Current Knowledge of Calcium Phosphate Chemistry and in
Particular Solid Surface-Water Interface Interactions
Petros G. Koutsoukos
Institute of Chemical Engineering and High Temperature Chemical Processes
(FORTH – ICEHT) and
Department of Chemical Engineering, University of
Patras
P.O. Box 1414, GR 26500 Patras, GREECE
Keywords: Calcium, phosphate, supersaturated solutions, kinetics of crystal
growth
Abstract
Phosphorus recovery from wastewater is determined from the transfer of
aqueous phosphate species into a solid form.
Depending on the solution
supersaturation a number of calcium phosphates may be formed from the
thermodynamically unstable amorphous calcium phosphate, to dicalcium
phosphate dihydrate, octacalcium phosphate to the most stable mineral phase,
hydroxyapatite.
The phase which forms and the interactions and kinetics
effects of water-soluble compounds on the nature and the kinetics of the
calcium phosphate salt formation can be modeled by experiments in which all
sensitive parameters are controlled.
This can be achieved by the constant
supersaturation method which allows for the identification of even transient
phases which dissolve rapidly at variable supersaturation. The seeded growth
of HAP at near neutral pH values, proceeds by a surface controlled
mechanism.
Water soluble impurities retard the crystallization process by
adsorption at the active growth sites. The relative effect of various additives
may be evaluated through the appropriate modeling of the adsorption process.
The case of L-serine is presented which even though is characterized by low
affinity for the hydroxyapatite substrate caused significant reduction of the
crystal growth rate.
1. Introduction
The precipitation and dissolution of calcium phosphates are processes of
considerable importance to waste water treatment and in particular to phosphorus
recovery an issue of increasing importance. It is reported that addition of lime makes
it possible to remove 85-90% of the inorganic orthophosphates present in wastewater
[1].
Although there is no general agreement concerning the mechanisms of calcium
phosphate precipitation, the consensus is that the chemistry of the aqueous phase from
which precipitation takes place is of paramount importance.
Model studies are needed for the assessment of the conditions most appropriate for
the removal and / or recovery of phosphorus from aqueous solutions in the form of
calcium phosphate salts. These studies however should be based on accurate
thermodynamic considerations which may be used next as guides for the appropriate
kinetics experiments. In the present paper an overview of the thermodynamics and
kinetics investigations in aqueous systems of calcium phosphate.
2. The calcium phosphate salts
The formation of calcium phosphate salts in aqueous solutions takes place
following the development of supersaturation. Supersaturation may be developed by
increasing the aqueous medium content in calcium and phosphate and / or the pH.
Moreover,
temperature
increase
contribute
to
the
solution
supersaturation
development because the sparingly soluble calcium phosphate salts have reverse
solubility. Following the establishment of supersaturation nucleation takes place.
Once the nuclei exceed a critical size, they grow further in the crystal growth proves
which takes place on the active growth sites of the crystallites. Depending on the
solution supersaturation, four well defined regions may be distinguished for the
calcium phosphate system. These regions are shown in figure 1. As may be seen the
driving force is the solution supersaturations, S, defined as:
S=
IAP
K 0s
(1)
where IAP is the ion activity product of the salt considered and K 0s the respective
thermodynamic solubility product.
Total Ca lcium / M
10-2
DCPA
DCPD
10-3
OCP
TCP
10-4
HAP
10-5
4
5
6
7
8
9
10
pH
Figure 1: Solubility isotherms of calcium phosphates. Calculated at 25ºC, NaCl 0.2
M
At very high supersaturations calcium phosphate precipitates spontaneously, a fact
demonstrated by the formation of cloudiness in the aqueous phase upon raising the
supersaturation.
Before reaching this region however, it is possible to prepare
solutions supersaturated with respect to calcium phosphate, but the precipitation takes
place past the lapse of measurable induction times, following the establishment of the
solution supersaturations.
Moreover, it is possible to prepare calcium phosphate
supersaturated solutions, which are stable. In these solutions precipitation does not
take place, unless they are seeded either with calcium phosphate seed crystals or with
substrates which may function as templates for the selective overgrowth of calcium
phosphates. The lower limit of this supersaturation range is the solubility of the
calcium phosphate considered (S=1). Below this limit, dissolution takes place. It is
thus reported that for pH 7.40 and a molar ratio of total calcium /total phosphate
concentration equal to 1.66, at calcium concentrations of 10 mM spontaneous
precipitation takes place and between 3 – 10 mM the precipitation takes place past the
lapse of induction times. Below 3 mM the supersaturated solutions are stable for long
periods of time [2].
When calcium phosphate is precipitated from highly
supersaturated solutions an unstable precursor phase has been reported to form. This
phase is characterized by the absence of peaks in the powder x-ray diffraction pattern
and is known as the amorphous calcium phosphate (ACP). The composition of ACP
appears to depend upon the precipitation conditions and is usually formed in
supersaturated solutions at pH>7.0 [3-6]. In slightly acidic calcium phosphate
solutions the monoclinic DCPD forms [7-9]. OCP is formed by the hydrolysis of
DCPD in solutions of pH 5-6 and may also be precipitates heterogeneously upon TCP
[10,11]. HAP is the thermodynamically most stable phase and often when precipitated
in the presence of foreign ions substitutions calcium, phosphate and / or hydroxyls by
some of these ions take place. Thus, substitutions of OH- by F- or Cl- ions, of the
phosphate by sulfate and carbonate and of the calcium by Sr2+, Mg2+ and Na+ ions
have been reported [12-16]. A considerable amount of the work done for the
identification of calcium phosphate minerals which precipitates spontaneously has
been based on the stoichiometric molar ratio of calcium to phosphate calculated from
the respective changes in the solutions. This ratio has been found in several cases to
be 1.45±0.05 which is considerably lower than the value of 1.67 corresponding to
HAP which is generally implied as the precipitating mineral. A number of different
precursor phases have been postulated to form including TCP [17-19], OCP [19, 20]
and DCPD [21].
3.
Thermodynamics
mineral
phases.
and
kinetics
of
Experimental
the
formation
methods
for
of
the
investigation of implants mineralization
Of primary importance is the development of supersaturation which is the driving
force for nucleation and provided that there is sufficient contact time with a foreign
substrate, deposition may take place [22].
Supersaturation is a measure of the
deviation of a dissolved salt from its equilibrium value. In figure 2 a typical solubility
diagram for a sparingly soluble salt of inverse solubility is shown. The solid line
corresponds to equilibrium. At a point A the solute is in equilibrium with the
corresponding solid salt. Any deviation from this equilibrium position may be
effected either isothermally (line AB), at constant solute concentration, increasing the
solution temperature (AC),
or by varying both concentration and temperature (AD).
A solution departing from equilibrium is bound to return to this state by the
precipitation of the excess solute. However for most of the scale forming sparingly
soluble salts, supersaturated solutions may be stable for practically infinite time
periods. These solutions are metastable and may return to equilibrium only when a
cause acts as e.g. the introduction of seed crystals of the salt corresponding to the
supersaturated solution.
B
Labile
Concentration
D
A
C
Metastable
Stable
Temperature
Figure 2. Solubility- Super solubility diagrams of a sparingly soluble salt with inverse
solubility.
There is however a threshold in the extent of deviation from equilibrium marked by
the dashed line in figure 2, which if reached, spontaneous precipitation occurs with or
without induction time preceding precipitation. This range of supersaturations defines
the labile region and the dashed line is known as the super solubility curve. It should
be noted that the super solubility curve is not well defined and depends on several
factors such as presence of foreign suspended particles, agitation, temperature, pH etc.
The formation and subsequent deposition of solids occurs only when the solution
conditions correspond to the metastable or the labile region. Below the solubility
curve fouling from scale deposits cannot take place. On the contrary, since at this
range the solutions are undersaturated dissolution is likely to take place, should any
crystals of the respective salt be present.
Supersaturation in solution can be developed in many ways including
temperature fluctuation, pH change, mixing of incompatible waters, increasing the
concentration by evaporation or solids dissolution etc. Although supersaturation is the
driving force for the formation of a salt, the exact values in which precipitation occurs
are quite different from salt to salt and as a rule, the degree of supersaturation needed
for a sparingly soluble salt is orders of magnitude higher than the corresponding value
for a soluble salt. Quantitatively, as already mentioned in equation (1), supersaturation
for sparingly soluble salts Mí+Aí- is defined as [23]:
(
(
1 /ν
) (α )
) (α )

 α Mm+
S=
α
 Mm+
ν+


s

ν−

∞ 
ν−
A α−
s
ν+
A α−
∞
 IP 
=  o
Ks
1 /ν
[2]
where subscripts s and ∞ refer to solution and equilibrium conditions respectively, á
denote the activities of the respective ions and í++í-= í.
IP and K 0s are the ion
products in the supersaturated solution and at equilibrium respectively.
Very
often
an
induction
time
elapses
between
the
achievement
of
supersaturation and the detection of the formation of the first crystals. This time,
defined as the induction time, ô, is considered to correspond to the time needed for the
development of supercritical nuclei. The induction time is inversely proportional to
the rate of nucleation and according to the classical nucleation theory the following
relationship may be written [24]:
log ô = A +
Bã 3s
[3]
3
( 2.303kT) log S
As soon as stable, supercritical nuclei have been formed
in a supersaturated solution they grow into crystals of
visible size. The rate of crystal growth may be defined
as the displacement velocity of a crystal face relative
to a fixed point of the crystal. This definition however
cannot
be
easily
applied
to
the
formation
of
polycrystalline deposits such as those encountered in the
mineral
deposits
formed
on
implants.
In
this
case,
experimentally the rates of growth may be expressed in
terms of the molar rate deposition by equation:
Rg =
1 dm
A dt
[4]
Where m is the number of moles of the solid deposited on a substrate in contact with
the supersaturated solution, e.g. seed crystals, or the surface of the implant, and A, the
surface area of the substrate.
The rate laws used to express the dependence of the rates as a function of the
solution supersaturation provide mechanistic information for the mechanism of the
formation of the mineral salt. At a microscopic scale and in analogy with the
mechanism of crystal growth in the vapor phase [25], the sequence of steps followed
for the growth of crystals are shown in figure 2:
1
3
2
Figure 3: Model for the steps involved in the process of crystal growth of the
supercritical nuclei
The steps involved in the crystal growth of the supercritical nuclei are as follows:
(i) Transport of lattice ions to the surface by convection ( step 1)
(ii) Transport of the lattice ions to the crystal surface by diffusion (step 1).
(iii) Adsorption at a step representing the emergence of a lattice dislocation at the
crystal surface (step 2).
(iv) Migration along the step, integration at a kink site on the step and partial or total
dehydration of the ions (step 3).
The rate of crystallization can be expressed in terms of the simple semiempirical
kinetics equation:
R g = k g f (S) σn
[5]
where kg is the rate constant for crystal growth, f(S) a function of the total number of
the available growth sites , n the apparent order of the crystal growth process and σ
the relative supersaturation, S1/9 -1.
When mass transport (step 1) is the rate
determining step the growth rate is given by eq. (6):
R d = kdó
[6]
where kd is the diffusion rate constant which is given by:
kd =
DõC∞
ä
[7]
where D is the mean diffusion coefficient of the lattice ions in solution, υ the molar
volume of the crystalline material, C∞ the solubility of the precipitating phase and δ
the thickness of the diffusion layer at the crystal surface [26-28].
From the mechanistic point of view it is possible to interpret kinetics data on
the basis of theoretical models the most important of which include adsorption and
diffusion-reaction. The concept of crystal growth proceeding on the basis of an
adsorbed monolayer of solute atoms, molecules or ion clusters was first suggested by
Volmer [29]. Through this monolayer it is possible to exchange ions or molecules
between the bulk solution and the crystal surface The rate in this case is [28]:
Rg′ = k ad σ
[8]
where the rate constant kad is given by:
k ad = a νad υC ∞
[9]
In equation (27),
a is the jump distance and ν ad the jump frequency of an ion into the
adsorption layer.
As may be seen, from the experimental point of view valuable
information may be obtained by measurements of the rates of precipitation on a
specific substrate as a function of the solution supersaturation.
4.Kinetics
measurements
hydroxyapatite
in
for
the
supersaturated
precipitation
calcium
of
phosphate
solutions in the absence and in the presence of ionized
organic compounds.
An example of the application of the methodology of
constant solution composition is the precipitation of
hydroxyapatite.
In wastewater, the presence of ionized
organic molecules or other ions affects the rates of
crystal growth because of adsorption processes on the
active growth sites of the crystals (steps and kink
sites).
Experiments in which supersaturation decreases
during
the
precipitation
cannot
provide
accurate
estimates of the retardation due to the additives when
they are adsorbed, because crystal growth and adsorption
take place at the same time.
Often adsorption involves
release or consumption of protons.
The presence of an
amino-acid, L-serine in the supersaturated solution on
the crystal growth rates of HAP was investigated.
L-
serine
in
contains
ionizable
groups
typically
found
organic compounds present in wastewater. The driving force for the
formation of HAP from a supersaturated solution is the change in Gibbs free energy,
ÄG, for the transfer from the supersaturated solution to equilibrium.
According to
equation (2):
∆G = −
Rg T
ν
ln
IP
K 0s
[10]
In Eq. [10] IP is the ion activity product: (Ca2+)5 (PO4 3-)3 (OH-), K 0s its solubility
product, í the number of ions (í=9 for HAP), Rg the gas constant and T the absolute
temperature. The ratio IP/ K 0s represents the degree of supersaturation, Ù, and was
computed by the computer code HYDRAQL [30] which is a free energy minimization
program taking into account all equilibria in the solution, mass balance and
electroneutrality conditions. The initial solution conditions and the initial rates of
HAP formation obtained, R, are summarized in Table 1. The experimental conditions
were selected so that the only phase which may be formed is HAP . This was verified
by the constancy of solution composition throughout the precipitation process.
In the absence of any inhibitor, the growth rate as a function of the solution
supersaturation was found to exhibit parabolic dependence, as may be seen in figure
4.
Rate / mol min -1 m-2
2.00 10-7
1.50 10-7
1.00 10-7
5.00 10-8
0
5
10
15
20
25
30
σ ΗΑΡ
Figure 4: Dependence of the rate of crystal growth of HAP on HAP seed crystals at
37ºC. (n): Present work; (s) ref. 31; (o) ref. 32
The second order dependence suggested that the mechanism of HAP crystal growth is
controlled by surface diffusion of the growth units to the active growth sites.
As may be seen from Table 1, concentrations of L-serine as low as 2.0x10-3 M
resulted in the inhibition of HAP crystal growth. At this concentration the rate of HAP
crystal growth was reduced by ca 25%. The inhibitory activity increased with
increasing L-serine concentration and may be related to: (i) formation of ion pairs
with calcium in the solution, thereby decreasing the driving force, i.e. the degree of
supersaturation for crystal growth, and (ii) to the blocking of crystal growth sites by
adsorption. Calculations were done by introducing in the computer code HYDRAQL
the formation equilibrium of the 1:1 Ca-serine ion pair with its stability constant
(logK=1.43 at 25°C) (25), showed that in the case of the maximum concentration of
serine (0.010 M) only 0.6 % of the total calcium contributes in the formation of the
aforementioned ion pair.
It is therefore evident that the presence of serine in the
concentration range investigated (1x10-3 – 1x10-2 M) does not affect to any significant
extent the concentration of free Ca2+ ions and therefore the degree of the solution
supersaturation with respect to HAP. Consequently, the inhibitory effect of L-serine
may be ascribed
growth sites.
to adsorption onto HAP and subsequent blocking of the active
Table 1. Experimental Conditions for the Crystallization of HAP on HAP seed
crystals in the presence of L-serine, at pH=7.4 and T=310.15° K: Cat , total calcium;
Pt , total phosphate. Ionic strength was adjusted by NaNO3 as inert electrolyte.
ÄG / KJ mol-1
Cat
Pt
[NaNO3 ]
Dt
10-4 mol
10-4 mol
10-3 mol
10-3 mol
dm-3
dm-3
dm-3
dm-3
1.50
0.90
1.50
0.00
2.51
1.99
0.86
-3.44
8.4
1.50
0.90
1.50
1.00
2.51
1.99
0.86
-3.44
8.4
1.50
0.90
1.50
2.00
2.51
1.99
0.86
-3.44
6.5
1.50
0.90
1.50
3.50
2.51
1.99
0.86
-3.43
4.9
1.50
0.90
1.50
5.00
2.51
1.99
0.87
-3.43
4.3
1.50
0.90
1.50
10.0
2.52
1.99
0.87
-3.42
2.0
DCPD OCP TCP
R
HAP
10-8 mol/min
m2
Assuming Langmuir – type adsorption, according to which the rate of HAP crystal
growth in the presence of the inhibitor, Ri, is given by [33]:
Ri = Ro (1-bθ)
[11]
where Ro is the crystallization rate in the absence of inhibitors and θ (0<θ<1) is the
fraction of the active growth sites occupied by the inhibitor adsorbed onto the HAP
seed crystals. According to the Langmuir isotherm:
1−θ=
In equation 12,
1
1
+K
L
C
[12]
i
the adsorption constant KL is the ratio of the rate constants for
adsorption and desorption respectively and is considered as a measure of the affinity
of the adsorbate for the adsorbent and Ci is the total equilibrium concentration of the
adsorbate (L-serine). Combination of equations 11 and 12 yields:
Ro
1
1
= +
R o − R i b bK LCi
[13]
Plots of the right hand side of equation 13 as a function of the inverse of the additive
concentration are expected to be linear. The plot according to equation 13, is shown
in figure 5.
2.60
2.40
R0/(R0-Ri)
2.20
2.00
1.80
1.60
1.40
1.20
1.00
0
50000
100000
150000
1/c i
Figure 5: Kinetic Langmuir-type plot for the effect of the presence of L-serine in the
crystal growth of HAP at 37 ºC.
In the case of serine, the linear fit of the kinetics data suggested that for the
concentration range investigated, the inhibitory activity of L-serine may be explained
by blocking of the active growth sites by adsorption. From the slope of the straight
line a value of 130 dm3 / mol was obtained for the affinity constant a value which, as
may be seen from the tabulation of similar values shown in table 2 [32], is rather low
in comparison with other, strong inhibitors of the HAP crystal growth.
Table 2: Comparative data for the affinities calculated from kinetics experiments of
the crystal growth of HAP in supersaturated solutions in the presence of the respective
compounds [32]
Inhibitor
107 KL
Sodium pyrophosphate
0.02
1-hydroxyethylidenephosphonic acid
0.13
Mellitic acid
0.16
Citric acid
0.002
1,2-dihydroxy-1,22.16
bis(dihydroxyphosphonyl)ethane
Zn 2+
3.02
1-hydroxyethylidene-1,1-diphosphonic
0.21
acid (EHDP)
The low affinity of HAP for L-serine may be corroborated from the analysis of
the equilibrium adsorption results. Figure 6 illustrates the adsorption isotherm of Lserine onto HAP, obtained experimentally at pH=7.4±0.3.
60
50
30
-1
2
Γ / m µmol
-1
40
20
10
0
0
1000
2000
-1
3000
3
C eq / dm mol
4000
-1
Figure 6: Serine surface excess on HAP as a function of the inverse of the
equilibrium serine concentration; pH 7.40, 0.01M KNO3 , 37°C
The Langmuir type isotherm obtained suggests adsorption on distinct, energetically
equivalent sites with no lateral interactions between the adsorbed species, which is in
agreement with the type of adsorption assumed in the analysis of the kinetics results.
In the presence of serine. The linear form of the Langmuir adsorption isotherm is:
1
Γ
=
1
Γm
+
1
K
L
Γm C eq
[31]
where Γ, Γm and Ceq represent respectively the surface concentration, the saturated
surface concentration (i.e. the surface concentration of adsorbate corresponding to
monolayer surface coverage), and the equilibrium solution concentration of L-serine..
From the intercept and slope of the linear regression the values 0.16 ìmol m-2 and 546
dm3 /mol are calculated for Γm and KL respectively. Although the values of the affinity
constant obtained from the study of the kinetics of precipitation of HAP on the HAP
seed crystals and of the adsorption of serine onto the HAP surface are different, they
are of the same order of magnitude
The results of the present work have shown that it is possible to model calcium
phosphate precipitation processes in complex aqueous media following careful
thermodynamic analysis of the driving force and precise kinetics measurements,
which can be achieved at conditions of constant supersaturation. Combination of the
thermodynamics calculations and kinetics measurements may clarify the conditions in
which the formation of transient phases take place and also provide reliable
information concerning the timescale of their existence in the aqueous media from
which phosphorus is removed.
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