- Email: [email protected]
Analysis of calcium hydroxyapatite dissolution in non-stoichiometric solutions
Colloids and Surfaces A: Physicochemicaland EngineeringAspects 121 (1997) 217-228
ELSEVIER
COLLOIDS SURFACES A
Analysis of calcium hydroxyapatite dissolution in non-stoichiometric solutions Ph. Schaad
b
F. Poumier b, J.C. Voegel
b, Ph. Gramain a,,
a Ecole Nationale Supdrieure de Chirnie de Montpellier, Laboratoire de Chimie Appliqude, CNRS, URA 1193, 8, rue de l'Ecole Normale, 34000 Montpellier, France b Centre de Recherches Odontologiques U424 INSERM, 1, Place de l'H6pital, 67000 Strasbourg, France
Received 29 July 1996; accepted 23 November 1996
Abstract The dissolution kinetics of calcium hydroxyapatite powder (HAP) are investigated under constant pH values of 5.0, 5.5 and 6.0, in solutions containing initially non-stoichiometric amounts of calcium and phosphate ions. Although a true steady state is never attained, it is possible to define a pseudo-steady state within a limited reaction domain. It is demonstrated that the kinetics follow an effective order of dissolution relative to the calcium activity gradient near to 1. This process is quantitatively evaluated by a rate reduction factor which characterizes the state of the interface. It is shown that calcium adsorption takes place at the interface during dissolution, and that the evolution of the HAP surface state is responsible for the non-attainment of a true steady state. In particular, for initial strong calcium undersaturations, the attainment of the pseudo-steady state is very long. At the pseudo-steady state, the rate reduction factor is only pH-dependent, but not on the composition of the initial solution. © 1997 Elsevier Science B.V. Keywords: Calcium hydroxyapatite dissolution; Non-stoichiometric solutions
1. Introduction It is now well established that an interpretation of the dissolution kinetics of calcium hydroxyapatite ( H A P ) in terms of a purely diffusion-limited process in the Nernst layer adjacent to the crystal surface, supposing that the driving force for dissolution is the equilibrium solubility of apatite, is not fully satisfying [1,2]. In order to explain the deviation from a simple diffusive process, two models of dissolution were proposed in recent years, both including a combined surface- and diffusion-controlled mecha-
* Corresponding author. Tel.: + 33 67 144365/01; Fax: + 33 67 147220/53. 0927-7757/97/$17.00 © 1997Elsevier Science B.V. All rights reserved PII S0927-7757 (96) 03977-5
nism. According to Nancollas et al. [3], using the model developed by Christoffersen et al. [4-7], a polynuclear or SurfaCe disloCa-ti0n mechanism occurs at the surface. Based on extensive experi! mental studies, Gramain et al. [1,8-10] pr6posed a dissolution model in which the diffusion process is restricted by the spontaneous formation at the solid interface of an adsorbed calcium-rich layer. The formation of this semi-permeable layer follows a linear adsorption isotherm until saturation and, in consequence, is in constant evolution during the early stages of the dissolution process. This model was based on the experimental observation of a strong calcium accumulation at the solid interface [8,10] and on the determining influence of the sample conditioning [9]. We demonstrate that for experimental conditions in which the ratio s of
218
Ph. Schaad et al. / Colloids" Surfaces A: Physicochem. Eng. Aspects 121 (1997) 217-228
calcium and phosphate ions present in solution is close to the theoretical value of s for HAP, the experimentally consumed proton and released calcium-ion rates are well described by a firstorder law with respect to the calcium activity gradient, and by a rate reduction factor associated with the semi-permeable layer. The aim of the present paper is to study the HAP dissolution by including the influence of the initial equilibrium conditions (stoichiometric and non-stoichiometric conditions) and to extend the previous model to non-stoichiometric conditions. For non-stoichiometric conditions, the calcium over phosphate ratio S in solution ( S = C a / P ) is not constant, but is time-dependent. Dissolution experiments were achieved at three different constant pH values (5.0, 5.5 and 6.0) by continuously recording the proton consumptions and calcium releases and by determining the phosphate concentration in the bulk before and after the dissolution step. For each pH value, three experimental equilibrium solutions were studied with initial So = Ca0/Po (initial calcium over phosphate ratio) higher, lower, or equal to the stoichiometric value. We demonstrate that, as in our previous studies, a first-order law related to the calcium activity gradient of HAP describes the data well. The structure of the paper is as follows. First, we analyze the equilibrium conditions of the experiments by determining the activities of the calcium, phosphate and hydroxyl ions. Later, we will show that for a restricted reaction domain where a quasi-steady state can be considered, a first-order law related to the calcium activity is observed.
2. Materials and methods
51 + 11 m 2 g - 1. For the solid sample used, calcium was determined by atomic absorption spectrophotometry and phosphate by a colorimetric method [11]. The SHApCa/P ratio obtained was 1.63 +_0.06, to be compared to the theoretical value of 1.677.
2.2. Solutions All salts used were of analytical grade and were dissolved in deionized water. Activity factors were calculated using the Debye H/ickel equation: logf = -AZ 2
v;
(1)
1 + Bai'~/~ where Zi represents the valence of the ith ion, # is the ionic strength of the solution, ai is the distance of the closest approach, and A and B are constants depending on the temperature and the dielectric constant of the solution. The values used for A and B were 0.5092 and 0.3286 x l0 s, respectively; those for al were 6 . 0 x l 0 - S c m for Ca 2+, 4 x 10 S cm for Ca 2+, 4 x 10 S cm for HzPO 4 and P O ] - and 3 . 5 x 1 0 - S c m for OH . For all experiments, using the evaporation law consistent with this equipment [12], corrections were systematically made in order to take into account volume variations due to evaporation and to acid injection. The experiments were carried out at three pH values (5.0, 5.5 and 6.0). For each pH value, three solutions were prepared (S1-$9) (Table 1). The composition of each solution containing 8.0 × 1 0 - 2 M KC1 corresponded to the solubility product of HAP (pKspnge=59.5+l.2) [10]. Solutions S1, $4 and $7 had an So value larger than 1.67, solutions $2, $5 and $8 an S o value close to 1.67, and $3, $6 and $9 an S o value smaller than 1.67.
2.1. H A P 2.3. Calcium, phosphate and proton determination Experiments were performed with 100 160 gm hydroxyapatite (HAP) platelets (Bio-Gel HTP, Bio-Rad Laboratories, Richmond, CA) prepared as described elsewhere [9]. The specific surface area, determined by the BET method (Laboratoire de Chimie des Mat6riaux Catalytiques, Strasbourg) for HAP was found to be
The detection limit for calcium and phosphate ions with a sufficient precision was about 5 x 10 .5 M. Above this value, the precision for calcium determination with the aid of the calciumspecific electrode is about 2%. This precision is comparable to that given by Margolis et al. [13].
Ph. Schaad et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 121 (1997) 217-228
219
Table 1 Initial and final equilibrium conditions of HAP equilibrated in solutions, saturated with respect to HAP but having So> 1.63 (S1, $4 and $7), So close to 1.63 ($2, $5 and $8) or So < 1.63 ($3, $6 and $9). At equilibrium, calcium and phosphate ions were determined experimentally. The ionic products (K~)calculated with respect to HAP. pK~= -log K±should be compared with pKs = 59.5 ± 1.2 [9] Equilibrium conditions
Initial conditions
s1 $2 $3 $4 $5 $6 $7 $8 $9
CaC12 (moll 1 x 104)
KHzPO4 (moll 1 x 104)
CaC12/ KH2PO4
pH (±0.1)
pKi (±1.2)
Ca0 (moll lx104) (_+2%)
Po (moll-lxl04) (± 10%)
So= Ca0/P0 (±12%)
pH (+0.1)
pKi (_+1.2)
5.00 3.00 1.00 3.00 1.50 0.50 3.00 hl0 0.50
0.60 1.75 9.90 0.30 0.90 6.00 0.15 0.65 3.00
8.30 1.70 0.10 10.0 1.70 0.08 20.0 1.70 0.16
6.3 6.3 6.3 6.6 6.6 6.6 6.8 6.8 6.8
59.7 59.5 59.6 59.3 59.9 59.9 59.7 59.9 59.6
5.3 3.0 1.0 3.0 1.5 0.7 3.3 hl 0.6
1.0 2.0 8.0 0.5 1.1 6.2 0.5 1.0 3.2
5.30 1.50 0.12 6.00 1.36 o. 11 6.60 hl0 0.18
6.3 6.4 6.4 6.7 6.7 6.7 7.0 6.9 6.9
58.9 59.0 59.3 59.1 59.2 58.7 59.1 58.8 58.7
It was estimated by c o m p a r i n g the calcium electrode responses with the a m o u n t s o f calcium added continuously to the bulk solution. F r o m these simulation experiments, it can be seen that the specific calcium electrode responses initially show a deficiency estimated to about 2% o f the calcium added. This deficiency lasts for about 2 0 r a i n [14]. For the released calcium, which is obtained by the difference between the calcium a m o u n t present at time t and the calcium a m o u n t present initially before the start o f dissolution, the precision is a b o u t 4%. Phosphate a m o u n t s present within the solution at different experimental stages were estimated by spectrophotometric analysis o f m o l y b d e n u m blue phosphate complexes using a Beckman Model 34 spectrophotometer. Thus, 1.5 ml aliquots were withdrawn f r o m the solution after 10 min powder settling and 3.5 ml o f reagent (0.5 ml ascorbic acid solution at 10% and 3 ml o f a (NH4)6MoT.4H20 solution at 0.42% in H2SO4 N ) were added. The O D at 820 n m was measured at 37°C after 1 h o f reaction [11, 15]. The precision in phosphate determination is about 10%. It is a b o u t 1.5% for the c o n s u m e d protons, mainly due to the errors in the bulk-volume determination. The error linked to the general reproductibility o f dissolution is a b o u t 10% for p r o t o n consumption, as well as for calcium and phosphate releases.
2.4. Experimental dissolution set-up The experimental apparatus has been described previously [12]. Briefly, it consists o f a reactor (Mettler, type DV702, Greifensee, Switzerland) with two titrators (Mettler, type DL21, Greifensee, Switzerland) connected to a recorder and interfaced to a microcomputer. The reactor, thermostated at 37°C, includes a stirring system operating at 1000 rpm, a water-tight cover and an argon bubbling system. A combined p H electrode (Mettler, type D G l l l , Greifensee, Switzerland) and a calcium electrode (Orion Research, type 94-09, Cambridge, U S A ) were used. The p H and calcium ion activities within the bulk solution were followed continuously with time. The p H and calcium electrode responses were checked by control experiments. For p H measurements after less than 1 rain, the p H electrode response corresponds to the p r o t o n bulk activity with a precision o f about p H ± 0.1. 2.5. Equilibration procedure 200 ml o f S1, $2 and $3 solution (100 ml for $4, $5 and $6 and 50 ml for $7, $8 and $9), corresponding to equilibrium conditions, were added to the reactor. The procedure starts with 1 h o f
220
Ph. Schaad et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 121 (1997) 217-228
electrode stabilization within the same solutions adjusted to their respective dissolving pH values of 5.0, 5.5 or 6.0. Then, the pH was precisely adjusted to the calculated equilibrium value and the required amount of HAP added to the solution for 2 h of equilibration. The amounts of HAP added were selected in order to attain thermodynamic equilibrium at each dissolving pH value without having dissolved more than 50% of the available HAP. For this reason we used 40 mg HAP for dissolution at pH 5.0 and 20 and 10 mg at pH 5.5 and 6.0, respectively. However, since it was demonstrated in previous studies [8] that the initial surface state strongly influences the whole dissolution process, and in this respect the amount of ions adsorbed is strongly dependent upon the solid/liquid ratio, all equilibrations were performed with a solid/liquid ratio of 0.2 g 1- 1, similar to the value used in our previous studies. After about 2 h of contact of HAP with the solution, the time necessary to attain equilibrium, the pH values reached were around 6.4 for experiments S1, $2 and $3, around 6.7 for experiments $4, $5 and $6, and around 6.9 for $7, $8 and $9 (see Table 1). Stirring was then stopped for about 10rain in order to allow the powder to settle, and the bulk solution was reduced to 50 ml ( 150 ml of solution was withdrawn for experiments S1, $2 and $3, and 50ml for experiments $4, $5 and $6). 1.5 ml of solution was also kept for phosphate determination.
2.6. Dissolution procedure For all experiments, HAP dissolution was initiated by 'a rapid decrease of the pH to the desired value. The volume of injected acid for the pH jump was systematically estimated from control (without HAP) experiments, and withdrawn from the total amount of injected acid for the estimation of protons consumed during dissolution. The volume of acid added at each injection was very low (0.01% of the 5 ml burette volume), and the bulk solution was stirred and perfectly homogenous. The desired pH value was reached after the first minute of HCI addition, and was kept constant by continuous (3.0 x 10 -z N) HC1 injection. The solid/liquid ratios varied in the dissolution period
from 0.2gl -t at pH6.0 to 0.4gl 1 at pH5.5 and 0.8g1-1 at pH5.0, which allowed us to explore the whole dissolution domain until the dissolution of less than 50% of the available HAP, when thermodynamic equilibrium was reached.
2.7. Solubility products of HAP at equilibrium (pH 7.0) and at dissolution equilibrium (pH 5.0, 5.5 and 6. O) The ionic products with respect to HAP were calculated after reaching equilibration and at the end of the dissolution period. They were evaluated using the Debye-Htickel approximation and the measured phosphate, calcium and ionic proton concentrations. The values found were compared to the solubility product of HAP (pK~pugp: 59.5 _+1.2) [101.
3. Results and discussion
The experimental approach used in this study consisted of following the dissolution kinetics of HAP with pH- and calcium-selective electrodes. HAP was first equilibrated at neutral pH in solutions containing different selected amounts of calcium and phosphate ions. The composition of these solutions was chosen so as to correspond to HAP saturation in a pH domain close to pH 7.0, in some cases with Ca/P ratios far from the HAP stoichiometry [(Ca/P)nke=l.63]. After reaching equilibrium, the pH was rapidly decreased and the protons taken up and calcium released were recorded continuously up to the final equilibrium. The ionic composition of the solutions at the initial equilibrium (before the start of dissolution) and at the end of the dissolution step are shown in Tables 1 and 2, respectively. These analyses, using pH and calcium electrodes and phosphate determination by a spectrophotometric method, allowed us to calculate the ionic products (Ki) of the solution with respect to HAP and to compare them with the solubility product (KspHAp)of HAP [10]. Ki is given by: Ki = [aCa 2+ ]5[aPO]- ]3[aOH ]
(2)
where aCa 2+, aPO 3- and aOH- correspond to
Ph. Schaad et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 121 (1997) 217-228
221
Table 2 Final bulk concentrations determined experimentally at the end of the dissolution stage, and amounts of calcium and phosphate released during the dissolution stage. The conversion percentage (last column) is estimated on the basis of released calcium. Ionic products (Ki) were calculated with respect to HAP.pK i = - l o g Ki should be compared with pK~ = 59.5 _+ 1.2 [9] pH of dissolution
S1 $2 $3 $4 $5 $6 $7 $8 $9
5.0
5.5
6.0
Final conditions
Amounts dissolved
Ca (moll-Ix104 ) (_+2%)
P (moll-~x104 ) (_+ 10%)
Ca/P (_+12%)
pKi (_+1.2)
Car (moll-ax104 ) (_+4%)
Pr (moll-Ix104 ) (_+ 10%)
Car/Pr (-+-14%)
HAP conversion (%)
40.0 38.2 37.5 17.6 12.6 11.9 6.5 5.8 3.5
21.0 23.3 27.6 8.8 8.0 13.2 3.2 5.4 6.4
1.90 1.63 1.35 2.00 1.57 0.90 2.03 1.07 0.54
59.6 59.0 59.5 59.6 59.2 59.5 59.0 59.2 59.4
35.7 35.9 36.8 14.8 11.0 11.5 3.3 4.5 2.8
20.4 21.2 20.0 8.3 7.0 6.4 2.4 4.1 2.6
1.75 1.69 1.84 1.78 1.57 1.79 1.37 1.01 1.07
45 45 46 37 32 29 17 22 14
the activities of the calcium, phosphate (PO]-) and hydroxyl ions, respectively. The same relation is defined for KspHAPby replacing the bulk activities with the saturating activities. The data shown in Table 1 indicate that at the end of equilibrium (before dissolution), all the solutions were saturated with respect to HAP (pKsp~A P = 59.5 _+1.2). Similarly, at the end of the dissolution steps and for the three pH values (5.0, 5.5, 6.0), when both the protons consumed and the calcium released remained unchanged within the solutions, saturation with respect to HAP was again observed (Table 2), even when the final conditions were far from Ca/P congruency. These results are in good agreement with those obtained by Hagen et al. [16] and by Brown [17], who showed that the thermodynamic equilibrium of HAP may also be reached in non-stoichiometric conditions. The amounts of HAP initially added were calculated in order to allow an HAP conversion of less than 50%, even when dissolution equilibrium was attained in the bulk. Moreover, this experimental method allowed us to explore concentrations which covered the domain ranging from the largely undersaturated conditions (at the beginning of the dissolution kinetics) until the attainment of saturation. Fig. 1 shows a typical example of proton consumption and calcium release kinetics at pH 5.0
with the different initial S0=Cao/Po ratios given in Table 1. The same type of kinetics is observed at pH 5.5 and 6.0. From such kinetics, the proton consumption rates JH (in mol g- 1 s - 1) are obtained by numerical derivation of the proton dissolution kinetics. Examination of these kinetics demonstrates that proton consumption is only little affected by the initial non-stoichiometric conditions, while the calcium release kinetics show greater differences. The interpretation of these kinetics requires knowledge of the variation of the ratio S = C a / P in solution during the dissolution process. S can easily be determined at each time from the initial conditions and the calcium release kinetics when the amounts of phosphate released during dissolution are known. The phosphate release kinetics are easily estimated from the proton or calcium kinetics when a congruent HAP dissolution is assumed. This hypothesis is justified since there is no apparent reason to suppose that the initial non-stoichiometric conditions influence the stoichiometry of the HAP decomposition under acidic conditions. Moreover, as demonstrated in Table 3 (columns 4 and 5), the total amounts of phosphate released at the end of the dissolution period (estimated from the colorimetric method) are comparable to the amounts estimated either from consumed protons or released calcium by supposing a congruent
222
Ph. Schaad et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 121 (1997) 217 228 6.0
E,
,
,
activity gradient (asCa aCa) and by the definition of a rate reduction factor 1/(1 + K ) :
,
5.0
p° a
x
T -5 E
JH = R J c a = R
4.0 $1 $2 $1
3.0
(a)
m c
pH
'
5.0
37"C
1.0
0 0 l
0
I
I
I
I
100 200 300 400 500 600
4.0 S -~
i
$
i
i
1
i
i
~
3.o
s2 -6 E
2.0
0
"o o gl
(3)
fo a
2.0
0.0
(asCa - aCa)"
with:
'7-
E
([+K)
1.0 [/
pH 5.0
F
370C
o
0.0
I
0
I
I
I
l
100 200 300 400 500 iO0 t i m e (rain)
Fig. 1. Proton uptake (a) and calcium release (b) kinetics at 37°C and pH 5.0, with a stirring speed of 1000 rpm, and in the presence of 8.0 x 10 2 M KC1 for experiments performed with solutions S1, $2 and $3 with 40 mg HAP.
dissolution. On this basis, the phosphate release kinetics were estimated from the proton consumption kinetics, which were determined with a better precision than the calcium release kinetics. The variation of S with dissolution time at p H 5.0, 5.5 and 6.0 is given in Fig. 2. Depending on the initial S o values and the pH, it is observed that S becomes nearly constant after 10 15% of conversion. It is clear that before this percentage, the dissolution process is far from steady-state. In previous studies [1,18, 19], we could demonstrate that when S remained close to the theoretical Ca/P ratio of HAP, the proton consumption rate Jn and calcium release rate Jc, were well described by a first-order law with respect to the calcium
K = - - and n = 1 Pca
(4)
where asCa represents the calcium activity at saturation at the solid interface, aCa is the calcium activity in the bulk solution, and n is the order of the reaction. R is the number of protons consumed when one calcium is released, and is pH-dependent, p0Ca represents the mass transfer coefficient in the Nernst layer in the absence of any chemical reaction, and PCa is the mass transfer coefficient characterising the permeability of the interfacial layer where the chemical reaction takes place. K defines the reduced permeability of the surface layer with respect to the Nernst layer, In order to check the validity of Eq. (3) in nonstoichiometric conditions, and more particularly the order of the reaction, plots of the proton flux versus asCa-aCa in log-log scales according to Eq. (3) are shown for the three p H values in Fig. 3Fig. 4Fig. 5. In each figure, the solid straight line represents the ideal slope of 1 (n = 1). Before discussing the results in greater depth, it is useful to consider the limits of the analysis of the kinetics imposed by the experimental conditions. The H A P used sample is platelet-shaped and the surface area can be considered as constant until a degree of conversion of 30% [ 1]. This value constitutes the higher limit of analysis. The lower limit can be defined from the S kinetics. It should be higher (or at least equal) than the beginning of the domain where the S ratio remains nearly constant, and for which a pseudo-steady state can be assumed. F r o m Figs. 3 5, it is clear that from 0 to 30% of conversion, the slopes decrease with increasing conversion, with a trend to stabilization around a value of I or close to 1. The initial slopes at high undersaturation correspond to values of n varying from 2 to 4. During this period, the hypothesis of the existence of a linear and constant interfacial gradient cannot be assumed. The strong
Ph. Schaad et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 121 (1997) 217-228
223
Table 3 Comparison between the experimentallyestimated phosphate amounts at the end of dissolution stage (Pr measured) determined by the molybdate complexation method, and the phosphate evaluated by considering the total amount of consumed proton (Pt from H) or of released calcium (Pr from Car) Experiment
pH of dissolution
Pr measured (moll-Ix104 ) (_+ 10%)
Pr from H consumption (moll lx104 ) (_+ 1.5%)
Pr from Car release (moll 1x104 ) (+4%)
SI $2 $3 $4 $5 $6 $7 $8 $9
5.0
20.4 21.2 20.0 8.3 7.0 6.4 2.4 4.1 2.6
22.2 21.5 22.8 8.5 7.1 6.5 2.1 3.0 1.9
21.3 21.4 22.0 8.9 7.7 6.9 1.9 2.7 1.7
5.5
6.0
6
~ ~ r - - - - - v - - - - T
5 4 3 2
$1
$2 •
1
o
o
o
---~
pH 5.0
•
"" ....
ooooo
o ° o ~
~ .
o°o°oo°°o.
$5
0
° ° °°°°°°+°
0
° ° ° o N
5
10
5 4 3
:,
5
20
25
50
H 5.5 "l
0
5
10
15
20
25
30
6
-,q'
5
~"~,~
4
~
pH 6.0
S8
2 1
Sg 0
5
10
15
20
conversion %
Fig. 2. S estimated from the ratio between the initial So= Cao/Po and Sr = Car/Pr, the ratio of released calcium (Cap detected by the specificelectrode) and released phosphate (from H uptake kinetics) vs. time at pH 5.0 (S1-$3), 5.5 ($4 $6) and 6.0 ($7 $9).
variations of n in the initial dissolution periods explain why the H A P sample conditionings and the origin of the H A P sample have such a considerable effect on the dissolution kinetics [8-10]. This demonstrates the determining role of the H A P interface in the dissolution process, and explains the important scattering of the n values already published. Using the constant composition technique, Nancollas et al. [20] studied the behavior of different apatites at a high degree of undersaturation and for a reaction conversion smaller than 10%. They obtained n values respectively equal to 4.2 for H A P prepared in their laboratory, 1.9 for extracted h u m a n enamel, 1.5 for h u m a n enamel and 1.0 for bovine enamel. More recently, Budz et al. [21,22], using the same technique, observed orders of respectively 5.05 and 5.43 for H A P reaction after 5 and 10% of conversion. These values are close to those reported by Christoffersen and Christoffersen [5]. Budz et al. [21] noted, however, that at lower undersaturations, the rates fall abruptly to much lower kinetic orders. An interpretation was given in terms of the possible presence of impurities or a modification of the surface properties as the reaction proceeds. Considering that the observations made during the initial dissolution period were representative of the general mechanism, the authors suggested that the decrease of the slope was related to the reaction mechanism itself, and explained it in terms of a polynuclear mechanism [5].
224
Ph. Schaad et al. / Colloids" Surfaces A." Physic•chem. Eng. Aspects 121 (1997) 217 228
conversion
conversion % .30 -6.0
20
10
r
,
30
0
i
T
I
::
-6.0
I ii
.~,~-"
-7.0 i
..,~.~
7
-6.0
i
.
o
." i."
T
T -6.5
--
O
- 6 . 5
E -7.0
o --
0
-6.5
6'1
-5 E
10
°°•°
-6.5
-7.0
20
-6.0
i
o -
-6.0
-7.0 i
- 6 . 0
i°* • °,~°°
-6.5
_7oH -3.50
s3 -3.25
-3.00
Iog(a - a )
-7.0
-3.6
-3.4
-3.2
Iog(a - o )
Fig. 3. Log JH vs. log (a,Ca-aCa) representation for experiments at pH 5.0 (S1 $3). Experimental data are compared with a straight line (solid line) of slope n = 1. The two solid vertical lines define the domain of validity obtained from the estimation of S and the conversion limit of 30%, and the dotted line corresponds to the conversion percentage where calcium adsorption is maximal.
Fig. 4. Log JH vs. log (asCa-aCa) representation for experiments at pH 5.5 ($4 $6). Experimental data are compared with a straight line (solid line) of slope n = 1. The two solid vertical lines define the domain of validity obtained from the determination of S and the conversion limit of 30%, and the dotted line corresponds to the conversion percentage where calcium adsorption is maximal.
A n a v e r a g e d slope ( T a b l e 4) was o b t a i n e d b y linear regression o f each kinetics (Figs. 3 - 5 ) b y considering the d o m a i n (vertical bars) defined b y the 30% c o n v e r s i o n limit a n d the beginning o f the d o m a i n where S r e m a i n s constant. F o r the nine experiments, the slopes v a r i e d f r o m 1.0 to 2.0 with a m e a n value o f 1.25_+0.25. In g o o d a g r e e m e n t with this result, W h i t e a n d N a n c o l l a s [3], a n d p a r t i c u l a r l y D a l a s et al. [23], o b s e r v e d a quasilinear d e p e n d e n c e between m i n e r a l i z a t i o n rates a n d u n d e r s a t u r a t i o n with an n value o f 1.25 _+0.18. A value slightly a b o v e unity is n o t surprising, since it is clear f r o m Figs. 2 - 5 t h a t a true steady state is never fully reached in the d o m a i n considered. H o w e v e r , this value s u p p o r t s the i n t e r p r e t a -
tion o f the d a t a a c c o r d i n g to a first-order law with respect to u n d e r s a t u r a t i o n , as for stoichiometric conditions. The initial d i s s o l u t i o n p e r i o d before the quasilinear regime is interesting to investigate since it is related to i m p o r t a n t interfacial exchanges. These exchanges constitute the basis o f the p r o p o s e d model, in which the rate decreases o f the dissolution process are i n t e r p r e t e d b y the f o r m a t i o n o f a s e m i - p e r m e a b l e layer due to an interfacial calcium a c c u m u l a t i o n occurring, m a i n l y in the initial dissolution times [8]. In this study, we investigated this aspect a n d systematically c a l c u l a t e d the o b s e r v e d calcium deficiencies A C a in the b u l k s o l u t i o n vs. time. We c a l c u l a t e d t h e m f r o m p r o t o n consumption and calcium release kinetics
Ph. Schaad et aL / Colloids Surfaces A: Physicochem. Eng. Aspects 121 (1997) 21~228 conversion
-6.5
30
20
Table 4 Evolution of S, n and 1/1 + K values at t = 0 (see Eq. (3) for experiments performed at pH 5.0 (S1 $3), 5.5 ($4-$6) and 6.0 ($7 $9). The slopes n were obtained from linear regression of the experimental data given in Figs. 3 5 between the lower and upper domain limits in the percentage of conversion. The rate reduction factors extrapolated to t = 0 1 / ( I + K ) , = 0 were obtained from a linear regression in the defined interval domain as shown in Fig. 7 for pH 5.0
%
10
0
.'"
$7
-6.0 ~. T
-8
E -7.0 -o= c,
.S
-7.5
o -
- 6 . 0
,
-6.5
,
i
-7.0 -7.5
-4.5
-4.0
- 5.5
Fig. 5. Log Jn vs. log (a~Ca-aCa) representation for experiments at pH 6.0 ($7 $9). Experimental data are compared with a straight line (solid line) of slope n = 1. The two solid vertical lines define the domain of validity obtained from the determination of S and the conversion limit of 30%, and the dotted line corresponds to the conversion percentage where calcium adsorption is maximal.
according to the relation
[HI
pH of dissolution
Mean S value (_+5%)
Slope n ( 4- 0.25 )
1/(1 + K ) x 1034- 0.1 at t = 0
SI $2 $3 $4 $5 $6 $7 $8 $9
5.0
2.1 1.6 1.0 2.5 1.6 0.8 2.6 1.5 0.4
1.1 1.4 1.0 1.3 1.0 1.5 1.2 1.3 2.0
0.60 0.64 0.64 0.80 0.90 1.10 0.80 1.30
-[Car]
5.5
6.0
" ~ ' ~
Iog(a -a)
A[Ca] = ~ -
Experiments n=l
-6.5
225
(5)
where R corresponds to the H/Ca ratio for the HAP used (R = 1.43 at pH 5.0, 1.38 at pH 5.5 and 1.36 at pH 6.0). Eq. (5) assumes that all the protons are exclusively consumed by ionic Ca and P exchanges. However, protons are also involved in the build up of the surface charge and the electrical double layer. It is assumed that both these mechanisms are rapid and fully achieved at the start of the dissolution process, since the start is preceeded by a period of 1 min, during which the pH is decreased from its equilibrium value (Table 1) to
the pH value of dissolution. The results obtained for the three pH values and different experimental conditions are represented in Fig. 6. At pH 5.0 and for the stoichiometric $2 solution, the calcium deficiency represents a deviation of 7%. This becomes 30% for the strongly calcium-deficient $3 solution, and is very low for the calcium-rich S1 solution. Similar observations were made at pH 5.5 and 6.0, with the calcium adsorption kinetics showing a maximum. The error of the estimation of the calcium deficit being around 5%, we conclude the existence of an effective general tendency towards interfacial calcium accumulation. The calcium bulk activities Cama x and the dissolution times z corresponding to the maximum amounts of calcium adsorbed A[Ca]m,× are shown in Table 5. For experiments $7 and $8 (pH 6), the effects are too small to be evaluated quantitatively. The adsorbed calcium amounts Fma. (in mol cm -z) can be estimated if one supposes that accumulated calcium is effectively adsorbed at the HAP surface. The values (Table 5) range from 1.47 to 13.4 x 10 l°mol cm -2, and are more than one order of magnitude higher than the value of 2.6x 10 H m o l c m - 2 estimated by Maf6 et al. [24], assuming a monolayer adsorption of calcium ions having an ionic radius corresponding to the
226
Ph. Schaad et al. / Colloids Surfaces A." Physicochem. Eng. Aspects 121 (1997) 217-228
6.0
.
.
.
.
i
.
.
.
.
i
.
.
.
.
i
.
.
.
.
3.0
0.0 0 2.0
/~ . . . . . . . . . . . . . . . . . 100 200 .......................
300
400
x
7_
1.0
$5
E "~
0.0 0 1.0
60 ....
120 180 , ..............
240
300
pH 6 . 0 $9 0.5
0.0 0
50 time
1 O0
150
200
(min)
Fig. 6. Calcium deficiency (3ca) obtained from the difference between the congruently released calcium estimated (from H-uptake kinetics) and released calcium, Car (detected by the specific electrode), vs. time.
Debye length. This suggests multilayer formation, as proposed in the layer model [25]. Moreover, the layer model supposes a permanent calcium accumulation during the dissolution process in relation with the increasing calcium concentration in the dissolving medium. This behavior seems to be verified by the results in Fig. 6, since a strong tendency for calcium accumulation is observed throughout the whole kinetics. In summary, the shape of the adsorption kinetics, with the existence of a maximum (in particular at pH 5.0), confirms the hypothesis of two distinct phenomena on the basis of the dissolution model. At initial times, calcium adsorption occurs to equilibrate the interface after the rapid pH decrease of the solution, and leads to the formation of the inhibiting calcium layer. The time which corresponds to the maximum amount of calcium adsorbed onto H A P is approximatively equal to the lower limit defining the constant-S domain. This time is defined in Figs. 3 and 4 by the vertical dotted lines. Moreover, the observed increase of adsorbed calcium ions (Table 5) when the pH decreases is in agreement with the decrease in auto-inhibition observed for higher pH values [1]. According to the layer model, this is due to the presence of divalent phosphate ions, which increases the permeability of the calcium layer, a phenomenon which is well documented in ionexchanging membranes [26]. In such conditions,
Table 5 Maximum amount of calcium ions /'max absorbed onto HAP and estimated from calcium deficiency A[Ca]maxobtained from the difference between congruentlyreleased calcium (estimated from H consumption) and released calcium (Car, estimated from calcium electrode), r is the time necessaryto attain Fma,, and [Ca]maxand is respresented by dotted line in Figs. 3 5 Experiments
pH of dissolution
[Ca]maxmeasured in the bulk (mol 1-1 x 104)
3[Ca]max (Ca deficiencyin the bulk) (mol 1-1 x 104)(_+0.5)
Fmax(adsorbed Ca on HAP)z (min) at maximum deficiency (mol cm -2 × 101°)
$1 $2 $3 $4 $5 $6 $7 $8 $9
5.0
22.0_+2.2 24.0_+2.4 25.0_+2.5 2.8_+0.25 2.3 _+0.25 2.8 _+0.25 1.8_+0.25 1.2_+0.25 < 1.2
0.6 2.0 5.5 0.5 0.8 1.6
1.47 40 4.90 80 13.4120 2.45 35 3.92 35 7.84100
0.6
5.88140
5.5 6.0
Ph. Schaad et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 121 (1997) 217-228
it becomes obvious that a true steady state is never achieved during HAP dissolution, except perhaps for high pH values. Since a first-order law describes the dissolution process, the phenomenological double-layer model described by Eq. (3) permits the study of the rate reduction factor which characterizes the inhibiting effect of the adherent calcium layer. It gives a quantitative evaluation of different factors capable of affecting the HAP interface and the dissolution mechanism. In particular, its evolution during the dissolution of HAP is interesting to study, since it describes the formation and reinforcement of the layer. 1 / ( I + K ) kinetics are given in Fig. 7 (pH 5), and, as observed in a previous study [1], 1/(1 + K ) decreases rapidly in the initial times, then decreases 8.0 6.0 4.0 2.0 0.0 0
5
10 15 20 25 30 35
0
5
10 15 20 25 30 35
8.0 6
6.0 4.0 2.0
227
linearly with time or levels off. The vertical lines in Fig. 7 define the considered pseudo-steady state domains, as in Figs. 3-5. The dotted lines indicate the conversion ratios corresponding to the maximum of accumulated calcium. According to the previous analysis, the initial rapid decrease of 1/(1 + K ) corresponds to the interfacial calcium accumulation period, and the linear domain to the establishment of a pseudo-steady state. From this linear behaviour, it is possible by extrapolation to define values of 1/(1 + K ) corresponding to t = 0 , which describes the permeability of the interface during the dissolution process at steady state. These extrapolated data avoid the need to evaluate these parameters at a given degree of saturation, as generally done in the analysis of HAP kinetics. The extrapolated 1/(1 + K ) values are shown in Table 4 and, as expected from comparison with the values obtained for stoichiometric conditions, show a similar dependence on pH [1]. At higher pH values, the permeability of the interface is higher and the non-steady state period is shorter. The initial So = Cao/Po composition does not seem to have any influence, except on the time necessary to attain the steady state. The lower the initial calcium concentration, the longer the time needed to reach the steady state. An interpretation in terms of calcium amounts necessary to form the adherent calcium-rich layer is in good agreement with the proposed model.
0.0 8.0
4. Conclusion
6.0 4.0
$3,
2.0
,
, ~
0.0
0
5
10 15 20 25 30 35 conversion %
Fig. 7. 1/(l+K)n vs. conversion percentage calculated with Eq. (3) for experiments realized with solutions S1, $2 and $3 (pH 5). Extrapolationsto t = 0 weredone from linear regression in the steady-state domain defined in Table 4. The two vertical lines definethe domain of validityobtained from the determination of S and the conversionlimit of 30%, and the dotted line corresponds to the conversion percentage where calcium adsorption is maximal.
The analysis of the HAP dissolution process in equilibrated solutions corresponding to different So = Cao/Po ratios demonstrates the important role played by the calcium ions adsorbed at the solid interface. In particular, we demonstrate that, due to interfacial ionic exchange and calcium accumulation, a pseudo-steady state is only attained after long reaction times. This explains the difficulties encountered in the study of HAP dissolution and the important scatter in the reaction orders reported in the literature. The present data demonstrates that the reaction order is close to 1 in a restricted experimental domain, and confirms for
228
Ph. Schaad et al. / Colloids" Surfaces A: Physicochem. Eng. Aspects 121 (1997) 217 228
n o n - s t o i c h i o m e t r i c c o n d i t i o n s the results o b t a i n e d for s t o i c h i o m e t r i c c o n d i t i o n s .
Acknowledgment O n e o f the a u t h o r s (P.S.) t h a n k s " l a F a c u l t 6 d ' O d o n t o l o g i e de S t r a s b o u r g " , F r a n c e , f o r financial s u p p o r t .
References [1] J.M. Thomann, J.C. Voegel and Ph. Gramain, Colloids Surfaces, 54 (1991) 145. [2] W. White and G.H. Nancollas, J. Dent. Res., 56 (1977) 524. [3] W.C. Chen and G.H. Nancollas, J. Dent. Res., 65 (1986) 663. [4] J. Christoffersen, M.R. Christoffersen and N. Kjaergaard, J. Cryst. Growth, 43 (1978) 501. [5] J. Christoffersen and M.R. Christoffersen, J. Cryst. Growth, 47 (1979) 671. [6] J. Christoffersen, J. Cryst. Growth, 48 (1980) 29. [7] J. Christoffersen and M.R. Christoffersen, J. Cryst. Growth, 57 (1982) 21. [8] Ph. Gramain, J.M. Thomann, M. Gumpper and J.C. Voegel, J. Colloid Interface Sci., 128 (1989) 370. [9] J.M. Thomann, J.C. Voegel and Ph. Gramain, Calcif. Tissue Int., 46 (1990) 121.
[10] Ph. Gramain, J.C. Voegel, M. Gumpper and J.M. Thomann, J. Colloid Interface Sci., 118 (1987) 148. [11] Ames, Methods Enzymol., 8 (1966) 115. [12] J.M. Thomann, P. Gasser, E. Br6s, J.C. Voegel and Ph. Gramain, Comput. Methods Programs Biomed., 31 (1990) 89. [13] H.C. Margolis and E.C. Moreno, Calcif. Tissue Int., 50 (1992) 137. [14] J.M. Thomann, Thesis, Strasbourg, 1989. [15] P.S. Chen, T.Y. Toribara and H. Warner, Anal. Chem., 28 (1956) 1756. [16] A.R. Hagen, Acta Odont. Scand., 33 (1975) 67. [17] W.E. Brown, J. Dent. Res., 53 (1974) 204. [18] Ph. Schaad, J.M. Thomann, J.C. Voegel and Ph. Gramain, Colloids Surfaces A: Physicochem. Eng. Aspects, 83 (1994) 285. [19] Ph. Schaad, J.M. Thomann, J.C. Voegel and Ph. Gramain, J. Colloid Interface Sci., 164 (1994) 291. [20] G.H. Nancollas and M.B. Tomson, Science, 200 (1978) 1059. [21] J.A. Budz, M. Lore and G.H. Nancollas, Adv. Dent. Res., 1 (1987) 314. [22] J.A. Budz and G.H. Nancollas, J. Cryst. Growth, 91 (1988) 490. [23] E. Dalas, J.K. Kallitsis and P.G. Koutsoukos, Langmuir, 7 (1991) 1822. [24] S. Maf6, J.A. Manzanares, H. Reiss, J.M. Thomann and Ph. Gramain, J. Phys. Chem., 96 (1992) 861. [25] J.M. Thomann, J.C. Voegel and Ph. Gramain, J. Colloid Interface Sci., 157 (1993) 369. [26] F. Hefferich, in Ion Exchange, McGraw-Hill, New York, 1962, p. 353.
ELSEVIER
COLLOIDS SURFACES A
Analysis of calcium hydroxyapatite dissolution in non-stoichiometric solutions Ph. Schaad
b
F. Poumier b, J.C. Voegel
b, Ph. Gramain a,,
a Ecole Nationale Supdrieure de Chirnie de Montpellier, Laboratoire de Chimie Appliqude, CNRS, URA 1193, 8, rue de l'Ecole Normale, 34000 Montpellier, France b Centre de Recherches Odontologiques U424 INSERM, 1, Place de l'H6pital, 67000 Strasbourg, France
Received 29 July 1996; accepted 23 November 1996
Abstract The dissolution kinetics of calcium hydroxyapatite powder (HAP) are investigated under constant pH values of 5.0, 5.5 and 6.0, in solutions containing initially non-stoichiometric amounts of calcium and phosphate ions. Although a true steady state is never attained, it is possible to define a pseudo-steady state within a limited reaction domain. It is demonstrated that the kinetics follow an effective order of dissolution relative to the calcium activity gradient near to 1. This process is quantitatively evaluated by a rate reduction factor which characterizes the state of the interface. It is shown that calcium adsorption takes place at the interface during dissolution, and that the evolution of the HAP surface state is responsible for the non-attainment of a true steady state. In particular, for initial strong calcium undersaturations, the attainment of the pseudo-steady state is very long. At the pseudo-steady state, the rate reduction factor is only pH-dependent, but not on the composition of the initial solution. © 1997 Elsevier Science B.V. Keywords: Calcium hydroxyapatite dissolution; Non-stoichiometric solutions
1. Introduction It is now well established that an interpretation of the dissolution kinetics of calcium hydroxyapatite ( H A P ) in terms of a purely diffusion-limited process in the Nernst layer adjacent to the crystal surface, supposing that the driving force for dissolution is the equilibrium solubility of apatite, is not fully satisfying [1,2]. In order to explain the deviation from a simple diffusive process, two models of dissolution were proposed in recent years, both including a combined surface- and diffusion-controlled mecha-
* Corresponding author. Tel.: + 33 67 144365/01; Fax: + 33 67 147220/53. 0927-7757/97/$17.00 © 1997Elsevier Science B.V. All rights reserved PII S0927-7757 (96) 03977-5
nism. According to Nancollas et al. [3], using the model developed by Christoffersen et al. [4-7], a polynuclear or SurfaCe disloCa-ti0n mechanism occurs at the surface. Based on extensive experi! mental studies, Gramain et al. [1,8-10] pr6posed a dissolution model in which the diffusion process is restricted by the spontaneous formation at the solid interface of an adsorbed calcium-rich layer. The formation of this semi-permeable layer follows a linear adsorption isotherm until saturation and, in consequence, is in constant evolution during the early stages of the dissolution process. This model was based on the experimental observation of a strong calcium accumulation at the solid interface [8,10] and on the determining influence of the sample conditioning [9]. We demonstrate that for experimental conditions in which the ratio s of
218
Ph. Schaad et al. / Colloids" Surfaces A: Physicochem. Eng. Aspects 121 (1997) 217-228
calcium and phosphate ions present in solution is close to the theoretical value of s for HAP, the experimentally consumed proton and released calcium-ion rates are well described by a firstorder law with respect to the calcium activity gradient, and by a rate reduction factor associated with the semi-permeable layer. The aim of the present paper is to study the HAP dissolution by including the influence of the initial equilibrium conditions (stoichiometric and non-stoichiometric conditions) and to extend the previous model to non-stoichiometric conditions. For non-stoichiometric conditions, the calcium over phosphate ratio S in solution ( S = C a / P ) is not constant, but is time-dependent. Dissolution experiments were achieved at three different constant pH values (5.0, 5.5 and 6.0) by continuously recording the proton consumptions and calcium releases and by determining the phosphate concentration in the bulk before and after the dissolution step. For each pH value, three experimental equilibrium solutions were studied with initial So = Ca0/Po (initial calcium over phosphate ratio) higher, lower, or equal to the stoichiometric value. We demonstrate that, as in our previous studies, a first-order law related to the calcium activity gradient of HAP describes the data well. The structure of the paper is as follows. First, we analyze the equilibrium conditions of the experiments by determining the activities of the calcium, phosphate and hydroxyl ions. Later, we will show that for a restricted reaction domain where a quasi-steady state can be considered, a first-order law related to the calcium activity is observed.
2. Materials and methods
51 + 11 m 2 g - 1. For the solid sample used, calcium was determined by atomic absorption spectrophotometry and phosphate by a colorimetric method [11]. The SHApCa/P ratio obtained was 1.63 +_0.06, to be compared to the theoretical value of 1.677.
2.2. Solutions All salts used were of analytical grade and were dissolved in deionized water. Activity factors were calculated using the Debye H/ickel equation: logf = -AZ 2
v;
(1)
1 + Bai'~/~ where Zi represents the valence of the ith ion, # is the ionic strength of the solution, ai is the distance of the closest approach, and A and B are constants depending on the temperature and the dielectric constant of the solution. The values used for A and B were 0.5092 and 0.3286 x l0 s, respectively; those for al were 6 . 0 x l 0 - S c m for Ca 2+, 4 x 10 S cm for Ca 2+, 4 x 10 S cm for HzPO 4 and P O ] - and 3 . 5 x 1 0 - S c m for OH . For all experiments, using the evaporation law consistent with this equipment [12], corrections were systematically made in order to take into account volume variations due to evaporation and to acid injection. The experiments were carried out at three pH values (5.0, 5.5 and 6.0). For each pH value, three solutions were prepared (S1-$9) (Table 1). The composition of each solution containing 8.0 × 1 0 - 2 M KC1 corresponded to the solubility product of HAP (pKspnge=59.5+l.2) [10]. Solutions S1, $4 and $7 had an So value larger than 1.67, solutions $2, $5 and $8 an S o value close to 1.67, and $3, $6 and $9 an S o value smaller than 1.67.
2.1. H A P 2.3. Calcium, phosphate and proton determination Experiments were performed with 100 160 gm hydroxyapatite (HAP) platelets (Bio-Gel HTP, Bio-Rad Laboratories, Richmond, CA) prepared as described elsewhere [9]. The specific surface area, determined by the BET method (Laboratoire de Chimie des Mat6riaux Catalytiques, Strasbourg) for HAP was found to be
The detection limit for calcium and phosphate ions with a sufficient precision was about 5 x 10 .5 M. Above this value, the precision for calcium determination with the aid of the calciumspecific electrode is about 2%. This precision is comparable to that given by Margolis et al. [13].
Ph. Schaad et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 121 (1997) 217-228
219
Table 1 Initial and final equilibrium conditions of HAP equilibrated in solutions, saturated with respect to HAP but having So> 1.63 (S1, $4 and $7), So close to 1.63 ($2, $5 and $8) or So < 1.63 ($3, $6 and $9). At equilibrium, calcium and phosphate ions were determined experimentally. The ionic products (K~)calculated with respect to HAP. pK~= -log K±should be compared with pKs = 59.5 ± 1.2 [9] Equilibrium conditions
Initial conditions
s1 $2 $3 $4 $5 $6 $7 $8 $9
CaC12 (moll 1 x 104)
KHzPO4 (moll 1 x 104)
CaC12/ KH2PO4
pH (±0.1)
pKi (±1.2)
Ca0 (moll lx104) (_+2%)
Po (moll-lxl04) (± 10%)
So= Ca0/P0 (±12%)
pH (+0.1)
pKi (_+1.2)
5.00 3.00 1.00 3.00 1.50 0.50 3.00 hl0 0.50
0.60 1.75 9.90 0.30 0.90 6.00 0.15 0.65 3.00
8.30 1.70 0.10 10.0 1.70 0.08 20.0 1.70 0.16
6.3 6.3 6.3 6.6 6.6 6.6 6.8 6.8 6.8
59.7 59.5 59.6 59.3 59.9 59.9 59.7 59.9 59.6
5.3 3.0 1.0 3.0 1.5 0.7 3.3 hl 0.6
1.0 2.0 8.0 0.5 1.1 6.2 0.5 1.0 3.2
5.30 1.50 0.12 6.00 1.36 o. 11 6.60 hl0 0.18
6.3 6.4 6.4 6.7 6.7 6.7 7.0 6.9 6.9
58.9 59.0 59.3 59.1 59.2 58.7 59.1 58.8 58.7
It was estimated by c o m p a r i n g the calcium electrode responses with the a m o u n t s o f calcium added continuously to the bulk solution. F r o m these simulation experiments, it can be seen that the specific calcium electrode responses initially show a deficiency estimated to about 2% o f the calcium added. This deficiency lasts for about 2 0 r a i n [14]. For the released calcium, which is obtained by the difference between the calcium a m o u n t present at time t and the calcium a m o u n t present initially before the start o f dissolution, the precision is a b o u t 4%. Phosphate a m o u n t s present within the solution at different experimental stages were estimated by spectrophotometric analysis o f m o l y b d e n u m blue phosphate complexes using a Beckman Model 34 spectrophotometer. Thus, 1.5 ml aliquots were withdrawn f r o m the solution after 10 min powder settling and 3.5 ml o f reagent (0.5 ml ascorbic acid solution at 10% and 3 ml o f a (NH4)6MoT.4H20 solution at 0.42% in H2SO4 N ) were added. The O D at 820 n m was measured at 37°C after 1 h o f reaction [11, 15]. The precision in phosphate determination is about 10%. It is a b o u t 1.5% for the c o n s u m e d protons, mainly due to the errors in the bulk-volume determination. The error linked to the general reproductibility o f dissolution is a b o u t 10% for p r o t o n consumption, as well as for calcium and phosphate releases.
2.4. Experimental dissolution set-up The experimental apparatus has been described previously [12]. Briefly, it consists o f a reactor (Mettler, type DV702, Greifensee, Switzerland) with two titrators (Mettler, type DL21, Greifensee, Switzerland) connected to a recorder and interfaced to a microcomputer. The reactor, thermostated at 37°C, includes a stirring system operating at 1000 rpm, a water-tight cover and an argon bubbling system. A combined p H electrode (Mettler, type D G l l l , Greifensee, Switzerland) and a calcium electrode (Orion Research, type 94-09, Cambridge, U S A ) were used. The p H and calcium ion activities within the bulk solution were followed continuously with time. The p H and calcium electrode responses were checked by control experiments. For p H measurements after less than 1 rain, the p H electrode response corresponds to the p r o t o n bulk activity with a precision o f about p H ± 0.1. 2.5. Equilibration procedure 200 ml o f S1, $2 and $3 solution (100 ml for $4, $5 and $6 and 50 ml for $7, $8 and $9), corresponding to equilibrium conditions, were added to the reactor. The procedure starts with 1 h o f
220
Ph. Schaad et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 121 (1997) 217-228
electrode stabilization within the same solutions adjusted to their respective dissolving pH values of 5.0, 5.5 or 6.0. Then, the pH was precisely adjusted to the calculated equilibrium value and the required amount of HAP added to the solution for 2 h of equilibration. The amounts of HAP added were selected in order to attain thermodynamic equilibrium at each dissolving pH value without having dissolved more than 50% of the available HAP. For this reason we used 40 mg HAP for dissolution at pH 5.0 and 20 and 10 mg at pH 5.5 and 6.0, respectively. However, since it was demonstrated in previous studies [8] that the initial surface state strongly influences the whole dissolution process, and in this respect the amount of ions adsorbed is strongly dependent upon the solid/liquid ratio, all equilibrations were performed with a solid/liquid ratio of 0.2 g 1- 1, similar to the value used in our previous studies. After about 2 h of contact of HAP with the solution, the time necessary to attain equilibrium, the pH values reached were around 6.4 for experiments S1, $2 and $3, around 6.7 for experiments $4, $5 and $6, and around 6.9 for $7, $8 and $9 (see Table 1). Stirring was then stopped for about 10rain in order to allow the powder to settle, and the bulk solution was reduced to 50 ml ( 150 ml of solution was withdrawn for experiments S1, $2 and $3, and 50ml for experiments $4, $5 and $6). 1.5 ml of solution was also kept for phosphate determination.
2.6. Dissolution procedure For all experiments, HAP dissolution was initiated by 'a rapid decrease of the pH to the desired value. The volume of injected acid for the pH jump was systematically estimated from control (without HAP) experiments, and withdrawn from the total amount of injected acid for the estimation of protons consumed during dissolution. The volume of acid added at each injection was very low (0.01% of the 5 ml burette volume), and the bulk solution was stirred and perfectly homogenous. The desired pH value was reached after the first minute of HCI addition, and was kept constant by continuous (3.0 x 10 -z N) HC1 injection. The solid/liquid ratios varied in the dissolution period
from 0.2gl -t at pH6.0 to 0.4gl 1 at pH5.5 and 0.8g1-1 at pH5.0, which allowed us to explore the whole dissolution domain until the dissolution of less than 50% of the available HAP, when thermodynamic equilibrium was reached.
2.7. Solubility products of HAP at equilibrium (pH 7.0) and at dissolution equilibrium (pH 5.0, 5.5 and 6. O) The ionic products with respect to HAP were calculated after reaching equilibration and at the end of the dissolution period. They were evaluated using the Debye-Htickel approximation and the measured phosphate, calcium and ionic proton concentrations. The values found were compared to the solubility product of HAP (pK~pugp: 59.5 _+1.2) [101.
3. Results and discussion
The experimental approach used in this study consisted of following the dissolution kinetics of HAP with pH- and calcium-selective electrodes. HAP was first equilibrated at neutral pH in solutions containing different selected amounts of calcium and phosphate ions. The composition of these solutions was chosen so as to correspond to HAP saturation in a pH domain close to pH 7.0, in some cases with Ca/P ratios far from the HAP stoichiometry [(Ca/P)nke=l.63]. After reaching equilibrium, the pH was rapidly decreased and the protons taken up and calcium released were recorded continuously up to the final equilibrium. The ionic composition of the solutions at the initial equilibrium (before the start of dissolution) and at the end of the dissolution step are shown in Tables 1 and 2, respectively. These analyses, using pH and calcium electrodes and phosphate determination by a spectrophotometric method, allowed us to calculate the ionic products (Ki) of the solution with respect to HAP and to compare them with the solubility product (KspHAp)of HAP [10]. Ki is given by: Ki = [aCa 2+ ]5[aPO]- ]3[aOH ]
(2)
where aCa 2+, aPO 3- and aOH- correspond to
Ph. Schaad et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 121 (1997) 217-228
221
Table 2 Final bulk concentrations determined experimentally at the end of the dissolution stage, and amounts of calcium and phosphate released during the dissolution stage. The conversion percentage (last column) is estimated on the basis of released calcium. Ionic products (Ki) were calculated with respect to HAP.pK i = - l o g Ki should be compared with pK~ = 59.5 _+ 1.2 [9] pH of dissolution
S1 $2 $3 $4 $5 $6 $7 $8 $9
5.0
5.5
6.0
Final conditions
Amounts dissolved
Ca (moll-Ix104 ) (_+2%)
P (moll-~x104 ) (_+ 10%)
Ca/P (_+12%)
pKi (_+1.2)
Car (moll-ax104 ) (_+4%)
Pr (moll-Ix104 ) (_+ 10%)
Car/Pr (-+-14%)
HAP conversion (%)
40.0 38.2 37.5 17.6 12.6 11.9 6.5 5.8 3.5
21.0 23.3 27.6 8.8 8.0 13.2 3.2 5.4 6.4
1.90 1.63 1.35 2.00 1.57 0.90 2.03 1.07 0.54
59.6 59.0 59.5 59.6 59.2 59.5 59.0 59.2 59.4
35.7 35.9 36.8 14.8 11.0 11.5 3.3 4.5 2.8
20.4 21.2 20.0 8.3 7.0 6.4 2.4 4.1 2.6
1.75 1.69 1.84 1.78 1.57 1.79 1.37 1.01 1.07
45 45 46 37 32 29 17 22 14
the activities of the calcium, phosphate (PO]-) and hydroxyl ions, respectively. The same relation is defined for KspHAPby replacing the bulk activities with the saturating activities. The data shown in Table 1 indicate that at the end of equilibrium (before dissolution), all the solutions were saturated with respect to HAP (pKsp~A P = 59.5 _+1.2). Similarly, at the end of the dissolution steps and for the three pH values (5.0, 5.5, 6.0), when both the protons consumed and the calcium released remained unchanged within the solutions, saturation with respect to HAP was again observed (Table 2), even when the final conditions were far from Ca/P congruency. These results are in good agreement with those obtained by Hagen et al. [16] and by Brown [17], who showed that the thermodynamic equilibrium of HAP may also be reached in non-stoichiometric conditions. The amounts of HAP initially added were calculated in order to allow an HAP conversion of less than 50%, even when dissolution equilibrium was attained in the bulk. Moreover, this experimental method allowed us to explore concentrations which covered the domain ranging from the largely undersaturated conditions (at the beginning of the dissolution kinetics) until the attainment of saturation. Fig. 1 shows a typical example of proton consumption and calcium release kinetics at pH 5.0
with the different initial S0=Cao/Po ratios given in Table 1. The same type of kinetics is observed at pH 5.5 and 6.0. From such kinetics, the proton consumption rates JH (in mol g- 1 s - 1) are obtained by numerical derivation of the proton dissolution kinetics. Examination of these kinetics demonstrates that proton consumption is only little affected by the initial non-stoichiometric conditions, while the calcium release kinetics show greater differences. The interpretation of these kinetics requires knowledge of the variation of the ratio S = C a / P in solution during the dissolution process. S can easily be determined at each time from the initial conditions and the calcium release kinetics when the amounts of phosphate released during dissolution are known. The phosphate release kinetics are easily estimated from the proton or calcium kinetics when a congruent HAP dissolution is assumed. This hypothesis is justified since there is no apparent reason to suppose that the initial non-stoichiometric conditions influence the stoichiometry of the HAP decomposition under acidic conditions. Moreover, as demonstrated in Table 3 (columns 4 and 5), the total amounts of phosphate released at the end of the dissolution period (estimated from the colorimetric method) are comparable to the amounts estimated either from consumed protons or released calcium by supposing a congruent
222
Ph. Schaad et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 121 (1997) 217 228 6.0
E,
,
,
activity gradient (asCa aCa) and by the definition of a rate reduction factor 1/(1 + K ) :
,
5.0
p° a
x
T -5 E
JH = R J c a = R
4.0 $1 $2 $1
3.0
(a)
m c
pH
'
5.0
37"C
1.0
0 0 l
0
I
I
I
I
100 200 300 400 500 600
4.0 S -~
i
$
i
i
1
i
i
~
3.o
s2 -6 E
2.0
0
"o o gl
(3)
fo a
2.0
0.0
(asCa - aCa)"
with:
'7-
E
([+K)
1.0 [/
pH 5.0
F
370C
o
0.0
I
0
I
I
I
l
100 200 300 400 500 iO0 t i m e (rain)
Fig. 1. Proton uptake (a) and calcium release (b) kinetics at 37°C and pH 5.0, with a stirring speed of 1000 rpm, and in the presence of 8.0 x 10 2 M KC1 for experiments performed with solutions S1, $2 and $3 with 40 mg HAP.
dissolution. On this basis, the phosphate release kinetics were estimated from the proton consumption kinetics, which were determined with a better precision than the calcium release kinetics. The variation of S with dissolution time at p H 5.0, 5.5 and 6.0 is given in Fig. 2. Depending on the initial S o values and the pH, it is observed that S becomes nearly constant after 10 15% of conversion. It is clear that before this percentage, the dissolution process is far from steady-state. In previous studies [1,18, 19], we could demonstrate that when S remained close to the theoretical Ca/P ratio of HAP, the proton consumption rate Jn and calcium release rate Jc, were well described by a first-order law with respect to the calcium
K = - - and n = 1 Pca
(4)
where asCa represents the calcium activity at saturation at the solid interface, aCa is the calcium activity in the bulk solution, and n is the order of the reaction. R is the number of protons consumed when one calcium is released, and is pH-dependent, p0Ca represents the mass transfer coefficient in the Nernst layer in the absence of any chemical reaction, and PCa is the mass transfer coefficient characterising the permeability of the interfacial layer where the chemical reaction takes place. K defines the reduced permeability of the surface layer with respect to the Nernst layer, In order to check the validity of Eq. (3) in nonstoichiometric conditions, and more particularly the order of the reaction, plots of the proton flux versus asCa-aCa in log-log scales according to Eq. (3) are shown for the three p H values in Fig. 3Fig. 4Fig. 5. In each figure, the solid straight line represents the ideal slope of 1 (n = 1). Before discussing the results in greater depth, it is useful to consider the limits of the analysis of the kinetics imposed by the experimental conditions. The H A P used sample is platelet-shaped and the surface area can be considered as constant until a degree of conversion of 30% [ 1]. This value constitutes the higher limit of analysis. The lower limit can be defined from the S kinetics. It should be higher (or at least equal) than the beginning of the domain where the S ratio remains nearly constant, and for which a pseudo-steady state can be assumed. F r o m Figs. 3 5, it is clear that from 0 to 30% of conversion, the slopes decrease with increasing conversion, with a trend to stabilization around a value of I or close to 1. The initial slopes at high undersaturation correspond to values of n varying from 2 to 4. During this period, the hypothesis of the existence of a linear and constant interfacial gradient cannot be assumed. The strong
Ph. Schaad et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 121 (1997) 217-228
223
Table 3 Comparison between the experimentallyestimated phosphate amounts at the end of dissolution stage (Pr measured) determined by the molybdate complexation method, and the phosphate evaluated by considering the total amount of consumed proton (Pt from H) or of released calcium (Pr from Car) Experiment
pH of dissolution
Pr measured (moll-Ix104 ) (_+ 10%)
Pr from H consumption (moll lx104 ) (_+ 1.5%)
Pr from Car release (moll 1x104 ) (+4%)
SI $2 $3 $4 $5 $6 $7 $8 $9
5.0
20.4 21.2 20.0 8.3 7.0 6.4 2.4 4.1 2.6
22.2 21.5 22.8 8.5 7.1 6.5 2.1 3.0 1.9
21.3 21.4 22.0 8.9 7.7 6.9 1.9 2.7 1.7
5.5
6.0
6
~ ~ r - - - - - v - - - - T
5 4 3 2
$1
$2 •
1
o
o
o
---~
pH 5.0
•
"" ....
ooooo
o ° o ~
~ .
o°o°oo°°o.
$5
0
° ° °°°°°°+°
0
° ° ° o N
5
10
5 4 3
:,
5
20
25
50
H 5.5 "l
0
5
10
15
20
25
30
6
-,q'
5
~"~,~
4
~
pH 6.0
S8
2 1
Sg 0
5
10
15
20
conversion %
Fig. 2. S estimated from the ratio between the initial So= Cao/Po and Sr = Car/Pr, the ratio of released calcium (Cap detected by the specificelectrode) and released phosphate (from H uptake kinetics) vs. time at pH 5.0 (S1-$3), 5.5 ($4 $6) and 6.0 ($7 $9).
variations of n in the initial dissolution periods explain why the H A P sample conditionings and the origin of the H A P sample have such a considerable effect on the dissolution kinetics [8-10]. This demonstrates the determining role of the H A P interface in the dissolution process, and explains the important scattering of the n values already published. Using the constant composition technique, Nancollas et al. [20] studied the behavior of different apatites at a high degree of undersaturation and for a reaction conversion smaller than 10%. They obtained n values respectively equal to 4.2 for H A P prepared in their laboratory, 1.9 for extracted h u m a n enamel, 1.5 for h u m a n enamel and 1.0 for bovine enamel. More recently, Budz et al. [21,22], using the same technique, observed orders of respectively 5.05 and 5.43 for H A P reaction after 5 and 10% of conversion. These values are close to those reported by Christoffersen and Christoffersen [5]. Budz et al. [21] noted, however, that at lower undersaturations, the rates fall abruptly to much lower kinetic orders. An interpretation was given in terms of the possible presence of impurities or a modification of the surface properties as the reaction proceeds. Considering that the observations made during the initial dissolution period were representative of the general mechanism, the authors suggested that the decrease of the slope was related to the reaction mechanism itself, and explained it in terms of a polynuclear mechanism [5].
224
Ph. Schaad et al. / Colloids" Surfaces A." Physic•chem. Eng. Aspects 121 (1997) 217 228
conversion
conversion % .30 -6.0
20
10
r
,
30
0
i
T
I
::
-6.0
I ii
.~,~-"
-7.0 i
..,~.~
7
-6.0
i
.
o
." i."
T
T -6.5
--
O
- 6 . 5
E -7.0
o --
0
-6.5
6'1
-5 E
10
°°•°
-6.5
-7.0
20
-6.0
i
o -
-6.0
-7.0 i
- 6 . 0
i°* • °,~°°
-6.5
_7oH -3.50
s3 -3.25
-3.00
Iog(a - a )
-7.0
-3.6
-3.4
-3.2
Iog(a - o )
Fig. 3. Log JH vs. log (a,Ca-aCa) representation for experiments at pH 5.0 (S1 $3). Experimental data are compared with a straight line (solid line) of slope n = 1. The two solid vertical lines define the domain of validity obtained from the estimation of S and the conversion limit of 30%, and the dotted line corresponds to the conversion percentage where calcium adsorption is maximal.
Fig. 4. Log JH vs. log (asCa-aCa) representation for experiments at pH 5.5 ($4 $6). Experimental data are compared with a straight line (solid line) of slope n = 1. The two solid vertical lines define the domain of validity obtained from the determination of S and the conversion limit of 30%, and the dotted line corresponds to the conversion percentage where calcium adsorption is maximal.
A n a v e r a g e d slope ( T a b l e 4) was o b t a i n e d b y linear regression o f each kinetics (Figs. 3 - 5 ) b y considering the d o m a i n (vertical bars) defined b y the 30% c o n v e r s i o n limit a n d the beginning o f the d o m a i n where S r e m a i n s constant. F o r the nine experiments, the slopes v a r i e d f r o m 1.0 to 2.0 with a m e a n value o f 1.25_+0.25. In g o o d a g r e e m e n t with this result, W h i t e a n d N a n c o l l a s [3], a n d p a r t i c u l a r l y D a l a s et al. [23], o b s e r v e d a quasilinear d e p e n d e n c e between m i n e r a l i z a t i o n rates a n d u n d e r s a t u r a t i o n with an n value o f 1.25 _+0.18. A value slightly a b o v e unity is n o t surprising, since it is clear f r o m Figs. 2 - 5 t h a t a true steady state is never fully reached in the d o m a i n considered. H o w e v e r , this value s u p p o r t s the i n t e r p r e t a -
tion o f the d a t a a c c o r d i n g to a first-order law with respect to u n d e r s a t u r a t i o n , as for stoichiometric conditions. The initial d i s s o l u t i o n p e r i o d before the quasilinear regime is interesting to investigate since it is related to i m p o r t a n t interfacial exchanges. These exchanges constitute the basis o f the p r o p o s e d model, in which the rate decreases o f the dissolution process are i n t e r p r e t e d b y the f o r m a t i o n o f a s e m i - p e r m e a b l e layer due to an interfacial calcium a c c u m u l a t i o n occurring, m a i n l y in the initial dissolution times [8]. In this study, we investigated this aspect a n d systematically c a l c u l a t e d the o b s e r v e d calcium deficiencies A C a in the b u l k s o l u t i o n vs. time. We c a l c u l a t e d t h e m f r o m p r o t o n consumption and calcium release kinetics
Ph. Schaad et aL / Colloids Surfaces A: Physicochem. Eng. Aspects 121 (1997) 21~228 conversion
-6.5
30
20
Table 4 Evolution of S, n and 1/1 + K values at t = 0 (see Eq. (3) for experiments performed at pH 5.0 (S1 $3), 5.5 ($4-$6) and 6.0 ($7 $9). The slopes n were obtained from linear regression of the experimental data given in Figs. 3 5 between the lower and upper domain limits in the percentage of conversion. The rate reduction factors extrapolated to t = 0 1 / ( I + K ) , = 0 were obtained from a linear regression in the defined interval domain as shown in Fig. 7 for pH 5.0
%
10
0
.'"
$7
-6.0 ~. T
-8
E -7.0 -o= c,
.S
-7.5
o -
- 6 . 0
,
-6.5
,
i
-7.0 -7.5
-4.5
-4.0
- 5.5
Fig. 5. Log Jn vs. log (a~Ca-aCa) representation for experiments at pH 6.0 ($7 $9). Experimental data are compared with a straight line (solid line) of slope n = 1. The two solid vertical lines define the domain of validity obtained from the determination of S and the conversion limit of 30%, and the dotted line corresponds to the conversion percentage where calcium adsorption is maximal.
according to the relation
[HI
pH of dissolution
Mean S value (_+5%)
Slope n ( 4- 0.25 )
1/(1 + K ) x 1034- 0.1 at t = 0
SI $2 $3 $4 $5 $6 $7 $8 $9
5.0
2.1 1.6 1.0 2.5 1.6 0.8 2.6 1.5 0.4
1.1 1.4 1.0 1.3 1.0 1.5 1.2 1.3 2.0
0.60 0.64 0.64 0.80 0.90 1.10 0.80 1.30
-[Car]
5.5
6.0
" ~ ' ~
Iog(a -a)
A[Ca] = ~ -
Experiments n=l
-6.5
225
(5)
where R corresponds to the H/Ca ratio for the HAP used (R = 1.43 at pH 5.0, 1.38 at pH 5.5 and 1.36 at pH 6.0). Eq. (5) assumes that all the protons are exclusively consumed by ionic Ca and P exchanges. However, protons are also involved in the build up of the surface charge and the electrical double layer. It is assumed that both these mechanisms are rapid and fully achieved at the start of the dissolution process, since the start is preceeded by a period of 1 min, during which the pH is decreased from its equilibrium value (Table 1) to
the pH value of dissolution. The results obtained for the three pH values and different experimental conditions are represented in Fig. 6. At pH 5.0 and for the stoichiometric $2 solution, the calcium deficiency represents a deviation of 7%. This becomes 30% for the strongly calcium-deficient $3 solution, and is very low for the calcium-rich S1 solution. Similar observations were made at pH 5.5 and 6.0, with the calcium adsorption kinetics showing a maximum. The error of the estimation of the calcium deficit being around 5%, we conclude the existence of an effective general tendency towards interfacial calcium accumulation. The calcium bulk activities Cama x and the dissolution times z corresponding to the maximum amounts of calcium adsorbed A[Ca]m,× are shown in Table 5. For experiments $7 and $8 (pH 6), the effects are too small to be evaluated quantitatively. The adsorbed calcium amounts Fma. (in mol cm -z) can be estimated if one supposes that accumulated calcium is effectively adsorbed at the HAP surface. The values (Table 5) range from 1.47 to 13.4 x 10 l°mol cm -2, and are more than one order of magnitude higher than the value of 2.6x 10 H m o l c m - 2 estimated by Maf6 et al. [24], assuming a monolayer adsorption of calcium ions having an ionic radius corresponding to the
226
Ph. Schaad et al. / Colloids Surfaces A." Physicochem. Eng. Aspects 121 (1997) 217-228
6.0
.
.
.
.
i
.
.
.
.
i
.
.
.
.
i
.
.
.
.
3.0
0.0 0 2.0
/~ . . . . . . . . . . . . . . . . . 100 200 .......................
300
400
x
7_
1.0
$5
E "~
0.0 0 1.0
60 ....
120 180 , ..............
240
300
pH 6 . 0 $9 0.5
0.0 0
50 time
1 O0
150
200
(min)
Fig. 6. Calcium deficiency (3ca) obtained from the difference between the congruently released calcium estimated (from H-uptake kinetics) and released calcium, Car (detected by the specific electrode), vs. time.
Debye length. This suggests multilayer formation, as proposed in the layer model [25]. Moreover, the layer model supposes a permanent calcium accumulation during the dissolution process in relation with the increasing calcium concentration in the dissolving medium. This behavior seems to be verified by the results in Fig. 6, since a strong tendency for calcium accumulation is observed throughout the whole kinetics. In summary, the shape of the adsorption kinetics, with the existence of a maximum (in particular at pH 5.0), confirms the hypothesis of two distinct phenomena on the basis of the dissolution model. At initial times, calcium adsorption occurs to equilibrate the interface after the rapid pH decrease of the solution, and leads to the formation of the inhibiting calcium layer. The time which corresponds to the maximum amount of calcium adsorbed onto H A P is approximatively equal to the lower limit defining the constant-S domain. This time is defined in Figs. 3 and 4 by the vertical dotted lines. Moreover, the observed increase of adsorbed calcium ions (Table 5) when the pH decreases is in agreement with the decrease in auto-inhibition observed for higher pH values [1]. According to the layer model, this is due to the presence of divalent phosphate ions, which increases the permeability of the calcium layer, a phenomenon which is well documented in ionexchanging membranes [26]. In such conditions,
Table 5 Maximum amount of calcium ions /'max absorbed onto HAP and estimated from calcium deficiency A[Ca]maxobtained from the difference between congruentlyreleased calcium (estimated from H consumption) and released calcium (Car, estimated from calcium electrode), r is the time necessaryto attain Fma,, and [Ca]maxand is respresented by dotted line in Figs. 3 5 Experiments
pH of dissolution
[Ca]maxmeasured in the bulk (mol 1-1 x 104)
3[Ca]max (Ca deficiencyin the bulk) (mol 1-1 x 104)(_+0.5)
Fmax(adsorbed Ca on HAP)z (min) at maximum deficiency (mol cm -2 × 101°)
$1 $2 $3 $4 $5 $6 $7 $8 $9
5.0
22.0_+2.2 24.0_+2.4 25.0_+2.5 2.8_+0.25 2.3 _+0.25 2.8 _+0.25 1.8_+0.25 1.2_+0.25 < 1.2
0.6 2.0 5.5 0.5 0.8 1.6
1.47 40 4.90 80 13.4120 2.45 35 3.92 35 7.84100
0.6
5.88140
5.5 6.0
Ph. Schaad et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 121 (1997) 217-228
it becomes obvious that a true steady state is never achieved during HAP dissolution, except perhaps for high pH values. Since a first-order law describes the dissolution process, the phenomenological double-layer model described by Eq. (3) permits the study of the rate reduction factor which characterizes the inhibiting effect of the adherent calcium layer. It gives a quantitative evaluation of different factors capable of affecting the HAP interface and the dissolution mechanism. In particular, its evolution during the dissolution of HAP is interesting to study, since it describes the formation and reinforcement of the layer. 1 / ( I + K ) kinetics are given in Fig. 7 (pH 5), and, as observed in a previous study [1], 1/(1 + K ) decreases rapidly in the initial times, then decreases 8.0 6.0 4.0 2.0 0.0 0
5
10 15 20 25 30 35
0
5
10 15 20 25 30 35
8.0 6
6.0 4.0 2.0
227
linearly with time or levels off. The vertical lines in Fig. 7 define the considered pseudo-steady state domains, as in Figs. 3-5. The dotted lines indicate the conversion ratios corresponding to the maximum of accumulated calcium. According to the previous analysis, the initial rapid decrease of 1/(1 + K ) corresponds to the interfacial calcium accumulation period, and the linear domain to the establishment of a pseudo-steady state. From this linear behaviour, it is possible by extrapolation to define values of 1/(1 + K ) corresponding to t = 0 , which describes the permeability of the interface during the dissolution process at steady state. These extrapolated data avoid the need to evaluate these parameters at a given degree of saturation, as generally done in the analysis of HAP kinetics. The extrapolated 1/(1 + K ) values are shown in Table 4 and, as expected from comparison with the values obtained for stoichiometric conditions, show a similar dependence on pH [1]. At higher pH values, the permeability of the interface is higher and the non-steady state period is shorter. The initial So = Cao/Po composition does not seem to have any influence, except on the time necessary to attain the steady state. The lower the initial calcium concentration, the longer the time needed to reach the steady state. An interpretation in terms of calcium amounts necessary to form the adherent calcium-rich layer is in good agreement with the proposed model.
0.0 8.0
4. Conclusion
6.0 4.0
$3,
2.0
,
, ~
0.0
0
5
10 15 20 25 30 35 conversion %
Fig. 7. 1/(l+K)n vs. conversion percentage calculated with Eq. (3) for experiments realized with solutions S1, $2 and $3 (pH 5). Extrapolationsto t = 0 weredone from linear regression in the steady-state domain defined in Table 4. The two vertical lines definethe domain of validityobtained from the determination of S and the conversionlimit of 30%, and the dotted line corresponds to the conversion percentage where calcium adsorption is maximal.
The analysis of the HAP dissolution process in equilibrated solutions corresponding to different So = Cao/Po ratios demonstrates the important role played by the calcium ions adsorbed at the solid interface. In particular, we demonstrate that, due to interfacial ionic exchange and calcium accumulation, a pseudo-steady state is only attained after long reaction times. This explains the difficulties encountered in the study of HAP dissolution and the important scatter in the reaction orders reported in the literature. The present data demonstrates that the reaction order is close to 1 in a restricted experimental domain, and confirms for
228
Ph. Schaad et al. / Colloids" Surfaces A: Physicochem. Eng. Aspects 121 (1997) 217 228
n o n - s t o i c h i o m e t r i c c o n d i t i o n s the results o b t a i n e d for s t o i c h i o m e t r i c c o n d i t i o n s .
Acknowledgment O n e o f the a u t h o r s (P.S.) t h a n k s " l a F a c u l t 6 d ' O d o n t o l o g i e de S t r a s b o u r g " , F r a n c e , f o r financial s u p p o r t .
References [1] J.M. Thomann, J.C. Voegel and Ph. Gramain, Colloids Surfaces, 54 (1991) 145. [2] W. White and G.H. Nancollas, J. Dent. Res., 56 (1977) 524. [3] W.C. Chen and G.H. Nancollas, J. Dent. Res., 65 (1986) 663. [4] J. Christoffersen, M.R. Christoffersen and N. Kjaergaard, J. Cryst. Growth, 43 (1978) 501. [5] J. Christoffersen and M.R. Christoffersen, J. Cryst. Growth, 47 (1979) 671. [6] J. Christoffersen, J. Cryst. Growth, 48 (1980) 29. [7] J. Christoffersen and M.R. Christoffersen, J. Cryst. Growth, 57 (1982) 21. [8] Ph. Gramain, J.M. Thomann, M. Gumpper and J.C. Voegel, J. Colloid Interface Sci., 128 (1989) 370. [9] J.M. Thomann, J.C. Voegel and Ph. Gramain, Calcif. Tissue Int., 46 (1990) 121.
[10] Ph. Gramain, J.C. Voegel, M. Gumpper and J.M. Thomann, J. Colloid Interface Sci., 118 (1987) 148. [11] Ames, Methods Enzymol., 8 (1966) 115. [12] J.M. Thomann, P. Gasser, E. Br6s, J.C. Voegel and Ph. Gramain, Comput. Methods Programs Biomed., 31 (1990) 89. [13] H.C. Margolis and E.C. Moreno, Calcif. Tissue Int., 50 (1992) 137. [14] J.M. Thomann, Thesis, Strasbourg, 1989. [15] P.S. Chen, T.Y. Toribara and H. Warner, Anal. Chem., 28 (1956) 1756. [16] A.R. Hagen, Acta Odont. Scand., 33 (1975) 67. [17] W.E. Brown, J. Dent. Res., 53 (1974) 204. [18] Ph. Schaad, J.M. Thomann, J.C. Voegel and Ph. Gramain, Colloids Surfaces A: Physicochem. Eng. Aspects, 83 (1994) 285. [19] Ph. Schaad, J.M. Thomann, J.C. Voegel and Ph. Gramain, J. Colloid Interface Sci., 164 (1994) 291. [20] G.H. Nancollas and M.B. Tomson, Science, 200 (1978) 1059. [21] J.A. Budz, M. Lore and G.H. Nancollas, Adv. Dent. Res., 1 (1987) 314. [22] J.A. Budz and G.H. Nancollas, J. Cryst. Growth, 91 (1988) 490. [23] E. Dalas, J.K. Kallitsis and P.G. Koutsoukos, Langmuir, 7 (1991) 1822. [24] S. Maf6, J.A. Manzanares, H. Reiss, J.M. Thomann and Ph. Gramain, J. Phys. Chem., 96 (1992) 861. [25] J.M. Thomann, J.C. Voegel and Ph. Gramain, J. Colloid Interface Sci., 157 (1993) 369. [26] F. Hefferich, in Ion Exchange, McGraw-Hill, New York, 1962, p. 353.