Water Assistance in Ion Transfer during Charge and Discharge Cycles

Article pubs.acs.org/JPCC

Water Assistance in Ion Transfer during Charge and Discharge Cycles Tomonori Ohba* Graduate School of Science, Chiba University, 1-33 Yayoi, Inage, Chiba 263-8522, Japan S Supporting Information *

ABSTRACT: Knowledge of the dynamic properties of electrolyte solutions during charge and discharge cycles is crucial for understanding and developing electric energy devices. Molecular dynamics simulations of aqueous NaCl solution in nanopores between charged graphene layers were performed to assess the dynamical mechanism of ion transfer. Ions moved to the oppositely charged graphene layer according to the strength of their partial charges. The ion hydration numbers increased during ion transfer, suggesting quick rearrangement of water molecules around the ions to form a hydration shell. The extent of hydrogen bonding also increased during ion transfer. Water molecules participating in ion transfer hydrated the ion and simultaneously maintained hydrogen bonding, supporting a quick ion transfer mechanism during charge and discharge cycles.

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interactions.22,23 High capacitance was observed with oscillatory capacitance variation when the ion size was close to the nanopore size.24−27 Capacitance also strongly depended on surface topography.28 Yang et al. proposed that chemically converted graphene layers have the advantages of being mechanically strong, highly conductive, and stable electrodes and thus could be used as novel high-capacitance electrodes.29,30 Significant desolvation was imposed in extremely narrow nanopores smaller than the solvated ion size, providing an anomalous increase in capacitance.26,31,32 In such narrow nanopores, the solvation structure was more ordered than that in wider nanopores.33,34 Levi et al. showed the direct evaluation of solvation numbers during cyclic voltammetry of electrolytes confined in carbon nanopores using a quartz crystal microbalance, and significant desolvation was seen.35 The desolvation in carbon nanopores was investigated using Monte Carlo and molecular dynamics (MD) simulations.32,34,36 We observed an enhancement in hydration shell formation in carbon nanopores despite the dehydration.37,38 On the other hand, hydration structure was retained in the LiCl aqueous solution in slit nanopores of 0.9−1.5 nm.39 The dynamics of ions in ionic liquids and electrolytes became slower with decreasing nanopore size.40,41 Kalluri proposed that nanopores composed of charged graphene layers concentrated oppositely charged ions.42,43 The structure of electrolyte solutions at a charged surface can be assumed based on Helmholtz, Gouy−Chapman, Gouy− Chapman−Stern, and Debye−Hückel models. A molecularlevel structural understanding of electrolyte solution behavior during charge and discharge cycles is needed to optimize

INTRODUCTION The development of rechargeable batteries, electrical doublelayer capacitors, and fuel cells is in particularly high demand because of the environmental performance and portability of these devices.1,2 To achieve these demands, it is crucial that batteries with high power density and high energy density are fabricated. Nanoporous carbons have received attention for use as electrode materials in electrochemical capacitors.3−9 Electrical double-layer capacitors have the advantage of high durability and rapid charge and discharge cycles when used in rechargeable batteries.10 The advantage is caused by ion transfer between two electrodes without a chemical reaction. Smooth ion transfer is necessary to obtain high performance in various batteries. Thus, understanding the structural and dynamic properties of electrolyte solutions is essential for future development of electric energy storage devices. The structural properties of electrolyte solutions have been investigated using various techniques, which reveal, for instance, hydration structure, coordination number, hydrogen bonding, and solvation energies.11−17 Ohtaki and Radnai reviewed the structure and dynamics of hydrated ions.18 Various properties of electrolyte solutions have been clarified in these studies. However, the behavior of electrolyte solutions confined in carbon nanospaces is much more complex than in the bulk phase, although a mechanistic understanding is needed for battery development. Carbon nanopores strongly influence the capacitance; subnanometer pores generated high-capacitance densities, as discussed by Chmiola et al.8,19 Comprehensive reviews on the anomalous properties of capacitors have been undertaken by Simon and Gogotsi.9,20 On the other hand, Centeno et al. showed that regular capacitance patterns were observed in 0.7−15 nm nanopores.21 Jiang et al. and Xing et al. proposed that the capacitance enhancement observed in subnanometer pores by density functional theory and molecular simulation was caused by a change in the ion−ion © 2015 American Chemical Society

Received: March 18, 2015 Revised: June 16, 2015 Published: June 25, 2015 15185

DOI: 10.1021/acs.jpcc.5b02631 J. Phys. Chem. C 2015, 119, 15185−15194

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The Journal of Physical Chemistry C battery efficiency. Recent studies using molecular simulation revealed the molecular structure of electrolytes in charged nanopores and significantly contributed to our understanding of molecular-level structures. Ions in less-charged nanopores moved more slowly than in bulk electrolyte solution.44 Smaller ions were more slowly inserted in the charged nanopores than larger ions because of a barrier for partitioning the ions into the nanopores.45 This was a result of larger ions weakly interacting with water such that hydrogen bonding between the water molecules surrounding the ion was the dominant interaction.46 However, ion hydration decreased the energy barrier for ion transport through hydrophobic nanopores and thus promoted ion penetration.47 Kalluri showed the structure of NaCl solutions on charged carbon surfaces and demonstrated strong ion−ion correlation near the surfaces.42 Despite these efforts, a full understanding of ion dynamics during charge and discharge cycles is still lacking. Graphene layers as electrodes have been attracting attention because of their novelty and high capacitance ability.29,30 In this study, I employ MD simulations of NaCl aqueous solutions on charged graphene layers to assess the dynamic properties of Na+ and Cl− ions near/on the interfaces of those graphene layers during charge and discharge cycles. I present the dynamic structure changes of ions and water during charge and discharge cycles and discuss the mechanism of ion transport and the roles of water.

Figure 1. (a) Partial charges of the graphene-layer carbon atoms at z = 1.0 nm. Carbon atoms at the opposite graphene layer have the opposite partial charge. (b) Average position of ions in the nanopore between the graphene layers during charge and discharge cycles by adding partial charges of ±0.02 (top), ±0.03 (middle), and ±0.04 e (bottom) on the carbon atoms.

of −0.02, −0.03, or −0.04 e on carbon atoms. During 40−60 ps, the graphene layers at z = +1.0 and −1.0 nm had the negative and positive partial charges, respectively. The partial charges were abruptly exchanged every 20 ps in this manner. These three charged graphene-layer models were used to evaluate the dynamic properties of ions and are referred to as weakly, intermediately, and strongly charged graphene layers according to the strength of partial charge. The partial charges were assumed to change suddenly every 20 ps during charge and discharge cycles. The partial charges were also changed every 40 and 100 ps for comparison. The intermolecular interactions used in the MD simulation were the TIP5P model for water and a combination of Lennard-Jones and simple point charge potentials.48,49 The potential parameters are as follows: εNa/kB = 43.0 K, σNa = 0.273 nm, qNa/e = +1.0 C; εCl/kB = 20.2 K, σCl = 0.486 nm, qCl/e = −1.0 C; and εH2O/kB = 80.5 K, σH2O = 0.312 nm, qH2O/e = ± 0.241 C. Simulations using the above simple point charge model reproduced experimental results well. Thus, the validity of the model was confirmed for instance by comparison with a canonical ensemble Monte Carlo (CEMC) simulation and previous reports of bulk electrolyte solutions.18,46,50,51 Although the different parameters produced somewhat different physical properties, the above potential parameters also described experimental properties such as structures well. Furthermore, our preceding studies indicated that the structures of electrolyte and water in confined carbon nanopores using the CEMC simulations agreed well with the experimental structures,38,52 although the comparison of dynamic properties has been inadequate. In this study, a simple point charge model was adopted to evaluate dynamic properties of electrolytes. The simple point charge model assumes the fixed partial charges, and thus, the nuclei and electrons were on the atomic center. The nonpolarizable simple point charge model is somewhat inadequate to reproduce experimental observations in a large molecular system. For instance, the polarizability of large halide anions at the air/water interface, which was similar to that in the gas phase, controlled the detailed behaviors.53−56 Despite its accuracy, the Cl− ion polarizability was neglected in this study because ion polarizability is significantly reduced in the condensed phase57 and

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METHODS MD simulations of an aqueous NaCl solution sandwiched between graphene layers were performed using a newly developed program. Two graphene layers were aligned vertically along the z-axis of the 2.951 × 2.982 × 100.0 nm3 unit cell and were located 2.0 nm away from each other, that is, at z = ±1.0 nm. Each graphene layer was composed of 936 carbon atoms. A variety of graphene-layer capacitance effects were also examined using models with different distances of 1, 2, 3, and 5 nm between graphene layers. Carbon atom partial charges were set at ±0.02, ±0.03, and ±0.04 e, as mentioned later in detail. Molecular numbers of Na+, Cl−, and water molecules were set at 5, 5, and 290 for the 1 nm distance; 10, 10, and 530 for the 2 nm distance; 16, 16, and 868 for the 3 nm distance; and 26, 26, and 1448 for the 5 nm distance, respectively, to correspond to a solution concentration and density of 0.9 mol L−1 and 1.0 g mL−1 (see also Table S1, Supporting Information). MD simulation of bulk electrolyte solution in the unit cell of 3.0 × 3.0 × 3.0 nm3 was also performed to assess the hydration number. The molecular numbers of Na+, Cl−, and water molecules were 16, 16, and 888, respectively. The MD simulation used the leapfrog Verlet integration algorithm in the NVT ensemble with coupling to a thermal bath held at approximately 300 K. The simulation was allowed to proceed for 120 ps using an integration time step of 0.5 fs. The molecular properties were obtained from the accumulation of three calculation cycles using three different initial molecular positions. The charged graphene model was established by application of a positive partial charge on a carbon atom of a graphene layer and a negative partial charge on that of the opposite graphene layer. Charge and discharge cycles were simulated by exchange of partial charges every 20 ps, as shown in Figure 1a. Both graphene layers had neutral charges up to 20 ps. During 20−40 ps, the graphene layer at z = +1.0 nm had the positive partial charges of +0.02, +0.03, or +0.04 e on carbon atoms, while the graphene layer at z = −1.0 nm had the negative partial charges 15186


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The Journal of Physical Chemistry C

Figure 2. (a) Partial charges of the graphene layer carbon atoms at z = 1.0 nm. Charge and discharge cycles were exchanged every 20 (top), 40 (middle), and 100 ps (bottom). (b) Average positions of ions in the nanopore between the graphene layers during charge and discharge cycles by adding partial charges of ±0.02 (left), ±0.03 (center), and ±0.04 e (right) on the carbon atoms. (c) Partial charge of the graphene layer carbon atoms at z = 1.0 nm in the long time scale simulation. (d) Average position of ions in the nanopore in the long time scale.

However, in the strongly charged model, ions quickly moved on the oppositely charged graphene layer and were able to make contact with the oppositely charged graphene layers. Thus, during the 20 ps charge and discharge cycles, the ions were unlikely to achieve equilibrium in the weakly and intermediately charged models, whereas the ions in the strongly charged model were almost in quasi-equilibrium. However, even in the weakly charged model, ion pairs were more separated by repetition of the charge and discharge cycles. The average positions in quasi-equilibrium were obtained from the relatively long time scale MD simulations at the positive charges for 1000 ps, as shown in Figure 2c and d. Here the average positions were obtained using only one initial position and, thus, could not be directly compared with those in Figure 2b. The longer charging process after 20 ps (the startup of the charging processes) suggested that ions quickly moved between 20 and 40 ps, and the average positions were rarely changed above 40 ps in the intermediately and strongly charged models. On the other hand, ions in the weakly charged model were fluctuated by formation of ion pairs. Thus, the 20 ps charge and discharge cycles were herein adopted to assess detailed dynamic properties of ions near the interface between electrolyte and graphene layers. The dynamic ion transport properties in Figure 2 and hydration number variations in Figure S4 (Supporting Information) were slightly influenced by differences in charge and discharge duration. The distance between electrodes also mainly influenced only the electric field. Thus, ion transport near electrodes could be assessed using these

partial charges dominantly control ion properties in this study. The potential well depth and collision diameter of a carbon atom were 30.14 K and 0.3416 nm, respectively.58,59 Periodic boundary conditions were applied for all three dimensions. Lorentz−Berthelot mixing rules were adopted for the LennardJones interaction between different molecular species, and the long-range Coulomb interactions were calculated using a threedimensional Ewald summation method.60,61 Here the longrange interactions in the z-direction were almost neglected owing to the large unit z-length. The MD simulations in 1000 ps were performed to obtain quasi-equilibrium positions at positive partial charges of +0.02, +0.03, and +0.04 e.

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RESULTS AND DISCUSSION Figure 1b shows the average positions of Na+ and Cl− ions in the nanopore between graphene layers, obtained from the snapshots in Figures S1−S3 (Supporting Information). Figure 2a and b also shows the partial charges of the graphene-layer carbon atoms at z = 1.0 nm and the average positions of Na+ and Cl− ions during the charge and discharge cycles every 20, 40, and 100 ps. The average positions were obtained from the averaged values of ions in those simulations using three different initial positions. Here the partial charges during charge and discharge cycles in Figures 1b and 2b correspond to those in Figures 1a and 2a, respectively. The charge and discharge cycles for longer periods separated the ions well in the weakly and intermediately charged models, as shown in Figure 2b. 15187


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Figure 3. Molecular distributions of Na+ (a, d, and g), Cl− ions (b, e, and h), and water (c, f, and (i) in the nanopores between weakly charged (V = ±0.02 e) (a−c), intermediately charged (V = ±0.03 e) (d−f), and strongly charged (V = ±0.04 e) (g−i) graphene layers.

moved to the oppositely charged graphene layers by 20 ps charging, whereas water was rarely influenced by the charge and discharge cycles. The molecular distributions within the graphene layers clearly indicated that some ion pairs were retained in the weakly and, even in the intermediately, charged models. Some Cl− ions especially remained on the same side of the same-charged graphene layer by forming ion pairs. This was a reason that Cl− ions were slowly moved to the oppositely charged graphene layer rather than Na+ ions. Ions were generally positioned on the oppositely charged graphene layer, and associated counterions were on the second-layer sites. In the strongly charged model, most ion pairs were separated, and ions were in contact with the oppositely charged graphene layers. The ion arrangements on the oppositely charged graphene layers were also observed in the equilibrium MD simulation.42 The average distances between Na+ and Cl− ions increased with increasing partial charge on the graphene. Both ions move gradually away from each other over time during charge and discharge cycles between 20 and 100 ps. Na+ ions appear to move faster than Cl− ions. Furthermore, Na+ ions were quickly attracted to and moved to similar positions of the Cl− ion after removing the partial charges. This is a result of the smaller molecular size of a Na+ ion than that of a Cl− ion. The quick ion transfer of smaller ions proceeds through an apparently different mechanism than ion insertion into a nanopore.45 The molecular distributions of ions in the positively charged processes at 40 and 80 ps, negatively charged processes at 60 and 100 ps, and charge release processes at 20 and 120 ps were different from each other, supporting the notion that ion transfer is a kinetically controlled process. Water forms six layers in the nanopores

simulation conditions, although actual charge and discharge cycles might have several billion times longer time scales and several million times wider electrodes than those in this study. Knowledge of ion transport on graphene layers is important for a complete understanding of the electrolyte mechanism because the ion potentials near the interface between electrolyte and graphene layers are very different from those in bulk, as mentioned later. In the uncharged state, before 20 ps, both ions have similar average positions. Some ions formed ion pairs near the center of those nanopores at that time. The oppositely charged ion species then became separated by donation of the partial charges during 20−40 ps. The average positions of Na+ and Cl− ions in a quasi-equilibrium state for the strongly charged graphene layers were at z = ±0.77 and ±0.69 nm, respectively, because the potential minimum positions of Na+ and Cl− ions were 0.78 and 0.69 nm, respectively, as described later (Figure 6b). The contact distances of Na+−C and Cl−−C are 0.3073 and 0.4138 nm, respectively, evaluated from Lorentz−Berthelot mixing rules, as mentioned above. This indicates that the contact positions of Na+ and Cl− ions with the graphene layers are roughly at z = ±0.69 and ±0.59 nm, respectively. Thus, the distances between the ions and graphene layers were at 0.08 and 0.10 nm shorter contact distances, suggesting a competition between exchange repulsion and electrostatic attraction. In the weakly charged model (V = ±0.02 e), the average ion positions remained near the center of the nanopore, and some ions were coordinated with the oppositely charged ions during charging, as shown in Figure S1 (Supporting Information). Figure 3a−i shows the molecular distributions during the charge and discharge cycles. Na+ and Cl− ions were 15188


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charge release process at 100 ps, the rate increases were again moderate. However, the transport rates still depended on the charge strength, or in other words, ions moved faster in the strongly charged model. Ions were strongly bound on the oppositely charged graphene layer in the strongly charged model, and thus the same ion species were concentrated on the surface. These same ion species were then quickly repelled mainly by coulomb repulsion when the polarity of the graphene layer was reversed. To evaluate the molecular transport mechanism during the charge and discharge cycles, molecular structures were evaluated from the snapshots in Figures S1−S3 (Supporting Information). The radial distribution functions show that Na+ and Cl− ions strongly interact with lone pairs and hydrogen atoms of water, respectively, over the entire time range (Figure S5, Supporting Information). The radial distribution functions suggested that no significant difference of those structures was observed in a nanopore and bulk electrolyte solution. Density functional theory of solvation structure in bulk electrolyte solution indicated that the hydration numbers of Na+ and Cl− ions were 4.9−5.5 and 6.0−6.5, respectively, determined by integration of the Na+ ion−H2O first peak below 0.32 nm and the Cl− ion−H2O first peak below 0.38 nm.62 The hydration numbers of Na+ and Cl− ions in bulk electrolyte solution in this simulation using the above definitions were 3.0 and 4.8, respectively. The smaller hydration numbers in a concentration of 0.9 mol L−1 than those in the density functional theory in dilute electrolyte solution are a result of ion pairs. Here the coordination numbers between Na+ and Cl− ions were 1.4. Thus, including the coordination numbers between Na+ and Cl− ions, those simulations agreed with each other. The hydration numbers obtained from the above definition could be compared with each other (Figure 5a−c), although the hydration numbers have some uncertainty. Coordination numbers between different ion species were obtained from the distance between these ions, using a cutoff distance of 0.426 nm for Na+−Cl−. The coordination numbers for water

between the graphene layers without regard to partial charges, and the distributions were rarely altered during charge and discharge cycles. The monolayer positions of water on the graphene layers were at z = ±0.70 nm. Thus, Na+ ions were closer to the graphene layers than water, whereas the Cl− ion positions were similar to those of water. Thus, both ions on the graphene layers should be partially dehydrated, as discussed below. The mobility of both ions and water was tracked from the average transport rates of ions and water in three dimensions, as shown in Figure 4, to evaluate their dynamical properties

Figure 4. Molecular mobility of Na+ and Cl− ions and water during charge and discharge cycles, calculated from the average velocities. The strength of the partial charges of carbon atoms were ±0.02 (a), ±0.03 (b), and ±0.04 e (c), as shown in Figure 1a.

during charge and discharge cycles. Here the average transport rates were calculated from the MD simulations using three different initial positions. Average velocities of Na+ and Cl− ions were approximately 700 and 400 m s−1 at the steady state, respectively. The rates of Na+ and Cl− ions were faster and slower than water, respectively, as the water velocity was nearly constant at around 500 m s−1. The rates of both ions significantly increased immediately after the partial charges were donated at 20 ps and reversed at 40, 60, and 80 ps, as a result of both ions moving to the oppositely charged graphene layer. The rates at 20 ps were seen to only slightly increase in the weakly charged graphene layers in Figure 4a. The rate increases at 20 ps were also moderate even in the intermediately and strongly charged graphene layers in Figure 4b and c. Conversely, intense rate increases were observed at the charge-reversal processes at 40, 60, and 80 ps; more than 1000 m s−1 for Na+ ions and 500 m s−1 for Cl− ions. The smaller Na+ ions move faster than the larger Cl− ions, although the partitioning effect of ions into nanopores from bulk electrolytes imposed slower transport of smaller ions.47 In the

Figure 5. Hydration numbers of Na+ and Cl− ions and coordination number between Na+ and Cl− (a−c). Numbers of hydrogen bonds of water in the nanopores and water surrounding Na+ and Cl− ions (d− f). The strengths of the partial charges of carbon atoms were ±0.02 (a, d), ±0.03 (b, e), and ±0.04 e (c, f), as shown in Figure 1a. 15189


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Figure 6. Potential profiles of Na+ (red curves) and Cl− ions (blue curves) for the strongly charged graphene layers (V = ±0.04 e). Here the graphene layers at positive and negative z positions have positive and negative partial charges of +0.04 e and −0.04 e, respectively. Graphene-layer distances were (a) 1.0, (b) 2.0, (c) 3.0, (d) 5.0 nm, (e) 10 nm, and (f) 100 nm.

surrounding Na+ and Cl− ions were 3−5 and 5−7, respectively. Hydration numbers of ions strongly depend on adjoining ions and contact with graphene layers. The average coordination numbers of water with Na+ and Cl− ions in the simulations were 3.0 and 5.3, respectively, before charging, that is, before 20 ps. The coordination number between Na+ and Cl− was nearly 2 before 20 ps, whereas ion pairs were decreased during the charge and discharge cycles (20−100 ps) and disappeared in the strongly charged model. Ion pairs were again formed in the charge release process after 100 ps. The water/ion coordination numbers were significantly increased to 4−5 for Na+ ions and to 6−7 for Cl− ions at the reverse-charge processes at 40, 60, and 80 ps. The coordination numbers between Na+ and Cl− were also slightly increased at those periods. The increases of the coordination number at the charge reversal are a result of intensive collision of ions with water, showing a direct proof of compelling transfer of ions. The average hydration numbers of Na+ and Cl− during the time scale of 120 ps were 3.4 and 5.4, respectively. Here the literature values of hydration numbers of Na+ and Cl− ions range from 4 to 8 and 5 to 8, respectively.18,32,50,51,63−65 The total coordination numbers of ions with water and counterions are shown in Figure S6 (Supporting Information). The coordination numbers of Na+ and Cl− ions before charging (below 20 ps) were 4.9 and 7.2, respectively. Those in the charging processes from 20 to 100 ps were approximately 4 and 6 for the intermediately and strongly charged processes, respectively, except for in the reverse-charged processes. On the other hand, the same coordination numbers were approximately 5 and 7 for the weakly charged process, respectively. The decoordination is due to strong ion adsorption to the oppositely charged graphene layers. The decrease of the coordination numbers with increasing charge density on graphene layers was also observed elsewhere.42 The

coordination numbers after charging (above 100 ps) were 4.7 and 6.8, respectively, indicating some persistence of the dehydrated structure. Thus, the hydration numbers of Na+ ions in this study were slightly smaller than the hydration numbers previously reported32 because of formation of ion pairs in the weakly charged model and contact with the graphene layers. When the graphene polarity was reversed, the hydration numbers increased suddenly, corresponding with the coordination numbers. The hydration numbers of Na+ and Cl− ions increased to as high as 5 and 7, respectively, during the charge-reversal processes for the intermediately and strongly charged processes. Therefore, water rearrangement was sufficiently faster than ion transfer because if water rearrangement was slower than ion transfer the hydration number would otherwise become smaller than its steady state value. Strong ion hydration could relate to smooth ion transfer, as mentioned in previous work.47 The extent of hydrogen bonding was assessed by defining hydrogen bonds between O and H atoms having intermolecular distances of less than 0.312 nm and having O− H−lone pair angles less than 140°, as shown in Figure 5d−f. The average number of hydrogen bonds for all the water molecules in the nanopores was 1.5. However, water molecules surrounding ions participated in only approximately 1.2 hydrogen bonds on average. This indicates that the extent of hydrogen bonding was significantly decreased for those water molecules involved in hydration shell formation.37,38 The hydrogen bonding numbers recovered to the overall average value at the charge-reversal processes. This indicated that hydration shell water molecules reformed their hydrogen bonding network just before release from the hydration shell. While the main focus of this study has been on graphene layers at the 2 nm distance, the dynamic properties of ions in 1, 3, and 5 nm nanopores are also briefly discussed. The potential profiles of Na+ and Cl− ions in Figure 6a−f show abrupt 15190


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Figure 7. Dependence of ion properties on distance between graphene layers with C partial charges of ±0.04 e. Average positions of Na+ (a) and Cl− ions (b) during the charge and discharge cycles in the nanopores between the graphene layers at distances of 1, 2, 3, and 5 nm. (c−f) Snapshots of electrolytes in the nanopores between graphene layers at 60 ps. Na+ and Cl− ions are depicted by green and yellow spheres, and water O and H atoms are depicted by blue and red spheres, respectively. (g−j) Molecular mobilities of ions and water.

nanopores, respectively, while those in the 1 nm nanopore were 4.9 and 8.9, respectively. An enhancement in hydration was also observed in 2 nm cylindrical nanopores, whereas dehydration was observed in cylindrical nanopores with diameters smaller than 1.4 nm.32,37 In the case of slit nanopores, dehydration was observed below the effective pore width of 0.7 nm, and extremely narrow pores repelled ions.33,39,66,67 Thus, the curvature effect is important for hydration and dehydration in narrow nanopores. On the other hand, those size dependences in the wider nanopores are a result of the strength of electric fields. For instance, the molecular mobility and hydration numbers for partial charges of ±0.04 e in the 5 nm nanopore were similar to those with partial charges of ±0.02 e in the 2 nm nanopores. Thus, the dynamic properties near interfaces on graphene layers were assessed here, although the distance between actual electrodes is many orders of magnitude larger than the distance between graphene layers in this study.

potential changes in nanopores narrower than 5 nm. The potential curves in the nanopores between 10 and 100 nm were only significantly changed near the interfaces of graphene layers, and the other, central regions showed only moderate changes. Thus, the electrolytes near/on the graphene layer interface are significant when observing the behaviors during charge and discharge cycles. Average ion positions shown in Figure 7a and b illustrate that ions slowly moved to the oppositely charged graphene layer in the wide nanopores because the electric field strength was weakened in the wider nanopores even with the same carbon atom partial charges. The snapshots in Figure 7c−f clearly indicate that some ion pairs remained intact, and ions moved slowly in the wider nanopores. In contrast, a higher mobility of both ions, as shown in Figure 7g−j, was observed for systems with narrower nanopores because of the strong electric fields, agreeing with the snapshots in Figure 7c−f. Thus, ions in the narrow nanopores quickly moved to the oppositely charged graphene layer, whereas in the wide nanopores ions gradually and continuously moved to the oppositely charged graphene layer. Figure 8a−d shows the hydration number changes of Na+ and Cl− ions during charge and discharge cycles in the nanopores of 1, 2, 3, and 5 nm widths. The average hydration numbers of Na+ and Cl− ions were approximately 3.5 and 2.5 in the 2, 3, and 5 nm

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CONCLUSIONS Dynamic structural changes of aqueous electrolyte solutions near/on the interfaces of graphene layers were evaluated from our MD simulations. Na+ and Cl− ions are quickly transferred to the stronger, oppositely charged graphene layers. Both ion 15191



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ACKNOWLEDGMENTS

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REFERENCES

This research was supported by the Japan Society for the Promotion of Science KAKENHI Grant Number 26706001 and 15K12261, a Research Fellowship from the Futaba Electronics Memorial Foundation, and Japan Gas Association.

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Figure 8. Hydration numbers of Na+ and Cl− ions and coordination number between Na+ and Cl−. Graphene-layer distances were (a) 1.0, (b) 2.0, (c) 3.0, and (d) 5.0 nm.

hydration numbers and hydrogen bonding extent of water surrounding the ions increased during ion transfer. That is, water around the ions was strongly hydrated and formed hydrogen bonds between water molecules during ion transfer. Thus, a smooth structural transformation of water molecules around ions facilitates quick ion transfer in the nanopore between charged graphene layers. Further studies using other ion species and porous electrodes are necessary to assess ion transfer mechanisms and size dependences.

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ASSOCIATED CONTENT

S Supporting Information *

Molecular numbers and densities in the calculation system, snapshots during the MD simulation, and hydration and coordination number on cycle duration, and radial distribution functions. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/ acs.jpcc.5b02631.

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AUTHOR INFORMATION

Corresponding Author

*Phone: 81-43-290-2779. E-mail: [email protected]. Notes

The authors declare no competing financial interest. 15192


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