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:

0sK

IAPS = (1)

where IAP is the ion activity product of the salt considered and 0sK the respective

thermodynamic solubility product.

10-5

10-4

10-3

10-2

4 5 6 7 8 9 10

Tot

al C

a lc

ium

/ M

pH

HAP

TCPOCP

DCPA

DCPD

Figure 1: Solubility isotherms of calcium phosphates. Calculated at 25C, 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 1.450.05 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 and kinetics of the formation of

mineral phases. Experimental methods for 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. C

once

ntra

tion

Temperature

Labile

Metastable

Stable

A

B

C

D

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 M+A- is defined as [23]:

S =a

M m +( )sn+

aAa-( )s

n-

aM m +( )

n+a

Aa-( )n-

1 /n

=IP

K so

1 /n

[2]

where subscripts s and refer to solution and equilibrium conditions respectively,

denote the activities of the respective ions and ++-= . IP and K s0 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, , 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]:

Slog)kT303.2(

BAlog 3

3s+= [3]

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:

dtdm

A1Rg = [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

2

3

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:

ngg )S(fkR s= [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 s

the relative supersaturation, S1/9-1. When mass transport (step 1) is the rate

determining step the growth rate is given by eq. (6):

kR dd = [6]

where kd is the diffusion rate constant which is given by:

CDkd

= [7]

where D is the mean diffusion coefficient of the lattice ions in solution, u the molar

volume of the crystalline material, C the solubility of the precipitating phase and d

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]:

R g = k ads [8]

where the rate constant kad is given by:

k ad = anad uC [9]

In equation (27), a is the jump distance and nad 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 for the precipitation of

hydroxyapatite in supersaturated calcium 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 contains ionizable groups typically found in

organic compounds present in wastewater. The driving force for the

formation of HAP from a supersaturated solution is the change in Gibbs free energy,

G, for the transfer from the supersaturated solution to equilibrium. According to

equation (2):

DG = -Rg T

nln

IP

K s0

[10]

In Eq. [10] IP is the ion activity product: (Ca2+)5 (PO43-)3 (OH-), K s0 its solubility

product, the number of ions (=9 for HAP), Rg the gas constant and T the absolute

temperature. The ratio IP/ K s0 represents the degree of supersaturation, , 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.

5.00 10-8

1.00 10-7

1.50 10-7

2.00 10-7

0 5 10 15 20 25 30

Rat

e / m

ol m

in-1

m-2

s HAR

Figure 4: Dependence of the rate of crystal growth of HAP on HAP seed crystals at

37C. (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 25C) (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 to adsorption onto HAP and subsequent blocking of the active

growth sites.

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.

Cat Pt [NaNO3] Dt G / KJ mol-1 R

10-4mol

dm-3

10-4mol

dm-3

10-3mol

dm-3

10-3mol

dm-3

DCPD OCP TCP HAP 10-8mol/min

m2

1.50

1.50

1.50

1.50

1.50

1.50

0.90

0.90

0.90

0.90

0.90

0.90

1.50

1.50

1.50

1.50

1.50

1.50

0.00

1.00

2.00

3.50

5.00

10.0

2.51

2.51

2.51

2.51

2.51

2.52

1.99

1.99

1.99

1.99

1.99

1.99

0.86

0.86

0.86

0.86

0.87

0.87

-3.44

-3.44

-3.44

-3.43

-3.43

-3.42

8.4

8.4

6.5

4.9

4.3

2.0

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-bq) [11]

where Ro is the crystallization rate in the absence of inhibitors and q (0

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.

1.00

1.20

1.40

1.60

1.80

2.00

2.20

2.40

2.60

0 50000 100000 150000

R0/

(R0-

Ri)

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 C.

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-1,2-bis(dihydroxyphosphonyl)ethane

2.16

Zn 2+ 3.02 1-hydroxyethylidene-1,1-diphosphonic acid (EHDP)

0.21

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 L-

serine onto HAP, obtained experimentally at pH=7.40.3.

0 1000 2000 3000 40000

10

20

30

40

50

60

G-1 /

m2 m

mol

-1

C eq-1 / dm

3 mol

-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, 37C

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

G=

1

Gm+

1

K L Gm C eq [31]

where G, Gm 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 mol m-2 and 546

dm3/mol are calculated for Gm 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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