Andrea Zen1,2,3, Tai Bui3,4,5, Tran Thi Bao Le6, Weparn J Tay4, Kuhan Chellappah4, Ian R Collins4, Richard D Rickman4, Alberto Striolo6,7, Angelos Michaelides3,5,8. 1. Dipartimento di Fisica Ettore Pancini, Università di Napoli Federico II, Monte S. Angelo, I-80126 Napoli, Italy. 2. Department of Earth Sciences, University College London, Gower Street, London WC1E 6BT, U.K. 3. Thomas Young Centre and London Centre for Nanotechnology, 17-19 Gordon Street, London WC1H 0AH, U.K. 4. BP Exploration Operating Co. Ltd, Chertsey Road, Thames TW16 7LN, U.K. 5. Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, U.K. 6. Department of Chemical Engineering, University College London, WC1E 7JE London, U.K. 7. School of Chemical, Biological and Materials Engineering, University of Oklahoma, Norman, Oklahoma 73019, United States. 8. Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K.
Abstract
The aggregation of clay particles in aqueous solution is a ubiquitous everyday process of broad environmental and technological importance. However, it is poorly understood at the all-important atomistic level since it depends on a complex and dynamic interplay of solvent-mediated electrostatic, hydrogen bonding, and dispersion interactions. With this in mind, we have performed an extensive set of classical molecular dynamics simulations (included enhanced sampling simulations) on the interactions between model kaolinite nanoparticles in pure and salty water. Our simulations reveal highly anisotropic behavior, in which the interaction between the nanoparticles varies from attractive to repulsive depending on the relative orientation of the nanoparticles. Detailed analysis reveals that at large separation (>1.5 nm), this interaction is dominated by electrostatic effects, whereas at smaller separations, the nature of the water hydration structure becomes critical. This study highlights an incredible richness in how clay nanoparticles interact, which should be accounted for in, for example, coarse-grained models of clay nanoparticle aggregation.
The aggregation of clay particles in aqueous solution is a ubiquitous everyday process of broad environmental and technological importance. However, it is poorly understood at the all-important atomistic level since it depends on a complex and dynamic interplay of solvent-mediated electrostatic, hydrogen bonding, and dispersion interactions. With this in mind, we have performed an extensive set of classical molecular dynamics simulations (included enhanced sampling simulations) on the interactions between model kaolinite nanoparticles in pure and salty water. Our simulations reveal highly anisotropic behavior, in which the interaction between the nanoparticles varies from attractive to repulsive depending on the relative orientation of the nanoparticles. Detailed analysis reveals that at large separation (>1.5 nm), this interaction is dominated by electrostatic effects, whereas at smaller separations, the nature of the water hydration structure becomes critical. This study highlights an incredible richness in how clay nanoparticles interact, which should be accounted for in, for example, coarse-grained models of clay nanoparticle aggregation.
Clay
particles are all around us: present in the Earth’s
crust, soil, the ocean floor, and the atmosphere as aerosols. Clays
have been extensively used since antiquity in pottery, as building
and writing materials, and more. Clays are also critical to contemporary
challenges: for example, as atmospheric ice nucleating agents, they
are relevant to climate change; the ability of clays to trap toxic
(including nuclear) waste is important for environmental remediation;
and as porous materials, they filter and dictate the flow of water
and other fluids through rocks.[1]Understanding the aggregation of individual clay particles into
larger agglomerates is critical to explaining and controlling the
behavior of clays in many of the above examples. However, at the atomic
scale, clay particle agglomeration is poorly understood. Partly, this
is down to the challenge of characterizing and tracking the agglomeration
of clay particles in solution but also because of the wealth of variables
that are inevitably relevant to the agglomeration process. Parameters
such as particle size, shape, chemical composition, temperature, pressure,
and solvent effects will all play a role.[2] A further challenge is the inherent chemical complexity of clay
particles: as (alumino)-silicate clays interact through a complex
interplay of electrostatic, hydrogen bonding, and van der Waals (vdW)
dispersion forces; with all these interactions mediated by the aqueous
electrolyte solution separating individual particles.[3]The inherent (and interesting) complexity of clay
particle aggregation
has motivated a large body of experimental[4−14] and computational[15−37] work aimed at understanding clay particle association under well-defined
conditions, as well as related questions about the structure and dynamics
of the water–clay interface. Being the simplest, one of the
most abundant, and also one of the most technologically relevant clays,
kaolinite (Al2(OH)4Si2O5), has emerged as a widely studied model system. Indeed, kaolinite
can now essentially be considered the “fruit fly” system
of physical chemistry/chemical physics research on clay particles.
However, the nature of kaolinite nanoparticle association under even
simple and well-defined conditions is still not understood. This is
what we aim to address in the current study through a systematic set
of computational studies, aiming specifically to understand the following
questions: (i) are the interactions between clay (nano)-particles
in solution attractive or repulsive?; (ii) does the nature of the
interaction depend on the facets of the (nano)-particles that interact
and if so to what extent?; (iii) what role does the aqueous solution
play in the association process?; and (iv) what are the length scale(s)
of the particle–particle interactions?To answer these
questions and to gain a better understanding of
the factors that influence kaolinite particle agglomeration in aqueous
solutions, we used molecular dynamics simulations to explore the association
of clay nanoparticles. Since kaolinite nanoparticles most often occur
as hexagonal platelets,[38] we modeled the
association of hexagonal clay nano-platelets. Figure a shows representation of the simulated nanoparticles.
In order to capture the role the (dynamic) solvent molecules play
in the association process, we computed potential of mean force (PMF)
curves between two kaolinite particles with varying orientations,
see Figure b, in both
pure and saline water environments. The contributions of interparticle
interactions are disentangled into the vdW and Coulombic potentials.
The effect of the hydration films on the PMF profiles is then investigated,
with a particular emphasis on the structural and dynamical properties
of water molecules confined between the two approaching surfaces.
As the presence/absence of ions in solution affects differently the
different contributions determining the overall interparticle interactions,
we are able to elucidate the effects of salt on the evaluated PMFs.
Figure 1
Overview
of the model kaolinite nanoparticles considered in this
study. (a) Representation of two kaolinite particles in the edge-to-face
orientation. The six edges (top) are called after their Miller indices
of the crystallographic structure,[39] and
the two inequivalent basal surfaces (bottom), (001) and (00–1),
are called gibbsite (G) and siloxane (S) faces, respectively, according
to the literature. White, red, gray, and yellow spheres represent
the hydrogen, oxygen, aluminum, and silicon atomic species, respectively.
We emphasize the five nonequivalent surfaces (the six edges are 2-by-2
equivalent) using different colors. (b) Nine representative orientations
of two kaolinite particles considered in this work.
Overview
of the model kaolinite nanoparticles considered in this
study. (a) Representation of two kaolinite particles in the edge-to-face
orientation. The six edges (top) are called after their Miller indices
of the crystallographic structure,[39] and
the two inequivalent basal surfaces (bottom), (001) and (00–1),
are called gibbsite (G) and siloxane (S) faces, respectively, according
to the literature. White, red, gray, and yellow spheres represent
the hydrogen, oxygen, aluminum, and silicon atomic species, respectively.
We emphasize the five nonequivalent surfaces (the six edges are 2-by-2
equivalent) using different colors. (b) Nine representative orientations
of two kaolinite particles considered in this work.
Computational Methods
The MD simulations employing force
field potentials have all been
performed using the LAMMPS package.[40] In
each simulation cell, there are two kaolinite nanoparticles and 10,000
to 11,000 water molecules. An image of the nanoparticles in the edge-to-face
configuration—but without any water present—is shown
in Figure a. An image
of the full simulation cell including the water molecules is shown
in Figure S1 of Supporting Information.
The kaolinite nanoparticles are prepared, as described in Section
S1 of Supporting Information. To simulate
the saline solution, sodium chloride ions corresponding to the salinity
of 1.2 M were added to the system. In line with ref (17), the simulation cell is
roughly 60 × 60 × 100 Å3. A simulation box
of this size is sufficiently large to avoid finite size effects, as
evidenced by: (i) the density of water, see Figures c and S10g–i of Supporting Information; and (ii) the diffusion coefficient
of water, see Figure S13 of Supporting Information, in the region between the two kaolinite particles, both of which
reach the bulk value. In the face-to-face orientation both the nanoparticles
have the basal faces parallel to the xy-plane, whereas
in the face-to-edge orientation, one nanoparticle (the lower in our
setups) has the basal faces parallel to the xy-plane,
and the other nanoparticle has the basal faces orthogonal to the xy-plane, and it is placed above the first nanoparticle.
Figure 3
Overview of the interaction
and the hydration for interfaces of
different thicknesses. (a) PMF profiles between two kaolinite particles
in pure and saline water systems for the gibbsite–siloxane
orientation. (b) Decomposition of particle–particle interactions:
vdW and Coulombic potentials as a function of the distance between
the two particles. (c–e) Density profiles of water, Na+, and Cl– along the Z-direction
of the simulation box calculated for the pure and saline water systems
at the particle–particle distance of 20, 10, and 6 Å,
respectively.
Force
Fields
The simulations employed the ClayFF potential[37,41−43] for kaolinite and the rigid SPC/E model[44] for water. The sodium, Na+, and chloride
ions, Cl–, were modeled as a single charged Lennard-Jones
sphere with parameters taken from the study of Smith and Dang without
polarizability.[45] Interactions between
unlike atom types were calculated using the standard Lorentz–Berthelot
mixing rules. The SHAKE algorithm[46] is
used to constrain the rigid water molecule and the OH distance in
the hydroxyl groups of kaolinite. Additional constraints on the kaolinite
atoms have been added to enhance the stability of the nanoparticles,
following previous work.[47,48] Real-space interactions
were truncated at 10 Å with corrections to the energy applied,
and a particle–particle–particle–mesh solver
was used to account for long-range electrostatics.[49] The integration step in the MD simulations is 1 fs. We
tested the above setup on the adsorption of a single water molecule
of the Na+ cation and Cl– anion on the
siloxane and gibbsite faces, and we registered reasonable agreement
with benchmark ab initio evaluations (see Section
S2 and Table S1 in Supporting Information), in agreement with other studies from the literature.[35,37,50]
Simulation Protocol
To simulate the system at the desired
temperature and pressure, an equilibrium simulation at a pressure
of 200 bar and temperature of 350 K was initially conducted for 1
ns in the NPT ensemble [constant number (N) of atoms/particles, pressure (P), and
temperature (T)]. Moreover, the system associated
to each specific orientation has been equilibrated in the NVT ensemble [constant number of atoms/particles, volume
(V), and temperature] at 350 K for over 1 ns by applying
separate Nosé-Hoover chain thermostats[51] to water and nanoparticles.The umbrella sampling (US) technique[52,53] was employed to evaluate the PMF among two nanoparticles using the
collective variable modules[54] implemented
in LAMMPS.[40] The computational details
for the US simulations are reported in the Supporting Information. In these simulations, a harmonic potential with
a force constant of 10 kcal/(mol·m2) or 50 kcal/(mol·m2) is used to keep the upper particle at a specific distance
from the bottom one to ensure good sampling overlap between adjacent
sampling windows. In both the face-to-face and face-to-edge orientations,
the lower nanoparticle is neither allowed to diffuse nor to rotate,
with its heavy atoms (Al and Si) tethered to their initial position
(using the fix spring/self-command in LAMMPS). The upper nanoparticle
is allowed to translate but not to rotate (heavy atoms are constrained
using the fix rigid command). The only exception is for the cases
of the edge-to-face orientations, where a short simulation (around
100 ps, prior to imposing the rotational constraints) was performed
to allow the upper particle to freely rotate and translate so that
the edge of the top particle can preferentially interact with the
basal surface of the bottom one. Consequently, the angle formed by
the two particles are not precisely 90° afterward (the deviation
is less than 10°). Note that the PMF is a function of the distance
among the nanoparticles. There are several different ways to quantify
this distance (see, for instance, Figure S1 in Supporting Information). The US constraint uses the distance
among the centers of mass of the heavy atoms (i.e., Al and Si) of
the two nanoparticles as it is easily computed in runtime during an
MD simulation. In the Results and Discussion section, we report the
results as a function of the minimum distance ΔZ among the heavy atoms of the two nanoparticles, which provides a
direct indication of the thickness of the interface and facilitates
the comparison among PMF curves relative to different orientations.
We note that the procedure described above was followed for each orientation
of the nanoparticles, as shown in Figure , panel (b) and discussed in the Results
and Discussion section.As noted above, the simulations reported
in this work have been
performed at 350 K, representing a typical temperature for inner earth
oil reservoirs. We also performed additional simulations at 450 K
on the gibbsite–siloxane orientation (see Section S4 and Figure
S5 in Supporting Information). The effect
of temperature on the PMF profile yields a minimal impact. This observation
is in agreement with the observations of Ho and Criscenti.[17] Finally, it is important that the US MD simulations
are long enough to sample properly the phase space. We performed some
preliminary calculations, which indicated that a reasonable level
of convergence in the PMF is already achieved when each US MD simulation
is 3 ns long or more, see Figure S4 of Supporting Information. In our production calculations, we used at least
5 ns long US simulations.
Results and Discussion
In the following sections, we first show and discuss the PMFs between
kaolinite nanoparticles at different orientations, followed by an
analysis of the energetic contributions of the free energy and how
it determines the attractive or repulsive nature of the interaction
between nanoparticles. We consider the structure of water and ions
at the interface and elucidate how they determine the qualitative
features of the PMF profile for narrow separation distances. Finally,
we discuss the diffusion of kaolinite particles in solution.
Orientation
Dependence of PMF Profiles
A hexagonal
kaolinite platelet has eight interfaces with water: two inequivalent
basal faces and six edges. A careful analysis of the six edges shows
that some of them are indeed very similar, and we can identify only
three inequivalent edges.[37,55] In particular, the
(0 1 0) edge is roughly equivalent to the (1 1 0), the (0 −1
0) edge is roughly equivalent to the (−1 −1 0) surface,
and the (1 −1 0) edge is roughly equivalent to the (−1
1 0) surface, see Figure . Thus, we limit our investigation to only one representative
edge for each equivalent class. This leads to three representative
edges: (0 1 0), (1 −1 0), and (0 −1 0). Therefore, in
aqueous solutions, we evaluated nine distinct PMFs for particle–particle
interactions, three of which are face-to-face oriented and six of
which are edge-to-edge oriented. In real systems, we expect the presence
of a variety of ions in water, either directly desorbed from rock
surfaces or in the form of mineral salts. In addition, given that
the kaolinite basal surface is polar,[56] ions in solution are likely to adsorb at the interface to compensate
for the dipoles present within the nanoparticle.[30] To account for these issues, we performed simulations in
both pure water and in the more realistic situation of saline water,
with a 1.2 M sodium chloride (NaCl) concentration.The PMF curves
obtained from our simulations are shown in Figure . We find that the PMF profiles are highly
dependent on the relative orientation between the two particles. In
particular, the gibbsite–siloxane orientation is the most attractive,
whereas the gibbsite–gibbsite and siloxane–siloxane
orientations are overall repulsive. This behavior is explained qualitatively,
at least for the pure water case, in terms of electrostatics, as a
kaolinite nanoparticle forms a dipole with the siloxane surface negatively
charged and the gibbsite surface positively charged. The face-to-edge
orientations exhibited a highly variable pattern of behavior, with
two out of six orientations being weakly attractive and the remaining
being overall repulsive. The face-to-edge PMFs are noticeably flatter
than the face-to-face PMFs. This is only in part explained by the
size of the interface: in our simulations, the face-to-face orientation
has an interface that is roughly 2.3 times larger than the face-to-edge,
while the free-energy barriers in the former are much larger than
a factor 2.3; see the plot of the PMF per surface area reported in
Figure S6 of Supporting Information. It
is likely that the atomically rough morphology of the edges prevents
the formation of highly pronounced hydration layers, as observed in
simulations conducted for hydrated crystalline versus amorphous silica,
which could reduce the intensity of the resultant PMF profiles.[57−59]
Figure 2
Interaction
between two kaolinite nanoparticles at different orientations.
(a–c) for face-to-face interfaces; (d–i) for edge-to-face
interfaces. Red and blue curves are the PMF profiles in pure water
and in 1.2 M of sodium chloride solution, respectively. They are obtained
from US simulations in the NVT ensemble at a temperature
of 350 K, employing the ClayFF atomic force field for the kaolinite
particles and the SPC/E water model. The abscissa, ΔZ, is the minimum distance among the “heavy”
atoms (i.e., Al or Si atomic species) of the two nanoparticles.
Interaction
between two kaolinite nanoparticles at different orientations.
(a–c) for face-to-face interfaces; (d–i) for edge-to-face
interfaces. Red and blue curves are the PMF profiles in pure water
and in 1.2 M of sodium chloride solution, respectively. They are obtained
from US simulations in the NVT ensemble at a temperature
of 350 K, employing the ClayFF atomic force field for the kaolinite
particles and the SPC/E water model. The abscissa, ΔZ, is the minimum distance among the “heavy”
atoms (i.e., Al or Si atomic species) of the two nanoparticles.The presence of ions in solution shows a significant
impact on
PMF profiles. Ions screen the long-range electrostatic interaction
between the two particles, especially in the face-to-face oriented
interfaces. In particular, siloxane–siloxane and gibbsite–gibbsite
orientations exhibit decreased repulsion at large distances when ions
are in solution. The greatest effect is observed on the interactions
between the particles along the gibbsite–gibbsite orientation,
where the PMF profile is repulsive in pure water but becomes attractive
in saline solution. In the case of gibbsite–siloxane, ions
reduce the attraction slightly between the two particles. We observed
the same trend for the effect of salt in the edge-to-face oriented
systems, namely, that salt decreases long-range interactions between
two particles. As a result, we found that in some systems, the PMF
changes from repulsive to attractive due to the presence of salts.
It is worth noting that in our calculations for the face-to-face orientations,
the PMF profiles are limited to a minimum distance of approximately
5 Å. This is due to the fact that the free-energy barrier is
very high at closer distances,[17] preventing
effective sampling of the phase space[16] even though the locations of the local minima and maxima can still
be identified (see Section S6 and Figure S7 of Supporting Information).
Short- and Long-Range Characteristics
of PMF Profiles
The PMF profiles, as shown in Figure , exhibit a common feature:
they are very corrugated
when the interface thickness ΔZ is smaller
than ca. 1.5 nm, and they are smoother for larger ΔZ. This allows us to distinguish between a short-range regime, characterized
by the presence of several local minima and free-energy barriers among
them in the PMF profile, and a relatively long regime.The gibbsite–siloxane
orientation shows the most intense effective attraction. In this section,
we report a deeper analysis of this specific orientation. Figure a zooms in on the gibbsite–siloxane PMF profiles obtained
with pure and saline water. In both cases, we clearly identify three
local minima, the first in the case of pure water being at ΔZ = 6.2 Å, the second at 9.9 Å, and the third
at 12.8 Å (as we can precisely infer from the analysis of the
US simulations, see Figure S7 of Supporting Information). In almost the same position, we have the minima for saline water.a The main difference between the PMF profiles obtained
in the pure and saline water is that the latter appears having no
long-range interactions, and the intensity of the PMF minima and maxima
changes slightly due to the presence of salt.Overview of the interaction
and the hydration for interfaces of
different thicknesses. (a) PMF profiles between two kaolinite particles
in pure and saline water systems for the gibbsite–siloxane
orientation. (b) Decomposition of particle–particle interactions:
vdW and Coulombic potentials as a function of the distance between
the two particles. (c–e) Density profiles of water, Na+, and Cl– along the Z-direction
of the simulation box calculated for the pure and saline water systems
at the particle–particle distance of 20, 10, and 6 Å,
respectively.The smoothness of the long range
and the corrugation of the short
range can be explained in terms of the structure of the water at the
interface. When the interface is thick (say, the separation between
the particles is larger than ca. 1.5 nm), the water in the middle
of the interface has the density of bulk liquid water at the conditions
considered. See, for instance, the case of ΔZ = 2 nm in Figure c. In contrast, at distances shorter than 1.5 nm, the simulations
show that water at the interface forms hydration layers, in a number
ranging from 1 to 3. See, for instance, the case of ΔZ = 1 nm in Figure d, having a bilayer of water between the particles or a single
layer in the case of ΔZ = 0.6 nm in Figure e. It shall be noticed
that the presence of two or three water layers at the interface between
liquid water and a solid surface is an expected feature on atomically
smooth solid surfaces, observed also in experiments.[60,61] In our system, water is in fact confined in the region between the
two nanoparticles, thus forming hydration layers on both the surfaces.
The minima in the PMF profiles correspond to the interparticle distances
that optimally accommodate 1, 2, or 3 layers, and the barriers between
the minima arise because the corresponding particle–particle
distances are energetically unfavorable.The plots in Figure c–e show that
the density of water at the interface is almost
the same for pure and saline water, the latter being slightly lower
due to the simultaneous presence of ions at the interface. However,
at the simulated salinity, the concentration of ions is almost negligible
compared to that of water, so in the plots, the density of Na+ and Cl– is magnified by a factor of 5.
We show in Figure c,d the different behavior of ions at the two kaolinite faces: the
gibbsite face shows a pronounced peak of Cl– anions,
and the siloxane face shows a quite smaller peak of the Na+ cations and the absence of any Cl– anion in its
proximity. Thus, ions distribute on the two kaolinite faces to counteract
the intrinsic surface charge, screening the interparticle Coulombic
interaction, in agreement with the literature.[6,23,29] This screening effect appears as the reason
for the lack of long-range interactions among the kaolinite particles
in saline solution, as observed in Figure a.To illustrate that the long-range
attraction of the two particles
is indeed due to the electrostatic interaction, we have disentangled
some of the contributions that sum up to determine the overall interaction
energy, and specifically the vdW and the Coulombic interparticle contributions.b The mean vdW and Coulombic contributions are plotted
in Figure b as a function
of the distance ΔZ. The vdW potential exhibits
a short-range effect, becoming negligible beyond 1 nm. The electrostatic
potential exhibits long-range features, as expected. Therefore, at
distances exceeding 1 nm, the interparticle interaction is mostly
due to electrostatics. We observed distinct differences in the interactions
depending on the orientation of the particles. When the two approaching
surfaces are dissimilar (i.e., gibbsite–siloxane), both the
vdW and electrostatic potentials yield attractive interactions. In
contrast, when the approaching surfaces are identical, for example,
gibbsite–gibbsite and siloxane–siloxane, we observe
a repulsive behavior (see Figure S8 of Supporting Information). This is due to the identical surface charges
on the two approaching particles. As discussed above, in saline water,
the ions deposit near the surfaces screening the long-range Coulombic
attraction/repulsion.
Role of the Hydration Film
Based
on the behavior of
the interparticle interaction energy, see in Figure b, the interparticle interactions should
yield smooth PMF curves. This is not the case, as observed in the
previous section, and the PMF profiles exhibit a corrugated shape
at distances ΔZ smaller than ca. 1.5 nm, see Figure . The solvent plays
an important role in determining this corrugation.[17,59,62] In our study, we found that when two particles
approach one another, their hydration films tend to migrate closer
together and merge into a single layer at short distances. We believe
that the compatibility of the two hydration films correlates with
the energetic and enthalpic cost of the particle–particle aggregation.More specifically, the aggregation of two particles at a specific
orientation should be favorable if the structure of the water confined
between the particles is similar to the structure of interfacial water
when the particles are far away and should be unfavorable otherwise.
Thus, we evaluated the distribution of the orientation of the water
molecules in the first hydration layer of the bottom particle in out
MD simulations. A comparison of the distributions obtained for the
different orientations and at different distances, ΔZ, is reported in Figure . Panels (b–d) show the results of the water
orientation distribution. As the two particles approach one another
in the siloxane–siloxane and gibbsite–gibbsite orientations,
the orientation of water molecules in the first hydration layer undergoes
a significant change. In contrast, in the case of gibbsite–siloxane
orientation, the distribution at various distances changes only slightly
as the two particles approach each other. Similar observations are
drown if we consider the one-dimensional density profiles for water
hydrogen and oxygen atoms along the Z-direction of
the simulation box for the three orientations, see Figure S10a–i
and Section S9 of Supporting Information. Thus, for the gibbsite–siloxane orientation, the energy
cost associated with changing the water orientation is expected to
be small, different from siloxane–siloxane and gibbsite–gibbsite
orientations. The above conclusion is supported also by the behavior
of the solvation free energy as a function of the interparticle separation,
which we have evaluated from our MD simulations and shown in Figure
S9 of Supporting Information (details are
in Section S8 of Supporting Information).
Figure 4
Orientation of water molecules at the interface. (a) Definition
of the angle formed between water dipole moments and the Z-direction of the simulation box. (b–d) Distribution of the
angle formed between the dipole vector of water molecules in the first
hydration layer and the Z-direction of the simulation
box. Color scheme represents the distributions at various particle–particle
separations.
Orientation of water molecules at the interface. (a) Definition
of the angle formed between water dipole moments and the Z-direction of the simulation box. (b–d) Distribution of the
angle formed between the dipole vector of water molecules in the first
hydration layer and the Z-direction of the simulation
box. Color scheme represents the distributions at various particle–particle
separations.The hydration film has also an
important effect on diffusion properties
of the approaching nanoparticles. It is well known that nanoparticles
in solution will exhibit a Brownian motion, with a diffusion coefficient
proportional to the temperature of the system and to the inverse of
the nanoparticle size, as prescribed by the Stokes–Einstein
relation. Is the diffusion coefficient of a nanoparticle affected
by the presence of a second nanoparticle? In which way? We evaluated
the diffusion coefficient of one nanoparticle at a given distance
from the other nanoparticle in our simulations using the approach
of refs (63)–[65] and described
in Section S13 of Supporting Information. Figure shows the
diffusion coefficients for each of the three face-to-face orientations,
both for pure and saline water. At an interparticle distance ΔZ larger than 1.5 nm, the diffusion coefficient reaches
a plateau of ca. 6 × 10–11 m2/s,
which appears as the bulk value of the diffusion coefficient. The
bulk value appears to be the same in pure and saline water. Closer
than 1.5 nm, the diffusion coefficient decreases, becoming as slow
as more than six times smaller than that in the bulk. The trend of
the diffusion coefficient as a function of the distance ΔZ appears only weakly affected by the specificity of the
face-to-face orientation and the presence or absence of salt in water.
However, it can be noticed that in saline water, the decrease in mobility
is more pronounced than that in pure water.
Figure 5
Diffusion coefficients
along the Z-direction of
the upper kaolinite particle in the simulation box as a function of
particle–particle separation calculated for different orientations
in pure water (left) and in saline water at 1.2 M NaCl concentration
(right).
Diffusion coefficients
along the Z-direction of
the upper kaolinite particle in the simulation box as a function of
particle–particle separation calculated for different orientations
in pure water (left) and in saline water at 1.2 M NaCl concentration
(right).This reduction of the nanoparticle
mobility can be explained by
the behavior of the hydration water. We have measured in our simulations
a sharp reduction of the diffusion coefficient of water in the proximity
of the nanoparticle faces, see Section S12 and Figure S13 of Supporting Information. Notice that this decrease
in the mobility of water, and the corresponding increase in viscosity,
is in good agreement with several experimental observations.[61,66] Moreover, experiments[67,68] also show that the
viscosity of water increases by roughly 10% with the concentration
of NaCl used in our study. The reduction of the nanoparticle mobility
when closer than 1.5 nm appears to be closely related with the increased
viscosity of the hydration film.
Conclusions
In
this work, we have used atomistic molecular dynamics simulations
and enhanced sampling techniques to investigate and characterize the
interaction between two nanoparticles of kaolinite. Kaolinite particles
have roughly the shape of an hexagonal prism, with the two basal faces
being inequivalent, as are the side edges. As such, the interaction
between two particles depends on their relative orientation. We studied
the three possible face-to-face orientations and all the representative
face-to-edge orientations.A remarkable anisotropy of the interaction
emerged. Face-to-edge
interfaces yield a PMF that is much flatter than face-to-face interfaces.
In the latter case, two of the orientations result in a repulsive
interaction and one, the interface between the inequivalent faces,
yields an attractive interaction. We notice that the PMF profiles
exhibit different features depending on the distance between the two
particle surfaces. On the one hand, by disentangling the contributions
that sum up to give the overall interaction energy, we infer that
the attractive or repulsive nature of the interaction, for distances
larger than ca. 1.5 nm, is determined mainly by electrostatics. On
the other hand, at shorter separations, the structure of water confined
between the particles has to be carefully understood as this determines
the interaction profile. We notice a tendency to form water
layers, which correspond to the local minima in the free energy which
yields a very corrugated PMF.We have evaluated the PMF profiles
in pure water and in saline
solution. In saline solution, the ions have a tendency to adsorb preferentially
on the basal faces of the particles, counteracting the intrinsic dipole
across the kaolinite particles. Therefore, ions screen the electrostatic
interparticle interaction, and the long-range PMF profiles show a
much weaker interaction in saline water than that in pure water. However,
ions do not appear to affect greatly the corrugation of the PMF profiles
at small particle–particle separations.Our characterization
of the interaction between kaolinite nanoparticles
can be compared with alternative theoretical approaches to characterize
the interaction energies between (nano)-particles. The most common
approach is the DLVO theory (named after Derjaguin, Landau, Verwey
and Overbeek), which is in general valid at large particle–particle
separations. We have here investigated the PMF profile up to 3 nm,
so our approach can be complementary to DLVO as it assesses the properties
of interfaces among particles at larger distances. The interval of
the PMF profile that we have investigated here is, we think, the most
relevant for the aggregation of particles and the formation of fines.
It can be used as a solid basis for further investigations aimed at
modeling the aggregation of several particles.Experiments based
on high-resolution atomic force microscopy have
already provided important information on the properties of clay interfaces.[4−9] They are mostly interpreted in the context of DLVO theory and are
used to estimate the surface charge distribution in clays at different
environmental conditions. Hopefully, new experiments performed between
isolated kaolinite particles and functionalized tips (including surface
charge measurements) could validate the results presented here and
provide further insights into the importance of the ionic environment
on particle aggregation.