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Atomistic simulations of cation hydration in sodium and calcium montmorillonite
nanopores
Guomin Yang, Ivars Neretnieks, and Michael Holmboe
Citation: The Journal of Chemical Physics 147, 084705 (2017); doi: 10.1063/1.4992001
View online: http://dx.doi.org/10.1063/1.4992001
View Table of Contents: http://aip.scitation.org/toc/jcp/147/8
Published by the American Institute of Physics
THE JOURNAL OF CHEMICAL PHYSICS 147, 084705 (2017)
Atomistic simulations of cation hydration in sodium and calcium
montmorillonite nanopores
Guomin Yang,1,a) Ivars Neretnieks,1and Michael Holmboe2
1Department of Chemical Engineering, Royal Institute of Technology, S-100 44 Stockholm, Sweden
2Department of Chemistry, Ume˚
a University, Ume˚
a, Sweden
(Received 25 June 2017; accepted 1 August 2017; published online 23 August 2017)
During the last four decades, numerous studies have been directed to the swelling smectite-rich clays
in the context of high-level radioactive waste applications and waste-liners for contaminated sites.
The swelling properties of clay mineral particles arise due to hydration of the interlayer cations
and the diffuse double layers formed near the negatively charged montmorillonite (MMT) surfaces.
To accurately study the cation hydration in the interlayer nanopores of MMT, solvent-solute and
solvent-clay surface interactions (i.e., the solvation effects and the shape effects) on the atomic level
should be taken into account, in contrast to many recent electric double layer based methodologies
using continuum models. Therefore, in this research we employed fully atomistic simulations using
classical molecular dynamics (MD) simulations, the software package GROMACS along with the
CLAYFF forcefield and the SPC/E water model. We present the ion distributions and the deformation
of the hydrated coordination structures, i.e., the hydration shells of Na+and Ca2+ in the interlayer,
respectively, for MMT in the first-layer, the second-layer, the third-layer, the fourth-layer, and the fifth-
layer (1W, 2W, 3W, 4W, and 5W) hydrate states. Our MD simulations show that Na+in Na-MMT
nanopores have an affinity to the ditrigonal cavities of the clay layers and form transient inner-sphere
complexes at about 3.8 Å from clay midplane at water contents less than the 5W hydration state.
However, these phenomena are not observed in Ca-MMT regardless of swelling states. For Na-MMT,
each Na+is coordinated to four water molecules and one oxygen atom of the clay basal-plane in
the first hydration shell at the 1W hydration state, and with five to six water molecules in the first
hydration shell within a radius of 3.1 Å at all higher water contents. In Ca-MMT, however each Ca2+
is coordinated to approximately seven water molecules in the first hydration shell at the 1W hydration
state and about eight water molecules in the first hydration shell within a radius of 3.3 Å at all higher
hydration states. Moreover, theMD results show that the complete hydration shells are nearly spherical
with an orthogonal coordination sphere. They could only be formed when the basal spacing d001
≥18.7 Å, i.e., approximately, the interlayer separation h≥10 Å. Comparison between DFT and MD
simulations shows that DFT failed to reproduce the outer-sphere complexes in the Stern-layer (within
∼5.0 Å from the clay basal-plane), observed in the MD simulations. Published by AIP Publishing.
[http://dx.doi.org/10.1063/1.4992001]
I. INTRODUCTION
Hydration of the interlayer ions and their ion distribu-
tions near the clay-water interface govern the underlying
mechanisms of clay swelling,1–8clay mineral precipitations,
as well as radionuclide migration and retardation in argilla-
ceous rocks. In these systems, the electric double layers
(EDL) formed near the charged surfaces, e.g., the negatively
charged clays make the clay swell or collapse.9–11 The sig-
nificance of EDL for biological systems and in industrial
technical processes has been well illustrated in the work of
Angell et al.12 Recently, the EDL of ionic liquids has been
cumulatively relevant in designing lithium ion batteries and
super-capacitors.13
In the theoretical study of the EDL of electrolyte solutions
and ionic liquids, the simplest model of the underlying EDL
a)Electronic mail: guomin@kth.se
theories is the so-called primitive model (PM), where ions
typically are modeled as hard spheres and where the water
molecules are only represented implicitly as a continuum,
using a uniform dielectric constant. In the PM, the hydration
effects simply are accounted for by increasing the radius of
the ions. The enlarged ionic radius thus corresponds to the
“hydrated ionic radius” representing the size of the ion plus
the hydration shell of tightly coordinated and oriented water
molecules around it. With decreasing interlayer distances (i.e.,
decreasing water content) the hydration shell may deform,
eventually resulting in water molecules being squeezed out
from the inner hydration shell. Under the condition when the
interlayer distances are smaller than 1 nm, equivalent to a basal
spacing of approximately 2 nm, using a “hydrated ionic radius”
for the ions and particles, therefore, might become incredibly
unphysical.10
In an effort to account for the molecular nature of the
solvent, the PM was extended to a three-component model
0021-9606/2017/147(8)/084705/8/$30.00 147, 084705-1 Published by AIP Publishing.
084705-2 Yang, Neretnieks, and Holmboe J. Chem. Phys. 147, 084705 (2017)
(3CM) in which the solvent molecules are represented by
neutral hard spheres, and the electrostatic part of the sol-
vent molecules is still described as a continuum with uniform
dielectric constant.14 The ion-ion interaction in the 3CM thus
remains exactly the same as in the PM, whereas the ion-
solvent and solvent-solvent interactions are simply represented
by the hard sphere repulsions. The structural and thermo-
dynamic properties of the simplest PM and 3CM have been
studied.10,11,14,15
Yet another useful model of solvated electrolytes or
ionic liquids that goes beyond the primitive model is the
dimer electrolyte model,16–24 in which the solvated cations
or ionic liquids are represented by a dimer consisting of two
tangentially tethered hard spheres one of which is neutral
and the other is positively charged. The ions are described
by a negatively charged hard sphere monomers in a sol-
vent that is a dielectric continuum. This dimer model has
successfully been implemented for canonical Monte Carlo
(CMC),25 and density functional theory of fluids (DFT),26
techniques for the prediction of structure and differential
capacitance of a planar EDL. Results from CMC simula-
tions have shown that the shape of cations influences the
double layer structure and capacitance substantially for a neg-
atively charged surface, but less so for a positively charged
wall.25
In all of the above models, the dielectric constant of water
is constant. In reality it decreases with increasing ion concen-
tration27,28 since the screening ability of the solvent (dielectric
permittivity) decreases as the concentration of ions increases.
Later, the so-called II+IW theory was proposed by taking into
account the contributions of ion-ion (II) and ion-water (IW)
interactions to the excess chemical potentials. In the II+IW
theory, the IW interaction contains the information of dielec-
tric constant about the ability of water to screen the ions.29–32 In
their work, the II interaction was obtained with Grand Canon-
ical Monte Carlo (GCMC) simulations on the basis of the PM
by using the Pauling radii of the charged hard spheres. The IW
interaction was calculated from Born’s treatment of hydra-
tion by employing the Born radii, which are not a physical
radii, rather an effective parameter with which the theoretic
results agreed with the experimental hydration free energy.33
This II+IW model has been increasingly applied to predict the
activity coefficients of ions in bulk ionic liquid for a variety
of systems of interest. To the best of our knowledge, however
the work of the II+IW model for the EDL of ionic liquids and
electrolytes (in the presence of external field) are still rarely
investigated.
For more than two decades, molecular modeling such as
Monte Carlo (MC) and molecular dynamics (MD) simula-
tions1,2,4–6,8,34–36 have proven to be valuable heuristic tech-
niques for studying the interlayer molecular structures and
the EDL properties of clay minerals, by explicitly considering
the water-water, clay-water, counter-ion-water, and counter-
ion-clay interactions on the atomic level. Nevertheless, MD
and MC simulations have limitations with regard to mod-
eling large system sizes and long time scales. Especially
MD simulations have been increasingly used for studying
the EDL in nanopores3,37–39 because of its ability to give
explicit and atomistic insight into water-mineral interface
phenomena, with software packages such as GROMACS40–44
and LAMMPS.45
With this in mind, this study was motivated by a pre-
vious work that used DFT and showed that the attractive
forces between the sheets under certain circumstances can be
switched to repulsive forces with increasing ion sizes.10 More-
over, the hydrated ionic radii used in DFT agree quite well with
experimental results in predicting the ion exchange equilibria
only when the interlayer separations are larger than about 10 Å.
It has been realized that the hard-sphere model (in which the
ionic diameters are adjustable parameters) used in DFT9,11
failed in describing the hydration shells of water molecules,
whereas this can be achieved by MD simulations. To study how
the deformation of hydration shells influences the properties of
compacted smectite clays, we employed classical MD simula-
tions taking into account all atom-atom interactions including
the water molecule interactions. Furthermore, the MD simu-
lations demonstrated under which conditions DFT modeling
becomes significantly inaccurate, and when it still can give
accurate results.
To summarize, in this research we report MD simula-
tion of the cation hydration in the interlayer nanopores of
Na and Ca-MMT at different water contents. In Sec. II, the
methodologies of MD simulations implemented with GRO-
MACS are described and illustrated. The interlayer structure
of cations and water molecules in Na- and Ca-MMT are dis-
cussed in Sec. III. The deformation of the hydration shells
is captured by MD when the swelling state is varied from
the fifth-layer hydrate (5W) to the first-layer hydrate (1W).
The structures of interlayer hydration and water molecules are
quantitatively described by the radial distribution functions
(RDF). In Sec. IV, the EDL structures computed by the MD
simulations are compared with the corresponding results from
the DFT calculations, to demonstrate under which conditions
DFT predictions become inaccurate.
II. MOLECULAR DYNAMIC SIMULATION METHOD
In this study, all-atom MD simulations were carried out
with the open source package GROMACS.41,44 All interatomic
interactions for and between water, the clay lattice, and the
interlayer ions, were modeled using the most popular SPC/E
water model,46 the well established CLAYFF forcefield47 and
the Åqvist48 and Joung-Cheatham parameters,49 respectively.
It has been verified that the combination of forcefields and
water models50,51 is superior in reproducing the overall density
profiles (by deriving them from the X-ray structure factors for
the hydrated clays plus adsorbed waters and ions and compar-
ing with experimental XRD data) for the crystalline hydrates
of smectites.
The CLAYFF forcefield uses partially charged atom types
and considers all interactions as non-bonded “ionic” inter-
actions, except for the hydroxyl O–H bond. The generated
charge defects (due to the isomorphic substitution of Al iii
with Mg ii) are distributed over the Mg atoms and all first-
neighbor oxygens, which carry charges that approximate the
water-oxygen in the SPC/E model, with which they also share
their Lennard-Jones parameters. Beyond a cutoff value of
1.0 nm, all interactions due to the Lennard-Jones potential
084705-3 Yang, Neretnieks, and Holmboe J. Chem. Phys. 147, 084705 (2017)
(VdW interactions) were truncated whereas the electrostatic
interactions were computed with the Particle-Mesh-Ewald
(PME) method.52
In this study we used a Wyoming-type MMT,5,53 having
a generic unit cell chemical formula of X+
0.66 Al3.33Mg0.66
[Si8]O20[OH]4, with a surface charge density of approxi-
mately 0.11 C m 2, which was compensated by the incor-
poration of cations into the interlayer region, e.g., 0.33 Ca2+
or 0.66 Na+per unit cell. X +
0.66 denotes the average 0.66 mono-
valent ions (corresponding to 0.33 divalent ion) needed to
counterbalance the negative lattice charge. In all the MD simu-
lations, the systems are modeled with two fully flexible parallel
MMT sheets (6 ×6×2 unit cells) stacked in the zdirection
(Fig. 1).
All MD runs were simulated at 298 K using a time step of
1 fs, and the integration of the equations of motion were per-
formed using the leap-frog algorithm. To generate equilibrated
systems, the initial configurations were prepared by (1) energy
minimization, using the steepest descent algorithm, followed
by (2) simulations using position restraints of the clay lattices
in the canonical NVT ensemble for 5 ns, and (3) simulations
for 5 ns in the isothermal-isobaric NPT ensemble using the
Berendsen barostat,54 at 1 bar and 298 K, to relax the MMT
layers and interlayer solutes in the x,y, and zdirection. The
final production runs were performed in the NVT ensemble at
298 K for 125 ns.
Interlayer density profiles for all atoms were calculated
from MD trajectory data using
ρi(z)=hNii/(xy∆z), (1)
where ρiis the number density of the atoms in region i, i.e.,
a sliced section located between zand z+∆z, and where hNii
is the ensemble averaged number of atoms within this region,
having a bin volume of xy∆zin Å3. Similarly, the radial dis-
tribution function is calculated from the trajectories using the
equation
gij(r)=DNjE . (ρj4πr2∆r), (2)
where DNjEis the ensemble averaged number of atoms jlocated
within the spherical shells at rand r+∆rcentered on the atom
i, and ρjis the average density of atom j. The radial distribution
FIG. 1. Snapshot of a MD simulation cell showing Ca-MMT in the 3W hydra-
tion state with an 11.7 Å wide interlayer nanopore containing Ca ions (green)
ions and water molecules. The clay mineral structure contains Si (yellow), Al
(pink), Mg (blue), O (red), and H (white) atoms.
functions can be integrated cumulatively and radially along the
radius r, giving the coordination number, CNij(r), of j-atoms
about the central i-atom,
CNij (r)=4π ρjXgij (r)r2∆r. (3)
III. MOLECULAR DYNAMICS SIMULATIONS
OF CATION HYDRATION
In the simulations studying hydration of interlayer cations,
the average interlayer distances were solely determined by the
number of water molecules in each interlayer, since there could
be no exchange of the water molecules or ions between the dif-
ferent adjacent layers. The water contents were varied from the
first-layer hydrate to the fifth-layer hydrate (i.e., 1W, 2W, 3W,
4W, and 5W), having 5, 10, 15, 20, and 25 H2O per unit cell of
MMT as recommended by Holmboe and Bourg38 for a typical
Wyoming type MMT, since these water loadings was shown
to reproduce experimental interlayer distances measured by
XRD.38,55
A. Interlayer structures
Figure 2presents the MD simulations of the interlayer ion
distributions for water hydrogen (HW), water oxygen (OW),
and cations along the z-axis in Na- and Ca-MMT,respectively.
In Fig. 2(a), the smectite basal spacing (d001) is shown to be
about 12.5 Å for Na-MMT in the 1W hydration state. It is seen
that the interlayer structures of the water molecules and Na ions
are symmetric along the midplane of the interlayer. In Fig. 2(a),
two shoulders of the HW density profiles located around 5 Å
from the clay midplane indicate that HW are attracted to the
ditrigonal cavities of the siloxane surfaces, likely interacting
through hydrogen bond with basal-plane oxygen atoms (at
about 3.2 Å from the clay midplane). OW and Na ions are
found located roughly equally around two planes with a small
offset from the interlayer midplane. The Na ions appear to be
forming the inner-sphere complexes (peaks about 5.7 Å from
the clay midplane) interacting with the octahedral charge site.
Nevertheless, two minor features in the Na ion distributions
are found to reside at around 3.8 Å from the clay midplane
because they are attracted to ditrigonal cavities and forming
transient inner-sphere surface complexes. Figure 2(b) shows a
basal spacing of 13.7 Å (slightly larger than the experimental
FIG. 2. Interlayer ion distributions as a function of interlayer separations for
(a) Na-MMT and (b) Ca-MMT in the 1W hydration state. Inserts show the Na
and Ca ion distributions magnified.
084705-4 Yang, Neretnieks, and Holmboe J. Chem. Phys. 147, 084705 (2017)
value) for Ca-MMT in 1W. It is seen that two small OW
peaks reside at the same place as the HW peaks in the wings
of distributions around 5 Å from the clay midplane. It indi-
cates that OW atoms located near the ditrigonal cavities of the
siloxane surfaces interacting with the clay hydrogen atoms.
Comparison between Na-MMT and Ca-MMT illustrate that
the Ca ions do not penetrate the ditrigonal cavities and show
a preference for outer-sphere complexes over inner-sphere
complexes.
Figure 3shows the ion distributions in the interlayer of
MMT in the 2W hydration state, resulting in a basal spac-
ing for both Na- and Ca-MMT of 15.6 Å, which is well in
line with the experimental basal spacing data in the work of
Holmboe et al.55 It is seen that the interlayer structures of HW
and OW in Na-MMT and Ca-MMT [Figs. 3(a) and 3(b)] are
very similar, and that the HW and OW distributions are sym-
metrically distributed around two planes with a small offset
from the interlayer midplane. For neither Na- nor Ca-MMT,
the OW atoms show no preference for the ditrigonal cavities
of the siloxane surfaces.
Figure 3(a) shows that the Na ions are mainly located
at the interlayer midplane, forming outer-sphere complexes
(peaks about 7.8 Å from the clay midplane) but also inner-
sphere complexes (peaks about 5.9 Å from the clay midplane).
Interestingly, even for the 2W hydration state, the Na ions
can form transient inner-sphere complexes with the ditrigonal
cavities (peaks about 3.8 Å from clay midplane) as shown
in the inserted plot [Fig. 3(a)]. The Ca ions, however, show
exclusively outer-sphere complexes within the interlayer water
molecules [Fig. 3(b)].
Figure 4shows the corresponding 3W hydration state
resulting in a basal spacing of approximately 18.7 Å for both
Na- and Ca-MMT (well in line with the experimental basal
spacing data, see Holmboe et al., 2012). In Fig. 4(a), the broad
and seemingly diffuse layer of Na ions was found, associated
with water molecules at the interlayer midplane, with two lay-
ers of outer-sphere complexes residing at about 7.6 Å from
the clay midplane, but still with two small shoulders located
around 5.9 Å indicating some residual inner-sphere complexes.
The transient inner-sphere complexes (peaks about 3.8 Å from
clay midplane shown in the interested plot) interacting with
the ditrigonal cavities seen at lower hydration states were also
FIG. 3. Interlayerion distributions as a function of interlayer separations from
MD simulations for (a) Na-MMT and (b) Ca-MMT in the 2W hydration state.
Inserts show the Na and Ca ion distributions magnified.
FIG. 4. Interlayer density profiles as a function of interlayer separations from
MD simulations for (a) Na-MMT and (b) Ca-MMT in the 3W hydration state.
Inserts show the Na and Ca ion distributions magnified.
found for Na-MMT in the 3W hydration state [Fig. 4(a)]. The
Na ion distributions display asymmetry in the transient inner-
sphere complexes as shown in the embedded plots, which
can be explained by the isomorphic substitution sites being
distributed randomly in the x-yplane, possibly creating a cer-
tain amount of heterogeneity in the surface charge density.
Figure 4(b) shows that there are only two shoulders in the Ca
ion distributions, located about 7.8 Å from the clay midplane,
without any significant diffuse or broad layer in the interlayer
midplane.
For the 4W hydration state, the basal spacing was found
to be approximately 21.7 Å for both Na- and Ca-MMT, shown
in Fig. 5. It is seen that both outer-sphere complexes and
diffuse-layer exist for both Na- and Ca-MMT in the 4W hydra-
tion state. Again, Fig. 5(a) shows the transient inner-sphere
complexes in ditrigonal cavities reside at 3.8 Å and residue
inner-sphere complexes at 5.9 Å from the clay midplane for
Na-MMT. Figure 5(b) illustrates that the diffuse layers appear
in Ca-MMT when the swelling reaches the 4W hydration
state.
For the 5W hydration state, the basal spacing was found
to be approximately 24.8 Å for both Na- and Ca-MMT.
Figure 6(a) shows a significant fraction of the Na ions reside
in outer-sphere complexes (peaks about 7.8 Å from the clay
midplane). The small peaks of Na ions at about 10.8 Å from
the clay midplane [Fig. 6(a)] indicate a complex exchange
FIG. 5. Interlayerion distributions as a function of interlayer separations from
MD simulations for (a) Na-MMT and (b) Ca-MMT in the 4W hydration state.
Inserts show the Na and Ca ion distributions magnified.
084705-5 Yang, Neretnieks, and Holmboe J. Chem. Phys. 147, 084705 (2017)
FIG. 6. Interlayer density profiles as a function of interlayer separations from
MD simulations for (a) Na-MMT and (b) Ca-MMT in the 5W hydration state.
Inserts show the Na and Ca ion distributions magnified.
between the diffuse-layer and outer-sphere complexes. It is
worth noting that the Na ions show no affinity to the ditrig-
onal cavities at this hydration state. Furthermore, it is seen
that the peaks of the diffuse-layer at the interlayer midplane in
Na-MMT disappeared [Fig. 6(a)], indicating that the Na ions
are solvated in the diffuse layer region. The Ca ions mainly
reside in outer-sphere complexes (peaks at about 7.7 Å from
the clay midplane) and are solvated in the diffuse layer region
as well [Fig. 6(b)]. It is worth noting that the water concen-
tration for Ca-MMT in the 5W is approximately 55 M, i.e.,
the water density is about 1.0 g/cm3at the interlayer midplane
indicating that the start of the formation of the bulk water
reservoir.
B. Structure of interlayer hydration
Figure 7(a) shows the radial distribution function (RDF)
between Na-OW (Na is the reference solute, OW represents
the ligand) from the simulations for Na-MMT in the 1W, 2W,
3W, 4W, and 5W hydration states. It is seen that the first peak
in the RDF is located at 2.34 Å for the 1W hydrate state.
For higher hydration states, the primary peak in the RDF’s
is found to reside at about 2.36 Å. This initial shift indicates
that the water molecules have more space to orient themselves
with increasing the interlayer separation. Figure 7(b) shows
the corresponding coordination number (CN) of Na coordi-
nating to OW. It is seen that, in the 1W hydrate state, there are
FIG. 8. Polyhedral structure of Na ions hydrated in the interlayer of Na-MMT
in (a) 1W and (b) 5W. Only Na ions (dark blue) and water oxygen atoms OW
(red) of the first hydration shell in the interlayer are shown. The clay mineral
structures are shaded for clarity.
four water molecules (i.e., OW) in the first hydration shell of
Na ion. Figure 8(a) further illustrates that for the 1W hydra-
tion state, each Na ion is coordinated to four water molecules
and one basal oxygen atom from the surface of MMT.
Figure 7(b) shows that the number of water molecules in the
first hydration shell is increased from four to six when increas-
ing the water content from the 1W to the 5W hydration state.
It is seen that each Na ion in the interlayer is coordinated by
five to six water molecules forming orthogonal coordination
sphere [Fig. 8(b)] with a radius of 3.1 Å [which is the posi-
tion of the first minimum in the RDF for Na-OW shown in
Fig. 7(a)] in the 5W hydration state. Figure 7(c) presents the
average distances of the nearest-neighbor and next nearest-
neighbor water molecules about a reference water molecule
are 2.74 Å (the first peak) and 4.66 Å (the second peak),
respectively. The average distance of hydrogen bond in the
interlayer is found to be about 1.9 Å [the first peak shown in
Fig. 7(d)].
Figure 9shows the corresponding data presented in Fig. 7,
but here data are shown for Ca-MMT at different hydration
states. In Fig. 9(a), the first peak of the RDF of Ca-OW is
shifted from 2.36 Å to 2.38 Å when the water content is
increased from the 1W to the 5W hydration state. There are
seven water molecules in the first shell of the Ca hydration
complex [Fig. 10(a)] when Ca-MMT is in the 1W hydra-
tion state. It is seen that the coordination number of water
molecules in the first hydration shell is increased from seven
to eight when increasing the water contents from 1W to 5W
FIG. 7. Graphs of interlayer (a) RDF
for Na-OW, (b) coordinate number
CNNa-OW (r), (c) RDF for OW-OW, and
(d) RDF for HW-OW in Na-MMT.
084705-6 Yang, Neretnieks, and Holmboe J. Chem. Phys. 147, 084705 (2017)
FIG. 9. Graphs of the interlayer (a)
RDF for Ca-OW, (b) coordinate num-
ber CNCa-OW (r), (c) RDF for OW-OW,
and (d) RDF for HW-OW in Ca-MMT.
[Fig. 9(b)]. Furthermore, at the 5W hydration state, each Ca
ion is coordinated to eight water molecules, forming orthog-
onal coordination sphere [Fig. 10(b)] with a radius of 3.3 Å
[which is the position of the first minimum in the RDF for Ca-
OW shown in Fig. 9(a)]. Figure 9(c) shows that the average
distances of the nearest-neighbor and next nearest-neighbor
water molecules about a reference molecule are 2.8 Å (the
first peak) and 4.55 Å (the second peak). The average distance
of hydrogen bond is about 1.8 Å (the first peak) as shown in
Fig. 9(d).
C. Deformation of hydration shells
Figure 11 shows the deformation of the hydration shells
coordinated around Ca ions in the 1W, 2W, 3W, and 5W hydra-
tion states. In Fig. 11, only the interlayer Ca ions (green) and
water oxygen atoms OW (red) in the first coordination shell
are shown. Figure 11(a) shows that there are about seven water
molecules coordinated around each Ca ion in the first hydra-
tion shell when Ca-MMT is in the 1W hydration state. It is
seen that the water molecules are squeezed out from the top
and bottom of the first shell and prefer to reside in the center of
a ring in the xy-plane, due to the limited space. For Ca-MMT
in the 2W hydration state, eight water molecules coordinate to
Ca in the first shell, as shown in Fig. 11(b). Only a minor defor-
mation of the first coordination water shell was observed [such
as the one in the right corner in Fig. 10(b)], since the hydration
FIG. 10. Polyhedral structure of Ca ions hydrated in the interlayer for Ca-
MMT in (a) 1W and (b) 5W. Ca ions (light blue) and water oxygen atoms OW
(red) of the first hydration shell in the interlayer are shown. The clay mineral
structures are shaded for clarity.
shells were found to be nearly spherical. Figure 11(c) shows
that Ca ions are fully hydrated forming evenly distributed
spherical shells for Ca-MMT in the 3W hydration state. In
Fig. 11(d), there are nearly eight water molecules coordinated
around each Ca ion in the first hydration shell for Ca-MMT in
the 5W hydration state. In Fig. 11(d), the complete hydration
shells are observed forming orthogonal coordination spheres
[Fig. 10(b)] with radius of approximately 3.3 Å without any
deformation.
D. Comparison between MD and classical DFT
on the EDL
The Stern-layer effect plays an essential role in explain-
ing the swelling mechanism of clay minerals. In order to reveal
under which conditions our previous modeling using density
functional theory (DFT) becomes increasingly inaccurate with
decreasing interlayer separation, we performed a compari-
son with MD simulations conducted in this study. The blue
curves presented in Fig. 12 come from the reference fluid
FIG. 11. Snapshot of MD simulations showing deformation of hydration
shells in the interlayer of Ca-MMT in (a) 1W, (b) 2W, (c) 3W, and (d) 5W. Only
Ca ions (green) and water oxygen atoms OW (red) of the first hydration shell
are shown in the picture. The clay mineral structures are shaded for clarity.
084705-7 Yang, Neretnieks, and Holmboe J. Chem. Phys. 147, 084705 (2017)
density/weighted correlation approach (RFD/WCA) within
the framework of DFT. The detailed information of the DFT
method can be found in the papers.9,11 The red curves are from
MD simulations. The gray dashed lines represent the midplane
to basal-plane distance (half a MMT layer). In the DFT cal-
culations, the diameters of Na and Ca ions from CLAYFF
forcefield47 were used. For simplicity, the ions were described
as hard spheres of equal size with point charges assumed
to be located at the ion centers, and the solvent represented
by a continuum with a uniform dielectric permittivity (εr
= 78.4) at room temperature (T= 298 K), next to charged
surfaces in the DFT calculations for the restricted primitive
model.
Figure 12(a) illustrates the MD simulation cell with
Na-MMT having an excess electrolyte concentration with
24 excess Na–Cl ions in a ten-layer hydration state (10 W),
containing 3600 H2O water molecules (containing 50 water
molecules per unit cell), and 13 776 atoms in total (including
atoms in clay mineral structure). The size of the simulation
cell was 31.0 Å ×54.2 Å ×82.9 Å (x×y×z), result-
ing in an equilibrated interlayer separation of approximately
30 Å. The corresponding DFT calculations were performed
for a similar system where Na-MMT system is in equilibrium
with a NaCl bulk solution of 0.62M. The bulk ion concentra-
tions were determined from the density profiles in middle of
the pore. The ionic diameters and the surface charge density
used in DFT system were 4.848 Å and 0.11 C m 2, respec-
tively, hence similar surface charge density used in the MD
simulations. It was shown that the DFT calculations success-
fully capture the diffuse ion swarm from approximately 5.0 Å
beyond the basal-plane in comparison with MD simulations.
However, the features of the main outer-sphere complexes
(within 5.0 Å from the basal-plane) and inner-sphere com-
plexes observed by MD simulations were not predicted by the
DFT results.
The MD simulations presented in Fig. 12(b) show a cor-
responding Ca-MMT MD system in the ten-layer hydration
state (10W), containing an additional 6 Ca and 12 Cl ions,
resulting in the cell dimensions of 31.0 Å ×54.2 Å ×83.2 Å
FIG. 12. Comparison of interlayer density profile from MD (red curves) and
DFT (blue curves) for (a) Na-MMT and (b) Ca-MMT. Solid curves repre-
sent the counter-ion distributions, and dashed curves represent the co-ion
distributions.
FIG. 13. Snapshot of MD simulations cell showing Ca-MMT in the ten-layer
hydrate. Ca2+ (green) ions, Cl (dark blue), and water molecules. The clay
mineral structure contains Si (yellow), Al (pink), Mg (light blue), O (red), and
H (white) atoms.
(x×y×z), see also Fig. 13. After reaching equilibrium, the
bulk CaCl2salt concentration was about 0.23M, and the inter-
layer separation approximately 31.6 Å. It is compared with the
corresponding DFT system in equilibrium with a 0.23M CaCl2
solution. Here, the ionic diameters and the surface charge den-
sity were 5.3 Å and 0.11 C m 2, respectively. Analogously to
the case with Na ions, the steric and hydration effects on the
Stern-layer are absent in the DFT predictions.
IV. CONCLUSIONS
To better understand the mechanism causing the swelling
of smectite clays and interlayer hydration, and the effects of ion
hydration on the molecular level for the EDL, we modeled Na-
and Ca-MMT at different water loadings using MD, explicitly
taking into account the interactions of the water molecules. The
MD results showed that the smectite basal spacing (d001) was
about 12.5 Å, with Na ion coordinated to four water molecules
and one basal oxygen atom from the surface of Na-MMT in
the 1W hydration state. It was found that Na-MMT resulted in
d001 of about 15.6 Å, 18.7 Å, 21.7 Å, and 24.8 Å in the 2W, 3W,
4W, and 5W hydration states, respectively, in which each Na
ion was coordinated to nearly six water molecules in the first
hydration shell within a radius of 3.1 Å. It was shown that Ca-
MMT in the 1W hydration state resulted in d001 of about 13.7 Å
(slightly larger than the experimental value), with Ca ion being
hydrated by approximately seven water molecules in its first
084705-8 Yang, Neretnieks, and Holmboe J. Chem. Phys. 147, 084705 (2017)
hydration shell, which was deformed and non-symmetrical. In
the 2W hydration state, d001 was found to be about 15.6 Å
for Ca-MMT (well in line with the experimental data), with
each Ca ion being hydrated by nearly eight water molecules
in the first shell. Only a minor deformation of the first coor-
dination water shell was observed for Ca-MMT in 2W, since
the hydration shells were found to be nearly spherical. For the
higher hydration states, it was found that the Ca ions were fully
hydrated with evenly distributed spherical coordination shells,
resulting in d001 of 18.7 Å, 21.7 Å, and 24.8 Å, respectively,
in the 3W, 4W, and 5W hydration state. Moreover, eight water
molecules were coordinated to Ca ion in the first coordination
shell, forming orthogonal coordination spheres with a radius
of about 3.3 Å. Hence, it was concluded that complete hydra-
tion shells could only be formed when the basal spacing is
larger than approximately 18.7 Å.
ACKNOWLEDGMENTS
The authors would like to acknowledge the financial
support of the Swedish Nuclear Fuel and Waste Manage-
ment Company (SKB). The simulations were performed on
resources provided by the Swedish National Infrastructure
for Computing (SNIC) at PDC and HPC2N Centers for High
Performance Computing.
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