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Sistema de Información Científica
Red de Revistas Científicas de América Latina y el Caribe, España y Portugal
Rev. Int. Contam. Ambie. 27 (2) 139-151, 2011
A UNIFIED SURFACE STRUCTURAL MODEL FOR FERRIHYDRITE: PROTON CHARGE,
ELECTROLYTE BINDING, AND ARSENATE ADSORPTION
Mario VILLALOBOS
1,2
and Juan ANTELO
3
1
Grupo de Biogeoquímica Ambiental, Facultad de Química,
2
Instituto de Geología, Universidad Na-
cional Autónoma de México (UNAM), Coyoacán, Ciudad Universitaria, México 04510 D.F., México.
mar.villa@stanfordalumni.org
3
Departamento de Edafología y Química Agrícola, Universidad de Santiago de Compostela, Rúa Lope Gómez
de Marzoa s/n, 15782 Santiago de Compostela, España
(Recibido marzo 2011, aceptado abril 2011)
Key words: ferrihydrite, surface structure, point of zero charge, speci±c surface area
ABSTRACT
Ferrihydrite (FH) is a common hydrous ferric oxide nanomineral in aqueous geo-
chemical environments. Its small particle sizes (1.5-5 nm) expose a very high speci±c
surface area at the mineral/water interface, and this may have considerable in²uence
on the transport and fate of a variety of trace and major elements through diverse
sorption processes. In particular, arsenate anions show a very high af±nity for Fe(III)
oxide surfaces, including FH, and their fate in contaminated environments is almost
invariably associated to these. The extremely small FH nanoparticles, which show high
particle aggregation when dried, preclude experimental determination of important
surface parameters for the thermodynamic description of its adsorption behavior, such
as available speci±c surface area in aqueous suspension. In the present work we have
compiled eight sets of published acid-base surface titration data for synthetic prepara-
tions of FH across a wide range of particle sizes, and uni±ed their description through
a face-distribution site-density model developed previously for goethite. We show that
the surface proton charge behavior of FH in conjunction with its As(V) adsorption
behavior may be adequately described using the af±nity constants derived for goethite,
by assuming the FH surface to be composed predominantly of singly-coordinated >OH
groups, with a site density equal to that of the (010) goethite face (
Pnma
space group).
Also, through the applied model the available speci±c surface area of each FH prepara-
tion in aqueous suspension may be successfully derived, showing values between 330
and 1120 m
2
/g. The implications of the results reported here are highly relevant for
predictive purposes of FH surface reactivity in general.
Palabras clave: ferrihidrita, estructura super±cial, punto de carga cero, área super±cial especí±ca
RESUMEN
La ferrihidrita (FH) es un nanomineral de óxido férrico hidratado común en ambientes
geoquímicos acuosos. Sus pequeños tamaños de partícula (1.5-5 nm) exponen una gran
área super±cial especí±ca en la interfaz mineral/agua, y esto puede tener una in²uencia
considerable en el transporte y destino de una variedad de elementos vestigiales y ma-
M. Villalobos and J. Antelo
140
Fig. 1.
Relationship between particle size and specifc surFace
area For Ferrihydrite, calculated assuming spherical par-
ticle shape and a fxed mass density oF 3.57 g/cm
3
(From
Murphy
et al.
1976).
200
1
2
Ferrihydrite diameter (nm)
Calculated specific surface area (m
2
/g)
3
4
5
6
7
300
400
500
600
700
800
900
1000
1100
1200
yores, a través de diversos procesos de sorción. En particular, los aniones de arseniato
muestran una gran afnidad por las superfcies de óxidos de ±e(III), incluyendo a la ±H,
y su destino en ambientes contaminados está casi invariablemente asociado a éstos.
Las nanopartículas extremadamente pequeñas de ±H, que muestran un alto grado de
agregación cuando se secan, impiden la determinación experimental de parámetros
superfciales importantes para la descripción termodinámica de su comportamiento
de adsorción, tales como el área superfcial específca disponible en suspensión. En el
presente trabajo hemos recopilado ocho series de datos de titulación superfcial ácido-
base publicadas de preparaciones sintéticas de ±H en un amplio intervalo de tamaños
de partícula y hemos unifcado su descripción a través de un modelo de distribución
de caras cristalinas - densidad de sitios desarrollado previamente para la goetita. Mos-
tramos que el comportamiento de carga superfcial protónica de la ±H junto con su
comportamiento de adsorción de As(V) se puede describir adecuadamente utilizando
las constantes de afnidad derivadas para la goetita, asumiendo la superfcie de la ±H
como compuesta predominantemente de grupos superfciales monocoordinados >OH,
con una densidad de sitios igual al de la cara (010) de la goetita (grupo espacial
Pnma
).
Además, a través del modelo aplicado se puede derivar exitosamente el área superfcial
específca disponible de cada preparación de ±H en suspensión acuosa, mostrando
valores entre 330 y 1120 m
2
/g. La implicación de los resultados que se reportan aquí
es altamente relevante para la predicción general de la reactividad superfcial de la ±H.
INTRODUCTION
±errihydrite (±H) is a very common ±e oxide
nanomineral and the frst solid product oF Fast hydro-
lysis oF aqueous ±e(III) solutions, or rapid oxidation
oF aqueous ±e(II), under normal ambient conditions
(Schwertmann and Cornell 2000). ThereFore, it is con-
sidered a “young” ±e oxide in natural environments,
occurring typically in lakes, streams, and hydromor-
phic soils. Its particle sizes range From 1.5 to 5 nm
(Murphy
et al.
1976, Janney
et al.
2000, Theng and
Yuang 2008) and cannot surpass 6 nm (Waychunas
and Zhang 2008) beFore transitioning to a more crys-
talline, usually goethite phase, under humid ambient
conditions (Schwertmann and Cornell 2000). These
small sizes ensure a large exposed specifc surFace area
(SSA) and thus, a high reactivity towards adsorption
oF ions in bio-geochemical environments. ThereFore,
±H when present has a considerable in²uence in the
transport oF trace and major ionic species, competing
Favorably through adsorptive mechanisms against
other colloidal minerals present. A thermodynamic
description oF its surFace reactivity is thereFore crucial
iF predictive modeling is desired on the mobility and
Fate oF geochemically and environmentally relevant
species in settings where ±H Forms.
One may calculate the speciFic surFace areas
(SSAs) theoretically exposed oF individual ±H
spherical nanoparticles (
Fig. 1
) as a Function oF their
diameter (
d
). The inverse relationship between
d
and SSA [SSA=(6/
r
)/
d
, where
r
= 3.57 g/cm
3
is the
mass density For two-line ±H; Murphy
et al.
1976]
results in large increments oF SSA when particle size
declines in this narrow size range (SSA increases
ca
. From 300 m
2
/g to 840 m
2
/g For a diFFerence oF
only 3.6 nm diameter;
Fig. 1
). The nanosize regime
oF ±H brings about experimental diFfculties in its
structural characterization and determination oF
its surFace reactivity. Considerably larger particle
aggregation ensues upon drying ±H suspensions,
especially oF Freshly-precipitated samples, causing
reduction oF exposed surFace area (to 200-300 m
2
/g;
Dzombak and Morel 1990), and thus precluding the
use oF N
2
-adsorption BET to determine reliable va-
A UNIFIED SURFACE STRUCTURAL MODEL FOR FERRIHYDRITE
141
lues for actual surface area exposed under aqueous
conditions. Therefore, this parameter is arbitrarily
chosen for surface area normalization of adsorption
data on FH and for their thermodynamic modeling.
Typical values recommended for modeling are in
an intermediate range from the theoretical interval
of
fgure 1
, of 600-650 m
2
/g (Dzombak and Morel
1990, Hiemstra and Van Riemsdijk 2009).
Recently, Hiemstra and Van Riemsdijk (2009)
have shown that the standard structural model for FH
(Drits
et al.
1993) may be used to propose a surface
structure based on that of goethite as a proxy. They
were successful in modeling proton and electrolyte
binding (Hiemstra and Van Riemsdijk 2009), and
U(VI) and carbonate adsorption to FH (Hiemstra
et al.
2009) using the charge distribution (CD) and
multi-site surface complexation (MUSIC) model, by
assuming the crystallographic site densities of goethi-
te faces (101), (010), and (210) (
Pnma
space group)
in equal proportions, as representing the FH surface.
Antelo
et al.
(2010) investigated the proton
charge and phosphate adsorption behavior of a FH
sample that was aged and dialyzed for several days,
and were also able to model the data by using the
same proportions of “goethite” faces, but required
assuming a speci±c surface area of
ca
. half the va-
lue of the former authors. However, in order to be
consistent with the above proportions of faces they
also required assuming different values of the sur-
face proton and electrolyte af±nity parameters from
those proposed by Hiemstra and Van Riemsdijk
(2009), as well as the optimal internal capacitance
considered, C
1
(0.74 F/m
2
vs.
1.15 F/m
2
in the latter
work), despite applying the same MUSIC model.
The goal of the present work was to continue on the
steps of Hiemstra and Van Riemsdijk (2009) Hiemstra
et al.
(2009) and Antelo
et al.
(2010) of using goethite
as a proxy for the FH surface, with the aim of unifying
the thermodynamic description of the FH surface
across all samples. To achieve this, we analyzed the
surface proton charge behavior of a larger number of
datasets published representing samples across the
whole range of particle sizes. The data were modeled
in a self-consistent manner, and the optimized af±nity
parameters generated offered a uni±ed picture with
those obtained for goethite from a previous work
(Salazar-Camacho and Villalobos 2010). An important
outcome of the modeling exercises were the values of
actual SSA exposed in aqueous FH suspensions.
In addition, the uni±ed surface acid and elec-
trolyte-binding parameters obtained were applied
to the successful description of arsenate adsorption
behavior to FH for two reliable data sets from the
literature (Raven
et al.
1998, Dixit and Hering 2003).
We should note that the data analysis and modeling
presented in this work apply to two-line FH, and due
to lack of adsorption data available for six-line FH no
inference can be drawn for this latter phase.
FERRIHYDRITE SURFACE PROTON
CHARGE ANALYSIS
Point o± zero net proton charge (PZNPC)
A large amount of work has been devoted to deter-
mine surface proton charge behavior of FH, of which
the resulting PZNPC values lie in the range of 7.9 to
8.2 (Dzombak and Morel 1990), with average and
median values near 8.0, and sometimes even lower
values (Kosmulski 2009). All of these were obtained
on freshly-precipitated and thus low-particle-sized FH
samples. However, recently, higher PZNPC values
have been obtained for FH samples that have been
both cleaned extensively and from which carbonate
has been rigorously excluded (
Table I
). Accompanying
this is the unavoidable process of “aging” effects of the
initially-obtained FH samples, most notably manifes-
ted in particle growth (to
ca
. 5 nm; Gilbert
et al.
2009).
In
table I
we have compiled eleven reports of
FH PZNPC, of which eight acid-base titration da-
tasets have been used in the analysis presented in
this study (note that no sample was dried in order to
avoid aggregation problems). We note that all fresh
and thus not rigorously de-carbonated FH samples
show consistently low values (7.9-8.1), whereas all
dialyzed and N
2
-purged samples after synthesis tend
towards higher values (8.6-8.7). These differences
from the values of freshly-precipitated FH samples
could be interpreted as real surface-driven changes
due to different proportions of crystal face distributions
exposed in both groups of samples. However, in the
case of the freshly-prepared Hsi FH sample (
Table I
;
Hsi and Langmuir 1985), for which a value of 8.15
was reported, we note further that in the same work
the PZNPC obtained for a 49 m
2
/g goethite was 8.3,
a value which is considerably lower than expected.
Normal PZNPC values for well-decarbonated goethi-
te preparations are found in the range 8.9 to 9.4 (Van
Geen
et al.
1994, Lumsdon and Evans 1994, Boily
et al.
2001, Villalobos
et al.
2003).
PZNPC values for goethite below 8.9 are attri-
buted to poor carbonate exclusion previous to acid-
base titration experiments (Zeltner and Anderson
1988, Lumsdon and Evans 1994, Villalobos and
M. Villalobos and J. Antelo
142
TABLE I.
SUMMARY OF FERRIHYDRITE PZNPC VALUES AND SYNTHESIS CONDITIONS FROM LITERATURE ACID-
BASE TITRATION DATASETS USED IN THE PRESENT WORK
Reference
a
pH of point of
zero net proton
charge (PZNPC)
reported
Conditions
after synthesis
and before use
Code in
present
work
b
Surface area
optimized in
present work
b
Value
Method
used
c
Aging time
Cleaning
method
Speci±c
surface
area (m
2
/g)
Corresponding
particle diameter
(nm)
(1)
8
CIP in titration
curves
“short”
“Rapid” wash
by dialysis
Yates
934
1.8
(2)
7.9
CIP in titration
curves
4 h
None
reported
Davis
1120
1.5
(3)
7.9-8.1
CIP in titration
curves
3 h
None
reported
Swallow
1120
1.5
(4)
8.15
d
CIP in titration
curves
4 h
None
reported
Hsi
840
2
(5)
8.5
CIP in titration
curves
Within
10 days
None
reported
Raven
840
2
(6)
8.7
IEP
unknown
Unknown
-
-
-
(7)
8.3
Stoichiometric
Reaction
Fe(III) + OH
-
3 weeks
None
reported
-
-
-
(8)
8.7
CIP in titration
curves
10 days
Dialysis,
15-h N
2
purging
Hofmann
650
2.6
(9)
8.6
CIP in titration
curves
Several
days
Dialysis
-
-
-
(10)
7.9
CIP in titration
curves
4 h
None
reported
Nagata
989
1.7
(11)
8.7
CIP in titration
curves
+2 days
Dialysis
after initial
aging,
overnight N
2
purging
Antelo
337
5
a
(1) Yates 1975 from Dzombak and Morel 1990; (2) Davis 1977 from Dzombak and Morel 1990; (3) Swallow
et al
. 1978; (4) Hsi
and Langmuir 1985; (5) Raven
et al
. 1998; Jain
et al
. 1999; (6) Dardenne
et al
. 2001 from Kosmulski 2002; (7) Spadini
et al
. 2003;
(8) Hofmann
et al
. 2005; (9) Gilbert
et al
. 2007, 2009; (10) Nagata
et al
. 2009; (11) Antelo
et al
. 2010.
b
A dash “-“ is placed if no dataset was available or used.
c
CIP = common intersection point from titration curves at ≥3 different ionic strengths. IEP = isoelectric point.
d
The value reported in the text is 7.9, but the actual CIP from the reported plot is 8.15. A CIP value of pH=8.3 for a 49 m
2
/g goethite
is reported in this work as well.
Leckie 2000), because the source of this carbonate
is atmospheric CO
2
, which acidi±es the medium,
and even small amounts of CO
2
dissolved cause
considerable underestimations in the measured PZ-
NPC (Villalobos and Leckie 2000). We know now
that a more reliable PZNPC for a 50 m
2
/g goethite
is 8.9 (Van Geen
et al.
1994). Therefore the goethite
titration data of Hsi and Langmuir (1985) must be
corrected by a value near 0.6 pH units. If the same
correction is applied to their FH sample a PZNPC of
8.75 is obtained, and we believe this may be a value
closer to the real one if carbonate could be excluded
from the extremely high SSA of the small nanopar-
ticles obtained when freshly precipitated. We believe
that the exposed SSA of freshly-prepared FH is so
high that despite efforts to exclude carbonate during
its synthesis, it is impossible to obtain carbonate-free
FH after synthesis, without additional efforts to expel
it (which in turn cause aging, particle growth, and
ensuing decrease in SSA).
In this manner, we propose here a uni±ed value
of 8.8 for the PZNPC of all FH samples across the
whole size range of occurrences.
Ferrihydrite surface proton charge behavior
If the surface proton charge of the different FH
samples analyzed is plotted normalized by FH mass
for equal ionic strengths, and after correcting (i.e.,
shifting) all to show a PZNPC of 8.8 (
Fig. 2a
) we
may identify three main sample behaviors. Samples
A UNIFIED SURFACE STRUCTURAL MODEL FOR FERRIHYDRITE
143
Fig. 2.
Experimental surface proton charge of seven ferrihydrite systems reported in
table I
, as a function of pH at ionic strength of
0.1 M, as normalized by (a) mass, and (b) surface area.
–80
–30
20
–1
–0.5
0
0.5
1.5
1
3
4
5
pH
pH
6
7
8
9
10
11
12
4
5
6
7
8
9
10
11
70
120
170
a)
b)
[H
+
]ads (C/g)
[H+]ads (mmol/m
2
)
Hsi & Langmuir –0.1 M
Davis, 0.1 M
Swallow –0.1 M
Antelo –0.1 M
Nagata –0.1 M
Hofmann –0.1 M
Raven –0.1 M NaCl
Hsi & Langmuir –0.1 M –840 m
2
/g
Davis, 0.1 M –1120 m
2
/g
Swallow –0.1 M –1120 m
2
/g
Antelo –0.1 M –337 m
2
/g
Nagata –0.1 M –989 m
2
/g
Hofmann –0.1 M –650 m
2
/g
Raven –0.1 M NaCl –840 m
2
/g
processed as freshly-prepared show the highest pro-
ton charging values for any given pH; then follows
the Hofmann FH sample (Hofmann
et al.
2005), and
least in charging is the Antelo FH sample. The main
difference between the latter two samples and the
freshly-prepared FH samples is the reported de-car-
bonation process carried out after synthesis (
table I
).
Since the actual exposed SSA is largely unknown
for all samples analyzed we may treat this as an adjus-
table parameter and we may ±nd the SSA relationship
between them that yields a congruent proton charging
behavior when data are normalized by surface area.
The actual SSA values depend obviously on what
particular value is assumed for the chosen starting
FH sample.
Figure 2b
shows the congruent beha-
vior for the optimal SSA values obtained from the
modeling exercise in the following section. Only the
Raven FH sample continues to show higher charging
because the electrolyte anion used was Cl
instead
of NO
3
as in all the rest. It is well-known that Cl
shows a stronger af±nity for the goethite surface than
NO
3
(Villalobos and Leckie 2000, Rahnemaie
et al.
2006), therefore the same may be expected for FH,
which causes higher proton charging at pH values
below the PZNPC (
Fig. 2b
).
Freshly-prepared FH samples show optimal SSA
values between 840 and 1120 m
2
/g, corresponding
to theoretical particle diameters between 2 and 1.5
nm. The Hofmann FH sample yielded an optimal
SSA of 650 m
2
/g (corresponding to 2.6 nm), which
is a value in the range typically used for general FH
modeling (Dzombak and Morel 1990, Hiemstra and
Van Riemsdijk 2009). Finally, the Antelo FH yielded
an optimal value of 337 m
2
/g (=5 nm), which is very
close to the one used by Antelo
et al
. (2010) to model
phosphate adsorption to this FH (350 m
2
/g), and the
corresponding particle size is close to that observed
by them using TEM. Also, the experimental BET-
SSA values obtained by Glbert
et al
. (2009) for 5 nm
FH particles at pH 5-8 are in the range 305-379 m
2
/g.
The optimal SSA results obtained strongly suggest
that, despite the fact that nanoparticle aggregation
has been demonstrated to occur in suspensions of
5-nm FH samples at pH values above 5 (Gilbert
et al.
2009), most or all surface area appears to be
available for proton, electrolyte, and as will be seen
below, for As(V) adsorption in the range of pH values
reported (
ca.
4-11), indicating that perhaps the FH
particle aggregation that occurs in suspension is not
suf±ciently tight to block its surface binding sites.
In other words, the aggregation framework of FH in
suspension is suf±ciently open and dynamic to not
render any surface site as unavailable.
MODELING FERRIHYDRITE SURFACE
REACTIVITY
Goethite surface as a proxy
Hiemstra and Van Riemsdijk (2009) proposed
a FH surface model based on equal proportions of
the goethite faces (101), (010), and (210). We found
that FH surface proton charge data may be modeled
with the same af±nity constants if the proportions of
goethite faces are varied, provided the SSA assumed
is also varied appropriately, because SSA is highly
correlated with the site density parameter. This effec-
tively means that equal simulations are obtained if
site densities are changed, by simultaneously chan-
ging SSAs in the opposite direction in an appropriate
magnitude. Since SSA is an unknown parameter, this
yields in±nite possibilities for choosing adequate
M. Villalobos and J. Antelo
144
TABLE II.
CD-MUSIC MODELING PARAMETERS THAT
YIELDED EQUAL OPTIMAL SIMULATIONS
FOR PROTON CHARGING OF THREE FERRI-
HYDRITE SYSTEMS*
Ferrihydrite
system
Optimal modeling parameters
Site density
(sites/nm
2
)
Specifc
sur±ace
area (m
2
/g)
>FeOH
1/2–
>Fe
3
O
1/2–
Antelo
6
8.8
1.2
0
350
325
Hsi
6
8.8
1.2
0
1000
950
Davis
6
8.8
1.2
0
1250
1200
*
For sel±-consistency, the parameters were fxed according to An-
telo
et al.
(2010) to the ±ollowing values: C
1
=0.74 F/m
2
, C
2
=0.93
F/m
2
, pH
pznpc
=8.7 = log K o± protonation o± both >FeOH
1/2-
and
Fe
3
O
1/2-
groups, log K(NO
3
)=–0.96, log K(K
+
)=–1.16 ±or
“Antelo” FH system, log K(Na
+
)=–0.60 ±or “Hsi” and “Davis”
FH systems.
The frst set corresponds to equal contribution o± ±aces (101),
(010), and (210).
The second set corresponds to the exclusive
presence o± ±ace (010) with 8.8 sites/nm
2
o± singly-coordinated
sites (Hiemstra and Van Riemsdijk 2009a; Dr. Vidal Barrón,
personal communication).
goethite ±aces proportions to describe FH sur±ace
proton charge behavior. For example, in
table II
we
show two optimal modeling combinations SSA-site
densities ±or three FH systems while fxing the other
parameters as previously obtained by Antelo
et al
.
(2010) in the ±ramework o± the simplifed (1-pK)
MUSIC model. For this we assumed two di±±erent
±ace distributions: equal contributions o± the above
three ±aces (with total proton-active site density =
7.2 sites/nm
2
), and the exclusive contribution o± ±ace
(010) (with total proton-active site density = 8.8 sites/
nm
2
). Obviously, in the latter case the SSA required
±or a correct description o± the sur±ace charge is lower
±or all FH systems, and in principle no particular ±ace
distribution seems more appropriate than the other.
The small FH particle size range (2-6 nm) and their
strong aggregation have proven to be an impediment
to get a reliable vision o± the FH crystal structure.
Recent structural studies by Michel
et al
. (2007,
2010) allow us to have a better picture o± the mine-
ral structure ±or the FH nanoparticles, but still more
in±ormation is needed able to recognize which are the
crystal ±aces that have more important contributions.
Nevertheless, i± As(V) adsorption data are inclu-
ded in this analysis, the adequate ±ace distribution
±or the modeling exercise was largely reduced to a
large contribution o± goethite ±ace (010), as will be
shown below.
General surface complexation modeling procedure
Sur±ace proton charge and arsenate adsorption
data were modeled using the Triple Layer sur±ace
complexation model in combination with aspects o±
the CD-MUSIC model, in which separate and explicit
site densities and a±fnities o± >FeOH, >Fe
2
OH, and
>Fe
3
OH sur±ace sites were considered. FITEQL 3.2
(Herbelin and Westall 1996) was used to optimize
values o± a±fnity parameters ±or the proton charging
and the As(V) adsorption data. Protons were assumed
to bind to >FeOH and >Fe
3
OH sites, while As(V)
was assumed to bind to >FeOH sites and adjacent
>Fe
2
OH groups (Salazar-Camacho and Villalobos
2010). From previous work on uni±ying the modeling
description o± goethite, the PZNPC o± >FeOH and
>Fe
3
OH sites were fxed to 8.8 and 9.66, respecti-
vely, and a
D
pKa o± 4 was established around each
(Salazar-Camacho and Villalobos 2010). Thus, only
electrolyte-binding constants were optimized to
describe the sur±ace charging behavior o± FH nano-
particles. For As(V) adsorption modeling all optimal
parameters obtained ±rom simulations o± titration
data were fxed, including the inner-layer capacitance
(
Table III
), and the a±fnity constants ±or the arsenate
ions were the only optimized parameters.
The complete list o± ±ormation reactions ±or
sur±ace species considered on >Fe
n
OH sites, where
n=1 is ±or singly-coordinated sites, and n=3 is ±or
triply-coordinated sites are:
>Fe
n
OH + H
+
= >Fe
n
OH
2
+
Log Ka
1 (n=1)
=6.8,
(n=2)
=7.66
>Fe
n
OH = >Fe
n
O
+ H
+
Log Ka
2 (n=1)
=-10.8,
(n=2)
=11.66
>Fe
n
OH + H
+
+ NO
3
/Cl
= >Fe
n
OH
2
+…
NO
3
/Cl
Log K
n
(NO
3
, ClO
4
) - optimized
>Fe
n
OH + Na
+
= >Fe
n
O
–…
Na
+
+ H
+
Log K
n
(Na
+
) - optimized
>FeOH + >Fe
2
OH + AsO
4
3-
+ H
+
= >FeO
-0.7
AsO
3
–1.3…
HOFe
2
< + H
2
O
Log K(As(V))
deprotonated
- optimized
>FeOH + >Fe
2
OH + AsO
4
3–
+ 2H
+
= >FeO
–0.7
AsO
3
H
–0.3…
HOFe
2
< + H
2
O
Log K(As(V))
protonated
- optimized
Proton surface charge modeling on ferrihydrite
In previous work with the more crystalline mineral
goethite (
a
-FeOOH - SSA ±rom 12 to 98 m
2
/g) we
A UNIFIED SURFACE STRUCTURAL MODEL FOR FERRIHYDRITE
145
TABLE III.
SUMMARY OF FERRIHYDRITE AND GOETHITE ELECTROLYTE AND ARSENATE BINDING
LOGARITHMIC CONSTANTS ON SINGLY-COORDINATED >FeOH SURFACE GROUPS
a
Mineral
K (NO
3
, ClO
4
)
K (Cl
)
K (Na
+
)
K (As(V))
Deprotonated
b
K (As(V))
Protonated
b
Ferrihydrite
c
8.1 ± 0.3
8.35
d
–9.5 ± 0.2
e
18.03 / 18.10
20.18 / 19.12
Goethite
f
8.02 ± 0.01
8.4 ± 0.2
–9.4 ± 0.2
e
18.75 ± 0.9
19.6 ± 0.3
a
Constants reported are based on a 1.0 M standard state. The pH of PZNPC was 8.8, and a
D
pKa of 4 was esta-
blished around it. C
2
values were 0.2 F/m
2
b
Values given are for Dixit / Raven systems, respectively. Optimal SSA for Dixit system was 989 m
2
/g, and
840 m
2
/g for Raven.
c
C
1
values were 0.64 ± 0.06 F/m
2
d
From the Raven system
e
Log K(K+) = –9.66 for ferrihydrite, and –9.99 for goethite (from the corresponding Antelo systems)
f
Taken from Salazar-Camacho and Villalobos (2010)
have found a value of 8.8 for the PZNPC of singly
(>FeOH) –coordinated surface groups, using a model
that combines the main tenets of the Triple Layer Mo-
del with some of those from the CD-MUSIC model
(Salazar-Camacho and Villalobos 2010). This value
coincides with the PZNPC of FH established above,
and strongly suggests that >FeOH groups are the major
contributors of the FH proton surface charge. This in
turn suggests that an adequate face distribution for
modeling purposes is one where face (010) predomi-
nates over face (101), because the latter contributes
with triply (>Fe
3
OH) –coordinated surface groups,
which were found previously to have a PZNPC of 9.66
(Salazar-Camacho and Villalobos 2010). Therefore,
the optimal face distribution for FH, from the modeling
perspective and tied to the other modeling parameters
used, is one where face (010) is the only face conside-
red. If another face distribution is considered, with the
inclusion of crystal face (101), and as a result with the
inclusion of triply coordinated groups, the optimized
values obtained for the electrolyte binding constants
compensate to maintain the PZNPC of 8.8, but the
simulations progressively worsen (i.e., yield higher
errors) as the contribution of face (101) is increased.
Additionally, the model for FH of exclusive
presence of face (010) yielded optimal electrolyte-
binding constants with values very close to those
obtained for goethite on singly-coordinated groups
(
Table III
). The logarithmic values for these cons-
tants were 8.07
versus
8.02 for NO
3
/ClO
4
binding
on FH and goethite, respectively; -9.50
versus
-9.41
for Na
+
binding on FH and goethite, respectively; and
8.35
versus
8.4 for Cl
binding on FH and goethite,
respectively (
Table III
). If face (101) was included in
the modeling, the optimal values for the electrolyte-
binding constants for FH diverged progressively
from those obtained for goethite, and this provides
additional support for the chosen FH surface model
of exclusive (010) face.
Figure 3
shows the optimal
simulations for the eight FH systems investigated.
These ²ndings are remarkable because they allow
uni²cation of the proton charging behavior of both
goethite and FH using the same values of acidity and
electrolyte-binding constants. The only parameters
adjusted further for FH were the SSA and the inner-
layer capacitance (C
1
). The optimal FH values for C
1
were 0.64 ± 0.06 F/m
2
, which are smaller than those
previously obtained for goethite by Salazar-Camacho
and Villalobos (2010). For SSA, the optimal values
are given in
table I
and were discussed above. These
values yielded congruency of surface charge behavior
when plotted normalized by surface area (
Fig. 2b
).
We should note that the results obtained from the
modeling exercise, suggesting that the optimal repre-
sentation of the FH surface is one where the goethite
(010) is the exclusive face present, is a macroscopic
result that bears no speci²c microscopic evidence.
As(V) adsorption modeling on ferrihydrite
Two FH systems were found in the literature with
reliable enough As(V) adsorption data to model:
Dixit (Dixit and Hering 2003) and Raven (Raven
et
al.
1998). Other systems published contained impor-
tant errors or did not report consistent data between
isotherms and pH adsorption edges. Yet another
system published with extensive As(V) adsorption
data reported exorbitant amounts of As(V) uptake
by FH (Pierce and Moore 1982), in which isotherms
showed ever increasing adsorption, with values
above 35 mmol/g at aqueous As(V) concentrations
of
ca
. 500
m
M and pH values ranging from 4 to 10.
These dramatic uptake values were impossible to
model as simple adsorption, and suggest that under
the experimental conditions imposed in this system,
coprecipitation processes occurred in the form of
Fe(III) arsenate solids (e.g., scorodite).
M. Villalobos and J. Antelo
146
Fig. 3.
Surface proton charge modeling of FH systems used, reported in
table I
: (a) Davis, Hsi, and Yates, (b) Nagata, (c) Raven,
(d) Hofmann, (e) Antelo, and (f) Swallow. Symbols denote experimental data and lines model simulations with parameters
described in
table III
pH
4
5
6
7
8
pH
3
5
7
9
11
13
9
10
11
pH
4
5
6
7
8
9
10
11
pH
4
5
6
7
8
9
10
11
a)
c)
d)
b)
–0.6
–0.4
–0.2
0
0.2
0.4
0.6
0.8
1
1.2
Proton charge (μmol/m
2
)
–0.6
–0.4
–0.2
0
0.2
0.4
0.6
0.8
1.2
1.4
1
Proton charge (μmol/m
2
)
–1.5
–1
–0.5
0
0.5
1
2
2.5
1.5
Proton charge (μmol/m
2
)
–1
–0.5
0
0.5
1
2
1.5
Proton charge (μmol/m
2
)
e)
f)
–1
–0.5
0
0.5
1
2
1.5
Proton charge (μmol/m
2
)
–1
–0.5
0.5
2
0
1
1.5
Proton charge (μmol/m
2
)
Davis
– I=0.001 M – 1120 m2/g
I=0.01 M
I=0.05 M
I=0.1 M
Davis
– I=0.01 M – 1120 m2/g
Davis
– I=0.1 M – 1120 m2/g
Hsi – I=0.001 M – 840 m2/g
Hsi – I=0.01 M – 840 m2/g
Hsi – I=0.1 M – 840 m2/g
Yates – I=0.01 M – 934 m2/g
I=0.01 M
I=0.05 M
I=0.1 M
I=0.01 M
I=0.03 M
I=0.1 M
I=0.3 M
I=0.01 M
I=0.1 M
I=0.5 M
pH
4
5
6
7
8
9
10
11
I=0.1 M
I=0.25 M
I=0.5 M
pH
3
5
7
9
11
13
Figure 4
shows the optimal As(V) adsorption
simulations for the Dixit system, according to the
parameters shown in
table III
. The optimal SSA for
this system was 989 m
2
/g, and this is consistent with
the fact that freshly-prepared FH samples were used
(Dixit and Hering, 2003). The pH adsorption edges
(
Fig. 4a
) and isotherm at pH 4 (
Fig. 4c
) were ade-
quately simulated, although the ±ts achieved for some
edges are not as close to those simulated previously for
goethite (Salazar-Camacho and Villalobos 2010). At
the higher As(V) loadings and lower pH values model
simulations slightly underestimated the adsorption
onto FH. The arsenate complex is monodentate on
singly-coordinated sites (
Fig. 5
), but occupies a second
A UNIFIED SURFACE STRUCTURAL MODEL FOR FERRIHYDRITE
147
a)
c)
b)
0.0
0.5
1.0
1.5
2.0
2.5
3
4
5
6
7
8
9
10
11
[As(V)]ads (μmol/m
2
)
pH
0.34 umol/m2
1.18 umol/m2
1.69 umol/m2
3.37 umol/m2
Total As(V) loading:
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
3
4
5
6
7
8
9
10
11
[As(V)]ads (μmol/m
2
)
pH
>FeO
–0.7
AsO
3
–1.3.
.
HOFe
2
<
>FeO
–0.7
AsO
3
H
–0.3.
.
HOFe
2
<
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0
50
100
150
200
250
300
350
400
450
500
[As(V)]ads (μmol/m
2
)
[As(V)]aq (μM)
Fig. 4.
Arsenate adsorption modeling of Dixit and Hering (2003) FH system at 0.03 g/L: (a) pH adsorption edges at four different
total As(V) loadings, (b) surface speciation example for 1.69
m
mol/m
2
total As(V) loading, and (c) adsorption isotherm at
pH 4. Symbols denote experimental data and lines model simulations with parameters described in table III.
adjacent doubly-coordinated site present on the (010)
face through H-bonds (Salazar-Camacho and Villalo-
bos 2010). This complex is dominant throughout the
pH range (
Fig. 4b
), but its protonated version becomes
relatively important at pH values below 5, and thus
predominates in the isotherm at pH 4 (
Fig. 4c
) above
10
m
M aqueous As(V) (not explicitly shown).
Previous studies suggest that arsenate adsorption
on iron oxides occurs via formation of bidentate
surface complexes, which may be protonated at low
pH values and deprotonated at intermediate to high
pH (Sherman and Randall 2003, Stachowicz
et al.
2006). In these, the presence of monodentate surface
complexes was considered to be a minor contribution.
However, a recent spectroscopic study by Loring
et
al.
(2009) con±rms that monodentate coordination is
the predominant form of arsenate adsorbed on iron
oxides. These authors also suggest that arsenate can
act as a H-bond acceptor or donor, depending on
the pH of the system, with adjacent surface groups
(>Fe
2
OH or >FeOH groups). At low pH values the
arsenate surface complex will be protonated and
acts as H-bond donor. From intermediate to high pH
values the arsenate complex will be deprotonated,
becoming a H-bond acceptor to the closest surface
sites (
Fig. 5
). H-bond formation on the arsenate com-
plexes increases their stability and favors arsenate
adsorption across the whole pH range.
Figure 6
shows the optimal simulations for the
Raven system. Again, the ±ts are quite acceptable but
a bit off in comparison to those for goethite. In this
system, the deprotonated complex predominates in
the isotherm at pH 9.2 (
Fig. 6
, not explicitly shown).
The model underestimates arsenate adsorption at
the lower pH values and higher loadings for both
systems. The explanation is not clear but may be
M. Villalobos and J. Antelo
148
Fig. 5
. Molecular structures of face (010) and of modeled As(V) surface complex bound to
singly- and doubly-coordinated sites
related to a larger uncertainty in the experimental
data reported under these conditions.
Figure 6c
shows a comparison of pH adsorption
edges between both systems for a very similar total
As(V) loading normalized by surface area (0.32-
0.34
m
mol/m
2
), and in both cases the lowest loading
analyzed. It is interesting to note that the edge for the
Dixit system where arsenate desorbs appears several
pH units earlier than that for the Raven system, des-
pite the fact that their SSAs are very similar (989
vs
.
840 m
2
/g), and all modeling parameters are also very
similar. The model, although slightly underestimating
arsenate adsorption at the higher pH values, predicts
quite well this difference in behavior. The explanation
for the large difference in both systems is that, despite
very similar total As(V)/>FeOH sites ratios (=0.021-
0.022) between both FH systems, the SSA of FH is
so high that at any particular pH, because the solids
concentrations used in each system are very different,
the aqueous OH
/>FeOH sites ratio also varies dra-
matically. The aqueous OH
/>FeOH sites ratio at any
given pH is much lower for the Raven system (2 g/L
vs
.
0.03 g/L for Dixit) and OH
ions exert less competition
against As(V) for the surface, and thus As(V) desorbs
at a later pH than in the Dixit system. This important
solids concentration effect on adsorption observed in
FH is unnoticeable in other mineral surfaces with much
lower SSA, such as goethite.
Arsenate adsorption on both FH systems was
described with the parameter set of
table III
.
The af±nity constants for the protonated surface
complex are slightly higher than those found for
the deprotonated complex, as expected; however,
the values for the protonated complex showed the
largest uncertainty between FH samples (one log
unit difference,
table III
). The reason for this is
that the isotherm data at low pH reported for both
systems showed high variability (
Figs. 4c
and
6b
).
Also, the Raven adsorption data in general showed
large uncertainties in the low-pH area (see arrows
in
Figs. 6a
and
b
). The larger experimental uncer-
tainties under low pH conditions and high As(V)
loadings makes it dif±cult for the model to provide
better ±ts, as was mentioned above.
The values for the af±nity constants obtained in
the As(V) adsorption simulations for both Dixit and
Raven FH systems are very close to, or within those
found for goethite (
Table III
). The agreement bet-
ween the af±nity constants for FH and for goethite is
better than that found by Antelo
et al.
(2010) in their
analysis of phosphate adsorption on FH nanoparticles
using the CD-MUSIC model. In their study they
found af±nity constants for FH between two and three
orders of magnitude lower than those of goethite,
although we should note that they considered forma-
tion of bidentate phosphate surface complexes. The
A UNIFIED SURFACE STRUCTURAL MODEL FOR FERRIHYDRITE
149
Fig. 6.
Arsenate adsorption modeling of Raven
et al.
(1998) ferrihydrite system at 2 g/L: (a) pH adsorption edges at three different
total As(V) loadings, (b) adsorption isotherms at pH 4.6 and 9.2, and (c) comparison of pH adsorption edge with Dixit and
Hering (2003) system for a similar total As(V) loading. Symbols denote experimental data and lines model simulations with
parameters described in
table III
. The arrow indicates a data point calculated from the corresponding isotherm (a), or pH
adsorption edge (b).
0.2
0.25
0.3
0.35
c)
a)
c)
3
4
5
6
7
8
9
10
11
12
[As(V)]ads (μmol/m
2
)
pH
0.34 umol/m2 - Dixit - 0.03 g/L
0.32 umol/m2 - Raven - 2 g/L
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
3
4
5
6
7
8
9
10
11
[As(V)]ads (μmol/m
2
)
pH
0.32 umol/m2
0.95 umol/m2
15.83 umol/m2
Total As(V) loading:
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
0
5
10
15
20
25
[As(V)]ads (μmol/m
2
)
[As(V)]aq (mM)
pH 4.6
pH 9.2
close agreement found in the present study supports
the use of the goethite surface structure as a proxy for
FH nanoparticle surfaces, as an acceptable approach
for modeling ion adsorption on this nanomineral.
CONCLUSIONS
Proton charging data for a set of eight ferrihydrite
(FH) preparations reported in the literature showed
widely variable mass-normalized values. Simulation
of the data through surface complexation modeling
allowed determination of the optimal speci±c surface
area values (SSA) exposed in suspension. Norma-
lizing proton adsorption data by these surface area
values provided surface charge congruency behavior
among FH samples, and in this manner, the surface
proton charge behavior per mass of any FH may be
used as a good diagnostics of the actual SSA expo-
sed in suspension. Despite the fact that nanoparticle
aggregation has been demonstrated to occur in sus-
pensions of 5-nm FH samples at pH values above 5
(Gilbert
et al.
2009), most or all surface area appears
to be available for proton, electrolyte, and As(V)
adsorption in the range of pH values reported (
ca.
4-11). Feshly-prepared FH samples showed the
highest SSA values (between 840 and 1120 m
2
/g),
corresponding to particle diameters of 1.5 to 2 nm,
whereas aged samples showed lower SSA values
(650 and 337 m
2
/g), corresponding to particle dia-
meters of 2.6 to 5 nm. We suggest the actual point
of zero net proton charge (PZNPC) for ferrihydrite
is 8.8, regardless of particle size. The lower values
reported for fresh FH samples are probably related
M. Villalobos and J. Antelo
150
to inefFcient exclusion of surface-bound carbonate
from CO
2
entrained, at the extremely high surface
area exposed on this nanomineral. Small amounts of
CO
2
entrained may cause underestimation of surface
proton charge and thus of the PZNPC.
The ±H surface may be successfully macroscopi-
cally modeled as composed exclusively of goethite
face (010), with a high density of singly-coordinated
>±eOH groups (8.8-9.1 sites/nm
2
), and no triply-
coordinated groups present. The optimized values of
all surface afFnity constants obtained for ±H were
very similar to those previously obtained for goethite
on singly-coordinated >±eOH sites, supporting the
above crystal-face model proposed, and indicating
that the goethite surface structure is a good proxy to
explain the adsorption behavior of ±H nanoparticles.
These results are highly relevant for environmen-
tal geochemical work, especially for aquatic systems
and hydromorphic soils, where ±H is present, be-
cause they allow in a simpliFed manner an accurate
prediction of the ±H surface reactivity based on that
of goethite, and thus of the adsorption behavior of
relevant species in these environments.
ACNOWLEDGEMENTS
J.A. would like to thank Vidal Barrón for the
fruitful discussions on the calculations of site densi-
ties for the different goethite faces. The authors are
grateful to Carlos Salazar-Camacho for preparing
fgure 5
. M.V. appreciates the Fnancial support from
PAPIIT Project IN112007 and I±S Project W/3912.
J.A thanks the Ministerio de Educación y Ciencia
for the Fnancial support under the research project
CTM2008-03455.
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