Journal of Hazardous Materials 244–245 (2013) 21–28
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Journal of Hazardous Materials
journal homepage: www.elsevier.com/locate/jhazmat
Molecular dynamics simulation of the diffusion of uranium species in clay pores
Liu Xiao-yu a , Wang Lu-hua a , Zheng Zhong a , Kang Ming-liang a , Li Chun a,b , Liu Chun-li a,∗
a
Beijing National Laboratory for Molecular Sciences, Radiochemistry and Radiation Chemistry Key Laboratory for Fundamental Science, College of Chemistry Molecular Engineering,
Peking University, Beijing 100871, China
b
State Nuclear Security Technology Center, Beijing 100037, China
h i g h l i g h t s
We investigated the diffusion behavior of Uranium species in montmorillonite pores using MD technique.
Our results indicated that different uranium species have distinct diffusion coefficients in clay pores.
The negative charged uranium complexes must be addressed in the safety assessment for geological disposal of nuclear wastes.
a r t i c l e
i n f o
Article history:
Received 25 August 2012
Received in revised form 1 November 2012
Accepted 13 November 2012
Available online 21 November 2012
Keywords:
Uranyl
Species
Diffusion
Molecular dynamics
Montmorillonite
a b s t r a c t
Molecular dynamics simulations were carried out to investigate the diffusive behavior of aqueous uranium species in montmorillonite pores. Three uranium species (UO2 2+ , UO2 CO3 , UO2 (CO3 )2 2− ) were
confirmed in both the adsorbed and diffuse layers. UO2 (CO3 )3 4− was neglected in the subsequent analysis due to its scare occurrence. The species-based diffusion coefficients in montmorillonite pores were
then calculated, and compared with the water mobility and their diffusivity in aqueous solution/feldspar
nanosized fractures. Three factors were considered that affected the diffusive behavior of the uranium
species: the mobility of water, the self-diffusion coefficient of the aqueous species, and the electrostatic
forces between the negatively charged surface and charged molecules. The mobility of U species in the
adsorbed layer decreased in the following sequence: UO2 2+ > UO2 CO3 > UO2 (CO3 )2 2− . In the diffuse layer,
we obtained the highest diffusion coefficient for UO2 (CO3 )2 2− with the value of 5.48 × 10−10 m2 s−1 , which
was faster than UO2 2+ . For these two charged species, the influence of electrostatic forces on the diffusion of solutes in the diffuse layer is overwhelming, whereas the influence of self-diffusion and water
mobility is minor. Our study demonstrated that the negatively charged uranyl carbonate complex must
be addressed in the safety assessment of potential radioactive waste disposal systems.
© 2012 Elsevier B.V. All rights reserved.
1. Introduction
The transport of uranium in the environment as a result of
human activities, such as mill tailings, mining, nuclear tests and
potential geological disposal of waste, is of great concern. The
diffusion and sorption of uranium in/onto a variety of natural
substrates have been experimentally studied for decades. These
minerals include clays [1–3], granite [4–6], iron oxy-hydroxides
[7–9] and zeolites [10,11]. Some novel materials have also been
synthesized for removal of uranium ions from contaminated media,
and its separation/extraction from solutions [12–14]. According to
recent spectroscopic and microscopic studies, the linear uranyl ion
(UO2 2+ ) is the predominant uranium species in the micro pores of
contaminated sediments from the Hanford Site [15,16] and in the
oxic groundwater system [17]. These studies implied that diffusion
∗ Corresponding author. Tel.: +86 10 62765905; fax: +86 10 62765905.
E-mail address: [email protected] (C.-l. Liu).
0304-3894/$ – see front matter © 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.jhazmat.2012.11.031
and accumulation of uranyl species in the micro pores play a significant role in the future fate of these species in the contaminated
natural media. Furthermore, Kerisit and Liu addressed the importance of ions diffuse in the micro pores, i.e., diffusion controls the
rates of reactant supply and product removal, thereby affecting the
local concentration gradient of chemical compositions, which, in
turn, influence further reactions and diffusion, thus leading to a
complex coupling between diffusion and geochemical and biogeochemical reactions [18].
The diffusion of uranium in various materials has been investigated to assess the risks associated with radioactive waste disposal
[5,6,19]. Furthermore, the obtained diffusion coefficients were used
to model the transport of uranium in subsurface sediments [20–23].
However, the uranyl self-diffusion coefficients, which are a critical
parameter, are inconsistent in the literature, and values ranging
from 0.426 to 0.759 m2 s−1 have been experimentally obtained in
solutions by various researchers [24–28]. In addition, due to the
coexistence of various U(VI) aqueous species in solution [29], it is
difficult to determine the self-diffusion coefficients for each uranyl
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X.-y. Liu et al. / Journal of Hazardous Materials 244–245 (2013) 21–28
species [30]. To date, the majority of experimental and modeling
diffusion studies have therefore assumed that all uranyl species
had the same diffusion coefficient [5,6,21]. To the best of our
knowledge, only Liu et al. have used a species-based model to investigate the transport properties of uranyl species [22,31]. In parallel
works, Kerisit and Liu used molecular dynamics (MD) simulations
to determine the self-diffusion coefficients of aqueous uranyl carbonate species (Mx UO2 (CO3 )y 2+2x−2y with M = Mg, Ca, or Sr) [18],
and they subsequently investigated the diffusion/adsorption of
Ca2 UO2 (CO3 )3 and of some of its constituent species, i.e., UO2 2+ ,
CO3 2− , and UO2 CO3 , in feldspar nanosized fractures [32]. Their
results indicated that (a) there are various diffusivities for different
U species; (b) the presence of the feldspar surface decreases the
diffusion coefficients of all the species considered in their work;
(c) the rate of decrease in the diffusion coefficients with decreasing
distance from the surface is greater for larger adsorbing species.
Molecular dynamics simulations have been used to obtain
solute dynamics properties for aqueous solution [18], structural
and dynamic properties for bulk water [33,34], and mineralwater interfaces [35–37]. Several works have also focused on the
influence of variable pore sizes and pore surface charges on the selfdiffusion coefficient of various species in porous media [35,38–40].
Our study is a parallel work to accompany the newly developing
diffusion methodology, namely the species-based diffusion concept. The overall purpose of this work is to provide the diffusion
coefficients for various uranyl species in montmorillonite pores
using the MD technique with an atomic-level insight. In addition,
our results will determine which uranyl specie is the most dangerous contaminant in subsurface environments. A prototypical
clay mineral, montmorillonite, was used to model the clay pores,
not only because of its prevalence in the environment, but also
its potential application as a barrier/backfill material in geological
repositories for nuclear wastes [41].
2. Computational methods
2.1. Geometry of the MD system
In our model, montmorillonite atomic coordinates were fixed
on the basis of the pyrophyllite structure reported by Bickmore
et al. [42], and this mineral structure was successfully used for
molecular dynamics simulations conducted by Bourg and Sposito
[43,44]. The negative structure charge in our model resulted from
the isomorphic substitutions of Al3+ by Mg2+ that randomly scattered only in the octahedral sheet, using an exclusion rule so that
two substitutions could not occur on two adjacent sites. The average unit cell formula is Na0.33 [Si8 ][Al3.67 Mg0.33 ]O20 (OH)4 , which
corresponds to a low-charge montmorillonite (0.33 e/unit cell). The
interlayer water structure is 11 water molecules per unit cell with
respect to 2 water layers, which is in agreement with XRD results on
water-saturated compacted Na-smectite at montmorillonite partial dry density between 1.0 and 1.5 kg/dm3 [45,46]. Charge deficits
were equilibrated by adding Na+ cations. Half of the total charge
was compensated by sodium cations in the interlayer, whereas the
other half was randomly placed in the pore region. The simulation is carried out for U/Ca/C compositions with 10/10/20 atoms
in the simulation cell, which approximately results in bulk concentrations of 0.05, 0.05 and 0.10 mol dm−3 , respectively. Prior to
the simulation, z-dimension of the cell was determined by equilibrating the system for 1000 ps at 298.15 K and constant gauge
pressure Pz = 0 (NPT ensemble simulation; the cell x and y dimensions were fixed, but the z-dimension was allowed to vary). Then,
the z-dimension of the cell that was obtained from the equilibration simulation was employed for the following 5000 ps production
simulation (NVT ensemble), which is called the primary simulation
Fig. 1. A snapshot of the MD simulation cell. This figure shows a uranyl containing
aqueous solution confined in a 36 Å wide montmorillonite pore between parallel
clay surfaces, with U (blue), C (gray), Na (purple), Ca (green), Cl (light green), O (red)
and H (white) atoms in the pore region and Si (yellow), Al (violet) in the clay mineral
structure. The clay surface on the right side is a periodic image of the clay surface
on the left side. (For interpretation of the references to color in this figure legend,
the reader is referred to the web version of this article.)
in this study. The periodically replicated simulation cell (Fig. 1)
contained two montmorillonite layers with an interlayer region
composed of 20 × 10 × 2 unit cells, and an aqueous pore space contained 11,120 water molecules, 66 sodium ions, 20 carbonate ions,
10 uranyl, and 10 calcium ions. The periodic conditions of the system in the production simulation were as follows: 104.04 × 89.84 Å
for the x y plane, z = 61.4 Å. A comparative simulation cell that did
not contain clay or compensative ions in solution was also built to
investigate the influence of the clay surfaces on the uranyl species
and their diffusivities.
2.2. Potential and code
The potential parameters for the montmorillonite, aqueous calcium and sodium ions in our model were taken from the CLAYFF
parameter set [47]. The potential parameter for UO2 2+ derived
from Guilbaud and Wipff [48,49] has been used to model a variety
of aqueous uranyl complexes [50–52] and their adsorption onto
clay basal planes [51,53–55]. Greathouse and co-workers modified the carbonate parameters in Ref. [51] to obtain satisfactory
configurations of uranyl carbonate complexes, and employed the
SPC water model in their studies [53,54]. Recently, Kerisit and Liu
successfully assembled a consistent set of potential parameters for
modeling alkaline-earth uranyl carbonate species in solution [18].
In this assembled model, the uranyl potential parameters were
from Guilbaud and Wipff [48,49], the carbonate parameters were
from Paveseet et al. [56], the calcium parameters were taken from
de Leeuw and Parker [57] and the SPC/E water model was used.
Selecting an adequate water model is critical for modeling the diffusion of aqueous species, because a rationally calculated water
diffusivity is the basis for obtaining a reasonable solute diffusion
coefficient. MD studies related to the aqueous diffusion problem
preferred the SPC/E model, which could more accurately reproduce the water diffusivity than the SPC water model [18,36,38,58].
Therefore, to make our results comparable with previous works, we
X.-y. Liu et al. / Journal of Hazardous Materials 244–245 (2013) 21–28
employed the same potential parameters taken from Greathouse
et al. [53,54] for the aqueous species (carbonate, uranyl) and the
extensively verified CLAYFF [59] for the montmorillonite and aqueous calcium ion, but SPC/E water model rather than the SPC water
model.
Discovery Studio software (Accelrys, Inc., San Diego, CA) was
used to build the simulation cells and to visualize results. All simulations were carried out with the LAMMPS software package [60].
The constant NVT (number, volume, temperature 298.15 K) or NPT
(number, pressure 0 atm, temperature 298.15 K) ensembles were
used with thermostat and barostat relaxation times of 0.1 ps and
0.5 ps, respectively. The electrostatic forces were calculated by
means of the Ewald summation method. The Verlet leapfrog integration algorithm was used to integrate the equations of motion
with a time step of 0.001 ps. All simulations were run for 5000 ps
(NVT) after an equilibration period of 1000 ps (NPT). This equilibration time was sufficient for our simulation to reach equilibrium.
2.3. Diffusion equation
The diffusion coefficient for the species of interest was determined using the well-known Einstein relationship [61]:
2Dt =
1
|r (t) − ri (0)|2 n i
(1)
where |ri (t) − r1 (0)|2 is the mean-square displacement (MSD) of a
diffusing molecule, ri (t) denotes the position of a diffusing molecule
i at time t, and n is the dimensionality of the system in which
the diffusion is considered. Unless specifically noted, all the diffusion coefficients computed in this work are those in the direction
parallel to the clay pore surfaces, and therefore, n equals 2.
The water diffusion coefficients were determined from the
oxygen atom positions, and U species diffusion coefficients were
calculated from the uranium coordinates. As mentioned above, one
goal of this work was to compare the diffusion of U species in
clay pores with that in aqueous solutions, and therefore, we followed the same protocol of Kerisit and Liu [18]: a configuration
was recorded every 0.2 ps, and 101 trajectories namely 20 ps length
23
were used to calculate the diffusion coefficients for the species of
interest.
3. Results and discussion
3.1. Distribution of Ions in the pore space
General information about the adsorption of ions was obtained
from U, C, Ca, and Na atomic density profiles (Fig. 2). The red vertical lines in Fig. 2 represent the coordinates of the most external
oxygen atoms in the montmorillonite layer. Montmorillonite was
simplified (only the external oxygen atoms are shown) because
we focus on the distribution of ions in the pore region, not the
clay structure. As indicated in Fig. 2, uranium adsorbed onto montmorillonite formed two prominent peaks at 29.2 Å and 58.4 Å,
which are approximately 4.5 Å away from the most external oxygen
atoms. This distance is slightly greater than the 4.0 Å obtained by
Greathouse et al., whose simulation contained less ion species and
used the SPC water model [53]. These two well-defined peaks are
considered to be an adsorption layer. Ions beyond these layers are
identified as being diffuse. Therefore, the pore space was divided
into three parts along the z-axis, namely two adsorbed layers and
one diffuse layer (30.6 Å < z <56.7 Å). As expected, the atomic density profile of uranium in the diffuse region (z = 30.6–56.7 Å) was
featureless with no peaks. However, there was a pronounced broad
shoulder between 31.0 Å and 38.0 Å. This shoulder can be assigned
to the formation of uranyl-carbonate complexes (see below). Note
that there is no other shoulder in the corresponding position, and
this asymmetry most likely originated from insufficient simulation
time.
In contrast to the uranium density profile, the C, Ca and Na ions
did not exhibit the same prominent peaks or well symmetric profiles (Fig. 2). Bourg et al. [44] and Tournassat et al. [58,62] presented
sharp and easily identified adsorbed peaks of sodium and calcium ions onto the montmorillonite basal planes. Nevertheless, the
atomic density profiles in this study for these two cations are more
diffuse. A possible reason for this discrepancy is the insufficient
simulation time, i.e., 5000 ps in our work vs 15,000 ps and 50,000 ps
in Tournassat et al. and Bourg et al., respectively. Additionally,
Fig. 2. Atomic density profiles for uranium, carbonate, calcium and sodium. The red vertical lines represent the coordinates of the most external oxygen atoms in the
montmorillonite layer. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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X.-y. Liu et al. / Journal of Hazardous Materials 244–245 (2013) 21–28
Fig. 3. Charge density profile within clay pore space as a function of z-coordinates.
the more complicated uranyl-carbonate–sodium ions–calcium ions
system that contains competition between the uranyl ions and
other cations for adsorbing to the clay surfaces may lead to the
difference as well.
In Fig. 2, a remarkable fraction of carbonates were present in the
region from 31.0 Å < z < 38.0 Å, and simultaneous shoulders of the
three cations were also present in this region. Carbonate is a wellknown ligand for uranyl and calcium ions. Consequently, these
cations formed complexes with the carbonate ligands, and these
charged species tend to be repelled by the negatively charged clay
surfaces and some free carbonates. These free carbonates attract
positively charged ions around them to maintain local electric neutrality. This can be verified by the charge density profile in Fig. 3.
This charge density profile is the charge density within the clay
pore spaces along z-direction. We integrated all the charged ions
within a slab with a thickness of 0.1 Å and converted the units to
C m−3 . Although C, Ca and Na are diffuse and poorly symmetrical
in the atomic density profiles, there are no shoulders in Fig. 3, and
the symmetry is considerably better. To understand the adsorption
in a complicated system, especially in the presence of ions that can
form complexes, in our opinion, not only should the atomic density profile, which provides information on the overall position of
the ions, be investigated but the charge density profile, which can
provide insight from the electric neutrality view within the pore
space, should also be considered.
In addition, comparing the first peaks of water with the
absorbate peaks in atomic density profile is a conventional method
to identify whether the formed surface complex is an inner-sphere
or outer-sphere surface complex [53,54]. There were intervening
water molecules between the first uranium atom peaks and the
siloxane surface, which implies the formation of an outer-sphere
complex (Fig. 4).
To investigate the species-based diffusion, we first analyzed the
uranyl-carbonate–calcium complexes that would form, and then
calculated their proportion during the simulation. Two parameters
were used to evaluate the possible complexes: 4.5 Å for the distance between the U atom in the uranyl species and calcium, and
3.1 Å between U and the C in carbonate. This protocol is similar to
the conventional radial distribution function (RDF), which counts
the numbers of atoms of interest that are present in a sphere with a
specific radius (4.5 Å for Ca and 3.1 Å for C). The position of the uranium atoms from each trajectory is considered to be the origin of the
sphere. For example, if there are two carbon atoms located less than
a distance of 3.1 Å from the central uranium atom, a bicarbonate
uranyl complex is proposed. Unexpectedly, the calculations did not
Fig. 4. Atomic density profiles for uranium (in blue), water (in red). (For interpretation of the references to color in this figure legend, the reader is referred to the web
version of this article.)
reveal the presence of uranyl-carbonate–calcium complexes, but
only uranyl (UO2 2+ ) and three other uranyl-carbonate complexes
(UO2 CO3 , UO2 (CO3 )2 2− and UO2 (CO3 )3 4− ). This result is consistent
with the radial distribution function calculation result (not shown
here), which exhibited a sharp peak at 2.84 Å for the carbon in carbonate and no apparent peak up to 4.5 Å for calcium. The results are
shown in Fig. 5 and Table 1. Approximately 90% of the uranyl species
are in the adsorbed layer of the clay pores, and UO2 2+ is the predominant species. Nevertheless, the neutral UO2 CO3 species prevails in
the aqueous solution. These two counterpart simulations demonstrate that the influence of the negatively charged clay surfaces on
the distribution of uranyl species is remarkable.
3.2. Diffusion of water
The distribution and self-diffusion of water provide unique
insights into the effect of water on the diffusion of uranyl species.
The water density was calculated based on the water oxygen position and the results are presented in Fig. 4. This figure reveals the
presence of a first adsorbed layer at a distance approximately 2.98 Å
from the topmost oxygen atoms in the clay. Another distinct peak
and a vague peak can also be observed. The water density fluctuations converge to the bulk density at 10–11 Å away from the
surface. In Fig. 4, the sharply adsorbed water layers of the first
group are primarily from electrostatic forces between the surface
hydroxyls groups and water molecules. The broader and shorter
peaks next to the first peaks indicate a weaker binding between
the clay basal plane and the second layers with respect to the first
group layers. This result leads the water diffusivity to decrease as
water molecules approach the surface because they experience an
increasing binding strength (see below).
From the trajectories, we first extracted each of the water
molecular self-diffusion coefficients in the directions parallel to
the montmorillonite basal plane, which would be referred to the
pore diffusion coefficient, Dp . Then, we averaged the obtained diffusion coefficients whose heights are approximately in the same
region, i.e., some water molecules diffuse into the adsorbed layer
z < 30.6 Å or z > 56.7 Å during a MSD calculation interval (20 ps in
our case). Finally, the averaged water diffusion coefficients in the
pore space at the adsorbed and diffuse layers are shown in Table 2.
Water has been experimentally used as a tracer to determine the
diffusion properties within intra-grain clay pore regions using neutron spin echo by Marry et al. [36]. The reported experimental value
X.-y. Liu et al. / Journal of Hazardous Materials 244–245 (2013) 21–28
25
Fig. 5. Atomic density profiles for various uranium species.
of D (can be considered as Dp of the adsorbed layer in our case)
is 2.8 ± 0.3 × 10−10 m2 s−1 , and the authors also carried out serial
MD simulations to obtain the values of 2.69–5.80 × 10−10 m2 s−1
depending on the various simulation conditions. The results in this
study are 1.5–2.5 times greater than the values reported by Marry
et al. [35,36]. This result is within our expectations, because the
pore width used by Marry et al. was 12.2 Å, which is considerably
less than the 36 Å used in our simulation. Additionally, Kerisit and
Liu reported that the diffusivity of water molecules decreased as
they approach the surface [32,37,38]. If we consider the region of
3–9 Å in Kerisit and Liu’s model [32] as the adsorbed layer and >9 Å
as the diffuse layer in our case, the water diffusivity would be in
the range of the results reported in Ref. [32] (Table 2).
3.3. Diffusion of uranium species
As discussed above, various uranium species formed in our simulation system and they existed in both the adsorbed layer and
the diffuse layer. Therefore, we need to determine if the same uranium species have the same diffusion coefficient in the adsorbed
layer and diffuse layer, or if different species exhibit the same
diffuse behavior in the same layer. Due to the ligands exchange
Table 1
Percentage of uranyl species.
Adsorbed layera
Diffuse layerb
Species
UO2 2+
UO2 CO3
UO2 (CO3 )2 2−
UO2 (CO3 )3 4−
UO2 2+
UO2 CO3
UO2 (CO3 )2 2−
UO2 (CO3 )3 4−
Proportionc
63.3%
12.7%
12.1%
0.0%
7.8%
0.5%
3.6%
0.0%
51.3%
32.9%
0.0%
d
Aqueous
15.8%
a
b
c
d
Adsorbed layer is within the external siloxane surface plus 6.0 Å (z < 30.6 Å or z > 56.7 Å).
Diffuse region is greater the imaginary “external adsorbed planes” (30.6 Å < z < 56.7 Å).
Results from the primary simulation that modeled the uranyl species diffuse in the clay pores.
Results of comparative simulation cell without clay and compensative ions in solution.
Table 2
Diffusion coefficients of uranyl species and water in pore space/aqueous solution.
Adsorbed layera
Diffuse layerb
UO2 2+
UO2 CO3
UO2 (CO3 )2 2−
D
Dd
3.6
0–5.6
2.5
0–4.0
1.4
De
Df
Aqueous solution
7.6
6.7
9.2
8.1
Species
c
a
b
c
d
e
f
5.5
7.5
H2 O
6.6
3.4–22.4
UO2 2+
UO2 CO3
UO2 (CO3 )2 2−
H2 O
4.2
5.6–7.8
3.0
4.0–7.4
5.5
24.2
22.4–25.5
28.3
27.9
This work, adsorbed layer is within the external siloxane surface plus 6.0 Å (z < 30.6 Å or z > 56.7 Å).
This work, diffuse region is greater than the imaginary “external adsorbed planes” (30.6 Å < z < 56.7 Å).
Primary simulation of this work, units are 10−10 m2 s−1 .
Estimated from Ref. [32], and we considered 3–9 Å in Ref. [32] as the adsorbed layer.
Obtained by Kerisit and Liu results in aqueous solution, units are 10−10 m2 s−1 [18].
Comparative simulation in this work without clay and compensative ions.
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X.-y. Liu et al. / Journal of Hazardous Materials 244–245 (2013) 21–28
reaction, the uranium atom is hardly present in a unique complex
form during the entire simulation run, and the most common phenomenon is the transformation between similar complexes, e.g.,
UO2 2+ /UO2 CO3 . Therefore, it is difficult to determine the diffusion
coefficient based on the U species. Therefore, during a calculation
interval (20 ps, 101 trajectories obtained for a calculation), the complex stoichiometric number was allowed to vary ±5%. For instance,
if UO2 CO3 is present in 98 trajectories from 101 consecutive trajectories while UO2 2+ exists in the other 3 trajectories, the complex
stoichiometric number would be UO2 (CO3 )0.97 , and we also assign
the calculated diffusion coefficient during this interval to UO2 CO3 .
Following these tactics, the diffusion coefficients for each of the
formed U complexes in the adsorbed layer/diffuse layer and aqueous solution were calculated (Table 2). The corresponding diffusion
coefficients for the U species in aqueous solution/feldspar nanosized fractures and the water diffusion coefficients obtained by
Kerisit et al. [18,32] are also listed in Table 2. The different simulation protocols employed for the last two rows in Table 2 are
briefly discussed here. 10 uranyl ions, 10 calcium ions and 20 carbonates were mixed with 11,120 water molecules in our case, and
the coefficients were calculated using the rule mentioned above.
However, the uranyl species diffusivities in the work of Kerisit
et al. were calculated from elaborately constructed simulation cells
that contained only one species per cell. Despite the various values in the last two rows of Table 2, the diffusivities of the uranyl
species have the same sequence: UO2 2+ > UO2 CO3 > UO2 (CO3 )2 2− .
Compared to the diffusion of U species in aqueous solution, the diffusion coefficients in clay pores are considerably lower. The diffuse
behavior of uranium species was primarily influenced by three factors in our case: the mobility of water, the self-diffusion coefficient
of the aqueous species and the electrostatic forces between the
negative surface and the charged molecules. As discussed above,
the water mobility in the adsorbed layer is slower than that in the
diffuse layer. Our results reveal a general rule that U species diffuse
faster in the bulk region than in the region near the clay surface.
This result can be attributed to the difference in water mobility, i.e.,
6.64 × 10−10 m2 s−1 in the adsorbed layer vs 24.17 × 10−10 m2 s−1 in
the diffuse layer. Comparison of the U species mobility in the pores
of montmorillonite and feldspar in Table 2 indicates that even the
neutral charged nanosized feldspar surfaces indeed decrease the
diffusivities of U species [32]. In this work, the negatively charged
clay surfaces of the montmorillonite appear to decrease the diffusivities more significantly. Also note that is that the mobility of
U species in the adsorbed layer of the montmorillonite decreases
as follows, UO2 2+ > UO2 CO3 > UO2 (CO3 )2 2− . This sequence is not
expected because the negatively charged species is expected to
move faster than the positively charged species near a negative
clay surface. One reason for this behavior may originate from the
difference in the self-diffusion coefficient, which was addressed
by Kerisit et al. [18]. Their calculated self-diffusion coefficients for
uranyl species have a general linear dependence on the inverse of
the equivalent spherical radius. In the adsorbed layer, the water
density is approximately two-times greater than that in the bulk
region, and a more ordered water structure will result in a higher
activation energy for larger aqueous species to diffuse. Kerisit
et al. recently confirmed that among the uranyl carbonate species
they modeled, the largest species, Ca2 UO2 (CO3 )3 , decreases more
quickly than that of the other species. Their MD simulations suggested that the relative effect of the mineral surface on the diffusion
of aqueous species increases with the size of the species. Therefore,
we believe that the mobility of water and the self-diffusion of U
species govern the diffuse of U species in the adsorbed layer, and
the electrostatic interaction is less important. Nevertheless, this
rule may not be applicable in the diffuse region. In this area, water
performs like bulk water, which means that the influence of water
mobility on the diffusion of the solute may be negligible and only
self-diffusion and electrostatic forces need to be considered. We
obtained the highest diffusion coefficient for UO2 (CO3 )2 2− , and it
is greater than that of UO2 2+ in the diffuse layer. Obviously, the
stronger attraction between UO2 2+ and clay surface significantly
decreases the mobility of positively charged species. The electrostatic force in this area may be overwhelming, whereas the
influence from self-diffusion is minor. Due to the negative charge
and the bulk-like water, it is reasonable to assume that the diffusion behavior of UO2 (CO3 )2 2− is similar to the aqueous solution.
In other words, this coefficient can be quantitatively comparable
to that of UO2 (CO3 )2 2− in aqueous solution. From Table 2, the
two diffusion coefficients are essentially equal. If we divide the
UO2 (CO3 )2 2− coefficient in the adsorbed and diffuse layers by the
water diffusion coefficient in the corresponding layers, the obtained
values are almost the same. This result indicates that the mobility
of UO2 (CO3 )2 2− is proportional to the mobility of water in the layer
where they diffuse, and that the negatively charged species diffuse
in the montmorillonite pores are primarily influenced by the water
mobility and their self-diffusion, not the electrostatic force from
the charged clay surface.
4. Conclusions
Molecular dynamics simulation was carried out to investigate
the diffusion behaviors of uranyl carbonate species in montmorillonite pores. In particular, the pore diffusion coefficients of
these species were calculated in terms of the developing speciesbased diffusion model. A variety of uranyl carbonate species
were identified in our simulation as the basis for future discussion on the species-based uranyl diffusion. Three predominant U
species (UO2 2+ , UO2 CO3 , UO2 (CO3 )2 2− ) were confirmed in both
the adsorbed and diffuse layers, whereas UO2 (CO3 )3 4− was scarce
and consequently neglected. The species-based uranyl diffusion
coefficients in montmorillonite pores were then calculated. The
results indicated that the mobility of water, the self-diffusion coefficient of the aqueous species, and the electrostatic forces between
the negatively charged surface and the charged molecules influence the diffusion of uranium species. However, these three factors
exhibited different significances depending on the charge of species
and layers where they are located. In the adsorbed layer, all the
U species are primarily influenced by the compact water layer
and their self-diffusion. However, in the diffuse layer, the electrostatic force is determinative. Interestingly, according to the
calculations, the influence from the water mobility on the diffusion of the negatively charged species UO2 (CO3 )2 2− is remarkable,
and UO2 (CO3 )2 2− is the most mobile U species in our calculation.
In summary, in terms of the species-based diffusion concept, this
study indicates that (1) various U species have different diffusive
behavior; (2) the charged montmorillonite surfaces decrease the
mobility of these species with respect to their aqueous diffusivities and influence the mineral surface on the diffusion of aqueous
species increases with the species size within the adsorbed layers;
and (3) the negatively charged species is the most dangerous contaminant in the safety assessment of potential radioactive waste
disposal systems with respect to their neutral or positively charged
counterparts.
Acknowledgements
We thank the financial support from the Special Foundation
for High-level Radioactive Waste Disposal (2007-840, 2012-851)
and National Natural Science Foundation of China (NSFC) (nos.
11075006 and 1026010). We are grateful to Dr. Christophe Tournassat (BRGM, French Geological Survey, Orléans, France) for his
kind pre-review on this manuscript.
X.-y. Liu et al. / Journal of Hazardous Materials 244–245 (2013) 21–28
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