Capacitive Energy Storage: Current and Future Challenges

Perspective pubs.acs.org/JPCL

Capacitive Energy Storage: Current and Future Challenges Jenel Vatamanu* and Dmitry Bedrov Department of Materials Science & Engineering, The University of Utah, 122 S. Central Campus Drive, Salt Lake City, Utah 84112, United States ABSTRACT: Capacitive energy storage devices are receiving increasing experimental and theoretical attention due to their enormous potential for energy applications. Current research in this field is focused on the improvement of both the energy and the power density of supercapacitors by optimizing the nanostructure of porous electrodes and the chemical structure/composition of the electrolytes. However, the understanding of the underlying correlations and the mechanisms of electric double layer formation near charged surfaces and inside nanoporous electrodes is complicated by the complex interplay of several molecular scale phenomena. This Perspective presents several aspects regarding the experimental and theoretical research in the field, discusses the current atomistic and molecular scale understanding of the mechanisms of energy and charge storage, and provides a brief outlook to the future developments and applications of these devices.

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remarkable properties of RTILs, which include their low viscosity, volatility, flammability, and melting point, a relatively large electrochemical, chemical, and thermal stability, excellent solvation properties, and good ionic conductivity, make these compounds ideally suited as electrolytes. The electrodes of EDLCs typically consist of a porous material with high electronic conductivity and large specific surface area. The energy storage in EDLCs is achieved due to the electrostatic interactions between the charged electrode surface and a fewnanometer thick layer of ordered electrolyte near the electrode surface. To date, the EDLCs are commonly utilized in high fidelity/ precision electronics, regenerative braking in electric vehicle transportation, flash photography, portable electronic devices, and many other applications. However, the main limitation of EDLCs is their relatively low energy density compared to EBs. Therefore, extensive theoretical and experimental research efforts are focusing on the design and optimization of novel materials and systems that can bring these devices to a new level. Understanding the behavior of the electrolyte (i.e., structural correlations, dynamical properties, charge separation, etc.) near the electrode surfaces, or the electric double layer (EDL) properties, is therefore one of the key aspects in revealing the mechanisms of charge storage in these devices and is important both from fundamental and practical considerations. This paper will discuss and review several key theoretical and experimental issues of non-Faradaic charge storage in EDLCs. The manuscript is intended as a rather brief overview of this fast growing field. While we attempted to acknowledge much of the extensive literature in this field, it is very clear that it would be impossible to cover all valuable work

n the context of increasing demand for efficient and nonpolluting energy, the theoretical and experimental research of electricity based energy storage devices increased significantly in the past decade. These devices can be divided in two main categories: those that involve redox reactions during charging/discharging cycles (e.g., electrochemical batteries and pseudocapacitors) and devices that involve no chemical processes (e.g., electric double layer supercapacitors or EDLCs). The electrochemical batteries (EBs) are commonly utilized for applications requiring a steady energy output over a long period of time, which makes them suitable for powering portable electronics or electric vehicles. However, the electrochemical reactions occurring in EBs during the charging/ discharging cycling eventually lead to the degradation of the electrode and electrolyte materials and, hence, limit the lifetime of these devices. Also because the redox reactions and the intercalation/deintercalation processes associated with the charge transport are accompanied by relatively large activation barriers, the time required to recharge EBs can be long and the delivered power is limited. The EDLCs, on the other hand, have emerged as very promising energy storage technologies for applications requiring shorter-term high burst of energy. These devices can charge/discharge very fast and do have significantly longer lifetime than EBs because they use non-Faradaic (i.e., purely electrostatic) processes for energy storage. Note that in many applications combining the supercapacitors with batteries can be optimal for energy delivery. The EDLCs are comprised of two oppositely charged electrodes and an electrolyte inserted between the electrodes. The latter usually contains a large amount of salt dissolved in a solvent (water or organic solvent) or can be entirely comprised of a molten salt. Recent advances in synthetic chemistry produced a number of organic molten salts that have a low melting temperature, that is, below 100 °C. These organic salts are also called room temperature ionic liquids (RTILs). The © 2015 American Chemical Society

Received: June 6, 2015 Accepted: August 26, 2015 Published: August 26, 2015 3594

DOI: 10.1021/acs.jpclett.5b01199 J. Phys. Chem. Lett. 2015, 6, 3594−3609

The Journal of Physical Chemistry Letters

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nanopores showed the necessity to use the fluctuating charge approach in order to correctly capture the kinetics of ion rearrangement inside conductive nanopores21 or the screening of electrostatic interactions between ions inside the nanopores due to induction of local image charges on nanopore walls.22 In the constant potential technique, the electrode charges are assigned either by imposing a fixed electrostatic potential on the electrode surface16,17,23 or by constraining the total electrode charge to a desired value and computing the electrode chemical potential as a Lagrange multiplier associated with this constrain.18 The modeling of the conducting electrode within the constant potential framework can be achieved with one single adjustable parameter, specifically the width of the Gaussian smeared charge assigned on the electrode atoms.16,24 This width can be tuned to quantitatively reproduce the wellknown results expected from classical electrostatics for the polarization of a conductor upon the approach of an external charge.17 Sprik et al.16 and Reed et al.17,25,26 found that a width of the Gaussian distribution of about 0.5 Å is optimal for most cases. The electrode charges can be assigned on a finer grid than the locations of the electrode atoms, as proposed by Golze et al.,21 resulting in a better stability and convergence of the method with respect to the adjustable parameter. Another important technical aspect regarding the molecular simulations of electrode−electrolyte interfaces is the handling of the periodic boundary conditions. Yeh et al.27 showed that for systems having large dipole moments (e.g., created by the intrinsic presence of oppositely charged electrodes) in the simulation cell, in order to correctly treat the long-range electrostatic interactions (typically done with Ewald type summations), the utilization of 2D symmetry (i.e., assuming the periodicity and performing the summation in the reciprocal space only in the directions perpendicular to the dipole) instead of the conventional 3D periodicity provides more accurate results. However, the utilization of the 2D-Ewald summation significantly increases the computational burden due to the necessity to separately handle the analytic term at the Fourier vector k = 0 (which has O(N2) associated computational cost)28,29 and the need for explicit integration along the asymmetry direction for the reciprocal terms at k ≠ 0 (which means significantly more k-points in that direction). This extra computational expense of the 2D-Ewald was resolved by Kawata and co-workers.30−33 Specifically, the term at k = 0 was handled with forward and backward spline interpolations on a regular grid,30,31 thus reducing the computational cost from O(N2) to O(N·n), where n is the order of interpolating splines. The reciprocal terms at k ≠ 0 were handled with a version of SPME adapted for 2D-symmetry,31−33 which takes advantage of the fast Fourier transform algorithm and reduces the computational cost to O(NlogN), and hence, the increase of the number of k-vectors for Fourier integration does not become computationally too expensive. Few comments have to be made in regard with the force fields utilized in modeling RTIL electrolytes at charged surfaces. Obviously, ab initio simulations are expected to provide the most complete theoretical description of the molecular and electronic characteristics and interactions between species, and some pioneering works in this regard were recently reported for example for RTILs near graphene and nanotubes34−36 or flavonols on graphenes.37 However, as the size of the electrode−electrolyte systems is large (typically tens of thousands of atoms) and the time scales required to access the EDL restructuring is on the order of multiple

in this brief presentation. Additional references to experimental and theoretical papers as well as comprehensive discussions of issues related to this research field can be found in the recent review papers by, for example, Fedorov et al.1 and Hayes et al.2 Issues related to electrode materials were reviewed by Zhang et al.3 and Gogotsi and co-workers.4,5 Chemical modifications of carbon-based electrode materials such as graphene and nanotubes are presented in the reviews of Tasis et al.,6 Georgakilas et al.,7 and Boukhvalov et al.8 The recent papers of Merlet et al.9 and Hughes et al.10 discussed specific theoretical and computational challenges in simulation of RTILs near charged surfaces. A comprehensive description of application of classical density functional methods to these systems are given by Wu et al.,11,12 Henderson et al.,13 and Woodward et al.14,15 Molecular Simulations of Electrode−Electrolyte Interfaces. Taking into account that the energy storage in EDLCs is achieved by a rearrangement of ions in a relatively thin interfacial layer near the electrode surface and that there are no redox reactions involved, the classical molecular dynamics (MD) simulation is an effective technique to study these processes at electrified interfaces. Utilizing accurate atomistic force fields, these simulations can provide quantitatively accurate predictions of the EDL structure and dynamics at charged surfaces. Two molecular simulation techniques are commonly utilized to simulate electrolytes near charged surfaces: (i) approaches that impose a constant and uniformly distributed charge on the electrode surface or (ii) more advanced methods that allow spatial and temporal fluctuations of the local charge on the electrode surface while constraining the applied electrode potential. In the fixed charge approach, a uniformly distributed charge over the electrode atoms/surface is set constant and the simulations sample the electrolyte response to such constant charge, therefore not including the effect of the electrode polarization by electrolyte. In the constant potential approach, on the other hand, the charge on the electrode atoms is allowed to fluctuate in order to satisfy the condition of minimizing the free energy of the system.16−18 In this case, the polarization of the electrode and the electrolyte restructuring in the EDL are coupled, which is physically a more realistic representation.

The classical molecular dynamics simulation is an effective technique to study processes at electrified interfaces. The constant charge approach can be straightforwardly implemented in any simulation code/software and it has been shown that for electrolytes near flat electrodes it predicts static properties (e.g., the EDL structure) in good agreement with simulations conducted using the constant potential approach.19 However, to capture correctly the evolution of EDL restructuring as well as the mobility of ions in the EDL, the constant potential (or fluctuating charge) approach is necessary.20,21 Wang et al.19 compared these two methods for a Li-salt in acetonitrile-based solvent and found good agreement for the EDL structure at low voltages (i.e., below 2 V electrode potential). However, at larger voltages there were noticeable differences in the EDL structure and Li distribution near the electrode surface. Also, for atomically rough surfaces the fluctuating charge approach is likely to be required in order to capture the electrostatic nonequivalence of the surface atoms. Importantly, studies of electrolytes confined inside 3595



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When an electrostatic potential (or charge) is applied on the electrode surface, the ionic electrolyte will restructure to compensate the electrode charge with an excess amount of counterions in the interfacial layer. Traditionally, this interfacial layer is referred to as EDL, although, as shown in a number of simulations and experiments, the electrode−electrolyte interface can have a multilayer structure of alternating counterions and co-ions (as can be seen in Figure 1a). The specific

nanoseconds, the ab initio simulations are computationally too prohibitive. The classical MD simulations with atomistically detailed force fields are expected to be the best candidates for this purpose as they can accurately capture the details of the electrostatic interactions and the chemical structure at the EDL/electrode interface. One also has an option of using either polarizable force fields (that include the effects of electronic polarizabilities via either induced dipoles or Drude oscillators) or nonpolarizable models with fixed partial atomic charges. The former is considered to be more accurate, in particular for electrolytes containing small ions such as Li+. For example, extensive work by Borodin et al.38−41 showed that the inclusion of the electronic polarizability is necessary to correctly reproduce the structure of the local coordination shell around Li+ as well as the dynamic and transport properties in systems containing Li-salts.42,43 An electrolyte containing large radius halide anions (such as iodine)44 is another example of a system requiring polarizable force fields in classical molecular simulations. The nonpolarizable force fields for ionic systems typically predict stronger interactions of ions with their local environments, which leads to smaller diffusion coefficients and higher viscosity predictions. At the same time, many RTILbased electrolytes comprised of larger ions can be modeled fairly accurately with atomistic nonpolarizable force fields or even with united atom models where groups of atoms (e.g., such as −CH2− or −CH3) are combined into a single force center.45,46 Among popular atomistic force fields used in MD simulations of RTILs and Li-salt based electrolytes are polarizable and nonpolarizable versions of the APPLE&P,38,39,41,47−49 nonpolarizable OPLS-AA force field,50−52 a recent version of CL/P force-field,53 polarizable force-fields with the polarizability represented with Drude oscillators54 or damped induced dipoles obtained using a force-matching fitting of results from ab initio MD simulations.55−57 In addition to atomistic force fields, often coarser-grained models are also used for modeling RTIL electrolytes. In these simulations, the whole ion can be represented using very few or even a single force center. Although the simulations using these types of models usually can provide very important qualitative understanding, they cannot take into account the details of the electrolyte chemical structure (i.e., the charge distribution on the ions) and hence they are not expected to be in quantitative agreement with experiments. In addition to the selection of the appropriate model for electrolyte, the choice of the electrode model is also very important. As an electrostatic potential difference is applied between two electrodes, a certain amount of charge will be accumulated on the electrode atoms and the physical model for the electrode representation (i.e., conducting, semiconducting, etc.) depends on the simulation scheme utilized to distribute the charges on the atoms. The choice of the electrode model will define the ability of the electrode to polarize in response to the electrolyte restructuring and, hence, can be very important even at a qualitative level. Furthermore, it might be important to take into account the semiconducting character of several carbon-based electrodes characterized by the density of states and quantum capacitance near the Fermi level.58−63 Electric Double Layer (EDL) Structure. Many macroscopic properties related to the charge storage in EDLCs can be correlated with the underlying electrode−electrolyte interfacial structure and its dependence on the applied electrode potential, and therefore, an understanding of the molecular scale electrode−electrolyte interfacial structure is very important.

Figure 1. Example of an EDL structure for (a) ion center-of-mass density, (b) cumulative space charge density and (c) Poisson potential as obtained from atomistic MD simulations of [C2mim][TFSI] RTIL at 393 K and a potential difference between electrodes of 7 V. In agreement with many experiments, the simulations probed a multilayer structuring of electrolyte near the electrode surface.

distribution of ions next to the electrode surface, the width of the electrode−electrolyte interface, and the response of the EDL structure to changes in the applied voltage are intriguing issues of great theoretical and practical interest. Several important insights into the EDL structure and the mechanisms of its formation were gained from theoretical studies based on analytical theories as well as from atomistic simulations. Earlier EDL models such as Gouy−Chapman,64,65 Stern,66 or more recent models proposed by Kornyshev,67 Oldham,68 or Yining69 predict a uniformly decreasing counterion charge density as a function of distance from the electrode surface both for condensed molten salts and diluted solutions of ions. However, a completely different picture of the EDL structure emerges from the analytical theories that account for the shortrange correlations between ions. Specifically, the classical density functional theory,15,70−75 the inhomogeneous or singlet versions of Ornstein−Zernike (OZ) based integral equation theories for atomic76−79 or molecular fluids,80−82 as well as the 3596



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The experimental analysis of the atomistic level structure of EDLs reveals a somewhat inconsistent picture depending on which technique is used for the measurements. The atomic force microscopy (AFM) or X-ray reflectometry on RTILs near charged electrode surfaces clearly reveal a multilayer EDL structure and an overscreened interfacial layer. For example, the X-ray reflectometry study by Yamamoto et al.87 of a RTIL electrolyte on Au(111) electrode showed the formation of multiple layers and overscreening of the interfacial layer. Similar EDL structuring was also found using the AFM technique.88 Likewise, RTILs with cations containing long alkyl tails (up to 18 carbon atoms) also generated multiple layer structured EDL, as was found with resonant soft X-ray reflectivity.89 Nishi et al.90 showed that the amplitude of these structural oscillations decreases with increasing temperature. The amplitude of the structural oscillations of EDL can also depend on the electrode polarity. For example Hayes et al.91 found that the structural oscillations of RTIL near Au(111) electrodes were more pronounced at the negative electrode, which is in good agreement with the predictions from recent molecular simulations.49 In agreement with Nishi et al.,90 up to six layers were observed by AFM measurements for several common RTILs on mica surface92 as well as on silica and graphite surfaces.93 An interesting case of EDL structure consisting of bilayer nanofilms was observed for RTILs containing ions with extended alkyl tails (up to 10 carbon atoms).94−96 On the other hand, another set of experiments based on sum frequency generation (SFG) spectroscopy suggested that a Helmholtz-like inner layer largely dominates the EDL structure. For example, Baldelli suggested an interpretation of the SFG spectroscopy of EDL structure97,98 that is consistent with the formation of a single strongly adsorbed (Helmholtz-like) layer and not with a multilayer structure.99 A dense interfacial layer was also suggested from in situ spectroscopic ellipsometry by Nishi et al.100 for four RTILs at Hg electrode. Other SFG spectroscopy101 in situ scanning tunneling miscroscopy,102 and solid-state nuclear magnetic resonance103 measurements for 1butyl-3-methylimidazolium (C4mim)/hexafluorophosphate (PF6) RTIL at Au and mica electrodes have reported a short and long-range order in the plane parallel to the electrode surface that was consistent with a strongly adsorbed crystal-like layer. Therefore, while the SFG spectroscopy and some other surface characterization techniques suggest strongly ordered Helmholtz layer of electrolyte near the electrode surface, the molecular simulations and the AFM and X-ray experiments point out toward a multilayer structure of EDLs. It is possible that the layers beyond the most strongly adsorbed ions cannot be seen by the SFG method. However, the source of this apparent discrepancy between the SFG measurements and other techniques requires further investigation. Dif ferential Capacitance (DC). The differential capacitance (DC), which is the measure of the change in the electrode charge upon a small change in the applied voltage, and its dependence on the electrode potential are key properties often reported by experiments because they can be, in principle, correlated with the changes in the EDL structure. Although the examination of the experimental literature shows a large variability in the DC dependence on voltage, a few generic trends can be inferred: the DC either can have a maximum at low voltages and decrease with increasing voltage (i.e., a bellshaped dependence of the DC on voltage) or it can show a minimum at low voltages (the U-shaped). Note that the Ushaped (at low voltages) DC becomes a camel-shaped

integral equation theories based on the Bogolyubov−Born− Green−Kirkwood−Yvon hierarchy83 predict an overscreening of the interfacial electrolyte layer followed by a sequence of multiple electrolyte layers in molten salts and concentrated ionic solutions. A Landau−Ginzburg type of free energy functional proposed by Bazant et al.84 was sufficient to predict overscreening, overcharging, the competition between them as a function of electrode potential, as well as multiple layer structuring near electrodes. In light of the singlet-based OZ integral equation theory, the appearance of a multilayer structure is related to the short-range correlations between ions. Specifically, Booth et al.85 showed that while a hypernetted chain closure (that accounts for the short-range correlations) can predict the structure oscillations and overscreening, the closure form that ignored the short-ranged correlations between ions led to a Gouy−Chapman type of behavior with no multilayers or overscreening.

Many macroscopic properties related to the charge storage in EDLCs can be correlated with the underlying electrode−electrolyte interfacial structure and its dependence on the applied electrode potential. The predicted electrolyte partitioning near the electrode surface in alternating layers rich in either counterions or co-ions extending over several nanometers from the surface as well as the overscreening of the interfacial layer were confirmed by an extensive number of atomistic simulations of molten salts,23,25 RTILs,45,47,49,86 as well as carbonates solutions containing Lisalts.42,43 A typical EDL structure obtained from simulations is exemplified in Figure 1 for a system consisting of [C2mim][TFSI] RTIL confined between two oppositely charged graphite electrodes with the potential difference of 7 V. Note that according to the extensive data from molecular simulations available in the literature, most RTILs generate density and charge profiles that are qualitatively similar to those shown in Figure 1. According to Figure 1, there are structural oscillations in ions’ density (Figure 1a), cumulative spatial charge distribution (Figure 1b), and screened Poisson potential (Figure 1c) that are extending over several nanometers from the electrode surface along the direction perpendicular to the surface. Specifically, the formation of multiple layers rich in either counterion or co-ion shown in Figure 1a generates an oscillatory spatial charge distribution as shown in Figure 1b. These oscillations decrease exponentially in amplitude with increasing the distance from the electrode. The resulting screened Poisson potential (Figure 1c) also oscillates near the electrode; however, it remains constant far away from the electrode, that is, in the bulk electrolyte region. This means that the ions several nanometers away from the electrode surface, that is, beyond the EDL multilayer structure, effectively do not feel any mean electrostatic field from the electrode surface. In other words, the multilayer structure formed near the electrode surface screens out the electrostatic field generated by electrodes. The relatively short-range width of the EDL (only a few nanometers) can be intuitively understood from the fact that the dense ionic liquids have high density of charges and, accordingly, a rather short Debye screening length. 3597



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with ions (i.e., within ΔU 4−5 V).110 At higher voltages (ΔU > 6−7 V), however, the simulations of realistic RTILs such as [C4mim][PF6]110,111 and [pyr13][FSI]45 showed a decay of DC scaling as ∝1/|Uelectrode|1/2, which is in perfect agreement with the asymptotic and system independent behavior predicted by the Kornyshev model.67 Many molecular simulations of conventional RTILs near flat electrode surfaces have predicted an absolute value of DC between 4 and 5.5 μF/ cm2.45−47,49,59,110,112−116 Similar values of capacitances, of around 5 μF/cm2, were predicted for solutions of RTILs in acetonitrile solvents117 and for Li-salts dissolved in carbonates.42,43 These theoretical predictions for DCs are in good quantitative agreement with the experimental works by Drüschler et al.,118 Alam et al.,119 Cannes et al.,120 and Costa et al.121,122 However, there are systems that do not follow this general trend. For example, although the recent experiments of Costa et al.122 also found almost flat capacitance dependence on electrode voltage for several RTILs near Pt and Au, the [C4mim][BF4] on Pt has generated a large DC peak at lower voltages as observed in the earlier work of Su et al.123 A similar spike in DC (of up to 20 μF/cm2) was generated by [C2mim][TFSI]124 and [C2mim][BF4]125 on Hg electrodes. Some simulations also reported sharp peaks in DC at low voltages. For example, simulations of Tazi et al.126 and calculations based on restricted primitive model127 showed that when the interactions between electrode−electrolyte were treated as polarizable,126 a strong peak in DC is generated at lower voltages. Another possible mechanism that has been suggested to explain the sharp peaks in DC near PZC is related to a strong ion pairing that dissociates upon a small increase in the electrode potential. However, Ma et al.14 using classical DFT calculations showed that even 100% ion-pairing would not dramatically change the nature of surface-ion interactions and the shape of DC. Another explanation for the appearance of strong peaks in DC in some systems can be directly related to the topography of the electrode surface structure. Earlier experimental work of Randin et al.128 showed that pyrolytic graphite generated larger capacitances than the electrode materials that had a smoother surface. Tang and co-workers129 have found a large influence of the graphite electrode orientation on the structure of Li-salt based electrolytes near electrodes. The study by Costa et al.121 of a series of RTILs and electrode surfaces found a dramatic impact of the electrode material and its surface structure on DC. These observations suggest that the atomic level surface topography of the electrode surface can also be very important in defining the correlations between the EDL structure and DC. Moreover, the metallic electrode surfaces can restructure in contact with electrolyte130,131 and the geometry of the formed patterns/islands can depend on the applied voltage.123 This electrode restructuring can complicate the interpretation of electrode capacitances. For carbon-based electrodes where such a restructuring is restricted by covalent bonds, a much stronger impact of electrode orientation on DC is expected, which appears to be consistent with the larger variability of experimentally reported DCs on various glassy-carbon electrodes. Several simulation works have focused on gaining a basic theoretical understanding of the role of surface roughness on the EDL structure and DC. As shown in the theoretical work of Tazi et al.126 for molten salts near Al(001) and Al(011) crystallographic faces and by us86 for [C2mim][FSI] RTIL on

dependence over an extended potential range because at large potentials the DC eventually reaches a maximum (due to surface crowding by ions) and then decreases with further potential increase. Such a behavior was explained at a fundamental level through simple EDL models proposed by Kornyshev67 and Oldham,68 which attributed this effect to be essentially steric in origin. As shown by Kornyshev, the mean field lattice-gas model predicts a “Fermi-like” distribution of ions near the surface if the ion excluded volume is considered. From such “Fermi-like” distributions one can understand the bell-shaped DC (and in general the decrease of DC with the increase of the electrode potential) as a manifestation of the steric exclusion effects due to the surface crowding effects. In contrast, if at low voltages the electrode surface is weakly populated by ions and there are many empty sites available for ions next to the surface then a fast (vs potential increase) ion accumulation is expected upon electrode potential increase, leading to a DC increase with voltage increase. Therefore, it is expected that the electrolytes with high density of ions near the electrode surface generate a bell-shaped DC, whereas electrolytes with low ion density generate a camel-shaped DC as predicted by both the Kornyshev67 model and the more complex classical DFT-based theories.13,104 Note that our simulations of RTILs at flat surfaces do show relatively small changes of the total interfacial density near the interface, which is consistent with the weak variation of DC vs electrode potential (see discussion below). Although qualitatively explainable from classical considerations using the Gouy−Chapman or the Kornyshev models, the physical origin of the U-shaped DC for electrolytes at semiconducting electrodes, such as pristine graphene, may be dominated by quantum effects. It is well known that the pristine graphene has the Dirac point at the K-point. Consistent with such a band structure, the density of states near the Fermi level is low resulting in a U-shaped dependence on the local surface potential around the Fermi level. Such low density of states diminishes the rates of electrode charge accumulation (and therefore the capacitance) as compared to a metallic surface that has high density of states and no gaps (or Dirac point) in its band structure near the Fermi level. This aspect can be understood at the phenomenological level by modeling the capacitance of the electrode with two serially connected capacitors: (i) a capacitor representing the quantum capacitance (Cq) of the electrode (defined by the band structure and the density of states of the electrode material), and (ii) the second capacitor representing the classical processes of electrolyte restructuring near the charged surface due to the EDL formation (CEDL). The presence of the Dirac point in the graphene structure implies a U-shaped Cq with very small values (below 1 μF/cm2) near the potential of zero charge (PZC). Such small values of Cq dominate the total electrode capacitance making it strongly U-shaped.59 However, the metallic character of graphene can be restored by doping with either p or n impurities (demonstrated to be experimentally feasible105−109) that moves the band gap away from the Fermi level62 or by generating vacancy defects, which introduce zigzag (metallic) edges that destroy the Dirac point and enhance the energy bands and the density of states near the Fermi level.60 As a common trend, the atomistic MD simulations on atomically flat, metallic electrode surfaces showed only a weak dependence of DC versus the applied potential (ΔU) in the range of potentials where the electrode surface is not saturated 3598



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Figure 2. (a) Differential capacitance as a function of the electrode potential for several types of surface topographies shown in the snapshots. (b) Derivative with respect to electrode potential of the total electrolyte charge located within certain distances d from electrode as a function of electrode potential. These derivatives were converted to units of μF/cm2 for easier comparison with DC. The data in panel b suggest that an interfacial layer with a width of ∼1.6 nm is sufficient to quantitatively capture the dependence of DC on the electrode potential.

In addition to the surface roughness, the curvature of the electrode surface can also influence the magnitude and shape of DC. A weak dependence of DC on the applied voltage was shown from simulations for curved (spherical and cylindrical) electrode geometries134 albeit with increased capacitances per surface area or per unit mass of electrode by as much as 40− 60% for spherical onion-like electrodes134 and up to ≈25% for (5,5) nanotubes.135 A significant increase of the gravimetric capacitance (almost 400% relative to the capacitances of flat surfaces or 250F/g) normalized per unit mass of the electrode was reported for the limiting case of cylindrical electrode geometry (a single wire of atoms) with a diameter comparable to ion sizes, i.e., very high curvature.136 This effect can be straightforwardly correlated with the packing and the overscreening due to the surface curvature of EDL.134 Finally, in the discussion of the EDL structure and DC a very interesting question is how do these two properties correlate? For example, how much of the multilayer structure shown in Figure 1a is essential to quantitatively determine the shape of DC as a function of electrode voltage such as the one shown e.g., in Figure 2a? Our recent MD simulations on [Cnmim][FSI] and [Cnmim][TFSI] RTILs (n = 2,4,6 and 8) showed that despite the extension of the multilayer structure up to 4−5 nm, the interfacial layer located within 0.5−0.6 nm from the electrode surface can qualitative capture the main features of the DC dependence on voltage. Also, an electrolyte layer within 1.4−2.0 nm from the electrode surface is sufficient to quantitatively explain the DC shape as a function of potential47,49 as illustrated in Figure 2b. In other words, the additional layers located beyond the 2 nm distance from the surface have a negligible contribution to DC. Nanoconf ined RTILs. As the non-Faradaic energy storage in supercapacitors is achieved at the electrode−electrolyte interface, the increase of the specific surface area (SSA) in porous electrodes remains an obvious route for increasing the energy density stored in these devices. The extensive research in increasing the SSA of porous materials is also motivated by recent experiments for organometallic frameworks, which probed SSA as large as 7000 m2/g137,138 and by theoretical

prismatic face graphite, the atomic-level corrugated surfaces can generate large peaks in DC at lower voltages. Pak et al. used ab initio simulations to study an RTIL near graphene60 and showed that certain types of graphene edges can almost double the EDL capacitance. Ho et al.132 reported a doubling of capacitance (as compared to atomically flat surfaces) for aqueous solution of NaCl by nanopatterning the graphene electrodes. For [pyr13][FSI] RTIL Xing et al.133 showed that the surface nanopatterning can generate a 50−70% increase in capacitance even at relatively large voltages (ΔU = 2−2.5 V). Furthermore, increasing the extent of the surface corrugation can result in large amplitude variations in DC with multiple minima and maxima as a function of potential as shown in Figure 2a.133 However, the capacitance enhancement and the peaks in DC disappear if the widths of the surface patterns are larger than the dimensions of the ions comprising the electrolyte.133 Interestingly, the chemical structure of ions has a more pronounced effect on the shape and magnitude of DC and on the EDL structure for corrugated surfaces than for atomically flat ones. For example, while the [Cnmim][FSI] and [Cnmim][TFSI] RTILs generate similar DC near the flat electrode surface, they show qualitatively different DC near the prismatic face of graphite.48,49 The body of work discussed above clearly indicates that the atomic scale topography of the electrode surfaces is one of the key characteristics influencing the charge storage in EDLCs, which has to be carefully characterized for each investigated system. Also, the surface roughness can be tuned to increase the energy storage.

The atomic scale topography of the electrode surfaces is one of the key characteristics influencing the charge storage in EDLCs, which has to be carefully characterized for each investigated system. 3599



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estimates of the upper limit of SSA in the range of 14 000 to 27 000 m2/g range.139 For the energy storage applications, however, porous electrode materials with good electronic conductivity and SSA ranging from 2000 to 3000 m2/g for various carbon fibers,140−142 carbide-derived carbon,4,143−145 aerogels,146−148 nanotubes,149−154 and 2D-microporous triazine-based frameworks155 to about 4000 m2/g for rice-hull based carbon156 and porous 3D-graphenes157 have been successfully prepared. The increase of the SSA in porous electrodes is usually accompanied by a decrease of the pore widths to nanometer dimensions. In such materials the electrolyte is experiencing qualitatively different (compared to bulk electrolyte) environments due to the nanoconfinement and a number of new intriguing phenomena such as accelerating dynamics,158−160 a sharp increase of capacitance,143 selective ion-flow,161,162 inverse osmosis and nanofiltration,163−165 and concentration gradient driven power sources166,167 were discovered for electrolytes in nanometer and subnanometer pores.

Figure 3. Summary of capacitance enhancements reported by several experiments for a variety of electrolytes on nanoporous electrodes.

given applied voltage (Uelectrode). The IC can be reported for individual electrodes or for the entire capacitor (ICcap). Note that in the latest case the contributions from both electrodes are accounted for. Most experimental capacitances discussed above and shown in Figure 3 are for the total capacitance, that is, include contributions from both electrodes (IC+ and IC−). The enhancement of the EDL capacitance in nanopores can be understood in light of the basic theoretical models proposed by Kondrat and Kornyshev.22 Specifically, due to the polarization of the conductive pore walls the strength of the electrostatic interactions between the inserted ions decreases exponentially as a function of the separation between ions. This screening of the electrostatic interactions increases with decreasing the pore width and when the pore width is roughly equal to the diameter of the ions these interactions become truly short-range.22 As a result of such strong screening, the counterions can pack closer to each other, generating the socalled “superionic states” or states of high density of counterions; the formation of such densely packed counterion states in narrow nanopores, therefore, is consistent with the increased values of capacitances.184 The original model was proposed for the slit nanopore geometry22 but similar results were obtained for cylindrical geometry as well.185,186 Kornyshev and co-workers provided the basic theoretical understanding of the mechanisms for ionic liquid electrolyte restructuring and charge storage in narrow nanoporous electrodes which can be summarized as follows: (i) at low voltages the primary mechanism for electrolyte restructuring is the co-ion removal from the pore,185 (ii) at higher voltages (around 1−2 V), a sharp phase transition consisting of a complete co-ion removal from the nanopore can occur, which generates a spike in DC at the corresponding voltage,22 and (iii) at even higher voltages where all co-ions are removed, further charge accumulation is possible by the counterion densification due to screening of the repulsive electrostatic interactions between the counterions by the nanoconfinement effects.186 These three regimes were later confirmed by atomistic simulations and are schematically illustrated in Figure 4 by ion density profiles and DC as a function of electrode voltage.187−190 The dependencies shown in Figure 4 are typical for what we observed for a number of various RTILs inside subnanometer pores. Near PZC the composition of electrolyte is changing in both electrodes with the increasing of the electrode potentials due to the expulsion of co-ions. At certain electrode potentials, an abrupt transition of complete expulsion of co-ions occurs. At this transition voltage, the total density of ions inside the nanopore decreases.

An electrolyte layer within 2.0 nm from the electrode surface is sufficient to quantitatively explain the DC shape as a function of potential. In the context of improving the energy density in supercapacitors, the experimental work of Largeot et al.168 was a turning point triggering extensive further experimental and theoretical research. This experimental work showed that it is possible to create nanoporous carbon based electrodes with well-controlled pore widths and polydispersity. In this work, it was reported that although the electrode materials with wider pores (with width >1 nm) have generated capacitances comparable to those for nonporous electrodes (i.e., about 7 μF/cm2), the subnanometer-wide pores showed a sharp increase in the capacitance with a maximum of ≈13 μF/cm2 for nanopores having 0.7 nm widths.168 Other experiments found similar enhancement for various carbon-based electrodes and electrolytes consisting of either RTILs or solutions with salts.169−172 For example, the more recent experiments of Li et al.173 reported capacitances of up to 14 μF/cm2 for their nanoporous structures, whereas Hsia et al.174 estimated their capacitances to ≈20 μF/cm2 (or volumetric capacitances of 2.5F/cm3) for 3D ultrathin carbon-based foams. On the other hand, Centeno and co-workers reported little or almost no variation of capacitances for solutions of ionic salts in acetonitrile solvent,175−178 although it is understood from classical DFT studies that the behavior of nanoconfined solutions of ions and neat RTILs can be quite different.179 Also, in recent simulation works Merlet et al.180,181 have utilized carbon-based nanoporous electrode structures obtained from reverse Monte Carlo technique and demonstrated an agreement between the simulation data and the experimental capacitance found by Largeot.168 Figure 3 summarizes the capacitance enhancement due to nanoconfinement from the experimental studies mentioned above and several other works that included data on flat (nonporous) electrodes.172,182,183 Note that in most of these works the energy storage was characterized by the integral capacitance (IC), which is a measure of how much charge is stored by the electrode for a 3600



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inside the pore will occur leading to a sharp increase in the DC and IC. We have observed this type of mechanism in simulations of [C2mim][TFSI] on the negative electrode comprised of an array of carbon-chains spaced at 7.2 Å.136 In principle, this type of transition can be expected for any RTIL electrolyte inside nanopores that have the width sufficiently small that the steric interactions do not allow the electrolyte to wet the uncharged pore, yet these repulsive interactions can be overcome by electrostatic interactions at some higher voltages. The role of the nonionic (albeit polar) solvents on the capacitance enhancement in nanopores was elucidated with classical DFT simulations. Jiang and co-workers showed that the presence of a nonionic solvent decreases the extent of capacitance enhancement as compared to RTIL electrolytes.179,192,196 This might explain the lack of substantial (if any) capacitance enhancement in Centeno et al. work mentioned above.176 It also appears that the capacitance enhancement for nonionic solvent based electrolytes can have a complex dependence on the solvent polarity showing a maximum at certain values of solvent dielectric constant.196 This issue certainly needs further and more systematic investigation by both experiments and atomistic simulations. Although many molecular simulations showed consistent trends on the capacitance enhancement for RTIL electrolytes inside nanoporous electrodes, the magnitude of the capacitance enhancement reported from most simulations for slit pores would still appear quantitatively in disagreement with experimental data. For example, although Feng et al.191 and Wu et al.188 reported ICs close to ≈9−10 μF/cm2, their corresponding capacitance for flat surfaces or wider pores was about ≈6.5−7 μF/cm2, hence a relative enhancement of only 40−50% was found for slit pores compared to 100% enhancement reported in experiments for the same electrolyte. Similarly, we found lower values of the relative capacitance enhancement for a variety of RTILs in slit-like nanopores with atomically smooth walls.189,190 Hence, some additional factors, rather than just the nanoconfinement and the resulting screening in smooth surface pores, should be contributing to the capacitance enhancement. As shown in Figure 5, the geometry and the topography of the nanopore walls can have a significant impact on the enhanced capacitance. While nanopores with atomically flat walls generated capacitances of up to 7−8 μF/cm2 for most RTILs, an additional (and significant) increase of capacitance for up to 10−11 μF/cm2 (or slightly more than 100% enhancement compared to the IC on flat surfaces) was possible for nanopores with atomically rough walls exposed to electrolyte.190 Therefore, we suggest that it is possible that a change in the nanopore structure from relatively smooth walls for wide pores to strongly rough/edgy walls for subnanometer pores can significantly contribute to the capacitance enhancement observed experimentally. Figure 6 illustrates this hypothesis and indicates that in wider pores the RTILs inside the nanoporous electrodes behave similar to what simulations predict for slit nanopores with flat walls, however, in subnanometer pores the behavior is more consistent with what simulations predict for nanopores with rough walls. In these rough pores, the enhancement mechanism consists of a combination of two factors: (i) an enhanced co-ion expulsion from the nanopore (i.e., the expulsion occurs at lower voltages than in slit pores) and (ii) a stronger condensation of counterions possible in rough pores.

Figure 4. Schematic representation of a typical DC and ion densities for a RTIL inserted in subnanometer slit pore, as a function of the electrode potential. The values on y axis represent a typical range obtained from MD simulations of RTILs and discussed in ref 190. These plots show a sharp co-ion expelling from the pore at a certain values of potentials, therefore generating large peaks in DC.

However, because of the increased charge separation (i.e., the co-ions were expelled from the pore) the DC has a spike at this voltage and overall a well-defined camel-shape dependence. At even larger potentials, the charge accumulation occurs through densification of counterions inside the nanopore. The presence of these sharp peaks in DC at the corresponding demixing potentials are the primary reasons for enhanced values of IC assuming that the IC was measured at potentials higher than those where the sharp expelling of co-ions from the nanopore occurs. Note that with increasing the nanopore width, it is possible to observe an oscillatory behavior of IC as a function of pore widths.179,188,191−193 In wider pores, the expulsion of coions is not as abrupt as for subnanometer pores shown in Figure 4 because in wider pores, the co-ions can avoid the electrostatic repulsions from the charged surface by accumulating toward the center of the pore and allowing the counterions to accumulate near the (oppositely charged) nanopore wall. Certain widths of the nanopore are more commensurate with the formed layer structure inside the nanopore and this leads to oscillations in capacitance. However, the capacitance enhancement at larger widths is only about 15% (relative to the nonporous electrodes), and hence, the largest enhancement is observed in the subnanometer pores where the nanopore width is comparable with the RTIL ion dimensions. In addition to the mechanism discussed above and shown in Figure 4, a couple of other possible capacitance enhancement mechanisms are possible in nanoporous electrodes. For example, in some systems, such as the [pyr13][FSI] RTIL, the change in the electrolyte composition inside the nanopore can occur without sharp transitions and abrupt expulsion of coins. In this case, the DC has an overall bell-shape with a maximum near PZC.190 Another type of capacitance enhancement mechanism was suggested by Kiyohara et al.194,195 for systems where the electrolyte does not wet the nanopore at low voltages. In this case, as the electrode potential increases, at a certain threshold potential a sharp counterion accumulation 3601



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The utilization of subnanometer pores to enhance the capacitance, however, can result in a slowing down of ion dynamics and hence the kinetics of the charging/discharging processes. This is an important drawback as it could negate the key advantage of the non-Faradaic energy storage, specifically the ability of these devices to charge/discharge faster and to deliver more power. It is then important to understand if it could be possible to design electrode materials that will generate high power densities despite the tight subnanometer confinement. Molecular simulations can predict how much power density can theoretically be expected from the capacitive storage in subnanometer pores. For example, shown in Figure 7

Figure 5. Integral capacitance (doubled) as a function of pore geometry as obtained from atomistic MD simulations. The potential difference between electrodes varied in simulations between 2 and 3 V, which is within the electrochemical stability window for many RTILs and of practical interest for energy storage applications. Nanopores with rough edges generated noticeable larger capacitances.

Figure 7. Kinetics of discharging of a nanoporous electrode by [pyr13][FSI] electrolyte. The initial system was equilibrated at a potential difference ΔU = 3 V. At time t = 0, ΔU was set to zero and the kinetics of discharging was monitored. Within 10 ns of simulations the system has discharged 90% of its original charge.

is the rate of discharge for a system comprised of a RTIL electrolyte and two slit-pore electrodes separated by 140 Å. The pores had the widths of 7.5 Å and the electrolyte was inserted over a ≈60 Å depth inside the slits. The system was initially charged and equilibrated at the potential difference between electrodes ΔU = 3 V. Then at time t = 0 the potential difference was set to ΔU = 0 V and the rate of the electrode discharging (due to the electrolyte rearrangement in the nanopore) was monitored as a function of time. As shown in Figure 7, the electrode loses about 90% of its initial charge over a time scale of 10 ns. Similar discharge rates were previously reported in ref 198. This result indicates that the rate of discharge under certain potential regimes can be very fast (and therefore the delivered power can be very high) if the nanopores are relatively short and there is a relatively short separation between the oppositely charged pores. We speculate that a design of 3D hierarchical nanostructures where the electrolyte has an easy access to the narrow yet short nanopores and the separation between the positive and negative electrodes is minimal will significantly advance the next generation of EDLCs with very high power rates. However, for such devices, it might be quite difficult to prevent overheating during discharging. From this consideration the RTILs are particularly attractive, as these electrolytes have a very low vapor pressure and, hence, can withstand substantial overheating without evaporation or boiling. Future Directions. Due to the great demand for efficient energy storage, the research in the field of electrified interfaces and supercapacitors is expected to increase significantly from both theoretical and experimental points of view. Theoretical

Figure 6. Comparison between the relative enhancement of capacitance for nanopores having atomically smooth and rough walls. Narrow nanopores with atomically rough walls can generate capacitance enhancement comparable to experiment. This picture is reprinted from the ACS Nano (ref 190). Copyright 2015, American Chemical Society.

Therefore, it appears that in order to maximize the charge storage in porous electrodes, the nanopores with rough/edgy walls are preferred. A limiting case of such electrodes would be a network of single chains or narrow strands of conjugated structures. The highest non-Faradaic capacitance (normalized per mass of electrode) predicted so far by simulations is ≈300− 350 F/g (at ΔU = 3 V) for arrays of conducting single chains.136 Similar range of IC (≈325 F/g) was recently shown experimentally for graphene aerogels by Jung et al.197 However, it should be noted that the electrochemical stability of such 1Dchains is lower than of 2D-graphene like structures, particularly at high voltages. Furthermore, these networks of 1D-chains can have low electronic conductivity, although this can be overcome by doping them with heteroatoms (e.g., metals).

It appears that in order to maximize the charge storage in porous electrodes, the nanopores with rough/edgy walls are preferred. 3602



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could have a great impact in social, medical, and military applications. These technologies will have to deal with the incorporation of the capacitive energy storage in textiles. Conductive yarns based on modified graphene oxide passivated with MnO2 were used to fabricate knittable, weaveable, and wearable supercapacitors214 that can have energy densities as high as 480 μF/cm2.215 Textile compatible capacitive storage was obtained recently by spraying and drying aqueous and acidic solutions of multiwall carbon nanotubes on Nafion membranes.216 On-a-chip capacitive storage can represent an interesting approach to power portable electronics that may possibly allow further miniaturization of electronics. Because of the small distance between the oppositely charged plates, the power density of the on-a-chip microsupercapacitors could be thousands of times higher than that from the conventional energy sources, therefore enabling faster operation.217,218 Also, integrating solar cells with supercapacitors can enable applications in self-powered smart-textiles or autonomous robotics. Self-powered “energy fibers”, which both collect the energy from the sun via a polymer-based solar cell and store it by the integrated supercapacitor, were recently demonstrated experimentally.219 Nanosupercapacitor energy storage could have intriguing applications in bioengineering and medicine. For example, the biocompatible DNA-based hydrogel the DNA can be used as a template for the layer-by-layer assembly of polyelectrolytes, polyanilines, or nanotubes to build nanosupercapacitors that subsequently can be used as implantable and biocompatible energy sources for in vivo applications.220,221 Although the opportunities for novel designs and applications of the capacitive energy storage devices are rapidly expanding, the complexity of correlations and mechanisms responsible for the charge storage and charging/discharging processes will necessitate molecular level understanding of the governing phenomena. In this regard, the enhancement of molecular simulation techniques as well as multiscale modeling approaches that can connect the atomic/molecular scale correlations with the macroscopic device performance will play an essential role.

research and in particular molecular simulations employing accurate force fields and models for electrolyte/electrode interface are in an excellent position to address the fundamental aspects regarding the EDL structure and the mechanisms of charge storage, which are still elusive and sometimes perhaps controversial. Having demonstrated the ability to provide quantitative agreement with the experimental data, these simulations can also help to elucidate the origins of the apparent disagreements between various experimental techniques. For example, the AFM measurements tend to predict a somewhat different (i.e., more structured and extended) EDL structure than the SFG spectroscopy. The electrochemical impedance spectroscopy, which is a widely utilized technique to measure the DC, usually predicts lower DCs as compared to the cyclic voltammetry199−201 and showed inconsistency with the galvanostatic charge/discharge method for several electrochemical systems.202−204 The origin of these disagreements between different techniques is still not well understood. The impedance spectroscopy methods require an equivalent circuit; however, the assignment of such a circuit is not unique and often it is hard to associate specific physical phenomena with chosen circuit elements or their combination.205 We believe that an understanding of these problems from a molecular scale perspective may be essential in facilitating the interpretation of experiments. Future research in capacitive energy storage could be critically important in deploying new technologies. In this regard, a few aspects will be briefly presented in the remainder of this Perspective. When the limit of non-Faradaic storage is reached, we anticipate that the future capacitive energy storage devices will utilize both the electrostatic and the pseudocapacitive (redox) mechanisms, as well as a variety of electrolytes beyond conventional RTILs or nonionic solvent-based electrolytes. It is an increasing trend to consider supercapacitors in combination with other energy storage or conversion devices. For example, a combination of both supercapacitor and Libattery enables regenerative braking and increased acceleration power in electric vehicles. Also, hybridization of fuel cells with supercapacitors or with both Li-batteries and supercapacitors206 can increase the fuel economy by as much as 24−28% in vehicle transportation.207 Therefore, even if the main source of energy is based on either fuel cell or electrochemical batteries, it should not be surprising that the supercapacitors will play a central role in future electric vehicles. Besides the increased energy and power density for automotive applications, there is a number of other applications where the supercapacitors will likely have a great future. For many of these applications the issue of miniaturization of the supercapacitors has to be addressed. Cheap, disposable, optically transparent capacitive storage devices are extremely important in designing flexible touch-screen based electronics. Such devices could, for example, replace the conventional paper printing with a dynamically/interactively changing text on a sheet-of-paper-thin touch-screen. These will require a fundamentally new approach in the design of ultralight capacitive energy storage.3,208 In principle, such devices can be based on conventional materials as it has been already demonstrated that paper,209,210 cellulose fibers,211 and wood-based212,213 supercapacitors are possible due to the excellent porosity of cellulose. “Smart” clothing comprised of wearable electronic textiles containing microcomputers incorporated in their structure that allows interaction with both the body and the environment

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare the following competing financial interest(s): The authors declare no conflict of interest regarding the material presented in this manuscript. Although Prof. Bedrov is a co-owner of the Wasatch Molecular Inc. (WMI), a small start-up company that specializes in consulting services and development of customized force fields for molecular simulations, the materials, results, and views presented here are the outcomes of the academic research that have been published in the open literature and are not related to WMI activities. Biographies Jenel Vatamanu received his B.Sc. from Dunarea de Jos University of Galati, Romania, M.Sc. from Al. I. Cuza University of Iasi, Romania (thesis advisor: Prof. Gelu Bourceanu), and Ph.D. from Queen’s University, Canada (thesis advisor: Prof. Natalie M. Cann). He holds a Research Associate position at the University of Utah Material Science and Engineering Department and his current research includes 3603



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Force Using Classical Density Functional Approach. J. Chem. Phys. 2015, 142, 174704. (15) Forsman, J.; Woodward, C. E.; Trulsson, M. A Classical Density Functional Theory of Ionic Liquids. J. Phys. Chem. B 2011, 115, 4606− 4612. (16) Siepmann, J. I.; Sprik, M. Influence of Surface Topology and Electrostatic Potential on Water/Electrode Systems. J. Chem. Phys. 1995, 102, 511−524. (17) 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. (18) Pastewka, L.; Järvi, T. T.; Mayrhofer, L.; Moseler, M. ChargeTransfer Model for Carbonaceous Electrodes in Polar Environments. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 83, 165418. (19) Wang, Z.; Yang, Y.; Olmsted, D. L.; Asta, M.; Laird, B. B. Evaluation of the Constant Potential Method in Simulating Electric Double-Layer Capacitors. J. Chem. Phys. 2014, 141, 184102. (20) Merlet, C.; Péan, C.; Rotenberg, B.; Madden, P. A.; Simon, P.; Salanne, M. Simulating Supercapacitors: Can We Model Electrodes as Constant Charge Surfaces? J. Phys. Chem. Lett. 2013, 4, 264−268. (21) Merlet, C.; Limmer, D. T.; Salanne, M.; van Roij, R.; Madden, P. A.; Chandler, D.; Rotenberg, B. The Electric Double Layer Has a Life of Its Own. J. Phys. Chem. C 2014, 118, 18291−18298. (22) Kondrat, S.; Kornyshev, A. Superionic State in Double-Layer Capacitors with Nanoporous Electrodes. J. Phys.: Condens. Matter 2011, 23, 022201. (23) 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. (24) Kiss, P. T.; Sega, M.; Baranyai, A. Efficient Handling of Gaussian Charge Distributions: An Application to Polarizable Molecular Models. J. Chem. Theory Comput. 2014, 10, 5513−5519. (25) Reed, S. K.; Madden, P. A.; Papadopoulos, A. Electrochemical Charge Transfer at a Metallic Electrode: A Simulation Study. J. Chem. Phys. 2008, 128, 124701. (26) Golze, D.; Iannuzzi, M.; Nguyen, M.-T.; Passerone, D.; Hutter, J. Simulation of Adsorption Processes at Metallic Interfaces: An Image Charge Augmented Qm/Mm Approach. J. Chem. Theory Comput. 2013, 9, 5086−5097. (27) Yeh, I.-C.; Berkowitz, M. L. Ewald Summation for Systems with Slab Geometry. J. Chem. Phys. 1999, 111, 3155−3162. (28) Heyes, D. M. Pressure Tensor of Partial-Charge and PointDipole Lattices with Bulk and Surface Geometries. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 49, 755−764. (29) Heyes, D. M. Molecular Dynamics of Ionic Solid and Liquid Surfaces. Phys. Rev. B: Condens. Matter Mater. Phys. 1984, 30, 2182− 2201. (30) Kawata, M.; Mikami, M. Rapid Calculation of Two-Dimensional Ewald Summation. Chem. Phys. Lett. 2001, 340, 157−164. (31) Kawata, M.; Mikami, M.; Nagashima, U. Computationally Efficient Method to Calculate the Coulomb Interactions in ThreeDimensional Systems with Two-Dimensional Periodicity. J. Chem. Phys. 2002, 116, 3430−3448. (32) Kawata, M.; Mikami, M.; Nagashima, U. Rapid Calculation of the Coulomb Component of the Stress Tensor for Three-Dimensional Systems with Two-Dimensional Periodicity. J. Chem. Phys. 2001, 115, 4457−4462. (33) Kawata, M.; Nagashima, U. Particle Mesh Ewald Method for Three-Dimensional Systems with Two-Dimensional Periodicity. Chem. Phys. Lett. 2001, 340, 165−172. (34) Pensado, A. S.; Malberg, F.; Gomes, M. F. C.; Padua, A. A. H.; Fernandez, J.; Kirchner, B. Interactions and Structure of Ionic Liquids on Graphene and Carbon Nanotubes Surfaces. RSC Adv. 2014, 4, 18017−18024. (35) Kirchner, B.; Hollóczki, O.; Canongia Lopes, J. N.; Pádua, A. A. H. Multiresolution Calculation of Ionic Liquids. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2015, 5, 202−214.

theoretical studies of electric phenomena and energy storage devices. Web site: https://faculty.utah.edu/u0615401-JENEL_VATAMANU/ biography/index.hml. Dmitry Bedrov received B.S. in Thermophysics at the Odessa State Academy of Refrigeration and Ph.D. in Chemical Engineering at the University of Utah, where he currently holds an Associate Professor position at the Materials Science and Engineering Department. His primary research focus is multiscale molecular modeling of materials for energy applications and soft-condensed matter. Web site: http:// www.eng.utah.edu/~bedrov/.

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ACKNOWLEDGMENTS The authors would like to acknowledge the support by the U.S. Department of Energy through the SISGR Program Grant Number DECS00001912 and by the Army Research Laboratory under Cooperative Agreement number W911NF12-2-0023. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. We gratefully acknowledge Dr. Oleg Borodin for useful discussions and for providing us with customized forcefields for the study of RTILs at charged electrodes. We would like to thank Dr. Mihaela Vatamanu for valuable comments and discussion of the manuscript.

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REFERENCES

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