Toward a Detailed Molecular Analysis of the Long-Range Swelling

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Toward a Detailed Molecular Analysis of the Long-Range Swelling Gap of Charged Rigid Lamellae Dispersed in Water A. Delville* CRMD-CNRS, 1B rue de la Ferollerie, 45071 Orleans Cedex 02, France ABSTRACT: Numerical simulations are performed to identify the thermodynamical origin of the long-range gap detected during the swelling of charged rigid lamellae neutralized by monovalent counterions. The short-ranged ion/lamella and water/ lamella van der Waals interactions are shown to be responsible for the large activation energy responsible for the coexistence between swollen and unswollen charged interface in the presence of bulk water. The variation of the amount of confined water molecules as a function of the interlamellar separation is determined by Grand Canonical Monte Carlo simulations, while the dynamical behavior of the confined ions and water molecules is analyzed by numerical simulations of Molecular Dynamics.

I. INTRODUCTION Aqueous dispersions of charged colloids are used in many industrial applications exploiting their stabilizing power induced by their long-range electrostatic coupling.1,2 In the presence of pure water, a large class of charged lamellae neutralized by monovalent counterions, like clay minerals36 and amphiphilic rigid membranes,713 exhibits a strange behavior not yet fully understood. At low water content, a so-called crystalline swelling is reported and corresponds to the transition between successive layers of confined water molecules.1,5,14 At high water content, continuous swelling results from the overlap1,2,8,15,16 of the layers of counterions condensed in the vicinity of the basal surface of the charged lamellae. Both behaviors were the subject of numerous experimental investigations1,314,1721 and are perfectly understood from a theoretical point of view. The last behavior (continuous swelling) is purely entropic and is well described1,2,8 in the framework of the Primitive Model22 by treating the solvent as a continuous medium. The analysis of crystalline swelling requires a molecular model of the lamella/water interface18,2332 to satisfactorily describe the hydration of the confined counterions20 whose enthalpy21 drives the water uptake of the charged lamellae. By contrast, in the intermediate regime corresponding to the transition between these two antagonistic swelling regimes, a gap was reported313 whose origin is not fully understood.32,33 The purpose of that study is to provide a molecular analysis of the lamella/water/lamella interfaces to identify the thermodynamic origin of the coexistence between swollen and unswollen lamellar phases. Previous analysis of that phenomenon was based on the detection of specific interactions between some surface sites located on the basal surface of the charged membrane and either the confined water molecules32 or the neutralizing counterions.33 Because this swelling gap is reported for a large class of materials313 without any structural similitude, we may reasonably expect to obtain r 2011 American Chemical Society

meaningful results by taking into account neither the detailed atomic structure of the charged lamella nor the exact location of its charged sites. By contrast, a molecular analysis of the solvent molecules appears necessary to describe satisfactorily the transition between the layered structure of the confined water molecules1,14 and the 3D network of hydrogen bonds occurring within the interlamellar space at larger separations.

II. METHODS The simulation cell (Figure 1) contains two charged lamellae (thickness 7 Å, section 6400 Å2, surface charge density 6.88 me Å2) neutralized by 176 sodium counterions. These parameters are selected to reproduce the geometrical and electrostatic properties of an isolated clay particle. The two fragments of lamellae are parallel to each other and divide the simulation cell in two subdomains corresponding respectively to the external and internal (or confined) fluids (see Figure 1). The ion contents of the two subdomains are the same to maintain their electroneutrality. The longitudinal separation between the two lamellae is defined as the minimum longitudinal distance between their two equatorial planes. It was varied between 20 and 40 Å, with a step of 1.25 Å, that is, small enough to detect the influence of water layering.1 While increasing the longitudinal size of the simulation cell as a function of the separation between the two lamellae, the longitudinal size of the external subdomain is kept constant, corresponding to an external separation of 50 Å between the two equatorial planes of the lamellae (see Figure 1). The water molecules are described by the classical SPCE model34 with a short-range van der Waals interaction described Received: September 8, 2011 Revised: November 18, 2011 Published: November 22, 2011 818

dx.doi.org/10.1021/jp208662y | J. Phys. Chem. C 2012, 116, 818–825

The Journal of Physical Chemistry C

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where zα stems for the longitudinal distance of the sodium ion or the oxygen atom of the water molecule from the equatorial plane of the lamella, L is the thickness of the clay lamella (7 Å), εOα and σOα are the classical LJ parameters (see eqs 1 and 2), and F is the average density of the VDW interacting sites within the lamella. To mimic clay particles, these parameters were selected to describe the water/oxygen and sodium/oxygen LJ interactions,30 while the parameter F matches the average density of oxygen atoms within the clay lamella (i.e., 0.052 atom/Å3). In the same manner, the lamella/lamella short-range interaction is given by: 2

( )3 4σ OO 12 1 1 2 þ 6 7 6 15 ðP LÞ8 ðP þ LÞ8 P8 7 2π 2 6 7 ( ) UðPÞ ¼ F εOO S6 7 6 3 1 1 2 7 4 σ 6 5 þ OO ðP LÞ2 ðP þ LÞ2 P2

ð4Þ where P is the separation between the two lamellae and S their section (6400 Å2). 3D periodic boundary conditions35 and minimum image convention35 are used to evaluate the interatomic potentials. Classical Ewald summation35,36 is used to reproduce the long range of the Coulomb potential cut by the minimum image convention. Accuracy better than 0.0005 is obtained37 by using 576 replicas with a damping parameter of 0.09 Å1. Because, at equilibrium, the longitudinal component of the pressure tensor is the same within each subdomain, it is evaluated from the longitudinal component of the force acting on each platelet. By deriving eqs 3 and 4, we obtain:

Figure 1. Snapshot illustrating one equilibrium configuration of the sodium counterions and water molecules confined between two fragments of rigid lamellae with a separation of 20 Å (see text). The two empty spaces between the three layers of water molecules are occupied by the rigid lamellae.

by the Lennard-Jones (LJ) potential: " # σ αβ 12 σαβ 6 Uαβ ðrÞ ¼ εαβ 2 r r

ð1Þ

where the indexes αβ describe the interacting sites. In the framework of the SPCE model of bulk water, the LJ parameters are30 σOO = 3.5532 Å, εOO = 14.877 kJ/mol, σNaNa = 2.6378 Å, and εNaNa = 0.5447 kJ/mol. The classical LorentzBerthelot relationships are used to determine the parameters describing the oxygensodium LJ potential: σONa ¼ 0:5ðσOO þ σNaNa Þ and εONa ¼

Pz, α ðzα Þ ¼

( )3 σ12 1 1 Oα 7 6 6 5 ð0:5L þ jzα jÞ10 ð 0:5L jzα jÞ10 7 6 ( )7 7 6 7 6 1 1 5 4 þ σ6 Oα 4 4 ð0:5L þ jzα jÞ ð 0:5L jzα jÞ 2

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi εOO εNaNa

ð2Þ The lamella/lamella, water/lamella, and sodium/lamella potentials also contain electrostatic and van der Waals contributions. The long-ranged electrostatic coupling is obtained by uniformly distributing the 88 elementary charges of each lamella within a squared network of 400 sites located within their equatorial plane. The short-ranged VDW coupling is obtained by integrating the corresponding Lennard-Jones (LJ) potentials over the whole volume of the lamella, leading to the ion/lamella and water/lamella potentials: Uα ðzα Þ ¼ 2πFεOα "

Z L=2 L=2

dz

Z ∞ 0

ð5Þ for the LJ contributions from the platelet/sodium and the platelet/water interactions, and ( )3 16σ12 1 1 2 OO þ 7 6 6 15 ðP LÞ9 ðP þ LÞ9 P9 7 4π 2 6 ( )7 F εOO 6 Pz ðPÞ ¼ 7 7 6 3 1 1 2 5 4 σ6 þ OO 3 3 3 P ðP LÞ ðP þ LÞ 2

r

ð6Þ

# σ 6O α 2 3 dr ¼ fr 2 þ ðz jzα jÞ2 g6 fr 2 þ ðz jzα jÞ g σ 12 Oα

" πFεOα

for the LJ contribution from the platelet/platelet interaction. Grand Canonical Monte Carlo (GCMC) simulations35,38 are first performed to determine the number of confined water molecules in equilibrium with a reservoir of bulk water. Simulations of Molecular Dynamics (MD)35 are later performed to extract dynamical information on the mobility of the confined water molecules. The quaternion procedure is used to describe water rotation in the framework of a generalized Verlet algorithm.35,39,40 A Berendsen thermostat41 is applied to each component of the translational and rotational kinetic energy of the water molecules.

( ) σ12 1 1 Oα 45 ð0:5L þ jzα jÞ9 ð 0:5L jzα jÞ9

( ) σ6O α 1 1 þ 3 ð0:5L þ jzα jÞ3 ð 0:5L jzα jÞ3

πFεOα zα Sjzα j

ð3Þ 819

dx.doi.org/10.1021/jp208662y |J. Phys. Chem. C 2012, 116, 818–825


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Figure 4. Concentration profiles of the neutralizing sodium counterions evaluated at interlamellar separations of 20, 30, and 40 Å, respectively.

Figure 2. Concentration profiles of the oxygen and hydrogen atoms pertaining to the water molecules confined between two fragments of rigid lamellae with a separation of 20 Å. The origin coincides with the equatorial plane of the charged lamellae. Negative and positive values of the abscissa correspond to water molecules pertaining to the internal and external subdomain, respectively.

Figure 5. Radial distribution function and mean hydration number characterizing the water organization in the vicinity of the sodium counterions confined in the internal and external subdomains limited by two clay fragments with a separation of 20 Å.

Figure 3. Local order parameter (cf., eq 7) of the water molecules confined evaluated at interlamellar separations of 20, 30, and 40 Å, respectively.

some preferential orientation: they direct one of their hydrogen atoms in the direction of the negatively charged wall to optimize their electrostatic energy. The local order parameter is used to quantify such specific ordering of the water molecules:

An elementary step of 0.5 fs is used to integrate the water and ionic trajectories.

P2 ðcosðθÞÞ ¼

III. RESULTS AND DISCUSSION

3 cosðθÞ2 1 2

ð7Þ

where θ is the angle between the bisector of the HOH angle and the longitudinal director. In addition to the strong ordering of the water molecules pertaining to the two hydration layers (i.e., at separations smaller than 10 Å), Figure 3 also exhibits a reduced local ordering of the water molecules up to separations as large as 15 Å, corresponding to a limiting lamella/lamella equatorial

A. Structure of the Confined Ions and Water Molecules. As displayed in Figure 2, the water molecules are strongly organized at contact with the rigid lamellae: the local water density increases drastically by reference to the bulk water density, and two hydration layers are clearly identified. As also displayed in Figure 1, the water molecules, at contact with the lamella, exhibit 820



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Figure 6. Variation of the interfacial water content determined by GCMC simulations (see text) as a function of the interlamellar separation. Figure 7. Variation of the longitudinal component of the total interfacial pressure and its contribution from the lamelle/lamella and ion/ lamella van der Waals interactions as a function of the interlamellar separation.

separation of 30 Å. Above that separation, water molecules behave like bulk water. As a consequence, the local ordering detected for the water molecules confined between lamellae with a separation of 20 Å differs significantly from the ordering reported at larger separations (see Figure 3) because of some interference between the water organizations induced by the two facing lamellae. Such specific ordering of the water molecules at contact with clay lamellae was previously detected by 2H NMR spectroscopy.4245 In addition to the structure of the confined water molecules, we have also analyzed the distribution of the neutralizing sodium cations within the interlamellar space. Figure 4 illustrates the influence of the separation between the two parallel lamellae on the overlap between their ionic diffuse layers of condensed counterions. Because the minimum sodium/lamella separation (7.5 ( 0.2 Å in Figure 4) is significantly larger than the minimum oxygen/lamella separation (6.0 ( 0.2 Å in Figure 2), one may reasonably expect that even condensed sodium counterions keep intact their first hydration sphere. This result is fully confirmed by the analysis of the radial distribution function of the water oxygen atoms around the sodium cations (see Figure 5). As displayed in Figure 5, the water content of the first hydration layers of both kinds of sodium counterion (5.86 ( 0.3 in the internal subdomain and 5.93 ( 0.3 in the external subdomain) does not exhibit significant difference and corresponds to fully hydrated sodium cations. Note that these results are obtained for a platelet/platelet separation of 20 Å. Because, at such separation, the major fraction of the sodium counterions confined in the internal subdomain is condensed in the vicinity of the clay surface (see Figure 4), one may conclude that the condensed sodium counterions have a nearly complete first hydration layer. This result is not surprising because previous measurements20 and numerical simulations2026 have clearly indentified sodium hydration as the driving force responsible for the water uptake by the clay interlayer. B. Swelling Pressure and Free Energy. The total number of water molecules confined between the charge lamellae increases linearly when their separation varies between 20 and 40 Å (see Figure 6). That result excludes any occurrence of water layering1 at water/lamella separations larger than 10 Å, in agreement with

the water concentration profiles displayed in Figure 2. Because, at equilibrium, the longitudinal component of the pressure tensor is the same in each subdomain, we derive it by calculating the net force acting on the rigid platelets. Surprisingly enough, the longitudinal component of the pressure exerted on the basal surface of the lamellae exhibits, in Figure 7, a strong oscillation in the same range of interlamellar separations. A careful analysis of the various contributions to the longitudinal pressure reveals that the electrostatic components of the lamella/lamella repulsion, the counterion/lamella attraction, and the water/ lamella interaction cancel out. The longitudinal pressure is thus totally driven by its short-ranged van der Waals contributions. Figure 7 also illustrates the reduced contributions from the lamella/lamella and ion/lamella VDW forces by comparison with the water/lamella contribution. The reduced contribution from the lamella/lamella VDW interaction is not surprising because of the large separations between the platelet: an attraction of the order of magnitude of 10 MPa occurs only at separations smaller than 18 Å (see Figure 7). Furthermore, the limited contribution from the ion/lamella VDW interactions results from various factors: • first, the parameters describing the range and the strength of the ion/oxygen LJ potential are smaller than those describing the oxygen/oxygen LJ potential (see eqs 1 and 2); • second, because of the complete hydration of the condensed sodium counterions (see Figure 5), the minimum sodium/platelet separation (∼7.5 Å in Figure 4) is always larger than the minimum oxygen/platelet separation (∼6 Å in Figure 2); • third, the local density of the oxygen atoms from the water molecules exceeds by 1 order of magnitude the maximum local density of the sodium counterions (see Figures 2 and 4). As a consequence, the net longitudinal pressure results from the VDW interactions between the charged lamellae and the confined water molecules. 821



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Figure 8. Variation of the interfacial free energy obtained by the integration of the interfacial pressure displayed in Figure 7 (see text). Figure 9. Velocity autocorrelation functions characterizing the mobility of the water molecules located, respectively, in the internal and external subdomains limited by two lamellae with a separation of 20 Å (see text).

The variation of the longitudinal pressure as a function of the platelet/platelet equatorial separation (see Figure 7) is fitted by a simple four-order polynomial law, whose integration gives the variation of the free energy predicted during the swelling of the interface: ΔFðzÞ ¼

Z z 40

Ptotal ðzÞ dz

the HOH bisector47 by reference with the longitudinal director: GðτÞ ¼ Æcosðθð0ÞÞcosðθðτÞÞæ

ð8Þ

As displayed in Figure 9, we obtain the nearly same velocity autocorrelation functions quantifying the radial mobility of the internal and external water molecules, corresponding to water molecules confined between lamellae with a separation of 20 and 50 Å, respectively. By contrast, the velocity autocorrelation functions quantifying the longitudinal mobility of the same water molecules differ significantly. However, the corresponding components of the self-diffusion tensors (see Figure 10), obtained by integration (see eq 9), appear similar and reach the order of magnitude of the bulk water mobility (i.e., 0.2 Å2/ps). This behavior was already detected by quasi-elastic neutron scattering experiments using either time-of-flight4854 or neutron spin echo52 techniques for the water molecules confined between clay lamellae with a separation of 15 Å. All of these QENS experiments confirm that, on the investigated time-scale (i.e., less than 1 ns), the apparent mobility of these confined water molecules is only slightly reduced by comparison with the mobility of bulk water. This result is also totally confirmed by numerical simulations of Molecular Dynamics,52,53 using different force fields to describe the clay/water and the clay/ion interactions. By contrast, a different behavior is reported for the water-mobility probed by NMR self-diffusion measurements55,56 on a much larger time-scale (i.e., larger than 1 ms). Under such conditions, the apparent mobility of the confined water molecules is monitored by the tortuosity56 of the diffusion space limited by the solid particles, and the water trajectories result then from the numerous elastic collisions with the surface of the clay platelets. As a consequence, the water molecules confined within dense clay sediments, with a high degree of alignment of their directors, exhibit an important reduction of their mobility in the longitudinal direction55,56 (i.e., perpendicular to the clay surface), while the radial mobility (i.e., parallel to the clay surface) is slightly reduced by comparison with that of bulk water.

where the clay interface with a separation of 40 Å is taken as the reference state. As displayed in Figure 8, the free energy profile is compatible with a coexistence of totally swollen lamellae with imperfectly swollen interfaces with a separation of 30 Å. Such a coexistence agrees qualitatively with the experimentally data.313 Because the leading contribution to the longitudinal pressure originates from the short-ranged water/lamella Lennard-Jones potentials, a more quantitative agreement should be obtained by slightly improving these van der Waals interactions. Finally, the activation free energy (5 ( 0.5 mJ/m2) appears negligible as compared to the hydration enthalpy of charged lamellae such as clay platelets (∼1 J/m2).21 However, by considering the large basal surface of these lamellar particles (S ≈ 102 μm2), we obtain a net activation free energy of 30 MJ/mol, large enough to stabilize the corresponding swelling gap over a broad range of temperature. C. Dynamical Properties. Simulations of Molecular Dynamics are useful to extract dynamical information on the mobility of the confined sodium counterions and water molecules, whose short-ranged interactions with the charged lamellae are responsible for the gap between the partially swollen lamellar systems. The three diagonal components of the tensor describing the self-diffusion coefficient of the confined water molecules are evaluated by integrating the autocorrelation functions of the molecular velocities:46 Dα, α ¼ lim

τf∞

Z τ 0

ÆB v α ð0Þ B v α ðtÞæ dt

ð10Þ

ð9Þ

while the orientational mobility of the confined water molecules is quantified by the autocorrelation function of the orientation of 822



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Figure 12. Mean squared displacement of the sodium counterions confined under the same condition as in Figure 9.

Figure 10. Variation, as a function of the upper time-limit, of the radial and longitudinal components of the self-diffusion tensor quantifying the mobility of the confined water molecules obtained by integration of the velocity autocorrelation functions displayed in Figure 9 (see text and eq 9).

as expected from the previous analysis (see Figures 13). As a conclusion, the dynamical behavior of the confined water molecules is similar to that of bulk water, and our MD simulations totally fail to detect even partially immobilized or quenched water molecules. Finally, the same approach should also be applied to quantify the mobility of the confined sodium counterions. Unfortunately, their velocity correlation function is not exploitable because the reduced number of sodium cations leads to very large statistical noise. By contrast, the mean squared displacement clearly indicates a radial mobility (0.15 Å2/ps in Figure 12) similar to that of the confined water molecules (see Figure 10). This result qualitatively agrees with the data obtained by NMR relaxometry58,59 and self-diffusion measurements60 performed on equivalent interfacial systems. Because of the geometrical confinement of the sodium cations, the long-time asymptotic behavior of the longitudinal component of the mean squared displacement cannot be exploited to extract the corresponding ionic mobility. The data displayed in Figure 12, however, confirm the complete lack of a long-time trapping of the monovalent counterions within some well generated by the electrostatic potential in the vicinity of the charged lamellae. D. Limitations and Prospects. Because of the size of the simulation cell (see section II), the longitudinal pressure displayed in Figure 7 cancels out at an interlamellar separation equal to 50 Å. The exact equation of state of such charged interfaces can be evaluated by adding a net repulsion evaluated by using the predictions of the Primitive Model (i.e., Pz ≈ 0.5 MPa).61,62 This approximation is fully justified because, at such separations, the water molecules are expected to behave as a continuum with the dielectric constant of bulk water. Note that the same model predicts a net repulsion of the order of magnitude of 10 MPa at interlamellar separations as small as 20 Å,62 in qualitative agreement with the results displayed in Figure 7. Because of the numerous hypotheses implied in these numerical simulations, this work should be considered as a first approach toward a comprehensive thermodynamical analysis of the long-range swelling gap detected for charged lamellae neutralized by monovalent counterions. As an example, the

Figure 11. Autocorrelation of the water directors quantifying the orientational correlation time of the water molecules confined under the same condition as in Figure 9.

Furthermore, the orientational mobility of the internal and external water molecules appears significantly different (see Figure 11). Yet a simple exponential fit leads to the nearly equivalent correlation times, that is, 3.2 ( 0.4 ps for the water molecules pertaining to the internal and external subdomains, roughly corresponding to the correlation time of bulk water.57 The same behavior was also reported by QENS experiments50,53 and numerical simulations of Molecular Dynamics53 for water molecules confined between clay lamellae with a period of 15 Å. The slight difference displayed in Figure 11 originates from the largest residual orientation of the most confined water molecules, 823



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longitudinal pressure (Figure 7) and the corresponding free energy (Figure 8) were obtained for a simple distribution of the electric charges of the lamellae: they are embedded in the equatorial plane and uniformly distributed on a fine grid with 0.22 electron per interacting site. In that context, it should be interesting to probe the influence of the localization63 of such charged sites at the basal surface of the lamellae with an accumulation of one electron located on randomly distributed sites. As stated by Gauss’s law, the average electric field will be exactly the same, but the local electric field can differ significantly, leading to possible modifications like a strong accumulation of counterions33 near such surface sites with different water organization,32 probably modifying the net longitudinal pressure. The same study should also be performed by modifying various geometrical and chemical parameters like the membrane thickness, its van der Waals short-range potentials and surface charge density, as well as the size and valence of the neutralizing counterions. A question concerns indeed the validity of the predictions of the Primitive Model concerning such charged interfaces neutralized by di- or trivalents62,64 counterions: to what extent does the predicted attraction induced by interionic correlations62,64 persist at separations small enough to invalidate the Primitive Model itself? Preliminary results were already obtained by using a very simple model of water molecules (Stockmayer fluid),65,66 and further investigations are required, implying more realistic modeling of the physicochemical properties of bulk water.6770 Finally, one may also wonder about the influence of the sign of the electric charges bearded by the lamellae. By using positively charged lamellae, we reasonably expect to obtain a different behavior not only because of an inversion of the residual water dipole in the vicinity of the charged interface (cf., Figure 3) but also because anion hydration induces a different organization57,71 of the water molecules pertaining to its first hydration sphere.

(5) Norrish, K. Discuss. Faraday Soc. 1954, 18, 120. (6) Zhang, Z. Z.; Low, P. F. J. Colloid Interface Sci. 1989, 133, 461. (7) Uang, Y. J.; Blum, F. D.; Friberg, S. E.; Wang, J. F. Langmuir 1992, 8, 1487. (8) Dubois, M.; Zemb, Th.; Belloni, L.; Delville, A.; Levitz, P.; Setton, R. J. Chem. Phys. 1992, 96, 2278. (9) Ockelford, J.; Timimi, B. A.; Nayaran, K. S.; Tiddy, G. J. T. J. Phys. Chem. 1993, 97, 6767. (10) Caboi, F.; Monduzzi, M. Langmuir 1996, 12, 3548. (11) McGrath, K. M.; Drummond, C. J. Colloid Polym. Sci. 1996, 274, 316. (12) Dubois, M.; Zemb, Th.; Fuller, N.; Rand, R. P.; Parsegian, V. A. J. Chem. Phys. 1998, 108, 7855. (13) Brotons, G.; Dubois, M.; Belloni, L.; Grillo, I.; Narayanan, T.; Zemb, Th. J. Chem. Phys. 2005, 123, 024704. (14) Ferrage, E.; Sakharov, B. A.; Michot, L. J.; Delville, A.; Bauer, A.; Lanson, B.; Grangeon, S.; Frapper, G.; Jimenez-Ruiz, M.; Cuello, G. J. J. Phys. Chem. C 2011, 115, 1867. (15) Marcus, R. A. J. Chem. Phys. 1955, 23, 1057. (16) Delville, A.; Laszlo, P. New J. Chem. 1989, 13, 481. (17) Cebula, D. J.; Thomas, R. K.; Middleton, S.; Ottewill, R. H.; White, J. W. Clays Clay Miner. 1979, 27, 39. (18) Skipper, N. T.; Williams, G. D.; de Siqueira, A.V.C.; Lobban, C.; Soper, A. K. Clay Miner. 2000, 35, 283. (19) Delville, A.; Letellier, M. Langmuir 1995, 11, 1361. (20) Rinnert, E.; Carteret, C.; Humbert, B.; Fragneto-Cusani, G.; Ramsay, J. D. F.; Delville, A.; Robert, J. L.; Bihannic, I.; Pelletier, M.; Michot, L. J. J. Phys. Chem. B 2005, 109, 23745. (21) Fripiat, J.; Cases, J.; Franc-ois, M.; Letellier, M. J. Colloid Interface Sci. 1982, 89, 378. (22) Carley, D. D. J. Chem. Phys. 1967, 46, 3783. (23) Boek, E. S.; Coveney, P. V.; Skipper, N. T. J. Am. Chem. Soc. 1995, 117, 12608. (24) Smith, D. E. Langmuir 1998, 14, 5959. (25) Sposito, G.; Skipper, N. E.; Sutton, R.; Park, S. H.; Soper, A. K.; Greathouse, J. A. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 3358. (26) Delville, A. Langmuir 1991, 7, 547. (27) Leote de Carvalho, R. J. F.; Skipper, N. T. J. Chem. Phys. 2001, 114, 3727. (28) Chavez-Paez, M.; dePablo, L.; dePablo, J. J. J. Chem. Phys. 2001, 114, 10948. (29) Mary, V.; Turq, P. J. Phys. Chem. B 2003, 107, 1832. (30) Cygan, R. T.; Liang, J. J.; Kalinichev, A. G. J. Phys. Chem. B 2004, 108, 1255. (31) Tambach, T. J.; Bolhuis, P. G.; Hensen, E. J. M.; Smit, B. Langmuir 2006, 22, 1223. (32) Meleshyn, A.; Bunnerberg, C. J. Chem. Phys. 2005, 122, 034705. (33) Forsman, J. Langmuir 2006, 22, 2975. (34) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. J. Phys. Chem. 1987, 91, 6269. (35) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendo Press: Oxford, 1994. (36) Heyes, D. M. Phys. Rev. B: Condens. Matter 1994, 49, 755. (37) Hummer, G. Chem. Phys. Lett. 1995, 235, 297. (38) Adams, D. J. Mol. Phys. 1974, 28, 1241. (39) Evans, D. J.; Murad, S. Mol. Phys. 1977, 34, 327. (40) Fincham, D. Mol. Simul. 1992, 8, 165. (41) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; DiNola, A.; Haak, J. R. J. Chem. Phys. 1984, 81, 3684. (42) Woessner, D. E.; Snowden, B. S., Jr. J. Chem. Phys. 1969, 50, 1516. (43) Delville, A.; Grandjean, J.; Laszlo, P. J. Phys. Chem. 1991, 95, 1383. (44) Petit, D.; Korb, J. P.; Delville, A.; Grandjean, J.; Laszlo, P. J. Magn. Reson. 1992, 96, 252. (45) Porion, P.; Faugere, A. M.; Michot, L. J.; Paineau, E.; Delville, A J. Phys. Chem. C 2011, 115, 14253. (46) Hansen, J. P.; McDonald, I. R. Theory of Simple Liquids; Academic Press: London, 1990.

IV. CONCLUSIONS This article is a first step toward a complete thermodynamical characterization of the long-range gap occurring during the swelling of charged rigid lamellae neutralized by monovalent counterions in the presence of bulk water. A molecular analysis of the confined water molecules and sodium counterions was used to identify the short-range water/lamella and ion/lamella van der Waals interactions as the origin of the activation energy responsible for the coexistence of swollen and unswollen interfaces. Furthermore, simulations of Molecular Dynamics clearly confirm the lack of long-time trapping of the confined ions or solvent molecules in some potential well in the vicinity of the charged surfaces. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

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