Ternary Complex Formation of Phosphate with Ca and Mg Ions
Binding to Ferrihydrite: Experiments and Mechanisms
Juan C. Mendez* and Tjisse Hiemstra

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ABSTRACT: Calcium (Ca) and magnesium (Mg) are the most abundant alkaline-
earth metal ions in nature, and their interaction with ferrihydrite (Fh) affects the
geochemical cycling of relevant ions, including phosphate (PO4). The interfacial
interactions of Ca and Mg (M2+) with PO4 have not been analyzed yet for freshly
precipitated Fh. Here, we studied experimentally this interaction in binary M2+-PO4
systems over a wide range of pH, M2+/PO4 ratios, and ion loadings. The primary
adsorption data were scaled to the surface area of Fh using a recent ion-probing
methodology that accounts for the size-dependent chemical composition of this
nanomaterial (FeO1.4(OH)0.2·nH2O). The results have been interpreted with the
charge distribution (CD) model, combined with a state-of-the-art structural surface
model for Fh. The CD coefficients have been derived independently using MO/
DFT/B3LYP/6-31+G** optimized geometries. M2+ and PO4 mutually enhance their
adsorption to Fh. This synergy results from the combined effect of ternary surface
complex formation and increased electrostatic interactions. The type of ternary
complex formed (anion- vs cation-bridged) depends on the relative binding affinities of the co-adsorbing ions. For our Ca-PO4
systems, modeling suggests the formation of two anion-bridged ternary complexes, i.e., (FeO)2PO2Ca and FeOPO3Ca. The
latter is most prominently present, leading to a relative increase in the fraction of monodentate PO4 complexes. In Mg-PO4 systems,
only the formation of the ternary FeOPO3Mg complex has been resolved. In the absence of Ca, the pH dependency of PO4
adsorption is stronger for Fh than for goethite, but this difference is largely, although not entirely, compensated in the presence of
Ca. This study enables the use of Fh as a proxy for the natural oxide fraction, which will contribute to improved understanding of the
mutual interactions of PO4 and M2+ in natural systems.

KEYWORDS: calcium, magnesium, iron oxides nanoparticles, surface complexation modeling, CD model,
cooperative and synergistic binding, electrostatic interactions, anion-bridged complexes

1. INTRODUCTION

Ferrihydrite (Fh) is a nanoparticulate Fe-(hydr)oxide present
in almost all natural systems including soils, aquifers, and
oceans, and it is also found in mine waste drainage water.1−3

Due to its relatively low surface energy in comparison to other
Fe-(hydr)oxides, Fh is the most thermodynamically stable Fe-
(hydr)oxide at a nanosize range of ∼2−8 nm.4 It is the earliest
Fe(III) product that precipitates and works as a precursor of
other more crystalline Fe-(hydr)oxides.5−7 Fh has a high ion
adsorption capacity and a large affinity for binding inorganic
ions and organic compounds.8−13 In the environment, the
(bio)geochemical cycle of many nutrients and pollutants is
largely determined by adsorption processes occurring at the
Fh−solution interface.1 Hence, grasping the interfacial
processes of ion binding is essential for understanding the
adsorption behavior of ions observed at the macroscopic scale.
A major reason for the extraordinarily high ion adsorption

capacity of Fh is its large specific surface area (SSA),14,15

which, for freshly precipitated Fh, is in the order of ∼600−
1100 m2 g−1.16 Moreover, Fh has a relatively high surface site

density of particularly singly coordinated (FeOH) groups,17

which are able to bind cations and anions. The singly (
FeOH) and triply (Fe3O) coordinated surface groups of Fh
may bind protons, resulting in a pH-dependent net surface
charge. The result is an amphoteric behavior of Fh being
important for the pH dependency of the adsorption of both
metal ions and oxyanions. The mechanisms of ion complex-
ation have been extensively studied for Fh in a long history of
in situ spectroscopy, quantum chemical computations, and
surface complexation modeling, e.g., refs 14 and 18−32.
Remarkably, the interaction of Ca and Mg with Fh nano-
particles has received relatively little attention, whereas both
elements are highly abundant in the environment and may

Received: December 17, 2019
Revised: March 19, 2020
Accepted: March 25, 2020
Published: March 25, 2020

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significantly affect the adsorption of other compounds,
particularly oxyanions, such as phosphate (PO4), arsenate
(AsO4), and selenite (SeO3).

33−36 In systems with well-
crystallized goethite, it has been shown that the adsorption of
PO4 and SeO3 increases in the presence of, respectively, the
alkaline-earth metal ions Ca and Sr.34,36,37 Qualitatively, similar
results have been reported for the adsorption of AsO4 and PO4
in the presence of Ca in systems with freeze-dried Fh.31

From a quantitative perspective, calcium (Ca2+) is generally
the most important metal cation in soil and groundwater.38

Across different environments, the solution concentration of
Ca varies over several orders, being low as ∼10−5 M and high
as 10−1 M. Magnesium ions (Mg2+) can also be abundant in
natural environments. It dominates the composition of divalent
cations in marine systems and is important in areas irrigated
with Mg-rich water.36,39 Both alkaline-earth cations (herein-
after jointly referred to as M2+) can specifically adsorb to the
surfaces of Fe-(hydr)oxides, affecting the physicochemical
properties of the mineral−solution interface and the
adsorption of organic and inorganic compounds,13,33−35

including PO4.
In aquatic and terrestrial systems, the PO4 availability is

largely controlled by adsorption to the nanosize fraction of Fe
and Al-(hydr)oxides40−42 that can be dissolved in an acid
ammonium oxalate solution.43,44 Thus, Fh can be considered
as a relevant model material for studying the mechanisms of
PO4 binding to the natural fraction of metal (hydr)oxides. In
most environments, PO4 ions are simultaneously present with
Ca and Mg ions and will interact in combination at the Fh−
solution interface. The adsorption of Ca promotes the binding
of PO4 to Fe-(hydr)oxides and vice versa.34,45 This cooperative
interaction has been noticed by soil chemists since long
ago,46,47 yet the mechanism of the pH-dependent interplay of
PO4 and Ca2+ ions at the surfaces of Fe-(hydr)oxides remains
indistinct. However, understanding and quantifying these
mutual interactions are highly relevant from a practical
perspective of soil chemical analysis. For predicting the
availability and mobility of PO4 in the environment, field
samples are often taken and routinely extracted with
unbuffered electrolyte solutions.48,49 These solutions may
strongly differ in the concentration of Ca, for instance, soil
extractions with 0.01 M CaCl2 solution50 vs soil extractions
with demineralized water.48 The differences in the Ca
concentration of the extracting solutions will affect the
equilibration of PO4.

48,51 Translation of these measurements
to field conditions not only requires insights into the interfacial
interactions of PO4 and the alkaline-earth metal ions but also
their quantification.
Three main mechanisms have been proposed for explaining

the synergistic interaction between PO4 and Ca2+ ions at
metal-(hydr)oxide surfaces, namely, (i) increase in the
interfacial electrostatic interactions; (ii) formation of ternary
surface complexes; and (iii) surface precipitation of Ca-PO4
mineral phases, which may be particularly relevant at high
adsorption densities.28,52−54 Moreover, formation of Fe-PO4-
Ca networks has been reported when Fe(III) coprecipitates in
the presence of PO4 and Ca2+ ions.55 A chemical interaction
between Ca and PO4 is conceivable as these ions can
precipitate in a range of minerals whose thermodynamic
stability increases at an increase in the Ca/PO4 ratio.56

Rationalizing the interfacial interaction between Ca and PO4
only on the basis of electrostatics has been done for
goethite,34,36 while the additional formation of a ternary Fe-

PO4-Ca complex has been assumed in the case of a freeze-
dried Fh material.31

For freeze-dried Fh, the cooperative interaction between Ca
and PO4 has been previously investigated.31 However, the ion
adsorption behavior of this material differs from that of freshly
prepared Fh because drying leads to irreversible aggregation of
the primary particles.57 This may lead to changes in the crystal
morphology, phase transformation of Fh,58 and undefined
reduction of the reactive surface area.59 Therefore, freshly
prepared Fh is chosen in the present study. For this material,
we have developed recently a methodology to determine the
reactive surface area in a consistent manner with the
description of the primary surface charge and specific ion
adsorption.59 For freshly prepared Fh, the cooperative
interaction of PO4 with Ca ions has never been studied nor
has it been done for Mg ions. Another advantage of using
freshly prepared Fh is the possibility to interpret the collected
adsorption data with advanced surface complexation modeling.
In addition, we consider freshly prepared Fh as a good proxy
for the natural Fe oxide fraction of soils and sediments since Fh
particles may precipitate without extensive aggregation if
formed in the presence of natural organic matter, which
contributes to the thermodynamic stability of Fh and prevents
its phase transformation into more stable Fe-(hydr)oxide
minerals.6,60,61

Based on the above, the objective of the present study is to
assess experimentally and by surface complexation modeling
the interaction of the alkaline-earth metal ions Ca2+ and Mg2+

with PO4 in systems with well-defined, freshly precipitated Fh.
In our analysis, we will apply a state-of-art modeling framework
that includes recent insights into the surface structure of Fh26

and the interfacial charge distribution of the complexes formed
that will be derived independently from MO/DFT/B3LYP/6-
31+G** optimized hydrated clusters. In addition, we will
account for the chemical heterogeneity of the reactive sites of
Fh for binding divalent metal ions, defining in our modeling
sites with high and low affinities for binding Ca2+ and Mg2+

ions.
For a consistent data interpretation, we will measure the SSA

of Fh with a recently developed ion-probing methodology59

that we will use to scale our primary adsorption data (ion/Fe
ratios). In this scaling, we will consistently account for the size
dependency of the molar mass of Fh. The latter is due to a
particle size-dependent contribution of chemisorbed water
(nH2O), completing the coordination spheres of Fe atoms at
the surface of Fh leading to FeO1.4(OH)0.2·nH2O.

17 The size-
dependent composition also affects the mass density ρnano (g
cm−3) of Fh. This ρnano will be used to translate the specific
surface area into a mean particle diameter that is used to derive
the values of the Stern layer capacitances of the compact part
of the electrical double layer because this nanomaterial is
strongly curved. All the abovementioned factors will be
collectively included in the present CD modeling approach
together with a recent evaluation of the primary charge of Fh.59

In our work, we will explore the ternary complex formation, for
which will be considering a suite of complexes as candidates to
describe our extensive adsorption dataset. Finally, we will
address the question of how much Fh differs from well-
crystallized goethite in relation to the cooperative binding of
Ca-PO4 and what are the possible implications of using these
materials as proxies for the natural oxide fraction.

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2. EXPERIMENTAL SECTION

Ultrapure water (18.2 MΩcm at 25 °C, 1 ppb TOC) and
chemical reactants of analytical grade were used to prepare all
stock solutions and Fh suspensions. Contact between solutions
and air was minimized to avoid the interference of CO2(g)
during the adsorption experiments.
2.1. Synthesis of Ferrihydrite. Fh was synthesized

according to Hiemstra et al.16 Briefly, ∼1.0 L of a solution
containing ∼3.7 mM Fe(NO3)3·9H2O dissolved in 0.01 M
HNO3 was titrated by adding a freshly prepared solution of
0.02 M NaOH. The NaOH solution was initially added at a
rate of ∼200 mL min−1 until a pH of ∼3.1 was reached.
Subsequently, additional base solution was added in ∼5 mL
increments until the suspension reached a final pH of ∼8.2.
Once the pH was stabilized (∼15 min), the Fh suspension was
centrifuged at 3300g for 45 min. Next, the supernatant was
carefully removed and the settled Fh particles were re-
suspended in a solution of 0.01 M NaNO3 to a final volume
of typically ∼160 mL. Each freshly prepared Fh suspension was
aged for 4 h at 20 °C in closed bottles before starting the
adsorption experiments. The total Fe concentration of each Fh
suspension was determined in a matrix of 0.8 M H2SO4 using
ICP-OES. Typically, the total Fe concentration in these
suspensions was 20.5 ± 0.5 mM (∼2 g L−1). The specific
surface area (m2 g−1) of each Fh batch was independently
measured using surface probing with PO4.

59 In this approach,
the pH-dependent adsorption of PO4 is measured in single-ion
systems. The primary adsorption data (i.e., mol PO4/mol Fe)
are then iteratively interpreted with the CD model, defining
the SSA as the only adjustable parameter and accounting for
the size dependency of the molar mass (Mnano) and mass
density (ρnano) of Fh, as well as the size dependency of the
Stern layer capacitance.59

2.2. Adsorption Experiments. The adsorption interaction
between the alkaline-earth cations (Ca and Mg) and PO4 was
evaluated in binary systems with freshly precipitated Fh. The
pH of the adsorption systems ranged between ∼5 and 10, and
the background electrolyte concentration was kept constant at
0.01 M NaNO3. Each adsorption system was prepared in 50
mL polypropylene tubes kept under moist-purified N2(g) to
prevent intrusion of CO2(g) during the preparation of the
systems. For the Ca-PO4 experiments, nine adsorption series
were prepared with different molar Ca:PO4:Fe ratios. Addi-
tional series with no Ca addition were prepared and used as a
reference for the adsorption of PO4 in single-ion systems. For
the Mg-PO4 experiments, three adsorption series were
prepared at different Mg:PO4:Fe ratios. Details about the
chemical conditions of each adsorption series are presented in
Tables S1 and S2 of the Supporting Information. The pH of
the adsorption systems was adjusted within the desired range
by adding 1.0−2.0 mL of 0.01 M solutions of either HNO3 or
NaOH. Stock solutions of NaH2PO4, Ca(NO3)2, and Mg-
(NO3)2 were used to add, respectively, the ions PO4

3−, Ca2+,
and Mg2+. To minimize the risk of any precipitation of Ca-PO4
and Mg-PO4 solid phases, the systems were pre-equilibrated
with PO4 for 1 h before the corresponding alkaline-earth ion
was added. The final volume of each adsorption system was
40.0 mL. All adsorption systems were constantly shaken (120
strokes/min) at 20 °C for 20 h, and next the suspensions were
centrifuged at 3330g for 20 min to separate the solid and liquid
phases. An aliquot of 10 mL was taken from the supernatant of
each adsorption system, filtered through a 0.45 μm membrane

filter, and acidified with HNO3 for analysis of the equilibrium
concentration of M2+ and PO4. The analysis was done using
either ICP-OES or ICP-MS, depending on the final
concentrations of the analyzed elements. The settled Fh
particles were re-suspended in the 50 mL polypropylene tube
to measure the equilibrium pH with a combined glass
electrode.

2.3. Modeling. 2.3.1. Charge Distribution (CD) Model.
The results of the M2+-PO4 adsorption experiments have been
interpreted with the charge distribution (CD) model62 in
combination with a recent multisite ion complexation
(MUSIC) model for Fh.26 Details about this structural surface
model are described in Section 2.3.2. The electrical double
layer (EDL) is described with the extended Stern layer
approach.63 Since Fh is an ultrasmall nanoparticle with a strong
surface curvature, the capacitance values (Cnano,1 and Cnano,2) of
the inner and outer Stern layers are made size-dependent,
using well-crystallized goethite as a reference with a near-zero
surface curvature.64 The primary surface charge is described
according to Mendez and Hiemstra.59

CD modeling was done with ECOSAT version 4.9.65 The
affinity constants (log K) of the adsorption reactions of the
ternary Fe-PO4-M

2+ complexes were optimized using the
program FIT version 2.581.66 The entire set of solution
speciation and primary protonation reactions used in the
modeling are presented, respectively, in Tables S3 and S4 of
the Supporting Information. Software Spartan18 parallel of
Wavefunction, Inc. was used to optimize the geometries of the
ternary Fe-PO4-Ca and Fe-PO4-Mg complexes with molecular
orbital (MO) calculations, applying density function theory
(DFT). This approach has been also applied to optimize the
geometries of the M2+67 and PO4

26 complexes adsorbed to Fh.
These optimized geometries were interpreted with Brown
valence analysis68,69 to assess the charge distribution of the
adsorbed complexes with a small correction for water dipole
orientation.63 The charge attribution to the surface plane
(Δz0) was based on the optimized MO/DFT geometries,
whereas the charge distribution over the Stern planes (Δz1 and
Δz2) was derived for the ternary complexes by fitting to the
experimental adsorption data. Details about the template of Fh
used in the geometry optimizations are given in Mendez and
Hiemstra.27

2.3.2. Multisite Ion Complexation Model for Fh. For Fh, a
new structural model has been proposed by Michel et al.70,71

The surface structure has been described by Hiemstra.17 Since
Fh particles are ultrasmall, the surface will dominantly
contribute to the overall behavior of this nanomaterial. Many
microscopic and macroscopic properties of Fh are size-
dependent. A whole suite of physical−chemical properties
can be understood from the difference in the polyhedral
composition of the mineral core and the surface.4,17,72,73 With
a surface structural analysis of this material, Hiemstra and
Zhao26 have developed a mechanistic multisite ion complex-
ation model for Fh, distinguishing various types of sites and
deriving corresponding densities. The model also includes the
size-dependent variation of the molar mass (Mnano) and the
mass density (ρnano) that results from the variable contribution
of chemisorbed water (nH2O) to the overall chemical
composition of Fh (FeO1.4(OH)0.2·nH2O).

16

In the above structural multisite model, three types of
surface groups have been defined, which differ in their
coordination number with Fe, i.e., singly (FeOH−0.5),
doubly (Fe2OH

0), and triply (Fe3O
−0.5) coordinated

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groups. Structurally, two types of singly coordinated groups
can be distinguished, i.e., FeOH(a)−0.5 and FeOH(b)−0.5,
which may form, respectively, either single-edge (1E) or
double-corner (2C) bidentate surface complexes having,
respectively, a surface density of Ns(a) = 3.0 ± 0.6 nm−2 and
Ns(b) = 2.8 ± 0.6 nm−2. Both types of singly coordinated
groups may also form single-corner (1C) monodentate surface
complexes. The triply coordinated groups do not participate in
ligand exchange reactions, but they contribute to the
development of the primary surface charge. At the surfaces
of Fh, different types of triply coordinated groups are found
with a large variation in their proton affinity (log KH). The
surface charge introduced by groups with a low log KH (
Fe3O

−0.5) is compensated by groups with a high log KH (
Fe3OH

+0.5), leading to an effective site density of Ns,(T) = 1.4 ±
0.5 nm−2, if the charging behavior of these triply coordinated
groups is represented by an equivalent surface site with a log
KH = ∼8.1, as for the singly coordinated groups.26 The 
Fe2OH

0 groups are presumably uncharged and do not react
with protons under common pH conditions. This model has
been applied to describe consistently the primary surface
charge59 and the adsorption of a range of oxyanions, such as
PO4, AsO4, As(OH)3,

26 Si(OH)4,
72 and CO3,

27 as well as the
adsorption of a series of alkaline-earth metal cations.67

2.3.3. Description of Ion Adsorption in Single Systems. In
a parallel study, we have shown that the CD model can
describe very well the adsorption of Ca2+ and Mg2+ (M2+) to

Fh in single-ion systems over a broad range of solution
conditions, comprising different initial M2+ concentrations and
molar M2+/Fe ratios, as well as pH and ionic strength levels.67

The data can be described by defining in the modeling the
formation of a binuclear bidentate complex according to

K

2 FeOH(b) M (FeOH(b)) M

log

z z0.5 2
2

1 0 1

BM

≡ + ↔ ≡− + − +Δ Δ

(1)

where Δz0 and Δz1 are the CD coefficients derived from the
Brown bond valence analysis applied to the MO/DFT
optimized geometries (Table 1). Bidentate complex formation
is supported by our combined interpretation of MO/DFT
geometry optimizations67 and EXAFS data for the adsorption
of divalent cation to Fe (hydr)oxides.25,37,74−76 This binding
mechanism is also supported by the thermodynamic analysis of
macroscopic data such as the H+/M2+ exchange ratio reported
for Ca77 and the marked pH dependency of Ca adsorption
observed in our adsorption experiments.
In that same parallel study, we have also shown that the

adsorption sites of Fh for binding M2+ exhibit chemical
heterogeneity, which is a common reported phenomenon for
the binding of metal ions to Fh.14,20,78 The high affinity sites
dominate the adsorption at low M2+ concentrations, and for
our Fh preparation, these surface sites have a density of Ns(bh)
= 0.32 ± 0.02 nm−2. The corresponding site density for the low

Table 1. Surface Species, CD Coefficients, and Fitted log K for the Binding Reactions of Ca and Mg to Fh Derived in Our
Parallel Studya67

species IDb FeOH(bl)−0.5 FeOH(bh)−0.5 Δz0c Δz1 Δz2 H+ Ca2+ Mg2+ log K ± SE

(FeOH)2Ca BCa(l) 2 0 0.94 1.06 0 0 1 0 2.64 ± 0.03
(FeOH)2Ca BCa(h) 0 2 0.94 1.06 0 0 1 0 5.13 ± 0.02
(FeOH)2Mg BMg(l) 2 0 0.89 1.11 0 0 0 1 1.87 ± 0.06
(FeOH)2Mg BMg(h) 0 2 0.89 1.11 0 0 0 1 4.09 ± 0.04

aThe surface site densities are from Hiemstra and Zhao26 with FeOH(a) = 3.0 nm−2, FeOH(b) = 2.8 nm−2, and Fe3O = 1.4 nm−2. Two
types of FeOH(b) groups were defined to account for site heterogeneity FeOH(bl) for low affinity and FeOH(bh) for high affinity, having
site densities of, respectively, 2.48 ± 0.02 and 0.32 ± 0.02 nm−2 for our Fh preparations. The capacitance values for the extended Stern layers of Fh
(Cnano,1 and Cnano,2) are size-dependent

59 (see Tables S1 and S2) and were calculated by taking as a reference the capacitance values of goethite (C1
= 0.90 F m−2 and C2 = 0.74 F m−2) bBCa(l) = bidentate (double-corner) Ca with low affinity sites; BCa(h) = bidentate (double-corner) Ca with
high affinity sites; BMg(l) = bidentate (double-corner) Mg with low affinity sites; BMg(h) = bidentate (double-corner) Mg with high affinity sites
cThe CD coefficients have been derived from MO/DFT optimized geometries.

Table 2. Surface Species, CD Coefficients, and Fitted log K for the Formation of Ternary Complexes in the Binary Systems
PO4-Ca (R2 = 0.99 and n = 72) and PO4-Mg (R2 = 0.99 and n = 22) with Fha

species ID FeOH(a)b FeOH(bl)d FeOH(bh)b Δz0 Δz1 Δz2 H+ M2+ PO4
−3 log K ± SEc

FeOPO3Ca
d MPCa(a) 1 0 0 0.24 −1.30 1.06 1 1 1 22.27 ± 0.12

FeOPO3Ca
d MPCa(bl) 0 1 0 0.24 −1.30 1.06 1 1 1 22.27 ± 0.12

FeOPO3Ca
d MPCa(bh) 0 0 1 0.24 −1.30 1.06 1 1 1 22.27 ± 0.12

(FeO)2PO2Ca
e BPCa(bl) 0 2 0 0.62 −1.08 1.46 2 1 1 30.09 ± 0.12

(FeO)2PO2Ca
e BPCa(bh) 0 0 2 0.62 −1.08 1.46 2 1 1 30.09 ± 0.12

FeOPO3Mgd MPMg(a) 1 0 0 0.22 −1.55 1.33 1 1 1 22.00 ± 0.10
FeOPO3Mgd MPMg(bl) 0 1 0 0.22 −1.55 1.33 1 1 1 22.00 ± 0.10
FeOPO3Mgd MPMg(bh) 0 0 1 0.22 −1.55 1.33 1 1 1 22.00 ± 0.10

aThe surface site densities are from Hiemstra and Zhao26 withFeOH(a) = 3 nm−2,FeOH(b) = 2.8 nm−2, andFe3O = 1.4 nm−2. Two types
of FeOH(b) groups were defined to account for the surface site heterogeneity of the adsorption of M2+ (FeOH(bl) and FeOH(bh) for low
and high affinities, respectively). bFeOH(a)−0.5 with PO4 forms only monodentate complexes, whereas FeOH(b)−0.5 forms both mono- and
bidentate (double corner) complexes (see section 2.3.2). clog K values derived in this study by fitting of the experimental data obtained in the
binary Ca-PO4 and Mg-PO4 systems. dΔz2 = 1.06 v.u. (± 0.06) can be explained as the Ca complexation to adsorbed PO4 in FeOPO3-Ca-
(OH2)n with remaining charge attribution of Ca to three OH2 ligands in the outer Stern plane. For the ternary complexes MPMg, a higher Δz2
value of 1.33 v.u. (± 0.07) suggest that Mg is more loosely bound to PO4 than Ca (see text). eΔz2 = 1.46 v.u. (± 0.17) can be explained as the Ca
complexation to adsorbed PO4 in (FeO)2PO2-Ca-(OH2)n with a charge attribution of Ca to four OH2 ligands in the outer Stern plane.

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affinity sites can be set to Ns(bl) = 2.48 nm−2, as the sum of
both types of FeOH(b) −0.5 groups is 2.8 nm−2.26

For describing the adsorption of PO4 in single-ion systems,
we have used the set of CD model parameters derived by
Hiemstra and Zhao.26 For the adsorption of oxyanions that
strongly interact with Fh such as PO4, we do not experience
explicitly in our modeling the presence of high affinity sites, in
line with previous suggestions given by Dzombak and Morel.14

Probably, the high affinity character of these sites is masked by
the already rather large PO4 loading of the low affinity sites.
Therefore, we have used in our modeling the same set of log K
values for PO4 binding to both types of FeOH(b)−0.5 groups
(Table 2 and Table S4).

3. RESULTS AND DISCUSSION

3.1. Interaction of Calcium and Magnesium with
Phosphate: Experimental Results. The interaction of the
alkaline-earth metal Ca with PO4 in Fh systems has been
studied extensively in the present work. In Figures 1 and 2, the
left panels show the adsorption edges of Ca to Fh in the binary
Ca-PO4 systems, whereas the right panels show the
corresponding PO4 adsorption data. In Figure 1, the upper
panels are for a total Ca concentration of ∼0.05 mM, and the
lower panels are for systems with a 5-fold higher concentration
of added Ca (∼0.25 mM). In Figure 2, we give the adsorption
data for binary Ca-PO4 systems with a higher Fh
concentration. This allows an accurate measurement of the

adsorption of Ca to Fh at higher total added Ca
concentrations, i.e., ∼1.0 mM (upper panels) and ∼0.62 mM
(lower panels). For comparison, we also present in Figures 1
and 2 the model predictions (dotted lines) and/or the
measured adsorption data (open symbols) of the correspond-
ing single-ion systems at the same initial ion loading.
At a given pH, the adsorption of Ca to Fh increases

simultaneously with an increase in the initial concentration of
PO4. In comparison to the single-ion systems, the adsorption
edges of Ca are significantly shifted toward lower pH values
(∼2.0 pH units) in the presence of PO4. For systems with the
same total Fe content, this shift of the adsorption edges is
more pronounced for systems with lower total molar Ca/PO4
ratios. Simultaneously, the adsorption of PO4 to Fh increases
in the presence of Ca, but the synergistic effect of Ca on the
PO4 adsorption is less pronounced than the corresponding
effect of PO4 on the adsorption of Ca.
The cooperative interaction of ions adsorbed to Fh was also

evaluated in the binary Mg-PO4 systems. Figure 3a,c shows
that in the presence of PO4, the adsorption edges of Mg are
shifted toward lower pH values (closed symbols), in
comparison to the adsorption of Mg in the single-ion systems
(open symbols). In Figure 3b, the adsorption of PO4 in the
absence (open symbols) and presence (closed symbols) of Mg
is compared for Fh systems with two different values for the
total molar Mg/PO4 ratios: 0.5 (circles) and 0.05 (squares).
The percentage of PO4 adsorbed increases in the presence of
Mg. Additionally, the pH dependency of the PO4 adsorption is

Figure 1. pH-dependent adsorption of Ca (left panels) and PO4 (right panels) in binary ion systems with Fh. The ionic strength was kept constant
at I = 0.01 M NaNO3, and the specific surface area of this Fh suspension was A = 684 ± 15 m2 g−1 with a corresponding molar mass ofMnano = 96.6
g mol−1 Fe. The symbols are the experimental data, and the lines are the CD model calculations obtained with the parameter sets of Tables 1 and 2.
The adsorption parameters of PO4 in single-ion systems are taken from Hiemstra and Zhao.26 The total concentrations of Fe, Ca, and PO4 are given
in each panel. The initial Ca loadings in systems a, b and c, d are equivalent to, respectively, ∼0.4 and ∼1.7 μmol m−2, and the equivalent initial
PO4 loadings vary from ∼2.0 to 3.9 μmol m−2. For comparison, model predictions are given for the corresponding single-ion systems, i.e., without
addition of either Ca or PO4 (dotted lines). For PO4, the adsorption in single-ion systems was additionally measured for each experimental
condition (open symbols). The adsorption of Ca and PO4 is promoted in the binary systems by mutual electrostatic interactions and the formation
of ternary PO4-Ca surface complexes.

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strongly reduced in the systems with a relatively high molar
Mg/PO4 ratio, e.g., ∼1.6 (Figure 3d).
The model lines in Figures 1−3 show the capability of the

CD model to describe accurately the interfacial interactions of
the alkaline-earth metal ions Ca and Mg with PO4 over a wide
range of conditions in the Fh systems. Synergy between these
cations and PO4 has been also reported for freeze-dried Fh,31

goethite (α-FeOOH),34−36 hydrous zirconium oxide
(HZO),79 and manganese dioxide (δ-MnO2).

80 However, the
dominant mechanisms explaining these interactions might
differ between these oxide materials. For Fh, details about the
mechanisms of synergetic binding will be discussed in the next
section.
3.2. Modeling and Mechanisms of M2+-PO4 Adsorp-

tion Synergy. 3.2.1. Effect of Electrostatic Interactions. The
adsorption of M2+ is significantly promoted by PO4 in all
binary systems in comparison to the corresponding single-ion
systems (dotted lines and/or open symbols in the left panels of
Figures 1−3). In contrast, the PO4 adsorption in the binary
systems (right panels in Figures 1−3) increases mainly at high
pH and high initial M2+ concentration due to the presence of
M2+. The reason for this difference is the higher affinity of PO4
for the adsorption to Fh, in comparison with the adsorption
affinity of M2+. The large quantities of adsorbed PO4 can
change substantially the net particle charge of Fh, whereas the
presence of M2+ in the binary systems affects notably less the
net particle charge, as it can be shown by modeling.
In the absence of specific ion adsorption, the point of zero

charge of Fh in NaNO3 solutions is pHPZC ≈ 8.1.59 Our CD

modeling shows that the adsorption of PO4 to Fh provokes a
decrease in the isoelectric point (IEP) to pHIEP ≈ 4.5−5.0
(Figure S1a). It implies that, under these conditions, a negative
double layer potential (ψ) is created in a major part of the pH
range of our study. This induces a shift of the adsorption edges
of Ca2+ and Mg2+ in the presence of PO4 (Figures 1−3) and
stimulates the formation of ternary surface species (Section
3.2.2). The binding of Ca2+ or Mg2+ ions in the binary systems
with PO4 partly compensates the negative charge created by
the adsorbed PO4 ions, and in turn, this promotes the
adsorption of PO4 in the binary systems, particularly at high
pH. It can be shown that at a sufficiently high Ca
concentration, binary Ca-PO4 systems with Fh may have two
pH values where the particle charge switches, i.e., two pHIEP
values, one at low pH and one at high pH (Figure S1b).
Figure 4 presents the concentrations of Ca (panel a) and

PO4 (panel b) in the equilibrium solution of the respective
single- (open symbols) and binary (closed symbols) Fh
systems. The experimental data of the binary systems cannot
be explained by using only the adsorption reactions found for
the single-ion systems (dotted lines) in the modeling. Figure 4
illustrates that mutual electrostatic interactions alone are not
enough to explain the adsorption data in binary Ca-PO4
systems. This finding contrasts with that in goethite systems,
in which the cooperative binding of Ca2+ and Mg2+ ions with
PO4 could be well predicted assuming only electrostatic
interactions.34−36 Differences in the adsorption interaction of
Ca-PO4 between Fh and goethite are discussed in Section 3.4.
In our Fh systems, the precipitation of a calcium phosphate

Figure 2. pH-dependent adsorption of Ca (left panels) and PO4 (right panels) in single- and binary ion systems with Fh in I = 0.01 M NaNO3. The
specific surface area of this Fh suspension was A = 684 ± 15 m2 g−1 with a corresponding molar mass of Mnano = 96.6 g mol−1 Fe. The total
concentrations of Fe, Ca, and PO4 are given in each panel. The initial loadings of Ca in systems a, b and c, d are equivalent to, respectively, ∼3.9
and ∼2.5 μmol m−2. The initial PO4 loadings are equivalent to ∼1.5−2.3 μmol m−2 in systems a, b and ∼2.5 in systems c, d. The closed symbols
and the full lines are, respectively, experimental data and CD model calculations for binary systems. For comparison, the model predictions are
given for single-ion systems, i.e., without addition of either Ca or PO4 (dotted lines). For PO4, the adsorption in single-ion systems was also
measured for each experimental condition (open symbols). The CD model parameter sets are given in Tables 1 and 2. The adsorption parameters
of PO4 in single-ion systems are taken from Hiemstra and Zhao.26 The capacitance values are given in Table S1.

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mineral cannot explain the significant reduction of concen-
trations in the Ca and PO4 systems neither, as illustrated in
Section 4 of the Supporting Information. For the Mg-PO4
systems, the same results are observed (Figure S4).
3.2.2. Formation of Ternary Ca-PO4 Surface Complexes.

The adsorption data of Ca and PO4 in the binary systems can
only be described by including in the modeling the formation
of ternary surface complexes. In general, Ca and PO4 have
contrasting affinities for binding to metal (hydr)oxides. Ca2+

ions have a much lower intrinsic affinity than PO4 ions for the
binding sites at the surface of Fh. However, Ca2+ ions do have
a high affinity for PO4, which is reflected by the increasing
stability of Ca-PO4 minerals at increasing molar Ca/PO4 ratio
of these minerals.56 In the case of ternary complex formation, it
is therefore more likely that Ca will bind to adsorbed PO4

rather than the opposite. This idea is supported by literature
data of Fe-PO4-Ca co-precipitation showing direct complex-
ation of PO4 to Fe(III) polymers, where these units form larger
networks that are interconnected by Ca2+ ions.55,81 High-
energy X-ray scattering with pair distribution function analysis
showed double-corner (FeO)2PO2 complexes linked
together by Ca ions bound as single-corner complexes55 with
a Ca-P distance of 360 pm. In situ spectroscopic studies have
also suggested the formation of PO4-bridged ternary complexes
with Ca in adsorption systems with hydrous zirconium oxide79

and titanium dioxide (TiO2).
82

The binding of Ca2+ cations to already adsorbed PO4 anions
(i.e., formation of anion-bridged ternary complexes) is also
supported by the modeling of the Ca and PO4 adsorption data
of our binary Ca-PO4 systems with Fh (Figures 1 and 2). Our
extensive modeling of these systems shows that the use of
cation-bridged ternary complexes (i.e., Fe-Ca-PO4) did not
provide a good description of the adsorption of both Ca and
PO4 in the binary systems. Instead, our modeling advocates the
formation of anion-bridged complexes, in which the Ca2+ ion is
located at a larger distance from the surface.
The formation reactions of the ternary complexes ultimately

derived after extensive modeling are

Figure 3. pH-dependent adsorption of (a, c) Mg and (b, d) PO4 in single- (open symbols) and binary (closed symbols) ion systems with Fh in I =
0.01 M NaNO3. The specific surface area of this Fh suspension was A = 720 ± 10 m2 g−1 with a corresponding molar mass of Mnano = 97.6 g mol−1

Fe. The symbols are the experimental data, and the lines are the CD model results obtained with the parameter sets of Tables 1 and 2. The
adsorption parameters of PO4 in single-ion systems are taken from Hiemstra and Zhao.26 The total concentrations of Fe, Mg, and PO4 are given in
each panel. The initial loadings of Mg are equivalent to ∼0.1 and ∼1.1 μmol m−2 in systems a, b and ∼2.0 μmol m−2 in systems c, d. The initial PO4
loadings are equivalent to, respectively, ∼2.2 and 1.3 μmol m−2 in systems a, b and c, d. For comparison, the respective adsorption series in single-
ion systems have been measured (open symbols) and/or modeled (dotted line). The capacitance values are given in Table S2.

Figure 4. Logarithm of the (a) Ca and (b) PO4 concentrations in the
equilibrium solution of systems with Fh in I = 0.01 M NaNO3. The
total Fe concentration was 3.9 mM, and the specific surface area of
this Fh suspension was A = 684 ± 15 m2g−1 with a respective molar
mass Mnano = 96.6 g mol−1 Fe. Closed symbols are for the binary Ca-
PO4 systems with total concentrations of Ca = 1.0 mM and PO4 = 0.6
mM, and the open symbols are for the single-ion systems. The dotted
lines are the CD model predictions using only the adsorption
parameters of the single-ion systems of Ca (Table 1) and PO4,

26

whereas the full lines are the modeling results including for the binary
systems the formation of ternary surface complexes (Table 2).

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K
FeOH H (aq) PO (aq)

Ca (aq)

FeO PO Ca H O(l)

log
z z z

0.5
4

3

2

0.5 0
3

1 2
2

MTC

≡ + +
+

↔ ≡ +

− + −

+

− +Δ Δ Δ
(2)

K
2 FeOH 2 H (aq) PO (aq)

Ca (aq)

(FeO) PO Ca 2 H O(l)

log
z z z

0.5
4

3

2

2
1 0

2
1 2

2

BTC

≡ + +
+

↔ ≡ +

− + −

+

− +Δ Δ Δ

(3)

where Δz0, Δz1, and Δz2 are the CD coefficients of the 0-,
1-, and 2-plane in the extended Stern layer model. The
corresponding set of adsorption parameters is given in Table 2.
For both the above surface complexes, the values of Δz0

have been derived with the Brown bond valence analysis68,69 of
the optimized geometries of these ternary complexes that we
obtained with MO/DFT/B3LYP/6-31+G** calculations
(Section 5 in the Supporting Information), whereas the values
of Δz1 and Δz2 were adjusted by fitting the model to the
adsorption data using the constraint Δztot = Δz0 + Δz1 + Δz2.
The optimized MO/DFT structures of the ternary complexes
defined with eqs 2 and 3 are represented in Figure 5a,b,

respectively. Both the mononuclear monodentate FeOPO3
complex (Figure 5a) and the binuclear bidentate
(FeO)2PO2 complex (Figure 5b) interact with Ca by
forming one single Ca-O-P bond. In the former complex, the
calculated Ca-P distance was 367 pm, and in the latter, it was
327 pm. In a hydrated calcium phosphate mineral, brushite
(CaHPO4·2H2O), a Ca-P distance of 370 ± 2 pm can be
found in the case of single Ca-O-P bridging, which is close to
the distance (360 pm) observed in (FeO)2PO2Ca net-
works55 and found also in hydroxyapatite. In brushite, a shorter
Ca-P distance of 312 pm is also found for single Ca-O-P
linkages.
The ternary complex in which PO4 is bound to Fh in a

monodentate configuration (MPCa) (eq 2) is the most
relevant ternary surface species for describing our experimental

data of the binary Ca-PO4 systems (see below Figure 6). This
complex can be formed with both types of singly coordinated

groups FeOH(a)−0.5 and FeOH(b)−0.5. A similar type of
complex was used by Antelo et al.31 for describing Ca-PO4
binary systems with freeze-dried Fh. However, their data set
covers a relatively small range of solution conditions compared
to our work, in which we collected adsorption data at a wider
range of Ca/Fe ratios. This allows us to reveal by modeling the
formation of an additional ternary complex (BPCa), in which
Ca is bound to an adsorbed PO4 present in the bidentate
configuration (eq 3). Moreover, in our modeling, we have
implemented the difference in high and low affinity sites for
Ca, enabling a good description of the Ca binding over a wide
range of Ca loadings. With the two ternary complexes resolved,
an excellent and consistent description of the simultaneous
adsorption of Ca and PO4 is possible (R

2 = 0.99 and n = 72),
as shown in Figures 1 and 2 with the modeled lines.
For the binary Mg-PO4 systems, only the formation of one

ternary complex is required for describing adequately the
interaction of these two ions with the surfaces of Fh (R2 = 0.99
and n = 22). In this ternary complex, PO4 is bound to Fh in a
monodentate configuration (MPMg), similar to that for the
ternary Fe-PO4-Ca complex formulated in eq 2. The respective
adsorption reaction is formulated as

Figure 5. Hydrated geometries of the ternary Fe-PO4-Ca complexes
optimized with MO/DFT/B3LYP/6-31+G**. (a) Single-corner
complex of FeOPO3 (d(Fe-P) = 348 pm) with a Ca ion that is
bound to PO4 as a Ca-O-P single-corner (1C) complex (d(P-Ca) =
367 pm), formed according to eq 2. (b) Double-corner complex of
(FeO)2PO2 (d(Fe-P) = 320 ± 4 pm) with a Ca ion that is bound to
PO4 as a Ca-O-P single-corner (1C) complex (d(P-Ca) = 327 pm),
formed according to eq 3. The Fe2(OH)6 (OH2)3PO4-Ca cluster (a)
has 26 water molecules for hydration and the other one (b) has 21.

Figure 6. pH-dependent surface speciation of PO4 (upper panels) and
Ca (lower panels) in the corresponding single-ion (left panels) and
binary Ca−PO4 (right panels) systems with Fh in 0.01 M NaNO3.
The conditions of the systems are similar to those of the adsorption
experiments shown in Figure 2a,b and Figure 4. The total Fe
concentration is 3.90 mM, and the specific surface area of Fh is A =
684 m2 g−1 with a corresponding molar mass of Mnano = 96.6 g mol−1.
The total PO4 and Ca concentrations are, respectively, 0.60 mM and
1.0 mM. For PO4: MH = monodentate protonated; MH2 =
monodentate doubly protonated; B = bidentate; BH = bidentate
protonated. For Ca: BCa(l) = bidentate at the low affinity sites;
BCa(h) = bidentate at the high affinity sites. For the ternary species:
MPCa = ternary complex in which PO4 is bound as a monodentate;
BPCa = ternary complex in which PO4 is bound as a bidentate. The
calculations have been done using the CD model with the parameter
sets of Tables 1, 2 and Table S4 in the Supporting Information.

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K
FeOH H (aq) PO (aq)

Mg (aq)

FeO PO Mg H O(l)

log
z z z

0.5
4

3

2

0.5 0
3

1 2
2

MTC

≡ + +
+

↔ ≡ +

− + −

+

− +Δ Δ Δ

(4)

Presently, we have not been able to clearly reveal the
formation of the ternary Fe-PO4-Mg complex, in which PO4 is
bound to Fh in a bidentate configuration (BPMg), as we did
resolve for the Ca-PO4 systems. Introduction of such BPMg
does not improve the description of our adsorption data in the
Mg-PO4 systems, and a large uncertainty is found in the fitting
of the CD coefficients of the 1- and 2-planes (i.e., Δz1 and
Δz2) of this ternary species. It must be noticed that for the Mg-
PO4 systems, we have collected a more limited dataset,
covering a narrower range of solution conditions in
comparison to the Ca-PO4 systems. This may have affected
the resolution of our modeling approach to distinguish the
potential formation of an additional ternary complex species.
Considering this constraint, we have implemented in our final
modeling only the formation of the ternary complex MPMg.
In the series of alkaline-earth metal ions, Ca2+ interacts

stronger than Mg2+ with Fh, which is reflected in its higher log
K values (Δlog K ≈ 0.9) for high and low affinity sites (Table
1). This difference in log K might be attributed to an exchange
of interfacial water, releasing Gibbs free energy.67 For the
formation of monodentate ternary complexes (eq 2 and 4), we
find a difference in affinity of Δlog KMTC ≈ 0.3 between the
ternary complexes with Ca and Mg, which is possibly also due
to an exchange of interfacial water because, in solution, both
association constants (CaHPO4

0(aq) and MgHPO4
0(aq)) are

rather similar.83 The stronger interaction of Ca with PO4 at the
surface of Fh can be also inferred from our MO/DFT
calculations. Ca2+ neutralizes the negative charge of PO4
ligands better than Mg2+, which leads to lower attribution of
the negative charge of PO4 to the surface and, consequently, to
slightly higher Δz0 values for the MPCa complex. In addition,
the fitted Δz2 value is higher for the MPMg than for the MPCa
complex (Table 2), suggesting that a higher fraction of Mg
charge is located in the outer Stern layer region. Overall, these
results suggest that Mg is more loosely bound to PO4 than Ca
at the surfaces of Fh. In Figure S6 of the Supporting
Information, we modeled the PO4 binding to Fh in the
presence of either Ca or Mg. At the same solution conditions
(i.e., pH and total M2+ concentration), the adsorption of PO4
is more enhanced in the presence of Ca in comparison to Mg.
In literature, formation of both anion-bridged (e.g., Fe-PO4-

M2+) and metal-bridged (e.g., Fe-M2+-PO4) ternary complexes
have been proposed.53 In general, the type of ternary
complexes formed would depend on the relative affinity of
the co-adsorbing ions for the Fe-(hydr)oxide surfaces.53 If the
anion interaction with the surface is relatively weak, metal-
bridged ternary complexes dominate, as found, for instance, in
Cd-SO4 and Pb-SO4 systems.28,84,85 In our case, the anion
(PO4

3−) is much stronger bound to Fh than the cation (Ca2+

or Mg2+) and this leads to the formation of anion-bridged
complexes.
In specific cases, it is also possible that both cations and

anions react directly with the surfaces,25,28,53 as found in Pb-
PO4 systems.86 In that type of complex, both ions are bound to
the surface in a monodentate manner, but there is an
additional chemical (lateral) interaction between the adsorbed
cation and anion.53 Conceptually, all charges are then located

in the inner Stern layer region (0- and 1-plane). When a
ternary anion-bridged surface complex is formed, part of the
complex (M2+) may physically enter the outer Stern layer
region (2-plane). This is found with our CD modeling for the
(FeO)2PO2-Ca and FeOPO3-Ca complexes. According to
the CD model, ∼two/thirds of the Ca charge in the
(FeO)2PO2-Ca complex is at the 2-plane (Δz2 = +1.46 ±
0.17 v.u.), which could suggest that ∼two/thirds of the Ca
ligands are in the outer Stern layer. This attribution of positive
charges of the ternary Fe-PO4-Ca complexes to the 2-plane will
have important implications for describing the pH-dependent
PO4 adsorption in Ca media, as it will be discussed in Section
3.4.

3.3. Surface Speciation: Single- vs Binary Ion
Systems. In Figure 6, the surface speciation of PO4 and Ca
in single-ion systems (left panels) is compared to the
corresponding surface speciation of these ions in the binary
Ca-PO4 systems (right panels). The calculations have been
done with the CD model and the simulated conditions of the
binary Ca-PO4 systems are similar to the experimental
conditions for the data shown in Figures 2a,b and 4.
In relation to the PO4 adsorption, comparing Figure 6a,b

shows that the Ca-PO4 synergy is more notorious at high pH
values, in agreement with our experimental results (Figures 1
and 2). The ternary complex formation is mainly due to the
formation of MPCa. The ternary complex formation reduces
the contribution of the bidentate PO4 surface complexes (B,
BH) to the overall PO4 adsorption, while the speciation of
both monodentate PO4 species (MH, MH2) is hardly affected.
A similar result is found for the PO4 surface speciation in
binary Mg-PO4 systems (Figure S5).
Comparing Figure 6c,d shows that the Ca adsorption

strongly increases in the presence of PO4. At low pH values, Ca
is mainly bound as a ternary complex in the binary Ca-PO4
systems. In the absence of PO4 (Figure 6c), hardly any Ca is
bound at low pH. The stimulating role of PO4 due to favorable
electrostatics is mainly visible at high pH. In the presence of
PO4, more Ca is clearly bound as bidentate species (BCa), as it
is evident from comparing Figure 6c,d. Especially, the Ca
adsorption to the low affinity sites (BCa(l)) is enhanced at
high pH conditions. The Ca binding to the high affinity sites
(BCa(h)) is hardly affected, which is due to near-saturation of
these sites, as observed already in the single-ion systems in the
absence of PO4.

3.4. Comparing Ferrihydrite and Goethite. The
synergistic interaction of Ca with PO4 has been studied
extensively in the past for well-crystallized goethite,34 allowing
us to compare it with the interaction presently measured for
Fh. In Figure 7, the PO4 adsorption isotherms of Fh (panel a)
and goethite (panel b) have been calculated for systems at pH
5 and 7 in the presence (symbols) and absence (lines) of Ca at
a constant ionic strength of 3 mM. In the absence of Ca, the
pH dependency of the PO4 adsorption is much larger for Fh
than for goethite, which can be attributed to more protonation
of adsorbed PO4 at low pH values.26 In the presence of Ca, the
pH dependency is much smaller for the reasons discussed
below.
The intrinsic difference in the pH dependency of the PO4

adsorption of Fh and goethite is illustrated in Figure 7a,b with
model lines calculated for systems at pH 5 and 7 in NaNO3
solution. This pH dependency is much higher for Fh than for
goethite. At pH 7, the PO4 adsorption in NaNO3 is very similar
for Fh and goethite (dotted lines). However, at pH 5 the

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adsorption of PO4 in NaNO3 is much higher for Fh (full lines)
than for goethite. As mentioned above, this is particularly due
to a difference in protonation of the adsorbed PO4 species.

26

For Fh (Figure 7a), the presence of Ca2+ hardly affects the PO4
adsorption at pH 5 (green squares vs full line), although some
Ca2+ ions do adsorb but this is mainly in the form of ternary
Fe-PO4-Ca complexes. The corresponding adsorbed Ca does
not have a strong electrostatic interaction with the other types
of adsorbed PO4 ions because a significant part of the Ca
charge is outside the inner Stern region according to our CD
analysis (see Δz2 in Table 2). In contrast, in the Ca-goethite,
there is a substantial increase in the PO4 adsorption at pH = 5
(Figure 7b), which is due to a strong electrostatic interaction
of the adsorbed Ca2+ ions with adsorbed PO4. For goethite,
most of the divalent charge of Ca2+ is present at the 1-plane
(Δz1) and acts on the negatively charge of the outer oxygen
ligands of PO4 that reside there. This strong electrostatic
interaction of Ca2+ also occurs at pH 7, increasing the PO4
adsorption to similar levels as that for pH 5. For Fh at pH 7,
the PO4 adsorption is also increased in the presence of Ca2+

(blue circles vs dotted line). However, this increase is mainly
due to the significant formation of ternary Ca-PO4 complexes,
and it is less important than the increase in the PO4 adsorption
on goethite by electrostatic interaction of the large fraction of
Ca2+ charges present in the 1-plane.
The abovementioned difference in the pH-dependent

adsorption behavior of PO4 for both Fe (hydr)oxide minerals
will be important in applications of surface complexation
modeling in natural systems. It is evident that the choice of a
proxy for the natural oxide fraction will be crucial for the
outcome of predictions, particularly the pH dependency, as
illustrated in Figure 7. In future applications to soils, this will
be evaluated.

4. CONCLUSIONS
In this study, the surface interaction of the alkaline-earth metal
ions Ca2+ and Mg2+ with adsorbed PO4 has been quantified for

well-characterized, freshly precipitated Fh. The collected data
have been interpreted with the CD model in combination with
a recently developed multisite ion complexation model for Fh,
in which reactive site densities are based on analysis of the
surface structure. In addition, high and low affinity (log K)
sites are distinguished in the model, derived from the
adsorption of alkaline-earth metal ions (M2+) covering a
wide range of surface loadings. The corresponding adsorption
densities have been quantified in a parallel study using single-
ion systems.67 According to that study, the alkaline-earth metal
ions form binuclear double-corner (2C) inner-sphere com-
plexes (FeOH)2

Δz0MΔz1, for which the CD coefficients have
been derived with a Brown bond valence analysis using MO/
DFT optimized geometries of complexes.
In the present study with binary M2+-PO4 systems, the

adsorption of Ca2+ and Mg2+ ions to Fh is found to be
enhanced in the presence of adsorbed PO4 and vice versa. For
Fh, this synergistic effect is due to the combined effect of an
enhanced electrostatic interaction and the formation of ternary
surface complexes. For the Ca-PO4 systems, our model reveals
the formation of two anion-bridged surface ternary complexes:
FeOPO3Ca and (FeO)2PO2Ca, the former being most
prominently present. The charge attribution to the surface
(Δz0) has been derived for both complexes from the MO/
DFT/B3LYP/6-31+G** optimized geometries. The Ca2+ ion
charge is distributed between the inner (Δz1) and outer Stern
(Δz2) plane, which we found by analysis of the adsorption data
with CD modeling. For the Mg-PO4 systems, only the
formation of the ternary complex FeOPO3Mg could be
revealed under the investigated adsorption conditions. Our
results are in line with the general notion that the dominant
type of ternary complex (i.e., metal-bridged vs anion-bridged)
depends on the relative affinity of the co-adsorbing ions for the
metal (hydr)oxide surface. PO4 has a significantly higher
intrinsic affinity than Ca and Mg for binding sites at the surface
of Fh, favoring the formation of anion-bridged ternary
complexes. This is indeed found in our CD modeling. In
addition, our modeling reveals that the distribution between
monodentate and bidentate surface complexes of PO4 is
different in the single-ion and binary systems. In the presence
of M2+, more PO4 is bound to Fh in a monodentate
configuration compared to the single-ion systems.
The pH dependency of the intrinsic PO4 adsorption in

NaNO3 solution is much larger for Fh than for goethite.
However, this difference is largely compensated by the binding
of Ca. For Fh, the increase in PO4 adsorption is predominantly
due to the formation of ternary Fe-PO4-Ca surface complexes,
and in the case of goethite, the increase is entirely due to a
mutual electrostatic interaction of adsorbed Ca2+ and PO4.
From an environmental perspective, the present study is highly
relevant because Ca2+ and Mg2+ ions are abundant in natural
systems. The interaction of Ca2+ and Mg2+ with the surfaces of
metal (hydr)oxides affects the chemical behavior and fate of
other important ions, particularly anions, as shown here for
PO4. Fh can be used as a proxy for the natural oxide fraction,
and application of the results of the present study will
contribute to improved understanding of the mutual
interactions of PO4 and M2+ in soils, aquifers, and natural
water bodies.

Figure 7. PO4 adsorption isotherms of (a) ferrihydrite and (b)
goethite at pH 5 and 7 in the absence (lines) and presence (symbols)
of Ca at a constant ionic strength of 3 mM. The intrinsic pH
dependency of the PO4 adsorption in the NaNO3 solutions is much
higher for Fh than for goethite (lines). This difference is largely,
though not entirely, compensated by the presence of Ca (symbols).
For Fh, the PO4 adsorption is increased by ternary Ca-PO4 complex
formation, particularly at high pH (Figure 6), and for goethite, the
increase is due to a strong electrostatic interaction of adsorbed Ca2+

by introducing positive charge mainly to the first Stern plane, where
the negatively charged outer ligands of the adsorbed PO4 ions reside
(see text). For Fh, the adsorption of PO4 has been calculated using
the parameter sets of Tables 1 and 2 and Table S4 in the Supporting
Information. For goethite, the adsorption has been calculated with the
parameter sets of Hiemstra et al.43

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■ ASSOCIATED CONTENT
*sı Supporting Information
The Supporting Information is available free of charge at
h t tps ://pubs . ac s .o rg/do i/10 .1021/acsea r thspace -
chem.9b00320.

Conditions of the batch adsorption experiments (1),
thermodynamic databases used in the modeling (2),
effect of phosphate adsorption on the net charge of
ferrihydrite (3), precipitation of Ca-PO4 minerals (4),
charge distribution of the ternary complexes (5),
modeling of Mg-PO4 interaction with no ternary
complex formation (6), surface speciation of PO4 and
Mg in ferrihydrite systems (7), and modeling PO4
binding: Ca vs Mg systems (8) (PDF)

■ AUTHOR INFORMATION
Corresponding Author
Juan C. Mendez − Soil Chemistry and Chemical Soil Quality
Group, Wageningen University, 6708 PB Wageningen, The
Netherlands; orcid.org/0000-0002-1658-400X;
Phone: +31 317 48 2342; Email: juan.mendezfernandez@
wur.nl

Author
Tjisse Hiemstra − Soil Chemistry and Chemical Soil Quality
Group, Wageningen University, 6708 PB Wageningen, The
Netherlands

Complete contact information is available at:
https://pubs.acs.org/10.1021/acsearthspacechem.9b00320

Notes
The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS
The grant provided by the University of Costa Rica (UCR) to
the first author is gratefully acknowledged. We thank the work
of He Wei and Frank van Raffe in collecting part of the Ca-PO4
and Mg-PO4 adsorption data, respectively. We also thank Peter
Nobels from the Chemistry and Biology Soil Laboratory
(CBLB) for his attentive work regarding the ICP-OES and
ICP-MS analyses.

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