Molecular Simulation of Ion-Specific Effects in Confined Electrolyte

Pierre-Andre Cazade , Remco Hartkamp , and Benoit Coasne ... Cabello-Aguilar , Adib Abou-Chaaya , Philippe Miele , Emmanuel Balanzat , Jean Marc Janot...
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J. Phys. Chem. C 2010, 114, 12245–12257

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Molecular Simulation of Ion-Specific Effects in Confined Electrolyte Solutions Using Polarizable Forcefields P.-A. Cazade,† J. Dweik,‡ B. Coasne,*,† F. Henn,† and J. Palmeri§ Institut Charles Gerhardt Montpellier, UMR 5253 CNRS, UniVersite Montpellier, ENSCM, 8 rue de l’Ecole Normale, 34296 Montpellier Cedex 05, France, Institut Europeen des Membranes, UMR 5635 CNRS, UniVersite Montpellier, Place Eugene Bataillon, 34095 Montpellier Cedex 5, France, and Laboratoire de Physique Theorique, UMR 5152 CNRS, IRSAMC, UniVersite Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse Cedex 4, France ReceiVed: April 29, 2010

This paper reports on a molecular dynamics study of aqueous electrolyte solutions confined in hydrophobic nanopores. We examined for the first time the effect of the size and polarizability of the ions on the structure and dynamics of the confined electrolyte solution by considering the series of sodium halides (NaX with X ) F, Cl, Br, and I). We also address the effect of pore size by varying the diameter of the nanochannel. As far as structural properties are concerned, the behavior of the NaF electrolyte solution significantly differs from that of the other sodium halide solutions. Because of their small size, Na and F in NaF are found to be significantly solvated by water. In addition, due to steric and hydrophobic effects [Chandler, D. Nature 2005, 437, 640.], Cl, Br, and I tend to be repelled from the regions where the density of water is larger. Ion-specific effects on the dynamics of water and ions are found to be minimized when the electrolyte solution is confined at the nanoscale in comparison to bulk water and the water-air interface. For instance, both the data for water and the ionic species indicate that the ratio of the self-diffusivity for the confined solution to that for the bulk is independent of the nature of the anion F, Cl, Br, and I. Moreover, while the average solvation times for Na in NaF and Na in NaX (X ) Cl, Br, I) significantly differ for bulk electrolyte solutions, they turn out to be very similar for the confined solutions. Such a leveling of the dynamical properties of the electrolyte solutions due to confinement is also observed on the pairing of the anions and cations. 1. Introduction Access to drinkable water has become one of the most important societal issues for the next decades.1 This has led many countries to find alternative sources of drinkable water such as dew, fog, undersea springs, and so forth.2 Unfortunately, these methods are either very expensive or inefficient for large scale applications. Another very common method for countries with direct access to the sea is seawater desalination using reverse-osmosis membranes.3 While this technology is widely used and has proven to be efficient, it remains very costly. The use of high pressure pumps represents an important energetic cost that prevents a wide-scale use of this technique. Moreover, the environmental impact of this technology is also an important issue as (1) salt rejection is often needlessly high and strongly concentrated salt solutions are rejected into the sea, and (2) washing the membranes requires chloride solutions. In this context, many investigations are being carried out to find more efficient and cheaper methods for seawater desalination. Thus, nanofiltration membranes are promising candidates for drinkable water production as they could allow a large volume of water to be desalinated while selectively rejecting the ions (and thereby minimizing the remineralization step after filtration).1,4,5 Moreover, such nanofilters, which could mimic certain biological * To whom correspondence should be addressed. E-mail: benoit. [email protected]. Phone: +33 4 67 16 34 59. Fax: +33 4 67 14 42 90. † Institut Charles Gerhardt Montpellier. ‡ Institut Europeen des Membranes. § Laboratoire de Physique Theorique.

membranes possessing ion channels, have proven to be highly useful thanks to their selectivity and enhanced flow of certain species. Despite the increasing number of experimental, theoretical, and molecular simulation studies on biological and inorganic nanomembranes, the physical origin of ion-specific effects on transport in nanochannels remains to be clarified. In this work, we report on a molecular simulation study of aqueous electrolyte solutions confined in a single nanopore. We address the effect of the size of the ions by considering the series of sodium halide electrolyte solutions NaX with X ) F, Cl, Br, and I. While all of the molecular simulation works reported in the literature treating confined electrolytes (see Section 2) were performed with nonpolarizable forcefields, the present study was carried out using polarizable forcefields for both the water molecules and the ions. The use of such more sophisticated models was motivated by the fact that many molecular simulation studies on interfacial electrolyte solutions (gas/liquid, liquid/liquid, and solid/liquid interfaces) revealed the crucial role played by polarizability.6-18 In our work, the hydrophobic nanomembrane is modeled as a single-walled carbon nanotube that corresponds to an ideal system allowing us to clarify the physics at play at the nanoscale.19 In addition to being useful tools for theoretical approaches of transport and confinement at the nanometric scale, carbon nanotubes are relevant for practical applications in nanofiltration and nanofluidics. Indeed, the carbon nanotubes can be prepared in various morphologies such as single or multiwalled nanotubes and their channel diameter is easily controlled to obtain a wide range of sizes. Moreover, they can be self-assembled in a membrane to obtain nanofluidics de-

10.1021/jp103880s  2010 American Chemical Society Published on Web 06/24/2010

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vices.19 In this work, we also determine the effect of confinement by varying the diameter of the carbon nanotube from D ) 1 to 3 nm. The structure and dynamics of the confined electrolyte solutions is investigated by means of molecular dynamics (MD). This molecular simulation technique, which gives access to structural, dynamical, and thermodynamical properties, is well suited to investigate the behavior of confined systems. In addition, periodic boundary conditions in the three dimensions of space were used to mimic an infinite nanotube in the z-direction. This approach, which is in contrast to what is usually done (pore + 2 reservoirs) is complementary to this general method. Indeed, ion transport in nanofilters can approximately be broken down into three steps, partitioning into the nanopore from the external feed solution, transport through the nanopore, and finally partitioning out of the nanopore into the external permeate solution. The approach adopted here allows us to focus in detail on the intermediate step of transport through the nanopore where diffusion and/or pairing-correlation effects modified with respect to the bulk by confinement may play an important role. The structure of water and ions confined in the carbon nanotubes is first investigated using radial density contours, pair correlation functions, and surface densities of solvating water molecules. The dynamical properties of the system are then determined by calculating mean square displacements, self-diffusion coefficients, and time correlation functions to estimate the average solvation and ion-pairing times as well as residence time at the carbon nanotube surface. The remainder of this paper is organized as follows. In Section 2, we report a brief review of the literature and state of the art of molecular simulation of confined electrolyte solutions. In Section 3, we present the simulation techniques and details about the models used to describe the carbon nanotube and aqueous electrolyte solutions. In Section 4, we discuss the results obtained concerning the structure and dynamics of water and ions confined in the carbon nanotubes. In Section 5, we summarize our results and present concluding remarks. 2. State of the Art Given the great challenge that represents obtaining desalination nanomembranes, many molecular simulation works have been reported on water20-24 and water and ions25-31 confined at the nanoscale in hydrophobic pores. Besides the increasing number of molecular simulation studies published on the confinement of aqueous electrolyte solutions, other authors have also considered confinement and transport of ions in biological systems.30,32,33 In what follows, we restrict ourselves to the review of the most recent but abundant theoretical and molecular simulation works published on the transport of aqueous electrolyte solutions in hydrophobic nanopores. Nicholson and Quirke34 reported one of the first molecular dynamics studies on the confinement of an aqueous solution of sodium chloride in a hydrophobic carbon nanotube. These authors addressed the effect of confinement on the structure, solvation, and pairing effect of ions. As in the case of bulk aqueous solutions, the latter phenomena are expected to play a key role in ion transport in nanoporous materials. The effect of confinement on the solvation sphere was also investigated by Shao et al.35 These authors examined the effect of the size and nature of the ions (Li, Na, K, F, and Cl), as well as the effect of the carbon nanotube diameter and temperature. The average solvation radius was found to be almost independent of confinement and temperature. Moreover, at ambient temperature, the average number of solvating molecules is close to its bulk counterpart for carbon nanotubes with pore sizes down to 1 nm. On the

Cazade et al. other hand, by considering the distribution of angles between the dipole of the solvating water molecules and the ions, Shao et al. found that the orientational ordering of water with respect to the cations is less marked than in the bulk while it is similar for anions. In agreement with these results, Ohba et al.36 found that confinement in carbon slit pores affects the solvation of divalent cations (Ca2+ in a CaCl2 solution). Surprisingly, these authors also showed that the number of solvating water molecules in the confined electrolyte solution is larger than the bulk. Recently, Huang et al.25,26 reported results from classical molecular dynamics of sodium chloride and sodium iodide electrolyte solutions confined in a hydrophobic slit pore. These authors found that the structure and ordering of the confined ions are mainly driven by the surface-induced structure of water. Sodium ions were found to be repelled from the surface as it is more favorable from an energetic point of view to have them solvated by water and remain far from a low dielectric interface. For the same reason, chloride ions also tend to be repelled from the surface. In contrast, due to their larger size, iodide ions are preferentially located near the surface where a water vaporlike phase is formed because of the hydrophobic nature of the substrate (this effect has been described in the literature as the air-cushion phenomenon).These results, which show that the hydrophobic solvation energy of the ions needs to be considered to account for such ion-specific effects, can be partly explained in terms of the hydrophobic effect (see ref 37 for a recent review by Chandler). Although Huang et al. did not use a polarizable ion model they did implicitly account for ion polarizability by artificially increasing the Lennard-Jones size of I- to correctly account for the propensity of large polarizable anions to migrate to areas of low water density. Of particular interest for the crossover regime between nanofiltration and reverse osmosis applications, Yang et al.28 studied the partitioning of cations (Na, K, Cs) in charged hydrophobic nanomembranes modeled as a single carbon nanotube (radius ) 0.335 nm ) diameter of water molecule) where some of the carbon atoms carry electrostatic charges. These authors showed that the selectivity, defined from the number of ions entering the nanopore, toward the different cations depends on the surface charge density. For intermediate surface charge densities, the selectivity of the carbon nanotube toward the K and Cs cations is shown to be larger than that toward the Na cations. As the surface charge density increases, the increase in the selectivity toward the K cations is larger than for the Cs and Na cations. This suggests that ion partitioning in nanopores not only depends on the electrostatic charge, but is also driven by free energy barriers arising from other types of interactions (if only ion charge played an important role, selectivity would not depend on the nature of the monovalent ions). These results on ion-specific effects are consistent with those reported by Huang et al. on the role of the hydrophobic solvation energy. It should be emphasized that the ion-specific effects reported above are not accounted for in the Gouy-Chapman model of the electrical double layer in which ions are only distinguished by their valence. As a result, several authors have proposed possible extensions of the space charge model to describe ion distribution in nanochannels. Among the most fundamental works, Schoch et al. recently reviewed the basis and concepts behind any theory of transport phenomena at the nanoscale.38 In particular, these authors discussed how classical theories based on the Poisson-Boltzmann and Navier-Stokes equations need to be modified to account for confinement and surface driven effects. Sparreboom et al.39 also recently reviewed

Ion-Specific Effects in Confined Electrolyte Solutions transport in nanofluidic devices and presented a model of the structure of ions in nanochannels that is based on the following three main factors (1) the presence of an external force such as an electric field or pressure gradient, (2) the various colloidal forces that encompass electrostatic and van der Waals interactions, the steric repulsion, and the hydrophobic forces,40,41 and (3) hydrostatic effects such as friction with the wall of the channel. In this review paper, the model reported by the authors was found to allow qualitative interpretation and prediction of nanofluidic transport phenomena. In their molecular simulation work, on sodium chloride and sodium iodide electrolyte solutions in a hydrophobic pore, Huang et al. also reported an analytical model based on the Poisson-Boltzmann equation that includes size-dependent hydrophobic solvation energy of the ions.27 Using this model, these authors showed that electrokinetic ion-specific effects are related to the size-dependence of the hydrophobic solvation energy. Moreover, the model suggests that anomalous electrokinetic effects such as a non-null zeta potential for uncharged pore surfaces in the case of asymmetrical anion/cation electrolytes are related to the affinity of large ions for the liquid/vapor interface, “air cushion” at the nanopore surface. In their work, Huang et al.26 also showed that the velocity profiles of the confined electrolyte solutions still obey macroscopic hydrodynamics even at the nanometric scale.26 For uncharged hydrophobic surfaces, the slip length was shown to be important, which leads to enhanced osmotic diffusion for fluids confined in superhydrophobic nanochannels.27,29 In contrast, the ζ-potential and flow rate in electro-osmosis processes were found to be independent of the slip length which suggests that, counterintuitively, the flow for a charge-neutral fluid is independent of the solid-fluid friction coefficient. In the case of hydrophilic surface, the authors found that the slip length is equal to zero as expected using the common no-slip boundary conditions. Xue et al.42 compared molecular dynamics simulations with the predictions of the space charge model in terms of ionic current of an electrolyte solution confined in a charged nanopore. These authors showed that for broad nanopores (with a radius larger than 1.5 nm) the theoretical predictions agree with the simulation results. However, for smaller nanopores, the ionic current obtained by molecular dynamics simulation is always smaller than the theoretical value. For a given pore size, the discrepancy between the two approaches increases as the surface charge increases. These authors also showed that the electro-osmosis contribution to the total flow cannot be neglected when the surface charge of the nanopore is high (around 1 e/nm2). While the works described above were obtained for nanochannels of a simple geometry and a regular surface, other authors have considered the case of more complex carbon nanotubes systems. Park et al.43 studied by means of molecular dynamics simulations the effect of the morphology of carbon nanotubes in the separation of KCl electrolyte solutions. These authors designed a Y-junction carbon nanotube with one branch positively charged and the other one negatively charged. As expected, this nanofluidics device proved its ability for separating K and Cl ions as they are transported within the negatively charged and positively charged channels, respectively. Xu and Aluru44 reported tight-binding calculations (semiempirical methods) of the screening of the electrostatic potential induced by a confined electrolyte solution in the case of semiconductor and metallic carbon nanotubes. Of particular interest for applications in chemical and biological sensing, these authors showed that measuring the electrostatic potential in the vicinity of the carbon nanotube outer surface allows distinguishing its conformation (armchair versus zigzag) and identifying the nature of the

J. Phys. Chem. C, Vol. 114, No. 28, 2010 12247 confined ions. It should be emphasized that the works reported above were carried out using nonequilibrium simulations in which an external field (electrostatic field, hydrostatic pressure or concentration gradient) is applied during the calculations. While the results reported above were obtained in the case of single isolated nanochannels, several authors also considered more realistic models of hydrophobic membranes where the system is composed of several nanochannels. Hummer and coworkers45 reported a molecular simulation study of osmotic transport of water in hexagonally packed carbon nanotubes (in their system, transport is forbidden between the carbon nanotubes as they are embedded in a polymeric membrane). In this work, the carbon nanotube membrane separates a pure water reservoir from an aqueous electrolyte (NaCl) reservoir. By imposing a hydrostatic pressure difference between the two reservoirs, the authors induced a large frictionless osmotic flow (5 water molecules per nanosecond) comparable to rates obtained with biological membranes. Such a slip-flow was found to be governed by the free energy barriers for water molecules to enter and leave the nanotubes. Later, the same group46 considered the same model of hydrophobic membranes and calculated the free energy barrier for the ions to enter the nanopores; this free energy barrier was found to be low (3-5.5 kJ/mol) for large nanopores (diameter greater than 1 nm) but increases as the nanochannel becomes narrower (120 kJ/mol). The authors showed that the latter dependence is due to the first solvation sphere that is affected for nanochannels smaller than ∼1 nm. In fact, in small nanotubes ions must lose their solvation sphere to pass through the membrane, which represents an important free energy cost. Finally, the authors also showed that ion transport in small nanochannels significantly depends on the structure of water (including the layering of the water molecules in the vicinity of the channel surface). In the spirit of the work by Hummer and co-workers, Corry47 also considered by means of molecular simulation the use of carbon nanotubebased nanomembranes for desalination. This author calculated the free energy barriers associated with ions and water molecules entering carbon nanotubes. The large energy barrier for small carbon nanotubes (100.4 kJ/mol for a diameter D ) 6.6 Å) decreases quickly with increasing nanotube diameter (down to 1.67 kJ/mol for a diameter D ) 9.3 Å). In any case, confinement prevents the ions and water molecules from being solvated to the same extent as in the bulk solutions. Such a decrease in ion solvation has an energetic cost, which is about 10.46 kJ/mol per lost solvating molecule. The latter energetic penalty is partly compensated by (1) the favorable van der Waals interaction between oxygen atoms of water and carbon atoms of the nanotube, (2) an increase in the average lifetime of hydrogen bonding between water molecules, and (3) the creation of new hydrogen bonds due to confinement that forces the water molecules to stay close to each other. In a recent paper, Suk et al.48 addressed the effect of an electric field on reverse osmosis in boronitride nanotubes. These authors reported that reverse osmosis is enhanced when an electric field is applied in the direction of the reverse-osmotic flow. This result is due to the orientation of the water dipole along the electric field that facilitates their mobility and transport. 3. Computational Details 3.1. Models for the Electrolyte Solution and Nanomembrane. Hydrophobic nanomembranes in our work were modeled as a single-wall carbon nanotube. We note that the latter system has to be considered as an ideal system that can be used to model electrolyte transport in hydrophobic nanomembranes.

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TABLE 1: Geometric Parameters for the Water Model POL3 and for the Carbon Nanotubes bond (Å) OH HOH CC

angle (deg)

1.000 109.47 1.418

TABLE 2: Interaction Parameters of the Models Used for the Simulationsa atomic label

qi (e)

Ri (Å3)

εii (kcal.mol-1)

σij (Å)

Na F Cl Br I O (POL3) H (POL3) C

1.000 -1.000 -1.000 -1.000 -1.000 0.730 0.365 0.000

0.240 0.600* 3.250 4.530 6.920 0.528 0.170 0.000

0.10000 0.10000 0.10000 0.10000 0.10000 0.15600

2.3359 3.1663 4.3387 4.6986 5.1494 3.2037

0.05564

3.4000

a qi is the partial charge, Ri is the polarizability, εii and σii are the parameters for the Lennard-Jones potential.

Carbon nanotubes were obtained from a graphene sheet wrapped around the x-axis in the armchair conformation. Two diameters D ) 1 and 3 nm were considered to address the effect of confinement on the properties of the electrolyte solutions in the nanomembranes. One notes here that the approximate diameter of a water molecule is about 0.3 nm, which implies that these choices of pore diameters correspond to about 3 and 10 water molecules. The nanotube length is equal to 71.224 Å. The confined electrolyte solutions were modeled using polarizable force fields as it has been shown that polarization is crucial for an accurate description of ionic solutions.6-16 Water was described in our simulations using the POL3 polarizable model of Kollman et al.49 In this model, each O and H atom of the rigid water molecule (the geometric parameters are listed in Table 1) possesses a partial charge that interacts through Coulombic forces. In addition, the oxygen atom of the water molecule is a center of repulsion/dispersion interactions that interacts through a Lennard-Jones potential. The polarization contribution is included by taking into account the polarizabilities of both the oxygen and hydrogen atoms. Cations and anions (NaX with X ) F, Cl, Br, and I) of the electrolyte solutions were described as single spheres with a formal charge (+1 for the cations and -1 for the anions). Each ion is a center of repulsion/dispersion interactions modeled using Lennard-Jones potentials. The Lennard-Jones parameters for the ions were taken from the work by Dang et al.50-53 on bulk electrolyte solutions. Polarizabilities for the anions and cations were taken from refs 51, 53, and 54. The different Lennard-Jones parameters, charges, and polarizabilities of the atoms and ions are listed in Table 2. Interactions between the ions, atoms of the water molecule, and carbon atoms of the nanotube were calculated as the sum of the Coulombic, polarization, and dispersion interactions with a repulsive short-range contribution. The energy Uk(rk) of the atom or ion k at a position rk is given by

Uk(rk) )

∑

j)(O,H,Na,X,C)

{ [( ) ( ) ] } 4εjk

σjk rjk

12

σjk 6 + rjk qjqk 1 - µkE(0) (1) k 4πε0rjk 2 -

where X ) F, Cl, Br, or I and rkj is the distance between atoms j and k (j, k ) O, H, Na, X or C). The first term in eq 1 is the

repulsive term that corresponds to the repulsive energy due to finite compressibility of electron clouds when approaching the atom or ion to a very short distance from the nanochannel surface or another atom or ion. The second term in eq 1 is the dispersion interaction. The energetic and geometric crossparameters εjk and σjk were obtained from the atom-like parameters using the Lorentz-Berthelot mixing rules.55 We note that εjk in eq 1 has to be expressed in Joule to be consistent with the Coulombic term. The third term in eq 1 is the Coulombic interaction between the charge of atom or ion k and that of atom or ion j. The fourth term is the polarization contribution of atom or ion k. µk is the relaxed polarization dipole of the atom or ion k resulting from the interaction with the charges and dipoles j, µk ) RkEkwhere Ek is the electrostatic field at rk due to the all of the charges and the dipoles and E(0) k is the electrostatic field at rk due to all of the charges, but not the dipoles. The atomic parameters for the electrolyte/electrolyte and electrolyte/nanotube interactions are given in Table 2. Interatomic energy contributions were calculated within a cutoff radius equal to 12 Å. The Coulombic energy was computed using the Ewald summation technique with the following parameters: a Gaussian width equal to R ) 0.227 Å-1 and kmax ) 12, 12, 16 along the x-, y-, and z-directions, respectively. The polarization energy was computed in the frame of the Car-Parrinello scheme.56 In eq 1, the energy function is only valid after minimization with respect to the fluctuating dipoles and is therefore equivalent to a zero temperature calculation; the Car-Parrinello method couples the dynamic dipoles with fictitious masses to a very low temperature heat bath to dynamically approximate in a faster way the zero-temperature energy. 3.2. Molecular Dynamics. Periodic boundary conditions in the three dimensions of space were used to mimic an infinite nanotube in the z-direction. The size of the simulation box in the x- and y-directions was chosen large enough to ensure negligible interactions between the electrolyte solution confined in the carbon nanotube and its periodic images (Lx,y ) 50 Å and 70 Å for the nanotubes with D ) 1 and 3 nm, respectively). The temperature was set to 300 K and the number of anion/ cation pairs, that is, 3 and 42 pairs for the D ) 1 and 3 nm nanotubes, respectively, correspond to a concentration of about 1.85 mol · L-1. A physically meaningful density of water molecules confined in the nanotube at a fugacity of 1 atm was obtained by first performing Grand Canonical Monte Carlo (GCMC) simulations (details can be found in the refs 57-59). The molecular dynamics simulations were performed with the AMBER9 software.60 Initial configurations were taken from the well-equilibrated GCMC calculations mentioned above. Trajectories were limited to 10 and 2 ns for the 1 and 3 nm carbon nanotubes, respectively, to keep the computing time reasonable. Trajectories were integrated using the leapfrog algorithm with a time step of 1 fs. The temperature was maintained constant using a Berendsen thermostat61 with a coupling time to the thermal bath equal to 0.1 ps. The properties and configurations of the system were stored each 1 ps. 4. Results 4.1. Structure and Organization of Confined Electrolytes. Figure 1 shows the radial density contour plots for the electrolyte solutions NaX (X ) F, Cl, Br, I) confined in the carbon nanotube with D ) 3 nm. These contour plots represent a map of the radial density for the water molecules, anions, cations within the nanochannel (each density map is integrated over the whole nanotube length). Figure 1 also shows typical molecular

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Figure 1. Contour plots showing the density distribution of sodium ions Na, halide ions X, and water molecules of electrolyte solutions NaX (X ) F, Cl, Br, I) at location (x,y) in a carbon nanotube of a diameter D ) 3.0 nm. The density increases from purple, blue, green, yellow, orange, and red. Electrolyte solutions are (from top to bottom) NaF, NaCl, NaBr, and NaI. For each contour plot, the associated radial density profiles are provided as Supporting Information. R ) 0 and 15 Å corresponds to the center of the nanotube and the wall of the nanotube, respectively. A typical molecular configuration is shown for each confined electrolyte solution. Gray segments are bonds between the carbon atoms of the nanotube while the white and red segments are the water molecules. Blue, yellow, green, brass, and pink spheres are the Na, F, Cl, Br, and I ions, respectively.

configurations to illustrate the positions of the different species. Independently of the electrolyte solution, the contour plots for water exhibit density maxima located at well-defined positions from the nanotube wall. The amplitude of these maxima decreases with increasing distance from the nanotube surface and the density tends toward the bulk value close to the pore center as water molecules recover their bulk properties (this can be seen in the radial density profiles F(r) provided in the Supporting Information). These density oscillations reveal the significant layering of water in the vicinity of the nanochannel wall. Such a spatial ordering of confined water is characteristic of water in hydrophobic or hydrophilic spaces.62-77 Interestingly, the density contour plots for confined water are nearly insensitive to the nature of the sodium halide ions. This result is confirmed by the fact that the density profiles were found to be almost identical to that obtained for pure water confined in the carbon nanotube (results not shown). This result shows that even for

salt concentrations 3 times larger than that of seawater the structure of confined water is mainly driven by interactions between water molecules and between water molecules and the nanochannel surface. This result is consistent with previous results reported by Huang et al.25,26 who found that the ion density profiles are mainly driven by the surface-induced water structure. We note that a similar conclusion has been reached in our recent molecular simulation study of water and ions confined in organic nanochannels where the structure of the different species was found to be independent of the nature of the ions. The contour plots for sodium also exhibit density oscillations, which reveal that cations tend to form layers at the nanotube surface (Figure 1). As in the case of water, such a spatial ordering of confined cations is only weakly sensitive to the nature of the anions. The density maxima for sodium are located at positions where the water density is low. These results suggest

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that the positional ordering of the cations is governed by their interaction with the confined water molecules. In fact, this configuration where sodium cations are sandwiched between water layers is favorable as it leads to higher solvation of the cations while being compatible with the layering imposed by the carbon nanotube. In particular, as will be seen below, the average surface density of solvating water molecules around sodium is very close to that for bulk electrolyte solutions. Such a significant solvation of sodium cations, observed both for bulk and confined electrolyte solutions, is due to their small size that only weakly perturbs the hydrogen bonding between water molecules. Moreover, given the hydrophobic nature of the neutral surface of the carbon nanotubes, there are no specific adsorption sites for charged species so that they tend to be repelled from the surface by steric and dielectric effects, the latter arising from the dielectric discontinuity between pore water and the nanopore carbon wall and outlying space. In contrast to the results for water and sodium cations, the density contour plots for anions depend on their nature (F, Cl, Br, I). On the one hand, fluoride anions occupy in a more homogeneous way the porous space within the carbon nanotube though layering is also observed for this anion (i.e., smooth density oscillations are observed in the corresponding contour plots). The locations of the density peaks for fluoride seem to be correlated with those for sodium cations; this result suggests that, as in bulk NaF solutions, the fluoride anions tend (1) to pair with the sodium cations and (2) to be solvated by water molecules (see below for a more detailed discussion of that issue). On the other hand, larger anions such as Cl, Br, and I exhibit a different behavior from F as marked density oscillations are observed in the contour plots. The latter plots for Cl, Br, and I anions exhibit a marked density maximum close to the carbon surface, which is located in between the first and second water layers. Such an inhomogeneous occupancy of the large anions indicates that ions tend to be repelled from the water layers as they become larger. This result can be explained in terms of the hydrophobic effect;37 that is, the free energy cost to solvate anions increases with increasing their size due to (1) the energy (enthalpic) penalty to break hydrogen bonding in liquid water and (2) the entropy cost of hydrating small cavities due to the dynamic reordering, or rigidifying, of the surrounding water hydrogen bond network (with little actual bond breaking). For solutes of the size of the ions studied here ( 10 Å corresponds to the layer of water molecules close to the carbon nanotube surface. The second region R < 7 Å corresponds to bulklike water confined in the nanotube center. To keep simple the discussion below, we do not consider water located in the second adsorbed layer, that is, 7 Å < R < 10 Å. Calculating the self-diffusion coefficient for water in each of the two regions above is a tedious task that requires very long simulations to obtain reliable statistics. Instead of performing such time-consuming calculations, we roughly estimated the dynamics of water in each region as the average mean square displacement along the direction z at a time τ0 ∼ 20 ps. The latter value, which is somewhat arbitrary, has been selected since no significant transfer between the different regions is observed below this duration. Figure 7 shows for water confined in the carbon nanotube. Both the data for pure water and water in the different electrolyte solutions are reported. The results for pure water show that due to the interaction with the atoms of the carbon nanotube the water molecules in the vicinity of the surface are slowed down compared to those located in the pore center. The latter finding is in full agreement with previous molecular simulations performed by Gubbins and co-workers.109 In contrast, the data for the confined electrolyte solutions indicate that diffusion of water in the first adsorbed layer is faster than that in the pore center. Such a result can be interpreted as follows. Because of the significant electrostatic interaction in the pore center with the confined ions, the water molecules are slowed down. Such a more significant slowing down of the water molecules by the ions in the pore center than by the carbon atoms at the nanotube surface is consistent with the fact the ion-water electrostatic interaction is stronger than the carbon-water van der Waals

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Figure 5. Mean square displacements (MSD) along the nanotube axis for water (top), sodium ions (middle), and halide ions X (bottom) in electrolyte solutions NaX (X ) F, Cl, Br, I) confined in the 3 nm carbon nanotube. For each species (water, Na, and X), the blue, green, red, and black lines correspond to results obtained for the NaF, NaCl, NaBr, and NaI electrolyte solutions, respectively. In the top panel, the dashed line corresponds to the results obtained for pure water confined in the 3 nm carbon nanotube.

interaction. The latter interpretation is supported by the fact that the diffusion of water becomes slower as the size of the anion decreases (for instance, ) 3.3 Å2 for water in the pore center with NaF while ) 5.6 Å2 for water in the pore center with NaI); indeed, as discussed above, the solvation of anions increases with decreasing anion size so that the average water/ion interaction increases. To get further information on the dynamical behavior of the confined electrolyte solutions, we calculated time correlation functions R(τ) between the ions and water molecules: Ni

Rij(τ) )

Nj

∑ ∑ 〈Θij(t)Θij(t + τ)〉t

1 1 Ni Nj i)1

(3)

j)1

where i and j denote a water molecule, an anion, or a cation. Θ(t) equals 1 if i and j are nearest neighbors at time t and 0 otherwise. i and j are considered nearest neighbors if the distance rij is smaller than the first minimum in the corresponding g(r) function (3.0 Å for Na-O). The brackets in eq 3 indicate that the value is averaged over a large number of molecular dynamics configurations. Because of the definition given above, Θ(t)Θ(t + τ) ) 1 if i and j are nearest neighbors at the times t and t + τ. Consequently, R(τ) gives the

Figure 6. (top) Self-diffusion coefficients of water molecules and ions for electrolyte solutions NaX (X ) F, Cl, Br, I). (bottom) Ration between the self-diffusion coefficient defined above and its bulk counterpart for the same electrolyte solutions and at the same concentration 1.8 mol L-1. O dots correspond to values obtained for sodium ions, 0 dots correspond to values obtained for halide ions, and 4 dots to values obtained for water molecules.

Figure 7. Average mean square displacement at τ ) 20 ps for water molecules of pure water confined in the carbon nanotube with D ) 3 nm. O dots correspond to values obtained in the bulk-like water at the nanotube center (R < 7 Å) and 0 dots to values obtained in the first adsorbed layer at the nanotube surface (R > 10 Å).

probability of having i and j paired at times t and t + τ. Such time correlation functions are of particular interest as they can be related to NMR data. Figure 8 shows the time correlation functions between the Na cation and the oxygen atoms of water O for the four electrolyte solutions NaX (X ) F, Cl, Br, I). Both the data for bulk and confined electrolyte solutions are shown. The latter time correlation functions allow us to estimate the average solvation times of the cations by the water molecules.73,76,110 Data for the bulk electrolyte solutions show that NaF exhibits

Ion-Specific Effects in Confined Electrolyte Solutions

Figure 8. Time correlation functions R(τ) between Na ions and O atoms of water molecules in electrolyte solutions NaX (X ) F, Cl, Br, I). The blue, green, red, and black lines correspond to results obtained for the NaF, NaCl, NaBr, and NaI electrolyte solutions, respectively. The solid lines are for electrolyte solutions confined in a 3 nm carbon nanotube while the dashed lines are for the corresponding bulk electrolyte solutions. The inset shows the same curves when plotted in a semilog scale.

a different dynamical behavior from the other sodium halides NaCl, NaBr, and NaI. Much longer average solvation times are observed for Na in NaF compared to the other electrolyte solutions. Interestingly, this difference between the sodium halide electrolyte solutions is attenuated upon confinement. Indeed, upon confinement, the average solvation time for Na in NaF is decreased compared to the bulk while that for Na in NaX (X ) Cl, Br, I) is increased. It should be emphasized that similar results have been obtained when looking at the solvation of the anions by the water molecules (results not shown). The correlation/pairing effect of cations and anions in bulk electrolyte solutions has been shown to play a significant role on the properties of the system. Indeed, the pairing effect is known to be the leading effect for salt solvation;111 significant pairing induces the formation of small salt clusters that favor crystallization.112 We also expect such an effect to be a key parameter in describing the dynamics of the confined electrolyte solutions. In particular, the formation of salt crystallites in nanopores can occlude the membranes and prevent nanofiltration. To estimate the average pairing time between the cations and anions, we show in Figure 9 the time correlation functions between Na and X (X ) F, Cl, Br, I). Both the data for confined and bulk electrolyte solutions are reported. Again, the data for the bulk electrolyte solutions show that NaF exhibits a different dynamical behavior from the other sodium halides NaCl, NaBr, NaI. Much longer pairing times are observed for NaF compared to the other electrolyte solutions. The difference between the sodium halide electrolyte solutions almost disappears upon confinement as very similar average pairing times are observed for the different electrolyte solutions. This result is consistent with our results above for the average solvation times showing that ion-specific dynamical effects are diminished when the electrolyte solutions is confined at the nanoscale. It should be noted that the time correlations between ions and water molecules and between cations and anions always tend to be zero. They become negligible beyond 300 ps. This indicates that there is a correlation between ion-pairing lifetime and solvation lifetime as they exhibit similar decorrelation time. The insets in Figure 8 and Figure 9, which show these correlation functions in semilog scale, reveal that the time correlation functions for the nanopores, unlike those for the bulk systems, do not exhibit a simple exponential decay. On the

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Figure 9. Time correlation functions R(τ) between Na and X ions in electrolyte solutions NaX (X ) F, Cl, Br, I). The blue, green, red, and black lines correspond to results obtained for the NaF, NaCl, NaBr, and NaI electrolyte solutions, respectively. The solid lines are for electrolyte solutions confined in a 3 nm carbon nanotube while the dashed lines are for the corresponding bulk electrolyte solutions. The inset shows the same curves when plotted in a semilog scale.

Figure 10. Time correlation functions R(τ) for the oxygen atoms of water in electrolyte solutions NaX (X ) F, Cl, Br, I) at the surface of the 3 nm carbon nanotube (see text). The blue, green, red, and black lines correspond to results obtained for NaF, NaCl, NaBr, and NaI electrolyte solutions, respectively. The inset shows the same curves in a semilog scale.

contrary, the functions look like stretched exponential functions. This suggests that the relaxation process is much more complex in the confined systems than in the bulk systems. It also indicates that these correlation functions result either from a distribution of times due to the heterogeneous nature of the system or from strongly correlated relaxation phenomena. Figure 10 shows the time correlation function of the water oxygen with the carbon nanotube surface. The latter function differs from that in eq 3 as it provides an estimate of the average time spent by the water molecules in the vicinity of the carbon surface Ni

Pi(τ) )

∑

1 〈Θ (t)Θi(t + τ)〉t Ni i)1 i

(4)

where θi(t) equals 1 if the water molecule i is located at time t within the first adsorbed layer and 0 otherwise. On the basis of the first minimum in the density profiles, a water molecule is considered within the first adsorbed layer if its position is such that R > 10 Å. Again, the brackets in eq 4 indicate that the value is averaged over a large number of molecular dynamics configura-

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tions. Because of the definition above, θ(t) · θ(t + τ) ) 1 if a water molecule is within the first adsorbed layer at the times t and t + τ. The water-surface time correlation functions in Figure 10 suggest that the average residence time of water at the carbon surface decreases as the size of the anion increases. This result is consistent with the fact that the self-diffusivity of water increases with increasing anion size. As a result, due to their faster diffusion, water molecules in electrolyte solutions with large ions tend to spend less time in the vicinity of the carbon surface. Nevertheless, it should be noted that the differences observed in terms of residence times between the electrolyte solutions are small. This result is consistent with the fact that the structure of water confined in the carbon nanotube is nearly insensitive to the nature of the ions, as it is mainly driven by the interaction with the surface. 5. Conclusion Water in the confined electrolyte solutions exhibits significant layering that is nearly insensitive to the nature of the sodium halide ions. Even for salt concentrations 3 times larger than that of seawater, the structure of confined water is mainly driven by the interactions between water molecules and between water molecules and the nanochannel surface. Sodium also tends to form layers at the nanotube surface that are sandwiched between water molecules. Such an ordering of the cations is governed by the ordering of the confined water molecules, as the latter configuration corresponds to higher solvation of the cations all the while being compatible with the layering imposed by the carbon nanotube. In contrast to the results for water and sodium cations, the structure of the anions depends on their nature (F, Cl, Br, I). On the one hand, fluoride anions occupy in a more homogeneous way the porous space within the carbon nanotube. On the other hand, larger anions, that is, Cl, Br, and I, exhibit a different behavior than F because the former tend to be more and more repelled from the water layers as their size increases. This result can be explained in terms of the steric/hydrophobic effect;37 that is, the hydrophobic contribution to the free energy cost of solvating ions increases with increasing ion size (roughly as the volume) due to the mainly entropic cost of hydrating small cavities. The average surface densities of solvating molecules around the cations and anions are very close to those in the bulk. This result confirms that water and ions tend to keep their relative organization even in the case of severe confinement. Moreover, the average surface density of water molecules in the first solvation sphere around the sodium ions ∼0.32 H2O/Å2 is nearly insensitive to the nature of the anion. The dynamics of the confined water molecules and ionic species was found to be slower than that for the bulk electrolyte solutions. Such reduced diffusion (∼40%) shows that the confinement effect at the nanoscale in carbon nanotubes significantly hinders the dynamics of the confined systems. In contrast to the structural properties that show different behaviors for NaF and NaX (X ) Cl, Br, I), the dynamical data for these systems suggest that confinement tends to attenuate certain ion specific differences seen in the bulk. For instance, both the data for water and the ionic species indicate that the ratio of the self-diffusivity for the confined electrolyte to that for the bulk is independent of the nature of the anion F, Cl, Br, I. Moreover, while the average solvation times for Na in NaF and Na in NaX (X ) Cl, Br, I) significantly differ for bulk solutions, they tend to be similar when considering the confined solutions. Such an attenuation of the dynamical properties of the electrolyte solutions due to confinement is also observed for the pairing of the anions and cations. While NaF bulk solution exhibits a very different pairing behavior (as seen in the time correlation

Cazade et al. functions) from the other sodium halide solutions (NaCl, NaBr, NaI), the difference nearly vanishes upon confinement. Finally, by looking at the water-surface time correlation functions, we show that the average residence time of water at the carbon surface does not drastically depend on the size of the anion. This result is consistent with the fact that the structure of water confined in the carbon nanotube is nearly insensitive to the nature of the ions as it is mainly driven by the interaction with the surface. Acknowledgment. We thank the French National Research Agency (ANR) for funding through the research project “SIMONANOMEM” (ANR-07-NANO-055-04). Calculations were performed using supercomputers at the Institut de De´veloppement et des Ressources en Informatique Scientifique (IDRIS, CNRS, Grant 96223). We are grateful to J. Moore and K. E. Gubbins for fruitful discussions on diffusion in nanopores and nanotubes. This paper also benefits from discussions with P. Bonnaud, P. Levitz, and R. Pellenq. Supporting Information Available: Additional simulation results. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Shannon, M. A.; Bohn, P. W.; Elimelech, M.; Georgiadis, J. G.; Marin˜as, B. J.; Mayes, A. M. Nature 2008, 452, 301–310. (2) Fleury, P.; Bakalowicz, M.; de Marsily, G. J. Hydrol. 2007, 339, 79–92. (3) http://news.bbc.co.uk/2/hi/europe/8161889.stm (accessed July 21, 2009). (4) Lefebvre, X.; Palmeri, J.; David, P. J. Phys. Chem. B 2004, 108, 16811–16824. (5) Chmiel, H.; Lefebvre, X.; Mavrov, V.; Noronha, M.; Palmeri, J. Computer Simulation of Nanofiltration, Membranes and Processes. In Handbook of Theoretical and Computational Nanotechnology; Rieth, M., Schommers, W., Eds.; American Scientific Publishers: Los Angeles, CA, 2006; Vol. 5, pp 93-214. (6) Caldwell, J. W.; Dang, L. X.; Kollman, P. A. J. Am. Chem. Soc. 1990, 112, 9145. (7) Dang, L. X.; Rice, J. E.; Caldwell, J. W.; Kollman, P. A. J. Am. Chem. Soc. 1991, 113, 2481. (8) Perera, L.; Berkowitz, M. L. J. Chem. Phys. 1991, 95, 7556. (9) Caldwell, J. W.; Kollman, P. A. J. Am. Chem. Soc. 1995, 117, 4177. (10) Shelly, J. C.; Sprik, M.; Klein, M. L. Langmuir 1993, 9, 916. (11) Marrone, T. J.; Hartsough, D. S.; Merz, K. M. J. J. Phys. Chem. 1994, 98, 1341. (12) Gregory, J. K.; Clary, D. C.; Liu, K.; Brown, M. G.; Saykally, R. J. Science 1997, 275, 814. (13) Dang, L. X.; Chang, T.-M. J. Chem. Phys. 1997, 106, 8149. (14) Dang, L. X. J. Phys. Chem. 1998, 102, 620. (15) Herce, D. H.; Perera, L.; Darden, T. A.; Sagui, C. J. Chem. Phys. 2005, 122, 24513–24522. (16) Chang, T.-M.; Dang, L. X. Chem. ReV. 2006, 106, 1305–1322. (17) Horinek, D.; Netz, R. R. Phys. ReV. Lett. 2007, 99, 226104. (18) Jungwirth, P.; Tobias, D. J. Chem. ReV. 2006, 106, 1259–1281. (19) Whitby, M.; Quirke, N. Nature Nano. 2007, 2, 87–94. (20) Qiao, Y.; Cao, G.; Chen, X. J. Am. Chem. Soc. 2007, 129, 2355. (21) Li, J.; Gong, X.; Lu, H.; Li, D.; Fang, H.; Zhou, R. Proc. Nat. Acad. Sci. U.S.A. 2007, 104, 3687–3692. (22) Romero-Vargas Castrill, S.; Giovambattista, N.; Aksay, I. A.; Debenedetti, P. G. J. Phys. Chem. B 2009, 113, 7973–7976. (23) Stanley, H. E. Z. Phys. Chem. 2009, 223, 939–956. (24) Nicotera, I.; Coppola, L.; Rossi, C. O.; Youssry, M.; Ranieri, G. A. J. Phys. Chem. B 2009, 113, 13935–13941. (25) Huang, D. M.; Cottin-Bizonne, C.; Ybert, C.; Bocquet, L. Phys. ReV. Lett. 2007, 100, 177801–177804. (26) Huang, D. M.; Cottin-Bizonne, C.; Ybert, C.; Bocquet, L. Langmuir 2008, 24, 1442–1450. (27) Huang, D. M.; Cottin-Bizonne, C.; Ybert, C.; Bocquet, L. Phys. ReV. Lett. 2008, 101, 64503–64506. (28) Yang, L.; Garde, S. J. Chem. Phys. 2007, 126, 84706–84713. (29) Ren, Y.; Stein, D. Nanotechnology 2008, 19, 195707–195712. (30) Va´cha, R.; Siu, S. W. I.; Petrov, M.; Bo¨ckmann, R. A. J. Phys. Chem. A 2009, 113, 7235–7243.

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