Differential Capacitance and Energetics of the Electrical Double Layer

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C: Energy Conversion and Storage; Energy and Charge Transport

Differential Capacitance and Energetic of the Electrical Double Layer of Graphene Oxide Supercapacitors. Impact of the Oxidation Degree Antenor José Paulista Neto, and Eudes Eterno Fileti J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b07349 • Publication Date (Web): 05 Sep 2018 Downloaded from http://pubs.acs.org on September 5, 2018

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The Journal of Physical Chemistry

Differential Capacitance and Energetic of the Electrical Double Layer of Graphene Oxide Supercapacitors. Impact of the Oxidation Degree Antenor J. Paulista Neto1 and Eudes Eterno Fileti*2

(1) Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, 09210-170, Santo André, SP, Brazil. (2) Instituto de Ciência e Tecnologia, Universidade Federal de São Paulo, 12247-014, São José dos Campos, SP, Brazil.

Abstract Graphene oxide based materials have been considered for potential energy storage applications, in particular supercapacitors. Here, for the first time, we present a detailed analysis of the properties of graphene oxide based supercapacitors as a function of both chemical composition and charge density on the electrodes. Differential capacitance was determined and the effect of the degree of oxidation of the electrodes was taken into account. Also, structural and energetic details on the electrode-electrolyte interaction and consequently the double-layer electric structure were analyzed. The differential capacitance value for all supercapacitors is within the range of 1.5 to 5.4 µF cm-2 in the ±3V window for the electrode potential and presents the highest value for the R20 system, which also had the highest mean integral capacitance. One important result is the gradual transition from bell-shaped to camelshaped as the degree of oxidation increases. The results presented here provide the missing complementing for a detailed and complete description of the properties of graphene oxide supercapacitors, indicating how they behave with the variation of charge density and degree of oxidation.

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Introduction Graphene-based materials have often been used as electrodes in chemical energy storage applications.1-7 This is due to the fact that graphene has unique physico-chemical properties such as a large specific area and wide electrochemical window that contribute crucially to the performance of the devices, having a theoretical capacity of up to ~21 µF cm-2, in the case of supercapacitors.8 However the strong π−π interactions between graphene sheets favor the formation of aggregates, significantly reducing their specific area, reducing the ionic mobility on their surface and, consequently, profoundly affecting their capacitive behavior.5 Therefore, in practice, its performance is always much lower than the expected value. A promising solution to overcome this problem is to employ an oxidized version of graphene, i.e., graphene oxide (GO).9-11 Although the insulating nature of GO limits its application as electrodes in supercapacitors, its reduced version, reduced graphene oxide (rGO), presents remarkable and advantageous characteristics for energy storage applications, such as its large specific area, chemical stability, good electrical conductivity and its amphiphilic nature.12-16 The amphiphilicity in rGO arises due to the formation of islands of hydrophilic groups separated by hydrophobic regions.15 This introduces pseudocapacitive effects to the electrode and ensures that the entire active surface can be accessible to the electrolyte.13-14 Therefore, such characteristics of the rGO have a direct reflection on the improvement of the properties of the oxide graphene based supercapacitors, such as its capacitance and cyclic stability.16 In the last decade, important advances in the use of GO-based materials for energy storage applications, in particular supercapacitors, have been achieved.17-19 Production of activated graphene (or porous carbon) through the chemical activation of exfoliated graphite oxide has made possible a great advance in the development of sophisticated 2D and 3D networks in meso-, micro- and nano-scales.20 This is due to the fact that the rational control of the electrode morphology contributes to the improvement their the electronic conductivity as


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well as the ion dynamics. In addition, the adjustment of surface properties (such as the electrostatic nature) can improve the affinity between the electrode and the ions and thus affect the ionic packing process.21-23 Therefore, by modulating the electrode structures and their corresponding surface properties we can improve the performance of the device in which it will be used.21-23 However, the computational modeling of these structures is still a challenge considering the incalculable possibilities for the morphological and chemical composition of each one of them. Nevertheless, recent computational works has provided important information on the efficiency of supercapacitors employing planar graphene oxide electrodes. For example, Kim and colleagues investigated several characteristics of graphene oxide and ionic liquid-based supercapacitors.1 Although their model considered only hydroxyl groups on the electrode their set of results is quite relevant and show that the capacitance of the electric double layer decreases with the increase of the oxidation degree of the electrode.1 Kerisit et al. investigated the effects of different oxygen groups, epoxy and hydroxyl, on five different concentrations on the capacitance of graphene oxide supercapacitors with the ionic liquid. It was verified that both the concentration and the type of the functional group reduce the capacitance of the supercapacitor, especially the OH group that favors the anion bonds with the functional groups of the electrodes, reducing their mobility and consequently reducing their performance.24 Jiang and colleagues explored the properties of reduced oxide electrodes in aqueous NaCl electrolytes and again it was observed that the reorientation of the electrolyte molecules near the electrode surface leads to a rearrangement of the net charge in the electric double layer (EDL).12 They verified that the effect of this charge rearrangement was to weaken the ionic mobility in the EDL which led to a significant reduction of the electrochemical capacitance.12 As far as we know, all the works that model graphene oxide supercapacitors report only its integral capacitance.1, 5, 12, 24-25 This property is in fact the most employed in applied


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works since it determines the energy density stored in a supercapacitor. However, differential capacitance provides the most detailed information about the physico-chemical processes that occur in the EDL.26 Therefore, since the differential capacitance is a quantitative measure of the response of the EDL structure to a change in the charge density of the electrode, its analysis is fundamental for the complete description of the behavior of the electric double layer, both theoretically and practically. In this work, we present a detailed analysis of the properties of graphene oxide based supercapacitors as a function of both chemical composition and charge density on the electrodes. Both integral and differential capacitance for each supercapacitor will be determined and the effect of the degree of oxidation of the electrodes will be taken into account. In addition, structural and energetic details on the electrode-electrolyte interaction and consequently the electric double layer structure will be analyzed.

Computational details Five different supercapacitors based on the BMIM-PF6 liquid ionic (1-butyl-3-methylimidazolium hexafluorophosphate) were investigated. For each of them, different electrodes were used, one of them being pure graphene and the other oxides of graphene in different degrees of oxidation. The degree of oxidation = 100 × ⁄ is defined as the ratio of the number of carbon of the graphene basal plane (cC) and the number of oxygen groups (cO) adsorbed on its surface.27 Unlike previous works that adopt to purely epoxy or purely hydroxyl functionalized graphene oxide electrodes,1 in this work we employ a more probable form for the graphene oxides, which consist of the basal graphene plane functionalized with both groups, oxides and hydroxyls, at an O/OH ratio of 2:1, as we used in previously work.2830

Table 1 shows the dimensions of each of the supercapacitors and their composition in

terms of the interaction sites. Molecular representation of the ions that compose the electrolyte, the electrodes and the supercapacitor is presented in Figure 1.


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Table 1: Composition of the investigated systems, separation distance between the electrodes (nm) and surface area do the electrodes (nm2). System # ion pairs # interaction sites d (nm) A (nm2) 550 18496 16.2 12.1 GRA 550 18800 15.3 12.8 R20 550 18896 14.8 13.2 R30 550 19040 15.4 12.8 R40 550 19160 15.2 13.0 R50

Figure 1: Molecular representation of the five electrodes used here e the ionic pair BMIM and PF6 from electrolyte. At bottom a representative charged supercapacitor equilibrate configuration.

Each supercapacitor was prepared so that the electrodes, rigid and separated by a distance d (see Table 1) delimit a volume capable of confining 550 ionic pairs of BMIM-PF6 (see Figure 1). The separation between the electrodes was adjusted in such a way that the density at the center of the supercapacitor is equal to the density of the pure liquid. This


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adjustment was made by means of preliminary semiisotropic NPT simulations without the typical vacuum layer without the electrodes. After obtaining the convergence of distance d, a vacuum slice of 22 nm was inserted between the electrodes in order to minimize their interaction and then all trajectories were produced at constant volume. These MD simulations were performed in the isothermal-isochoric ensemble (N, V, T) at 450 K. The potential model used to simulate the BMIM-PF6 ionic liquid was developed by Lopes and Padua.31 For the electrodes we used the model developed by us and that was successfully used in the thermodynamic and structural description of graphene oxides in various physicochemical conditions.28-30 Namely, in this model, the partial electric charges were calculated using quantum mechanical calculations. Such electric charges were obtained at B3LYP/6-31G(d,p) theoretical level using CHELPG scheme. Thus, the charges for the O(epoxy), O(hydroxyl), H(hydroxyl) and C(sp2) atoms were respectively -0.36e, -0.70e, +0.40e and +0.30e. These average values are similar to those determined by Stauffer, by the DFT charge scaling, which was performed to take into account the polarization effect of an aqueous environment.32 Graphene electrodes were simulated as a non-polarizable assembly of carbon atoms fixed in its hexagonal lattice with distance C-C of 1.42 nm.4, 33 Each supercapacitor was simulated at 11 different surface charge densities from

= 0

(discharged

ultracapacitor)

to

= ±12 C

(±0.75 )

evenly

incremented by 1.2 C . It is important to note that the electrostatic potential corresponding to the higher charge densities may go beyond the values supported by the ionic liquids under experimental conditions.34 In any case, it is interesting to simulate the properties of the supercapacitor under these conditions and to understand how they could behave in high potentials. In addition, we emphasize that this range for the charge density encompasses all the typical densities used to investigate graphene-based supercapacitors. All supercapacitors were simulated for 25.0 ns of which the first 5ns were discarded. The integration time-step was of 2.0 fs and the coordinates and intermediate thermodynamic


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quantities were saved every 0.2 ps. All reported MD simulations were performed using the GROMACS 2016 molecular simulation engine.35-38

Results & Discussion The main characteristic of an electrochemical supercapacitor is the formation of an electric double layer (EDL) near the surface of the electrodes. This double layer can be described both from a structural and an energetic point of view. Figure 2 shows the number density profiles for the GRA, R20 and R50 supercapacitors (the others are shown in the supporting material). In red, the distribution of cations BMIM near the negative electrode and, in blue, the distribution of anions PF6 near the positive electrode.

Figure 2. Number ion densities (in nm-3) of anions (in blue) and cations (in red) near the positive and negative electrodes, respectively. The distributions, calculated for center of mass of the ions, are presented as a function of the charge density magnitude ( ) and of distance between electrodes, z (nm).


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As expected we observed the typical pronounced fluctuation of the number density at EDL for all cases. Such an oscillatory pattern of number density near the surface of an electrode has already been observed for several other planar electrodes supercapacitors previously investigated.4, 24, 39-41 Naturally, the structuring, characterized by the first peak of the profile, increases as the charge density increases. This increase is more significant for graphene, for which at = 0 the height of the first peak of the cation distribution (in red) is ~110 nm-3 and at = ±12 C it is ~150 nm-3. This difference diminishes with the increase of the degree of oxidation in the electrode. For example, for R50 system the peak height varies with the charge density over a smaller range, from ~95 nm-3 to ~105 nm-3. Another important aspect to be analyzed is that in the pure graphene electrode the level of structuring is much higher than for the oxidized electrodes, especially for the cations, which interact much more strongly with the hydrophobic surface of the graphene. This is characterized by a much sharper first peak, ie higher and narrower than that observed for graphene oxide electrodes. This conclusion suggests that entropic effects that arise in the electrolyte reorganization at the electrode surface may be determinant for an accurate description of the EDL. Thermodynamic aspects (entropic and enthalpic) should be considered in a rigorous treatment. However, the energetic aspect of the EDL formation process, in terms of electrodeelectrolyte interactions, can provide important information to understand this process. In Figures 3A and 3B we present two different quantitative energy analyzes involving both components of Coulomb and van der Waals. We observed that the electrode-electrolyte electrostatic interaction (Figure 3A) depend on the oxidation level of the electrode, being zero for graphene and maximum (-130 kJ mol-1 per unit area) for the electrode R30. An even higher electrostatic interaction could be expected for higher oxygen concentrations (R> 30%), however we see that such interaction is -105 and -115 kJ mol-1 for the R40 and R50 electrodes, respectively. This behavior, as discussed previously, is attributed to steric factors


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that prevent further interaction through hydrogen bonds between the medium and graphene oxide.24 With increasing charge density on the electrodes, the electrostatic interaction increases gradually, except for R50 system, for which this interaction remains practically constant. In particular for graphene, its electrostatic interaction is zero, at = 0 and grows (in magnitude) quadratically with , in a range of 0 to -50 kJ mol-1. For the reduced graphene oxide, R = 20%, this quadratic variation can still be observed in the same range, but ranging from -50 to -125 kJ mol-1. As the R increases, the electrostatic interaction varies each time any less.

Figure 3: Electrode-electrolyte interaction energies in kJ mol-1 nm-2. The contributions of Coulomb (Coul) and van der Waals (vdW) of the electrodes-electrolytes interaction energy are shown in panels (A) and (B), respectively. In panel C, the red (negative electrode) and blue (positive electrode) bars represent the total interaction energy (Coul + vdW) of the electrolyte with the electrodes, respectively of each capacitor. These energies were normalized with respect to the electrode area and their values were multiplied by -1 for the sake of clarity. ACS Paragon Plus Environment

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In Figure 3B, we observe that the van der Waals interactions, for = 0, vary between -155 and -190 kJ mol-1 for all electrodes. It is interesting to note that although the oxides present a greater number of sites for weak interactions, since it includes additional groups O and OH, pure graphene electrode interacts most strongly with the electrolyte through van der Waals interactions. Note that, pure graphene shows greater reduction in the interaction with the increase of the density of charge, ranging from -190 to -165 kJ mol-1. This reduction in the van der Waals interaction, observed for all electrodes, is related to the strong electrostatic attraction that strongly compresses the EDL on the surface of the electrodes reducing the distances between the sites and favoring the repulsive term of the potential of Lennard-Jones. An interesting consequence (see Figure S2 in SI) is that the total interaction energy (Coul + vdW) of the electrodes with high oxidation degree remains practically constant with respect to the charge density of the electrodes. However, for the GRA and R20 systems, this same energy gradually decreases as the charge density of the electrodes increases. In general, it is interesting to note that although both contributions are expressive, the energetic part of the electrode-electrolyte interaction is dominated by the van der Waals terms, mainly for the lower charge densities. The interaction between the ionic liquid and the positive and negative electrodes in each supercapacitor leads to an inherent asymmetry that has a reflection on the properties of the device. Figure 3C allows to evaluate and quantify this asymmetry in terms of the interaction total energy between the electrolyte and both positive (blue bars) and the negative (red bars) electrodes. In general, for all supercapacitors the electrolyte interacts more strongly with the negative electrode, except for the R20 system, for which we observe an inverse behavior and the interaction of the electrolyte with both electrodes is only similar for high charge densities. This is due to the fact that, for reduced oxides and graphene, the interactions are strongly dominated by the van der Waals interactions, favored by the oxide topology that


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is characterized by the formation of hydrophilic islands separated by relatively large hydrophobic regions. In addition, as the oxidation degree increases, it is possible to observe the increase of the asymmetry and a lower interaction of the electrolyte with the positive electrode. The computational determination of the electrical properties of a supercapacitor is usually made based on the electrostatic potential profile, (). This potential can be obtained by integrating the Poisson equation, given by:19 1 () = −

" "#

( − ! ) $" ( ! )% !

where is the permittivity of vacuum at − ! distance along to the normal of the electrodes surface and $" ( ! ) is the local charge density due to the atomic charge distribution of each ionic species.19 From the electrostatic potential, we can then obtain both capacitances, integral (CI) and differential (CD). For this we determine the total potential drop across the device as && = & '()*+,- − & ./'()*+,- where & = ')0(1-, − )/1-, is calculated for both charge and uncharged electrode situations. In this way, the integral capacitance can be obtained by the ratio between the charge density and the drop potential, 2 =

| |4 &&, while

the differential capacitance is obtained by the rate of change of surface charge density as a function of the drop potential on a given electrode, - = %/%. Figure 4 shows the electrostatic potential profiles for three of the five supercapacitors studied here (the other are presented at SI). The profiles are presented as a function of the separation between the electrodes and also as a function of the charge density. At top of the Figure 4, we present a single profile for graphene, for a single charge density, indicating how the electrode potentials were taken. Note that electrode potential is obtained by the difference between the potential value at the electrode surface and the potential at the bulk region. The other plots at Figure 4 show the superposition of the potential profiles for all charge densities. ACS Paragon Plus Environment

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Figure 4: Electrostatic potential profiles, (), for all supercapacitor as a function of the distance, z, from the electrodes and the charge density, σ. At top, a single profile indicating precisely how the electrode potential is obtained, ie: & = ,6,'0*1-, − 7.68 . In the middle, we present a superposition of the graphs and at bottom, a cascade representation to facilitate the direct comparison of the effect of increasing the density of charge on the potential profile. In all cases the expected oscillatory pattern was obtained, that is, the electrostatic potential reaches the highest value on the surface of the electrode and, from there, it oscillates until reaching a constant value in the electrolyte bulk. Comparison of the potential profiles for graphene and reduced graphene oxide (R20) show that both have a similar potential drop in the electric double layer, with peaks in the potential profile around 3.3 V on the positive electrode. On the other hand, both GRA and R20 present significant differences in relation to R50. For this the potential peak in the electric double layer reaches 6.2 V, a value that is due to the strong hydrophilic character of the R50, which favors a greater electrostatic electrodeelectrolyte interaction. We can also observe that for all supercapacitors, the electrostatic potential at the electrode surface increases in magnitude as the charge density increases.


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This increase is related to the virtually linear increase of the drop potential across the supercapacitors as the charge density increases. This behavior is shown in Figure 5A and is consistent with the behavior of several previously simulated systems.19 An interesting feature of these systems is the relatively high value obtained for the potential zero charge (PZC) for some of the supercapacitors. Unlike graphene, for which all interaction sites are uncharged, graphene oxide presents partial charges at all of its functionalized sites even when the electrode is discharged. The effect of small asymmetries in the charge distribution can manifest in the electrostatic potential calculations and thus affect the PZC. For example, the graph shows that the PZC for graphene and R40 systems is close to zero (for the graphene system this PZC vales are consistent with previous theoretical studies), for R20 and R30 are close to -1V and for R50 it is close to +1V. Thus, no dependence of the PZC with the oxidation degree of the electrode can be established and probably the PZC value depends on the specific morphology used for each graphene oxide.

Figure 5: Electrical properties of ultracapacitors. a) variation of the electrostatic potential drop as a function of the charge density. b) integral capacitance as a function of the potential drop. c) energy density stored in the supercapacitor as a function of the potential drop. ACS Paragon Plus Environment

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Figure 5B shows the dependence of the integral capacitance with the voltage on the supercapacitor. For all cases, the capacitance varies drastically for values of potential less than 1V and presents constant behavior for high potentials. The graphene-based supercapacitor, for example, presents integral capacitance close to zero for potential zero and a value around ~2 µF cm-2 for potentials above 1V. Reduced graphene oxide present the greatest variation in lower potential. The value of its integral capacitance reaches a maximum of 6.8 µF cm-2 at 0.4V and reduces to a value around 3 µF cm-2 for potentials above 2V. The average value of the integral capacitance, for potentials above 1V is 2.2, 2.4, 2.1, 1.5 and 1.3 µF cm-2 for the GRA, R20, R30, R40 and R50 systems, respectively. There are no direct comparisons we can make with previous results, since this is the first work to explore graphene oxide electrodes functionalized with both O and OH groups simultaneously. However, we can establish connections with values obtained for similar supercapacitors. Jiang and colleagues studied reduced graphene oxide supercapacitors functionalized purely with O or OH using aqueous electrolyte NaCl.12 They found that the integral capacitance at a potential of about 2V is 2.6 µF cm-2. This value is lower than that found here for the supercapacitor R20, from 3.0 µF cm2

to the same potential. Kim and colleagues investigated GO/EMIM-BF4 supercapacitors over

a complete range of oxidation grades, from 0 to 100%. For a charge density of 7 µC cm-2 the authors found capacitances of 2.6, 2.3 and 2.2 µF cm-2 for the GRA, R40 and R20 electrodes, respectively.1 Vijayakumar et al. determined a supercapacitor rGO/BMIM-OTf purely functional with OH groups an integral capacitance 3.1 µF cm-2 for an oxidation degree of 20%.24 This value coincidentally is very close to that found here, 2.9 µF cm-2, despite the difference between the electrolytes and the chemical and morphological composition of the electrodes. This series of comparisons between supercapacitors involving electrodes functionalized only with O or only with OH. Both types of capacitors have capacitances similar to ours, which are O/OH hybrids. Thus, such a comparison suggests that the


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performance of graphene oxide supercapacitors has little or no dependence on pure or mixed O/OH functionalization. The density energy stored in a capacitor can be determined by 9 = 2 [ΔΔ] /2=, where = is the volume of the capacitor. However, it is important to keep in mind that this expression is accurate only for cases in which 2 is constant. We see from Figure 5B that this is not the case here, so the following values are accurate only for the potential range where 2 is approximately constant, ie for ΔΔ > 2=. Figure 5C describes how energy storage varies for each of the supercapacitors. Quadratic behavior is naturally observed for all systems so that energy increases with potential through the supercapacitor. In addition, we observed that systematically the storage capacity increases as the degree of oxidation decreases, that is, graphene and reduced graphene oxide systems are the most efficient devices among all investigated. Table 2 presents the values of energy stored as a function of the potential in the supercapacitor. For a physically relevant comparison, all values compared refer to the same potential. For example, at a potential of 4V, the energy density decreases from 14.3 J cm-1 to 7.8 J cm-3 as the degree of oxidation increases. Table 2. Stored energy density in each ultracapacitor, u, (J cm-3) compared at several potential differences ∆∆Φ, (V). Stored energy density, u, (J cm-3) ∆∆Φ (V) GRA R20 R30 R40 R50 1.0 0.8 1.1 0.7 0.4 0.4 2.0 3.6 4.2 3.2 2.5 1.9 3.0 8.1 9.5 7.0 5.4 4.4 4.0 14.3 16.1 12.4 9.3 7.8 5.0 22.9 26.4 20.8 15.6 13.2 6.0 29.1 21.6 18.6 7.0 28.9 25.4

As mentioned in the Introduction, the energy storage capacity of an electrochemical supercapacitor depends on the integral of the differential capacitance, which is a quantitative measure of the response of the electric double layer structure to a change in the charge density


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of the electrode.42-43 In addition, a fundamental understanding of EDL is often obtained by differential capacitance using electrochemical impedance spectroscopy.43-45 This analysis allows a comprehensive view on the properties of EDL in particular on the ionic orientation after the application of electric fields and consequently on the mechanism of charge accumulation on the surface of the electrode.26 Although integral capacitance is the most used in applied studies, because it quantifies the energy density of the EDL, the differential capacitances give much more information about the physical-chemical processes at play. Therefore, understanding the correlation of the EDL with the differential capacitance is important both from the theoretical and practical points of view, and for the first time this is carried for GO based supercapacitor.

Figure 6: (A) Charge density (σ) at graphene electrode versus potential drop (∆∆Φ) across the supercapacitor. (B-F) differential capacitance (CD) as a function of the potential drop for all supercapacitors investigated here. In (A), the circles represent data from MD simulations and the solid line is fit from polynomial smoothing of the data.

As we saw before, the CD, defined as a derivative of the surface charge density of the electrode in relation to the potential of the electrode. Different forms of CD-∆∆Φ curves have been observed experimentally and predicted computationally, including bell- and camelshaped types for supercapacitors with planar electrodes, indicating that the differential


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capacitance is closely associated with the potential of the electrode.39,

46-49

The analytical

expression derived by Kornyshev suggests that the shape of these curves is a function of many parameters such as the size, configuration and non-electrostatic interaction of ions with the surface of the electrode.50 Here, the differential capacitance was determined through the analytical derivative of the polynomial fitting of the correlation σ-∆∆Φ. This fitting is shown in Figure 6A for the graphene electrode. The other figures (6B-6F) present the differential capacitance as a function of the potential drop. We see that for all supercapacitors the differential capacitance presents a dependence with the potential of the bell or camel type. For GRA, R20 and R30 supercapacitors (figures 6B-6D), the CD-∆∆Φ curves is unsymmetrical bell-shaped with maxima in a small potential range with the peak position at negative values, while the R50 (figure 6F) is symmetrical camel-shaped with well-defined minimum at more positive potential. This is consistent with the theoretical models, which predict that for planar electrodes in ionic liquids the differential capacitance must be in camel-shaped with a minimum near PZC or one with a bell shape with a maximum in low potential regions.39, 47-48 The differential capacitance value for all supercapacitors is within the range of 1.5 to 5.4 µF cm-2 in the ±3V window for the electrode potential and presents the highest value for the R20 system, which also had the highest mean integral capacitance. This window of values is in good agreement with the majority of simulations of RTILs on flat surfaces that typically predict almost a constant DC with an average value between 4 and 5.5 µF cm-2 within a potential window of ±2 V.51-53 One important result is the gradual transition from bell-shaped to camel-shaped as the degree of oxidation increases. This transition was found experimentally by Ohsaka et. al. in an extensive study on the structure of glassy carbon (GC) in BMIBF4.44 Note that this transition begins with R40, which presents a more diffuse differential capacitance curve and is completed in the R50 system which shows a clear camelshaped dependence, with maxima of about 4.1 µF cm-2 around -2.8 and 3.2V. As it was observed through the density profiles (Figure 2), the structuring of the ions is greater for the


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pure graphene than for the oxidized electrodes. In addition, both pure graphene and reduced graphene oxide (R20) are the electrodes that interact most strongly with the electrolyte through the van der Waals interactions (Figure 3B). These factors can be related to this transition, which is expected based on EDL theories.46,

50

The systems with more reduced

electrodes (R < 30%) present a high overall number density due to van der Waals interaction with the electrolyte, i.e. the EDL is sufficiently incompressible, further increase in applied potential will not lead to increase in electrode charge, therefore a bell-shaped DC dependence should be expected. On the other hand, the EDL structure for the oxidized electrodes shows relatively low density and, hence, can accommodate more ions without significant free energy penalty, leading to the U-shaped DC dependence near PZC. At higher potentials, the total density of ions saturates on both electrodes the DC reaches its maxima resulting therefore in an overall camel-shaped DC.

Conclusions Atomistic molecular dynamics simulations were used to determine the properties of supercapacitors of graphene oxide based electrodes. The description was made both in terms of the degree of oxidation of the electrode and in terms of its charge density. Energy analysis shows that although both Coulomb and van der Waals contributions are expressive, the energetic part of the electrode-electrolyte interaction is dominated by the van der Waals terms, mainly for the lower charge densities. In general, for all supercapacitors, the total interaction between the ionic liquid and the positive and negative electrodes is more strong for the negative electrode. This interaction asymmetry is related to the known inherent electrostatic asymmetry that impacts the properties of the device. For all cases, it was verified that the integral capacitance varies drastically for values of potential less than 1V and presents a constant behavior for high values of potentials. Reduced graphene oxide is the one with the greatest variation in lower potential. The average


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value of the integral capacitance, for potentials above 1V is 2.2, 2.4, 2.1, 1.5 and 1.3 µF cm-2 for the GRA, R20, R30, R40 and R50 systems, respectively. The corresponding storage capacity was found to increases as the degree of oxidation decreases, that is, graphene and reduced graphene oxide systems are the most efficient devices among all investigated. The differential capacitance value for all supercapacitors is within the range of 1.5 to 5.4 µF cm-2 in the ±3V window for the electrode potential and presents the highest value for the R20 system, which also had the highest mean integral capacitance. One important result is the gradual transition from bell-shaped to camel-shaped as the degree of oxidation increases. This transition begins with R40, which presents a more diffuse differential capacitance curve and is completed in the R50 system which shows a clear camel-shaped dependence, with maxima of about 4.1 µF cm-2 around -2.8 and 3.2V. The factors that justify this transition are related to the differential accumulation and structuring of the ions near the surface of the more oxidized electrodes, which leads to the U-shaped DC dependence near PZC. At higher potentials, as the total density of ions saturates on both electrodes the DC reaches its maxima resulting therefore in an overall camel-shaped DC. The set of results presented here provides the missing complement for a detailed and complete description of the properties of graphene oxide supercapacitors, indicating how they behave with the variation of charge density and degree of oxidation. Graphene oxides have been used in storage energy applications in several different ways. For example, it has been an important material considered for hybrid structures and 3D architectures, both employed in EDL storing energy.21-23, 54 Therefore the results presented here may be useful for the rational development of such sophisticated structures.

Supporting Information Complementary information is provided in the supporting material. In this file we present the ion number densities and electrostatic potential profiles, both as a function of the charge


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density and of distance between electrodes for all investigated systems. Electrode-electrolyte total interaction energies for all supercapacitors are also presented.

Acknowledgments E.E.F. is funded through CNPq and FAPESP (Grant number: 2017/11631-2).

Contact Information Any correspondence concerning this work can be forwarded to [email protected] (E.E.F) or [email protected] (A.J.P.N)

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TOC Graphic


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Differential Capacitance and Energetics of the Electrical Double Layer

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