ARTICLE pubs.acs.org/JPCC
Aqueous NaCl Solutions within Charged Carbon-Slit Pores: Partition Coefficients and Density Distributions from Molecular Dynamics Simulations Raja Kirthi Kalluri, Deepthi Konatham, and Alberto Striolo* School of Chemical, Biological and Materials Engineering, The University of Oklahoma, Norman, Oklahoma 73019, United States ABSTRACT: Molecular dynamics simulations have been employed to study the structural properties of aqueous electrolytes confined within graphene pores. The effects of pore size and graphene surface charge density were quantified by calculating ionic density profiles within the pores and pore-bulk partition coefficients. Carbon-slit pores of width 0.9, 1.2, and 1.6 nm were considered. The graphene surfaces were charged with densities ranging from 0 (neutral pore), 20, 30, and 40 μC/cm2, simulating various applied voltages. Aqueous solutions of NaCl at 1.51.6 M concentrations were considered at ambient conditions. When the graphene sheets are neutral, most electrolytes remain outside of the pores. The few sodium and chloride ions that are found within the pores remain preferentially at the center of pores, where they can be hydrated. As the graphene surface charge density increases, more Na+ and Cl enter the pores. At the maximum graphene surface charge density considered (40 μC/cm2) the ionic concentration within the pores can be ∼10 times as high as that outside of the pores, with the maximum partition coefficient obtained when the pore width is 1.2 nm. In all pores, when the surface charge density is 40 μC/cm2 the ions move toward the charged graphene surfaces because of counterion condensation effects, at the expense of losing part of their hydration shells. In some instances our results reveal the formation of multiple layers of adsorbed electrolytes near a charged graphene surface. These layers appear to form because of a number of effects including surfaceion electrostatic interactions, hydration phenomena, and also ionion correlations, especially at the maximum surface charge densities considered within the 1.2 nm wide pores. The results presented are useful for designing graphene-based electric double layer capacitors.
1. INTRODUCTION Toward deploying renewable energy sources, it is crucial to develop efficient and cost-effective technologies to store electricity. To be useful for large-scale applications, energy-storage devices should be reasonably priced, capable of numerous charge/ discharge cycles without loss of efficiency, environmentally friendly, efficient, and reliable in a wide range of temperatures. Electric energy can be stored in batteries or electrochemical capacitors.1 Traditional batteries are currently plagued by a number of practical problems including high cost, limited stability over extended charge/discharge cycles, and slow power delivery or uptake. One possible alternative to batteries is represented by electric double-layer capacitors (EDLCs). EDLCs are electrochemical energy storage devices. Because the capacitance arises from electrostatic charge accumulation at the electrolyte/electrode surface and can be enhanced by increasing the electrodes interfacial area and by decreasing the charge separation distance, it largely depends on the type of electrodes used and on the type of electrolytes.2 Porous carbons are finding large applications because of their high surface area. To maximize performance, the pores should be easily accesible to the electrolytes. Significant technological advances have recently been achieved for EDLCs. Because of their extremely high power densities, incomparable cycle life, stability, and reliability, EDLCs are finding applications in devices such as uninterruptible power systems (UPS), memory back-up systems, and even emergency doors in Airbus A380 airplanes.2 The current major limitation for r 2011 American Chemical Society
the widespread application of EDLC is their limited energy density, which can be as little as one-fifteenth to one-thirtieth that of electrochemical batteries.2,3 Aqueous and organic electrolytes are employed for EDLCs. Although aqueous electrolytes generally yield higher power density, their low decomposition voltage (e1 V) places a limit on the energy density that can be achieved. Organic electrolytes allow a higher cell voltage, to ∼2.5 V, but are affected by relatively low ionic conductivity.2,3 To devise EDLCs with increased energy and power density, a better understanding is necessary regarding how electrolytes pack and diffuse within narrow charged pores. Different materials, including activated porous carbons and carbon nanotubes (CNTs), are used as EDLC electrodes.4 Zhang et al.2 provided a review regarding carbon-based electrode materials for EDLCs. Among carbon-based electrodes, graphene is currently attracting significant attention. Its excellent electron transfer behavior, high surface area, and its unique two-dimensional nature render graphene-based porous materials very attractive as EDLCs electrodes. Liang et al.5 showed that graphene-based electrodes with appropriate defects (encapsulated metal or metal oxide nanoparticles) and optimized alignment display enhanced capacitive behavior and good cycling performance. Graphene-based Received: April 2, 2011 Revised: June 3, 2011 Published: June 08, 2011 13786
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Figure 1. Representative simulation snapshots of the systems composed by electrolyte solution between carbon-slit pores of widths 1.6 nm (left), 1.2 nm (middle), and 0.9 nm (right). Gray spheres represent carbon atoms. Red and white represent oxygen and hydrogen atoms of water. Yellow and green represent chloride and sodium ions, respectively.
materials with large surface area yield dramatically increased capacitance in EDLCs.5 Various experiments have shown that the high electrical conductivity of graphene electrodes provides consistently good performance over a wide range of scan rates for both aqueous and organic electrolytes.5,6 The recent interest on EDLCs is due in part to the gamechanging experimental results from Gogotsi, Simon, and coworkers.7 These results point to a charge storage mechanism whereby the partial removal of the solvation shell and the increased confinement of the ions within a porous electrode lead to increased capacitance. The unexpected effect was reported for pores of size 0.69 nm and naturally contributed to stimulate enormous interest toward understanding structure and dynamics of electrolyte solutions confined in sub-nanometer pores. Many simulation studies have been reported on this subject. Federov et al.8 studied dense assemblies of charged Lennard-Jones spheres between charged walls, focusing on the effect of surface charge density on ion screening. Lynden-Bell et al.9 studied the hydration and mobility of electrolyte solutions inside a repulsive channel, showing that in a narrow pore the ionic hydration shell is incomplete and that the ionic diffusion is slower than that in the bulk. Yang et al.10 reported MD simulations for negatively charged CNTs interacting with aqueous Na+, K+, and Cs+. At a sufficiently high CNT charge (e.g., qCNT = 5e) it was thermodynamically favorable for all three ions to partition into the pore. Shim et al.11 showed that CNTs of diameter less than 1 nm are too small to accommodate bulky EMI+ and BF4 ions without the assistance of electrostatic interactions. Feng et al.12 quantified the energy cost for small inorganic ions to enter polarizable subnanometer pores. Their simulations suggest that Na+ and Cl ions entering a 0.82 nm wide slit pore must overcome a free energy penalty of less than 14 kJ/mol, much smaller than that encountered to enter CNTs of diameter 0.82 nm (∼120 kJ/mol). Tang et al.13 studied aqueous K+ and Cl confined in cylindrical pores of radius from 15.8 to 4.75 Å. The results showed a decrease in ionic hydration, water hydrogen bonding, and ionic conductivity as the cylindrical pore radius decreases. These and other results confirm that interactions between ions, ion hydration, as well as pore surface charge density contribute to determine selectivity and penetration of ions into sub-nanometer pores.1417 In this study we employ equilibrium molecular dynamics simulations to quantify the effect of surface charge density and pore width on the partition of aqueous NaCl electrolytes between bulk and confined regions and on the electrolytes distribution within the pores. Carbon-slit pores of widths 0.9, 1.2, and 1.6 nm are considered. The results are consistent with a competition between poreion electrostatic interactions and ion hydration forces that are affected by pore width. The remainder of the paper is organized as follows. In section 2 we describe
simulation methods and algorithms, in section 3 we discuss our results, and in section 4 we summarize our conclusions.
2. SIMULATION METHODS AND ALGORITHMS Within our simulation box, two graphite slabs were considered facing each other along the Z direction to represent slit-shaped pores. The graphite slabs below and above the slit-shaped pore volume consist of three and four graphene sheets, respectively, separated by 3.35 Å. The simulation box is periodic in the X, Y, and Z directions. An odd number of graphene sheets was chosen to represent the solid substrates (i.e., seven graphene layers along the periodic Z direction) so that two mirror-image graphene sheets face each other across the pore volume. The dimensions of each graphene sheet along the X and Y directions are 22.4 and 21.3 Å, respectively. Three pore sizes of 1.6, 1.2, and 0.9 nm were considered (the pore width refers to the center-to-center distance between carbon atoms of the bottommost layer of the top slab and the topmost layer of the bottom slab). The graphite slabs are surrounded by aqueous electrolyte solutions (water, sodium, and chloride ions) between the slabs and on both sides (a region of thickness ∼2.5 nm outside the pores is provided on each side of the graphitic pore) along the X direction. Because of periodic boundary conditions, the carbonslit pores are effectively infinite along the Y direction. The initial configuration is built with water and ions placed outside of the slit pore, in the “bulk” region. As the simulation progresses, water and ions fill the pore. In Figure 1 we report representative simulation snapshots of the three systems considered. From left to right, the pore width decreases from 1.6 to 1.2 to 0.9 nm. The simulation boxes are filled with water and NaCl. The number of water molecules in each simulation box was adjusted to secure the formation of a liquid film outside of the pore volume thick enough to approximate bulk liquid properties. For computational accuracy, it is desirable to simulate a bulk system as large as possible, but limitations due to computing power impose a practical limit on the size of the systems that can be simulated. As a compromise, the region meant to replicate bulk properties in our simulations is of thickness ∼5 nm. Because most simulation and experimental results for interfacial water suggest that a surface perturbs the properties of water for up to 11.5 nm from the solid, bulk properties should be obtained outside of the pore volume. We confirmed that bulk properties were reproduced far from the graphitic pores by analyzing the water density, which in those regions corresponds to that of bulk liquid water at ambient conditions. To further confirm the achievement of bulklike properties outside of the pores it would be desirable to implement grand canonical Monte Carlo simulations or to conduct molecular dynamics studies for systems much bigger than those considered here. However, both approaches require 13787
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Table 1. Composition of the Three Simulated Systemsa number of molecules
a
pore width (Å)
water
Na+ and Cl
ionic strength (M)
16
1776
51
1.59
12
1134
32
1.56
9
1216
33
1.51
All simulations were conducted at ambient conditions.
computational resources significantly larger than the massive ones employed herein. The simulated NaCl concentration in all cases was 1.51.6 M, chosen to replicate typical experimental EDLC conditions. The atomic composition of each of the three systems of Figure 1 is given in Table 1. Water is modeled using the simple point charge extended (SPC/E) model, which is a rigid three-site model known to reproduce adequately the structural and dynamic properties of water (pair correlation functions and self-diffusion coefficient) at ambient conditions.18 Bond lengths and angles in water molecules were kept fixed using the SHAKE algorithm.19 Carbon atoms in the graphene sheets are held stationary and modeled as Lennard-Jones spheres employing the parameters proposed by Cheng and Steele.20 The potential parameters implemented to simulate sodium (Na+) and chloride (Cl) ions were fitted for the SPC/E water model by Dang and collaborators to reproduce accurately the bulk liquid structural properties.21 These parameters have been used previously to study ion mobility in water.22 As commonly done in simulation studies,23 the applied voltage is described as a uniform distribution of electrical charges on the carbon atoms. The topmost graphene sheet of the bottom slab is modeled as the anode (by placing positive charges on the carbon atoms) and the bottommost graphene sheet of the top slab is modeled as the cathode (by placing negative charges on the carbon atoms). Equal but opposite charges are placed on the carbon atoms of the anode and the cathode to secure electroneutrality. Under this representation each carbon-slit pore of Figure 1 represents a capacitor. Different surface charge densities can be obtained by varying the electronic charges on the carbon atoms. Three surface charge densities of 40, 30, and 20 μC/cm2 were used. The effect of image charges was not considered. As the electrolyte concentration increases, this approximation is expected to become less severe because of screening.24 To conduct all-atom molecular dynamics simulations, we employed the simulation package LAMMPS.25 The dispersive interactions were modeled with 12-6 Lennard-Jones (LJ) potentials. The LJ parameters for unlike interactions were determined using the LorentzBerthelot mixing rules.26 The cutoff distance for all interactions was set to 9 Å, and the long-range electrostatic interactions were treated using the particle mesh Ewald summation method.27 The system temperature was maintained at 300 K by using the Nose-Hoover thermostat28,29 with a relaxation time of 10 fs. The simulations were conducted implementing both the NPT and the NVT ensembles, at different stages.26 Each system was initially simulated in the NPT ensemble at 1 atmosphere pressure and 300 K until water and electrolytes penetrated the pores and the systems reached constant volume. Then the simulations were conducted in the NVT ensemble at 300 K for 5 ns with a time step of 1 fs. At this point the carbon-slit pores
were charged. After uniform charges were placed on the carbon atoms, simulations were carried out for a total of 15 ns. This was considered sufficient to ensure equilibration because the density profiles for the ions inside the pore showed little changes during the last 8 ns of each simulation run. The results from the last 5 ns were used for analysis. The results discussed herein are averages over four independent simulations for each pore width and charge density considered. For each pore width, the final configurations obtained at the maximum surface charge density were used to initiate simulations at lower surface charge densities. The final results from these latter simulations reproduced those obtained from other initial configurations, further corroborating that the simulations discussed were properly converged.
3. RESULTS 3A. Partition Coefficients. The design of the simulation box, see Figure 1, allows us to estimate the distribution of electrolytes between the “bulk” and the porous volume as the surface charge density increases on the carbon-slit pores. The partition coefficient (Γ) was calculated as the ratio of ionic concentration in the pore versus that in the bulk
Γ¼
Cpore Cbulk
ð1Þ
The two concentrations Cpore and Cbulk are calculated by counting the number of ions, as well as water molecules, within the slit pore and within the region outside the pore. The region outside the pore considered for these calculations corresponds to the one along the X axis of the simulation box where no carbon atoms are found (see Figure 1). The partition coefficient is calculated for both Na+ and Cl ions as a function of pore width and of graphene surface charge density. The results are shown in Figure 2. Admittedly, the results in Figure 2 are probably dependent, to some extent, on the size of the simulated system. For example, should the X dimesion of the carbon-slit pores be larger than that considered here, it is likely that more ions will be attracted from the bulk to inside the pores at any surface charge density simulated, possibly leading to lower bulk concentrations and higher partition coefficients. Nevertheless, our results are useful for quantifying the effect of pore width on the partition coefficient for a given surface charge density, although they should be considered specific for the system simulated herein. Quantification of size effects is at present prohibitive in terms of computational resources. In all pores and for both Na+ and Cl ions, our results suggest that when the graphene surface charge density is zero the partition coefficient is less than unity, indicating that the ions reside preferentially in the bulk region. Our results suggest that the ions can be found within the largest neutral pore simulated (1.6 nm) but that their concentration is very low within the other two neutral pores. This observation is related to the sizes of the hydrated Na+ and Cl ions (0.72 and 0.66 nm, respectively), which are comparable to the width of the smaller pores simulated. The effective pore widths for the H = 0.9 and for the H = 1.2 nm pores are ∼0.57 and ∼0.90 nm, respectively, when excluded-volume effects are considered. Should the ions penetrate the neutral 0.9 nm pores, they would lose part of their hydration shell, which, as suggested by a number of simulation results,10,12 is associated with energetic penalties. When the pores are 1.6 nm in width (effective pore width ∼1.27 nm), the ions can penetrate the pore without necessarily losing their hydration 13788
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Figure 2. Partition coefficient for sodium (left) and chloride (right) ions as a function of graphene surface charge density. Different symbols are for pores of different widths (filled circles for H = 1.6 nm, empty circles for H = 1.2 nm, inverted triangles for H = 0.9 nm). Lines are guides to the eye. Symbols are larger than error bars.
shell. However, our simulation results suggest that even in this case the electrolytes preferentially reside in the bulk water. This is probably due to entropic reasons, as the hydrated ions inside the neutral pores will remain far from the solid surfaces, the free volume accessible to them is limited. As the graphene surface charge increases, our results suggest that more of the available ions enter the pores rather than residing in the bulk. For the wider pore considered (H = 1.6 nm), when the surface charge densities are larger than 20 μC/cm2, the partition coefficient is slightly larger than unity (1.2 ( 0.1), indicating that the concentration of both electrolytes within the slit pores is only slightly larger than that in the bulk, clearly because of attractive interactions between the charged surfaces and the electrolytes. Evidently such small electrolyte concentrations are sufficient to neutralize the charged graphene surfaces. For the H = 1.2 nm pore we observe that increasing the graphene surface charge density has a strong effect on the partition coefficient. The results can be understood when the effective pore size is considered (∼0.90 nm). Both hydrated ions can enter the H = 1.2 nm pores without experiencing significant energetic penalties. As the surface charge density increases, the poreion electrostatic interaction becomes more and more favorable. However, because these observations hold true also for the H = 1.6 nm pore, our partition coefficient results imply that some other phenomena occur when NaCl adsorb within the highly charged H = 1.2 nm pore. It should also be pointed out that while the partition coefficient for the H = 1.2 nm pore appears to increase gradually as the graphene surface charge density increases to 30 μC/cm2, there appears to be a much more significant increase when the surface charge density increases from 30 to 40 μC/cm2. It is possible that a combination of effects including strong electrostatic attractions between the charged graphene surfaces and the electrolytes, and confinement effects due to the reduced pore width compared to the H = 1.6 nm pore contribute to a pronounced loss of the hydration shell for adsorbed ions, which in turn may lead to enhanced ionion correlations. Evidence of such effects is provided below. For the H = 0.9 nm pore our results are qualitatively comparable to those just discussed for the H = 1.2 nm pores (i.e., the partition coefficient increases as the surface charge density increases). However, our results show that the partition coefficient remains very small, comparable to unity, as long as the surface charge density is 30 μC/cm2 or less. This is probably due
to the effective pore size (∼0.57 nm). Because to penetrate the H = 0.9 nm pores, the ions must lose part of their hydration water, overcoming a large energetic barrier,12 the concentration of the ions inside the pores remains lower than, or at most comparable to, that in the bulk. When the graphene surface charge density increases to 40 μC/cm2, our results show a large increase in the partition coefficient, which reaches ∼4. At this surface charge density the poreion electrostatic interactions become dominant and the ions are attracted inside the pores even at the expense of losing part of their hydration shells. The results discussed in this section appear to be consistent with the experimental data reported by Gogotsi and co-workers,7 which suggest that ions can penetrate sub-nanometer pores upon losing the hydration shell. However, our results also show that the partition coefficient is maximized for the H = 1.2 nm pores, suggesting that such pores might be optimal for the production of EDLCs when aqueous NaCl solutions are employed as electrolytes. Because these pores are larger than necessary for the complete loss of hydration shell for NaCl electrolytes, and because the partition coefficient obtained is much larger than that obtained for narrower, as well as wider pores, it is likely that other phenomena in addition to the perturbation of the hydration shell are responsible for these unexpected observations. To elucidate such phenomena, in the following sections we quantify the distribution of water and electrolytes within the various carbon-slit pores. 3B. Density Distributions within Neutral Pores. The density profiles of ions and water within pores of different width are shown in Figure 3, where distances are measured from the center of the carbon atoms of the topmost graphene sheet of the bottom graphitic slab. Depending on the pore widths considered, the positions Z = 1.6, 1.2, or 0.9 nm correspond to the bottommost graphene layer of the top graphitic slab (see Figure 1 for pore geometry). In all three pores, as expected, our results show that the confined water molecules yield well-defined density layers near each of the solid surfaces. The intensity of the density layers at contact with the graphene surfaces increases as the pore width decreases. In the H = 0.9 nm pores we observe the formation of two well-defined layers given by the position of the oxygen atoms of water. The density profile for the hydrogen atoms shows multiple peaks, because of the formation of hydrogen bonds between water molecules in the two layers. As the pore width increases to H = 1.2 nm, the two defined layers of oxygen atoms 13789
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Figure 3. Density profiles for oxygen (continuous black) and hydrogen atoms of water (dotted gray), sodium (dashed red), and chloride ions (dash-dot green) within neutral slit-shaped pores. Panels a, b, and c are for pores of width H = 1.6, 1.2, and 0.9 nm, respectively. In all cases, Z = 0 Å corresponds to the atomic center of the carbon atoms of the topmost graphene sheet of the bottom slab. Because of the large difference in density, the density profiles for O and H atoms of water are shown on the left y axis; those for Na+ and Cl ions are shown in the secondary y axis on the right.
Figure 4. Density profiles for oxygen (continuous black) and hydrogen atoms of water (dotted gray), sodium (dashed red), and chloride ions (dash-dot green) within slit-shaped pores. Panels a, b, and c are for pores of width H = 1.6, 1.2, and 0.9 nm, respectively. In all cases, Z = 0 Å corresponds to the atomic center of the positively charged carbon atoms of the topmost graphene of the bottom graphite slab. Because of the large difference in density, the density profiles for O and H atoms are shown on the left y axis; those for Na+ and Cl ions are shown in the secondary axis on the right. The graphene surface charge density is 40 μC/cm2.
near the graphitic surfaces are coupled to a third layer in the center of the pore. Within the H = 1.6 nm pores the results show the formation of four density layers formed by the oxygen atoms of water. The density distribution of the hydrogen atoms in this pore is qualitatively similar to that of the oxygen atoms, suggesting the formation of hydrogen bonds between water molecules within the same layers. These results are consistent with simulation results reported for water confined within slit-shaped carbon pores,30,31 suggesting that the presence of electrolytes does not affect significantly the structural properties of confined water. This is not too surprising when we consider the low concentrations of electrolytes within the pores, as indicated by the partition coefficients of Figure 2. Please note that the number density of ions (right axis in Figure 3) is ∼23 orders of magnitude lower than that of water molecules. For an analysis of the hydrogenbond network of water molecules confined within narrow carbon-slit pores, we refer the interested reader to refs 30 and 31. The density profiles shown in Figure 3 for Na+ and Cl ions in all pores considered are not perfectly symmetric. This is due to the small number of electrolytes within the pore (see Figure 2), which limits the statistical accuracy of our analysis. Despite this deficiency, our data show that both Na+ and Cl ions concentrate within the center of the pores, independent of the pore width. Note that the ionic density is significantly lower in the H = 0.9 and H = 1.2 nm pores than in the H = 1.6 nm ones, as expected from the partition coefficient results. On the basis of our results for aqueous NaCl confined within silica-based slit-shaped nanopores,17 it was expected that the Na+ ions would accumulate
in correspondence to local maxima in the density profile of oxygen atoms of water. Our results show that this is not always the case. In the H = 1.6 and H = 0.9 nm pores the Na+ ions appear to accumulate in regions depleted of oxygen atoms of water. Within the H = 1.2 nm the Na+ ions seem to instead accumulate in regions correspondent to maxima, as well as minima in the density of oxygen atoms. There appears to be a competition between the Na+ ions to incorporate within the water layers (the size of Na+ ions is comparable to that of water molecules) or to pack in between oxygen layers. In both cases, the Na+ ions interact favorably with the negatively charged oxygen atoms of water. The distribution of the Cl ions appears to be uniform near the centers of the H = 0.9 and the H = 1.6 nm pores, although some correlations seem to exist between the density profile of Cl and that of Na+ ions, especially within the H = 1.2 nm pores. The density profiles of sodium and chloride ions obtained are consistent with previously obtained results,32 although the NaCl concentrations considered here (∼35% by weight depending on the pore width) are much lower than those considered in ref 32. 3C. Density Distribution as a Function of Graphene Surface Charge Density. In contrast to the results shown in section 3B for atomic density distribution within neutral pores, we report in Figure 4 the atomic density distributions within the various pores simulated when the surface charge density is 40 μC/cm2, the maximum considered here. At this surface charge density the counterions move toward the graphene surfaces because of electrostatic attractions, leading to counterion adsorption. Our 13790
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The Journal of Physical Chemistry C results reveal that charging the pores has also a pronounced effect on the structure of confined water, which changes compared to that of neutral pores (Figure 3) because of two phenomena, both related to the graphene surface charge density. As the surface charge density increases, the orientation of interfacial water changes, leading to changes in the density profiles. The second phenomenon is due to the adsorption of electrolytes onto the charged surfaces. As the ions adsorb, they affect the water molecules within their hydration shells. To rationalize the results in Figure 4 it helps to remember that the topmost graphene layer of the bottom slab is positively charged, while the bottommost graphene layer of top slab is negatively charged (see Figure 1 for pore geometry). Near the positively charged surface (Z = 0) our results show that the orientation of interfacial water molecules changes significantly compared to results obtained in the neutral pores. In particular, the position of the density peaks representative of the oxygen atoms is closer to the surface than that representative of the hydrogen atoms. This is consistent with a water orientation in which most of the hydrogen atoms point away from the charged surface. On the contrary, near the negatively charged surface (Z = 1.6, 1.2, and 0.9 nm for the three pores) our results show that the hydrogen atoms of water are closer to the graphene surface than the oxygen atoms are. By comparing the position of the hydrogen peaks to those of the oxygen peaks, we conclude that one of the hydrogen atoms of interfacial water is directly pointing toward the charged surface, while the other is pointed away. Similar analysis has been reported previously for interfacial water molecules on other substrates.33,34 In addition to the orientation of interfacial water, its local density is much larger when the graphene surfaces bear 40 μC/cm2 than when they are neutral (compare Figure 3 to Figure 4). Further, the structural perturbation observed for confined water appears to span the entire pore width, except for the widest pore considered. As suggested by prior simulations on different substrates,17,35 the density profile for confined water is probably related to the distribution of ions within the pores. At the graphene surface charge density considered in Figure 4, we observe a pronounced association of the ions with the charged surfaces. Note that, as described in Figure 2, the concentration of both Na+ and Cl ions is larger than that in the bulk for all three pores considered in Figure 4. In the H = 1.2 nm pores the ionic concentration in the pores is almost 10 times that in the bulk, while in the H = 1.6 nm pores the concentration within the pores is only about twice that in the bulk. In all pores we observe pronounced layering of the ions. The Cl ions accumulate in proximity of the positively charged surface (Z = 0.0 nm), yielding one well-defined layer of density ∼0.0350.04 atoms/Å3 (the actual density depends on pore width). The position of this layer is embedded with the first layer of hydrogen atoms, suggesting a possible interaction between the Cl ions and the positively charged hydrogen atoms of water. In the H = 1.6 nm pore there appears to be the presence of a small second Cl layer further from the surface, although its features are obscured due to statistical uncertainty. The second Cl layer appears very clearly in the H = 1.2 and in the H = 0.9 nm pores. In both cases the position of this layer is located at about 0.55 nm from the positively charged surface. This second layer is well-defined in the two narrow pores because the ionic concentration is much larger than that in the H = 1.6 nm pore. It is also interesting to point out that a third dense layer is formed by Cl ions not far from the positively charged surface (Z ∼ 1.2 nm in
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Figure 5. Representative simulation snapshot obtained for the H = 1.6 nm pore at surface charge density of 40 μC/cm2. Only Na+ ions and water molecules within two selected layers are shown: (a) first and (b) second layers near the negatively charged surface. Gray spheres represent carbon atoms; red and white spheres represent oxygen and hydrogen of water; green spheres represent sodium ions. For clarity, the remaining carbon atoms, water molecules, and NaCl electrolytes in and out of the pore are not shown. The top graphene surface is negatively charged; the bottom one is positively charged.
the H = 1.6 nm pore, and Z ∼ 0.8 nm in the H = 1.2 nm pore). Because of its position in proximity of the layer formed by Na+ ions, the Cl ions probably occupy this layer because of electrostatic attractions to the positively charged sodium ions. This layer cannot form in the H = 0.9 nm pore because this pore is simply too narrow. It is worth pointing out that the intensity of the third peak of Cl ions is much larger within the H = 1.2 nm pore than within the H = 1.6 nm pore. More details will be discussed later regarding this feature. In analogy with the results just discussed for the Cl ions, even the confined Na+ ions show pronounced layering, although these ions accumulate in proximity of the negatively charged surface. The behavior of Na+ ions is however quantitatively different compared to that of the Cl ones. In detail, we observe the formation of two dense Na+ layers within the H = 1.6 nm pore, where the ionic concentration is only approximately twice that in the bulk. The Na+ closest to the negatively charged surface appears to be sandwiched between the layer of hydrogen atoms of water next to the surface and the first layer of oxygen atoms of water. The second Na+ layer is found in correspondence to a region depleted of oxygen atoms of water, in between two peaks formed by oxygen atoms. The first Na+ peak is so close to the negatively charged surface that Na+ ions must lose their hydration shells, while in the second layer Na+ ions can be fully hydrated. To visualize these structural phenomena, we report in Figure 5 details of representative simulation snapshots. On the left panel we show the Na+ ions within the first layer, with the correspondent water molecules. As expected from the density profiles just discussed, the Na+ ions have lost part of their hydration shells. On the right panel we show the Na+ ions, together with water molecules, that are found within the second layer near the negatively charged surface. These ions are fully hydrated. Within the H = 0.9 nm pore, where the sodium concentration in the pore is ∼4 times that in the bulk, we observe the formation of one wide peak next to the negatively charged surface. This peak is associated with a shoulder further from the graphene surface. We also observe the formation of a second well-defined peak at Z ∼ 0.45 nm. It appears that sodium ions within the H = 0.9 nm pore are only found within these two layers (the density goes to zero in other locations). The Na+ peak closest to the 13791
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The Journal of Physical Chemistry C negatively charged surface is found sandwiched between the first layer of oxygen atoms and the first layer of hydrogen atoms of water. The Na+ peak at Z ∼ 0.45 nm is found in a position that corresponds to a minimum in the density of oxygen atoms of water, suggesting that this position may have been chosen not only because of electrostatic interactions but also because of excluded-volume effects. Within the H = 1.2 nm pore, where the ionic concentration is almost 10 times that in the bulk, Na+ ions show the formation of one pronounced peak at contact with the negatively charged surface (Z ∼ 0.97 nm). The position of this peak is sandwiched between the position of the dense first layers formed by oxygen and hydrogen atoms of water. It should be pointed out that the intensity of the first Na+ peak near the negatively charged surface is much larger within the H = 1.2 nm pore than in any other pore considered here. Even within the H = 1.2 nm pore we observe the formation of a second layer of Na+ ions, much less intense than the first peak. This second peak (barely visible in Figure 4 but more clear in section 3D) is found at Z ∼ 0.75 nm, where the Na+ ions appear to be correlated to the Cl ions found at Z ∼ 0.8 nm. Although this sequence of Na+ and Cl ion peaks next to the negatively charged surfaces appears to be a clear signature of counterion condensation effects coupled to ionion correlations, based on the results of Qiao et al.,36,37 it is also possible that the second Na+ layer is due to ion hydration (i.e., the second Na+ layer may represent hydrated ions near the charged surface, as suggested by the right panel in Figure 5). In all cases discussed above, because the position of the first dense peak of either Na+ or Cl ions near the oppositely charged surfaces does not allow the formation of a complete hydration shell, our results suggest that the electrolytes condense near the oppositely charged surfaces at the expense of losing part of their hydration shells. These observations are quantified in Figure 6, where we report the average number of water molecules found within the first hydration shell of Na+ ions (this number is defined as the coordination number), as a function of the pore width and of the graphene surface charge density. The ions considered for the calculations in Figure 6 are all those found within the various pores. Some of these Na+ ions are in contact with the graphene surface; some are near the center of the pores. In the bulk the coordination number for Na+ ions was found to be ∼6.3 ( 0.1, which is in agreement with simulation results reported in the literature.38,39 When the pores are neutral, the coordination number for Na+ ions inside the pores decreases as the pore width decreases, because of excluded-volume effects. For each pore width, as the graphene surface charge density increases the hydration number further decreases because the Na+ ions adsorb onto the charged surface. In general, for a given surface charge density the hydration number decreases as the pore width decreases, except when the surface charged density is 40 μC/cm2, in which case our results suggest that the minimum in the hydration number for confined Na+ ions is found when the pore width is H = 1.2 nm. This observation is directly related to the very large local density found for Na+ ions at contact with the negatively charged surface within the H = 1.2 nm pore at 40 μC/cm2. As most Na+ ions within the H = 1.2 nm pore adsorb onto the surface at this surface charge density, their hydration shell cannot be complete, leading to the minimum in hydration number. 3D. Surface Charge Density Effects on the Distribution of Sodium Ions. The density profiles of sodium ions within the three different pores simulated as a function of surface charge density are shown in Figure 7. It can be seen that as the charge density decreases from 40 μC/cm2, sodium ions tend to move away from
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Figure 6. Hydration number for Na+ ions confined within carbon-slit pores of width H = 1.6, 1.2, and 0.9 nm. The results are shown as a function of the surface charge density. Lines are guide to the eye.
the graphene surface to the center of the pore. This occurs because the ions prefer to be hydrated unless the surface is so highly charged that electrostatic interactions overcome the energetic barriers related to the loss of the hydration shell. At the graphene surface charge density of 20 μC/cm2 our results show the formation of one dense peak at Z ∼ 1.15 nm in the H = 1.6 nm pore, Z ∼ 0.75 nm in the H = 1.2 nm pore, and Z ∼ 0.45 nm in the H = 0.9 nm pore. The position of these peaks corresponds to the position of the second adsorbed Na+ peak observed for the three pores when the surface charge density is 40 μC/cm2. This observation further reinforces the hypothesis that the Na+ ions within this peak are adsorbed near the charged surface while maintaining intact their hydration shell. Clearly, the electrostatic attraction to the negatively charged graphene surfaces is too weak to perturb the hydration shell. At the surface charge density of 30 μC/cm2 our results show the formation of a well-defined layer of Na+ ions adsorbed in contact with the charged surfaces. For the H = 1.6 and H = 1.2 nm pores the positions of these peaks correspond to the positions of the first adsorbed Na+ ion peaks formed on the 40 μC/cm2 surface, although the peak intensity is always lower for the 30 than for the 40 μC/cm2 surface charge density. It is interesting to point out that the first Na+ adsorbed peak within the H = 0.9 nm pore at 30 μC/cm2 is found in the position correspondent to the shoulder of the first adsorbed Na+ peak within the same pore when the surface charge density is 40 μC/cm2. This anomalous behavior may be due to the relatively low density of Na+ ions within the H = 0.9 nm pore, and possibly to both ionion and ionwater correlations. At the surface charge density of 40 μC/cm2, the density distributions described in Figure 4 are obtained. The biggest changes in the density distribution are obtained as the surface charge density increases from 30 to 40 μC/cm2 for the H = 1.2 and the H = 0.9 nm pores, in which cases increasing the graphene surface charge density leads to dramatic increases in the concentration of the Na+ ions within the pores, as shown in Figure 2. However, while within the H = 1.2 nm pore it appears that most Na+ ions adsorb at contact with the negatively charged surface, leading to the highest local atomic density obtained in any of the cases considered in Figure 7, the Na+ ions found within the H = 0.9 nm pore appear to be equally distributed between two layers, one in contact with the negatively charged surface, the other 13792
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The Journal of Physical Chemistry C
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Figure 7. Density profiles for Na+ ions within slit-shaped pores. From top to bottom, the three panels are for pores of width H = 1.6, 1.2, and 0.9 nm, respectively. Results are shown as a function of graphene surface charge density, ranging from 20 to 40 μC/cm2. Z = 0.0 nm corresponds to positively charged graphene surface. The negatively charged surface is found at Z = 1.6, 1.2, and 0.9 nm, respectively, for the three pores considered.
Figure 8. Density profiles for Cl ions within slit-shaped pores. From top to bottom the three panels are for pores of widths H = 1.6, 1.2, and 0.9 nm, respectively. Results are shown as a function of graphene surface charge density, ranging from 20 to 40 μC/cm2. The graphene surface at Z = 0.0 nm is positively charged.
closer to the layer of chloride ions. Even within the H = 1.6 nm pore our results show a large increase in Na+ atomic density at contact with the negatively charged surface coupled with an increase in local density in the second layer. These results suggest that both partially dehydrated and completely hydrated Na+ ions are found near the negatively charged surfaces, as detailed in Figure 5. 3E. Surface Charge Density Effects on the Distribution of Chloride Ions. The density profiles of chloride ions obtained
from our simulations inside the pores of various widths as a function of the graphene surface charge density are shown in Figure 8. The results are qualitatively similar to those discussed in the previous section for Na+, but they show some important differences. The differences appear to be due to the fact that the hydration shell for Cl ions is less rigid than that for the smaller Na+ ions. The coordination number of chloride is found to be ∼7.1 ( 0.12 in bulk water, in agreement with literature observations.38,39 For neutral pores, the coordination number of 13793
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The Journal of Physical Chemistry C chloride is found to be 6.8 ( 0.1, 6.7 ( 0.3, 6.6 ( 0.3 for pore widths of 1.6, 1.2, and 0.9 nm, respectively, suggesting that the hydration shell for Cl ions is in part perturbed when the ions enter any of the pores considered here. When the pores are charged, the coordination number of chloride is found to decrease to ∼5.2 ( 0.1 for the Cl ions inside the pores. This value for the hydration number does not change significantly when either the pore width or the surface charge density change from 20 to 40 μC/cm2. This observation suggests that, limited to the conditions considered here, Cl ions adsorbed within charged pores are most likely found near the positively charged surfaces, independent of surface charge density. For the H = 1.6 nm pore the Cl ions accumulate near the pore center when the pore is neutral (Figure 3). As the surface charge density increases to 20 μC/cm2, our results (Figure 8, top panel) show the formation of a first peak at contact with the positively charged surface at Z = 0.35 nm. It appears that most of the Cl ions are preferentially found near the positively charged surface rather than hydrated at the pore center. As the surface charge density increases, the intensity of the first adsorbed peak increases, but the peak position changes only minimally (the layer gets closer to the charged surface). At the maximum surface charge density considered, several density peaks are observed within the pore, as described in Figure 4, probably because of ionion correlations. Results analogous to those just discussed are found for the H = 1.2 nm pore, with the exception that our results show the formation of two adsorbed layers near the positively charged surface for surface charge densities of 20 and 30 μC/cm2. The second layer could be consistent with the adsorption of hydrated Cl ions. However, because the second layer of chloride ions, at Z ∼ 0.55 nm, is found near the layer of sodium ions at Z ∼ 0.75 nm, it is possible that ClNa+ correlations are responsible for this feature. At the surface charge density of 40 μC/cm2 we observe the formation of three Cl layers, two just described and the third one found near the negatively charged surface. As discussed earlier, for this surface charge density our results show a dramatic increase in the concentration of the Na+ ions within the H = 1.2 nm pore and the consequent formation of a very dense adsorbed Na+ layer at contact with the negatively charged graphene surface. The third peak of Cl ions is observed near this dense layer of Na+ ions. The fact that these two layers are found very close to each other suggests the possibility that ionion correlations become dominant within the H = 1.2 nm pore at the conditions considered. To explore this possibility, we report in Figure 9 one representative simulation snapshot for Cl and Na+ ions adsorbed within the H = 1.2 nm pore charged with surface charge density of 40 μC/cm2. Water molecules are not shown for clarity. All ions inside the pore are shown. The Na+ ions, shown as green spheres, form a dense layer at contact with the negatively charged graphene surface. The Cl ions are shown as spheres of three colors. Those Cl ions found at contact with the positively charged surface are shown in yellow, those in the second layer in blue, and those in the third layer in red. Visual inspection of both side and top view of the simulation snapshot (left and right panels of Figure 9, respectively) reveals a strong ionion correlation between the Na+ ions near the negatively charged surface and the third layer of Cl ions. These correlations are most likely responsible for the enhanced partition coefficient for NaCl ions inside the H = 1.2 nm pore at a surface charge density of 40 μC/cm2. Because our simulations have explored the effects of a surface charge density of 40 μC/cm2
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Figure 9. Representative simulation snapshot for H = 1.2 nm pore at surface charge density of 40 μC/cm2. The graphene surfaces below and above the pore volume are charged positively and negatively, respectively. Panels a and b provide side and top views, respectively. Only electrolytes within the pore volume are shown for clarity. Gray spheres represent carbon atoms, and green spheres represent sodium ions. Chloride ions are shown in yellow, blue, and red depending on their position within the first, second, and third layer identified by the density profiles of Figure 8, middle panel.
even for the H = 1.6 nm pore, large enough for structures such as those observed in Figure 9 to form, the natural question is why the partition coefficient was found to be smaller for the wider pore at equal surface charge density. It appears that, within the configuration considered here (one negatively charged pore surface facing a positively charged surface across the pore volume), the H = 1.2 nm pore width enhances the concentration of confined NaCl electrolytes because it allows easy penetration of the ions without significantly altering their hydration shells, it promotes ion adsorption on the charged surfaces upon disruption of the hydration shell, and in addition it promotes stabilization of the confined electrolytes via strong ionion correlations. Within the H = 0.9 nm pore there is no strong evidence of layering for Cl ions when the surface charge density is 20 μC/cm2 because of the few ions that enter the pore. As the surface charge density increases to 30 μC/cm2, our results provide evidence for a first adsorbed layer, although not very dense. As the surface charge density increases further, the ionic concentration within the pore is ∼4 times that in the bulk, leading to pronounced layering for confined Cl ions, described in Figure 4. Our results suggest that although the H = 0.9 nm pores are small enough to force both Na+ and Cl ions to lose their hydration shells as they enter the pores, they are too small to promote enhanced concentrations for the confined electrolytes via ionion correlations.
4. CONCLUSIONS In summary, we have reported the results of a number of equilibrium molecular dynamics simulations conducted to study the distribution of NaCl electrolytes between bulk aqueous systems and slit-shaped carbon pores of different widths and different surface charge densities. The pore widths considered are 0.9, 1.2, and 1.6 nm. The applied surface charge density ranges from 0 (neutral pores) to 40 μC/cm2. These simulations are conducted to better understand the competing tendency of the electrolytes to be hydrated by water molecules (which is not possible within subnanometer pores) and to be adsorbed near oppositely charged surfaces. It was found that ionion correlations are important for understanding the distribution of electrolytes within charged carbon-based pores. In all pores considered the concentration of ions is very low when the surface charge density is zero (partition coefficient 13794
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The Journal of Physical Chemistry C generally less than unity). As the surface charge density increases, the amount of electrolytes that preferentially distribute within the pores increases. While this effect is not very strong on the H = 1.6 nm pores, for which the partition coefficient is never much larger than 2, dramatic increases in the ionic concentration within the H = 1.2 and the H = 0.9 nm pores with comparison to the bulk are found when the surface charge density is of ∼40 μC/cm2. At this surface charge density the ionic concentration within the H = 1.2 nm pore can be ∼10 times larger than that in the bulk. Density profiles for oxygen and hydrogen atoms of water, as well as those for Cl and Na+ ions within the pores at all conditions considered are used to elucidate surfaceion, ion ion, and ionwater correlations. At the largest surface charge densities considered, because of the large ionic density within the pores, we find strong evidence of ionion correlations. Overall, our results, despite the approximations necessarily made to permit the massive simulations performed (polarization as well as image charge effects were neglected), appear to be in qualitative agreement with a number of literature reports, both from simulation and from experiment, and suggest that to design optimum electrodes for electric double layer capacitors one needs to carefully consider the properties of the hydrated and nonhydrated ions, and their tendency to associate because of electrostatic effects. For aqueous NaCl electrolytes our results suggest that, under the capacitor configuration considered in our simulations, best performance is attained when the pores are neither too narrow nor too wide. To increase the ion concentration within the charged pores, it appears important to minimize the energy penalty experienced by the ions as they enter the charged pores (it is desirable to only mildly perturb the ions hydration shell) as well as to maximize favorable ionion correlations by carefully controlling the pore width. The width of the carbon-slit pores necessary to attain enhanced partition coefficients most likely depends on the composition of the aqueous electrolyte and, in particular, on the size of the ions employed.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
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’ ACKNOWLEDGMENT This work was supported, in part, by the US Department of Energy, under Contract Number DE-FG02-09ER46618. Generous allocations of computing time were provided by the Oklahoma Supercomputer Center for Education and Research (OSCER) and by the National Energy Resources Supercomputer Center (NERSC). The authors wish to thank Dr. Dimitrios Argyris for helpful discussions. ’ REFERENCES (1) Conway, B. E. Electrochemical supercapacitors: scientific fundamentals and technological applications; Kluwer Academic/Plenum Publishers: New York, 1999. (2) Zhang, L. L.; Zhao, X. S. Chem. Soc. Rev. 2009, 38, 2520. (3) Winter, M; Brodd, R. J. Chem. Rev. 2004, 104, 4245. (4) Simon, P.; Gogotsi, Y. Nat. Mater. 2008, 7, 845. (5) Liang, M.; Luo, B.; Zhi Int. J. Energy Res. 2009, 33, 1161. (6) Stoller, M. D.; Park, S.; Zhu, Y.; An, J.; Ruoff, R. S. Nano Lett. 2008, 8, 3498. (7) Chmiola, J.; Largeot, C.; Taberna, P. L.; Simon, P.; Gogotsi, Y. Angew. Chem. 2008, 120, 3440. 13795
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