Geochimica et Cosmochimica Acta, Vol. 67, No. 5, pp. 1017–1030, 2003
Copyright © 2003 Elsevier Science Ltd
Printed in the USA. All rights reserved
0016-7037/03 $30.00 ⫹ .00
Pergamon
doi:10.1016/S0016-7037(02)01228-0
The effects of Mg2ⴙ and Hⴙ on apatite nucleation at silica surfaces
NITA SAHAI*
Department of Geology and Geophysics, University of Wisconsin, 1215 W. Dayton St., Madison, WI 53706, USA
(Received December 21, 2001; accepted in revised form September 17, 2002)
Abstract—Apatite (Ca10[PO4]6[OH]2) precipitation from aqueous solutions involves multiple steps, such as
nucleation of a precursor calcium phosphate phase, cluster aggregation, crystal growth, and transformation to
apatite, which are affected by the presence of other ions in solution. I report the mechanisms by which two
ions common in natural solutions, Mg2⫹ and H⫹, affect heterogeneous calcium phosphate nucleation on the
amorphous silica surface. Copyright © 2003 Elsevier Science Ltd
rine pore waters, from which authigenic apatite forms, and
mammalian blood, from which apatite precipitates as bone and
teeth, suggests that similar reaction mechanisms are involved in
heterogeneous apatite nucleation in both systems.
Ab initio molecular orbital calculations of structures and energies of model clusters were performed at the Hartree-Fock level
using effective core potentials and valence double-␨ basis sets
with polarization functions. Solvation was represented by explicit hydration and by a modified Born model. The model
molecular clusters are considered to be reaction intermediates
that closely follow transition states in elementary rate-determining steps. Calculated reaction energies are then related to
transition state energies by invoking Hammond’s postulate.
The elementary reactions are assumed to be Ca2⫹ and Mg2⫹
inner-sphere or outer-sphere surface complexation, followed by
phosphate attachment at the reactive surface site. At the ambient pH values of 6 to 9, the surface site is partially deprotonated
and represented as Si3O6H5(H2O)3⫺, where H2O represents the
explicitly hydrating water molecules.
The rate at which the hexaquo cation forms a surface complex decreases as Mg2⫹ outer sphere ⬎ Mg2⫹ inner sphere ⬎
Ca2⫹ inner sphere. Faster Mg2⫹ sorption is driven by gasphase electrostatic attraction, despite slower Mg(H2O)6 dehydration compared to Ca(H2O)62⫹. Mg2⫹ sorbs rapidly, blocking access of nucleating surface sites to Ca2⫹. HPO42⫺ attaches
directly to the Ca inner-sphere complex, forming the
Si3O6H5CaHPO4(H2O)3⫺ critical nucleus. The outer-sphere
Mg2⫹ surface complex has to convert to the inner-sphere
attachment
to
form
complex
for
HPO42⫺
Si3O6H5MgHPO4(H2O)3⫺. HPO42⫺ attachment at the Ca2⫹
inner-sphere complex is faster than at the Mg2⫹ inner-sphere
complex. Apatite nucleation is thus retarded but not entirely
prevented from solutions with high Mg/Ca ratios, where Mg2⫹
would otherwise have had the thermodynamic advantage. The
geochemical implication is that the Mg/Ca ratio of pore water
does not need to be altered significantly from seawater composition by ad hoc processes to allow authigenic apatite precipitation.
Protons catalyze apatite precipitation by affecting surface
charge and surface tension. Apatite is close to its point of zero
surface charge (pH 7 to 8) at the ambient circumneutral pH
values. At low surface charge, Lippman’s equation suggests a
reduction in the interfacial tension between adjacent critical
nuclei and solutions, thus promoting nucleation and growth.
The broad similarity in chemical composition between ma-
1. INTRODUCTION
1.1. Motivation
Authigenic apatite is precipitated in the pore spaces of relatively shallow marine sediments during early diagenesis. The
precipitates are often overgrowths on detrital skeletal material
or on authigenic amorphous silica. Similarly, bioapatite (dahllite in our bones and francollite in our teeth) precipitation is
promoted by silica bioceramics, which are used as orthopedic
and dental prosthetic implants. The composition of marine pore
water, from which authigenic apatite is formed, is close to that
of average seawater. The pH is ⬃7 to 8, ionic strength ⬃0.6
mol/L, total dissolved magnesium (MgT) ⬃ 5 mmol/L, total
dissolved calcium (CaT) ⬃15 mmol/L, and total dissolved
inorganic phosphorous (PT) ⬃20 to 100 ␮mol/L (Froelich et
al., 1988; Van Cappellen, 1991; Jarvis et al., 1994). Typical
compositions are shown in Table 1. Mammalian blood, from
which bioapatite precipitates, has a composition broadly similar
to that of marine pore water (Table 1). These similarities
suggest that the inorganic reaction pathways for heterogeneous
apatite nucleation are very similar in the natural environment
and in organisms.
The literature on apatite crystal nucleation and growth is
enormous, so only a few studies are cited here (e.g., Martens
and Harriss, 1970; Nancollas and Tomazic, 1974; Garside,
1982; Nielsen, 1984; Arends et al., 1987; Christoffersen et al.,
1989, 1996; Van Cappellen, 1991; Elliot, 1994). In general, the
precipitation reaction consists of separate steps, including critical nucleus formation of a precursor phase, crystal growth, and
phase transition. A cluster is a critical nucleus if it is just large
enough to be at thermodynamic equilibrium with respect to
precipitation and dissolution. Further enlargement of the cluster
is called crystal growth. The net precipitation reaction depends
on a host of factors, including the degree of supersaturation,
pH, ionic strength, Ca/P ratios, and the presence of other ions
such as Mg2⫹, CO32⫺, and F⫺. The effect of these variables on
crystal growth has been well studied, but less is known about
their influence on nucleation. In particular, there are few studies
* ([email protected]).
1017
1018
N. Sahai
Table 1. Compositions of different fluids that are normally supersaturated with respect to apatite: average seawater and average pore water
(Table 2-1 in Van Capellen’s [1991] thesis) and human blood plasma
(Kokubo et al., 1990).
Ion
Average
seawater
(mm)
Average
pore water
(mm)
Human
blood plasma
(mmol)
pH
Na⫹
K⫹
Ca2⫹
Mg2⫹
Cl–
HCO3–
HPO42–
⬃7.5 to 8
486
10.6
10.7
54.7
566
1.93 (⫹ CO32–)
10–4 to 10–3
⬃6.5 to 8.5
486
10.6
10.7
54.7
566
5.6 (⫹ CO32–)
1.5 ⫻ 10–2
7.3
142.0
5.0
2.5
1.5
103.0
27.0
1.0
on apatite nucleation at the surface of a chemically distinct
solid such as amorphous silica.
The precise mechanisms by which surfaces promote heterogeneous apatite precipitation are not known because of the
difficulty in characterizing the earliest angstrom- or nanometersized solid precipitates. By their very definition, molecular
orbital (MO) calculations provide the ideal theoretical tool for
studying reactions at this scale. The aim of the present study is
to use ab initio MO calculations to examine the effects of Mg2⫹
and H⫹ ions on the heterogeneous nucleation of the calcium
phosphate precursor at the amorphous silica surface.
sphere adsorption of calcium at the Si3O6H5⫺ site, followed by
attachment of the HPO42⫺ ion, resulting in the formation of the
critical nucleus. In terms of model clusters, the pathway is
represented as Si3O6H5(H2O)3⫺ 3 Si3O6H5Ca(H2O)6⫹ 3
Si3O6H5CaHPO4(H2O)3⫺. The real nucleating cluster is larger
than a single ⬎CaHPO4 unit and is represented as
Si3O6H5[CaHPO4]n(H2O)3⫺, where n ⫽ 2 to 3, and ⬎ indicates attachment to the underlying silica surface site. The
alternative mechanism involving initial phosphate adsorption
on silica followed by calcium attachment is less favorable
(Sahai and Tossell, 2000). On the basis of an extensive literature review of empirical studies, we hypothesized a polynuclear
mechanism whereby cluster nucleation at negatively charged
surface sites is followed by cluster aggregation, crystal growth
and solid-state phase transformation to apatite (Christoffersen
et al., 1996; Kanzaki et al., 1998, 2001; Da Costa et al., 1998;
Rodriguez-Clemente et al., 1998; Coreño et al., 2001).
The effects of Mg2⫹ and H⫹ ions on crystal growth are
summarized here (e.g., Nielsen, 1984; Zawacki et al., 1986;
Van Cappellen and Berner, 1991). Mg2⫹ inhibits apatite crystal
growth. It has been proposed that Mg2⫹ blocks growth sites,
and the inhibitory effect is normally accepted as reflecting the
slower dehydration rate of the aqueous Mg2⫹ ion compared to
Ca2⫹. The rate of apatite growth is increased by H⫹ at intermediate pH 6 ⱕ pH ⱕ 10. It has been suggested that protonation of PO43⫺ groups on the apatite crystal facilitates exchange
of phosphate between the solution and crystal (Christoffersen
1.2. Background
Homogeneous nucleation of apatite is very slow, even from
supersaturated solutions, because of the energetic costs involved, so heterogeneous nucleation is probably common. Microscopic apatite crystals forming natural phosphorite deposits
often occur as overgrowths on detrital skeletal material (e.g.,
the photomicrographs in Baturin, 2000). The common association of phosphorites with marine microfossils has led to conjectures that organic surfaces or microorganisms are involved
in authigenic apatite precipitation. After an extensive review of
the literature, Krajewski et al. (1994) concluded that almost any
surface is capable of promoting apatite nucleation, especially
under natural conditions where mineral surfaces are ubiquitous.
In the absence of direct evidence for the involvement of controlled biomineralization, induced mineralization due to high
total dissolved phosphate concentration in marine pore waters
provides a sufficient explanation for phosphorite deposit formation. The high inorganic phosphorous content is due to the
accumulation and decay of organisms. The terms controlled
mineralization and induced mineralization are used here in the
sense described by Lowenstam and Weiner (1989, pp. 26 –28).
In a previous study, we used MO calculations to identify the
surface site that is responsible for catalyzing nucleation of the
earliest calcium phosphate cluster on amorphous silica surfaces
and to determine the mechanism by which it is effected (Sahai
and Tossell, 2000). At the intermediate pH of marine pore
water and blood, the partially deprotonated three-ring,
Si3O6H5⫺, is the active site on silica surfaces for calcium
phosphate nucleation. The negative potential at the oxygen
atom initially promotes dehydration of the calcium ion as it
adsorbs. The most likely reaction pathway involves inner-
Table 2. Calculated gas-phase energies (E0gas) using polarized double-␨ valence basis set and effective core potentials (Stevens et al.,
1992). 1 Hartree ⫽ 627.6 kcal mol– ⫽ 2626 k mol–.
Cluster
⫹
H
H2O0
Mg(H2O)62⫹
Ca(H2O)62⫹
HPO4(H2O)42–
H2PO4(H2O)4–
Si3O6H6(H2O)30 C3v symmetry imposed
Si3O6H6Mg(H2O)62⫹ inner sphere
Si3O6H6Ca(H2O)62⫹ inner sphere
Si3O6H6(H2O)3Mg(H2O)32⫹ outer sphere
Si3O6H6(H2O)3Ca(H2O)32⫹ outer sphere
Si3O6H6MgHPO4(H2O)30
Si3O6H6CaHPO4(H2O)30
Si3O6H5(H2O)3–
Si3O6H5Mg(H2O)6⫹ inner sphere
Si3O6H5Ca(H2O)6⫹ inner sphere
Si3O6H5(H2O)3Mg(H2O)3⫹ outer sphere
Si3O6H5MgHPO4(H2O)3–
Si3O6H5CaHPO4(H2O)3–
Si3O6H3(H2O)33–C3v symmetry imposed
Si3O6H3Mg(H2O)6– inner sphere
Si3O6H3Ca(H2O)6– inner sphere
Si3O6H6 · Mg · (OH)3 · (H2O)31– surface hydroxide;
started out as Si3O6H3(H2O)3Mg(H2O)3–
Si3O6H6Ca 䡠 (OH)3(H2O)3– surface hydroxide; started
out as Si3O6H3(H2O)3Ca(H2O)3–
Si3O6H3MgHPO4(H2O)33–
Si3O6H3CaHPO4(H2O)33– monodentate
Si3O6H4CaHPO4(H2O)32– started out as
Si3O6H5CaPO4(H2O)32–
E0gas
(Hartree)
0.00
–16.8434
–101.5667
–101.4738
–137.2503
–137.9160
–159.9456
–210.9984
–210.902(5)
–211.289(9)
–211.13(6)
–230.762(4)
–230.65(5)
–159.390(4)
–210.7178
–210.606(1)
–210.77(9)
–230.27(1)
–230.16(2)
–157.9902
–209.7852
–209.6566
–209.78(2)
–209.6668
–228.921
–228.79(4)
–229.534(5)
Apatite nucleation at silica surfaces
1019
Fig. 1. Surface protonation levels of the Si three-ring site: (a) fully protonated, (b) partially deprotonated, and (c) fully
deprotonated. Key to atoms: open circles ⫽ H, square hatched circles ⫽ O, striped circles ⫽ Si.
and Christoffersen, 1981, 1982; Arends et al., 1987; Van Cappellen and Berner, 1991). In the present paper, ab initio calculations are used to determine the effects of Mg2⫹ and H⫹ on
heterogeneous nucleation of apatite at the chemically distinct
surface of silica.
2. COMPUTATIONAL DETAILS
2.1. Model Assumptions
As in our previous study (Sahai and Tossell, 2000), I assume
here that the nucleation reaction consists of elementary steps.
The silica surface is negatively charged at the circumneutral pH
of marine pore water and human blood. Adsorption of alkaline
earth metal ions is assumed to be driven largely by electrostatic
forces. Note that the term cluster is used here to refer to model
molecules or ions. Model clusters are distinct from the terms
nucleating cluster and critical nucleus in the context of homogeneous or heterogeneous nucleation.
The model clusters are assumed to represent reaction intermediates at progressive stages of the reaction, with structures very
close to the corresponding activated complexes (Sahai and Tossell,
2000). The formation energies of the intermediate species can then
be related to the energies of the transition states (Hammond, 1955;
Taube, 1959). According to Hammond’s (1955) postulate, “if two
states, as for example, a transition state and an intermediate, occur
consecutively during a reaction progress and have nearly the same
energy content, their interconversion will involve only a small
reorganization of the molecular structure.” This allows the results
to be interpreted in terms of reaction mechanisms without actually
identifying the activated complexes directly.
1020
N. Sahai
Table 3. Solvation enthalpy (⌬H0solv) for each molecule or cluster
calculated according to Rashin and Honig’s (1985) modified Born
equation: ⌬H0solv ⫽ –166.9 z2/re in kcal/mol–1, and using effective radii
(re) as determined by the SCRF Volume option in Gaussian 94. 1
Hartree ⫽ 627.6 kcal/mol–1.
Cluster
H⫹
H2O
Mg(H2O)62⫹
Ca(H2O)62⫹
HPO4(H2O)42–
H2PO4(H2O)4–
Si3O6H6(H2O)30
Si3O6H6Mg(H2O)62⫹
Si3O6H6Ca(H2O)62⫹
Si3O6H6(H2O)3Mg(H2O)32⫹
Si3O6H6(H2O)3Ca(H2O)32⫹
Si3O6H6MgHPO4(H2O)30
Si3O6H6CaHPO4(H2O)30
Si3O6H5(H2O)3–
Si3O6H5Mg(H2O)6⫹
Si3O6H5Ca(H2O)6⫹
Si3O6H5(H2O)3Mg(H2O)3⫹
Si3O6H5MgHPO4(H2O)3–
Si3O6H5CaHPO4(H2O)3–
Si3O6H3(H2O)33–
Si3O6H3Mg(H2O)6–
Si3O6H3Ca(H2O)6–
Si3O6H6Mg(OH)3(H2O)3–
Si3O6H6Ca(OH)3(H2O)3–
Si3O6H3MgHPO4(H2O)33–
Si3O6H3CaHPO4(H2O)33–
a
b
re (Å)
⌬H0solv
(Hartree)
3.94
3.98
3.79
3.54
4.90
5.19
5.26
5.15
5.43
5.18
5.25
4.53
5.20
5.13
5.22
5.39
4.95
4.83
5.30
5.16
5.21
5.26
5.43
5.51
–0.4259a
–0.0158b
–0.26998
–0.26727
–0.28067
–0.0791
0.0000
–0.2050
–0.20223
–0.20655
–0.19590
0.00
0.00
–0.058705
–0.0511
–0.051839
–0.0509
–0.049338
–0.053724
–0.49553
–0.0502
–0.051538
–0.0510
–0.050558
–0.4408
–0.4344
From Tawa et al. (1998).
Experimental ⌬H0vap of water from Ben Naim and Marcus (1984).
As detailed below, the free energy (G) term is assumed to be
dominated by the enthalpy (H) term, which is in turn dominated
by the internal energy (E) term (Sauer and Ahlrichs, 1990;
Fleischer et al., 1993). When comparing two similar elementary
reaction steps, the reaction with the more negative energy will
be the more facile pathway. The sum of all elementary steps
involving adsorption of Mg(H2O)62⫹ or Ca(H2O)62⫹ and
HPO4(H2O)4⫺ at the active surface site represents the overall
free energy of critical nucleus formation.
2.2. Geometry Optimizations
Structural optimizations and energy calculations for clusters
were carried out using the quantum chemistry software packages GAMESS, Gaussian 94, and Gaussian 98 (Schmidt et al.,
1993; Frisch et al., 1995, 1998). Optimizations were done at the
self-consistent field level using effective core potentials and
valence double-␨ basis sets with polarization functions (Stevens
et al., 1992). The Hartree-Fock computational level implies that
no corrections are made for electron correlation. The use of
effective core potentials means that core electrons are ignored,
and only the energy of the valence electrons is calculated. Basis
set truncation error and basis set superposition error are ignored.
The optimized geometries correspond to stationary points on
the potential energy surface, thus representing local extrema.
Because these points are assumed to be intermediates very
close to transition states, their formation energies track the
transition-state energies for each elementary step. Results are
reported in Table 2. Optimizations were performed without any
symmetry constraints, except as noted.
The active site for ⬎CaHPO4 nucleation at the silica surface is
the planar three-ring represented in the model by Si3O6H6 (Sahai
and Tossell, 2000). Different protonation levels are modeled as
fully protonated (Si3O6H6), partially deprotonated (Si3O6H5⫺),
and fully deprotonated (Si3O6H33⫺) (Fig. 1). Planar three-ring
structures are characterized by their distinctive Raman vibrational frequency at 605 cm⫺1 (Galeener, 1982; Brinker et al.,
1988) and have been modeled previously (e.g., West and Wallace,
1993; Tossell, 1996; Sahai and Tossell, 2000). Explicitly hydrated aqueous ions examined include Ca(H2O)62⫹,
Mg(H2O)62⫹,
H2PO4(H2O)4⫺,
HPO4(H2O)42⫺,
and
PO4(H2O)43⫺. Sorbed metal ions at different surface protonation levels are represented by model clusters such as Si3O6H6M
(H2O)62⫹, Si3O6H5M(H2O)6⫹, and Si3O6H3M(H2O)6⫺; sorbed
calcium phosphates are represented as Si3O6H6MHPO4(H2O)30,
Si3O6H5MHPO4(H2O)3⫺, and Si3O6H3MHPO4(H2O)33⫺,
where M is Ca2⫹ or Mg2⫹. The clusters shown in the figures
below were created with the molecular drawing software MacMolPlt (Bode and Gordon, 1998).
2.3. Energies
Energies are calculated at the same computational level as
the geometry optimizations (Table 2).The MO calculations
yield values of internal energy (E). Reaction energies are calculated as the difference between energies of products and
reactants (⌬Er). For small to medium-sized basis sets, the
relative ranking of formation energies of reactions is the same
at different computational levels, regardless of the inclusion or
neglect of basis set superposition error and of electron correlation (Sahai and Tossell, 2001). Reaction enthalpy (⌬Hr) is
assumed to be dominated by the ⌬Er term (Sauer and Ahlrichs,
1990; Fleischer et al., 1993). Thermal and entropic contributions to the free energy of reactions are not calculated because
of the prohibitive computational cost for the larger clusters
considered in this study. In short, it is assumed that ⌬Egas, r ⬇
⌬Hgas, r ⬇ ⌬H0gas, r ⬇ ⌬G0gas, r. A negative or positive value
for a calculated reaction enthalpy suggests that the reaction is
exothermic or endothermic only at standard state and does not
necessarily indicate whether the reaction will proceed spontaneously under the ambient conditions.
2.4. Treatment of Solvation
For aqueous reactions, solvation enthalpies (⌬H0solv, r) must
be added to the gas-phase enthalpies. The experimental ⌬H0vap
of water, equal to ⫺0.0158 Hartree, is taken as a measure of its
solvation enthalpy (Ben Naim and Marcus, 1984). The Born
solvation energy of H⫹ is difficult to calculate because the
radius is undefined, so I adopted the theoretical value of
⫺0.4259 Hartree (Tawa et al., 1998). Solvation enthalpy of
other molecules is calculated using a modified Born model,
which assumes a spherical solute cavity in the solvent’s dielectric continuum (Rashin and Honig, 1985) (Table 3). The effective radius of the solute cavity is estimated by using the SCRF
Volume option in Gaussian 94 and Gaussian 98. Stevens et al.’s
Apatite nucleation at silica surfaces
1021
Fig. 2. Reaction intermediates for Mg2⫹ adsorption: (a) and (b) inner sphere and outer sphere at the fully protonated level,
(c) and (d) inner sphere and outer sphere at the partially deprotonated level, and (e) surface hydroxide at the fully
deprotonated level. Key to atoms: open circles ⫽ H, square hatched circles ⫽ O, striped circles ⫽ Si, dark stippled circles
⫽ Mg.
(1992) basis set was not available in Gaussian 94, so the
“LanL2DZ” basis set with effective core potential was used for the
volume calculations (Frisch and Frisch, 1999, p. 34) (Table 3).
In the chemical formulae, I have not indicated the free water
molecules to be different from those directly bonded with the
metal ions. This is because the number of associated water
molecules would change if a different number of water molecules was used in the model clusters. The water molecules are
included to provide some degree of explicit hydration, which
accounts for short-range hydration effects. The number of
water molecules should not be taken literally.
The combination of explicit waters of hydration to account
for short-range hydration forces and the addition of a continuum contribution to account for long-range effects is a commonly used approach (e.g., Claverle et al., 1978; Freitas et al.,
1992; Keith and Frisch, 1994; Parchment et al., 1996; Tossell,
1999). Despite such considerations, there are still significant
sources of uncertainty in estimating solvation energies (Sahai
and Tossell, 2000) because of the inherent limitations of continuum solvation models. The limitations are mitigated somewhat by our interest in relative reaction energies rather than in
absolute values.
It is difficult to obtain absolute error estimates on calculated
reaction enthalpies. The present computational level should,
nevertheless, provide meaningful estimates of the relative stability of different species (Sahai and Tossell, 2001). Water
exchange rates or lifetimes of Mg2⫹ and Ca2⫹ can be used to
support this assertion. In Table 3, the ⌬H0solv of Mg2⫹ is more
negative than that of Ca2⫹, consistent with the former’s larger
charge-to-radius ratio. This implies that a water molecule is
more tightly held to Mg2⫹ and therefore is more difficult to
exchange with bulk water, so its rate of exchange should be
1022
N. Sahai
Table 4. Calculated reaction enthalpies (⌬H0r) in atomic units of Hartree for Mg2⫹ and Ca2⫹ sorption on silica rings. Gas-phase energies (⌬E0gas)
consistent with the polarized SBK basis set (Stevens et al., 1992). Solvation enthalpy (⌬H0solv) calculated according to Rashin and Honig’s (1985)
modified Born equation and using effective radii (re) as determined by the SCRF Volume option in Gaussian 94 (Frisch et al., 1995). ⌬H0r ⫽ ⌬H0gas, r
⫹ ⌬H 0solv, r, where we have assumed ⌬H0r ⬇ ⌬E0gas, r. 1 Hartree ⫽ 627.6 kcal mol⫺1.
#
M2⫹
surface
complex
formed
1.
Inner sphere
2.
Outer
sphere
3.
Inner sphere
4.
Outer
sphere
5.
Inner sphere
6.
Surface
hydroxide
a
Mg2⫹
Reaction
Sorption at Si3O6H6
Si3O6H6(H2O)3 ⫹ M(H2O)62⫹ ⫽
Si3O6H6M(H2O)62⫹ ⫹ 3H2O
Si3O6H6(H2O)3 ⫹ M(H2O)62⫹ ⫽
Si3O6H6(H2O)3M(H2O)32⫹ ⫹ 3H2O
Sorption at Si3O6H5–
Si3O6H5(H2O)3– ⫹ M(H2O)62⫹ ⫽
Si3O6H5M(H2O)6⫹ ⫹ 3H2O
Si3O6H5(H2O)3– ⫹ M(H2O)62⫹ ⫽
Si3O6H5(H2O)3M(H2O)3⫹ ⫹ 3H2O
Sorption at Si3O6H33–
Si3O6H3(H2O)33– ⫹ M(H2O)62⫹ ⫽
Si3O6H3M(H2O)6– ⫹ 3H2O
Si3O6H3(H2O)33– ⫹ M(H2O)62⫹ ⫽
Si3O6H6M(OH)3(H2O)3– ⫹ 3H2O
Ca2⫹
⌬H0gas, r
⌬H0solv, r
⌬H0r
⌬H0gas, r
⌬H0solv, r
⌬H0r
⌬H0r, Mg2⫹–
⌬H0r, Ca2⫹
–0.0163
⫹0.0176
⫹0.0013
–0.0133
⫹0.0222
⫹0.0089
–0.0076
–0.3078
⫹0.0160
–0.2918
–0.2468
⫹0.0102
–0.2366
–0.0552
–0.2909
⫹0.2302
–0.0606
–0.2709
⫹0.2242
–0.0467
–0.0139
–0.3521
⫹0.2304
–0.1217
—
—
—
N.D.a
–0.7585
⫹0.6679
–0.0906
–0.7228
⫹0.6687
–0.0541
–0.0365
–0.7553
⫹0.6671
–0.0882
–0.7330
⫹0.6696
–0.0634
–0.0248
N.D. ⫽ not defined; no stable outer-sphere geometry located for Ca2⫹, so no energy reported.
slower. This result is consistent with the empirical value of 10⫺6
to 10⫺5 s for the lifetime of the Mg2⫹-H2O bond compared to
10⫺8 s for Ca2⫹ (Israelachvili, 1992). A similar justification of the
reliability of relative adsorption energies, by comparison with
experimental data, is provided below in section 3.1.3.
3. RESULTS
3.1. Step 1: Metal Ion Sorption
3.1.1. Mg2⫹ surface complexation
Magnesium sorption at different surface protonation levels is
shown in Figures 2a to 2d. Inner-sphere complexation, where
Mg2⫹ is directly bonded to the surface oxygens, is obtained at
all surface protonation levels and is shown for the fully protonated (Fig. 2a) and partially protonated (Fig. 2c) levels. Structures were also obtained where water molecules are present between the surface and the Mg2⫹ cation, forming outer-sphere
complexes (Figs. 2b and 2d). In the case of Si3O6H3 (H2O)33⫺, the
outer-sphere complex was unstable such that during optimization,
the surface oxide anions (⬎SiO⫺) pulled off one H⫹ from each
of three water molecules between the surface and the Mg2⫹
ion. In this process, the surface oxide anions were converted to
silanol sites (⬎SOH), leaving behind three hydroxide groups
attached to the magnesium ion, yielding Si3O6H6Mg
(OH)3(H2O)3⫺. The resulting complex is termed a surface
hydroxide here (Fig. 2e). The reaction energies for Mg2⫹
surface-complex formation are calculated in Table 4.
3.1.2. Ca2⫹ surface complexation
Structures analogous to the Mg2⫹ surface complexes are
obtained for calcium sorption in most cases, and reaction energies are calculated in Table 4. Selected calcium surface
complexes shown here are the outer-sphere geometry at the
fully protonated level (Fig. 3a), the inner-sphere complex at the
partially protonated level (Fig. 3b), and the surface hydroxide
at the fully deprotonated level (Fig. 3c). Unlike Mg2⫹, a
stationary point was not located for the outer-sphere Ca2⫹
complex at the partially protonated Si3O6H5(H2O)3⫺ surface.
3.1.3. Comparison of Mg2⫹ and Ca2⫹ surface complexation
For both Mg2⫹ and Ca2⫹, ⌬H0r of inner-sphere surface
complexation becomes more negative as pH increases and
protonation level of the surface decreases (Table 4). Second,
the most stable surface complex at each protonation level is
different for the two ions. For Mg2⫹, the outer-sphere complex
is the most stable form at the fully protonated and the partially
deprotonated levels, and the inner-sphere complex becomes
more stable at the completely deprotonated level. The most
stable Ca2⫹ complex changes from outer sphere to inner sphere
to surface hydroxide as surface protonation level decreases. At
the Si3O6H5(H2O)3⫺ level expected at circumneutral pH, the
surface complexes in decreasing order of relative stability are
Mg2⫹ outer sphere ⬎ Mg2⫹ inner sphere ⬎ Ca2⫹ inner sphere.
Using Hammond’s postulate, this is also the order of decreasing
facility for adsorption and decreasing rate of reaction.
The effect of solvation can be separated from the overall
reaction energy in Table 4. For reaction mechanisms 1, 5, and
6, the ⌬H0solv, r values for the Mg2⫹ surface complexes are less
positive (more favorable) than the Ca2⫹ values. This result
suggests that that the Mg2⫹ ion is more readily (faster rate)
desolvated to form the inner-sphere complex compared to the
Ca2⫹ inner-sphere complex. For mechanisms 2 and 3, however,
the Mg2⫹ ions are more difficult to desolvate than Ca2⫹. These
results indicate that the difficulty in desolvating and adsorbing
Mg2⫹ is not always greater than that for Ca2⫹. Furthermore, a
comparison of ⌬H0solv, r for reactions 3 and 4 shows that the
rate of adsorption of Mg2⫹ depends on the type of surface
complex being formed, and the difference is driven by gasphase contributions, not by differences in desolvation rate.
Finally, the values in the last column of Table 4 represent the
stability of Mg2⫹ compared to Ca2⫹ complexes. A negative value
Apatite nucleation at silica surfaces
1023
Fig. 3. Reaction intermediates for Ca2⫹ adsorption: (a) outer sphere at the fully protonated level, (b) inner sphere at the
partially deprotonated level, and (c) surface hydroxide at the fully deprotonated level. Key to atoms: open circles ⫽ H,
square hatched circles ⫽ O, striped circles ⫽ Si, light stippled circles ⫽ Ca.
of ⌬H0r, Mg2⫹ ⫺ ⌬H0r, Ca2⫹ implies that the Mg2⫹ complex is more
stable than the Ca2⫹ analog. For each type of complex, Mg2⫹ is
more strongly sorbed than Ca2⫹. In addition, the Mg2⫹ innersphere complex is increasingly favored over the Ca2⫹ analog as
the surface protonation level decreases. Both these results are
consistent with experimentally measured pH edges for Mg2⫹ and
Ca2⫹ on the surface of quartz (Vuceta, 1976, pp. 100 –101).
3.2. Step 2: Phosphate Ion Attachment
3.2.1. Comparison of H2PO4⫺, HPO42⫺, and PO43⫺
attachment to sorbed calcium
The effect of pH on phosphate was modeled previously by
calculating attachment energies of H2PO4⫺, HPO42⫺, and
PO43⫺ at all surface protonation levels on the Ca2⫹-sorbed
sites (Sahai and Tossell, 2000). The attachment energies of
H2PO4⫺ and HPO42⫺ are compared in Table 5. Their relative
stabilities are represented by the difference ⌬H0r, HPO42⫺ ⫺
⌬H0r, H2PO4⫺. A negative value indicates that the reaction
involving HPO42⫺ is more favorable than the one involving
H2PO4⫺. For the fully protonated and partially protonated
rings, the gas-phase reaction energies are more favorable for
HPO42⫺ than for H2PO4⫺, and the solvation energy change is
more favorable for the H2PO4⫺ complexes. The reverse situation holds at the totally deprotonated surface site, where the
H2PO4⫺ surface complexes are more favored in the gas phase, and
the solvation energy change is more favorable for the HPO42⫺
surface complexes. As a result, there is no consistent pattern for
the ⌬H0r, HPO42⫺ ⫺ ⌬H0r, H2PO4⫺ values in Table 5. Finally,
for both HPO42⫺ and H2PO4⫺, the more stable surface cluster
1024
N. Sahai
Table 5. Calculated reaction enthalpies (⌬H0r, Hartree) of HPO4(H2O)42– and HPO4(H2O)4– attachment to Ca surface complexes.
#
7a.
Starting Ca2⫹
surface
complex
Inner sphere
7b.
8a.
Outer sphere
8b.
9a.
Inner sphere
9b.
10a.
Outer sphere
11a.
Inner sphere
11b.
12a.
12b.
Surface hydroxide
Ca2⫹
Reaction
Sorption at Si3O6H6
Si3O6H6M(H2O)32⫹ ⫹ HPO4(H2O)42– ⫽
Si3O6H6MHPO4(H2O)30⫹7H2O
Si3O6H6M(H2O)32⫹ ⫹ H2PO4(H2O)4– ⫽
Si3O6H6MH2PO4(H2O)3⫹ ⫹ 7H2O
Si3O6H6(H2O)3M(H2O)32⫹ ⫹ HPO4(H2O)42– ⫽
Si3O6H6MHPO4(H2O)30 ⫹ 7H2O
Si3O6H6(H2O)3M(H2O)32⫹ ⫹ H2PO4(H2O)4– ⫽
Si3O6H6MH2PO4(H2O)3⫹ ⫹ 7H2O
Sorption at Si3O6H5–
Si3O6H5M(H2O)3⫹ ⫹ HPO4(H2O)42– ⫽
Si3O6H5MHPO4(H2O)3–⫹ 7H2O
Si3O6H5M(H2O)3⫹ ⫹ H2PO4(H2O)4– ⫽
Si3O6H5MH2PO4(H2O)30⫹ 7H2O
Si3O6H5M(H2O)3⫹ ⫹ H2PO4(H2O)4– ⫽
Si3O6H5MH2PO4(H2O)30 ⫹ 7H2O
Sorption at Si3O6H33–
Si3O6H3M(H2O)3– ⫹ HPO4(H2O)42– ⫽
Si3O6H3MHPO4(H2O)33–⫹ 7H2O
Si3O6H3M(H2O)3– ⫹ H2PO4(H2O)4– ⫽
Si3O6H3MH2PO4(H2O)32– ⫹ 7H2O
Si3O6H6(OH)3M(H2O)3– ⫹ HPO4(H2O)42– ⫽
Si3O6H3MHPO4(H2O)3 ⫹ 7H2O
Si3O6H6(OH)3M(H2O)3– ⫹ H2PO4(H2O)4– ⫽
Si3O6H3MH2PO4(H2O)32–⫹ 7H2O
⌬H0gas, r
⌬H0solv,r
⌬H0r
–0.406
⫹0.3397
–0.0663
–0.1376
⫹0.1141
–0.0235
–0.1725
⫹0.3520
⫹0.1795
⫹0.0959
⫹0.1264
⫹0.0222
–0.2082
⫹0.1282
–0.0800
–0.0429
⫹0.0045
–0.0384
—
—
⫹0.2091
–0.2454
–0.0363
⫹0.1530
–0.1950
–0.0420
⫹0.2193
–0.2463
–0.027
⫹0.1632
–0.1959
–0.0327
⌬H0r, HPO42–
⌬H0r, H2PO4⫺
–0.0428
–0.0043
–0.0416
⫹0.0057
⫹0.0057
A geometry optimization for a ⬎CaPO4 surface cluster was attempted. The cluster was started out as Si3O6H5CaPO4(H2O)32–, but during
optimization, it went to Si3O6H4CaHPO4(H2O)32–. The energy for formation of this cluster is not reported in the present table.
is the one formed by attachment to the inner-sphere calcium
surface complex. The surface cluster formed by HPO42⫺ attachment at Si3O6H5Ca⫹ is Si3O6H5CaHPO4(H2O)3⫺ (Fig. 4a). A
similar geometry is obtained for Si3O6H5CaH2PO4(H2O)30
(not shown).
Geometry optimization for PO4(H2O)43⫺ attachment at
Si3O6H5Ca(H2O)3⫹ was also attempted, starting with the cluster Si3O6H5CaPO4(H2O)32⫺. During geometry optimization,
the PO43⫺ ion plucked one H⫹ atom from one surface silanol
site, leaving behind a deprotonated surface site and forming the
stable surface complex Si3O6H4CaHPO4(H2O)32⫺ (not
shown). This calculation indicates that at intermediate pH conditions where Si3O6H5(H2O)3⫺ is the surface protonation level,
the ⬎CaHPO4 cluster is favored over the ⬎CaPO4⫺ cluster.
In summary, HPO42⫺ is preferred over H2PO4⫺ or PO43⫺
for attachment at intermediate pH, resulting in the nucleating
cluster Si3O6H5 CaHPO4(H2O)3⫺ (Fig. 4a). HPO42⫺ is also the
dominant form of phosphoric acid at the intermediate pH of
marine pore water and blood. Thus, there is both kinetic and
thermodynamic advantage to HPO42⫺ attachment. In the following section, therefore, the attachment of only HPO42⫺ to
the Mg2⫹ surface complex is considered.
3.2.2. HPO42⫺ attachment to sorbed magnesium
The surface cluster formed at the partially deprotonated site
is Si3O6H5MgHPO4(H2O)3⫺ (Fig. 4b). The energy of HPO42⫺
adsorption at the Mg2⫹- and Ca2⫹-sorbed sites is calculated in
Table 6. In the case of Mg2⫹, HPO42⫺ attachment at the
inner-sphere complex is easiest at the Si3O6H6(H2O)3 and the
Si3O6H5(H2O)3⫺ protonation levels, and attachment at the
surface hydroxide is easiest at Si3O6H3(H2O)33⫺.
Ca2⫹ is favored over Mg2⫹ in reactions 7 to 12 of Table 6
(⌬H0r, Mg2⫹ ⫺ ⌬H0r, Ca2⫹ ⬎ 0). The mechanism involving the
inner-sphere Mg2⫹ complex at Si3O6H5(H2O)3⫺ (reaction 9) is
less favorable than Ca2⫹ by 0.0452 Hartree or 28.36 kcal
mol⫺1. The relative stability for M2⫹ attachment and
⬎MHPO4 formation at intermediate pH decreases as Ca2⫹
inner sphere ⬎ Mg2⫹ inner sphere ⬎ Mg2⫹ outer sphere. By
Hammond’s postulate, this is also the sequence for HPO42⫺
attachment rate. No value is reported for ⌬H0r of reaction 10
because no stationary point was found for the Ca2⫹ outersphere surface complex.
3.3. Overall Reaction: >MgHPO4 or >CaHPO4 Cluster
Nucleation
The net reaction energy for adsorption of Mg(H2O)62⫹,
Ca(H2O)62⫹, and HPO4(H2O)4⫺ on the silica three-ring at
different protonation levels is summarized in Table 7. These
reaction energies are related to ⌬H0r and ⌬G0r for formation of
⬎MHPO4 clusters. The formation of ⬎MgHPO4 is favored as
surface protonation level decreases. Thus, the inhibitory effect
of Mg2⫹ is counteracted by the catalytic effect of surface
protonation, consistent with empirical observation of the opposing effects of Mg2⫹ and pH. A consistent trend with pH is
not seen for ⬎CaHPO4 formation.
Apatite nucleation at silica surfaces
1025
Fig. 4. Reaction intermediates for HPO42⫺ attachment to the (a) Ca2⫹-sorbed site and the (b) Mg2⫹-sorbed site, at the
partially deprotonated level. Key to atoms as in Figures 2 and 3.
4. DISCUSSION
2ⴙ
4.1. Kinetic Effect of Mg
4.1.1. Most facile pathways at each protonation level
The information indicating the fastest pathways from Tables
4 and 6 is summarized in Table 8. The entries in Table 8 refer
to the reaction intermediate closest in structure to a nearby
transition state. The rows labeled “M2⫹ adsorption,” where
M2⫹ is Ca2⫹ or Mg2⫹, indicate the fastest formed M2⫹ surface
complex, i.e., products of reactions 1 to 6. The rows labeled
“starting M2⫹ surface complex for HPO42⫺ attachment” show
the reactants of reactions 7 to 12 that provide the fastest
pathways for ⬎MHPO4 surface cluster formation. The reaction
intermediates at the ambient circumneutral pH values for Ca2⫹
and Mg2⫹, respectively, are shown in Figures 5 and 6.
4.1.2. Desolvation vs. Surface-Poisoning effects at
intermediate pH
The rate of cation surface complexation decreases as Mg2⫹
outer sphere ⬎ Mg2⫹ inner sphere ⬎ Ca2⫹ inner sphere. Using
values from Tables 2 and 3, we see that conversion of the outer-
1026
N. Sahai
Table 6. Calculated reaction enthalpies (⌬H0r, Hartree) for HPO4(H2O)42– attachment to cation surface complexes.
Mg2⫹
Starting M2⫹
surface complex
#
⌬H0gas, r
Reaction
Sorption at Si3O6H6
–0.4175
Si3O6H6M(H2O)32⫹ ⫹
HPO4(H2O)42– ⫽
0
Si3O6H6MHPO4(H2O)3 ⫹ 7H2O
8. Outer sphere
Si3O6H6(H2O)3M(H2O)32⫹ ⫹
–0.1256
HPO4(H2O)42– ⫽
Si3O6H6MHPO4(H2O)30 ⫹ 7H2O
Sorption at Si3O6H5–
9. Inner sphere
Si3O6H5M(H2O)3⫹ ⫹ HPO4(H2O)42– –0.2067
⫽ Si3O6H5MHPO4(H2O)3–
⫹7H2O
10. Outer sphere
Si3O6H5(H2O)3M(H2O)3⫹ ⫹
–0.1455
HPO4(H2O)42– ⫽
Si3O6H5MHPO4(H2O)30 ⫹ 7H2O
Sorption at Si3O6H33–
11. Inner sphere
Si3O6H3M(H2O)3– ⫹ HPO4(H2O)42– ⫹0.2107
⫽ Si3O6H3MHPO4(H2O)33– ⫹
7H2O
12. Surface hydroxide Si3O6H6(OH)3M(H2O)3– ⫹
⫹0.2075
HPO4(H2O)42– ⫽
Si3O6H3MHPO4(H2O)33– ⫹ 7H2O
7. Inner sphere
a
Ca2⫹
⌬H0solv, r
⌬H0r
⌬H0gas, r
⌬H0solv, r
⌬H0r
⌬H0r, Mg2⫹–
⌬H0r, Ca2⫹
⫹0.3751
–0.0424
–0.406
⫹0.3397
–0.0663
⫹0.00239
⫹0.3766
⫹0.2510
–0.1725
⫹0.3520 ⫹0.1795
⫹0.0715
⫹0.1719
–0.0348
–0.2082
⫹0.1282
–0.0800
⫹0.0452
⫹0.1717
⫹0.0262
—
—
—
N.D.a
–0.2205
–0.0098
⫹0.2091
–0.2454
–0.0363
⫹0.0265
–0.2197
–0.0122
⫹0.2193
–0.2463
–0.027
⫹0.0148
N.D. ⫽ not defined; no stable outer-sphere geometry located for Ca2⫹, so no energy reported.
The rate of HPO42⫺ attachment follows exactly the opposite
sequence to cation adsorption. In terms of attachment rate, Mg
outer sphere ⬍ Mg inner sphere ⬍ Ca inner sphere complex.
HPO42⫺ attachment is less favorable for Mg2⫹ than for Ca2⫹
in terms of both ⌬H0gas, r and ⌬H0solv, r (reaction 9). Thus,
Mg2⫹ inhibits apatite nucleation by exerting its influence only
in the first elementary step, i.e., cation adsorption.
sphere Mg2⫹ to the inner-sphere Mg2⫹ surface complex,
Si3O6H5(H2O)3Mg(H2O)3⫹ 3 Si3O6H5Mg(H2O)6⫹, has positive values of ⌬H0gas, r, ⌬H0solv, r, and ⌬H0r ⫽
⫹0.0611 Hartree or ⫹38.35 kcal mol⫺1, so this should be a slow
step compared to the Ca2⫹ analog, where the outer-sphere complex, presumably, is so unstable that not even a stationary point
was located on the potential energy surface. The dehydration of
the Mg(H2O)62⫹ ion to form the inner-sphere surface complex is
also more difficult than for Ca2⫹, as reflected in the more positive
⌬H0solv, r of reaction 3 for Mg2⫹. Both these results are consistent
with empirically obtained dehydration frequencies or water-exchange lifetimes (Nielsen, 1984; Israelachvili, 1992, p. 55), which
show that aqueous Mg2⫹ dehydration is slower than aqueous
Ca2⫹ dehydration. It is perhaps intuitive to expect that the rate of
dehydration of the ion should correlate with the rate of ion adsorption and incorporation into a growing crystal and, hence, the
crystal growth rate. The present results, however, show that although Mg(H2O)62⫹ dehydration is slower than that of
Ca(H2O)62⫹, Mg2⫹ adsorption is faster, being driven by
gas-phase electrostatic effects. Thus, the ease of Mg(H2O)2⫹
desolvation vs. the Ca(H2O)2⫹ ion is not the controlling factor.
This is a new result, not expected from crystal growth theories.
Mg2⫹ exerts its influence by blocking Ca2⫹ adsorption.
4.2. Kinetic Effect of Hⴙ on Cluster Nucleation,
Aggregation, and Crystal Growth
Nucleation and growth of clusters from solution requires
that the surface energy (surface tension) between the cluster
and the solution or between two adjacent clusters be overcome. Surface tension (␴) depends on surface charge density
(␳s) according to the Lippman equation (e.g., Adamson and
Gast, 1997, p. 195):
d␴
⫽ – ␳ s,
d␺
(1)
where ␺ is the surface potential. Protons affect surface charge
and surface potential. Thus, pH can affect interfacial tension.
Table 7. Overall reaction enthalpies (⌬H0r, Hartree) for ⬎MgHPO4 and ⬎CaHPO4 surface cluster formation.
Mg2⫹
⌬H
0
#
Reaction
13.
Si3O6H6(H2O)3 ⫹ M(H2O)6 ⫹ HPO4(H2O)4 ⫽
Si3O6H6MHPO4(H2O)30 ⫹ 10H2O
Si3O6H5(H2O)3– ⫹ M(H2O)62⫹ ⫹ HPO4(H2O)42– ⫽
Si3O6H5MHPO4(H2O)3– ⫹ 10H2O
Si3O6H3(H2O)33– ⫹ M(H2O)62⫹ ⫹ HPO4(H2O)42–
⫽ Si3O6H3MHPO4(H2O)33– ⫹ 10H2O
14.
15.
0
2⫹
2–
⌬H
0
gas, r
Ca2⫹
⌬H
0
solv, r
⌬H
0
r
⌬H
0
gas, r
⌬H
0
solv, r
r
⌬H0r, MgHPO4–
⌬H0r, CaHPO4
–0.4338
⫹0.3927
–0.0411
–0.4188
⫹0.3622
–0.0571
⫹0.016
–0.4976
⫹0.4020
–0.0956
–0.4803
⫹0.3596
–0.1307
⫹0.0351
–0.5478
⫹0.4474
–0.1004
–0.5137
⫹0.4233
–0.0904
–0.01
Apatite nucleation at silica surfaces
1027
Table 8. Summary of most likely pathway for ⬎CaHPO4 and ⬎MgHPO4 surface nucleation.
Most facile mechanism
Reaction step2
pH 3
Low pH,
three-ring,
fully protonated
Ca2– adsorption
HPO42– attachment
Mg2– adsorption
HPO42– attachment
Resulting ⬎Ca2⫹ surface complex
Starting ⬎Ca2⫹ surface complex for HPO42– attachment
Resulting ⬎Mg2⫹ surface complex
Starting ⬎Mg2⫹ surface complex for HPO42– attachment
Outer sphere
Inner sphere
Outer sphere
Inner sphere
Intermediate pH,
three-ring,
partially protonated
Inner sphere
Inner sphere
Outer sphere
Inner sphere
High pH,
three-ring,
fully deprotonated
Surface hydroxide
Inner sphere
Inner sphere
Surface hydroxide
Fig. 5. Most facile pathway for ⬎CaHPO4 surface cluster nucleation at intermediate pH characteristic of marine pore
water, seawater, and human blood plasma solutions. Key to atoms as in Figure 3.
1028
N. Sahai
Fig. 6. Most facile pathway for ⬎MgHPO4 surface cluster nucleation at intermediate pH. Reaction rates relative to the
corresponding Ca2⫹ reaction are shown by arrows. The rate of conversion of the outer-sphere Mg2⫹ surface complex to the
inner-sphere complex refers to Mg2⫹ itself without comparison to Ca2⫹. Key to atoms as in Figure 2.
The pH of the point of zero charge (pHPZC) is ⬃8 and
reduces to ⬃7 when carbonate is present in solution (Wu et al.,
1991) as in seawater, marine pore fluids, and blood. In the
intermediate pH range, a near-neutral surface charge would
exist on the nuclei of calcium phosphate. Under these conditions, the CaHPO4-solution interfacial tension would be reduced, thus promoting a faster rate of nucleation and crystal
growth. A similar surface tension effect is observed in the growth
of precipitated gypsum and amorphous silica particles by “particle
bridging” (Schukin and Kontorovich, 1985). The process involves
the bridging of nanometer-sized crystalline or amorphous particles by elimination of the dispersion medium between them.
5. IMPLICATIONS
5.1. Marine Pore Water Compositions
It is known empirically that Mg2⫹ inhibits calcium phosphate nucleationas and growth. If the aqueous activity of
Mg2⫹ is much larger than that of Ca2⫹, then Mg2⫹ also has
an added thermodynamic advantage over Ca2⫹ in the ratelimiting step. At the large Mg/Ca ratio of ⬃5 of marine pore
water and seawater, it is difficult to imagine how any apatite
could precipitate from such a solution. To circumvent this
puzzle, various ad hoc geochemical processes have been proposed
in the literature that would bring about a reduction in the Mg/Ca
ratio and allow calcium phosphate to form (Slansky, 1986, pp.
88 –93, 100 –102). But some of the proposed geochemical scenarios are not realistic and cannot bring about the required degree of
reduction in the Mg/Ca ratio.
A fundamental flaw in the previous studies was the implicit
assumption that both Mg2⫹ and Ca2⫹ follow identical reaction
pathways. The present study, however, shows that ⬎MgHPO4
and ⬎CaHPO4 nucleation follow different pathways. A high
Mg/Ca ratio benefits Mg2⫹ only in the first step, but because
the overall ⌬G0r for CaHPO4 is faster, Ca2⫹ ultimately prevails. A smaller reduction of Mg/Ca ratio is now no longer a
necessary condition for apatite nucleation. This result eliminates the need to invoke unrealistic ad hoc geochemical processes for apatite precipitation.
5.2. Bone and Tooth Apatite Precipitation
We have previously calculated the energies, Raman/infrared
vibrational frequencies, and 29Si and 31P nuclear magnetic
Apatite nucleation at silica surfaces
resonance chemical shifts for the clusters Si3O6H5(H2O)3⫺ 3
Si3O6H5Ca(H2O)6⫹ 3 Si3O6H5CaHPO4(H2O)3⫺ (Sahai and
Tossell, 2000). The calculations were consistent with measured
spectral values for the earliest mineral phase isolated from a
2-week-old chicken embryo and with calcium phosphate precipitated in vitro on a silica bioceramic surface from a synthetic
blood solution (Roberts et al., 1992; Wu et al., 1994; Pereira et
al., 1995). These similarities suggested the fascinating possibility that the inorganic reaction pathway for nucleation of
apatite from marine pore water on authigenic silica is similar to
the pathway for bone and tooth apatite nucleation from blood at
silica bioceramic surfaces. The in vivo reaction for bone and
tooth growth, in the absence of silica bioceramics, may involve
negatively charged phosphorylated amino acid residues on protein surfaces (Glimcher, 1989; Sahai, unpublished data).
6. SUMMARY
Ab initio Hartree-Fock calculations were used to obtain the
geometries and energies of molecular clusters that are assumed
to represent reaction intermediates close to transition states for
elementary steps in heterogeneous apatite nucleation. Calculated relative reaction energies are assumed to track relative
activation enthalpies of corresponding reactions for the Mg2⫹
and Ca2⫹ ions.
Mg2⫹ does not inhibit heterogeneous nucleation of an amorphous ⬎CaHPO4 precursor because of the slow dehydration
kinetics of the aqueous Mg2⫹ ion, nor does it directly compete
with the most facile pathway followed by the Ca2⫹ ion. Rather,
fast electrostatically driven adsorption of Mg2⫹ blocks the
access of Ca2⫹ ions to reactive surface sites. Precursor nucleation, cluster aggregation, and crystal growth are fastest in the
intermediate pH range because low surface charge on apatite
lowers interfacial tension between adjacent critical nuclei.
The results suggest that special pore water compositions
produced by ad hoc geochemical processes are not required for
apatite precipitation. The mechanism for inorganic bone and
tooth apatite nucleation from blood on amorphous silica bioceramic implant surfaces is probably similar to apatite nucleation from pore water on authigenic amorphous silica.
Acknowledgments—I thank the reviewers and the associate editor, Dr.
A. Mucci, for their constructive comments; the guest editors, Drs.
Kevin Rosso and Udo Becker, for their invitation to submit a manuscript to this special issue; and Prof. Eugene Schukin at Johns Hopkins
University for insight into the Lippman equation. Financial support
came from “faculty startup” funds provided by the University of
Wisconsin.
Associate editor: A. Mucci
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