 7. Fuerstenau, D. W., Pure Appl. Chem. 24, 135 (1970). 8. Somasundaran, P., J. Colloid Interface Sci. 27, 659 (1968). 9. Bell, L. C., Posner, A. M., and Quirk, J. P., J. Colloid Interface Sci. 42, 250 (1973). 10. Myers, H. M., Caries Res. ll(Suppl. 1), 141 (1977). 11. Saleeb, F. Z., and deBruyn, P. L., J. Electroanal. Chem. 37, 99 (1972). 12, Parks, G. A., Chem. Rev. 65, 177 (1965). 13. Parks, G. A., Adv, Chem. Series No. 67 ACS, 121 (1967). 14. Honig, E. P., and Hengst, J. H. Th., J. Colloid Interface Sci. 29, 510 (1969). 15. Roman, R. J., Fuerstenau, M. C., and Seidel, D. C., Trans. A I M E 56 (1968). 16. Miller, J. D., and Hiskey, J. B., J. Colloid Interface Sci. 41, 567 (1972). 17. Stumm, W., and Morgan, J. J., "Aquatic Chemistry," p. 197. Wiley (Interscience), New York, 1970. 18. Toth, K., J. Dent. Res. 52, 533 (1973). 19. Asenden, R., Arch. Oral Biol. 18, 133 (1973). 20. Parkins, F. M., J. Dent. Res. 51, 1346 (1972). 21. Wei, S. H. Y., J. Dent. Res. 53, 57 (1974). 22. Moreno, E. C., Kresale, M., and Zahradnik, R. T., Caries Res. ll(Supp. 1), 142 (1977). 23. Brudevold, F., Savory, A., Gardner, D. E., Spinelli, M., and Speirs, R., Arch. Oral Biol. 8, 167 (1963). 24. Spinelli, M. A., Brudevold, F., and Moreno, E., Arch. Oral Biol. 16, 187 (1971). 25. Lin, L. J., The Adsorption of Fluoride Ions by Hydroxyapatite from Aqueous Solutions, M.S. Thesis, University of California, Berkeley, 1978. 26. Mishra, R. K., Chander, S., and Fuerstenau, D. W. ,Appl. Colloids Surfaces, to be published.