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Surface Diffusion and Adsorption in Supercapacitors Ali Eftekhari ACS Sustainable Chem. Eng., Just Accepted Manuscript • DOI: 10.1021/ acssuschemeng.8b01075 • Publication Date (Web): 07 Sep 2018 Downloaded from http://pubs.acs.org on October 1, 2018

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ACS Sustainable Chemistry & Engineering

Surface Diffusion and Adsorption in Supercapacitors

Ali Eftekhari Belfast Academy, 2 Queens Road, Belfast BT3 9FG, United Kingdom Email: [email protected] Abstract The prospect of double layer capacitors relies on the high specific surface area provided by microporosity of carbon. Since there is not enough space within narrow micropores for forming a double layer, recent theoretical/computational studies have aimed at explaining the mechanism in micropores. The problem is that the available models suggest substantial differences in the mechanism of energy storage by microporous and other types of carbon, but the electrochemical behaviours are similar to a significant degree. Here, a conceptual model is proposed empirically, which is in full agreement with the experimental data reported in the literature, to reasonably explain a universal mechanism of all carbon-based capacitors including microporous, mesoporous, graphene, etc. It is described that none of the available models for double layer charging from Helmholtz to Graham is valid for carbon-based capacitors, as no double layer is formed within the micropores, as well as the partial contribution of double layer charging in larger pores or on graphene sheets. The mechanism of charge accumulation in supercapacitors is based on the adsorption of electroactive species over active sites of the carbon nanomaterial, and the surface diffusion of the adsorbed species collects the charge over the high surface area of carbon. The rate-determining step is usually controlled by the availability of active sites, which defines the rate capability of supercapacitors. This explains why the rate capability of double layer capacitors is much lower than the theoretical expectations, and why the alignment of graphene sheets results in fast performance in the so-called kilohertz supercapacitors. Any factors, such as narrow pores and irregularities, slowing down the subsequent surface diffusion cause the deviation from ideal capacitive behaviour. The present paper attempts to highlight two points: surface diffusion might be a critical step in the mechanism of supercapacitors (probably a rate-determining step) and if narrow micropores exhibit capacitive behaviour without forming a double layer, larger pores may do the same since no sudden change in the capacitive behaviour with response to the pore size is observed (to represent a crucial change in the mechanism). Keywords: Supercapacitors; Carbon nanomaterials; Microporous carbon; Adsorption; Pseudocapacitance; Graphene Page 1 of 28 ACS Paragon Plus Environment

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Introduction

The story of supercapacitor was started by the idea that high surface area carbons can facilitate the appearance of strong double layer charging. Since the electrochemical accessibility defines the effective surface area, investigations of the relationship between the capacitive performance and the carbon morphology have been a hot topic of debate in this area during the recent years. In the case of microporous carbons, the prime question is the dependence of the capacitive performance on the pore size, which has been widely inspected experimentally and computationally. Chen and coworkers reported that if excluding the surface area provided by micropores smaller than the ions, the capacitance is proportional to the specific surface area.1 Nevertheless, it is known that the capacitance has a nonlinear dependency on the pore size.2-6 A breakthrough was the works of Simon and Gogotsi reporting the optimum value of 0.7 nm.7 In fact, they proposed that the pore size should be matched to the ion size.

The crucially important fact is that 0.7-nm micropores can only accommodate a single ion, and there is no space for the formation of a double layer. Hence, no double layer is formed in the range of microporosity. This means that there is, at least, a type of the so-called double layer, which stores energy with a mechanism other than double layer charging. In this case, despite the inappropriateness of the classic title, the arising question is if other types of carbon-based capacitors work based on the classic double layer view or there is a universal mechanism for all carbons from narrow micropores to flat graphene sheets. The latter possibility is more likely, as there has been no experimental evidence differentiating the electrochemical behaviour of these carbon nanomaterials. This makes the mechanism of energy storage in micropores critically important.

Available Models for Micropores

Several models have been proposed to explain the charge separation within micropores (see8 and the references therein). It should be emphasised that none of these models has been proved experimentally or theoretically because these models are based on fundamental assumptions, Page 2 of 28 ACS Paragon Plus Environment

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which have not been verified. All of these models are somehow speculative one way or another because there is a basic assumption about the underlying mechanism, which is not universally proved. The computational studies normally calculate the capacitive performance for various pore sizes with the given assumption, but since there is no systematic experimental data for a set of standard samples with calibrated pore sizes, these computational calculations cannot be verified. On the other hand, the rationale of these models is somehow confusing as some models still assume a double layer within the mesopores. For instance, Zhang et al. proposed a visual model in which five ions are arranged circularly in the cylindrical pore and claimed that the pore size should be minimised to keep the ions closely packed.1 In this case, the repulsion between the ions is too strong to expect a fast diffusion within the pores, which is a requirement for fast charging/discharging of supercapacitors. Furthermore, they used the classic capacitor equation based on the distance between the adsorbed ion and the pore wall. This is indeed the inner Helmholtz layer, and in the absence of the outer Helmholtz layer, it is not a double layer.

The validity of the Helmholtz model is not an issue here since the modifications made to the classic model of double layer charging make the situation even worse. The Helmholtz model assumes the thinnest possible arrangement of the two layers. In this case, a double layer should be formed within the radius (not diameter) of a pore. This is an important matter usually ignored in the literature; species of the same charge should be adsorbed on the pore walls throughout. Thus, the minimum diameter for the formation of the Helmholtz double layer is about 3nm. This makes a generalisation that micropores cannot provide capacitance by the classic double layer charging. Since the modern models for the double layer from Stern to Graham are based on the fact that the outer Helmholtz layer is not closely aligned with the inner Helmholtz layer and spread into the electrolyte, the minimum diameter for the double layer charging is even larger, and a fraction of mesopores are incapable of double layer charging in its classic sense.

The most common model for micropores is the random distribution of opposite charges in a micropore9-12 in which the exciting co-ions leave the micropore upon charging. Forse et al. stated that NMR is the only technique, which can detect the pre-existence of co-ions in the micropores12, but the cited experimental data were based on a carbon sample with an average pore size of 0.9 nm. This means a significant number of micropores were larger than a single-ion width, and the NMR data could reflect the coexistence of ions in larger micropores. On the other hand, some Page 3 of 28 ACS Paragon Plus Environment


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other reports, particularly for pure ionic liquids having poor wettability, suggest no or partial initial filling.13 In any case, this model proposes that each opposite ion should push the main ions out of the micropore to be extracted, and then, the main ion should be inserted into the micropore. Despite the fact that from a rational perspective, this process is unlikely to occur; this process is controlled by two one-dimensional diffusion steps.14 Thus, this system should be electrochemically under diffusion control regime. However, it is well known that this class of supercapacitors have a linear time dependency.15 On the other hand, this model does not explain two phenomena: how are the ions desolvated and ordered in term of the orientation to fit into micropores in the absence of any driving force (before charging)?

In two recent papers16-17, it has been conceptually explained that the available models for microporous supercapacitors are not rationally valid16 and the impedance model of supercapacitor indicates a diffusion process as an analogue to batteries (though at a different range of frequency).17 By matching these two models, it is attempted to propose a conceptual model for a possible mechanism of microporous supercapacitors. Similar to other models of microporous supercapacitors, the present one cannot be directly examined experimentally due to the scarcity of reliable uniform reference materials, but the present model better fits with the commonly accepted experimental facts. On the other hand, the purpose is not to propose the ultimate mechanism, but to foster the rationale for future research endeavours.

Adsorption (Physisorption vs. Chemisorption)

Figures 1a and 1b compare the possibility of perpendicular adsorption on the graphene basal plane with adsorption at the edge, which is accompanied by surface diffusion. In the former case, which is based on the common sense of classic double layer charging, surface diffusion has no significant impact on the capacitive performance. The key point is the type of adsorption rather than the direction of diffusion. Adsorption is a broad term, which covers a wide range of surface interactions including physisorption and chemisorption. To avoid any controversy, the distinction between physisorption and chemisorption depicted in this Section is entirely based on the classification made by IUPAC.18

Physisorption (also called van der Waals adsorption) is based on van der Waals interactions.18 This Page 4 of 28 ACS Paragon Plus Environment

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is the case illustrated in Figure 1a where charge species are physically adsorbed on the basal plane. In this case, the uniform distribution of π electrons over the sp2 carbon atoms provides an ideal opportunity for the uniform formation of the Helmholtz inner layer. Since the physically adsorbed species retain their initial charge, the opposite ions form the outer Helmholtz layer where a classic double layer is formed.

Figure 1. (a) Perpendicular physisorption on the basal plane of graphene or carbon nanotube, and (b) chemisorption and surface diffusion at the edge of graphene or carbon nanotube.

Chemisorption is much more complicated than physisorption and covers a broad range of possibilities including irreversible chemical transformation.18 Depending on the chemical bond formed, chemisorption involves electron transfer between interacting species to some degree. Usually, the adsorption energy (i.e., the activation energy for the formation of a chemical bond) is higher for chemisorption, as compared with physisorption (i.e., not activated adsorption). However, this can be a legitimate comparison for identical surface sites only. The dangling atoms at the graphene edge are considerably active and easily participate in a chemical reaction. Therefore, chemisorption at the graphene edge is more likely than physisorption on the basal plane.19

The edge atoms or defects in the graphene structure as displayed in Figure 1b are electron accepting/donating adsorption sites resulting in the so-called charge transfer adsorption as defined by IUPAC.18 Where the activation energy of adsorption is smaller than kT (k is the Boltzmann constant and T the temperature), the adsorbed species are mobile, as opposed to immobile adsorbents, which are localised. Hence, the species adsorbed at the dangling atoms are Page 5 of 28 ACS Paragon Plus Environment


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mobile to diffuse along the basal plane. This is indeed the central ideal of this paper.

As there is no distinct line between physisorption and chemisorption, there is none between chemisorption and surface intercalation too. For instance, RuO2 is a pioneering and characteristic pseudocapacitive material with a well-defined pseudocapacitance. However, the redox system is indeed based on a Faradaic reaction at the surface and sub-surface. In this case, the mechanism of energy storage is by charge storage rather than the characteristic charge separation of double layer. In other words, the surface of RuO2 is not charged to form the outer Helmholtz layer. An extreme case is when reducing the size of intercalation materials.20 The intercalation mechanism is still the same, but the Faradaic reaction occurs at the surface (or more precisely, within the lateral unit cell) where no solid-state diffusion occurs. Although the latter is not a genuine chemisorption, it is characterised as pseudocapacitance. It has been discussed that pseudocapacitance is not because of chemisorption or a surface-only mechanism, but the distribution of redox sites at different levels of energy.20 Therefore, the redox sites participate in the same Faradaic reaction at different potentials, and the result is a capacitive-like response (the so-called pseudocapacitance). The reason that pseudocapacitance is usually observed at the surface rather than bulk is the uniformity of the ordered crystal structure (the redox sites are almost identical therein).

In the case of physisorption (Figure 1a), the uniformity of the graphene basal plane is an advantageous feature assisting the formation of an ideal inner Helmholtz layer. Note that all the double layer models proposed after Helmholtz attempted to clarify that the outer Helmholtz layer is very complicated and spreads into the bulk solution even if the inner Helmholtz layer is ideally uniform. Disturbing the uniform charge distribution over π electrons of the basal plane (e.g., by doping) alters the structure of the inner Helmholtz layer. The higher capacitance of nitrogendoped carbon is usually referred to the contribution of both capacitive and Faradaic current.21-24

The theoretical capacity for physisorption is the surface coverage by a monolayer of a closepacked array of the adsorbent and for chemisorption is the number of active sites. This implies that the theoretical capacity of double layer charging is higher for the capacitance by the double layer charging as compared with pseudocapacitance, as all the surface can contribute to physisorption, but specific adsorption sites can facilitate chemisorption. Therefore, if double layer Page 6 of 28 ACS Paragon Plus Environment

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charging is complete, replacing the physisorption with a chemisorption mechanism (at the doped sites) should not increase the overall energy storage capacity. Unless the non-uniformity of charge can contribute to the dominant mechanism as will be discussed below.

Experimental Facts

As emphasised, all available models have been derived based on a typical experimental data, which might be universally true or not. Regardless of the theoretical or computational calculation, there is no direct theoretical explanation of the underlying phenomenon. Hence, each prospective model should explain a wide range of commonly accepted experimental facts. By a rational analysis of the experimental data reported in the literature and the commonly accepted facts, the general requirements for developing any mechanistic model can be summarised as

1. There is no major difference between the mechanism of microporous and mesoporous carbons. By increasing the pore size from 0.7 nm to the mesopore range, the electrochemical performance (including capacitance, rate capability, response shape, etc.) gradually changes. If assuming that charge separation in micropores is by ion exchange and in mesopores by double layer charging, a massive change in the electrochemical performance should be observed when passing a threshold (e.g., a few orders of magnitude higher rate capability for mesoporous carbon where the double layer formation is fast as compared with the diffusion-controlled ion-exchange in microporous carbon), but no experimental data suggests this. 2. All the experimental data indicate that the electrochemical behaviour of microporous carbon is not under diffusion control (to be precise, one-dimensional diffusion, as will be described later). This is indeed one of the most solid facts about this class of supercapacitors. Hence, onedimensional diffusion should not be the rate-determining step in a proposing model. 3. Aluminium electrolytic capacitors form a thin passive film, which serves as the dielectric. This process is obviously under mass transfer control, and thus, slower than the double layer charging, which is the result of ion rearrangement in the vicinity of the electrode/electrolyte interface (Figure 2a). Thus, one expects a higher rate capability for the double layer capacitors. In practice, carbon-based capacitors are a few orders of magnitude slower than electrolytic capacitors.25

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Figure 2. (a) A schematic illustration of the classic Helmholtz double layer, (b) insertion of single ions into micropores, and (c) formation of double layer in mesopores. The circles indicates the active edge carbon atoms facilitating the initial adsorption and the arrows show the surface diffusion of ions into the micropores. Note that the organic ions from ionic liquids reported in the literature are asymmetric and when matching their sizes with the 0.7-nm micropores, they can enter in one direction only.

4. If changing the orientation of graphene sheets or carbon nanotubes, the rate capability can be increased by a few orders of magnitude.25-36 Why should the double layer formation be orientation-sensitive? Note that this is not due to the electrochemical accessibility, as no such change occurs for the specific capacitance. 5. Altering the uniform charge distribution on graphene by doping or introducing defects improve not only the overall energy storage capacity but also the rate capability.21-24 Even if assuming that both capacitance and pseudocapacitance can occur in parallel, the latter is strongly kineticallycontrolled and should be slower than double layer charging. Page 8 of 28 ACS Paragon Plus Environment

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Deducing the Model

The present model is based on a rational deduction of the facts presented by the experimental data reported in the literature.

1. The ions are adsorbed on the mesopore walls rather than floating as a charged ion in the oppositely charged cylinder. XPS studies have shown that the counterions are electrochemically adsorbed on the carbon surface.37 On the other hand, most of the ions under consideration, particularly organic ions of ionic liquids, have asymmetrical geometry and non-uniform charge density. Thus, they move towards a wall depending on the ion orientation even by applying a small potential (Figure 2b). As a result, the movement of the counterions within micropores is through surface diffusion rather than diffusion freely within the electrolyte. 2. If the adsorbed ions are not subject to surface diffusion (i.e., immobile localised adsorbents), the first ions adsorbed at the pore mouth will block the entrance (Figure 2b). Consider the mandatory ion orientation for entering the micropore.16 This is also a reason that a pure IL electrolyte does not entirely fill small micropore because there is no thermodynamical justification for the specific orientation of the ions to orderly fill the micropores. 3. If the ions are adsorbed on the carbon surface, the adsorption should occur at the carbon sites with least energy, which are obviously dangling and edge atoms. This is indeed a known fact in the realm of electrochemistry, particularly in the case of graphene.19 This is well understood from a classic statement by Grahame in the 1940s38 that "If the surface is not smooth and homogeneous, the current density will not be uniform. For reasons of geometry alone, a surface which is rough cannot be expected to have a uniform current density, and the difficulty is exaggerated by the fact that a rough surface will probably be chemically inhomogeneous as well, so that the electrochemical reaction may well favour certain catalytically active spots." This statement appropriately matches the electronic structure of carbon nanomaterials. Except for the sp2 carbon atoms in the graphene hexagonal structure, carbon atoms are electronically different depending on the neighbouring bonds. As the dangling atoms on the edge of graphene are prone to be functionalised by various groups, the carbon atoms are at the pore mouth. Therefore, the anions are adsorbed at the edge atoms over the pore (Figure 2b). In practice, introducing defects into the graphene structure significantly enhances the capacitive performance due to the increased Page 9 of 28 ACS Paragon Plus Environment


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number of edge atoms facilitating the adsorption step.39-41 In the case of microporous carbon, graphitisation of the pore walls results in a higher capacitance.42 In addition to better electrical conductivity, vertical graphitic walls provide adsorption sites and sp2 surface for the ion mobility. This is also in agreement with the experimentally observed desolvation of ions entering micropores.43-45 4. The mobile adsorbed ions make the large surface area of carbon accessible even deep within small micropores. Three factors cause the diffusion of the adsorbed anion deep into the pore: (i) repulsion by the anions accumulated at the electrode/electrolyte interface. (ii) Non-uniform charge distribution because of the adsorbed anion at the pore edge favouring the pore depth. (iii) Easy (less interactive) surface diffusion of the adsorbed atoms deep within the pore (it is somehow similar to the spillover mechanism in electrocatalysis).

Surface Diffusion

Since the diffusion occurs on the micropore wall rather than within the micropore, the diffusion is no longer one-dimensional. Instead, the Fick's law should be solved for a cylindrical diffusion

(1) where c is the concentration, D the diffusion coefficient, r the radius, and φ the angle. Since there is no concentration gradient along r (the diffusion is along the surface not perpendicular to the pore wall), the first term can be eliminated. Solving this equation with the common boundary conditions, the flux will be proportional to t–1 instead of t–1/2; detailed mathematical solutions can be found in the relevant textbooks46-47). If spreading the pore wall to form a flat sheet of graphene, the Fick's second law can be solved with the Cartesian coordinates along two dimension. It is convenient to solve the Fick's second law in two-dimension via the fundamental solutions by the Green function using diffusion kernel (aka, heat kernel). The general solution is

(2) by using the Fick's first law, the current can be expressed as (3) This is an analogue to the classic Cottrel equation for one-dimensional diffusion. In the same Page 10 of 28 ACS Paragon Plus Environment

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fashion, the direct dependence of the peak current to the potential scan rate in cyclic voltammetry can be obtained. The point is that surface diffusion is two-dimensional for all carbon nanomaterials, and thus, the experimentally verified direct dependence of the capacitance on the scan rate48 is satisfied by the current model. In fact, this dependence is justified by the assumption that the electrochemical system is not under diffusion control since diffusion is not a rate-determining step in the double layer formation. However, this is not in agreement with the low rate capability of the carbon capacitors in comparison with the double layer charging.

Impedance Model

Impedance spectroscopy can shed light on the physical significance of this model. As a general reference, the impedance spectrum of a porous carbon capacitor is illustrated in Figure 3a. In practice, the low-frequency capacitance may overshadow other parts, but the undergoing competitions are of the utmost importance. The strength of the diffusion-controlled region also suggests the importance of diffusion within the micropores. This factor may seem simple but is the centrepiece of carbon capacitors, as it is believed that diffusion has no impact on the performance of double layer capacitors (see, for example, numerous works differentiating supercapacitors and batteries by relying on diffusion-independence15). In fact, the impedance models reveal that increasing the contribution of pores in the capacitive behaviour strengthen the role of diffusionbased processes.49

Figure 3. (a) Impedance model of a microporous carbon capacitor exhibiting three different regions.



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(b) Increasing the load mass or the film thickness. (c) Reducing the size of the pore mouth (similar dependency can be found for the pore size too). The representation of the impedance behaviour shown in the Nyquest diagrams (a-c) are illustrated in the corresponding Bode plots (d,e).

The frequency-dependent response is usually interpreted as the AC signal entering the micropores at low frequency. Although this impression is not incorrect, a more conceptual understanding is required to interpret the impedance spectra. Impedance measurement at each point is indeed a cycle of charging/discharging at the given frequency. The frequency is proportional to the potential scan rate in cyclic voltammetry. For instance, a frequency of 1 Hz means charging and discharging the electrode with a potential scan rate of 10 mV s–1 over a potential window of 5 mV (i.e., the amplitude in the experiment setting). The impedance spectra show the phase differences, representing the competition between the capacitive charge accumulation and resistance against the charge transfer, at different charge/discharge rates.

As discussed in17, the induction signal at high frequencies (as illustrated by the dashed line in Figure 3a) can be attributed to the anomalous magnetic properties of the carbon edge sites rather than the usual assumption of the instrumental artefacts. However, it cannot be directly used as a reliable signal in the present model. Examining the impedance spectrum at the three competing regions can provide invaluable information about the underlying mechanism of the supercapacitor:

(i) The characteristic semi-circle at high frequency is the competition between the outer double layer charging and the charge transfer resistance at the electrode/electrolyte interface. The corresponding Faradaic reaction is the adsorption of electroactive species at high energy carbon sites (i.e., defects, dangling atoms, functional groups, etc.). Since this reaction is kinetically controlled, the charge transfer resistance occurs at lower frequencies where the flow of the Faradaic current is meaningful. Note that with the so-called charge transfer adsorption, the adsorbed species forms a chemical bond sharing electrons with the electrode atoms, and do not have the same charge as electrostatic adsorption (physisorption) to form the inner Helmholtz layer. For a higher number of active sites, the charge transfer resistance reduces, and the semicircle diminishes. By exposing the graphene edges in a conical architecture, the supercapacitor exhibits a close to ideal behaviour even at the potential scan rate of 500 V s–1 as the semi-circle disappears.50-51 Page 12 of 28 ACS Paragon Plus Environment

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(ii) The diagonal line at the middle range of frequencies is indeed a diffusion-controlled Warburg impedance as a result of the Faradaic adsorption of the electroactive species at specific sites, as proposed by the present model. This region in Figure 3a is known as the distributed constant-type equivalent circuit in the transmission line model corresponds to the pore resistance.52 When increasing the material load (Figure 3b), the diffusion within the interconnected porosity in a thicker film is slower, and thus, this region is expanded in a broader range of frequency.53-55 The length of this region depends on two factors: how fast is the adsorption process and how fast is the diffusion of electroactive species within the interconnected (macro/meso)porosity. Almost all of the ultrafast supercapacitors reported in the literature are based on vertically aligned graphene sheets25-33 or carbon nanotubes34-36 where the edge sites are spread within the electrolyte, and the rate-determining role of the diffusion vanishes. Similar performance can be obtained by creating edge atoms within the graphene sheet by forming periodic holes.56 In the case of carbon nanotubes when the tubes are too small to preserve the vertical position, the rate capability significantly weakens as the edge sites are hidden within the carbon matrix and not directly exposed.36 Even in the case of ordered mesoporous carbon, the presence of graphitic sites at the pore mouth can result in fast performing supercapacitor.57

(iii) The low-frequency behaviour of an ideal capacitor is a vertical line in which the real impedance remains constant. However, in practice, there is a positive deviation from the vertical line due to the limiting factor of the slow diffusion within the micropores (Figure 3c). This deviation is indeed the competition arisen from the rate-determining role of the surface diffusion of the adsorbed species over the pore walls. Theoretical calculations indicate that this deviation is stronger for smaller pores.49,58 In the ideal behaviour, the adsorbed species are mobile enough to accumulate the charge with a capacitive-like response. Increasing the temperature during the synthesis of vertically aligned graphene sheets may result in the formation of a more ordered surface, and thus, the specific capacitance is enhanced by the temperature while the deviation in the third region is reduced.33 However, the thermal treatment heals the edge defects facilitating the initial adsorption, to some degree, and thus, the rate capability is weakened.

A similar deviation was theoretically predicted by Keiser et al. four decades ago by altering the pore mouth.59 Unfortunately, these behaviours have not yet been verified experimentally for Page 13 of 28 ACS Paragon Plus Environment


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microporous materials due to the difficulty in controlling the shape of micropores for the corresponding experiments. Nevertheless, the theoretical reasoning is fairly justifiable. This indicates that the pore mouth size can strengthen the diffusion impact in a capacitive system. Similar impedance behaviour can be observed when increasing the material load or density where obviously the diffusion is slower.54-55 Quite interestingly, as an analogue to the solid-state diffusion, the capacitance is strongly dependent on the pore directions as well as the pore size. By controlling the pore direction in a series of microporous carbons with similar pore sizes, the capacitance was improved by 50%.42 Furthermore, the impedance spectra exhibited the disappearance of the diffusion component.

This model explains two important factors in the capacitive behaviour of microporous carbon: nonlinear dependence of capacitance on the pore size and rate capability as a function of pore size. The maximum capacitance is achieved when the micropore allows the insertion of single ion only due to maximum occupation and minimum interactions. When the pore is slightly larger, two ions compete to enter the micropore. However, when the pore is significantly larger, two ions can simultaneously enter the pore without hindering interactions. This phenomenon can be well understood by a similar example from the intercalation of alkali metal ions into graphite. The size of K+ ion matches the interlayer spacing of graphite for single ion diffusion, and Li+ ion is much smaller than the graphite interlayer, and thus the insertion of multiple ions simultaneously is possible. While K and Li cations can be successfully intercalated into graphite, the intercalation of Na+ is thermodynamically unfavourable due to the size of Na+ cation in comparison with the graphite interlayer causing the interaction between the inserting cations.60

All carbon-based supercapacitors obey this model, although the semicircle is not always observed. The disappearance of the first two regions is due to the visual dominance of the third region where the impedance resolution (the number of points) is not enough to show the high-frequency behaviour. This feature can be seen in the phase diagram (Figure 3d,e), as all cases show similar patterns indicating the occurrence of the first and second regions. If only the third region occurs, then the phase diagram should be a horizontal line at a constant phase according to the deviation slope, but it has never been the case in the works reported in the literature.


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Rate Capability

An essential requirement of supercapacitors is the capability for fast charging/discharging. Theoretically, double layer capacitors should be quite fast because the double layer can be charged and discharged by displacement of ions in the vicinity of the electrode/electrolyte interface, whereas the charge/discharge of batteries is limited by the slow solid-state diffusion.20 According to the model presented above, carbon-based supercapacitors are not independent of diffusion control. Although no concentration gradient is formed as a result of a Faradaic reaction, the ions still should diffuse through the micropores, which can be considered as an analogue to the solid-state diffusion. The rate capability of carbon-based supercapacitors significantly decreases by decreasing the pore size.61 In other words, reducing the pore size might maximise the capacitance but at the cost of weakening the rate capability by making the diffusion slower.

In impedance measurements, the frequency is directly translated into the timescale. The value of f3 in Fig. 3(a) is proportional to the rate capability of the capacitor. This means that the capacitor can be charged/discharges with higher rates if the third region in the impedance model is started at higher frequencies. The reason is that at shorter timescales, the micropores can be used for the entrapment of the corresponding ions. Note that this does not necessarily mean that the diffusion is faster within the micropores. The diffusion coefficient within the micropores can be estimated from the slope of the third region regardless of the frequency at which the region is started. The micropore accessibility is mainly related to the pore mouth and its interconnection within the whole matrix. The second region is not always distinguishable, but the shrinking semicircle indicates the possibilities of faster adsorption, which is accompanied by a better rate capability.62

The Model in Action

To show the practical applicability of this model, let us interpret a typical impedance study reported in the literature.63 Figure 4 shows the CVs and impedance spectra of three similar microporous carbons. By interpreting the three impedance regions, one can find an excellent agreement with the CV data. The sample (Burley 800-900) with the fastest diffusion within micropores (as can be judged from the lower pore resistance) shows the highest specific Page 15 of 28 ACS Paragon Plus Environment


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capacitance. The sample (Burley 800) with the highest polarisation resistance has the most deformation in the rectangular CV. In the absence of carbon edge atoms, the initial adsorption needs a higher overpotential, and thus, the capacitance is lower at lower potentials (and vice versa during the reverse scan). The second number in the samples represents the calcination temperature. Obviously, thermal treatment has increased the graphitisation and activated the edge atoms at the end of hexagonal carbon architecture. Moreover, the capacitance of Burley 800 at high temperatures is higher than the other two samples. This might be affected by fast diffusion within the interconnected porosity. At high potentials, the presence of the lower number of adsorption sites is somehow compensated by the excess overpotentials. Albeit, an accurate comparison needs the values of transition frequencies as demonstrated in Figure 3a to realise the corresponding scales. Overall, this simple example shows how the model proposed here can be practically used by researchers to discover the pitfalls of each material under consideration.

Figure 4. Electrochemical properties of two-electrode cells built from Burley 800, Burley 800-800 and Burley 800-900 in 1 M Li2SO4: (a) cyclic voltammograms (5 mV s–1); (b) Nyquist plots. Reproduced with permission.63 Copyright 2015, Elsevier.

In a similar fashion, the rate capability of a capacitor can be estimated by the impedance model. When comparing similar microporous carbons, a higher power density is obtained when the f3 is larger.5 The distance between f2 and f3 indicates the capacitive contribution by the meso- and macroporosity. Since the majority of porosity in high surface area carbons is provided by micropores, the capacitor performance is mainly controlled by the third region in the impedance spectroscopy, and a high f3 can guarantee a better rate capability.

Concluding Remarks

It should be emphasised that the present paper does not aim to propose the ultimate mechanism Page 16 of 28 ACS Paragon Plus Environment

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of supercapacitors. Instead, it was clarified that supercapacitors should have a common mechanism. It is not reasonable to assume some supercapacitors work based on the double layer charging, and microporous carbon by the inclusion of single counterions; because both types show similar electrochemical behaviours. The model presented here may seem speculative, but this is precisely the point of this paper: the vague point of the mechanism of supercapacitors is the basic assumption, which is made speculatively in every model. Theoretical or computational calculations do not give legitimacy to a model as the validity of the basic assumption is the key question. Similar to the example model (i.e., the most common one for microporous carbon in the literature), the basic assumption is based on a typical data, which do not justify the validity of the assumption. Therefore, every model should satisfy a broad range of experimental facts, commonly accepted through numerous reports. The present model may seem speculative, but it satisfies more experimental facts as compared with other models available in the literature.

The charge storage mechanism in double layer capacitors utilising carbon nanomaterials is not based on the formation of a double layer in its classical form. Instead, accommodation of individual ions within micropores facilitates the charge separation for energy storage. The conceptual model proposed here differentiates this mechanism from the commonly believed double layer formation or diffusion of single ions within micropores. The model has been rationally connected with the corresponding impedance model to provide a practical guide for the analysis of experimental results. Most of the models reported in the literature have been developed based on molecular dynamics or similar computational simulations or supported by the corresponding calculations. However, this strategy does not lead us very far, as there is no systematic experimental data available to prove or disprove the simulations. Therefore, the present model was kept conceptual to highlight the underlying mechanism. Only a wide range of experimental examination of the proposed surface diffusion can prove or disprove the present model. To the best of my knowledge, there is no commonly accepted experimental fact (or a common phenomenon) in the literature contradicting the present model.

The Model Rationale Owing to the chemical reactivity of the dangling atoms, defective sites, and some functional groups, chemisorption at graphene or similar carbonaceous nanomaterials is facile and may occur before/faster than physisorption at the basal plane. In this case, the low activation energy of the Page 17 of 28 ACS Paragon Plus Environment


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adsorption guarantees mobile non-localised adsorbents, which can diffuse over the graphene basal plane as a result of the generated concentration gradient. Then, the active adsorption sites are freed for the subsequent adsorption. In this scenario, two processes might be the ratedetermining step, the chemisorption and the surface diffusion. This model is very simple but can explain the electrochemical performance of various carbon-based supercapacitors. This model can present a new perspective to consider the critical role of chemisorption and surface diffusion.

This model highlighted that if considering the classic double layer charging model as the main energy storage mechanism of carbon-based supercapacitors, the presence of dopants and defects should be disadvantageous because physisorption is faster and provides a higher energy storage capacity. However, this is indeed against the experimental facts. On the other hand, the idea of a separate contribution of capacitance and pseudocapacitance (double layer charging and Faradaic reaction, respectively) does not seem reasonable because introducing pseudocapacitive adsorption sites reduces the surface area for physisorption. There is no point to replace physisorption in favour of slower and weaker chemisorption if assuming the physisorption can proceed with the double layer charging. Hence, chemisorption or pseudocapacitance can contribute to the overall capacity if contributing to the whole mechanism.

Recommendations for Impedance Experiments Although impedance spectroscopy is a popular technique in studies of supercapacitors, almost all papers simply use it as a proof of the presence of a capacitive impedance without in-depth analysis. The present model provides a handy manual for interpreting the impedance spectra to explain the capacitive behaviour of a system under investigation. The following points can guide researchers to better plan the impedance experiments for adapting the model presented here.

(i) The impedance spectra of microporous carbons should theoretically display all of the regions introduced above. If some regions are not visible, they are probably smaller than the dominant one. In this case, a higher resolution setting (using a higher number of points) is required to distinguish all the regions.

(ii) Depending on the pore size and electrolyte, the diffusion process might not be fast enough to complete the charge accumulation within the micropores. Thus, it is sometimes necessary to Page 18 of 28 ACS Paragon Plus Environment

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conduct the impedance experiment within a wider range of low frequencies, which obviously makes the experiments painfully longer.

(iii) The frequencies at which transitions between regions happen should be reported, though it is not common in the literature. Since these frequencies can be directly translated into the sensing scale can assist in comparative studies of the data reported in the literature to find the ratedetermining factors in the design of the carbon nanomaterials for supercapacitors. Note that the regions I and III have a nature of the constant phase element (CPE) in the equivalent circuit, which is affected by a series of different factors including various types of irregularities. Therefore, these regions cannot be directly used for calculating the corresponding parameters such as the diffusion coefficient.



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References [1] Zhang, L.; Yang, X.; Zhang, F.; Long, G.; Zhang, T.; Leng, K.; Zhang, Y.; Huang, Y.; Ma, Y.; Zhang, M.; Chen, Y. Controlling the Effective Surface Area and Pore Size Distribution of sp2 Carbon Materials and Their Impact on the Capacitance Performance of These Materials. J. Am. Chem. Soc., 2013, 135, DOI 10.1021/ja402552h [2] Feng, G.; Cummings, P. T. Supercapacitor Capacitance Exhibits Oscillatory Behavior As a Function of Nanopore Size. J. Phys. Chem. Lett., 2011, 2, DOI 10.1021/jz201312e [3] Jiang, D.; Jin, Z.; Wu, J. Oscillation of Capacitance Inside Nanopores. Nano Lett., 2011, 11, DOI 10.1021/nl202952d [4] Jiang, D.; Jin, Z.; Henderson, D.; Wu, J. Solvent Effect on the Pore-Size Dependence of an Organic Electrolyte Supercapacitor. J. Phys. Chem. Lett., 2012, 3, DOI 10.1021/jz3004624 [5] Garcia, B. B.; Feaver, A. M.; Zhang, Q.; Champion, R. D.; Cao, G.; Fister, T. T.; Nagle, K. P.; Seidler, G. T. Effect of Pore Morphology on the Electrochemical Properties of Electric Double Layer Carbon Cryogel Supercapacitors. J. Appl. Phys., 2008, 104, DOI 10.1063/1.2949263 [6] Zhang, C.; Zhang, R.; Xing, B.; Cheng, G.; Xie, Y.; Qiao, W.; Zhan, L.; Liang, X.; Ling, L. Effect of Pore Structure on the Electrochemical Performance of Coal-Based Activated Carbons in NonAqueous Electrolyte. New Carbon Mater., 2010, 25, DOI 10.1016/S1872-5805(09)60020-2 [7] Largeot, C.; Portet, C.; Chmiola, J.; Taberna, P.; Gogotsi, Y.; Simon, P. Relation Between the Ion Size and Pore Size for an Electric Double-Layer Capacitor. J. Am. Chem. Soc., 2008, 130, DOI 10.1021/ja7106178 [8] Burt, R.; Birkett, G.; Zhao, X. S. A Review of Molecular Modelling of Electric Double Layer Capacitors. Phys. Chem. Chem. Phys., 2014, 16, DOI 10.1039/c3cp55186e [9] Wu, P.; Huang, J.; Meunier, V.; Sumpter, B. G.; Qiao, R. Voltage Dependent Charge Storage Modes and Capacity in Subnanometer Pores. J. Phys. Chem. Lett., 2012, 3, DOI 10.1021/jz300506j [10] Rochester, C. C.; Pruessner, G.; Kornyshev, A. A. Statistical Mechanics of ‘Unwanted Electroactuation’ in Nanoporous Supercapacitors. Electrochim. Acta, 2015, 174, DOI 10.1016/j.electacta.2015.04.064 [11] A Lee, A.; Kondrat, S.; Oshanin, G.; Kornyshev, A. A. Charging Dynamics of Supercapacitors with Narrow Cylindrical Nanopores. Nanotechnology, 2014, 25, DOI 10.1088/09574484/25/31/315401


Page 21 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


[12] Forse, A. C.; Merlet, C.; Griffin, J. M.; Grey, C. P. New Perspectives on the Charging Mechanisms of Supercapacitors. J. Am. Chem. Soc., 2016, 138, DOI 10.1021/jacs.6b02115 [13] Boukhalfa, S.; Gordon, D.; He, L.; Melnichenko, Y. B.; Nitta, N.; Magasinski, A.; Yushin, G. In Situ Small Angle Neutron Scattering Revealing Ion Sorption in Microporous Carbon Electrical Double Layer Capacitors. ACS Nano, 2014, 8, DOI 10.1021/nn406077n [14] Kondrat, S.; Kornyshev, A. Charging Dynamics and Optimization of Nanoporous Supercapacitors. J. Phys. Chem. C, 2013, 117, DOI 10.1021/jp400558y [15] Simon, P.; Gogotsi, Y.; Dunn, B. Where Do Batteries End and Supercapacitors Begin?. Science, 2014, 343, DOI 10.1126/science.1249625 [16] Eftekhari, A. On the Mechanism of Microporous Carbon Supercapacitors. Mater. Today Chem., 2018, 7, DOI 10.1016/j.mtchem.2017.11.004 [17] Eftekhari, A. The Mechanism of Ultrafast Supercapacitors. J. Mater. Chem. A, 2018, 6, DOI 10.1039/c7ta10013b [18] Burwell, R. L. Definitions, Terminology and Symbols in Colloid and Surface Chemistry. Pure Appl. Chem., 1976, 46, DOI 10.1351/pac197646010071 [19] Eftekhari, A.; García, H. The Necessity of Structural Irregularities for the Chemical Applications of Graphene. Mater. Today Chem., 2017, 4, DOI 10.1016/j.mtchem.2017.02.003 [20] Eftekhari, A.; Mohamedi, M. Tailoring Pseudocapactive Materials from a Mechanistic Perspective. Mater. Today Energy, 2017, 6, DOI 10.1016/j.mtener.2017.10.009 [21] Kang, D.; Moon, J. H. Lithographically Defined Three-Dimensional Pore-Patterned Carbon with Nitrogen Doping for High-Performance Ultrathin Supercapacitor Applications. Sci. Rep., 2014, 4, DOI 10.1038/srep05392 [22] Hu, Y.; Liu, H.; Ke, Q.; Wang, J. Effects of Nitrogen Doping on Supercapacitor Performance of a Mesoporous Carbon Electrode Produced by a Hydrothermal Soft-Templating Process. J. Mater. Chem. A, 2014, 2, DOI 10.1039/c4ta01269k [23] Zeng, J.; Cao, Q.; Jing, B.; Peng, X. Hierarchical Porous Nitrogen Doping Activated Carbon with High Performance for Supercapacitor Electrodes. RSC Adv., 2016, 6, DOI 10.1039/c5ra23735a [24] Ni, M.; Huang, Z.; Lian, Y.; Chen, R.; Zhang, X.; Nie, H.; Yang, W. Synergistic Doping for Pseudocapacitance Sites in Alkaline Carbon Supercapacitors. ChemElectroChem, 2018, 5, DOI 10.1002/celc.201700972



Page 22 of 33

[25] Miller, J. R.; Outlaw, R. A.; Holloway, B. C. Graphene Double-Layer Capacitor with AC LineFiltering Performance. Science, 2010, 329, DOI 10.1126/science.1194372 [26] Miller, J. R.; Outlaw, R.; Holloway, B. Graphene Electric Double Layer Capacitor with Ultra-HighPower Performance. Electrochim. Acta, 2011, 56, DOI 10.1016/j.electacta.2011.05.122 [27] Sheng, K.; Sun, Y.; Li, C.; Yuan, W.; Shi, G. Ultrahigh-Rate Supercapacitors Based on Eletrochemically Reduced Graphene Oxide for AC Line-Filtering. Sci. Rep., 2012, 2, DOI 10.1038/srep00247 [28] Shao, Y.; El-Kady, M. F.; Lin, C.; Zhu, G.; Marsh, K. L.; Hwang, J. Y.; Zhang, Q.; Li, Y.; Wang, H.; Kaner, R. B. 3D Freeze-Casting of Cellular Graphene Films for Ultrahigh-Power-Density Supercapacitors. Adv. Mater., 2016, 28, DOI 10.1002/adma.201506157 [29] Yoon, Y.; Lee, K.; Kwon, S.; Seo, S.; Yoo, H.; Kim, S.; Shin, Y.; Park, Y.; Kim, D.; Choi, J.; Lee, H. Vertical Alignments of Graphene Sheets Spatially and Densely Piled for Fast Ion Diffusion in Compact Supercapacitors. ACS Nano, 2014, 8, DOI 10.1021/nn500150j [30] Quan, B.; Meng, Y.; Li, L.; Yao, Z.; Liu, Z.; Wang, K.; Wei, Z.; Gu, C.; Li, J. Vertical Few-Layer Graphene/metalized Si-Nanocone Arrays As 3D Electrodes for Solid-State Supercapacitors with Large Areal Capacitance and Superior Rate Capability. Appl. Surf. Sci., 2017, 404, DOI 10.1016/j.apsusc.2017.01.312 [31] Cai, M.; Outlaw, R. A.; Butler, S. M.; Miller, J. R. A High Density of Vertically-Oriented Graphenes for Use in Electric Double Layer Capacitors. Carbon, 2012, 50, DOI 10.1016/j.carbon.2012.07.035 [32] Ren, G.; Pan, X.; Bayne, S.; Fan, Z. Kilohertz Ultrafast Electrochemical Supercapacitors Based on Perpendicularly-Oriented Graphene Grown Inside of Nickel Foam. Carbon, 2014, 71, DOI 10.1016/j.carbon.2014.01.017 [33] Cai, M.; Outlaw, R. A.; Quinlan, R. A.; Premathilake, D.; Butler, S. M.; Miller, J. R. Fast Response, Vertically Oriented Graphene Nanosheet Electric Double Layer Capacitors Synthesized from C2H2. ACS Nano, 2014, 8, DOI 10.1021/nn5009319 [34] Wang, W.; Ozkan, M.; Ozkan, C. S. Ultrafast High Energy Supercapacitors Based on Pillared Graphene Nanostructures. J. Mater. Chem. A, 2016, 4, DOI 10.1039/c5ta07615c [35] Lin, J.; Zhang, C.; Yan, Z.; Zhu, Y.; Peng, Z.; Hauge, R. H.; Natelson, D.; Tour, J. M. 3-Dimensional Graphene Carbon Nanotube Carpet-Based Microsupercapacitors with High Electrochemical Performance. Nano Lett., 2013, 13, DOI 10.1021/nl3034976


Page 23 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


[36] Ghosh, A.; Le, V. T.; Bae, J. J.; Lee, Y. H. TLM-PSD Model for Optimization of Energy and Power Density of Vertically Aligned Carbon Nanotube Supercapacitor. Sci. Rep., 2013, 3, DOI 10.1038/srep02939 [37] Kruusma, J.; Tonisoo, A.; Pärna, R.; Nõmmiste, E.; Lust, E. In Situ XPS Studies of Electrochemically Positively Polarized Molybdenum Carbide Derived Carbon Double Layer Capacitor Electrode. J. Electrochem. Soc., 2014, 161, DOI 10.1149/2.0641409jes [38] Grahame, D. C. Fiftieth Anniversary: Mathematical Theory of the Faradaic Admittance. J. Electrochem. Soc., 1952, 99, DOI 10.1149/1.2779638 [39] Zhu, J.; Childress, A. S.; Karakaya, M.; Dandeliya, S.; Srivastava, A.; Lin, Y.; Rao, A. M.; Podila, R. Defect-Engineered Graphene for High-Energy- and High-Power-Density Supercapacitor Devices. Adv. Mater., 2016, 28, DOI 10.1002/adma.201602028 [40] Taluja, Y.; SanthiBhushan, B.; Yadav, S.; Srivastava, A. Defect and Functionalized Graphene for Supercapacitor Electrodes. Superlattices Microstruct., 2016, 98, DOI 10.1016/j.spmi.2016.08.044 [41] Luo, G.; Liu, L.; Zhang, J.; Li, G.; Wang, B.; Zhao, J. Hole Defects and Nitrogen Doping in Graphene: Implication for Supercapacitor Applications. ACS Appl. Mater. Interfaces, 2013, 5, DOI 10.1021/am403427h [42] Kajdos, A.; Kvit, A.; Jones, F.; Jagiello, J.; Yushin, G. Tailoring the Pore Alignment for Rapid Ion Transport in Microporous Carbons. J. Am. Chem. Soc., 2010, 132, DOI 10.1021/ja910307x [43] Levi, M. D.; Levy, N.; Sigalov, S.; Salitra, G.; Aurbach, D.; Maier, J. Electrochemical Quartz Crystal Microbalance (EQCM) Studies of Ions and Solvents Insertion into Highly Porous Activated Carbons. J. Am. Chem. Soc., 2010, 132, DOI 10.1021/ja104391g [44] Péan, C.; Daffos, B.; Rotenberg, B.; Levitz, P.; Haefele, M.; Taberna, P.; Simon, P.; Salanne, M. Confinement, Desolvation, And Electrosorption Effects on the Diffusion of Ions in Nanoporous Carbon Electrodes. J. Am. Chem. Soc., 2015, 137, DOI 10.1021/jacs.5b07416 [45] Jäckel, N.; Rodner, M.; Schreiber, A.; Jeongwook, J.; Zeiger, M.; Aslan, M.; Weingarth, D.; Presser, V. Anomalous or Regular Capacitance? The Influence of Pore Size Dispersity on Double-Layer Formation. J. Power Sources, 2016, 326, DOI 10.1016/j.jpowsour.2016.03.015 [46] Crank, J. The Mathematics of Diffusion, 2nd Edition, Oxford University Press, UK, 1986. [47] Carslaw, H. S.; Jaeger, J. C. Conduction of Heat in Solids, 2nd Edition, Oxford University Press, UK, 1986.



Page 24 of 33

[48] Costentin, C.; Porter, T. R.; Savéant, J. How Do Pseudocapacitors Store Energy? Theoretical Analysis and Experimental Illustration. ACS Appl. Mater. Interfaces, 2017, 9, DOI 10.1021/acsami.6b14100 [49] Jurczakowski, R.; Hitz, C.; Lasia, A. Impedance of Porous Au Based Electrodes. J. Electroanal. Chem., 2004, 572, DOI 10.1016/j.jelechem.2004.01.008 [50] Ren, G.; Li, S.; Fan, Z.; Hoque, M. N. F.; Fan, Z. Ultrahigh-Rate Supercapacitors with Large Capacitance Based on Edge Oriented Graphene Coated Carbonized Cellulous Paper As Flexible Freestanding Electrodes. J. Power Sources, 2016, 325, DOI 10.1016/j.jpowsour.2016.06.021 [51] Ren, G.; Hoque, M. N. F.; Liu, J.; Warzywoda, J.; Fan, Z. Perpendicular Edge Oriented Graphene Foam Supporting Orthogonal TiO2(B) Nanosheets As Freestanding Electrode for Lithium Ion Battery. Nano Energy, 2016, 21, DOI 10.1016/j.nanoen.2016.01.010 [52] Itagaki, M.; Suzuki, S.; Shitanda, I.; Watanabe, K.; Nakazawa, H. Impedance Analysis on Electric Double Layer Capacitor with Transmission Line Model. J. Power Sources, 2007, 164, DOI 10.1016/j.jpowsour.2006.09.077 [53] Candy, J.; Fouilloux, P.; Keddam, M.; Takenouti, H. The Characterization of Porous Electrodes by Impedance Measurements. Electrochim. Acta, 1981, 26, DOI 10.1016/0013-4686(81)85072-4 [54] Cericola, D.; Spahr, M. E. Impedance Spectroscopic Studies of the Porous Structure of Electrodes Containing Graphite Materials with Different Particle Size and Shape. Electrochim. Acta, 2016, 191, DOI 10.1016/j.electacta.2016.01.121 [55] Kötz, R.; Carlen, M. Principles and Applications of Electrochemical Capacitors. Electrochim. Acta, 2000, 45, DOI 10.1016/S0013-4686(00)00354-6 [56] Zhou, Q.; Zhang, M.; Chen, J.; Hong, J.; Shi, G. Nitrogen-Doped Holey Graphene Film-Based Ultrafast Electrochemical Capacitors. ACS Appl. Mater. Interfaces, 2016, 8, DOI 10.1021/acsami.6b05601 [57] Yoo, Y.; Kim, M.; Kim, J.; Kim, Y. S.; Kim, W. Fast-Response Supercapacitors with Graphitic Ordered Mesoporous Carbons and Carbon Nanotubes for AC Line Filtering. J. Mater. Chem. A, 2016, 4, DOI 10.1039/c6ta00921b [58] Song, H.; Jung, Y.; Lee, K.; Dao, L. H. Electrochemical Impedance Spectroscopy of Porous Electrodes: the Effect of Pore Size Distribution. Electrochim. Acta, 1999, 44, DOI 10.1016/S0013-4686(99)00121-8 [59] Keiser, H.; Beccu, K.; Gutjahr, M. Abschätzung Der Porenstruktur Poröser Elektroden Aus


Page 25 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Impedanzmessungen. Electrochim. Acta, 1976, 21, DOI 10.1016/0013-4686(76)85147-X [60] Wang, Z.; Selbach, S. M.; Grande, T. Van Der Waals Density Functional Study of the Energetics of Alkali Metal Intercalation in Graphite. RSC Adv., 2014, 4, DOI 10.1039/C3RA47187J [61] Qu, D.; Shi, H. Studies of Activated Carbons Used in Double-Layer Capacitors. J. Power Sources, 1998, 74, DOI 10.1016/S0378-7753(98)00038-X [62] Zhang, L.; Shi, G. Preparation of Highly Conductive Graphene Hydrogels for Fabricating Supercapacitors with High Rate Capability. J. Phys. Chem. C, 2011, 115, DOI 10.1021/jp204036a [63] Kleszyk, P.; Ratajczak, P.; Skowron, P.; Jagiello, J.; Abbas, Q.; Frackowiak, E.; Béguin, F. Carbons with Narrow Pore Size Distribution Prepared by Simultaneous Carbonization and SelfActivation of Tobacco Stems and Their Application to Supercapacitors. Carbon, 2015, 81, DOI 10.1016/j.carbon.2014.09.043



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Figure Captions

Figure 1. (a) Perpendicular physisorption on the basal plane of graphene or carbon nanotube, and (b) chemisorption and surface diffusion at the edge of graphene or carbon nanotube.

Figure 2. (a) A schematic illustration of the classic Helmholtz double layer, (b) insertion of single ions into micropores, and (c) formation of double layer in mesopores. The circles indicates the active edge carbon atoms facilitating the initial adsorption and the arrows show the surface diffusion of ions into the micropores. Note that the organic ions from ionic liquids reported in the literature are asymmetric and when matching their sizes with the 0.7-nm micropores, they can enter in one direction only.

Figure 3. (a) Impedance model of a microporous carbon capacitor exhibiting three different regions. (b) Increasing the load mass or the film thickness. (c) Reducing the size of the pore mouth (similar dependency can be found for the pore size too). The representation of the impedance behaviour shown in the Nyquest diagrams (a-c) are illustrated in the corresponding Bode plots (d,e).

Figure 4. Electrochemical properties of two-electrode cells built from Burley 800, Burley 800-800 and Burley 800-900 in 1 M Li2SO4: (a) cyclic voltammograms (5 mV s–1); (b) Nyquist plots. Reproduced with permission.63 Copyright 2015, Elsevier.


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Equations in LaTeX format

Equation 1 \frac{\partial c}{\partial t} = D \Bigg(\frac{1}{r}\frac{∂}{∂r}\Big(r\frac{∂c}{∂r}\Big) + \frac{1}{r^2}\frac{\partial^2 c}{\partial φ} + \frac{\partial^2 c}{\partial z^2}\Bigg) Equation 2 c = \frac{1}{\sqrt{(4πDt)^n}} exp\Big(\frac{x^2}{4Dt}\Big) Equation 3 i = \frac{nFADC^*}{πt}



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For Table of Contents Use Only. Graphical Abstract Capacitive behaviour on carbon nanomaterials starts with a chemisorption at active sites and surface diffusion over the basal plane.


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FIgure 1

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Figure 2


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Figure 3



Figure 4 562x238mm (72 x 72 DPI)


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GRAPHICAL ABSTRACT: Instead of forming a classic double layer, electroactive species are chemisorbed at specific adsorption sites and diffuse along the basal plane.


Surface Diffusion and Adsorption in Supercapacitors - ACS Publications

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