Charge storage at the nanoscale: understanding the trends from the molecular scale perspective

Jenel Vatamanu *ab, Oleg Borodin a, Marco Olguin a, Gleb Yushin c and Dmitry Bedrov *b
aElectrochemistry Branch, Sensors and Electron Devices Directorate, Army Research Laboratory, 2800 Powder Mill Rd., Adelphi, MD 20703, USA. E-mail: jenel.vatamanu@utah.edu
bMaterials Science & Engineering Department, University of Utah, 122 South Central Campus Drive, Salt Lake City, UT 84112, USA. E-mail: d.bedrov@utah.edu
cSchool of Materials Science, Georgia Institute of Technology, 771 Ferst Dr. NW, Atlanta, GA 30332, USA

Received 13th June 2017 , Accepted 29th August 2017

First published on 29th August 2017


Supercapacitors or electrical double layer (EDL) capacitors store charge via rearrangement of ions in electrolytes and their adsorption on electrode surfaces. They are actively researched for multiple applications requiring longer cycling life, broader operational temperature ranges, and higher power density compared to batteries. Recent developments in nanostructured carbon-based electrodes with a high specific surface area have demonstrated the potential to significantly increase the energy density of supercapacitors. Molecular modeling of electrolytes near charged electrode surfaces has provided key insights into the fundamental aspects of charge storage at the nanoscale, including an understanding of the mechanisms of ion adsorption and dynamics at flat surfaces and inside nanopores, and the influence of curvature, roughness, and electronic structure of electrode surfaces. Here we review these molecular modeling findings for EDL capacitors, dual ion batteries and pseudo-capacitors together with available experimental observations and put this analysis into the perspective of future developments in this field. Current research trends and future directions are discussed.


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Jenel Vatamanu

Jenel Vatamanu received his B.Sc. from Dunarea de Jos University, Galati, Romania, M. Sc. from Al. I. Cuza University, Iasi, Romania, and Ph.D. from Queen's University, Canada. His research background is in physical and theoretical chemistry. His current research focuses on electricity based energy storage devices, faradaic and non-faradaic phenomena at electrified interfaces, ion transport in nanopores, electrodeposition, dendrite formation in Li-ion batteries, and the implementation of efficient techniques for large scale atomistic simulations.

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Oleg Borodin

Oleg Borodin is a scientist at the Electrochemistry Branch of the Army Research Laboratory (ARL), Adelphi, MD, working on multiscale modeling of materials for energy storage applications. His expertise includes quantum chemistry calculations and high throughput screening of electrochemical reactions in electrolytes and at electrode/electrolyte interfaces, MD simulations of liquid, ionic liquid, polymeric and solid electrolytes for lithium battery applications, SEI components, and electric double layer structures.

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Marco Olguin

Marco Olguin obtained both a B.S. and a M.S. degree in Chemistry from the University of Texas at El Paso. He then joined the Computational Science Program at the University of Texas at El Paso in 2010 for his doctoral studies on an excited state DFT method implemented in the NRLMOL code under the supervision of Prof. Tunna Baruah and Prof. Rajendra Zope. Since joining the Computational Science Program at the University of Texas at El Paso, he has continuously worked with High Performance Computing (HPC) systems running large scale simulations. He is currently working as a postdoctoral research associate at the US Army Research Laboratory under Dr Oleg Borodin, where he performs computational molecular modeling in application to energy storage systems.

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Gleb Yushin

Gleb Yushin is a Professor at the School of Materials and Engineering at the Georgia Institute of Technology, a co-Founder of Sila Nanotechnologies, Inc. (an engineered materials company focused on dramatically improving energy storage) and a co-Editor-in-Chief of Materials Today. Prof. Yushin's research is mostly focused on advancing energy storage materials and devices for electronic devices, transportation and grid applications. Prof. Yushin has co-authored over 40 patents and patent applications, over 110 invited and keynote presentations and seminars and over 140 publications on nanostructured materials for energy related applications, which received over 16,000 citations.

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Dmitry Bedrov

Dmitry Bedrov is an Associate Professor at the Department of Materials Science & Engineering at the University of Utah, and a co-founder and the President of Wastach Molecular, Inc. (a consulting company focused on multiscale modeling of materials and systems). Prof. Bedrov research is focused on multiscale modeling of complex systems and materials, with specific emphasis on energy storage and conversion devices, including batteries, supercapacitors, and fuel cells. Prof. Bedrov has published over 145 publications.


1. Introduction

The increasing demand for efficient, reliable and affordable energy storage devices stimulated research into faradaic and non-faradaic phenomena occurring at electrode–electrolyte interfaces. In faradaic devices, such as batteries or pseudo-capacitors, charge is stored due to electrochemical reactions occurring at electrodes. In contrast, capacitors store energy via non-faradaic processes (i.e., involving physical phenomena without chemical reactions). Depending on the type of material and charge storage mechanism involved there are three types of capacitive storage devices: dielectric capacitors, electrolytic capacitors and electric double layer capacitors (EDLCs) or supercapacitors.1,2 In dielectric capacitors, the space between electrodes is filled with a dielectric material and the energy storage involves reorientation of material local dipoles such that they oppose the externally applied electrostatic field between the plates. These capacitors have the fastest charge–discharge rate, operate at high voltages (kV) and in alternating current. However, the stored energy normalized per mass of dielectric material in this type of capacitor is small, as shown in Fig. 1. The energy density of dielectric capacitors can be increased by the utilization of dielectrics with high electric permittivity or ferroelectrics, e.g., class II ceramic capacitors.3,4 Electrolytic capacitors are comprised of two metal electrodes, typically made of aluminum, tantalum or niobium, with an ion conducting liquid or solid electrolyte between one of the electrodes and a dielectric material formed by the oxidation of the surface of the other electrode.5 These capacitors are commonly utilized in electronics or as power supplies and their current market size exceeds US$6 billions per year.1,6,7 Among the disadvantages of electrolytic capacitors are their relatively short lifetime and large leakage currents.
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Fig. 1 Ragone plot illustrating the power versus energy density for various electricity based energy storage devices. Figure is based on data compiled from several sources.24,249–254

EDLCs, on the other hand, are usually comprised of porous electrodes and liquid electrolytes. The charge storage is achieved via double layer restructuring due to an applied electric field causing ion diffusion and adsorption at the electrode surface or inside the nanoscopic pores. As the energy in EDLCs is stored within their thin interfacial layer, the enhancement of the energy density arises primarily from the increased specific surface area (SSA) of the porous electrodes. Currently, activated carbon is one of the most commonly used electrode materials made by charring and partially oxidizing the precursor using steam or carbon dioxide to create or enhance nanoscopic pores, often followed by purification to reduce impurities. While coconut shell-derived activated carbon (SSA of around 2000 m2 g−1) is a popular, low cost ($4 for commodity activated carbon and $15 per kg for EDLC-grade carbon in 2013) material that has been considered as the most commonly used material for practical applications in EDLCs,8 other natural precursor derived activated carbons9,10 as well as more advanced C-based materials have been widely investigated by academic groups.8,9,11,12 Extensive experimental work focused on understanding and design of nanostructured materials for energy storage applications enabled an increase in the SSA of C-based porous electrodes from a few hundreds of m2 g−1 in powders or activated carbons to 2000–3500 m2 g−1 in various carbide-derived carbons (CDCs), C-onions, zeolite or silica or alumina-templated carbons, Kroll carbons, graphene, polymer-derived carbons, vertically aligned C-nanotubes, aerogels, nanotubes and carbon-fibers.2,9,11,13–22 Recent research showed that it is technically possible to synthesize porous electrode materials based on 3D-graphenes with a SSA as large as 4000 m2 g−1.23 Many of these nanostructured materials, such as nanotubes or 3D-graphenes, unfortunately, have a low packing density resulting in low volumetric energy density.24 Low volume density electrode materials increase the amount (and hence the weight and cost) of inactive components present in EDLCs such as the bulk electrolyte, current collectors, separator, binder, connectors, and packaging therefore making such low-density electrodes much less attractive for the assembly of thin electrode cells.8,24 Hence, both volumetric and gravimetric energy densities as well as electrode thickness need to be considered as performance metrics in addition to the commonly considered parameters of capacitance per unit surface area or per mass of electrode material.

In comparison with dielectric and electrolytic capacitors, EDLCs with highly porous electrodes achieve the highest non-faradaic capacitance and charge/energy density25 making them suitable for applications requiring intermediate power density over longer-time discharge, e.g., emergency doors, memory backups, car starters, detonators, pulsed lasers, pacemaker devices, defibrillators, electric forklifts, cranes, and even electric buses and trains.8 Almost half of today's supercapacitor production is devoted to electric vehicle transportation (EVT).26 In EVT, the addition of supercapacitors to electrochemical batteries or fuel cells enables regenerative braking and faster acceleration, increases the overall energetic efficiency up to 20–25% and improves the life-time of batteries.27,28 EVT based exclusively on supercapacitors (or the so-called capa vehicles) was already tested as a non-polluting and energy efficient alternative for inner-city transportation that requires multiple stops (where recharging could be done in as little as half a minute) and relatively short distances (few miles) between stops. Such supercapacitor-only based EVT apparently is 20–50% more energy efficient than over-the-line electric vehicles (trolleys and electric trains).29 EDLCs are also utilized in bridge power applications, where immediate power availability may be difficult to achieve, such as in Uninterruptible Power Supply (UPS) systems utilizing generators, fuel cells or flywheels as the main power backup. EDLC burst power applications are still limited to frequencies lower than 100 Hz and often sacrifice the energy density to increase the power density.30 Supercapacitors could also be ideal for storing relatively small amounts of solar, mechanical, and thermal energy harvested from (relatively small) environmental energy fluxes.31–33 For example, traffic speed indicators or video cameras could be powered by a combination of solar cells and supercapacitors. Supercapacitors can be scaled to any desired size from nano/micro-meter in electronics to locomotive/wagon size (of tens of tons) in railroad transportation.

Because of the inherent advantages of reversible charge storage, it is expected that the demand for non-faradaic energy storage will increase in the near future. Specifically, it is projected that the supercapacitor market will rise from about US$1 billion per year today to several billions in the next few decades.7,29 However, the larger scale deployment of supercapacitors will depend on how the current and future research addresses their shortcomings which will be discussed in the next sections.

EDLC electrolytes are usually based on aqueous or aprotic organic based solvents, such as propylene carbonate (PC) or acetonitrile (AN). Electrolytes with aqueous solvents at typical salt concentrations (0.1–3 M) are often considered for high rate applications due to their higher conductivity but they suffer from narrow electrochemical stability windows, thus limiting the device energy density. Recent extension of the aqueous electrolyte electrochemical stability window to 3 V by increasing salt concentration has offered an intriguing possibility to further increase the aqueous EDLC energy density by suppression of the oxygen evolution at the positive electrodes and pushing anodic stability to higher voltages.34–38 Aprotic solvents have intermediate stability and rate characteristics between aqueous electrolytes and room temperature ionic liquids (RTILs) and were shown to be able to operate at extremely low temperatures down to −70 °C provided that the electrode porosity and microstructure are carefully optimized.39 RTILs consist of relatively bulky organic ions that are liquid at room temperature. They yield acceptable ionic conductivity, low vapor pressure, toxicity and flammability, which makes them attractive candidates for EDLCs if their cost can be reduced.40,41 Also, a wide variety of possible chemical structures of cations and anions suitable for RTILs allows for further chemical tailoring of these liquids to obtain the desired properties. In some cases, the addition of an aprotic solvent to RTILs is useful because the solvent can decrease the viscosity, increase the mobility of ions, and extend the lower end of the operating temperatures. The usage of asymmetric (in size and shape) ions or mixtures of ionic liquids also provided a viable strategy for extending the liquid range to lower temperatures beyond the melting point of traditional solvents.42

Unlike continuous double layer formation that occurs in EDLCs with increasing voltage, anion insertion into graphite occurs at well-defined potentials, typically around 4–5 V vs. Li/Li+. Such anion intercalation expands the graphite interlayer spacing to dimensions comparable to the smallest pore sizes used in EDLCs, giving rise to some similarity between them as we discuss below. Due to a well-defined anion intercalation potential that is analogous in many ways to lithium intercalation in graphite, devices relying on both anion and cation faradaic reactions are classified as dual-ion batteries (DIBs). In addition, in DIBs with all-carbon electrodes, alloyed anodes could replace graphite negative electrodes leading to a further increase in the energy density of DIBs. DIBs offer intermediate energy density between lithium ion batteries (LIBs) and EDLCs as shown in Fig. 1. Some of the challenges of DIBs are a relatively low volumetric capacity (compared to LIBs) experimentally observed in the graphite cathode and the need to identify electrolytes that are compatible with the relatively high cathode voltages (4–5 V vs. Li/Li+). DIB energy density is determined by the capacity of electrodes, voltage between electrodes and ability of the electrolyte to provide both lithium cations and anions for intercalation into the anode and cathode. Thus, it is important to choose electrolytes with high salt solubility and conductivity over a wide concentration range in addition to ensuring that the electrolyte is electrochemically compatible with both electrodes. Unlike DIBs, current LIBs rely on shuttling lithium ions between the graphite negative anode and intercalation cathode and do not rely on the electrolyte as the only source of ions for intercalation. LIB specific density is largely determined by electrode capacities and voltage between electrodes after accounting for the weight of the electrolyte, current collectors, separator and packaging. Current LIBs require electrolytes that are either electrochemically stable at the electrode potentials during charging or form a stable ionically conducting and electrically insulating passivation layer to kinetically protect the electrolyte from undesirable redox reactions at the electrodes. A high gravimetric and, especially, high volumetric capacity and voltage of LIBs cathodes, such as lithium cobalt oxide and lithium nickel cobalt manganese oxide, yield high energy densities for LIBs (see Fig. 1) when paired with graphite or alloyed anodes, making LIBs the technology of choice for portable electronics, hybrid and electric vehicles, and power tools.43

In EDLC and DIB devices discussed above, molecular scale phenomena are key in controlling the performance and design strategies. These phenomena include (i) more efficient packing of ions in the EDL or inside pores at lower voltages to increase the capacitance; (ii) role of quantum capacitance to ensure that it is not a limiting factor; (iii) faster transport of ions inside the pores; (iv) intercalation kinetics for faradaic devices; (v) improved electrochemical stability of electrolytes to expand the electrochemical window or to control the passivation layer for hybrid devices; (vi) design of hybrid micro- and macro-porous architectures to optimize transport and capacitance. Below we will discuss these molecular scale phenomena and their influence on the efficiency of energy storage devices.

2. Common challenges for capacitive energy storage

Lower energy density than in batteries

The current generation of commercially available supercapacitors can store a few (≈1–5) W h kg−1 (ref. 44) which is less than 2.5% of the energy density stored by typical LIBs (≈150–250 W h kg−1).9,43 Supercapacitors with energy densities of around 5–10 W h kg−1 currently represent the higher end of the technology.45,46 However, recent research showed that significantly larger non-faradaic capacitances are possible. For example, modified graphene pores47 can achieve an energy density of 20 W h kg−1 and have an excellent power retention of ≈97% after tens of thousands of cycles. Unfortunately, carbon surface functionalization often leads to a faster self-discharge. Integrating capacitors with pseudo-capacitors or utilizing asymmetric faradaic/non-faradaic supercapacitors can also increase the energy density by at least one order of magnitude, albeit at the expense of losing power density and shortening the lifetime.

Higher production cost

Despite the higher cost of EDLCs per kWh (ranging today between $3000 and $6000 per kW per h)48 compared to the cost of Li-ion-batteries ($150–$300 per kW per h),48 the longer life-time of EDLCs (10–20 years) compared to batteries (1–5 years) makes them attractive for certain applications requiring long lifetime and pulse power, especially if their production cost can be further reduced.49

Lower operating voltage

In order to stay within the electrochemical stability window of the electrolyte, supercapacitors operate at relatively low potentials, typically 1–2 V, in some cases up to 3 V. This disadvantage can be addressed through the design of new generations of electrochemically stable electrolytes. Some recent studies indicated that RTILs might be stable at potentials above 3.5–4 V.50–53 Electrolyte long-term stability is also dictated by carbon electrode impurities. Supercapacitor grade carbon is a premium activated carbon which is purified to reduce ash below 1% and to reduce halogen and iron impurities below 100 ppm to enable extended cycling.8 It is not clear whether a further reduction in impurities needed to increase the cycling life is economically justified. Note that supercapacitors are connected either serially or via a combination of serial and parallel connections to achieve the desired potential while maintaining high capacitances. This approach requires balancing electronic circuitry to avoid overcharging, which leads to energy losses and cell voltages of 20–24 V.54

The potential is not constant during discharge

In contrast to LIB and DIBs, supercapacitors do not provide a steady constant potential during their discharge at constant current, but instead the potential decreases linearly as the stored energy is consumed. This could limit the maximum amount of delivered energy when it is not desirable to reduce the operating potential below a certain value. However, depending on the potential range, this disadvantage can be alleviated by the use of additional electronic circuitry (such as DC-to-DC step-up converters55) that flattens out the potential slope vs. time.

Higher leakages and faster self-discharge

A charged supercapacitor at infinite external resistance (or disconnected from an external circuit) will eventually lose charge and voltage over time. While some batteries can hold charge for months, supercapacitors will lose up to 20–90% of the initial charge in less than one month. This phenomenon, also called leakage or self-discharge,56 is extremely important because it effectively excludes EDLCs as viable long-term energy storage devices and limits their application in short-term non-faradaic charge buffers.

High dielectric absorption or soakage

Discharged capacitors can retain or gain some residual charge if left in an open circuit. Such charge retention can present an electrocution hazard. For this reason, supercapacitor electrodes are connected with a conducting wire (short-circuited) during transport or other maintenance. To summarize, for the supercapacitor technology to evolve beyond the short-term, high-power applications, the challenges mentioned above have to be addressed and the energy-normalized EDLC cell-level cost should be further reduced. Extensive theoretical, simulation and experimental studies have focused on some of these issues and identified future research directions to further improve the supercapacitor technology. Modeling and simulation studies are playing an increasingly important role in understanding the underlying molecular scale mechanisms involved in charge storage. In this regard, atomistic simulations are currently sufficiently accurate for reliable predictions and to assist the experiments. In this paper we critically review the modeling predictions reported over the last decade and give a new perspective on the data. Connection with recent experimental work will be presented throughout the paper.

3. Modeling the electrode–electrolyte interfaces

Classical molecular dynamics (MD) simulations are well suited for the examination of non-faradaic processes consisting of ion rearrangements within the EDL structure due to electrostatic interactions. However, there are a couple of aspects of concern regarding the simulation of electrode–electrolyte systems using classical MD: (i) model/force field selection for the electrolyte and (ii) representation of electrodes. It is important to emphasize that an appropriate choice of the electrolyte and electrode models can influence not only the quantitative accuracy of simulation predictions, but also the physical aspect studied at a qualitative level.57 A few comments regarding the model choice for simulations of supercapacitors are in order.

In molecular simulations, typically, electrolytes are treated using non-polarizable force fields. For many systems, including RTILs comprised of relatively bulky ions, such an approach provides a quite reasonable estimate of the EDL structure (assuming that the force field originally was parameterized to reproduce the bulk properties of the considered electrolyte). However, often such force fields, in order to improve the description of dynamical properties, scale the ion charges to ±0.7–0.9e values in an attempt to effectively capture the induced polarization and charge transfer effects.58 While this approximation might work well for bulk RTILs, it is not clear what consequence it will have near charged electrode surfaces where the electrolyte typically forms structured layers and hence isotropic bulk approximations are no longer valid. Moreover, in the case of solvent/salt electrolytes (e.g., a Li–salt solution in carbonate-based solvent mixtures), ignoring the electronic polarizability of certain chemical groups can lead to significant errors regarding the local coordination structure and dynamics of ions both in bulk electrolytes and at interfaces with electrodes. As shown by Borodin et al.,59 the inclusion of polarizabilities via induced dipoles for electrolytes containing small radius ions can dramatically improve the accuracy of prediction of thermodynamic, structural, and, particularly, dynamic properties. Therefore, a more reliable approach for classical simulations of electrode–electrolyte systems is to treat electrolytes using polarizable models, despite their somewhat larger computational cost. In this regard, it is interesting to point out several recent efforts to develop polarizable coarse-grained models for ionic systems60–62 that attempt to preserve the important induced polarization effects operative in these systems, yet to reduce the computational cost via coarse-graining.

The choice of the electrode model can also be very important to correctly capture the studied interfacial phenomena. Many simulation studies utilize a constant and uniformly distributed charge on the electrode surface, i.e., not taking into account the electrode polarizability due to EDL restructuring. However, as pointed out by Merlet et al.,57 there are instances where electrode polarizability must be considered. For example, to accurately describe the ion dynamics inside nanopores,63 the capacitance enhancement in nanoconfinements or at rough surfaces and the strong electrostatic screening resulting in “superionic states” in nanoconfinements all require the electrodes to be treated as explicitly polarizable.

The electrode polarizability can be implemented by allowing the electrode charges to fluctuate during simulations, such that the electronic characteristics of modeled electrode materials are accurately reproduced.64,65 For example, for metallic electrodes the charge equilibration scheme must place most of the charge (i.e., more than 95%) at the surface of the electrode and reproduce the well-known image charge results.66,67 The basic idea of charge equilibration techniques is to compute a set of charges that minimizes the total electrostatic free energy of the system subject to a constraint that a specified electrostatic potential is imposed on the electrode. To impose the desired field on the electrode, besides the standard electrostatic interactions, an energy term representing the work (W) needed to bring charges qi on each electrode atom i at an electrochemical potential μi, i.e., W = −Σqiμi, is added.64,66,68 The fluctuant electrode charges are typically treated as Gaussian distributed.69 These charges are then computed by minimizing the total free energy with respect to the charges on electrode atoms. For classical molecular mechanics the grid over which the fluctuant charges are assigned typically is the same as the location of electrode atoms;66 combined classic and quantum-mechanics, on the other hand, explored finer electrode charge grid commensurate with grids from ab initio computations.70 From a technical viewpoint, the free energy minimization implies finding a solution for the system of linear (or sometimes non-linear) equations for all electrode charges qi by self-consistent iterations. Such a procedure can however significantly increase the computational cost of simulations.

There is abundant literature regarding various charge equilibration schemes. The particular choice of the scheme utilized for electrodes should take into account the physical aspects of the studied electrode material. For example, for metallic electrodes, the charge equilibration scheme proposed by Reed et al.66 to assign Gaussian distributed charges at the location of the electrode atoms has shown to be quite reliable even for complex geometries. However, if electrodes are semiconducting (i.e., with a band gap at the Fermi level) then a different charge equilibration scheme that can empirically correlate the energy and the density of states variation with electrostatic potential68 would be more accurate. For electrodes comprised of atoms of different chemical identities more complex charge equilibration techniques, such as QeQ71 or split-charge,72 might be required.

4. Structural properties of the electric double layer

In this section, we discuss recent theoretical and experimental advances in understanding the structure of the electrode–electrolyte interface, the EDL capacitance, and the energy density stored by various electrolytes in different electrode structures. We reiterate that the energy/charge stored by a capacitor can be quantified with the integral capacitance (CI). The CI is defined as the ratio between the electrode charge σ (normalized either per unit SSA or mass of the electrode) and the applied potential ΔU between electrodes, CI = σ/(ΔU/2). For the characterization of the electrode–electrolyte interface and the sensitivity of its properties to the electrode potential, the differential capacitance (CD) defined as the derivative of the electrode charge with respect to the electrode potential, CD = dσ/dUelectrode, is commonly used in both experiments and modeling. The electrode potential (Uelectrode) is readily available from simulations by integrating the Poisson equation of the ensemble averaged charge distribution from the electrode surface to the bulk electrolyte.

The fundamental understanding of CI and CD magnitudes and their dependence on voltage, temperature, and the chemical structure of the electrode and electrolyte is key to elucidating correlations between the structural changes within the EDL and routes to achieve capacitance enhancement. For example, in light of simple EDL models73 one would associate the increase of capacitance upon increasing the electrode potential with low concentration of ions near the electrode surface. In contrast, a decrease of capacitance as the electrode is charged can be caused by ion crowding and oversaturation at the surface. Also, sharp peaks in CD at certain voltages can indicate possible phase transitions within the interfacial layer.

As an electric field (or charge) is applied on the electrode, the ionic electrolyte will restructure such that it will diminish (or screen out) the impact of the applied field. Extensive experimental work based on atomic force microscopy and theoretical work based on MD simulations showed a consistent picture regarding the EDL structure formed at the electrode–electrolyte interface. Specifically, in pure RTIL and concentrated electrolytes, layers locally rich in either counterions or coions are formed near the surface along the direction perpendicular to the electrode surface. It is quite remarkable that AFM experiments reached a level of resolution that can accurately pinpoint individual electrolyte layers near the electrode surface.74 This EDL structure generates space charge oscillations in the electrolyte, as exemplified in Fig. 2. For pure RTILs it is often the case that the innermost electrolyte layer near the surface (about 5–6 Å width next to the electrode) can be over-screened at low voltages, meaning that it can contain more counter-charge than the charge on the electrode. This extra (over-screened) charge in the innermost layer is then compensated by the net co-ion charge in the follow-up layers of the electrolyte formed near the surface such that the total charge on the electrode is equal and opposite in sign to the total charge in the entire EDL structure. Interestingly, solutions of ions in aprotic solvents also generated multiple structural layers near the electrode qualitatively similar to those of RTILs.75 These structural oscillations in the electrolyte are fairly short-ranged, specifically they extend over a few nanometers from the electrode surface, typically 3–5 nm for pure RTILs and 1–2 nm for solutions.75 Low temperature, high solute concentration, and high electrolyte density can extend the range of these oscillations.


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Fig. 2 Typical distribution of average ion density (a), cumulative space charge (b) and the Poisson potential (c) observed for a room temperature ionic liquid between two charged electrodes. The local electrolyte structuring near electrode surfaces consists of several successive layers rich either in co-ions or in counterions and generates space charge near electrodes that completely screen out the applied electrostatic field within 2–3 nanometers from the surface. The panels (d) and (e) show the distribution of ions in the interfacial layer for a c2mim-TFSI RTIL and panels (f) and (g) for TEA-BF4 solution in acetonitrile solvent at various electrode voltages. This figure is based on the simulations presented in ref. 96 and 255 for a RTIL (c2mim-TFSI) and ref. 75 for a solution of ions (TEA-BF4 in AN).

The multilayer structure formed near the surface screens out and limits the range in the ability for the electrostatic field to penetrate inside the electrolyte. This aspect can be illustrated by the variation of the screened Poisson potential with respect to the distance from the electrode. As illustrated in Fig. 2, within a couple of nanometers from the electrode surface the density oscillations vanished and the Poisson potential in the electrolyte becomes almost constant, indicating that the externally applied field is mostly screened out. Note that recent AFM measurements76,77 revealed the presence of relatively weak forces between two charged mica surfaces with a pure RTIL electrolyte in between. These forces extended to large surface separations and therefore suggest a relatively large Debye screening length in pure RTILs and the presence of a broad (7–8 nm) diffuse layer. There is an ongoing debate regarding whether this effect can be explained by considering RTILs as concentrated solutions of ionic pairs with a small number of “defects” (free ions that are unpaired with counterions) or as concentrated ionic melt of free ions with very few paired ions. However, the magnitudes of the observed forces indicate that the amount of charge accumulated in the diffuse layer outside the first couple of nanometers (i.e., in the region between 2 nm and 7 nm away from the electrode surface) will be negligible compared to the charge stored close to the surface. Therefore, in RTIL electrolytes the majority of the charge storage effectively occurs within this thin (couple nanometers) layer of electrolyte next to the surface.

Despite having a multilayer structure, the adsorption/desorption and reorientation of ions in the innermost layer as a function of electrode potential are expected to have the main contribution to the magnitude of the capacitance. Although quantitative experimental characterization of ion distribution at the surface is challenging, appropriately tuned atomistic simulations can address this issue quite straightforwardly. Fig. 3 compares the dependence of ion density in the interfacial layer (defined as 5 Å electrolyte width from the surface) on the electrode potential obtained from simulations of 1-butyl-3-methylimidazolium bis(fluoromethylsulfonyl)imide (c4mim-TFSI) pure RTIL and a solution of tetraethylammonium tetrafluoroborate (TEA-BF4) in AN. As illustrated in Fig. 3, the solution of ions behaves differently from pure RTILs. Specifically, in solutions, as the surface becomes weakly charged (or near the potential of zero charge, PZC) the co-ions are almost completely repelled from the surface and the counter-ions accumulate with increasing potential.75,78 Somewhat smaller changes in ion adsorption/desorption from the interfacial layer were observed for the smaller Li+ ions in carbonate solvents.79 Such behavior for Li+ at the electrode interface is attributed to the strong coordination of Li+ by oxygen atoms from carbonate solvent molecules.80 In contrast to ionic solutions, pure RTILs require electrode potentials as large as 2 V (relative to the PZC) to repel the co-ions from the electrode surface and about 3 V to saturate the innermost layer with counter-ions. Therefore, within the electrode potential window of −2 V to +2 V the dominant mechanism of charging the interfacial layer in RTIL electrolytes involves a monotonic swapping of co-ions and counter-ions as the potential varies, while for ionic solutions it primarily involves the accumulation of solvated counter-ions next to the charged surface that is relatively depleted of co-ions. The mechanism of monotonic swaps of co-ions and counter-ions in RTILs is consistent with the weakly changing CDvs. potential observed both experimentally81,82 and theoretically83 for these systems.


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Fig. 3 The dependence of surface layer ion density for the innermost adsorbed electrolyte layer near a flat electrode (within 5 Å from the electrode surface) and within the same layer inside a 7.5 Å slit pore for (a) c4mim-TFSI RTIL and (b) a solution of TEA-BF4 in AN. The dashed lines represent data for the electrolyte inside the 7.5 Å width slit pore and the symbols represent data for the electrolyte near a flat electrode surface. The left y-axis shows the total number of ion centers of mass in the layer per 1 nm2 cross-sectional area. The right y-axis shows the density in units of number of C atoms from one graphene sheet per counterion in the interfacial layer. The flat electrode and the pore surface were modeled as graphene layers. Other details regarding these simulations can be found in ref. 75, 96 and 110.

Considering the difference in the mechanism of ion adsorption/desorption for pure RTILs and ionic solutions observed in Fig. 3, one should expect a noticeably different behavior of the CDvs. voltage for these two types of electrolytes. For example, in electrolytes with solvated ions the EDL restructuring should be more sensitive to the electrode potential change than in RTILs. As a result, at low voltages the solutions of ions might generate a larger CD than ionic liquids. Considering steric aspects (i.e., surface not crowded with ions) both the Gouy–Chapman and the mean field theories predict a sharp increase of capacitance vs. potential increase for diluted solutions. Models based on the mean field theories,73,84,85 however, tend to over-predict the magnitude of capacitance for both solutions and RTILs as shown for example by Breitsprecher et al.86 (see Fig. 4a). Quantitative predictions of theoretical models for the EDL structure and capacitance can be significantly improved based on classical density functional approaches87–90 (which are quite popular for EDL studies), mean field91,92 or integral equation theories.93,94 In contrast to basic EDL theories, various atomistic simulations predict consistent trends and variations of CD for RTIL electrolytes and solutions of ions as illustrated in Fig. 4b.75,95,96 Specifically, there is a rather weak dependence of CD on the applied voltage within the potential range defined by the electrochemical stability window of commonly used electrolytes (roughly between −3 V and +3 V). Typical values of CD for these electrolytes range between 4 and 6 μF cm−2. At larger voltages, i.e., above ±3 V, the electrode surface becomes crowded with counter-ions and CD begins to decrease. While such a behavior is expected for RTILs, it is surprising that several solutions of ions show a similar dependence of CD on the potential, which is not consistent with the Gouy–Chapman theory prediction.75 This clearly indicates a more complex influence of polar solvent molecules on the delicate balance of electrolyte structuring near the electrode surface. We believe that the observed deviation from the expected Gouy–Chapman behavior can be rationalized by taking into account a strong adsorption of solvent molecules onto the charged electrode surface (as expected for polar solvents) and by a large energy penalty required to de-solvate the ions.


image file: c7ta05153k-f4.tif
Fig. 4 (a) Differential capacitance obtained from mean field theory (MFT) calculations (solid lines) compared to that from molecular dynamics simulations (symbols) for the electrolyte represented by a coarse grained model from ref. 86. The quantities y (from simulations) and γ (from MFT) are defined in ref. 86 as measures of how much denser counterions can be in the interfacial layer than in the bulk fluid. Smaller γ and y represent environments with more empty space near the surface and therefore counterions can be packed to higher density near the surface as compared to bulk density. Both simulations and MFT predict a transition from camel-shaped CD at lower y and γ to a bell shaped CD for crowded surfaces (which correspond to large y in MD and γ in MFT). At moderate values of electrode potentials, the mean field theories predict significantly larger capacitances than molecular dynamics simulations. Data are extracted from ref. 86. (b) Differential capacitance of ideal Gouy–Chapman solution is compared to the differential capacitance of TEA-BF4 in AN using data from ref. 75 and the c2mim-TFSI RTIL using data from ref. 255. Interestingly, the chemically realistic models for solutions of ions can generate noticeably different capacitances compared to those obtained by MFT using simple models.

The atomic scale structure of the electrode surface can also affect the EDL structure dramatically and hence influence the magnitude of the capacitance and its dependence on the applied voltage. Fig. 5 compares CDvs. electrode potential for a typical RTIL and an ionic solution on atomically flat and rough electrode surfaces. For the latter, the roughness patterns have dimensions comparable to the dimensions of electrolyte ions. For ionic solutions the surface roughness does not significantly change the overall capacitance and its dependence on the electrode potential. However, for pure RTILs the surface roughness noticeably affects the capacitance dependence and leads to increased values.97–100 In contrast to smooth surfaces, the electrodes with high density of atomically rough patterns can generate multiple minima and maxima in CD with magnitude variations as much as 400% (from 4 to ≈16 μF cm−2)99 and increase the CI by almost 100% as compared to that of atomically flat surfaces.98 The increase in capacitance by a certain type of graphene rough edge is illustrated in Fig. 5b based on the DFT calculation by Zhan et al.100 Such behavior of the CD on rough electrodes can be explained by the presence of large local electric fields at the edges of the roughness features. These large local fields facilitate the co-ion/counter-ion separation in the EDL.101 Simulation studies found that the CI increase at the rough electrodes is comparable to the CI observed in narrow nanopores, which will be discussed in the next section. Curved electrodes can also increase the capacitance by as much as 100% (or up to 10–12 μF cm−2) compared to atomically smooth and flat electrodes, as has been shown both by theory and experiments for C-onions and C-nanotubes.97,102 Similar to atomically flat surfaces the electrodes comprised of curved nanoparticles generate almost constant CDvs. potential in a wide range of potentials (Fig. 5c).103


image file: c7ta05153k-f5.tif
Fig. 5 (a) The influence of electrode surface topography on CD dependence for RTILs and solutions obtained from MD simulations described in ref. 75 and 83. The pyr13-FSI RTIL was simulated as described in ref. 83. The solution of ions consisted of c2mim-BF4 in AN solvent as described in ref. 75. (b) The dependence of CD on electrode surface curvature predicted from classical DFT calculations256 for coarse grained models of RTILs.

Finally, it was found that temperature has a rather modest impact on the EDL structure and the CD of electrodes with atomically smooth surfaces81 but a more pronounced effect for the electrodes with atomically rough surfaces.83,103 For rough electrodes, the increase of temperature smoothens out the magnitude of the oscillations between the minima and maxima of CD while maintaining the overall similar σ = f(U) dependence and therefore similar CI.83 Both simulations83,103 and experiments81 reported a slight decrease in capacitance as the temperature increases, with the exception of a narrow range of voltages for atomically rough surfaces where the overall broadening of peaks in CDvs. electrode potential can lead to an increase of CD with T at a specific Uelectrode.

5. Electrolytes in charged nanopores

An ever-increasing need to increase the electrode surface area in order to achieve a higher capacitance without resorting to low or ultralow density materials with a low volumetric energy density led to the consideration of nanoporous materials with pore widths comparable to ion diameters. Clearly, the ionic packing in such narrow pores might noticeably deviate from the ionic packing in EDLs at “open” electrode surfaces, i.e., electrode surfaces in contact with the bulk electrolyte, hence suggesting that the charge storage mechanism can be different. For example, carbide derived carbon (CDC) electrodes with sub-nanometer size pores demonstrated an increased area-normalized capacitance up to 13–14 μF cm−2, which is almost double the capacitances of the same electrolyte in mesopores or at open electrodes.25,104,105 As shown by Largeot et al.105 for a RTIL electrolyte (c2mim-TFSI), a sharp increase in capacitance is possible in sub-nanometer pores with widths comparable to ion dimensions. This enhancement however vanishes when the pore widths are modified by as little as 0.5 Å. In other words, by carefully controlling the pore widths and their polydispersity (or their lack off),105 in principle, a doubling of the stored energy density is possible. Note that the experimental measurements of the carbon specific surface area generally rely on simplified gas sorption models that often use inappropriate (for small nanopores) assumptions and do not consider a realistic shape of the pores. As such, these estimations and thus the area-normalized capacitance values should be considered only qualitatively. Other, more direct studies of ion sorption in pores of various sizes, such as small angle neutron scattering,106,107 are typically significantly more expensive.

The experimentally observed increase of the capacitance of narrow pores has raised an intriguing theoretical question of why sub-nanometer pores allow supposedly denser countercharge packing and enhanced capacitances. Kornyshev and co-workers elucidated one of the physical origins explaining this phenomenon. They demonstrated that the charge distribution generated by ions on polarized metallic walls results in enhanced screening of electrostatic interactions between ions inside charged nanopores.108 Therefore, the electrostatic repulsion between ions with the same charge becomes short-ranged and as a result of such strong screening, it is then possible to densely pack electrode counterions inside a nanopore generating the so-called “superionic states”108 that lead to increased capacitance.105 According to this model and subsequent extensive molecular simulations using simplified coarse-grained models, the CI enhancement in slit nanopores is originated either from a sharp (vs. potential) expulsion of co-ions from charged nanopores at a certain value of the electrode potential or from the fast swapping of co-ions and counter-ions occurring at low voltages.109–111

Atomistic simulations probed this phenomenon for a variety of RTILs and reported mixed results. For nanopores with atomically smooth surfaces, such as slits or nanotubes, typical RTILs generated a smaller capacitance enhancement than reported experimentally. Specifically, depending on the electrolyte and the force field utilized in simulations, several simulation studies showed about 50% enhancement in CI for sub-nanometer (slit) pores relative to mesopores, or CI with values around 8–9 μF cm−2.109,110,112 Also, multiple simulations109,113 and classical DFT calculations114,115 showed a complex oscillating dependence of the capacitance on the pore width (Fig. 6a). The utilization of asymmetric pores (corresponding to a setup where positive and negative pores had different available volumes for the corresponding ion insertion) was shown to further increase the energy density if the ratio of volumes available for the ions on the positive and negative electrodes was commensurate with the asymmetry of electrolyte anion and cation dimensions110,116,117 (see Fig. 6b). Capacitance enhancements as much as 100% (compared to flat electrodes) were observed in the simulations of NaCl aqueous solution in slit pores tighter than 2 nm,118 which is in agreement with classical DFT theory that correlated the dielectric constant of the solvent with the capacitance enhancement.119


image file: c7ta05153k-f6.tif
Fig. 6 (a) A typical dependence of the integral capacitance (CI) on the pore width for an RTIL inserted into a slit pore as obtained from MD simulations. An increase of capacitance is observed in narrow pores followed by oscillating dependence at larger pore widths. Reproduced from ref. 113 with permission of the American Chemical Society. (b) The dependence of CI on the anode/cathode mass ratio for asymmetric pores. This panel shows that the capacitances can be further optimized by tuning the asymmetry between electrodes to match with the chemical structure of the electrolyte. Reproduced from ref. 117 with permission of the American Chemical Society. (c) The dependence of the pore capacitance (CI) relative to the capacitance of the same electrolyte on a flat unconfined electrode (CI-flat) on the pore width for the RTIL inside slit pores with flat and rough wall surfaces. Pores with atomically rough walls, whose surface topography combines the nanoconfinement effect with surface roughness and curvature, can generate additional capacitance enhancement as compared to pores with smooth surfaces. The symbols represent data from MD simulations while the blue line is based the experimental data from ref. 105. Reproduced from ref. 110 with permission of the American Chemical Society. (d) Differential capacitance versus voltage inside a 1D pore simulated using the Ising model. Reproduced from ref. 120 with permission of the Royal Society of Chemistry. The potential scale is in reduced units as defined in ref. 120. (e) Differential capacitance versus potential for 2D slit pores. Reproduced from ref. 110 with permission of the American Chemical Society.

More complex nanopore geometries were also investigated. A systematic study of the charge density enhancement inside pores, as a function of the pore structure, found that pores having surface roughness patterns can significantly enhance the capacitance.110 For example, simulations of nanopores with atomically rough surfaces predicted CI as large as 11–12 μF cm−2 for typical RTIL electrolytes (see Fig. 6c), demonstrating that the atomic scale surface roughness of nanopore walls (expected to be present in realistic carbon based subnanometer wide pores) can further increase the stored energy density110 and is a desirable feature of the electrode structure. The additional CI enhancement in nanopores with atomically rough walls is related to the same phenomena observed for the open electrodes with atomically rough surfaces discussed above. The high local electrostatic fields generated at the edges of rough patterns facilitate the co-ion expulsion from the pore and therefore the co-ion/counter-ion de-mixing in such nanopores occurs at lower voltages compared to nanopores with atomically smooth walls. While the overall enhancement of CI in nanopores with atomically rough walls is still only 50% compared to open electrodes with the same surface structure, the absolute values of CI predicted by atomistic simulations in such nanopores are much closer to experimentally reported values for the same electrolytes and pore dimensions.

The electrolyte structural changes inside charged nanopores can be summarized as follows. At low voltages, charge is accumulated inside the pore by swapping the co-ions with counter-ions. The observed capacitance enhancement is usually related to a sharp (with respect to voltage change) de-mixing (sometimes considered as a first-order phase transition) of co-ions and counter-ions inside the nanopore at some intermediate voltage (electrode potential around 1–2 V for typical RTILs). At this voltage, the co-ions completely leave the pore and only counter-ions are left inside the nanopore. While the total density of ions inside the nanopore at this transition voltage can drop, the stored charge density is increasing due to co-ion and counter-ion separation. In order to maximize the enhancement in CI, it is desirable that such de-mixing of ions occurs at similar voltages on both the negative and the positive electrode, leading to peaks in CD on both electrodes. Both slit110 and cylindrical120,121 pores generated peaks in capacitance (Fig. 6d and e), suggesting that such behavior is a fundamental characteristic of interactions of electrolyte species in confined environments.122 As the electrode potential is increased further (i.e., high voltages) the charge accumulation occurs via counter-ion condensation. However, there is a limit (due to ions' excluded volume) to how much the counter-ions can pack. Several studies showed that the capacitance enhancement inside carbon based nanoporous electrodes is limited to a ΔU of 2–3 V and it diminishes significantly at potential differences higher than 6 V.110

To further comprehend the influence of nanoconfinement on the electrolyte charge reorganization, we have compared the variation of the co- and counter-ion charge density in the innermost layer of the unconfined electrolyte (i.e., in the EDL at the open structure electrode) as a function of voltage with the behavior of the electrolyte inside charged nanopores. Fig. 2a and b show the cumulative charge density inside the nanopore normalized per unit surface area as a function of voltage. In both cases the atomic structures of the electrode surfaces (i.e., the nanopore walls and for the open structure electrode) are the same. A quick glance uncovers a surprising similarity between the ionic responses to the applied potential during electrode charging for the nanoconfined and open structures. This similarity suggests that the nanoconfinement effects on the electrolyte layer near the surface are relatively small and the composition of the electrolyte inside nanopores can be approximated by the composition of the inner Helmholtz layer at the open electrode. Examination of the differences indicates that a more pronounced variation for the confined system vs. open one in the region of 0–1 V for the c4mim cation leads to higher capacitance in this voltage range. Similarly, the TFSI anion desorbs from the nanopore somewhat more expediently than from the open surface with the potential decreasing from −1 to −2 V. Another observation is that at high voltages (>2 V or <−2 V) the counter-ion density is higher in the nanopore compared to that near the open electrode, with a larger difference observed for the positive electrode. The analysis of realistic materials is complicated by irregular pore shapes that can have broad distributions and have varying electronic properties. In order to start addressing such more realistic representations Merlet et al.123 simulated CDC pore structures reconstructed using a reverse Monte Carlo technique124 from experimental data. They categorized the charge enhancement as a function of the local pore structure/geometric pattern and identified steric environments that enhance the capacitances.123 Finally, the asymmetry in charge storage mechanisms vs. electrode polarity, consisting of cation adsorption in the negative pores and anion–cation exchange in the positive pores was observed experimentally with in situ NMR spectroscopy.125 Similar asymmetry of charge storage inside positive and negative nanopores were observed for RTILs inside narrow pores in other experimental125–128 and simulation studies.110

Similar to RTILs, the solutions of ions can also enhance the CI in sub-nanometer pores,129 albeit to a smaller extent.130 In order to obtain a sufficiently high concentration of ions inside nanopores such that the CI is enhanced compared to open structure electrodes, the ions should first de-solvate at least partially upon insertion and then displace the solvent from the pore. Snapshots illustrating the ionic composition inside a 7.5 Å width slit nanopore at several potentials are shown in Fig. 7 both for a typical RTIL and a solution of ions.


image file: c7ta05153k-f7.tif
Fig. 7 Snapshots showing the distribution of ions inside a 7.5 Å width slit pore for electrolytes consisting of a solution of ions and a RTIL at several different potential differences between electrodes. The TEA and c2mim ions are colored blue, BF4 is green, and the AN is colored red/pink. Details regarding simulation conditions based on which these snapshots were generated are given in ref. 75 and 110.

6. Dual-ion intercalation into graphite

The ability to control ion insertion into graphite is also of great importance to the development of DIBs, which is a promising energy storage technology due to several environmental, safety, and material cost benefits over the state-of-the-art Li-ion batteries. For example, the mining and processing of rather expensive and toxic cobalt and nickel metals needed for commercially used nickel and cobalt containing cathodes may cause adverse respiratory, pulmonary, and neurological effects in those exposed. The lack of appropriate personal protection in some of the metal mining facilities in developing countries is a major concern. As such, the possible use of graphite as a lower-cost, broadly available and safer electrode material for both the anode and the cathode may be an attractive alternative.

The electrochemical energy storage mechanism in this system consists of the simultaneous intercalation of Li+ or K+ cations into the graphite negative electrode or usage of Al metal and intercalation of the anion into the graphite positive electrode during charging, with anion intercalation proceeding in well-defined and sequential phases.131–147 One of the challenges of DIBs is a relatively low volumetric capacity experimentally observed for the graphite cathode compared to LIBs. Another challenge is the need to identify suitable electrolyte mixtures that exhibit a high oxidative stability at the graphite cathode and, in addition, form a stable solid electrolyte interphase (SEI) at the graphite anode, permitting stable and highly reversible ion intercalation/de-intercalation into graphite electrodes at operating voltages up to 5 V that is often at the limit of electrolyte oxidative stability.133–136,138,144,148 Electrolyte oxidation if often coupled with H-transfer reactions between solvents or solvents and anions with different reactions occurring at different potentials.149–151

A number of electrolytes were examined for use in a dual ion battery including propylene carbonate (PC), ethylene carbonate (EC), diethyl carbonate (DEC), and dimethyl carbonate (DMC), as well as dimethyl sulfoxide (DMSO), dimethylformamide (DMF), and ethyl methyl sulfone (EMS) doped with LiPF6, LiTFSI and other salts.131 DIBs with ionic liquids and IL-solvents such as EMS showed good capacity and efficiency.133,134,136,138,144 Recent work by Read et al.135 demonstrated that electrolytes based on monofluoroethylene carbonate (FEC) and ethylmethyl carbonate (EMC) exhibited high oxidative stability on graphite cathodes and formed stable SEIs on graphite anodes that allowed for full dual-graphite electrochemical cells to be evaluated for energy storage applications. Among various electrolyte mixtures used in dual-graphite batteries to successfully achieve reversible cycling performance, a noteworthy requirement to obtain a sufficiently high energy density is an electrolyte with a high molarity. A recently reported integrated DIB design consisting of an Al film deposited by magnetron sputtering onto one side of a 3D porous glass fiber separator forming a porous anode and cathode natural graphite directly loaded onto the other side of the separator with an Al film deposited on the cathode top achieved good rate performance up to 120 C with a high capacity of 116.1 mA h g−1 (charging/discharging within 30 s) using a 4 m LiPF6 EMC −4% vinylene carbonate additive as the electrolyte.145

Experimental findings indicate that different electrolyte solvents result in a similar stage-I graphite anion intercalated structure suggesting that the solvent does not dictate the structure/distribution of ions inside the graphite and hence may play an auxiliary role in the intercalation process. The structure and arrangement of anions in the graphite will set the limits on critical performance parameters for the dual-graphite cell, where the intercalant structure determines the discharge capacity and affects the graphite lattice expansion/contraction properties. To better understand these correlations DFT calculations have been used to investigate the graphite intercalation structure with PF6 as the anion. In particular, these studies aim to map the anion intercalate composition with the well-defined staging phases de-lineated by the voltage vs. specific capacity profiles, as given in the in situ work of Read et al.135,137 The in situ XRD and dilatometry results provide evidence for specific compositions being formed at the onset of each of the identified staging phases during the anion intercalation process (i.e., charging). The following sequence of phase formation observed upon charge was proposed:

C24PF6(IV) → C24PF6(III) → C24PF6(II) → C20PF6(II) → C24PF6(I) → C20PF6(I)

A conventional and practical interpretation of stage transitions views domains of intercalant as sliding along the graphite galleries to create local arrangements of stage n (n > 0) compositions. To model the nano-domains of the intercalant formed in each graphite layer for the various stage n phases within the DFT the super-cell approach would require a very computationally expensive model due to the large size of the simulation cell. Therefore, the authors have adopted four different model systems corresponding to various concentrations of anion intercalant within the stage-I composition. The model systems employed assume a full graphite gallery intercalation with PF6 anions in an ordered configuration as shown in Fig. 8. The progression of phase changes shown in Fig. 8a to d would correspond to the following stage transition scheme:

C48PF6(I) → C24PF6(I) → C20PF6(I) → C12PF6(I)


image file: c7ta05153k-f8.tif
Fig. 8 Optimized structures of the four GIC model systems. Color coding: carbon (gray); phosphorous (orange); fluorine (green). (a) C48PF6; (b) C24PF6; (c) C20PF6; (d) C12PF6; (e) orthographic perspective highlighting the stage (I) model of the supercell employed in DFT calculations; (f) voltage versus capacity plot for the four stage (I) model systems (M. Olguin and O. Borodin, unpublished results). (g) Systematic illustration of the staging mechanism for (i) graphite, (ii) stage-4, (iii) stage-2, and (iv) stage-1 of the AlCl4 anion; RE (in eV) is the relative energetics for the same concentrations from Bhauriyal et al.142 Reproduced with permission from the Royal Society of Chemistry.

We expect the calculated capacity values as a function of voltage to be higher than the reported experimental values due to the assumption of full stage-I graphite layer intercalation in this model system. Staging phenomena will be reported later. The intercalation voltage was calculated as follows:

ΔE = (E[GrPF6] − E[Gr] − nanion(E[LiPF6(s)] − E[LiPF6(g)]) + nanion × E[Li(bulk)]/nLi)/nanion
where E[GrPF6] is the electronic energy of the GIC structure containing nanion, E[Gr] corresponds to the electronic energy of the graphite system, E[LiPF6(s)] represents the solvation energy for the contact ion pair and was estimated using PBE/6-31+G(d,p) DFT using a cluster-continuum approach with LiPF6(PC)3 treated explicitly and solvent beyond the first solvation shell implicitly using a PCM model with the PC parameter,152E[LiPF6(g)] is the electronic energy of the isolated (gas-phase) contact ion pair, E[Li(bulk)] corresponds to the electronic energy of bulk Li metal, nanion denotes the number of PF6 anions, and nLi denotes the number of Li atoms in the Li bulk model system.

The DFT predictions show that a cathode capacity of 100–140 mA h g−1 can potentially be achieved using LiPF6-based electrolytes that are stable up to 5 V (Fig. 8). An increase in capacity requires a significant increase of the electrode voltage beyond 5 V that is currently not supported by traditional liquid electrolytes. While overestimating the experimentally determined capacity at 5 V (ref. 135 and 137) by ∼30%, DFT calculations accurately predict the plateau around 4.9–5 V for PF6 intercalation. Since the DFT calculations were performed at 0 K, it is expected that the inclusion of entropic effects in MD simulations at room temperature will result in lower PF6 intercalation capacities.

A comparison of the PF6intercalation in graphite examined by DFT with the anion populations in the smallest nanopores obtained from MD simulations as shown in Fig. 3a uncovers intriguing similarities. First, the curves yield a similar number of anions per carbon at 5 V between electrodes: 16 carbon atoms per PF6 anion in DFT calculations (Fig. 8) and ∼20 carbons per larger TFSI anions in MD simulations (Fig. 3a). Intriguingly, in both cases the slope changes around 5 V (2 V vs. the PZC in Fig. 3a), indicating that the work to densify ions within the hard nano-carbon or graphite pore is significantly higher beyond 5 V when the pore is filled primarily with counterions only.

The energetics of staging were examined for the AlCl4 anions in graphite using DFT calculations as shown in Fig. 8g. This study demonstrated on the molecular level that intercalation into a single gallery is favored until it reaches its maximum occupancy before starting to fill adjacent empty galleries. This behavior can be understood on the basis of ion–ion Coulomb repulsion and interlayer van der Waals attraction142 and is in accord with the DFT studies of lithium staging.153,154

Importantly, the overall electrolyte weight and concentration should also be considered during supercapacitor and dual-ion carbon battery optimization. In a typical 1 M PC-based electrolyte composition, the weight of PC solvent per anion is about 60 heavy atoms per anion, which is higher than the weight of carbons at the C24/PF6 stage of dual ion intercalation compounds or an equivalent EDL capacitor. Increasing the electrolyte ion concentration or switching to more expensive RTIL electrolytes would result in a higher energy density. It is consistent with the need to utilize highly concentrated electrolytes suggested in the pioneering work by Dahn et al. that focused on the effect of the maximum salt concentration difference in the electrolyte between fully discharged and fully charged states.131 In fact, improved energy density was demonstrated by increasing LiPF6 salt concentration essentially up to the solubility limit.141

Achieving a fast diffusion coefficient of PF6 or other anions in graphite is important for realizing high charge–discharge rates using large graphite flakes. The PF6 anion diffusion coefficient was estimated using a galvanostatic intermittent titration technique (GITT) yielding values between 10−11 cm2 s−1 and 10−14 cm2 s−1 depending on the electrode voltage.140 The measured activation energy of 0.366 eV is slightly higher than the 0.23 eV value for the PF6 anion hopping barrier obtained from DFT calculations.140 Similar barriers from 0.308 eV to 0.4 eV were reported for lithium diffusion in graphite.155 We find it somewhat unexpected because the estimated PF6 chemical diffusion coefficient is significantly lower than the Li+ cation diffusion coefficient parallel to the graphene plane of 10−7 cm2 s−1 reported from DFT calculations.155 A much higher TFSI anion diffusion coefficient was also predicted in MD simulations of the TFSI anion in a 0.75 nm slit pore yielding a TFSI self-diffusion coefficient almost as high as those of bulk ionic liquids (∼10−5 to 10−6 cm2 s−1) as will be discussed below in detail.156

The anion intercalation in graphite was recently extended to Al-graphite batteries using a IL-based electrolyte achieving an energy density of 68.7 W h kg−1 (based on 110 mA h g−1 cathode capacity and the masses of active materials in the electrodes and electrolyte).147 A novel potassium ion-based DIB utilized a potassium ion containing, IL-based electrolyte and showed promise for stationary (“grid”) energy storage by employing environmentally friendly, abundant and recyclable materials with a capacity retention of 95% after 1500 cycles.132

7. Electronic properties of carbon-based electrodes – quantum capacitance

The electrode materials for high power energy storage applications should have high electronic conductivity and thus preferably no gaps in their band structure (BS) at operating voltages. However, pristine graphene is a rather poor electrode material for such applications, because it is a semiconductor. The band structure of graphene is cone-shaped at the K-point due to the existence of the Dirac point (Fig. 9a).157,158 As a result of such a band structure, graphene has a V-shape dependence of the density of states as a function of local gate voltage with a minimum at the Fermi level (Fig. 9b).159 Nanotubes, on the other hand, have an almost constant density of states within approximately 1 eV (depending on tube diameter) from the Fermi level, and then a sharp increase at larger voltages.158,160 The presence of BS gaps at operating potentials is undesired because it diminishes the electronic conductivity and decreases the total stored charge as compared to metallic electrodes at similar electrode potentials.25,159,161,162
image file: c7ta05153k-f9.tif
Fig. 9 (a) Band structure of graphene illustrating the cone-shape dependence at the K-point (which also corresponds to a Dirac point). Such a band structure results in a small number of quantum states for electrons at (or near) the Fermi level, as shown in panel (b). The panels a and b are reproduced from ref. 175 with permission of the IOP science. Lower density of states (DOS) near the Fermi level for pristine semiconducting graphene diminishes the quantum capacitance (CQ) near the Fermi level160,162 and the total electrode capacitance (Ct), as shown in panel (c). The dashed blue line in panel (c) corresponds to the estimated capacitance near the doped graphene electrode and shows that the metallicity of graphene-based electrodes can significantly be increased by appropriately doping and/or inserting vacancies. The capacitance CEDL used to calculate Ct in panel (c) was obtained from simulations of the c2mim-TFSI RTIL near a flat metallic electrode, while CQ was obtained using a fixed band structure approach as shown in ref. 175 (d) the influence of increasing number of graphene layers used for the electrode on CQ. Reproduced from ref. 257 with permission of the American Chemical Society. (e) The role of graphene edges in enhancing the CQ as illustrated in ref. 100. Zig-zag edges increase CQ while armchair edges generate no capacitance enhancement or slightly diminish it as compared to basal graphene. Reproduced from ref. 100 with permission of Elsevier. (f) The influence of surface curvature and strain defects on CQ obtained from DFT calculations. Reproduced from ref. 174 with permission of the American Chemical Society.

The decrease of the total electrode capacitance due to the semiconducting nature of several carbon-based electrodes can be understood from the concept of “quantum capacitance” CQ. In classical conductors, the charge carriers (free electrons) obey Boltzmann statistics at equilibrium. However in a quantum Fermi gas the fermions obey additional constraints due to Fermi occupation rules of energy levels. These extra, quantum in nature, constraints have a net effect of only partly screening the field of a test charge and this effect can be represented in an equivalent circuit with the so-called quantum capacitance.163 For energy storage systems, the total electrode capacitance can be modeled as two serially connected capacitors: one capacitor representing the quantum effects in the electrode, CQ, and the other representing the classical effects of electrolyte ordering within the EDL (CEDL = CI or CD discussed above). Because the total capacitance of the electrode is defined as 1/Ct = 1/CEDL + 1/CQ, the smaller of CEDL or CQ is the limiting factor defining the value of the total capacitance. For electronically conductive (metallic) electrodes, CQ is very large and hence the limiting factor is the CEDL. However, for semiconducting electrodes, if CQ is less than CEDL then the former begins to dominate the performance of the energy storage device. This is illustrated in Fig. 9c where Ct values obtained from molecular simulation of conducting and semiconducting (single graphene sheet) electrodes with a RTIL electrolyte are compared.

As the research in this area moves towards the design of functionalized carbon-based electrodes164–166 that could end up with large band gaps and correspondingly low quantum capacitance, we would expect that the issue of restoring or increasing the pore metallicity will be an important aspect in the design of novel electrodes for energy storage. Both experiments and ab initio computations show that the metallicity of a semiconducting electrode can be increased by (i) doping graphene with heteroatoms which moves the band gap away from the Fermi level,167–170 (ii) generating vacancy defects171,172 in graphene, which destroys the Dirac point, (iii) generating a large density of zig-zag (metallic) graphene edges,100,173 and (iv) generating curved structures that increase both quantum and EDL capacitance174–178 (see Fig. 9d and e).

8. Dynamics inside nanopores and in the EDL

As the charge storage in supercapacitors involves reversible adsorption/desorption of ions, EDLCs can deliver higher power and recharge faster than batteries. It is however important to understand if these advantages will still hold in newer generations of porous materials with subnanometer widths and exceptionally high SSAs. In this regard, extensive research is dedicated to the study of the dynamic processes occurring within the EDL and the kinetics of charging/discharging of supercapacitors. Utilizing MD simulations, the dynamic properties of ions in supercapacitors can be studied following two routes: (i) “statically” from electrode–electrolyte interfaces or pores at equilibrium and (ii) “dynamically” when the systems are charged/discharged under non-equilibrium conditions following an imposed potential regime. We begin our discussion with results from the “static” approach.

Multiple studies showed the heterogeneity of electrolyte ion dynamics depending on the ion distance from the electrode surface. Specifically, in very wide pores or in non-porous systems the differences in the local structure within the EDL lead to significantly slower dynamics of the ions next to the surface than of the ions away from the surface or in the bulk electrolyte.179 An increase of the electrode potential further decreases the mobility of the ions in the interfacial layer, while an increase of temperature increases (as expected) the diffusion of the ions near the surface.

In contrast to mesopores, in tight (sub-nanometer) pores, instances of both slowing and accelerating of ion dynamics were reported.180 Note that intuitively one would expect that tight nanoconfinement slows down the ion diffusion because of steric obstructions. Strikingly however both basic theories and simulations with simple spherical ions found that an acceleration of ion dynamics (relative to dynamics in the bulk electrolyte) is actually possible in charged nanopores.181 Microporous zeolite-templated carbons with straightly aligned pores demonstrated outstanding rate performance when used in EDLCs.182 These experimental and modeling results raised the possibility that sub-nanometer pores optimizing the capacitance might actually deliver a higher power than wider pores.

Atomistic simulations of realistic RTILs in nanoconfinement presented an intriguingly complex picture. Specifically, for c2mim-TFSI inserted at various potentials from −2 to +2 V in slit pores which are comparable to the ionic diameter (i.e., 7.5 Å width) surprisingly large variations in ion diffusion coefficients, over about three orders of magnitude, were observed as a function of pore charge and inserted electrolyte composition.183 The dependence of ionic mobility on the surface potential can be summarized as follows. In uncharged pores the ion diffusion coefficients are significantly (almost two orders of magnitude) lower than in the bulk electrolyte. Upon charging the pore, the ion diffusion coefficients increase generating a U-shaped dependence on pore charge. However, how fast the dynamics accelerate vs. pore charging depends on the chemical structure of the electrolyte. For spherical ions this increase in dynamics is very sensitive to voltage, while for more complex (realistic) RTILs, such as c2mim-TFSI, the diffusion coefficients remain almost constant within a rather large range of dilated pore charge, e.g. between −1.0e per nm2 and +0.5e per nm2, and then they sharply increase at higher voltages.183

The dependence of the ion dynamics on pore widths can also be surprising. One would expect that the increase of pore widths relaxes steric constraints and therefore increases the ion dynamics, as probed for simple spherical ions. However, for complex (realistic) RTILs it was shown that the formation of multiple layers combined with the interlocking between co- and counter-ions can slow down the ion dynamics in wider pores as compared to sub-nanometer ones.183

Non-equilibrium atomistic simulations181,184 clarified the stages of EDL formation and the pore charging mechanism. In agreement with basic theories, these studies revealed a two-step mechanism of EDL formation: (i) a fast electrolyte arrangement near the electrode surface consisting initially of co-ion removal from the innermost layer followed by counter-ion migration next to the surface and (ii) a slow process of ion transport from one electrode to the other in order to balance the charges. Exemplified in Fig. 10 are the charge and discharge curves for a RTIL in a slit pore. For sub-nanometer pores the rates of charging and discharging are remarkably fast, i.e., 90% of charging and 50% of discharging occur within 10 ns. The charging process occurs with an initial condensation of the total density of the inserted electrolyte followed by a relaxation of the density due to excess co-ion removal. For the discharging the dominant mechanism is ion swapping. However, this asymmetry between charging and discharging is possible because systems are driven under far from equilibrium conditions in the particular setup of simulations. Specifically, due to the small distance between oppositely charged electrodes possible in MD simulations, the bulk ions in the initial perturbed configurations (that are not equilibrated) are subject to large fields184 which act as strong driving forces. In typical experiments the distance between the electrodes are three to four orders of magnitude larger than in simulations, thereby significantly slowing down the charge–discharge rates of supercapacitors. On the other hand, supercapacitors with an interdigitated configuration of electrodes that results in a smaller distance between the cathode and anode surfaces can deliver higher power.185,186 Therefore, the timescales shown in Fig. 10 demonstrate the upper limits of the power densities in such nanostructured devices.


image file: c7ta05153k-f10.tif
Fig. 10 The dynamics of charging/discharging of a slit pore filled with a RTIL. For distance between pores of tens of nanometers (accessible to atomistic simulations), the large fields generated when the potential is turned on or off drive the charging or discharging processes very fast (50% to 90% change in composition inside the pore). The simulated system consisted of c2mim-FSI at 393 K as presented in ref. 258.

The transmission line model appears to fit well with trends from MD for charging of CDC nanopores.187 For these complex pores NMR studies indicate that the dominant mechanism of charging appears to be co-ion/counter-ion swaps rather than countercharge accumulation.188 The chemical nature of the pore can dramatically change the mechanisms and the charging rates, specifically ionophobic pores accelerate the dynamics while ionophilic pores slow it down.189 The mechanism of charging ionophobic pores is dominated by counter-ion diffusion into an empty pore. Swapping of ions appears to be a dominant mechanism for the charging of ionophilic pores.

9. Pseudocapacitors and hybrid capacitors

Numerous transition metal oxides can store charge via surface redox reactions in addition to EDL formation, resulting in pseudocapacitive charge storage. Three types of mechanisms can lead to pseudocapacitance: (i) underpotential electrodeposition of metal ions on a chemically different substrate, (ii) reversible ion insertion into metal oxides190–194 (commonly within a surface layer or as interconnected nanowires195) without destroying/changing the initial crystal structure and (iii) redox reactions in conducting polymers196 or polyoxometalates.197–199 The faradaic capacitance is expected to increase as the potential increases due to increasing the driving force (or the overpotential); however, if electrochemical reactions are sufficiently fast such that the surface becomes depopulated of active sites, then the overall rate of the reaction could decrease upon further potential increase. These two opposite effects can generate, for an electrochemical process occurring at the surface of an electrode, a bell-shaped faradaic capacitance dependence on the potential with a sharp maximum. Besides faradaic capacitance, pseudocapacitors will necessarily have some non-faradaic EDL capacitance because the electrolyte ordering at the porous surface is inherent at any voltage or electrode geometry. The non-faradaic capacitance is elevated within the typical electrochemical window. For example, modeling of RuO2 pseudocapacitive behavior indicated that below the PZC the capacitive behavior is governed by the hydrogen adsorption reaction on the surface; above the PZC, the capacitive behavior is dominated by EDL formation.200 While the non-faradaic capacitance typically varies within 60–200 F g−1, the faradaic capacitances achieved by pseudocapacitance mechanisms can reach capacitances ranging from 1000 to 2000 F g−1. The energy densities of pseudocapacitors may reach tens (10–30) of W h kg−1, which is significantly larger than those of EDLCs (of 1–5 W h kg−1). While in electrochemical batteries ion insertion into the electrode bulk phase is involved, in pseudocapacitors the redox reactions occur mostly at the surface, which contributes to faster electrochemical responses (i.e., higher power and faster charging) than in batteries. In pseudocapacitors, the cyclic voltammetry (CV) curves for an individual electrode are similar to those of non-faradaic EDLCs (i.e., no large spikes) despite the involved charge transfer.201

The discovery of conducting polymers opened new possibilities in multiple research fields from energy storage via pseudocapacitance to advanced molecular engineering.202,203 For example, conducting polymers can make possible flexible supercapacitors that can be essential in powering up newer generations of smart portable foldable/flexible electronics. These polymers consist of an extended conjugated π-electron cloud and p or n doping atoms. Their chemical structures contain aromatic rings and/or double bonds with or without heteroatoms, e.g., polyanilines, polyindoles, polyacetylene, polypyrrole, polythiophene, etc.196 Commonly used doping heteroatoms are N, O, S, or transition metals.204 The main disadvantages of porous electrodes comprised of conducting polymers are (i) low mechanic stability and low lifetime because of the high extent of swelling/shrinking during charge/discharge cycles, (ii) relatively low electrochemical stability at higher potentials, and (iii) the difficulty to dope conducting polymers via oxidation and unavailability of a larger variety of chemical structures for negative electrodes. Importantly, the mechanical stability and cycling ability of conducting polymers can be significantly improved by the preparation of core–shell arrays of conducting polymers with metal oxides such as RuO2 or MnO2, and by co-deposition with carbon composites based on, e.g., carbon onions, nanotubes or graphene.205–210

Pseudocapacitance higher than that of conducting polymers can be obtained through ion insertion into conductive metal oxides. A very high capacitance (700 F g−1) and power density were demonstrated by proton insertion in RuO2 oxide.211 As ruthenium oxides are expensive, recent research focuses on identifying metal oxides (or composites with conducting polymers, with porous metal nanostructures or with nanocarbons) that are significantly cheaper, as well as identifying solvents stable at higher voltages. Aqueous solvents typically require low potentials (up to 1.2 V). The utilization of aprotic solvents for alkali metal solutions can substantially increase the operating potential window of pseudocapacitors even up to 4 V.212

As mentioned, negative porous structures for pseudocapacitors can be difficult to prepare. The so-called asymmetric supercapacitors overcame this disadvantage by combining faradaic and non-faradaic electrodes as follows: the negative electrode (based on porous carbon) is non-faradaic while the positive electrode (based on conducting polymers,213 metal oxides214 or composites215,216) is faradaic. The typical energy density of these capacitors can reach 10–30 W h kg−1.217 A hybrid/asymmetric aqueous intercalation battery using activated carbon as an electrochemical double-layer capacitor material in conjunction with an alkali-ion intercalation λ-MnO2 cathode material and aqueous electrolyte was proposed.218 However, the majority of the activated carbon in the anode of this device was subsequently replaced with the insertion compound NaTi2(PO4)3 leading to a battery with a similar long-term stability.218 Research in this field addresses the issue of carefully tuning the electrodes and electrolytes to take advantage of both non-faradaic (EDL) and faradaic charge storage mechanisms and to extend the usable potential window.219

10. Future research and concluding remarks

A diverse set of electric devices requires energy storage with markedly different power, energy and lifetime requirements. EDL and hybrid capacitors and ion intercalation devices will play an important role in future energy storage. For non-faradaic supercapacitors, the preparation of porous materials with a high specific surface area and sub-nanometer pore widths could significantly increase the capacitance. There is a tradeoff between increasing energy and power density that could, at least partially, be addressed by an appropriate choice of electrolyte and controlling the porosity distribution of electrodes. Increasing the energy density by increasing the operating voltage requires not only more electrolyte but also a reduction of impurities in carbon electrodes which increases the production cost. The low cost of the currently used carbons and organic electrolytes presents a formidable barrier to the adoption of the new generation of designed carbons in EDLCs and more expensive ionic liquids.8

DIBs offer higher energy density than EDLCs but require further improvements of electrolyte oxidative stability to extend the cycle life that is currently significantly lower compared to that of EDLCs that operate at lower voltages within electrolyte and electrode stability limits. DIBs have lower power density than EDLCs due to intercalation steps and formation of the SEI on the anode to kinetically extend the electrochemical stability window. The DIB energy density is cathode limited. Cathode capacity is typically around 20 carbons per anion such as PF6 or TFSI and requires much higher voltages in order to overcome anion – anion repulsion that is often beyond electrolyte oxidation stability in contrast to anodes where graphite accommodates one Li+ per six carbons. Because the electrolyte in DIBs serves as a source of both cations and anions needed for the intercalation reaction, increasing salt solubility is important in addition to ensuring that the electrolyte is electrochemically stable and has sufficient conductivity in the concentration range that DIBs experience during their operation. A combination of ion intercalation and EDL mechanisms offers additional design parameters to tailor energy and power densities to specific applications that have not been sufficiently explored.

For pseudocapacitors, which can store more charge than EDLCs, it is important to increase their lifetime and cycling ability while decreasing the material cost. The mechanical stability of the pseudocapacitive electrodes might be significantly improved by the utilization of composite materials of conducting polymers or metal oxides with porous carbon. Organometallic frameworks are also promising candidates for high energy density supercapacitors because they can store charge via both non-faradaic and pseudocapacitive processes220,221 and have high specific surface areas.

Another possibility to optimize the power and energy densities is the utilization of supercapacitor-battery asymmetric devices, where at least one of the electrodes is faradaic (or pseudocapacitive). This concept was demonstrated, for example, by Zhang et al.222 and Zhao et al.223 with porous carbon (having EDL capacitance) as the positive electrode and Fe3O4/graphene222 or nanoconfined Li4Ti5O12/porous carbon223 composites as negative electrodes (having faradaic capacitance involving Li-insertion into Fe3O4 or Li4Ti5O12 as in Li-ion batteries). The C–Li4Ti5O12/C cells can be charged or discharged very fast.223 Similarly, hybrids with electrodes containing a mixture of nitroxide–polymer (which store charge pseudocapacitively) with LiFePO4 (which is a typical Li-battery cathode involving Li insertion in the bulk electrode) have improved power and energy densities because of the initial fast electrochemical response of the pseudocapacitive polymer which later transfers charge to bulk LiFePO4.224

C-based pores (graphene, nanotubes, and various porous carbons) can be chemically modified, or functionalized, by either inserting hetero-atoms (N, P, S, and B) within the C-framework, or by attaching certain chemical groups (OH, OR, COOR, NR2, etc.) to C atoms in order to achieve desired properties.225,226 Such pore modifications can increase the energy density via both non-faradaic and pseudocapacitive mechanisms as well as via increase in quantum capacitance. The functionalized porous C can be tuned for specialized applications in medicine, nanoelectronics, energy fibers, all-solid227,228 supercapacitors for flexible/foldable devices, etc. Gaining a better understanding of which functional groups may lead to slower self-discharge and how it depends on the electrolyte composition and applied potential is important for future optimization of the chemical functionalization strategy.

Of practical interest to EDLCs, DIBs and hybrid devices is the decrease of the production cost of electrolytes and electrode materials. With respect to electrolytes, the replacement of more expensive Li–salts with cheaper alternatives consisting of Na or Mg solutes could be promising for both supercapacitors and electrochemical batteries.229,230 As for electrodes, experiments showed many options to prepare porous materials for energy storage from renewable or waste products21,22,231,232 such as wood,233,234 paper/cellulose,235 plants such as hemp,236–238 recycled cigarette filters,239 recycled plastic materials,240 scrap waste tires,241 and conversion of biomass237,242–245 or bio-waste,246–248 thereby potentially significantly reducing the cost and having a positive environmental impact.

Computational chemistry and molecular modeling could play an important role in assisting experiments and providing insight to complex realistic systems, particularly with increasing electrolyte packing in nanoconfined geometries for high power density, understanding supercapacitor self-discharge and degradation mechanisms, elucidating the role of impurities in charge–discharge rates, predicting the device lifetime, and predicting mechanisms of faradaic processes in batteries, pseudocapacitors, and hybrid devices.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

The authors gratefully acknowledge the support from a project sponsored by the Army Research Laboratory under Cooperative Agreement Number W911NF-12-2-0023. 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 ARL or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. JV acknowledges support through ORAU (contract #W911NF-16-2-0107) from the U.S. Army Research Laboratory. MO was supported by an Oak Ridge Associated Universities (ORAU) Postdoctoral Fellowship. GY and OB acknowledge partial support from the NASA Minority University Research and Education Project (MUREP) project (NASA grant NNX15AP44A and IAA NND16AA29I). Dr Jeffrey Read (ARL) is acknowledged for critical reading of the manuscript and numerous suggestions.

References

  1. A. Nishino, Capacitors: operating principles, current market and technical trends, J. Power Sources, 1996, 60(2), 137–147 CrossRef CAS .
  2. P. Simon and Y. Gogotsi, Materials for electrochemical capacitors, Nat. Mater., 2008, 7(11), 845–854 CrossRef CAS PubMed .
  3. M. J. Pan and C. A. Randall, A brief introduction to ceramic capacitors, IEEE Electr. Insul. Mag., 2010, 26(3), 44–50 CrossRef .
  4. A. González, E. Goikolea, J. A. Barrena and R. Mysyk, Review on supercapacitors: Technologies and materials, Renewable Sustainable Energy Rev., 2016, 58, 1189–1206 CrossRef .
  5. L. Wei and G. Yushin, Capacitive Electric Storage, in World Scientific Handbook of Energy, ed. G. M. Crawley, 2013, vol. 3, pp. 373–404 Search PubMed .
  6. H. Business, Electronic Capacitors Industry report, https://business.highbeam.com/industry-reports/equipment/electronic-capacitors Search PubMed.
  7. M. Jayalakshmi and K. Balasubramanian, Simple capacitors to supercapacitors – An overview, Int. J. Electrochem. Sci., 2008, 3(11), 1196–1217 CAS .
  8. L. Weinstein and R. Dash, Supercapacitor carbons Have exotic carbons failed?, Mater. Today, 2013, 16(10), 356–357 CrossRef .
  9. W. Gu and G. Yushin, Review of nanostructured carbon materials for electrochemical capacitor applications: advantages and limitations of activated carbon, carbide-derived carbon, zeolite-templated carbon, carbon aerogels, carbon nanotubes, onion-like carbon, and graphene, Wiley Interdiscip. Rev.: Energy Environ., 2014, 3(5), 424–473 CrossRef CAS .
  10. L. Wei and G. Yushin, Electrical double layer capacitors with activated sucrose-derived carbon electrodes, Carbon, 2011, 49(14), 4830–4838 CrossRef CAS .
  11. L. Wei, M. Sevilla, A. B. Fuertes, R. Mokaya and G. Yushin, Polypyrrole-Derived Activated Carbons for High-Performance Electrical Double-Layer Capacitors with Ionic Liquid Electrolyte, Adv. Funct. Mater., 2012, 22(4), 827–834 CrossRef CAS .
  12. N.-S. Choi, Z. Chen, S. A. Freunberger, X. Ji, Y.-K. Sun, K. Amine, G. Yushin, L. F. Nazar, J. Cho and P. G. Bruce, Challenges Facing Lithium Batteries and Electrical Double-Layer Capacitors, Angew. Chem., Int. Ed., 2012, 51(40), 9994–10024 CrossRef CAS PubMed .
  13. H. Zhong, F. Xu, Z. Li, R. Fu and D. Wu, High-energy supercapacitors based on hierarchical porous carbon with an ultrahigh ion-accessible surface area in ionic liquid electrolytes, Nanoscale, 2013, 5(11), 4678–4682 RSC .
  14. Y. Li, Z. Li and P. K. Shen, Simultaneous Formation of Ultrahigh Surface Area and Three-Dimensional Hierarchical Porous Graphene-Like Networks for Fast and Highly Stable Supercapacitors, Adv. Mater., 2013, 25(17), 2474–2480 CrossRef CAS PubMed .
  15. M. R. Arcila-Velez, J. Zhu, A. Childress, M. Karakaya, R. Podila, A. M. Rao and M. E. Roberts, Roll-to-roll synthesis of vertically aligned carbon nanotube electrodes for electrical double layer capacitors, Nano Energy, 2014, 8, 9–16 CrossRef CAS .
  16. M. Oschatz, S. Boukhalfa, W. Nickel, J. P. Hofmann, C. Fischer, G. Yushin and S. Kaskel, Carbide-derived carbon aerogels with tunable pore structure as versatile electrode material in high power supercapacitors, Carbon, 2017, 113, 283–291 CrossRef CAS .
  17. J. S. Moon, H. Kim, D.-C. Lee, J. T. Lee and G. Yushin, Increasing Capacitance of Zeolite-Templated Carbons in Electric Double Layer Capacitors, J. Electrochem. Soc., 2015, 162(5), A5070–A5076 CrossRef CAS .
  18. M. Oschatz, S. Boukhalfa, W. Nickel, J. T. Lee, S. Klosz, L. Borchardt, A. Eychmueller, G. Yushin and S. Kaskel, Kroll-carbons based on silica and alumina templates as high-rate electrode materials in electrochemical double-layer capacitors, J. Mater. Chem. A, 2014, 2(14), 5131–5139 CAS .
  19. Y. Korenblit and G. Yushin, Carbide-Derived Carbons, 2014, pp. 303–329 Search PubMed .
  20. L. Wei, N. Nitta and G. Yushin, Lithographically Patterned Thin Activated Carbon Films as a New Technology Platform for On-Chip Devices, ACS Nano, 2013, 7(8), 6498–6506 CrossRef CAS PubMed .
  21. W. Gu, M. Sevilla, A. Magasinski, A. F. Fuertes and G. Yushin, Sulfur-Containing Activated Carbons with Greatly Reduced Content of Bottle Neck Pores for Double-Layer Capacitors: a Case Study for Pseudocapacitance Detection, Energy Environ. Sci., 2013, 6, 2465–2476 CAS .
  22. L. Wei, M. Sevilla, A. B. Fuertesc, R. Mokaya and G. Yushin, Hydrothermal Carbonisation of Abundant Renewable Natural Organic Chemicals for High-Performance Supercapacitor Electrodes, Adv. Energy Mater., 2011, 1, 356–361 CrossRef CAS .
  23. L. Zhang, F. Zhang, X. Yang, G. Long, Y. Wu, T. Zhang, K. Leng, Y. Huang, Y. Ma, A. Yu and Y. Chen, Porous 3D graphene-based bulk materials with exceptional high surface area and excellent conductivity for supercapacitors, Sci. Rep., 2013, 3, 1408 CrossRef PubMed .
  24. Y. Gogotsi and P. Simon, True Performance Metrics in Electrochemical Energy Storage, Science, 2011, 334(6058), 917–918 CrossRef CAS PubMed .
  25. H. Ji, X. Zhao, Z. Qiao, J. Jung, Y. Zhu, Y. Lu, L. L. Zhang, A. H. MacDonald and R. S. Ruoff, Capacitance of carbon-based electrical double-layer capacitors, Nat. Commun., 2014, 5, 3317 Search PubMed .
  26. E. Karden, S. Ploumen, B. Fricke, T. Miller and K. Snyder, Energy storage devices for future hybrid electric vehicles, J. Power Sources, 2007, 168(1), 2–11 CrossRef CAS .
  27. H. Zhao and A. F. Burke, Fuel Cell Powered Vehicles Using Supercapacitors – Device Characteristics, Control Strategies, and Simulation Results, Fuel Cells, 2010, 10(5), 879–896 CrossRef CAS .
  28. P. Thounthong, S. Raël and B. Davat, Energy management of fuel cell/battery/supercapacitor hybrid power source for vehicle applications, J. Power Sources, 2009, 193(1), 376–385 CrossRef CAS .
  29. M. Winter and R. J. Brodd, What Are Batteries, Fuel Cells, and Supercapacitors?, Chem. Rev., 2004, 104(10), 4245–4270 CrossRef CAS PubMed .
  30. D. Pech, M. Brunet, H. Durou, P. H. Huang, V. Mochalin, Y. Gogotsi, P. L. Taberna and P. Simon, Ultrahigh-power micrometre-sized supercapacitors based on onion-like carbon, Nat. Nanotechnol., 2010, 5(9), 651–654 CrossRef CAS PubMed .
  31. Z. Zhao, S. Wang and C. You, Piezoelectric Micro-power Generation to Charge Supercapacitor with Optimized Duty Cycle, J. Intell. Mater. Syst. Struct., 2010, 21(11), 1131–1140 CrossRef CAS .
  32. X. Xia, J. Luo, Z. Zeng, C. Guan, Y. Zhang, J. Tu, H. Zhang and H. J. Fan, Integrated photoelectrochemical energy storage: solar hydrogen generation and supercapacitor, Sci. Rep., 2012, 2, 981 CrossRef PubMed .
  33. E. Stavrinidou, R. Gabrielsson, K. P. R. Nilsson, S. K. Singh, J. F. Franco-Gonzalez, A. V. Volkov, M. P. Jonsson, A. Grimoldi, M. Elgland, I. V. Zozoulenko, D. T. Simon and M. Berggren, In vivo polymerization and manufacturing of wires and supercapacitors in plants, Proc. Natl. Acad. Sci. U. S. A., 2017, 114(11), 2807–2812 CrossRef CAS PubMed .
  34. L. Suo, O. Borodin, W. Sun, X. Fan, C. Yang, F. Wang, T. Gao, Z. Ma, M. Schroeder, A. von Cresce, S. M. Russell, M. Armand, A. Angell, K. Xu and C. Wang, Advanced High-Voltage Aqueous Lithium-Ion Battery Enabled by “Water-in-Bisalt” Electrolyte, Angew. Chem., Int. Ed., 2016, 55(25), 7136–7141 CrossRef CAS PubMed .
  35. L. Suo, F. Han, X. Fan, H. Liu, K. Xu and C. Wang, “Water-in-Salt” electrolytes enable green and safe Li-ion batteries for large scale electric energy storage applications, J. Mater. Chem. A, 2016, 4(17), 6639–6644 CAS .
  36. F. Wang, Y. Lin, L. Suo, X. Fan, T. Gao, C. Yang, F. Han, Y. Qi, K. Xu and C. Wang, Stabilizing high voltage LiCoO2 cathode in aqueous electrolyte with interphase-forming additive, Energy Environ. Sci., 2016, 9(12), 3666–3673 CAS .
  37. Y. Yamada, K. Usui, K. Sodeyama, S. Ko, Y. Tateyama and A. Yamada, Hydrate-melt electrolytes for high-energy-density aqueous batteries, Nat. Energy, 2016, 1, 16129 CrossRef CAS .
  38. L. Suo, O. Borodin, Y. Wang, X. Rong, W. Sun, X. Fan, S. Xu, M. A. Schroeder, A. V. Cresce, F. Wang, C. Yang, Y.-S. Hu, K. Xu and C. Wang, “Water-in-Salt” Electrolyte Makes Aqueous Sodium-Ion Battery Safe, Green, and Long-Lasting, Adv. Energy Mater., 2017, 1701189 CrossRef .
  39. Y. Korenblit, A. Kajdos, W. C. West, M. C. Smart, E. J. Brandon, A. Kvit, J. Jagiello and G. Yushin, In Situ Studies of Ion Transport in Microporous Supercapacitor Electrodes at Ultralow Temperatures, Adv. Funct. Mater., 2012, 22(8), 1655–1662 CrossRef CAS .
  40. M. V. Fedorov and A. A. Kornyshev, Ionic Liquids at Electrified Interfaces, Chem. Rev., 2014, 114(5), 2978–3036 CrossRef CAS PubMed .
  41. R. Hayes, G. G. Warr and R. Atkin, Structure and Nanostructure in Ionic Liquids, Chem. Rev., 2015, 115(13), 6357–6426 CrossRef CAS PubMed .
  42. R. Lin, P.-L. Taberna, S. Fantini, V. Presser, C. R. Pérez, F. Malbosc, N. L. Rupesinghe, K. B. K. Teo, Y. Gogotsi and P. Simon, Capacitive Energy Storage from −50 to 100 °C Using an Ionic Liquid Electrolyte, J. Phys. Chem. Lett., 2011, 2(19), 2396–2401 CrossRef CAS .
  43. N. Nitta, F. Wu, J. T. Lee and G. Yushin, Li-ion battery materials: present and future, Mater. Today, 2015, 18(5), 252–264 CrossRef CAS .
  44. V. V. N. Obreja, On the performance of supercapacitors with electrodes based on carbon nanotubes and carbon activated material—A review, Phys. E, 2008, 40(7), 2596–2605 CrossRef CAS .
  45. Z. Yu, L. Tetard, L. Zhai and J. Thomas, Supercapacitor electrode materials: nanostructures from 0 to 3 dimensions, Energy Environ. Sci., 2015, 8(3), 702–730 CAS .
  46. J. R. Miller and A. F. Burke, Electrochemical capacitors: Challenges and opportunities for real-world applications, Electrochem. Soc. Interface, 2008, 17(1), 53–57 CAS .
  47. M. F. El-Kady, V. Strong, S. Dubin and R. B. Kaner, Laser Scribing of High-Performance and Flexible Graphene-Based Electrochemical Capacitors, Science, 2012, 335(6074), 1326–1330 CrossRef CAS PubMed .
  48. I. Hadjipaschalis, A. Poullikkas and V. Efthimiou, Overview of current and future energy storage technologies for electric power applications, Renewable Sustainable Energy Rev., 2009, 13(6–7), 1513–1522 CrossRef .
  49. M. Conte, Supercapacitors Technical Requirements for New Applications, Fuel Cells, 2010, 10(5), 806–818 CrossRef CAS .
  50. S. P. Ong, O. Andreussi, Y. Wu, N. Marzari and G. Ceder, Electrochemical Windows of Room-Temperature Ionic Liquids from Molecular Dynamics and Density Functional Theory Calculations, Chem. Mater., 2011, 23(11), 2979–2986 CrossRef CAS .
  51. P. A. Z. Suarez, C. S. Consorti, R. F. d. Souza, J. Dupont and R. S. Gonçalves, Electrochemical Behavior of Vitreous Glass Carbon and Platinum Electrodes in the Ionic Liquid 1-n-Butyl-3-Methylimidazolium Trifluoroacetate, J. Braz. Chem. Soc., 2002, 13, 106–109 CrossRef CAS .
  52. N. De Vos, C. Maton and C. V. Stevens, Electrochemical Stability of Ionic Liquids: General Influences and Degradation Mechanisms, ChemElectroChem, 2014, 1(8), 1258–1270 CrossRef CAS .
  53. M. Hayyan, F. S. Mjalli, M. A. Hashim, I. M. AlNashef and T. X. Mei, Investigating the electrochemical windows of ionic liquids, J. Ind. Eng. Chem., 2013, 19(1), 106–112 CrossRef CAS .
  54. Y. Gogotsi, Materials science: Energy storage wrapped up, Nature, 2014, 509(7502), 568–570 CrossRef CAS PubMed .
  55. W. Li and X. He, Review of Nonisolated High-Step-Up DC/DC Converters in Photovoltaic Grid-Connected Applications, IEEE Trans. Ind. Electron., 2011, 58(4), 1239–1250 CrossRef .
  56. H. A. Andreas, Self-Discharge in Electrochemical Capacitors: A Perspective Article, J. Electrochem. Soc., 2015, 162(5), A5047–A5053 CrossRef CAS .
  57. C. Merlet, C. Péan, B. Rotenberg, P. A. Madden, P. Simon and M. Salanne, Simulating Supercapacitors: Can We Model Electrodes As Constant Charge Surfaces?, J. Phys. Chem. Lett., 2013, 4(2), 264–268 CrossRef CAS PubMed .
  58. V. V. Chaban and O. V. Prezhdo, Nanoscale Carbon Greatly Enhances Mobility of a Highly Viscous Ionic Liquid, ACS Nano, 2014, 8(8), 8190–8197 CrossRef CAS PubMed .
  59. O. Borodin, Polarizable Force Field Development and Molecular Dynamics Simulations of Ionic Liquids, J. Phys. Chem. B, 2009, 113(33), 11463–11478 CrossRef CAS PubMed .
  60. F. Dommert, K. Wendler, R. Berger, L. Delle Site and C. Holm, Force Fields for Studying the Structure and Dynamics of Ionic Liquids: A Critical Review of Recent Developments, ChemPhysChem, 2012, 13(7), 1625–1637 CrossRef CAS PubMed .
  61. T. Köddermann, D. Reith and R. Ludwig, Comparison of Force Fields on the Basis of Various Model Approaches—How To Design the Best Model for the [CnMIM][NTf2] Family of Ionic Liquids, ChemPhysChem, 2013, 14(14), 3368–3374 CrossRef PubMed .
  62. C. Y. Son, J. G. McDaniel, J. R. Schmidt, Q. Cui and A. Yethiraj, First-Principles United Atom Force Field for the Ionic Liquid BMIM + BF4: An Alternative to Charge Scaling, J. Phys. Chem. B, 2016, 120(14), 3560–3568 CrossRef CAS PubMed .
  63. J. B. Haskins and J. W. Lawson, Evaluation of molecular dynamics simulation methods for ionic liquid electric double layers, J. Chem. Phys., 2016, 144(18), 184707 CrossRef PubMed .
  64. J. I. Siepmann and M. Sprik, Influence of surface topology and electrostatic potential on water/electrode systems, J. Chem. Phys., 1995, 102(1), 511–524 CrossRef CAS .
  65. Z. Wang, Y. Yang, D. L. Olmsted, M. Asta and B. B. Laird, Evaluation of the constant potential method in simulating electric double-layer capacitors, J. Chem. Phys., 2014, 141(18), 184102 CrossRef PubMed .
  66. S. K. Reed, O. J. Lanning and P. A. Madden, Electrochemical interface between an ionic liquid and a model metallic electrode, J. Chem. Phys., 2007, 126(8), 084704 CrossRef PubMed .
  67. S. K. Reed, P. A. Madden and A. Papadopoulos, Electrochemical charge transfer at a metallic electrode: A simulation study, J. Chem. Phys., 2008, 128(12), 124701 CrossRef PubMed .
  68. L. Pastewka, T. T. Järvi, L. Mayrhofer and M. Moseler, Charge-transfer model for carbonaceous electrodes in polar environments, Phys. Rev. B: Condens. Matter Mater. Phys., 2011, 83(16), 165418 CrossRef .
  69. P. T. Kiss, M. Sega and A. Baranyai, Efficient Handling of Gaussian Charge Distributions: An Application to Polarizable Molecular Models, J. Chem. Theory Comput., 2014, 10(12), 5513–5519 CrossRef CAS PubMed .
  70. D. Golze, M. Iannuzzi, M.-T. Nguyen, D. Passerone and J. Hutter, Simulation of Adsorption Processes at Metallic Interfaces: An Image Charge Augmented QM/MM Approach, J. Chem. Theory Comput., 2013, 9(11), 5086–5097 CrossRef CAS PubMed .
  71. C. E. Wilmer, K. C. Kim and R. Q. Snurr, An Extended Charge Equilibration Method, J. Phys. Chem. Lett., 2012, 3(17), 2506–2511 CrossRef CAS PubMed .
  72. R. A. Nistor and M. H. Müser, Dielectric properties of solids in the regular and split-charge equilibration formalisms, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 79(10), 104303 CrossRef .
  73. A. A. Kornyshev, Double-Layer in Ionic Liquids:[thin space (1/6-em)] Paradigm Change?, J. Phys. Chem. B, 2007, 111(20), 5545–5557 CrossRef CAS PubMed .
  74. R. Yamamoto, H. Morisaki, O. Sakata, H. Shimotani, H. Yuan, Y. Iwasa, T. Kimura and Y. Wakabayashi, External electric field dependence of the structure of the electric double layer at an ionic liquid/Au interface, Appl. Phys. Lett., 2012, 101(5), 053122 CrossRef .
  75. J. Vatamanu, M. Vatamanu, O. Borodin and D. Bedrov, A comparative study of room temperature ionic liquids and their organic solvent mixtures near charged electrodes, J. Phys.: Condens. Matter, 2016, 28(46), 464002 CrossRef PubMed .
  76. M. A. Gebbie, M. Valtiner, X. Banquy, E. T. Fox, W. A. Henderson and J. N. Israelachvili, Ionic liquids behave as dilute electrolyte solutions, Proc. Natl. Acad. Sci. U. S. A., 2013, 110(24), 9674–9679 CrossRef CAS PubMed .
  77. H. Jung, M. Lee, B. C. Yeo, K.-R. Lee and S. S. Han, Atomistic Observation of the Lithiation and Delithiation Behaviors of Silicon Nanowires Using Reactive Molecular Dynamics Simulations, J. Phys. Chem. C, 2015, 119(7), 3447–3455 CAS .
  78. C. Merlet, M. Salanne, B. Rotenberg and P. A. Madden, Influence of solvation on the structural and capacitive properties of electrical double layer capacitors, Electrochim. Acta, 2013, 101, 262–271 CrossRef CAS .
  79. J. Vatamanu, O. Borodin and G. D. Smith, 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, 2011, 116(1), 1114–1121 Search PubMed .
  80. O. Borodin, G. D. Smith and W. Henderson, Li+ Cation Environment, Transport, and Mechanical Properties of the LiTFSI Doped N-Methyl-N-alkylpyrrolidinium+TFSI-Ionic Liquids, J. Phys. Chem. B, 2006, 110(34), 16879–16886 CrossRef CAS PubMed .
  81. M. Druschler, N. Borisenko, J. Wallauer, C. Winter, B. Huber, F. Endres and B. Roling, 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(15), 5090–5099 RSC .
  82. C. Cannes, H. Cachet, C. Debiemme-Chouvy, C. Deslouis, J. de Sanoit, C. Le Naour and V. A. Zinovyeva, Double Layer at [BuMeIm][Tf2N] Ionic Liquid-Pt or -C Material Interfaces, J. Phys. Chem. C, 2013, 117(44), 22915–22925 CAS .
  83. J. Vatamanu, L. Xing, W. Li and D. Bedrov, Influence of temperature on the capacitance of ionic liquid electrolytes on charged surfaces, Phys. Chem. Chem. Phys., 2014, 16(11), 5174–5182 RSC .
  84. K. B. Oldham, A Gouy–Chapman–Stern model of the double layer at a (metal)/(ionic liquid) interface, J. Electroanal. Chem., 2008, 613(2), 131–138 CrossRef CAS .
  85. H. Yining, H. Shanghui and Y. Tianying, A mean-field theory on the differential capacitance of asymmetric ionic liquid electrolytes, J. Phys.: Condens. Matter, 2014, 26(28), 284103 CrossRef PubMed .
  86. K. Breitsprecher, P. Kosovan and C. Holm, Coarse-grained simulations of an ionic liquid-based capacitor: I. Density, ion size, and valency effects, J. Phys.: Condens. Matter, 2014, 26(28), 284108 CrossRef PubMed .
  87. D. Henderson, S. Lamperski, L. Bari Bhuiyan and J. Wu, The tail effect on the shape of an electrical double layer differential capacitance curve, J. Chem. Phys., 2013, 138(14), 144704 CrossRef PubMed .
  88. D. Henderson, D.-e. Jiang, Z. Jin and J. Wu, Application of Density Functional Theory To Study the Double Layer of an Electrolyte with an Explicit Dimer Model for the Solvent, J. Phys. Chem. B, 2012, 116(36), 11356–11361 CrossRef CAS PubMed .
  89. D.-e. Jiang, D. Meng and J. Wu, Density functional theory for differential capacitance of planar electric double layers in ionic liquids, Chem. Phys. Lett., 2011, 504(4–6), 153–158 CrossRef CAS .
  90. J. Forsman, C. E. Woodward and M. Trulsson, A Classical Density Functional Theory of Ionic Liquids, J. Phys. Chem. B, 2011, 115(16), 4606–4612 CrossRef CAS PubMed .
  91. J. Reszko-Zygmunt, S. Sokołowski, D. Henderson and D. Boda, Temperature dependence of the double layer capacitance for the restricted primitive model of an electrolyte solution from a density functional approach, J. Chem. Phys., 2005, 122(8), 084504 CrossRef CAS PubMed .
  92. S. Lamperski, C. W. Outhwaite and L. B. Bhuiyan, The Electric Double-Layer Differential Capacitance at and near Zero Surface Charge for a Restricted Primitive Model Electrolyte, J. Phys. Chem. B, 2009, 113(26), 8925–8929 CrossRef CAS PubMed .
  93. L. Sarkisov and P. R. Van Tassel, Theories of molecular fluids confined in disordered porous materials, J. Phys.: Condens. Matter, 2008, 20, 333101 CrossRef .
  94. S. Woelki, H.-H. Kohler and H. Krienke, A Singlet-RISM Theory for Solid/Liquid Interfaces Part I:[thin space (1/6-em)] Uncharged Walls, J. Phys. Chem. B, 2007, 111(47), 13386–13397 CrossRef CAS PubMed .
  95. H. Yang, J. Yang, Z. Bo, X. Chen, X. Shuai, J. Kong, J. Yan and K. Cen, Kinetic-Dominated Charging Mechanism within Representative Aqueous Electrolyte-based Electric Double-Layer Capacitors, J. Phys. Chem. Lett., 2017, 3703–3710 CrossRef CAS PubMed .
  96. Z. Hu, J. Vatamanu, O. Borodin and D. Bedrov, A comparative study of alkylimidazolium room temperature ionic liquids with FSI and TFSI anions near charged electrodes, Electrochim. Acta, 2014, 145, 40–52 CrossRef CAS .
  97. H. Yang, X. Zhang, J. Yang, Z. Bo, M. Hu, J. Yan and K. Cen, Molecular Origin of Electric Double-Layer Capacitance at Multilayer Graphene Edges, J. Phys. Chem. Lett., 2017, 8(1), 153–160 CrossRef CAS PubMed .
  98. T. A. Ho and A. Striolo, Capacitance enhancement via electrode patterning, J. Chem. Phys., 2013, 139(20), 204708 CrossRef PubMed .
  99. L. Xing, J. Vatamanu, G. D. Smith and D. Bedrov, 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(9), 1124–1129 CrossRef CAS PubMed .
  100. C. Zhan, Y. Zhang, P. T. Cummings and D.-e. Jiang, Computational insight into the capacitive performance of graphene edge planes, Carbon, 2017, 116, 278–285 CrossRef CAS .
  101. J. Vatamanu, Z. Hu, D. Bedrov, C. Perez and Y. Gogotsi, Increasing Energy Storage in Electrochemical Capacitors with Ionic Liquid Electrolytes and Nanostructured Carbon Electrodes, J. Phys. Chem. Lett., 2013, 4(17), 2829–2837 CrossRef CAS .
  102. G. Feng, D.-e. Jiang and P. T. Cummings, Curvature Effect on the Capacitance of Electric Double Layers at Ionic Liquid/Onion-Like Carbon Interfaces, J. Chem. Theory Comput., 2012, 8(3), 1058–1063 CrossRef CAS PubMed .
  103. G. Feng, S. Li, J. S. Atchison, V. Presser and P. T. Cummings, Molecular Insights into Carbon Nanotube Supercapacitors: Capacitance Independent of Voltage and Temperature, J. Phys. Chem. C, 2013, 117(18), 9178–9186 CAS .
  104. R. Lin, P. L. Taberna, J. Chmiola, D. Guay, Y. Gogotsi and P. Simon, 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(1), A7–A12 CrossRef CAS .
  105. C. Largeot, C. Portet, J. Chmiola, P.-L. Taberna, Y. Gogotsi and P. Simon, Relation between the Ion Size and Pore Size for an Electric Double-Layer Capacitor, J. Am. Chem. Soc., 2008, 130(9), 2730–2731 CrossRef CAS PubMed .
  106. S. Boukhalfa, D. Gordon, L. He, Y. B. Melnichenko, N. Nitta, A. Magasinski and G. Yushin, In Situ Small Angle Neutron Scattering Revealing Ion Sorption in Microporous Carbon Electrical Double Layer Capacitors, ACS Nano, 2014, 8(3), 2495–2503 CrossRef CAS PubMed .
  107. S. Boukhalfa, L. He, Y. B. Melnichenko and G. Yushin, Small-Angle Neutron Scattering for In Situ Probing of Ion Adsorption Inside Micropores, Angew. Chem., Int. Ed., 2013, 52(17), 4618–4622 CrossRef CAS PubMed .
  108. S. Kondrat and A. Kornyshev, Superionic state in double-layer capacitors with nanoporous electrodes, J. Phys.: Condens. Matter, 2011, 23(2), 022201 CrossRef CAS PubMed .
  109. G. Feng and P. T. Cummings, Supercapacitor Capacitance Exhibits Oscillatory Behavior as a Function of Nanopore Size, J. Phys. Chem. Lett., 2011, 2(22), 2859–2864 CrossRef CAS .
  110. J. Vatamanu, M. Vatamanu and D. Bedrov, Non-Faradaic Energy Storage by Room Temperature Ionic Liquids in Nanoporous Electrodes, ACS Nano, 2015, 9(6), 5999–6017 CrossRef CAS PubMed .
  111. P. Wu, J. Huang, V. Meunier, B. G. Sumpter and R. Qiao, Voltage Dependent Charge Storage Modes and Capacity in Subnanometer Pores, J. Phys. Chem. Lett., 2012, 3(13), 1732–1737 CrossRef CAS PubMed .
  112. Z. S. Wu, K. Parvez, X. Feng and K. Müllen, Graphene-based in-plane micro-supercapacitors with high power and energy densities, Nat. Commun., 2013, 4, 2487 Search PubMed .
  113. P. Wu, J. Huang, V. Meunier, B. G. Sumpter and R. Qiao, Complex Capacitance Scaling in Ionic Liquids-Filled Nanopores, ACS Nano, 2011, 5(11), 9044–9051 CrossRef CAS PubMed .
  114. D. Henderson, Oscillations in the capacitance of a nanopore containing an electrolyte due to pore width and nonzero size ions, J. Colloid Interface Sci., 2012, 374(1), 345–347 CrossRef CAS PubMed .
  115. D.-e. Jiang, Z. Jin, D. Henderson and J. Wu, Solvent Effect on the Pore-Size Dependence of an Organic Electrolyte Supercapacitor, J. Phys. Chem. Lett., 2012, 3(13), 1727–1731 CrossRef CAS PubMed .
  116. K. L. van Aken, M. Beidaghi and Y. Gogotsi, Formulation of Ionic-Liquid Electrolyte To Expand the Voltage Window of Supercapacitors, Angew. Chem., Int. Ed., 2015, 54(16), 4806–4809 CrossRef CAS PubMed .
  117. S. R. Varanasi and S. K. Bhatia, Optimal Electrode Mass Ratio in Nanoporous Carbon Electrochemical Supercapacitors, J. Phys. Chem. C, 2016, 120(49), 27925–27933 CAS .
  118. Y. Qiu and Y. Chen, Capacitance Performance of Sub-2 nm Graphene Nanochannels in Aqueous Electrolyte, J. Phys. Chem. C, 2015, 119(42), 23813–23819 CAS .
  119. D.-e. Jiang and J. Wu, Unusual effects of solvent polarity on capacitance for organic electrolytes in a nanoporous electrode, Nanoscale, 2014, 6(10), 5545–5550 RSC .
  120. A. A. Kornyshev, The simplest model of charge storage in single file metallic nanopores, Faraday Discuss., 2013, 164, 117–133 RSC .
  121. S. Kondrat and A. A. Kornyshev, Pressing a spring: what does it take to maximize the energy storage in nanoporous supercapacitors?, Nanoscale Horiz., 2016, 1(1), 45–52 RSC .
  122. L. Mohammadzadeh, P. Quaino and W. Schmickler, Interactions of anions and cations in carbon nanotubes, Faraday Discuss., 2016, 193, 415–426 RSC .
  123. C. Merlet, C. Péan, B. Rotenberg, P. A. Madden, B. Daffos, P. L. Taberna, P. Simon and M. Salanne, Highly confined ions store charge more efficiently in supercapacitors, Nat. Commun., 2013, 4, 2701 CAS .
  124. S. K. Jain, R. J. M. Pellenq, J. P. Pikunic and K. E. Gubbins, Molecular Modeling of Porous Carbons Using the Hybrid Reverse Monte Carlo Method, Langmuir, 2006, 22(24), 9942–9948 CrossRef CAS PubMed .
  125. J. M. Griffin, A. C. Forse, W.-Y. Tsai, P.-L. Taberna, P. Simon and C. P. Grey, In situ NMR and electrochemical quartz crystal microbalance techniques reveal the structure of the electrical double layer in supercapacitors, Nat. Mater., 2015, 14(8), 812–819 CrossRef CAS PubMed .
  126. H. Wang, T. K. J. Köster, N. M. Trease, J. Ségalini, P.-L. Taberna, P. Simon, Y. Gogotsi and C. P. Grey, Real-Time NMR Studies of Electrochemical Double-Layer Capacitors, J. Am. Chem. Soc., 2011, 133(48), 19270–19273 CrossRef CAS PubMed .
  127. L. Hu, D. Guo, G. Feng, H. Li and T. Zhai, Asymmetric Behavior of Positive and Negative Electrodes in Carbon/Carbon Supercapacitors and Its Underlying Mechanism, J. Phys. Chem. C, 2016, 120(43), 24675–24681 CAS .
  128. C. Prehal, C. Koczwara, N. Jäckel, A. Schreiber, M. Burian, H. Amenitsch, M. A. Hartmann, V. Presser and O. Paris, Quantification of ion confinement and desolvation in nanoporous carbon supercapacitors with modelling and in situ X-ray scattering, Nat. Energy, 2017, 2, 16215 CrossRef .
  129. J. Chmiola, G. Yushin, Y. Gogotsi, C. Portet, P. Simon and P. L. Taberna, Anomalous increase in carbon capacitance at pore sizes less than 1 nanometer, Science, 2006, 313(5794), 1760–1763 CrossRef CAS PubMed .
  130. T. A. Centeno, O. Sereda and F. Stoeckli, Capacitance in carbon pores of 0.7 to 15 nm: a regular pattern, Phys. Chem. Chem. Phys., 2011, 13(27), 12403–12406 RSC .
  131. J. R. Dahn and J. A. Seel, Energy and Capacity Projections for Practical Dual-Graphite Cells, J. Electrochem. Soc., 2000, 147(3), 899–901 CrossRef CAS .
  132. K. Beltrop, S. Beuker, A. Heckmann, M. Winter and T. Placke, Alternative electrochemical energy storage: potassium-based dual-graphite batteries, Energy Environ. Sci., 2017 DOI:10.10.1039/c7ee01535f .
  133. T. Placke, O. Fromm, S. F. Lux, P. Bieker, S. Rothermel, H.-W. Meyer, S. Passerini and M. Winter, Reversible Intercalation of Bis(trifluoromethanesulfonyl)imide Anions from an Ionic Liquid Electrolyte into Graphite for High Performance Dual-Ion Cells, J. Electrochem. Soc., 2012, 159(11), A1755–A1765 CrossRef CAS .
  134. X. Qi, B. Blizanac, A. DuPasquier, P. Meister, T. Placke, M. Oljaca, J. Li and M. Winter, Investigation of PF6- and TFSI- anion intercalation into graphitized carbon blacks and its influence on high voltage lithium ion batteries, Phys. Chem. Chem. Phys., 2014, 16(46), 25306–25313 RSC .
  135. J. A. Read, A. V. Cresce, M. H. Ervin and K. Xu, Dual-graphite chemistry enabled by a high voltage electrolyte, Energy Environ. Sci., 2014, 7(2), 617–620 CAS .
  136. S. Rothermel, P. Meister, G. Schmuelling, O. Fromm, H. W. Meyer, S. Nowak, M. Winter and T. Placke, Dual-graphite cells based on the reversible intercalation of bis(trifluoromethanesulfonyl)imide anions from an ionic liquid electrolyte, Energy Environ. Sci., 2014, 7(10), 3412–3423 CAS .
  137. J. A. Read, In Situ Studies on the Electrochemical Intercalation of Hexafluorophosphate Anion in Graphite with Selective Cointercalation of Solvent, J. Phys. Chem. C, 2015, 119(16), 8438–8446 CAS .
  138. K. Beltrop, P. Meister, S. Klein, A. Heckmann, M. Grunebaum, H. D. Wiemhofer, M. Winter and T. Placke, Does Size really Matter? New Insights into the Intercalation Behavior of Anions into a Graphite-Based Positive Electrode for Dual-Ion Batteries, Electrochim. Acta, 2016, 209, 44–55 CrossRef CAS .
  139. T. Fukutsuka, F. Yamane, K. Miyazaki and T. Abe, Electrochemical Intercalation of Bis(fluorosulfonyl)amide Anion into Graphite, J. Electrochem. Soc., 2016, 163(3), A499–A503 CrossRef CAS .
  140. S. Miyoshi, T. Akbay, T. Kurihara, T. Fukuda, A. T. Staykov, S. Ida and T. Ishihara, Fast Diffusivity of PF6 Anions in Graphitic Carbon for a Dual-Carbon Rechargeable Battery with Superior Rate Property, J. Phys. Chem. C, 2016, 120(40), 22887–22894 CAS .
  141. S. Miyoshi, H. Nagano, T. Fukuda, T. Kurihara, M. Watanabe, S. Ida and T. Ishihara, Dual-Carbon Battery Using High Concentration LiPF6 in Dimethyl Carbonate (DMC) Electrolyte, J. Electrochem. Soc., 2016, 163(7), A1206–A1213 CrossRef CAS .
  142. P. Bhauriyal, A. Mahata and B. Pathak, The staging mechanism of AlCl4 intercalation in a graphite electrode for an aluminium-ion battery, Phys. Chem. Chem. Phys., 2017, 19(11), 7980–7989 RSC .
  143. H. Fan, L. Qi and H. Wang, Hexafluorophosphate anion intercalation into graphite electrode from methyl propionate, Solid State Ionics, 2017, 300, 169–174 CrossRef CAS .
  144. J. Fan, Z. Zhang, Y. Liu, A. Wang, L. Li and W. Yuan, An excellent rechargeable PP14TFSI ionic liquid dual-ion battery, Chem. Commun., 2017, 53(51), 6891–6894 RSC .
  145. C. Jiang, Y. Fang, J. Lang and Y. Tang, Integrated Configuration Design for Ultrafast Rechargeable Dual-Ion Battery, Adv. Energy Mater., 2017, 1700913 CrossRef .
  146. I. A. Rodríguez-Pérez and X. Ji, Anion Hosting Cathodes in Dual-Ion Batteries, ACS Energy Lett., 2017, 1762–1770 CrossRef .
  147. D.-Y. Wang, C.-Y. Wei, M.-C. Lin, C.-J. Pan, H.-L. Chou, H.-A. Chen, M. Gong, Y. Wu, C. Yuan, M. Angell, Y.-J. Hsieh, Y.-H. Chen, C.-Y. Wen, C.-W. Chen, B.-J. Hwang, C.-C. Chen and H. Dai, Advanced rechargeable aluminium ion battery with a high-quality natural graphite cathode, Nat. Commun., 2017, 8, 14283 CrossRef CAS PubMed .
  148. O. Borodin, Molecular Modeling of Electrolytes, in Electrolytes for Lithium and Lithium-Ion Batteries, ed. T. R. Jow, K. Xu, O. Borodin and M. Ue, Springer, New York, 2014, vol. 58, pp. 371–401 Search PubMed .
  149. S. A. Delp, O. Borodin, M. Olguin, C. G. Eisner, J. L. Allen and T. R. Jow, Importance of Reduction and Oxidation Stability of High Voltage Electrolytes and Additives, Electrochim. Acta, 2016, 209, 498–510 CrossRef CAS .
  150. O. Borodin, W. Behl and T. R. Jow, Oxidative Stability and Initial Decomposition Reactions of Carbonate, Sulfone, and Alkyl Phosphate-Based Electrolytes, J. Phys. Chem. C, 2013, 117(17), 8661–8682 CAS .
  151. O. Borodin, M. Olguin, C. E. Spear, K. Leiter and J. Knap, Towards high throughput screening of electrochemical stability of battery electrolytes, Nanotechnology, 2015, 26(35), 354003 CrossRef PubMed .
  152. N. Chapman, O. Borodin, T. Yoon, C. C. Nguyen and B. L. Lucht, Spectroscopic and Density Functional Theory Characterization of Common Lithium Salt Solvates in Carbonate Electrolytes for Lithium Batteries, J. Phys. Chem. C, 2017, 121(4), 2135–2148 CAS .
  153. Y. Okamoto, Density Functional Theory Calculations of Alkali Metal (Li, Na, and K) Graphite Intercalation Compounds, J. Phys. Chem. C, 2014, 118(1), 16–19 CAS .
  154. K. Persson, Y. Hinuma, Y. S. Meng, A. Van der Ven and G. Ceder, Thermodynamic and kinetic properties of the Li-graphite system from first-principles calculations, Phys. Rev. B: Condens. Matter Mater. Phys., 2010, 82, 125416 CrossRef .
  155. K. Persson, V. A. Sethuraman, L. J. Hardwick, Y. Hinuma, Y. S. Meng, A. van der Ven, V. Srinivasan, R. Kostecki and G. Ceder, Lithium Diffusion in Graphitic Carbon, J. Phys. Chem. Lett., 2010, 1(8), 1176–1180 CrossRef CAS .
  156. Y. He, R. Qiao, J. Vatamanu, O. Borodin, D. Bedrov, J. Huang and B. G. Sumpter, Importance of Ion Packing on the Dynamics of Ionic Liquids during Micropore Charging, J. Phys. Chem. Lett., 2016, 7(1), 36–42 CrossRef CAS PubMed .
  157. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys., 2009, 81(1), 109–162 CrossRef CAS .
  158. N. M. Aziz, A. A. Attia, H. P. Adel and R. A. Riham, Simulation of the Band Structure of Graphene and Carbon Nanotube, J. Phys.: Conf. Ser., 2012, 343(1), 012076 Search PubMed .
  159. E. Paek, A. J. Pak, K. E. Kweon and G. S. Hwang, On the Origin of the Enhanced Supercapacitor Performance of Nitrogen-Doped Graphene, J. Phys. Chem. C, 2013, 117(11), 5610–5616 CAS .
  160. J. Dai, J. Li, H. Zeng and X. Cui, Measurements on quantum capacitance of individual single walled carbon nanotubes, Appl. Phys. Lett., 2009, 94(9), 093114 CrossRef .
  161. M. D. Stoller, C. W. Magnuson, Y. Zhu, S. Murali, J. W. Suk, R. Piner and R. S. Ruoff, Interfacial capacitance of single layer graphene, Energy Environ. Sci., 2011, 4(11), 4685–4689 CAS .
  162. E. Uesugi, H. Goto, R. Eguchi, A. Fujiwara and Y. Kubozono, Electric double-layer capacitance between an ionic liquid and few-layer graphene, Sci. Rep., 2013, 3, 1595 CrossRef PubMed .
  163. S. Luryi, Quantum capacitance devices, Appl. Phys. Lett., 1988, 52(6), 501–503 CrossRef .
  164. H. Gao, L. Song, W. Guo, L. Huang, D. Yang, F. Wang, Y. Zuo, X. Fan, Z. Liu, W. Gao, R. Vajtai, K. Hackenberg and P. M. Ajayan, A simple method to synthesize continuous large area nitrogen-doped graphene, Carbon, 2012, 50(12), 4476–4482 CrossRef CAS .
  165. C. Wang, Y. Zhou, L. He, T.-W. Ng, G. Hong, Q.-H. Wu, F. Gao, C.-S. Lee and W. Zhang, In situ nitrogen-doped graphene grown from polydimethylsiloxane by plasma enhanced chemical vapor deposition, Nanoscale, 2013, 5(2), 600–605 RSC .
  166. M. D. Stoller, S. Park, Y. Zhu, J. An and R. S. Ruoff, Graphene-Based Ultracapacitors, Nano Lett., 2008, 8(10), 3498–3502 CrossRef CAS PubMed .
  167. N. Ketabi, T. de Boer, M. Karakaya, J. Zhu, R. Podila, A. M. Rao, E. Z. Kurmaev and A. Moewes, Tuning the electronic structure of graphene through nitrogen doping: experiment and theory, RSC Adv., 2016, 6(61), 56721–56727 RSC .
  168. P. Hu, D. Meng, G. Ren, R. Yan and X. Peng, Nitrogen-doped mesoporous carbon thin film for binder-free supercapacitor, Applied Materials Today, 2016, 5, 1–8 CrossRef .
  169. C. Zhan, Y. Zhang, P. T. Cummings and D.-e. Jiang, Enhancing graphene capacitance by nitrogen: effects of doping configuration and concentration, Phys. Chem. Chem. Phys., 2016, 18, 4668–4674 RSC .
  170. M. Fan, Z.-Q. Feng, C. Zhu, X. Chen, C. Chen, J. Yang and D. Sun, Recent progress in 2D or 3D N-doped graphene synthesis and the characterizations, properties, and modulations of N species, J. Mater. Sci., 2016, 51(23), 10323–10349 CrossRef CAS .
  171. J. Zhu, A. S. Childress, M. Karakaya, S. Dandeliya, A. Srivastava, Y. Lin, A. M. Rao and R. Podila, Defect-Engineered Graphene for High-Energy- and High-Power-Density Supercapacitor Devices, Adv. Mater., 2016, 28(33), 7185–7192 CrossRef CAS PubMed .
  172. A. Dey, A. Chroneos, N. S. J. Braithwaite, R. P. Gandhiraman and S. Krishnamurthy, Plasma engineering of graphene, Appl. Phys. Rev., 2016, 3(2), 021301 Search PubMed .
  173. R. Narayanan, H. Yamada, M. Karakaya, R. Podila, A. M. Rao and P. R. Bandaru, Modulation of the Electrostatic and Quantum Capacitances of Few Layered Graphenes through Plasma Processing, Nano Lett., 2015, 15(5), 3067–3072 CrossRef CAS PubMed .
  174. B. C. Wood, T. Ogitsu, M. Otani and J. Biener, First-Principles-Inspired Design Strategies for Graphene-Based Supercapacitor Electrodes, J. Phys. Chem. C, 2013, 118(1), 4–15 Search PubMed .
  175. J. Vatamanu, X. Ni, F. Liu and D. Bedrov, Tailoring graphene-based electrodes from semiconducting to metallic to increase the energy density in supercapacitors, Nanotechnology, 2015, 26(46), 464001 CrossRef PubMed .
  176. A. J. Pak, E. Paek and G. S. Hwang, Tailoring the performance of graphene-based supercapacitors using topological defects: A theoretical assessment, Carbon, 2014, 68, 734–741 CrossRef CAS .
  177. B. Wang, L. Tsetseris and S. T. Pantelides, Introduction of nitrogen with controllable configuration into graphene via vacancies and edges, J. Mater. Chem. A, 2013, 1(47), 14927–14934 CAS .
  178. D. Weingarth, M. Zeiger, N. Jäckel, M. Aslan, G. Feng and V. Presser, Graphitization as a Universal Tool to Tailor the Potential-Dependent Capacitance of Carbon Supercapacitors, Adv. Energy Mater., 2014, 4(13), 1400316 CrossRef .
  179. R. Singh, J. Monk and F. R. Hung, Heterogeneity in the Dynamics of the Ionic Liquid [BMIM+][PF6] Confined in a Slit Nanopore, J. Phys. Chem. C, 2011, 115(33), 16544–16554 CAS .
  180. C. Iacob, J. R. Sangoro, W. K. Kipnusu, R. Valiullin, J. Karger and F. Kremer, Enhanced charge transport in nano-confined ionic liquids, Soft Matter, 2012, 8(2), 289–293 RSC .
  181. S. Kondrat, P. Wu, R. Qiao and A. A. Kornyshev, Accelerating charging dynamics in subnanometre pores, Nat. Mater., 2014, 13(4), 387–393 CrossRef CAS PubMed .
  182. A. Kajdos, A. Kvit, F. Jones, J. Jagiello and G. Yushin, Tailoring the Pore Alignment for Rapid Ion Transport in Microporous Carbons, J. Am. Chem. Soc., 2010, 132(10), 3252 CrossRef CAS PubMed .
  183. Y. He, R. Qiao, J. Vatamanu, O. Borodin, D. Bedrov, J. Huang and B. G. Sumpter, Importance of Ion Packing on the Dynamics of Ionic Liquids during Micropore Charging, J. Phys. Chem. Lett., 2016, 7(1), 36–42 CrossRef CAS PubMed .
  184. J. Xikai, H. Jingsong, Z. Hui, G. S. Bobby and Q. Rui, Dynamics of electrical double layer formation in room-temperature ionic liquids under constant-current charging conditions, J. Phys.: Condens. Matter, 2014, 26(28), 284109 CrossRef PubMed .
  185. C. Zhao, C. Wang, R. Gorkin Iii, S. Beirne, K. Shu and G. G. Wallace, Three dimensional (3D) printed electrodes for interdigitated supercapacitors, Electrochem. Commun., 2014, 41, 20–23 CrossRef CAS .
  186. R. Kumar, R. Savu, E. Joanni, A. R. Vaz, M. A. Canesqui, R. K. Singh, R. A. Timm, L. T. Kubota and S. A. Moshkalev, Fabrication of interdigitated micro-supercapacitor devices by direct laser writing onto ultra-thin, flexible and free-standing graphite oxide films, RSC Adv., 2016, 6(88), 84769–84776 RSC .
  187. C. Péan, C. Merlet, B. Rotenberg, P. A. Madden, P.-L. Taberna, B. Daffos, M. Salanne and P. Simon, On the Dynamics of Charging in Nanoporous Carbon-Based Supercapacitors, ACS Nano, 2014, 8(2), 1576–1583 CrossRef PubMed .
  188. A. C. Forse, C. Merlet, J. M. Griffin and C. P. Grey, New Perspectives on the Charging Mechanisms of Supercapacitors, J. Am. Chem. Soc., 2016, 138(18), 5731–5744 CrossRef CAS PubMed .
  189. A. L. Alpha, K. Svyatoslav, O. Gleb and A. K. Alexei, Charging dynamics of supercapacitors with narrow cylindrical nanopores, Nanotechnology, 2014, 25(31), 315401 CrossRef PubMed .
  190. M. Zhi, C. Xiang, J. Li, M. Li and N. Wu, Nanostructured carbon–metal oxide composite electrodes for supercapacitors: a review, Nanoscale, 2013, 5(1), 72–88 RSC .
  191. W. Wei, X. Cui, W. Chen and D. G. Ivey, Manganese oxide-based materials as electrochemical supercapacitor electrodes, Chem. Soc. Rev., 2011, 40(3), 1697–1721 RSC .
  192. H. Jiang, J. Ma and C. Z. Li, Mesoporous Carbon Incorporated Metal Oxide Nanomaterials as Supercapacitor Electrodes, Adv. Mater., 2012, 24(30), 4197–4202 CrossRef CAS PubMed .
  193. X. Lu, Y. Zeng, M. Yu, T. Zhai, C. Liang, S. Xie, M.-S. Balogun and Y. Tong, Oxygen-Deficient Hematite Nanorods as High-Performance and Novel Negative Electrodes for Flexible Asymmetric Supercapacitors, Adv. Mater., 2014, 26(19), 3148–3155 CrossRef CAS PubMed .
  194. K. A. Owusu, L. Qu, J. Li, Z. Wang, K. Zhao, C. Yang, K. M. Hercule, C. Lin, C. Shi, Q. Wei, L. Zhou and L. Mai, Low-crystalline iron oxide hydroxide nanoparticle anode for high-performance supercapacitors, Nat. Commun., 2017, 8, 14264 CrossRef PubMed .
  195. J. Dong, Y. Jiang, Q. Li, Q. Wei, W. Yang, S. Tan, X. Xu, Q. An and L. Mai, Pseudocapacitive titanium oxynitride mesoporous nanowires with iso-oriented nanocrystals for ultrahigh-rate sodium ion hybrid capacitors, J. Mater. Chem. A, 2017, 5(22), 10827–10835 CAS .
  196. G. A. Snook, P. Kao and A. S. Best, Conducting-polymer-based supercapacitor devices and electrodes, J. Power Sources, 2011, 196(1), 1–12 CrossRef CAS .
  197. C. Hu, E. Zhao, N. Nitta, A. Magasinski, G. Berdichevsky and G. Yushin, Aqueous solutions of acidic ionic liquids for enhanced stability of polyoxometalate-carbon supercapacitor electrodes, J. Power Sources, 2016, 326, 569–574 CrossRef CAS .
  198. Y. F. Song and R. Tsunashima, Recent advances on polyoxometalate-based molecular and composite materials, Chem. Soc. Rev., 2012, 41(22), 7384–7402 RSC .
  199. J. Alcaniz-Monge, G. Trautwein, S. Parres-Esclapez and J. A. Macia-Agullo, Influence of microporosity of activated carbons as a support of polyoxometalates, Microporous Mesoporous Mater., 2008, 115(3), 440–446 CrossRef CAS .
  200. C. Zhan, C. Lian, Y. Zhang, M. W. Thompson, Y. Xie, J. Wu, P. R. C. Kent, P. T. Cummings, D.-e. Jiang and D. J. Wesolowski, Computational Insights into Materials and Interfaces for Capacitive Energy Storage, Adv. Sci., 2017, 1700059 CrossRef PubMed .
  201. T. Brousse, D. Bélanger and J. W. Long, To Be or Not To Be Pseudocapacitive?, J. Electrochem. Soc., 2015, 162(5), A5185–A5189 CrossRef CAS .
  202. S. A. Ebrahim, M. E. Harb, M. M. Soliman and M. B. Tayel, Preparation and characterization of a pseudocapacitor electrode by spraying a conducting polymer onto a flexible substrate, J. Taibah Univ. Sci., 2016, 10(2), 281–285 CrossRef .
  203. A. M. Bryan, L. M. Santino, Y. Lu, S. Acharya and J. M. D'Arcy, Conducting Polymers for Pseudocapacitive Energy Storage, Chem. Mater., 2016, 28(17), 5989–5998 CrossRef CAS .
  204. T. K. Das and S. Prusty, Review on Conducting Polymers and Their Applications, Polym.-Plast. Technol. Eng., 2012, 51(14), 1487–1500 CrossRef CAS .
  205. C. Xia, W. Chen, X. Wang, M. N. Hedhili, N. Wei and H. N. Alshareef, Highly Stable Supercapacitors with Conducting Polymer Core–Shell Electrodes for Energy Storage Applications, Adv. Energy Mater., 2015, 5(8), 1401805 CrossRef .
  206. J. Duay, E. Gillette, R. Liu and S. B. Lee, Highly flexible pseudocapacitor based on freestanding heterogeneous MnO2/conductive polymer nanowire arrays, Phys. Chem. Chem. Phys., 2012, 14(10), 3329–3337 RSC .
  207. C. Peng, J. Jin and G. Z. Chen, A comparative study on electrochemical co-deposition and capacitance of composite films of conducting polymers and carbon nanotubes, Electrochim. Acta, 2007, 53(2), 525–537 CrossRef CAS .
  208. F. Alvi, M. K. Ram, P. A. Basnayaka, E. Stefanakos, Y. Goswami and A. Kumar, Graphene–polyethylenedioxythiophene conducting polymer nanocomposite based supercapacitor, Electrochim. Acta, 2011, 56(25), 9406–9412 CrossRef CAS .
  209. I. Kovalenko, D. G. Bucknall and G. Yushin, Detonation Nanodiamond and Onion-Like-Carbon-Embedded Polyaniline for Supercapacitors, Adv. Funct. Mater., 2010, 20(22), 3979–3986 CrossRef CAS .
  210. J. Benson, I. Kovalenko, S. Boukhalfa, D. Lashmore, M. Sanghadasa and G. Yushin, Multifunctional CNT–Polymer Composites for Ultra-Tough Structural Supercapacitors and Desalination Devices, Adv. Mater., 2013, 25(45), 6625–6632 CrossRef CAS PubMed .
  211. J. P. Zheng and T. R. Jow, A New Charge Storage Mechanism for Electrochemical Capacitors, J. Electrochem. Soc., 1995, 142(1), L6–L8 CrossRef CAS .
  212. M. Moshkovich, Y. Gofer and D. Aurbach, Investigation of the Electrochemical Windows of Aprotic Alkali Metal (Li, Na, K) Salt Solutions, J. Electrochem. Soc., 2001, 148(4), E155–E167 CrossRef CAS .
  213. Y. Zhou, H. Xu, N. Lachman, M. Ghaffari, S. Wu, Y. Liu, A. Ugur, K. K. Gleason, B. L. Wardle and Q. M. Zhang, Advanced asymmetric supercapacitor based on conducting polymer and aligned carbon nanotubes with controlled nanomorphology, Nano Energy, 2014, 9, 176–185 CrossRef CAS .
  214. C.-S. Dai, P.-Y. Chien, J.-Y. Lin, S.-W. Chou, W.-K. Wu, P.-H. Li, K.-Y. Wu and T.-W. Lin, Hierarchically Structured Ni3S2/Carbon Nanotube Composites as High Performance Cathode Materials for Asymmetric Supercapacitors, ACS Appl. Mater. Interfaces, 2013, 5(22), 12168–12174 CAS .
  215. T.-W. Lin, C.-S. Dai and K.-C. Hung, High Energy Density Asymmetric Supercapacitor Based on NiOOH/Ni3S2/3D Graphene and Fe3O4/Graphene Composite Electrodes, Sci. Rep., 2014, 4, 7274 CrossRef CAS PubMed .
  216. S. Sun, S. Wang, S. Li, Y. Li, Y.-H. Zhang, J. Chen, Z. Zhang, S. Fang and P. Wang, Asymmetric supercapacitors based on NiCo2O4/three dimensional graphene composite and three dimensional graphene with high energy density, J. Mater. Chem. A, 2016, 4, 18646–18653 CAS .
  217. F. Wang, S. Xiao, Y. Hou, C. Hu, L. Liu and Y. Wu, Electrode materials for aqueous asymmetric supercapacitors, RSC Adv., 2013, 3(32), 13059–13084 RSC .
  218. J. F. Whitacre, S. Shanbhag, A. Mohamed, A. Polonsky, K. Carlisle, J. Gulakowski, W. Wu, C. Smith, L. Cooney, D. Blackwood, J. C. Dandrea and C. Truchot, A Polyionic, Large-Format Energy Storage Device Using an Aqueous Electrolyte and Thick-Format Composite NaTi2(PO4)(3)/Activated Carbon Negative Electrodes, Energy Technol., 2015, 3(1), 20–31 CrossRef CAS .
  219. F. Li, H. Chen, X. Y. Liu, S. J. Zhu, J. Q. Jia, C. H. Xu, F. Dong, Z. Q. Wen and Y. X. Zhang, Low-cost high-performance asymmetric supercapacitors based on Co2AlO4@MnO2 nanosheets and Fe3O4 nanoflakes, J. Mater. Chem. A, 2016, 4(6), 2096–2104 CAS .
  220. K. M. Choi, H. M. Jeong, J. H. Park, Y.-B. Zhang, J. K. Kang and O. M. Yaghi, Supercapacitors of Nanocrystalline Metal–Organic Frameworks, ACS Nano, 2014, 8(7), 7451–7457 CrossRef CAS PubMed .
  221. X. Liu, C. Shi, C. Zhai, M. Cheng, Q. Liu and G. Wang, Cobalt-Based Layered Metal–Organic Framework as an Ultrahigh Capacity Supercapacitor Electrode Material, ACS Appl. Mater. Interfaces, 2016, 8(7), 4585–4591 CAS .
  222. F. Zhang, T. Zhang, X. Yang, L. Zhang, K. Leng, Y. Huang and Y. Chen, A high-performance supercapacitor-battery hybrid energy storage device based on graphene-enhanced electrode materials with ultrahigh energy density, Energy Environ. Sci., 2013, 6(5), 1623–1632 CAS .
  223. E. Zhao, C. Qin, H.-R. Jung, G. Berdichevsky, A. Nese, S. Marder and G. Yushin, Lithium Titanate Confined in Carbon Nanopores for Asymmetric supercapacitors, ACS Nano, 2016, 10(4), 3977–3984 CrossRef CAS PubMed .
  224. W. Guo, S. Xin, M. Ji, Y. Guo and L. Wan, Supercapacitor-battery hybrid energy storage devices from an aqueous nitroxide radical active material, Chin. Sci. Bull., 2011, 56(23), 2433–2436 CrossRef CAS .
  225. D. Liu, C. Fu, N. Zhang, H. Zhou and Y. Kuang, Three-Dimensional Porous Nitrogen doped Graphene Hydrogel for High Energy Density supercapacitors, Electrochim. Acta, 2016, 213, 291–297 CrossRef CAS .
  226. V. Georgakilas, M. Otyepka, A. B. Bourlinos, V. Chandra, N. Kim, K. C. Kemp, P. Hobza, R. Zboril and K. S. Kim, Functionalization of Graphene: Covalent and Non-Covalent Approaches, Derivatives and Applications, Chem. Rev., 2012, 112(11), 6156–6214 CrossRef CAS PubMed .
  227. T. Chen, Y. Tang, Y. Qiao, Z. Liu, W. Guo, J. Song, S. Mu, S. Yu, Y. Zhao and F. Gao, All-solid-state high performance asymmetric supercapacitors based on novel MnS nanocrystal and activated carbon materials, Sci. Rep., 2016, 6, 23289 CrossRef CAS PubMed .
  228. Y. Liu, B. Weng, J. M. Razal, Q. Xu, C. Zhao, Y. Hou, S. Seyedin, R. Jalili, G. G. Wallace and J. Chen, High-Performance Flexible All-Solid-State Supercapacitor from Large Free-Standing Graphene-PEDOT/PSS Films, Sci. Rep., 2015, 5, 17045 CrossRef CAS PubMed .
  229. Z. Chen, V. Augustyn, X. Jia, Q. Xiao, B. Dunn and Y. Lu, High-Performance Sodium-Ion Pseudocapacitors Based on Hierarchically Porous Nanowire Composites, ACS Nano, 2012, 6(5), 4319–4327 CrossRef CAS PubMed .
  230. H. Li, L. Peng, Y. Zhu, X. Zhang and G. Yu, Achieving High-Energy–High-Power Density in a Flexible Quasi-Solid-State Sodium Ion Capacitor, Nano Lett., 2016, 16(9), 5938–5943 CrossRef CAS PubMed .
  231. L. Wei and G. Yushin, Nanostructured activated carbons from natural precursors for electrical double layer capacitors, Nano Energy, 2012, 1(4), 552–565 CrossRef CAS .
  232. J. Liu, Y. Deng, X. Li and L. Wang, Promising Nitrogen-Rich Porous Carbons Derived from One-Step Calcium Chloride Activation of Biomass-Based Waste for High Performance Supercapacitors, ACS Sustainable Chem. Eng., 2016, 4(1), 177–187 CrossRef CAS .
  233. J. Jiang, L. Zhang, X. Wang, N. Holm, K. Rajagopalan, F. Chen and S. Ma, Highly ordered macroporous woody biochar with ultra-high carbon content as supercapacitor electrodes, Electrochim. Acta, 2013, 113, 481–489 CrossRef CAS .
  234. H. Jin, X. Wang, Z. Gu and J. Polin, Carbon materials from high ash biochar for supercapacitor and improvement of capacitance with HNO3 surface oxidation, J. Power Sources, 2013, 236, 285–292 CrossRef CAS .
  235. J. Cai, H. Niu, Z. Li, Y. Du, P. Cizek, Z. Xie, H. Xiong and T. Lin, High-Performance Supercapacitor Electrode Materials from Cellulose-Derived Carbon Nanofibers, ACS Appl. Mater. Interfaces, 2015, 7(27), 14946–14953 CAS .
  236. H. Zhu, W. Luo, P. N. Ciesielski, Z. Fang, J. Y. Zhu, G. Henriksson, M. E. Himmel and L. Hu, Wood-Derived Materials for Green Electronics, Biological Devices, and Energy Applications, Chem. Rev., 2016, 116(16), 9305–9374 CrossRef CAS PubMed .
  237. M. Sevilla, W. Gu, C. Falco, M. M. Titirici, A. B. Fuertes and G. Yushin, Hydrothermal synthesis of microalgae-derived microporous carbons for electrochemical capacitors, J. Power Sources, 2014, 267, 26–32 CrossRef CAS .
  238. H. Wang, Z. Xu, A. Kohandehghan, Z. Li, K. Cui, X. Tan, T. J. Stephenson, C. K. King'ondu, C. M. B. Holt, B. C. Olsen, J. K. Tak, D. Harfield, A. O. Anyia and D. Mitlin, Interconnected Carbon Nanosheets Derived from Hemp for Ultrafast Supercapacitors with High Energy, ACS Nano, 2013, 7(6), 5131–5141 CrossRef CAS PubMed .
  239. L. Minzae, K. Gil-Pyo, S. Hyeon Don, P. Soomin and Y. Jongheop, Preparation of energy storage material derived from a used cigarette filter for a supercapacitor electrode, Nanotechnology, 2014, 25(34), 345601 CrossRef PubMed .
  240. M. Boota, M. P. Paranthaman, A. K. Naskar, Y. Li, K. Akato and Y. Gogotsi, Waste Tire Derived Carbon–Polymer Composite Paper as Pseudocapacitive Electrode with Long Cycle Life, ChemSusChem, 2015, 8(21), 3576–3581 CrossRef CAS PubMed .
  241. M. Zhi, F. Yang, F. Meng, M. Li, A. Manivannan and N. Wu, Effects of Pore Structure on Performance of An Activated-Carbon Supercapacitor Electrode Recycled from Scrap Waste Tires, ACS Sustainable Chem. Eng., 2014, 2(7), 1592–1598 CrossRef CAS .
  242. A. Jain, R. Balasubramanian and M. P. Srinivasan, Hydrothermal conversion of biomass waste to activated carbon with high porosity: A review, Chem. Eng. J., 2016, 283, 789–805 CrossRef CAS .
  243. K. Jurewicz and K. Babeł, Efficient Capacitor Materials from Active Carbons Based on Coconut Shell/Melamine Precursors, Energy Fuels, 2010, 24(6), 3429–3435 CrossRef CAS .
  244. J. Wang, P. Nie, B. Ding, S. Dong, X. Hao, H. Dou and X. Zhang, Biomass derived carbon for energy storage devices, J. Mater. Chem. A, 2017, 5(6), 2411–2428 CAS .
  245. J. Jiang, High Temperature Monolithic Biochar Supercapacitor Using Ionic Liquid Electrolyte, J. Electrochem. Soc., 2017, 164(8), H5043–H5048 CrossRef CAS .
  246. W. Tian, Q. Gao, Y. Tan and Z. Li, Unusual interconnected graphitized carbon nanosheets as the electrode of high-rate ionic liquid-based supercapacitor, Carbon, 2017, 119, 287–295 CrossRef CAS .
  247. P. Sennu, H.-J. Choi, S.-G. Baek, V. Aravindan and Y.-S. Lee, Tube-like carbon for Li-ion capacitors derived from the environmentally undesirable plant: Prosopis juliflora, Carbon, 2016, 98, 58–66 CrossRef CAS .
  248. J. Deng, M. Li and Y. Wang, Biomass-derived carbon: synthesis and applications in energy storage and conversion, Green Chem., 2016, 18(18), 4824–4854 RSC .
  249. B. D. McCloskey, Expanding the Ragone Plot: Pushing the Limits of Energy Storage, J. Phys. Chem. Lett., 2015, 6(18), 3592–3593 CrossRef CAS PubMed .
  250. T. Christen and M. W. Carlen, Theory of Ragone plots, J. Power Sources, 2000, 91(2), 210–216 CrossRef CAS .
  251. Y. Zhai, Y. Dou, D. Zhao, P. F. Fulvio, R. T. Mayes and S. Dai, Carbon Materials for Chemical Capacitive Energy Storage, Adv. Mater., 2011, 23(42), 4828–4850 CrossRef CAS PubMed .
  252. S. Faraji and F. N. Ani, Microwave-assisted synthesis of metal oxide/hydroxide composite electrodes for high power supercapacitors – A review, J. Power Sources, 2014, 263, 338–360 CrossRef CAS .
  253. X. Rui, H. Tan and Q. Yan, Nanostructured metal sulfides for energy storage, Nanoscale, 2014, 6(17), 9889–9924 RSC .
  254. D. Pech, M. Brunet, H. Durou, P. Huang, V. Mochalin, Y. Gogotsi, P.-L. Taberna and P. Simon, Ultrahigh-power micrometre-sized supercapacitors based on onion-like carbon, Nat. Nanotechnol., 2010, 5(9), 651–654 CrossRef CAS PubMed .
  255. J. Vatamanu, O. Borodin, D. Bedrov and G. D. Smith, 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(14), 7940–7951 CAS .
  256. K. Ma, C. E. Woodward and J. Forsman, Classical Density Functional Study on Interfacial Structure and Differential Capacitance of Ionic Liquids near Charged Surfaces, J. Phys. Chem. C, 2014, 118(29), 15825–15834 CAS .
  257. C. Zhan, J. Neal, J. Wu and D.-e. Jiang, Quantum Effects on the Capacitance of Graphene-Based Electrodes, J. Phys. Chem. C, 2015, 119(39), 22297–22303 CAS .
  258. J. Vatamanu and D. Bedrov, Capacitive Energy Storage: Current and Future Challenges, J. Phys. Chem. Lett., 2015, 6(18), 3594–3609 CrossRef CAS PubMed .

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