On the Atomistic Nature of Capacitance Enhancement Generated by

Dec 15, 2012 - The latter aspect is not only difficult to measure, but as has been demonstrated by recent theoretical calculations(10) can be crucial ...
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On the Atomistic Nature of Capacitance Enhancement Generated by Ionic Liquid Electrolyte Confined in Subnanometer Pores Lidan Xing,†,‡ Jenel Vatamanu,*,† Oleg Borodin,§ and Dmitry Bedrov*,† †

Department of Materials Science and Engineering, University of Utah, 122 South Central Campus Drive, Salt Lake City, Utah 84112, United States ‡ School of Chemistry and Environment, South China Normal University, Guangzhou 510006, China § Electrochemistry Branch, U.S. Army Research Laboratory, 2800 Powder Mill Road, Adelphi, Maryland 20783, United States S Supporting Information *

ABSTRACT: The capacitance enhancement experimentally observed in electrodes with complex morphology of random subnanometer wide pores is an intriguing phenomena, yet the mechanisms for such enhancement are not completely understood. Our atomistic molecular dynamics simulations demonstrate that in subnanometer slit-geometry nanopores, a factor of 2 capacitance enhancement (compared to a flat electrode) is possible for the 1-ethyl-3-methylimidazolium (EMIM)−bis(trifluoro-methylsulfonyl)imide (TFSI) ionic liquid electrolyte. This capacitance enhancement is a result of a fast charge separation inside the nanopore due to abrupt expulsion of co-ions from the pore while maintaining an elevated counterion density due to strong screening of electrostatic repulsive interactions by the conductive pore. Importantly, we find that the capacitance enhancement can be very asymmetric. For the negatively charged 7.5 Å wide pore, the integral capacitance is 100% larger than on a flat surface; however, on the positive electrode, almost no enhancement is observed. Detailed analysis of structure and composition of electrolyte inside nanopores shows that the capacitance enhancement and the shape of differential capacitance strongly depend on the details of the ion chemical structure and a delicate balance of ion−surface and ion−ion interactions. SECTION: Energy Conversion and Storage; Energy and Charge Transport

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the electrode nanopores has been suggested. On the other hand, experiments of Centeno et al.6 with a variety of nanoporous carbon-based electrodes and [N(C2H5)4][BF4]/ ACN electrolyte showed no variation of capacitance as a function of pore diameter. Rather small changes of capacitance with pore width were also reported in refs 7−9. However, it is very hard to compare different studies due to large differences in materials structure, binder content, crystallinity, and, more importantly, the control of PSD. The latter aspect is not only difficult to measure, but as has been demonstrated by recent theoretical calculations10 can be crucial for the extent of capacitance enhancement in nanopores, i.e., a wide PSD can significantly reduce or eliminate the capacitance enhancement. Taking this into account as well as that different electrodes (even if made out of carbon) can also differ in electronic conductivity, surface group content, surface group species, defect density, and so on, the discrepancy between experimental results discussed above are not surprising. This also points out that a more systematic and controlled investigation of electrolyte properties and mechanisms of capacitance enhancement in nanoporous electrodes is needed.

ubstantial efforts are dedicated to improve the energy density in electric double layer (EDL) capacitors (or supercapacitors) through (i) design and synthesis of roomtemperature ionic liquids (RTIL) with high electrochemical stability and extended liquid range at low temperatures, (ii) preparation of high specific surface area porous electrodes, and (iii) optimization and control of width/geometry of the nanopores. The relationships between the pore diameter, the applied voltage and the integral capacitance (IC) have been a topic of extensive discussion and research since a substantial increase in capacitance was observed for [N(C2H5)4][BF4]/ acetonitrile (ACN) electrolyte on carbide-derived carbon (CDC) nanoporous electrodes with subnanometer wide pores.1−3 These studies showed a sharp peak in capacitance for pore width of 7−8 Å. The CDC has a very narrow pore size distribution (PSD) and, thus, allows a much more comprehensive understanding of pore size versus capacitance correlations compared to, e.g., activated carbon. Largelot et al.4 also showed a 90−100% increase in capacitance for 1-ethyl3-methylimidazolium (EMIM)-bis(trifluoro-methylsulfonyl)imide (TFSI) RTIL inserted in carbon-based nanoporous electrodes with nanopore dimensions matching ions size, while Barbieri et al.5 observed almost doubling of the capacitance by comparing different activated carbons with various pore characteristics. Therefore, a potentially new route to increase the energy density of EDL capacitors by tuning the widths of © 2012 American Chemical Society

Received: November 3, 2012 Accepted: December 15, 2012 Published: December 15, 2012 132

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from charges on the nanopore walls. They also showed that at reasonably high potentials and pore sizes comparable to ions diameter an abrupt change in ion composition can occur with co-ions leaving the nanopore while counterions continue to increase their packing due to screened electrostatic interactions. Utilizing MC simulations of a simple monatomic electrolyte and explicitly scaling electrostatic interactions in nanopores according to their model, Kondrat et al.21 showed that the capacitance could indeed increase with reduction of pore size. In that work, authors concluded that in order to observe a peak in the differential capacitance (DC), the charge accumulation in the nanopore due to co-ion/counterion swapping has to be accompanied by an increase of the total ion density in the pore. Interestingly, in these simulations, no abrupt demixing of coins and counterions was observed as a function of electrode potential. However, whether the assumptions of superscreening model as well as the predicted trends between DC and ion packing/composition still hold for realistic ions remained unclear. In this work, utilizing atomistic MD simulations we bring new insight into the mechanism(s) of capacitance enhancement for realistic RTIL in contact with nanoporous electrodes through systematic investigation of the DC of EDL. In light of the Kornyshev model,20 the conductive nature of the electrode surface is essential for screening out the repulsion between counterions and allowing their dense packing inside the nanopore. Therefore, in our simulations, electrode surfaces were represented as a conductor capable to adjust its surface charge (i.e., polarize) in response to EDL restructuring. This approach is physically more realistic compared to simulations that employed a fixed and uniform charge distribution on the pore surface.22−24 The electrode polarizability was modeled using flexible Gaussian-distributed25,26 electrode charges that were calculated iteratively subject to the condition of electrostatic energy minimization at the imposed potential on electrodes.27−30 This approach insures that the same potential (rather than the charge) is generated on all atoms representing the electrode. The [EMIM][TFSI] RTIL was used as electrolyte and modeled using a combined explicit atom(EA)/united-atom(UA) nonpolarizable force field reported previously.31 Electrolytes containing imidazolium-based salts have been extensively investigated both experimentally4,32 and from simulations (e.g., refs 33−35). Details and specific parameters of the simulation protocol are provided in the Supporting Information (SI). Here we only briefly mention the most important aspects. All simulations were conducted at 393 K to allow faster relaxation/ equilibration of electrolyte structure such that it is accessible to atomistic MD simulation time scales. Note that both experiment36 and simulations of similar RTIL on flat electrodes37−39 showed that, in the temperature range between 20 and 100 °C, the dependence of DC as a function of electrode potential does not change qualitatively, and its magnitude is only slightly effected. A similar trend in DC was probed with more recent analytical theories.40,41 Also, experimental measurements of Largeot et al.4 for [EMIM][TFSI] RTIL on CDC carbon electrodes, which reported the capacitance enhancement in subnanometer wide pores, were conducted at elevated (333 K) temperature. Taking into account that due to the dominance of electrostatic interactions between ions, the liquid structure of the RTIL does not change significantly in this temperature range, we expect that the phenomena and mechanisms

A number of molecular dynamics (MD) and Monte Carlo (MC) simulations have attempted to provide insight into this topic and produced several intriguing and sometimes controversial results as well. For electrolyte inserted between various nanotubes in the carbon nanotube forest, Yang et al.11 showed only a small (about 11%) increase in capacitance, from 5.5 to 6.1 μF/cm2, with decreasing spacing between nanotubes. Kalugin et al.12 showed a nontrivial coupling between the structure and dynamics of electrolyte confined inside nanotubes and the correlation of nanopore size with the supercapacitor performance. Simulations of Wu et al.13 and Feng et al.14 for slit-geometry nanopores showed only a 40% increase of the capacitance for subnanometer wide pores compared to larger pores (or flat electrodes) and suggested a complex (i.e., nonmonotonic) dependence of the capacitance on pore width. Using classical DFT method Jiang et al.15 found that the capacitance of electrolyte comprised of charged hard spheres has an oscillatory dependence as a function of pore size with the maximum capacitance for pore size comparable to ion diameters. Recent classical DFT study of [N(C2H5)4][BF4]/ ACN electrolyte by the same authors, showed only a marginal (8 Å), the charge accumulation is almost linear as a function of electrode potential. However, for pore widths less than 8 Å, the rate of charge accumulation becomes asymmetric between the positive and negative electrodes. Specifically, while the increase of σ on the positive electrode remains almost linear, on the negative electrode abrupt changes around −0.25 V and −0.7 V are observed for the 7.2 Å and 7.5 Å wide pores, respectively. Figure 2b shows the dependence of the DC as a function of Uelectrode. On the flat graphite, the [EMIM][TFSI] shows little variation in the overall camel-shaped DC30 with the magnitude varying between 4.0 and 5.2 μF/cm2. In relatively wide pores, 11−15 Å, a more pronounced dependence of DC as a function of potential is observed (see the inset of Figure 2b) as compared to the flat electrode. The DC generated by the 11 Å pore is bell-shaped, while the DC generated by the 15 Å pore is U-shaped without showing signs of saturation even at ±1.5 V

obtained from our simulations at 393 K are very similar to those observed at lower temperatures. The number of ionic pairs representing electrolyte varied between 189 and 311 depending on the nanopore width (see Table 1 in the SI). Two explicit electrodes were used to confine the electrolyte as illustrated in Figure 1. The electrodes consisted of graphene walls with slit-geometry nanopores formed by parallel layers of graphene sheets separated at distances of 7.2, 7.5, 8, 11, and 15 Å and the depth of the slits of about 80 Å. The walls exposed to the bulk electrolyte were not charged; only the slit nanopores were subjected to the applied potential, therefore the generated capacitance was due to EDL restructuring in the nanopore. The separation between electrodes was ∼115 Å. Simulations with applied potential differences between electrodes (ΔU) ranging from 0 to 3 V have been conducted for each nanopore width. Utilizing trajectories obtained from simulations, the charge density profiles ρ(z), where z is the extended direction of our simulation cell (see Figure 1), were computed. These profiles were utilized to obtain the electrostatic potential profile ϕ(z) between electrodes using a numerical integration of the 1DPoisson equation, ∇z[ε0(∇zϕ(z))] = −ρ(z) . The electrode potential Uelectrode was obtained from the potential drop within the EDL (i.e., between electrode surface and bulk electrolyte) relative to the potential of zero charge (PZC), Uelectrode = ϕelectrode - ϕbulk − PZC. The PZC was defined as the potential 134

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For the flat surface and larger pores (11 and 15 Å), the IC on both electrodes is very similar and fluctuates between 5 and 5.5 μF/cm2, which is in a good agreement with our previous extensive simulations of various RTILs on flat graphite electrodes30,36,37 as well as with recent experiments that carefully separated the fast capacitive process of electrolyte ordering on the surface35 and reported DCs of around 6 μF/ cm2 (or bellow depending on potential) for several RTILs on flat surfaces and at elevated temperatures. Madden and coworkers have also reported similar values of capacitance42 on the flat surface from MD simulations using a coarse-grained model and a constant potential methodology. However, for the pores width below nanometer, a qualitatively different behavior of IC on positive and negative electrodes is observed that has not been discussed before. On the positive electrode, there is very little IC enhancement upon reduction of the pore width. The highest IC in the positive pore (∼6.2 μF/cm2 for the 7.2 Å pore) is only a modest increase (about 20%) compared to the flat surface (∼5.1 μF/cm2). A strikingly different behavior of IC versus pore width is seen on the negative electrode. Specifically, a significant IC enhancement for the 7.5 Å pore is observed, reaching a value of 10.1 μF/cm2 (or 133 F/g see SI for details of units conversion), which is almost a 100% increase compared to the value for the flat electrode. The observed relative enhancement on the negative electrode is comparable with enhancements reported in ref 4 for the same RTIL on CDC electrodes. Note that in comparison with this particular experimental data, the ICs (per unit surface area electrode) obtained from our simulations are systematically lower by about 30% for all pore widths and the flat surface. A head-to-head comparison of absolute values of IC from experiment and simulations is difficult, mainly because in experiments, electrodes have random pores and determination of the specific surface area is difficult. Furthermore, the inherent difficulties in determining the absolute capacitances even on flat surfaces have been discussed in the literature.43 Therefore, we believe that the best measure of capacitance enhancement is the ratio between the IC in the pores and that on the flat surfaces as determined by the same method. The observed asymmetry in the IC enhancement is intriguing. First, it is clearly undesirable because it diminishes the total IC of the capacitor, which can be determined from 1/ ICtotal = 1/IC++1/IC−. Hence, even when the negative electrode capacitance (IC−) doubles upon reduction of the pore width but the IC+ stays unchanged, the ICtotal will only increase by 1/3. Therefore, due to observed asymmetry, the capacitor ICtotal derived from our simulations would not show the same extent as in experiments. Nevertheless, to the best of our knowledge, this is the first modeling study that shows that factor of 2 capacitance enhancement on a single electrode can be achieved in principle. Note that previous simulations of this RTIL only showed an increase of 40% for the slit geometry nanopores on each electrode.14,18 Second, in agreement with experimental data of Largelot et al., Figure 3 also shows that the range of pore widths where the enhancement is observed is remarkably narrow, indicating that the polydispersity in the pore width of nanoporous electrodes used in experiments has to be very small to maximize this effect. The asymmetry in the capacitance between the positive and negative nanoporous electrodes is surprising and raises a fundamental question: Where it is coming from? If the screening of electrostatic repulsion between ions by the conductive walls plays an important role as suggested by the

and DC values being considerably larger than those on the flat graphite surface or in the 11 Å pore. Previous simulations14−16 have shown that the IC can have a complex oscillatory dependence on pore width. Therefore, the qualitative changes in DC shape (from a bell-shape to a U-shape) seen in Figure 2b for 11 and 15 Å pores are likely the primary sources for such oscillatory behavior of IC. As the pore width is reduced to 8 Å, a clear increase in DC is observed in the negative range of electrode potential. Reduction of the pore width to 7.5 and 7.2 Å shifts this feature closer to PZC, resulting in a well-defined peak in DC. For the 7.5 Å pore, we see a sharp increase of DC from ∼7 to almost 20 μF/cm2 at Uelectrode∼ −0.6 V, which corresponds to the abrupt changes in σ shown in Figure 2a. The observed peak in DC is relatively narrow, such that at −1 V DC drops back to ∼6 μF/cm2. Interestingly, the DCs obtained for 7.5 Å and 8 Å pores are very asymmetric with respect to electrode polarity: there is a significant capacitance enhancement on the negative electrode, but there is no increase on the positive electrode. Figure 2 indicates that for the 8 Å pore the maximum in DC has not been reached at −1.5 V and it is possible that further reduction of negative potential can result in even larger values of DC for this pore. Finally, for the 7.2 Å pore, the DC has an overall bellshaped dependence showing a DC enhancement in the potential range between −0.7 V to +0.5 V with a peak at about −0.25 V and a maximum value of 12 μF/cm2. Figure 3 shows the IC as a function of pore width for the potential difference between electrodes of ΔU = 3 V. Note that

Figure 3. The dependence of the IC as a function pore width for the negative and positive electrodes at the applied potential difference between electrodes ΔU = 3 V. Also shown are the corresponding values for the positive and negative electrodes (relative to bulk electrolyte).

in large pores and on flat electrodes the Uelectrode on the positive and negative electrodes are almost equal in absolute values (roughly ±0.5ΔU). However, for smaller pores, where details of chemical structure of EMIM and TFSI (charge distribution, molecular conformation and orientation in the pore) as well as ion composition (see discussion below) play an important role in polarization of electrode surface, the electrode potentials can be quite asymmetric for an imposed ΔU. For example, in the 7.5 Å nanopore, the applied potential difference of ΔU = 3 V results in −1 V and +2 V electrode potentials as indicated in Figure 3. 135

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Analysis of TFSI−TFSI interactions inside pores resulted in similar screening of electrostatic interactions as for EMIM ions, indicating that in the subnanometer pores, both, EMIM ions in the negative pore and TFSI ions in the positive pore would have similar short-ranged electrostatic repulsion between ions and therefore both can pack densely. Hence, the observed asymmetry in capacitance enhancement on negative and positive electrodes is not due to differences in the superscreening of TFSI−TFSI and EMIM−EMIM interactions inside the corresponding electrodes. However, we found that due to details of charge distribution within EMIM and TFSI ions, a TFSI anion confined in the narrow pore would have a noticeably stronger (compared to EMIM) electrostatic interaction with the charged pore walls. On the negative electrode, this interaction is repulsive promoting TFSI expulsion, while on the positive it is attractive. We also would like to point out that the ability of electrodes to polarize in response to electrolyte restructuring implemented in our simulations might play an important role in this regard. The instantaneous charge distribution on the nanopore surface can be quite broad and significantly deviate from the average value of charge per atom corresponding to a certain (fixed) electrode potential (see Figure 1 in the SI). In the narrow pores, these charge distributions can become bimodal and quite asymmetric, therefore locally generating environments less repulsive for coions and stabilizing their retention in the nanopore. This effect would not be possible in simulations with fixed, homogeneous charge distribution. Next we analyze electrolyte structure and its composition inside the pores as a function of Uelectrode and pore width and correlate these data with trends observed for the capacitance. Figure 5 shows the cross-sectional density profiles of ions in the nanopore for several pore sizes at various potentials. At PZC, in larger pores (11 Å and 15 Å), there is enough space between the pore walls to accommodate at least three layers of ions. In the 11 Å wide pore, the uncharged walls preferentially adsorb EMIM cations while TFSI anions partition to the middle. However, in the 15 Å wide nanopore, there is not enough space to accommodate five alternating layers of ions, while four layers are energetically unfavorable if one of the ions (e.g., EMIM at PZC) preferentially partitions to the surface. Therefore, in the 15 Å pore, a two-layer structure (with both layers having cations and anions but cations preferentially sitting at the surface) and an ion-depleted region in the middle of the nanopore is observed. We believe that the bell-shape and Ushape DC dependencies observed in Figure 2 for the 11 Å and 15 Å pores, respectively, are directly related to the differences in the ion packing/distribution inside pores near PZC. In the 11 Å pore, the ions are already tightly packed at the PZC. In such configuration, there is not much flexibility in electrolyte structure for ions separation or for increase of ion density with increase of Uelectrode and, therefore, the DC decreases resulting in a bell-shape dependence. In the 15 Å pore, on the other hand, the extra free volume in the middle of the pore can facilitate ion separations as well as allow an increase of the overall ion density in the pore leading to a U-shape DC behavior near PZC. In this pore, as the potential increases further, we expect the DC eventually to start decreasing and become a camel-shape due to the surface saturation effect.44 As the Uelectrode becomes negative the amount of EMIM in the surface layers is increasing while the amount of TFSI in the middle of the pore is decreasing both in the 11 and 15 Å pores as expected. However, on the positive electrode an interesting

Kondrat and Kornyshev model, then similar (but opposite in sign) ion packing/compositions should be observed independently of electrode polarity? To address these questions, we first examine what kind of asymptotic behavior of charge−charge interactions is obtained from electrode polarization scheme employed in our simulations and how that agrees with prediction of the Kondrat and Kornyshev model. Note that both approaches use the same fundamental basis; however, simulations use an iterative approach to obtain a numerical solution while the model derives an analytical decay of the field around a confined ion and represents interaction between two ions with an effective screening function. As a test case, we have computed the total electrostatic interaction between two EMIM ions confined in a slit pore of various widths with conductive walls. Figure 4 shows the total electrostatic

Figure 4. The dependence of the total electrostatic energy between two EMIM ions as a function of their separation as obtained from a simulation of two EMIM ions confined between two graphite planes and no other ions present in the system. Solid lines show the fit by the first term of the expansion describing screened interactions between ions in the nanopore as suggested by Kornyshev model U ∼ A exp(−πr/L)/(rL)0.5. r is the distance between the ions centers of mass, and L is the nanopore width.

interaction energy (including screening due to induced charges on the pore walls) between two ions inside nanopores as a function of their center-of-mass separation. Compared to unscreened interactions between two EMIM ions in vacuum, we see a significant reduction in the repulsion energy between ions inside nanopores, consistent with Kondrat and Kornyshev prediction. Moreover, the obtained dependence of electrostatic energy can be nicely fit with the first term of the series expansion A exp(−πr/L)/(rL)0.5 derived by the their model, where r is the distance between two ions, L is the pore width, and A is a prefactor that includes the influence of the dielectric medium and geometric details. Figure 4 shows that in the 7.5 Å pore when two EMIMs are at separations comparable to ion effective size (∼7−8 Å), they only have repulsion energy on the order of 4−6 kT, which is still accessible due to thermal fluctuations as well as it can be compensated/offset by the attractive van der Waals interactions. Therefore, in this pore, the EMIM ions can pack quite densely, even if there are no TFSI ions around to screen out the electrostatic repulsion. In the 15 Å pore, this level of repulsive energy corresponds to about 14 Å separation, indicating that one could expect a significantly lower packing density of EMIM ions in the larger nanopore upon complete ion separation. 136

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Figure 5. The nanopore cross-sectional density profiles of TFSI (dashed) and EMIM (solid) ions at several potentials (columns: −1 V, PZC, and +1 V) and nanopore widths (rows: 7.5, 11, and 15 Å).

Figure 6. DC and the cumulative density profiles of ions as a function of electrode potential for 7.2 Å (a,b), 7.5 Å (c,d), and 11 Å (e,f) wide pores. Cumulative densities are offset by the corresponding value at the PZC. The absolute values of these cumulative densities are shown in SI.

difference in structure between these two pores can be observed. In the 11 Å nanopore charged to +1 V, we do not

see the center-of-mass of TFSI anions partitioning on the positively charged walls of the surface. While the amount of 137

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packing density in the pore. These abrupt changes in ion density and composition lead to significantly increased DC in the −0.7 to −0.9 V potential range (Figure 6c). Therefore, the demixing of ions at −0.7 V provides sufficient charge separation that, despite a noticeable drop in the total ionic density inside the nanopore it still leads to a pronounced DC spike. Hence, the observed in our system capacitance enhancement in narrow pores is not due to ion densification in the pore but rather due to a sharp ion demixing. Wu et al. also reported similar phenomena in their simulation of [EMIM][BF4] in the 7.8 Å wide pore and suggested that removal of the co-ions energetically is more effective at these conditions than ion swapping.13 The sharp co-ion/counterion separation has been predicted by the Kondrat and Kornyshev model,20 but apparently this demixing transition was not observed in their follow-up MC simulations using effective (screened) ion−ion interactions derived from the model.21 Instead, the maximum in DC in ref 21 was observed where the ion densification and ion separation in the pore were maximized. In contrast, our simulations show that densification of total number of ions is not crucial for obtaining maximum in DC. Once the co-ions are expelled from the pore, we expect that the densification of pure counterion phase becomes responsible for the charge accumulation. The effectiveness of this latter mechanism certainly strongly depends on the extent of screening of electrostatic interactions discussed above. Nevertheless, after demixing, the pure counterions phase can still be compressed significantly filling the extra available space generated by expelled co-ions. If such counterion compression can be achieved at potentials where electrolyte is still electrochemically stable, then the IC can either slightly increase or maintain its elevated enhancement as the ΔU increases. In even narrower pore, i.e., 7.2 Å, another qualitative change can be observed. In this pore, increasing the positive potential on the electrode results in a relative pronounced increase of TFSI density accompanied by an almost constant number of EMIM, therefore leading to a noticeable increase of the total number of ions in the pore from PZC up to 0.5 V. As the negative value of the electrode potential increases, the TFSI ion density also drops quickly while the number of EMIM ions slightly increases. At −0.5 V the 7.2 Å pore is essentially depleted of co-ions. Therefore in the potential range −0.5 V to −1.5 V a densification of EMIM counterions is the only mechanism to increase the electrode charge. As shown in Figure 6b, the counterion densification is not fast enough (vs potential) to maintain elevated DC, and hence the DC decreases with potential below −0.5 V. This behavior further supports our observation that the co-ion depletion from the pore, rather than counterion densification, is the main factor leading to the peak in DC and the capacitance enhancement in subnanometer pores. The observed changes in the ion density/ composition lead to a relatively broad peak in DC in the potential range between −0.7 V and +0.7 V. The extension of the DC peak into positive range of potentials leads to some enhancement in IC on the positive electrode as can be seen in Figure 3, but at the same time to a significant drop of IC on the negative electrode. It is possible that further reduction of nanopore width would result in even further increase of IC on the positive electrode. However, taking into account geometric constrains of the pore and ion sizes it is hard to expect this to be higher than the maximum observed for the negative electrode in the 7.5 Å pore.

EMIM in the nanopore decreases and its distribution across the nanopore becomes more homogeneous, Figure 5 still shows that the centers-of-mass of EMIM are much closer to the surfaces than those of TFSI. Such, unexpected behavior can be explained by the orientation of TFSI ions. In the positively charged 11 Å nanopore, TFSI ions can orient perpendicular to the surface and expose negatively charged O and F atoms to both nanopore walls, keeping the molecular center-of-mass in the middle of the pore. This orientation allows more contacts between negatively charged atoms and nanopore walls than a parallel alignment of TFSI along one of the surfaces. Separation between surfaces in the 15 Å nanopore is too large for a single TFSI ion to bridge the surfaces, therefore, leading to the formation of two TFSI layers (with parallel alignment of TFSI to the surface) that replace EMIM ions at the nanopore walls as positive potential increases. As the pore size is reduced below 8 Å, the electrolyte structure inside the pore transitions from a multilayer structure observed in larger pores to a single layer as illustrated in Figure 5 for the 7.5 Å pore. In these narrower pores, the steric geometric constrains of the nanopore do not allow multilayer formation and the electrolyte structure becomes single-layered with both types of ions mixed in the layer. Note, that in pores with a single-layer structure, the co-ions are in direct contact with electrostatically repulsive surface with a limited screening provided by the counterions within the layer. As the potential increases in these subnanometer pores, the ion population changes with co-ion depleting the nanopore. Figure 6 shows the cumulative density for each ion type and for the total ion density in the pores as a function of electrode potential. Also shown are the corresponding DC dependencies. The densities were offset by the corresponding value at the PZC and normalized by the unit surface area to facilitate comparison of pores with different widths. For pores wider than 8 Å, we observe that the increase of the counterion and the decrease of co-ion densities are almost linear with increase of Uelectrode. Interestingly, the total ion density on the negative electrode increases only slightly with increasing electrode potential, while on the positive electrode it decreases, likely reflecting small differences in the effective molar volumes of confined counterions. However, the overall effect in total ion density change is less than 15%. In these larger pores, the primary mechanism for the surface charge accumulation is due to swapping of co-ions with counterions as originally suggested by the Kondrat and Kornyshev model.20,21 For the 7.5 Å pore, the charging of the positive electrode results in a similar monotonic ion swapping as in larger pores. However, in this pore, the total number of ions stays almost constant as a function of electrode potential. On the negative electrode, a qualitatively different behavior is observed. At the electrode potential of −0.7 V, a sharp drop of the co-ion density is observed, while the counterion density does not change significantly, indicating that the pore can maintain the density of counterions despite the fact that after demixing the electrostatic repulsion between counterions is not screened by co-ions. This behavior can be explained by the strong screening of electrostatic interactions between counterions by the conductive wall as has been illustrated in Figure 4. The observed changes in co-ion and counterion densities result in an effective drop of the total density of inserted ions. Note, that at PZC, the average total number of ions in the 7.5 Å pore is about 2 ions/nm2. Hence, the observed drop by 0.6 ions/nm2 seen in Figure 6d represents a significant reduction in the ion 138

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To summarize, our MD simulations of [EMIM][TFSI] RTIL on nanoporous conductive electrodes showed that a factor of 2 enhancement in electrode capacitance can be obtained by simulations using subnanometer-wide slit-geometry pores. The main factor responsible for the capacitance enhancement is a demixing transition inside the narrow pore due to co-ions sharply leaving the pore above a certain electrode potential threshold, combined with the ability of the conductive pore to maintain elevated densities of counterions after demixing. In agreement with the superscreening model, our simulations showed that the ion−ion electrostatic interactions inside the subnanometer pores decay exponentially with the ion separation and therefore are short-ranged. As a result of such strong screening, counterions can pack densely inside pore and maintain elevated densities after co-ions are expelled from the pore. In wider pores, where multiple layers of ions can be accommodated, no abrupt changes in ion composition or density and, hence, no significant enhancement in capacitance has been observed. However, in these pores an oscillatory character of IC as a function of pore width can be associated with the change of DC dependence from a bell-shape to a Ushape as a function of electrode potential. Finally, we find that the DC enhancement is observed only on the negative electrode. This asymmetry in IC and DC enhancement for positive and negative electrodes indicates that details of chemical structure and specific interactions between ions and with the electrode surfaces play an important role in controlling the charge separation in nanopores. We believe this can be useful to design RTIL compositions and electrode structures and separately tune the specific cation/anion/electrode combinations for optimal energy storage on positive and negative electrodes.

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ASSOCIATED CONTENT

Details of simulation protocol and system set up as well as additional data on ionic composition, electrolyte density, and distribution of charge density profiles inside nanopores are provided as a function of pore width and electrode potential. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (J.V.); [email protected] (D.B.). Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Chimola, J.; Yushin, G.; Gogotsi, Y.; Portet, C.; Simon, P.; Taberna, P. Anomalous Increase in Carbon Capacitance at Pore Sizes Less than 1 Nanometer. Science 2006, 313, 1760−1763. (2) Simon, P.; Gogotsi, Y. Materials for Electrochemical Capacitors. Nat. Mater. 2008, 7, 845−854. (3) Lin, R.; Taberna, P. L.; Chimola, J.; Guay, D.; Gogotsi, Y.; Simon, P. Microelectrode Study of Pore Size, Ion Size, and Solvent Effects on the Charge/Discharge Behavior of Microporous Carbons for Electrical Double-Layer Capacitors. J. Electrochem. Soc. 2009, 156, A7−A12. (4) Largeot, C.; Portet, C.; Chmiola, J.; Taberna, J. C.; Gogotsi, Y.; Simon, P. Relation Between the Ion Size and Pore Size for an Electric Double-Layer Capacitor. J. Am. Chem. Soc. 2008, 130, 2730−2731. (5) Barbieri, O.; Hahn, M.; Herzog, A.; Kötz, R. Capacitance Limits of High Surface Area Activated Carbons for Double Layer Capacitors. Carbon 2005, 43, 1303−1310. (6) Centeno, T. A.; Sereda, O.; Stoeckli, F. Capacitance in Carbon Pores of 0.7 to 15 nm: A Regular Pattern. Phys. Chem. Chem. Phys. 2011, 13, 12403−12406. (7) Fernández, J. A.; Arulepp, M.; Leis, J.; Stoeckli, F.; Centeno, T. EDLC Performance of Carbide-Derived Carbons in Aprotic and Acidic Electrolytes. Electrochim. Acta 2008, 53, 7111−7116. (8) Lota, G.; Centeno, T. A.; Frackowiak, E.; Stoeckli, F. Improvement of the Structural and Chemical Properties of a Commercial Activated Carbon for Its Application in Electrochemical Capacitors. Electrochim. Acta 2008, 53, 2210−2216. (9) Centeno, T. A.; Hahn, M.; Fernández, J. A.; Kötz, R.; Stoeckli, F. Correlation Between Capacitances of Porous Carbons in Acidic and Aprotic EDLC Electrolytes. Electrochem. Commun. 2007, 9, 1242− 1246. (10) Kondrat, S.; Pérez, C. R.; Presser, V.; Gogotsi, Y.; Kornyshev, A. A. Effect of Pore Size and Its Dispersity on the Energy Storage in Nanoporous Supercapacitors. Energy Environ. Sci. 2012, 5, 6476−6479. (11) Yang, L.; Fishbine, B. H.; Migliori, A.; Pratt, L. R. Molecular Simulation of Electric Double-Layer Capacitors Based on Carbon Nanotube Forests. J. Am. Chem. Soc. 2009, 131, 12373−12376. (12) Kalugin, O. N.; Chaban, V. V.; Loskutov, V. V.; Prezhdo, O. V. Uniform Diffusion of Acetonitrile Inside Carbon Nanotubes Favors Supercapacitor Performance. Nano Lett. 2008, 8, 2126−2130. (13) Wu, P.; Huang, J.; Meunier, V.; Sumpter, B. G.; Qiao, R. Complex Capacitance Scaling in Ionic Liquids-Filled Nanopores. ACS Nano 2011, 5, 9044−9051. (14) Feng, G.; Cummings, P. T. Supercapacitor Capacitance Exhibits Oscillatory Behavior as a Function of Nanopore Size. J. Phys. Chem. Lett. 2011, 2, 2859−2864. (15) Jiang, D.; Jin, Z.; Wu, J. Oscillation of Capacitance inside Nanopores. Nano Lett. 2011, 11, 5373−5377. (16) Jiang, D.; Jin, Z.; Henderson, D.; Wu, J. Solvent Effect on the Pore-Size Dependence of an Organic Electrolyte Supercapacitor. J. Phys. Chem. Lett. 2012, 3, 1727−1731. (17) Henderson, D. Oscillations in the Capacitance of a Nanopore Containing an Electrolyte due to Pore Width and Nonzero Size Ions. J. Colloid Interface Sci. 2012, 374, 345−347. (18) Wu, P.; Huang, J.; Meunier, V.; Sumpter, B. G.; Qiao, R. Voltage Dependent Charge Storage Modes and Capacity in Subnanometer Pores. J. Phys. Chem. Lett. 2012, 3, 1732−1737. (19) Merlet, C.; Rotenberg, B.; Madden, P. A.; Taberna, P.-L.; Simon, P.; Gogotsi, Y.; Salanne, M. On the Molecular Origin of Supercapacitance in Nanoporous Carbon Electrodes. Nat. Mater. 2012, 11, 306−310. (20) Kondrat, S.; Kornyshev, A. Superionic State in Double-Layer Capacitors with Nanoporous Electrodes. J. Phys.: Condens. Matter. 2011, 23, 022201−5. (21) Kondrat, S.; Georgi, N.; Fedorov, M. V.; Kornishev, A. A Superionic State in Nano-porous Double-Layer Capacitors: Insights from Monte Carlo Simulations. Phys. Chem. Chem. Phys. 2011, 13, 11359−11366.

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ACKNOWLEDGMENTS

The authors are grateful to the Department of Energy under Contract Grant DE-SC0001912 to the University of Utah. This research used computational resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. L.X. acknowledges financial support of the Natural Science Foundation of Guangdong Province, China (grant no. 1035106310 1000001). 139

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(22) Singh, R.; Monk, J.; Hung, F. R. Heterogeneity in the Dynamics of the Ionic Liquid [BMIM+] [PF6−] Confined in a Slit Nanopore. J. Phys. Chem. C 2011, 115, 16544−16554. (23) Shim, Y.; Jung, Y.; Kim, H. J. Graphene-Based Supercapacitors: A Computer Simulation Study. J. Phys. Chem. C 2011, 115, 23574− 23583. (24) Yang, L.; Brian, B. H.; Migliori, A.; Pratt, L. R. Molecular Simulation of Electric Double-Layer Capacitors Based on Carbon Nanotube Forests. J. Am. Chem. Soc. 2009, 131, 12373−12376. (25) Siepmann, J. I.; Sprik, M. Influence of Surface Topology and Electrostatic Potential on Water/ Electrode Systems. J. Chem. Phys. 1995, 102, 511−524. (26) Xing, L.; Vatamanu, J.; Smith, G. D.; Bedrov, D. Nanopatterning of Electrode Surfaces as a Potential Route to Improve the Energy Density of Electric Double-Layer Capacitors: Insight from Molecular Simulations. J. Phys. Chem. Lett. 2012, 3, 1124−1129. (27) Reed, S. K.; Lanning, O. J.; Madden, P. A. Electrochemical Interface between an Ionic Liquid and a Model Metallic Electrode. J. Chem. Phys. 2007, 126, 084704−13. (28) Vatamanu, J.; Borodin, O.; Smith, G. D. Molecular Dynamics Simulations of Atomically Flat and Nanoporous Electrodes with a Molten Salt Electrolyte. Phys. Chem. Chem. Phys. 2010, 12, 170−182. (29) Vatamanu, J.; Borodin, O.; Smith, G. D. Molecular Dynamics Simulation Studies of the Structure of a Mixed Carbonate/LiPF6 Electrolyte Near Graphite Surface as a Function of Electrode Potential. J. Phys. Chem. C 2012, 116, 1114−1121. (30) Xing, L.; Vatamanu, J.; Borodin, O.; Smith, G. D.; Bedrov, D. Electrode/Electrolyte Interface in Sulfolane-Based Electrolytes for LiIon Batteries: A Molecular Dynamics Simulation Study. J. Phys. Chem. C. 2012, 116, 23871−23881. (31) Vatamanu, J.; Borodin, O.; Bedrov, D.; Smith, G. D. Molecular Dynamics Simulation Study of the Interfacial Structure and Differential Capacitance of Alkylimidazolium Bis(trifluoromethanesulfonyl)imide [Cnmim][TFSI] Ionic Liquids at Graphite Electrodes. J. Phys. Chem. C 2012, 116, 7940−7951. (32) Hardwick, L. J.; Holzapfel, M.; Wokaun, A.; Novak, P. Raman Study of Lithium Coordination in EMIM-TFSI Additive Systems as Lithium-Ion Battery Ionic Liquid Electrolytes. J. Raman Spectrosc. 2007, 38, 110−112. (33) Borodin, O. Polarizable Force Field Development and Molecular Dynamics Simulations of Ionic Liquids. J. Phys. Chem. B 2009, 113, 11463−11478. (34) Chaban, V. V.; Voroshylova, I. V.; Kalugin, O. N.; New Force, A. Field Model for the Simulation of Transport Properties of Imidazolium-Based Ionic Liquid. Phys. Chem. Chem. Phys. 2011, 13, 7910−7920. (35) Chaban, V. V.; Voroshylova, I. V.; Kalugin, O. N.; Prezhdo, O. V. Acetonitrile Boosts Conductivity of Imidazolium Ionic Liquids. J. Phys. Chem. B 2012, 116, 7719−7727. (36) Druschler, M.; Borisenko, N.; Wallauer, J.; Winter, C.; Huber, B.; Endresb, F.; Roling, B. New Insights into the Interface Between a Single-Crystalline Metal Electrode and an Extremely Pure Ionic Liquid: Slow Interfacial Processes and the Influence of Temperature on Interfacial Dynamics. Phys. Chem. Chem. Phys. 2012, 14, 5090− 5099. (37) Vatamanu, J.; Borodin, O.; Smith, G. D. Molecular Simulations of the Electric Double Layer Structure, Differential Capacitance, and Charging Kinetics for N-Methyl-N-propylpyrrolidinium Bis(fluorosulfonyl)imide at Graphite Electrodes. J. Phys. Chem. B 2011, 115, 3073−3084. (38) Vatamanu, J.; Borodin, O.; Smith, G. D. Molecular Insights into the Potential and Temperature Dependences of the Differential Capacitance of a Room-Temperature Ionic Liquid at Graphite Electrodes. J. Am. Chem. Soc. 2010, 132, 14825−14833. (39) Vatamanu, J.; Cao, L.; Borodin, O.; Bedrov, D.; Smith, G. D. On the Influence of Surface Topography on the Electric Double Layer Structure and Differential Capacitance of Graphite/Ionic Liquid Interfaces. J. Phys. Chem. Lett. 2011, 2, 2267−2272.

(40) Bhuiyan, L. B.; Lamperski, S. On the Interfacial Capacitance of an Electrolyte at a Metallic Electrode around Zero Surface Charge. Mol. Phys. 2012, DOI: 10.1080/00268976.2012.745954. (41) Bhuiyan, L. B.; Lamperski, S.; Wu, J. Z.; Henderson, D. Monte Carlo Simulation for the Double Layer Structure of an Ionic Liquid Using a Dimer Model: A Comparison with the Density Functional Theory. J. Phys. Chem. B 2012, 116, 10364−10370. (42) Merlet, C.; Salanne, M.; Rotenberg, B.; Madden, P. A. Imidazolium Ionic Liquid Interfaces with Vapor and Graphite: Interfacial Tension and Capacitance from Coarse-Grained Molecular Simulations. J. Phys. Chem. C 2011, 115, 16613−16618. (43) Gnahm, M.; Pajkossy, T.; Kolb, D. M. The Interface Between Au(111) and an Ionic Liquid. Electrochim. Acta 2010, 55, 6212−6217. (44) Kornyshev, A. A. Double-Layer in Ionic Liquids: Paradigm Change? J. Phys. Chem. B 2007, 111, 5545−5557.

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