Driving Force for the Hydration of the Swelling Clays: Case of Montmorillonites Saturated with Alkaline-Earth Cations
Fabrice Salles a, Jean-Marc Douillard a, Olivier Bildstein b, Cedric Gaudin a, Benedicte Prelot a, Jerzy
Zajac a, Henri Van Damme c
a Institut Charles Gerhardt, UMR 5253 CNRS-UM2-ENSCM-UM1, Université Montpellier II, Place E. Bataillon,
34095 Montpellier Cedex 5, France
b CEA, DEN, DTN Cadarache, F-13108 Saint Paul Les Durance, France
c ESPCI-Paris Tech., UMR 7615, CNRS-UPMC-ESPCI, 10 Rue Vauquelin, 75231 Paris Cedex 05, France
AUTHOR EMAIL ADDRESS: fabrice.salles@um2.fr
KEYWORDS. Hydration Energy, Surface, Electrostatic Calculations, Interlayer cations, Cation Exchange
ABSTRACT: Important structural modifications occur in swelling clays upon water adsorption. The multi-scale evolution
of the swelling clays structure is usually evidenced by various experimental techniques. However the driving force behind
such phenomena is still not thoroughly understood. It appears strongly dependent on the nature of the interlayer cation.
In the case of montmorillonites saturated with alkaline cations, it was inferred that the compensating cation or the layer
surface could control the hydration process and thus the opening of the interlayer space, depending on the nature of the
interlayer cation. In the present study, emphasis is put on the impact of divalent alkaline-earth cations compensating the
layer charge in montmorillonites. Since no experimental technique offers the possibility of directly determining the hydration contributions related to interlayer cations and layer surfaces, an approach based on the combination of electrostatic calculations and immersion data is developed here, as already validated in the case of montmorillonites saturated
by alkaline cations. This methodology allows to estimate the hydration energy for divalent interlayer cations and therefore to shed a new light on the driving force for hydration process occurring in montmorillonites saturated with alkalineearth cations. Firstly the surface energy values obtained from the electrostatic calculations based on the Electronegativity
Equalization Method vary from 450 mJ.m-2 for Mg-montmorillonite to 1100 mJ.m-² for Ba-montmorillonite. Secondly,
considering both the hydration energy for cations and layer surfaces, the driving force for the hydration of alkaline-earth
saturated montmorillonites can be attributed to the interlayer cation in the case of Mg-, Ca-, Sr-montmorillonites and to
the interlayer surface in the case of Ba-montmorillonites. These results explain the differences in behavior upon water
adsorption as a function of the nature of the interlayer cation, thereby allowing the macroscopic swelling trends to be
better understood. The knowledge of hydration processes occurring in homoionic montmorillonites saturated with both
the alkaline and the alkaline-earth cations may be of great importance to explain the behavior of natural clay samples
where mixtures of the two types of interlayer cation are present and also provides valuable information on the cation
exchange occurring in the swelling clays.
Introduction
Smectite clays, often called swelling clays, are involved
in various industrial processes or fundamental research
activities, such as water treatment,1 greenhouse gas sequestration,2 radioactive waste storage,3-5 planetology,6
oilfield 7 or climatology.8 Their high specific surface areas
(up to 760 m².g-1), high cation-exchange capacities, as well
as propensity to macroscopic swelling are of primary
interest. The microscopic structures are composed of
negatively charged silicate layers interacting with interlayer cations and adsorbed water molecules. The impact
of the water molecules on the swelling clay structure was
evidenced for smectites with different physical states
(shales, pasty muds, gels and dilute aqueous solutions) as
a function of the hydration state.9 To analyze the swelling
in such materials, the interaction between water molecules and the microscopic structure has to be evaluated.
At the macroscopic scale, the swelling of the smectitetype samples was evidenced as the increase in the apparent sample volume during adsorption of water. At the
microscopic level, the description was much more complex owing to the multiscale structure of smectite clays
and to the intermolecular forces acting between layers,
cations and water.10
The ideal microscopic structure of smectite-type clays is
composed by a stack of silicate layers separated by perfect
cleavage planes (Figure 1). The phyllosilicate is made by
sandwiching a sheet of Mg2+ or Al3+ ions in the octahedral
coordination between two sheets of SiO4 tetrahedra. Ionic
substitutions can occur in the octahedral or tetrahedral
sheet, and the silicate layers bear a negative charge compensated by interlayer cations, which are naturally mono(Na+, K+) or divalent (Ca2+ or Mg2+). To this regard, when
montmorillonite is altered, in contact for instance with
saline water, it may undergo structural modifications
leading to the removal of Mg2+ from the octahedral sheets
towards the interlayer space.11 The present study focuses
on montmorillonites, i.e. a class of swelling clays bearing
electric charge mainly due to octahedral substitutions
(see Figure 1). The compensating cations considered here
belong to the family of alkaline-earth metals and include
Mg2+, Ca2+, Sr2+, and Ba2+.
ized by calculating the hydration energy for alkaline cations and layer surfaces in the MX-type structures. The
driving force for hydration was shown to be strongly dependent on the nature of the interlayer cation,28 the
swelling inhibitor effect of the Cs+ cation being clearly
evidenced.22
Even if a multi-scale description was established,3,10,18,19,
it was also well accepted that the main energetic component for the clay hydration comes from the interlayer
space.22
29
Some multi-scale simulations were also performed on
swelling clays but only few of them provide a global vision
of the hydration process.30 Molecular simulations mainly
focused on a microscopic description of the mechanisms
involved in the hydration processes.31 The nature of the
interlayer cation, the position and the number of substitutions in swelling clays strongly influence upon the hydration capacity and the swelling capacity.32-40 Indeed the
electrostatic interaction has been shown to be the most
important component of the energy in montmorillonites
compared to the dispersion interactions,41 confirming that
the electrostatic charge of the interlayer cation and therefore its hydration ability is a key parameter to understand
the hydration process occurring in swelling clays.42 The
development of new force field taking into account the
polarization of the ions is in progress but still too complex
to be implemented for large systems.43 Furthermore a
large hydration energy for cations results in a large mobility upon hydration which explains the capacity of exchanging these interlayer cations in the MX structures. 4446
Figure 1. Unit cell considered in the partial charge calculations
for divalent montmorillonites: Si (purple), O (red), H (small balls
in cyan), Al (cyan), Mg (green), divalent cations (brown)
It was previously shown for alkaline or alkaline-earth
compensating cations that the nature of the interlayer
cation strongly influenced the interlayer space opening,
characterized by X-Ray Diffraction,12-17 at the dry state as
well as upon water adsorption.18-21 The total amount of
adsorbed water is also modified, as recently observed,19
thereby leading to important differences in (i) the specific
surface area available for water, (ii) the structural evolution of the montmorillonites (MX) samples, as well as (iii)
the repartition of water molecules in the different
pores.6,19,22-24 As far as the impact of the interlayer cation
on water adsorption is concerned, the smallest alkaline
cations (Li+ and Na+) were found to interact strongly with
water molecules imposing a strong swelling in the interlayer space in agreement with other studies.25,26 In contrast, the largest alkaline cations (K+, Rb+ and Cs+) interacted with few water molecules resulting in small impact
on the structures.22,27 These results were further rational-
It follows from all above studies that the determination
of the hydration energy is necessary to understand the
variety of processes occurring in swelling clays, such as
cation exchange, multi-scale hydration process and structure evolution. Moreover the relationship between swelling and hydration energy for divalent interlayer cations is
not trivial,7 neither are the causes of differences in the
hydration mechanism.26 The intention of the present
study is to estimate the impact of alkaline-earth cations,
as compensating ions in the MX structures, on the hydration process. In a first stage, it was possible to calculate
the surface energy of MXs saturated with alkaline-earth
cations, estimated from the energy of the cohesion between layers. With the injection of immersion data issued
from literature, both the hydration enthalpy of a cation
confined in the interlayer space and the hydration enthalpy of the layer surface could be extracted. Based on
the indications obtained when applying such a strategy,
the driving force for the hydration mechanism in the MX
structures was discussed to shed more light on the effect
of the nature of the interlayer alkali-earth cation.
Computational Section
1. Lattice energy
The first step of the calculation corresponds to the lattice energy in a crystal with the use of the Madelung matrix. This matrix represents the electrostatic influence
relative to the different positions of the atoms constituting the crystal. For the purpose of calculation, the whole
crystal structure (including H atoms), the space-group of
the crystal and the formal charges must be known, as
detailed elsewhere.47 The electrostatic part of the lattice
energy, corresponding to the actual attractive part of this
energy when considering ionic solids,48-49 is then obtained
from the following expression:
N a M e2
Ue  
re
[1]
The effective electrical charge located on a chemical species interacting via chemical bonds is related to the capacity of atoms to attract electrons. This is formally included in the term of electronegativity. Another concept
may be also introduced so as to describe quantitatively
the chemical bonds: the hardness being a measure of the
resistance of a chemical species to change its electronic
configuration.50 These two concepts have been extended
in the framework of density functional theory.51 In this
theory, the chemical potential µ of the electrons of the
system studied is the derivative of the energy, E, with
respect to the number of electrons, N, at a constant external potential, ν, and it is equivalent to the electronegativity χ:
[2]
The hardness η is then defined as,
[3]
Practically, the overall distribution of the electron density
around atoms is calculated in a molecule or a crystal using the above notions and as a function of the scales chosen for electronegativity and hardness. To reach such an
electronic density, the chemical potential equalization
method has to be applied to different atomic charge
clouds upon bond formation, and then it is possible to
determine the atomic charges. The calculation is trivial
for diatomic molecules A-B: for any electron transfer dN
from B to A at the internuclear distance r, where the
change in energy is described as follows:
 E 
 E

dE  
 
 N A  N B ,r  N B
 
 E 
  dN   
dr
 r  N A , N B
 N A ,r 
The equalization of the effective electronegativities of A
and B is ensured by the change dN of the effective atomic
charges qi. Based on the above-mentioned definition of
the hardness, a relation can be derived between the atomo
2. Atomic charge
 2E 
  
   2   

 N   N 
[5]
ic electronegativities  i , the charges qi, the hardnesses
where Ue, Na, M, e and re correspond, respectively, to the
lattice energy, the Avogadro number, the Madelung constant, the electron charge and the internuclear distance.
The choice of re is discussed in more details elsewhere.47
In this case, the crystal is supposed to be fully ionic.
  E / N    
 E 

 E 


 dN
0  
 
 N A  N B , re  N B  N A , re 
[4]
In this case, the equilibrium imposes the condition dr = 0
(i.e. r = re, where re is the equilibrium internucleus distance) and dE = 0. Hence Eq. 4 is simplified as follows,
i and the resulting mean electronegativity  which
corresponds to the mean electronegativity value after
taking into account the effect of the partial charges:
 A   A0   A q A   B0   B qB   B  
[6a]
which results in the charge:
qA 
 B0   A0
 A B
[6b]
From this equation, the difference in electronegativity can
be considered as driving the electron transfer in contrast
with the sum of hardnesses which is opposed to this
transfer.
The calculation becomes more complex when passing to
crystals, where forces act at relatively long distances and
where spatial summation is rather to be done. It is thus
necessary to know the electronegativities, the hardnesses
and the equilibrium distances for all atoms in the crystal.
For the purpose of the present study, the Allen electronegativity scale is adopted, as being related to spectroscopic characteristics of the atom.49,52 In addition, the
present model includes the hardness scale linked to the
radius of the atom considered as a sphere with a uniformly distributed electric charge q.53 The radius is taken equal
to the size of the diffuse orbital of the element (this hardness scale is detailed by Henry 53). In this formulation, the
calculation is independent of the assumptions or relative
scales but it depends only on physical values that can be
determined by spectroscopic techniques or quantum
calculations. Another important advantage of such a
model is the fact that no value of the charge of a chosen
atom has to be assumed, which is unfortunately often the
case in the calculations reported in the literature.54-56 The
hardness values used in this work have been collected in
Table 1.
Atom
Hardness (pm)
Si
O
Mg
106,8
45
127,9
Al
H
Mg
131,2
53
127.9
Ca
Sr
Ba
169
183
206
Table 1. Atom hardness values adopted for the purpose of calculations following Ref. 53 and 58.
a finite layer, especially, great changes in the electrostatic
energy are observed when developing various models of a
layer.28 The energy can be finally extrapolated to a value
representing a layer infinite in two directions of the space
and finite in the third one. With this assumption in mind,
the other parts of the energy (mainly due to dispersive
forces) are considered as being insensitive to any modification of the layer dimensions. The difference in the electrostatic energy expressed as per unit surface area can be
considered as the total variation of the attractive energy
between a semi-infinite layer and an infinite crystal (see
Figure 2).48 Finally, this energy can be viewed as the cohesive energy of the crystal, corresponding to the energy
required when separating the layers composing the crystal. The energy difference between the crystal and the
finite layer is divided by the surface area of the layer,
directly determined from the crystallographic data.
3. Calculations for crystals and layers
The mean electronegativity for an infinite crystal is determined by the following equation:
  i0 
e
40ri
qi 
1
40
n
M
j 1
i, j
eq j
n
with the condition:
q  z
i 1
i
[7]
The Madelung tensor Mi,j takes into account the geometry
of the crystal studied, by directly computing it from atom
positions using routine procedures. The computation of
the atomic charges qi is then straightforward. When this
distribution is established, Henry’s summation, developed
in the Partial Atomic Charge and Hardness Analysis
(PACHA) formalism,53 leads to the Electrostatic Balance
(EB):
EB 
e2 n n
 M i, j qi q j 
8Z0 i 1 j 1
Figure 2. Structures considered for the calculations: (a) infinite
crystal for montmorillonites and (b) semi-infinite lamella according a and b axes.
The unit cell and the c-axis are also reported.
[8]
If the ionic charges are considered instead of the atomic
charges in Eq. 8, this results in calculation of the electrostatic part of the lattice energy, Ue, defined previously in
Eq. 1 (note that the summation of the Madelung tensor
gives the Madelung constant). Then, the EB parameter
corresponds to the effective electrostatic part of the bond
energy. It has already been shown that the electrostatic
part of the energy, including also the repulsive forces,
attains, at first approximation, about 90% of the attractive
part.49 Furthermore, the electrostatic calculation in a 2D
lamellae structure is difficult to be implemented and very
expensive in computer memory.57 Instead 2D finite structures are considered for calculation since the results are
close to those obtained in calculation with a semi-infinite
crystal. In particular, the energy evolution as a function of
the number of atoms converges to that observed for the
2D infinite crystal.28
Accordingly, some modifications of long-range forces are
supposed to occur when comparing an infinite crystal and
The following equation can be used to calculate the cohesion energy of a solid per unit surface area:
attr
U coh
 U (crystal )  U (layer )  EB(crystal )  EB(layer ) Asc
[9]
where
c
s
A is the surface area of the layer shown in Fig. 2.
If such a layer is built along two crystal axes, proportionally to the cell dimensions, it is easy to relate the surface
area involved in the defined process to the molecular
lengths, linked in turn with the a, b and c cell parameters.
By definition, the energy of cohesion per unit surface area
is twice the surface energy.49 In the case of clays, the calculation following the above procedure results in the
energy of cohesion between different layers along the caxis, which is perpendicular to the ideal plane of cleavage.28,58
Crystallographic structures
Any meaningful calculation should be done only on a
MX structure with precise atom positions as a starting
point. The Tsipursky and Drits structure 59 has been cho-
sen in the present consideration. In such a structure, the c
parameter in the unit cell is modified as a function of the
nature of the interlayer cation. The corresponding crystallographic data are given in Table 2.
Crystallographic formula
Space Group
a (nm)
b (nm)
Alpha
Beta
Gamma
M Si16Al6Mg2O48H8
P1
0.517
1.788
90
90
90
c (nm) for Mg
c (nm) for Ca
c (nm) for Sr
c (nm) for Ba
0.975
0.980
1.003
1.021
Table 2. Crystallographic parameters for montmorillonites and cvalues for the montmorillonites saturated with alkaline-earth
cations adopted following Ref. 59
MX is a phyllosilicate formed by aluminosilicate layers
stacked above one another, each layer being composed of
silicon, aluminium, magnesium and oxygen atoms (see
Figure 1). A simplified formula is: (Na, 0.5Ca)0.6
(Al,Mg)4Si8O20(OH)4, nH2O, where Na and Ca cations are
the interlayer ions placed between the aluminosilicate
layers. In the type of structure considered here, neither
the existence of tetrahedral substitutions (Al instead of Si)
nor the presence of the iron atoms in the layer are taken
into account, because of the small number of substitutions in tetrahedral sites and the small amount of iron.
These assumptions are commonly accepted in other papers.28,54-56
Within the layer, an octahedral substitution can occur
and this corresponds to a partial replacement of aluminium atoms by magnesium ones in an octahedral sheet. A
negative charge appears due to such substitutions and it
must be compensated by interlayer cations. Generally,
Na+, Ca2+, Mg2+ are present as interlayer cations in the
natural samples For the purpose of the present work, such
alkaline-earth cations as Mg2+, Ca2+, Sr2+, and Ba2+ are
considered.
The MX structure can be built up either using the C2/m
or C2 space group. With the PACHA code, the C2 symmetry appears much simpler to be processed with the
Tsipurski and Drits structure.59 In this case, the cell dimensions for the Na-MX are: a= 0.517±0.002 nm,
b=0.894±0.002 nm, c=0.995±0.006 nm, β=99°54’±30’. The
insertion of alkaline-earth cations into the interlayer
space involves both the consideration of a double unit cell
with respect to the b parameter and the modification of
the c value, following the interlayer opening necessary for
a given alkaline-earth cation. The unit cell parameters are
taken from the literature.60-61 Moreover the alkaline-earth
cations are supposed to occupy similar adsorption sites as
the alkaline ones. In line with the previous papers,28 the
same Mg/Al ratio corresponding to one (+2) charge per
O48H8 is considered.
It is necessary to note that the simulated structures do
not contain any water molecules since the surface energy
of MX at the dry state is really needed. In addition, the
ideal simulated structures (i.e. without any structural
defects) present a perfect cleavage plane, which is generally difficult to achieve experimentally. Furthermore no
distorsion on the a and b parameters has been imposed to
the silicate layer at the dry state or because of the insertion of different interlayer cations.
Results and Discussion
1.
Surface Energies of MXs Saturated with AlkalineEarth Cations
The partial charges are determined for the different atoms
constituting the structure and are expressed using the
unit of electron charge for Ca-MX (Table 3). Similar
charges for the framework are obtained in the case of
MXs saturated with other alkaline-earth cations using the
same strategy.28 Finally only the partial charge of the
interlayer cation strongly varies. The comparison of the
framework partial charges with those reported for MXs
saturated with the alkaline cations 28 provides similar
trends: the Al atom is still considered as the most charged
framework species, even if two types of aluminium can be
distinguished: one close to the OH group and another one
close to O-Si groups. The charge differences are relatively
important and they vary in the range of 0.85 to 0.90 and
of 1.30 to 1.40, respectively. This effect has been already
observed in the case of MXs compensated with alkaline
cations. It is worth noting that the relative order of the
different charges assigned to the atoms obtained here is
consistent with others studies using partial charges implemented in molecular dynamics and Monte Carlo simulations.7,31,44,55,62
The replacement of an interlayer cation by another alkaline-earth cation does not modify drastically the charges
of the other elements, nor does the trend in the distribution of charges among these elements. Only the atomic
charge of the interlayer cation depends on its nature. In
the case of Mg- and Ca-MX, the partial charges of the
interlayer cation are close to 1 and 2, respectively, mainly
due to the difference of the cation radius. The Sr- and BaMX structures bear charges equal to 2.38 and 3.08, respectively. This means that the stoichiometry adopted in the
present model of MX is valid in the case of Mg2+ and Ca2+,
but not for Sr2+ and Ba2+ as interlayer cations. Nevertheless, the atomic charge variation calculated for a given
interlayer cation also reflects the strength of its bonding
to the layers. This force increases from Mg2+ to Ba2+,
which is consistent with the results of the hydration ability as evaluated by immersion calorimetry and X-Ray
diffraction.60,61
H
O
Al
Si
Mg
Ca
Charges
0.123
-0.546
1.196
0.859
1.143
2.007
Table 3. Partial charges obtained for the Ca-containing montmorillonite
The EB energy of the layer varies with the length of the
layer, i.e., with the number of atoms considered in the
calculation, and reaches a plateau obtained when the
number of atoms used in the computation reaches about
2000 giving the surface energy value E (in mJ.m-2) according to Eq. 9 (Figure 3). 28
Figure 3. Surface energy evolution as a function of the cation
radius.
The (ab) face is assumed is assumed to be representative
of the overall surface of a crystal of MX in natural conditions. The resulting energy values can be thus viewed as
the surface energies of the various systems, because the
ab surfaces are obtained by an ideal cleavage. These results fall in line with the surface energy of nonswelling
clays or silicas estimated using a very different approach
based on experimental results.63 For example, the surface
energies of kaolinites and illites, being close to the dry
MX, were found to be about 376 and 458 mJ.m-2 respectively. The electrostatic model calculations provided similar results for nonswelling clays, as already published
elsewhere.28,64,65 This agreement validates our approach
and the use of electrostatic values to estimate the surface
energy. From these calculations, the surface energy values
calculated here for the divalent MXs are found to be larger than those obtained for the nonswelling clays. The
comparison with the values observed for the MXs saturated with alkaline cations shows that the highest value is
reached in the case of Ba-MX.28,58,66 Finally, the surface
energy sequence at the dry state increases in the following
order: Li < Na < Mg < K < Rb < Ca < Sr < Cs < Ba. As the
surface energy probes the ability of the structure to open,
the cohesion of the interlayer space in Li-MX is thus
weaker than that determined in Ba-MX. This evolution is
consistent with the trends given from the X-Ray Diffraction data for montmorillonites saturated with alkali and
alkali-earth cations. 15,16,25,60,61 In addition, in the case of a
mixture of interlayer cations (Na+ and Ca2+), the Ca2+ are
found preferentially in the interlayer space, while the Na+
are located in mesopores.67-69
2. Decomposition of Immersion Enthalpies.
The surface energy determined for the dry state can be
related to the immersion enthalpy, immH, by the following definition: immH = HSL-H°S
[10]
where H°S is the surface enthalpy for the dry state and HSL
is the surface enthalpy for the liquid-solid interface.
By plotting the values of immH as a function of the surface energy for the dry state, the slope of the curve should
be equal to -1, as was confirmed in the case of nonswelling
clays (kaolinite, serpentine, chlorite and talc) (e.g., see
Figure 4).28 When one keeps the slope equal to -1, the
intercept of the immH vs. H°S plot should provide the
liquid-vapour interfacial enthalpy, HLV, for water. A good
agreement is again observed with the theoretical value of
118.5 mJ.m-², as reported previously for the MXs saturated
with alkaline cations and as shown in Figure 4.
In the case of MXs saturated with alkaline-earth cations,
the enthalpy of immersion and the Harkins Jura specific
surface area considered from literature in the present
study, were measured by Berend et al. (see Table 4).60-61
The plot of the surface energy for the dry state, as calculated in the previous section, as a function of the immersion enthalpy is shown in Figure 5. In this case, the slope
is positive and equal to 2.066 (far from the expected value
of -1 (Eq. 10)).This means that the compound with the
highest cohesion energy (Ba-MX) does not interact
strongly with water and appears therefore to be the most
difficult to be hydrated.
Immersion Heat
Specific
Surface Area
Immersion
(J g-1)
(m²g-1)
(mJ m-²)
Mg
148
50
2960
Ca
131
63
2079
Sr
104
63
1651
Ba
86,4
53
1630
Montmorillonites
Table 4. Heats of immersion and Harkins-Jura specific surface
areas selected for montmorillonites saturated with alkaline-earth
cations.60
These results can be rationalized in the following way. In
immersion experiments performed with nonswelling
clays, layer hydration is the only process occurring. In
contrast, owing to the presence of exchangeable and hydrating cations, the immersion process in swelling clays
can be decomposed at least into three elementary processes: layer hydration, cation hydration and swelling.
Figure 5 shows that the slope of the curve linking the
surface energy at the dry state with the immersion enthalpy is opposite in sign, with respect to the theoretical
value, when only layer hydration is considered (i.e., nonswelling clay behaviour). Hence the discrepancy may be
assigned to the hydration enthalpy of the interlayer cations and to the swelling energy, corresponding to the
For non-swelling
compounds the
(kaolinite,
serpentine,
talc,
energy required
to separate
silicate
layers.
ed from Eq. 11. The results and the evolution of the hydration energy as a function of the cation radius are shown in
Figure 6.
chlorite)
Surface Energy (mJ/m2 )
0
0
200
400
600
800
1000
1200
-100
Immersion enthalpy (mJ/m2)
-200
-300
S
T
K
-400
-500
 immHNS = Ehydration layer
-600
-700
Domain of
Swelling
Clays
-800
-900
y = 118,5 -x
C
Figure 5. Relationship between the experimental immersion
enthalpy for exchanged montmorillonite samples (issued from
references 60 and 61) and the theoretical surface energy for
divalent montmorillonites obtained from the electrostatic
calculations.
-1000
The immersion enthalpy of a swelling clay can thus be
decomposed by referring to the calibration curve obtained for nonswelling counterparts in Fig. 4. The energy
of cation hydration can be consequently determined from
the following equation:
Ehydration of cation =immH – Eswelling – Ehydration of layer
[11]
The swelling energy, Eswelling, can be estimated using electrostatic model calculations 28 as the difference between
two successive surface energy values for different interlayer space distances. By this way, the evolution of the
swelling energy can be evaluated as a function of the
interlayer distance. For each surface energy calculation,
the partial charge distribution is needed to evaluate the
infinite crystal energy and the lamellae energy (the 2D
infinite crystal). The results confirm that the contribution
of the swelling energy is small compared to the dry energy
and is limited to 50 mJ.m-² at the most. This gives an
important argument for neglecting the contribution of
the swelling energy in the calculations.
3. Hydration Energy for cations and surface layer
Assuming that the swelling energy can be neglected, the
layer hydration energy can be directly determined from
the appropriate calibration curve in Figure 4, as explained
in the previous paragraph. Figure 5 illustrates the M-MX
layer hydration process decomposed on the basis of the
surface energy for the dry state. Knowing the layer hydration energy, the cation hydration energy is then calculat-
500
Hydration Energy (mJ.m-2)
Figure 4. Evolution of the experimental immersion enthalpy as a
function of the theoretical surface energies for non-swelling
clays: kaolinite (K), talc (T), serpentine (S) and chlorite (C) (from
the experimental results56 and electrostatic calculations58,63-65).
0
Surface
-500
Ca
-1000
Mg
Sr
-1500
Ba
-2000
-2500
Cation
-3000
80
90
100
110
120
130
140
150
Cation radius (Å)
Figure 6. Evolution of the hydration energy for both surface and
cation (in mJ m-2) obtained from the model developed here to
distinguish each composante of hydration energy as a function
of the nature of the interlayer cation in the case of divalent
montmorillonites.
Straight lines represent the hydration energy values for the
cation while the dash lines represent the surface hydration energy.
Generally speaking, the trend observed in the cation hydration energy is in agreement with the Hofmeister series
and with the results obtained by Monte Carlo and other
types modelling.54-56,70 This trend is also supported by
Molecular Dynamics simulations performed in the case of
zeolites saturated by alkali-earth cations.70 The hydration
energies for various interlayer cations determined in the
present work parallel well with the hydration energy
trends of these cations in aqueous solutions. The hydration energies for cations in the clay structure are system-
atically smaller than those obtained in bulk water (Figure
7). Two effects may be invoked to explain this difference.
Firstly, one can consider that the number of water molecules surrounding a cation in its hydration shell is smaller
when it is located in the interlayer space compared to the
situation in bulk water due to the confinement imposed
by the quasi 2D porosity in the interlayer space. This fact
is admitted in adsorption at the Solid-Liquid interface,
where the hydration contributions to the differential
enthalpy of adsorption are of the same order of magnitude than the hydration energies obtained here.22,27 Secondly, an additional amount of energy is necessary to
eventually separate the cation from the clay surface. This
phenomenon is endothermic. However, such a movement
of ions cannot produce a great energy variation and thus
it can be neglected here. In any case, such an effect cannot be quantified without the use of other experimental
techniques, such as conductivity experiments. 27 Moreover, in our calculations, we did not take into account the
possible rearrangement of the silicate layer (modification
of the unit cell parameters according to a or b or possible
rearrangement of the framework atoms ), a phenomenon
which is evidenced in other flexible solids. 72-74 In addition,
the high hydration energy values calculated for the alkaliearth cations in montmorillonites explain the relatively
ability of the interlayer space to open compared to
montmorillonites saturated by alkali cations.22,27,60,61
Hydration Energy of the Cation
in Bulk Water (kJ.mol-1)
-500
Sr
-550
Ba
Finally, the results obtained in the framework of this
study may be confronted with the experimental adsorption isotherm and XRD data. Trends similar to the ones
observed here were deduced on the basis of the structure
models applied to analyse the XRD profiles as a function
of relative humidity.15 Indeed the Mg and Ca-MXs were
found to hydrate at lower pressures than the Sr- and BaMXs. The immersion heat obtained in calorimetry measurements followed the same trend as a function of the
nature of the alkaline-earth cation.60,61,77
In accordance with the values obtained for the hydration
energy of both the cation and the layer surface, the hydration mechanism can be now extended to include the conclusions referring to alkaline cations. Alkaline cations
possessing high hydration energy (Li+ and Na+) are relatively mobile in the interlayer space. In the case of alkaline-earth cations, Mg2+ and Ca2+ are mobile in the interlayer space, while Ba2+ should be strongly linked to the
clay layer. This conclusion is first supported by the analysis of the ratio between the hydration energy determined
for the cation in bulk water and in the interlayer space, as
well as its impact on the cation exchange.78-80
Conclusions
-600
Ca
-650
-700
Mg
-750
-800
-220 -200 -180 -160 -140 -120 -100 -80
of the hydration of the clay structure (Figure 6). The cation-water interaction provides smaller energy contribution
in this MX, which does not promote the hydration process. The intermediate case is observed for Sr-MX where
the two contributions are equivalent. Such a result is
validated by previous Molecular Dynamics simulations
performed for Mg-montmorillonite, where the Mg2+ interlayer cation were found to be hydrated with 6 H2O while
the layer surface barely interact with water molecules.75-76
-60
-40
Hydration Energy for the Interlayer Cation (kJ.mol-1)
Figure 7. Relationship between the hydration enthalpy of a given
cation in aqueous solution (from Gershel 80) and the hydration
energy calculated from our electrostatic calculations and the
methodology to estimate the different parts of the hydration
energy in the case of divalent montmorillonites.
Based on the different contributions to the overall hydration energy, it is possible to elucidate the driving force for
hydration in swelling clays. As illustrated in Figure 6, the
driving force is strongly dependent on the nature of the
interlayer cation. For Mg- and Ca-MX clays, hydration of
the interlayer cation is highly exothermic and its energy
exceeds that of the silicate layer hydration. The driving
force for the hydration in these minerals is clearly related
to the hydration of the interlayer cation. In the case of BaMX, the surface contribution is the most important part
The understanding of the hydration phenomenon is essential to predict the behaviour of smectite clays. In the
present paper, the task of correlating the results of electrostatic calculations with the experimental data taken
from the literature was undertaken so as to achieve this
objective. Using the calculation methodology, the surface
energy of MXs saturated with alkaline-earth cations at the
dry state was determined.
It appears that the larger the interlayer cation, the higher
the surface energy at the dry state, reaching a good
agreement with the previous results obtained for alkaline
interlayer cations. Furthermore, it was possible to calculate the hydration energy values for a cation and a layer
surface, based on the heat of immersion data. These results are of great importance for predicting the driving
force for hydration in the MX structure, being generally a
function of the nature of the interlayer cation. The cation
hydration favours the overall process in the case of Mg2+
and Ca2+ as interlayer cations, whereas the hydration of
layer surface has the predominant effect in Ba-MX. It is
worth noting that the surface energy at the dry state and
hydration energy values are consistent with the experimental data for MX saturated with alkaline-earth cations.
An important consequence of these results concerns the
prediction of the cation ability to diffuse and to be ex-
changed: cations possessing high hydration energy are
relatively mobile in the interlayer space.
AUTHOR INFORMATION
Corresponding Author
Dr Fabrice SALLES
Institut Charles Gerhardt, UMR 5253 CNRS-UM2-ENSCMUM1, Université Montpellier II, Place E. Bataillon, 34095
Montpellier Cedex 5, France
fabrice.salles@um2.fr
Author Contributions
The manuscript was written through contributions of all
authors. / All authors have given approval to the final version
of the manuscript. / ‡These authors contributed equally.
(match statement to author names with a symbol)
ACKNOWLEDGMENT
The authors acknowledge, with gratitude, financial support
for this research from the GNR FORPRO network (a research
network of French National Centre for Scientific Research
CNRS and National Agency for Radioactive Waste Management ANDRA).
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Chem. Mater.
Driving Force for the Hydration of the Swelling Clays: Case of Montmorillonites Saturated
with Alkaline-Earth Cations
Using electrostatic calculations, we determine
the surface energy for the dry state in swelling
clays such as montmorillonites presenting a
ideal plane of cleavage. From this results and
combining with immersion data, both the
hydration energy values for the cations and the
layer surface are determined and allow us to
elucidate the driving forces for the montmorillonites saturated with alkaline-earth cations.
500
Hydration Energy (mJ.m-2)
Fabrice Salles*, Jean-Marc Douillard,
Olivier Bildstein, Cedric Gaudin, Benedicte
Prelot, Jerzy Zajac and Henri Van Damme
0
Surface
-500
Ca
-1000
Mg
Sr
-1500
Ba
-2000
-2500
Cation
-3000
80
90
100
110
120
130
140
150
Cation radius (Å)
11