Graphene Oxide Supercapacitors: A Computer Simulation Study - The

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Graphene Oxide Supercapacitors: A Computer Simulation Study Andrew D. DeYoung,† Sang-Won Park,‡ Nilesh R. Dhumal,† Youngseon Shim,‡,∥ YounJoon Jung,*,‡ and Hyung J. Kim*,†,§,⊥ †

Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States Department of Chemistry, Seoul National University, Seoul 151-747, Korea § School of Computational Sciences, Korea Institute for Advanced Study, Seoul 130-722, Korea ‡

S Supporting Information *

ABSTRACT: Supercapacitors with graphene oxide (GO) electrodes in a parallel plate configuration are studied with molecular dynamics (MD) simulations. The full range of electrode oxidation from 0% (pure graphene) to 100% (fully oxidized GO) is investigated by decorating the graphene surface with hydroxyl groups. The ionic liquid 1-ethyl-3methylimidazolium tetrafluoroborate (EMI+BF4−) is examined as an electrolyte. Capacitance tends to decrease with increasing electrode oxidation, in agreement with several recent measurements. This trend is attributed to the decreasing reorganization ability of ions near the electrode and a widening gap in the double layer structures as the density of hydroxyl groups on the electrode surface increases.

1. INTRODUCTION Electric double layer capacitors (EDLCs), or supercapacitors, have attracted much attention, as they offer high power densities and reasonable energy densities for energy storage devices.1 A prototypical EDLC consists of two parallel electrodes that confine an electrolyte. Graphene-based materials are a promising alternative to conventional electrode materials due to graphene’s remarkable properties, including high surface area, electrical conductivity and mechanical stiffness, and efficient electrolyte wetting.2,3 Ionic liquids (ILs), meanwhile, are an exciting alternative to conventional electrolytes by virtue of their wide electrochemical window, low volatility, and high thermal stability.4 Since the combination of graphene-based electrodes and IL electrolytes promises excellent supercapacitor performance, many recent experimental studies have focused on such systems.5−7 Computational studiestypically MD simulationshave followed suit.8−23 However, characterizing the exact spatial and chemical structure of graphene-based electrodes is difficult. Perhaps because of this difficulty, and to keep model descriptions simple, most prior computational studies of such supercapacitors have used pure graphene as model electrodes. Yet, oxide impurities are likely to persist, despite strong reduction treatments, and thus graphene is sometimes referred to as “reduced graphene oxide” in the literature.24 According to X-ray photoelectron spectroscopy and NMR studies, hydroxyl and epoxide moieties are the predominant oxide groups in graphene oxide.25 The key question we undertake in this paper is whether the oxidation of graphene leads to an increase or decrease in the © XXXX American Chemical Society

device capacitance and how. This is a question of some experimental debate; while some studies suggest that graphene oxide electrodes give higher capacitance than those of relatively pure graphene,26,27 others suggest that oxidation leads to lower capacitance.28−34 To address this issue, we investigate how the oxidation of graphene electrodes influences electrolyte structure near the electrode surface and thus capacitance. While both non-MD35−41 and MD methods35,42−47 have been applied toward understanding the structure and mechanical properties of graphene oxide (GO), to our knowledge, computational studies of GO−liquid interfaces have not been reported thus far. In this initial study, we will consider only hydroxyl groups as the oxidative groups of graphene and postpone the electrode oxidation by epoxides for a future study. The outline of this paper is as follows: A brief description of the models and methods employed in the present study is given in section 2. In section 3, simulation results for cell voltage and specific capacitance of GO supercapacitors, in particular, their variations with electrode oxidation, are presented. The factors governing these variations and their molecular mechanisms are also analyzed there. Section 4 concludes our report.

2. SIMULATION MODELS AND METHODS The simulation system consists of an electrolyte confined between two GO electrodes in the parallel-plate configuration (Figure 1). As in refs 16−18, two different types of electrolytes were considered: a pure ionic liquid (IL) and an organic Received: July 21, 2014

A

dx.doi.org/10.1021/jp5072583 | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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The entire oxidation range of GO was studied; we considered 11 cases of differing levels of electrode oxidation, in which 0, 5, 10, 20, 25, 30, 40, 60, 70, 80, and 100% of the carbon atoms were oxidized with OH groups. While highly oxidized GO close to 100% may not be practical, its inclusion in the analysis yields a more complete insight into the influence of oxidation. Carbon atoms in adjacent pairs that were to be oxidized were chosen randomly; i.e., OH pairs in a trans conformation were distributed randomly on the graphene surface. In Figure 1, GO electrodes thus oxidized at the 10% level are used in the IL supercapacitor. To investigate the influence of the spatial arrangement of oxidation on capacitance, we have also considered a regular distribution of OH pairs in a crystalline pattern in the 25% and 40% oxidation cases. Additionally, an alternate random distribution was simulated at 25% oxidation. MD simulations were performed in the canonical ensemble at 350 K using the GROMACS package.58 The simulation cell was an orthorhombic box with dimensions 3.396 × 3.431 × 30.0 nm3, and periodic boundary conditions were applied. Long-range electrostatic interactions were computed using the particle-mesh-Ewald method with a 2D correction factor.59 In this initial effort, which focuses mainly on the qualitative understanding of the effect of electrode oxidation, the GO electrodes were uniformly charged by assigning partial charges to the carbon atoms so that surface charge densities of σS = ±0.43e/nm2 and 0corresponding to ±5e and 0 total electrode chargeswere achieved (e = elementary charge). Hereafter, these two cases will be referred to as the charged and discharged supercapacitors, respectively. The electrode situated at z = −z0 (electrode 1) was charged positively while the electrode at z0 (electrode 2) was charged negatively. For each charged supercapacitor, we simulated at least 10 different trajectories. In the discharged case, five trajectories were simulated. For each trajectory, simulation was carried out with 6 ns of annealing from 700 to 350 K and 4 ns of equilibration at 350 K, followed by a 10 ns production run. Ensemble averages were computed using 10 independent 10 ns production trajectories thus generated for the charged case and five trajectories for the discharged case.

Figure 1. Model supercapacitor system with pure EMI+BF4−. The GO electrodes are 10% oxidized.

electrolyte (OE). The IL system comprises 512 pairs of 1-ethyl3-methylimidazolium (EMI+) and tetrafluoroborate (BF4−) ions, while the OE system is composed of 62 EMI+BF4− pairs and 634 acetonitrile molecules, corresponding to a ∼1.3 M solution of EMI+BF4− in acetonitrile. In this paper, we will focus mainly on the IL system, while only the result for capacitance is given of the OE system. Two GO electrodes, each modeled as a flat, rigid graphene sheet with area 3.396 × 3.431 nm2, are separated by d (=6.6 nm) and situated at z = ±z0 (z0 = 3.3 nm) parallel to the xyplane. Each electrode consists of 448 carbon atoms and is decorated by hydroxyl (−OH) moieties, which are the sole oxidative groups present in our model, as mentioned above. Hereafter, we will use Cox to denote explicitly oxidized carbon atoms that are directly bonded to hydroxyl oxygen atoms, while Cun refers to unoxidized carbon atoms of GO. The geometry of the Cox−OH moieties employed in the simulations was based on ab initio calculations using the B3LYP/3-21G hybrid functional (see the Supporting Information for details). The OH groups are placed in adjacent pairs with the O−Cox−Cox− O dihedral in a trans conformation. Two Cox atoms of each oxidized pair are shifted by 0.1 Å toward each other and positioned off the graphene plane by 0.4 Å in the direction of their respective OH groups. The resulting Cox−Cox and Cox− Cun bond lengths, 1.515 and 1.502 Å, associated with an oxidized pair, are greater than the Cun−Cun value, 1.415 Å.48 The OPLS-AA force field49 was used to describe the hydroxyl groups. All other force field parameters were the same as in previous MD studies of Kim and co-workers.16−18,50,51 Specifically, the Lennard-Jones parameters ϵ = 43.2 K and σ = 0.34 nm were employed for graphene C atoms,52 which were frozen during simulations. For IL, the parameters for EMI+ were taken from refs 53 and 54, while those for BF4− were from refs 55 and 56. For CH3CN, the fully flexible six-site description of ref 57 was employed. We note that electronic polarizability is ignored in our model description (see below). Nonetheless, the potential model employed here describes reasonably well graphene and other carbon-based supercapacitors, according to prior studies.16−18,50,51

3. RESULTS AND DISCUSSION 3.1. Electric Potential. We begin by considering the cell voltage ΔΦcell, i.e., the electric potential difference between electrodes 1 and 2, and its change ΔΔΦcell with charging of the supercapacitor ΔΦcell = Φ(z = −z 0) − Φ(z = z 0); ΔΔΦcell = ΔΦcell (charged) − ΔΦcell (discharged)

(1)

The electric potential Φ(z) needed in eq 1 is obtained by integrating the Poisson equation8,60 Φ(z) = −4π ∑ α

ρα̅ (z) = A 0−1

z

∫−z

dz′(z − z′) ρα̅ (z′); 0

x0

y0

0

0

∫−x ∫−y

dx′dy′ ρα (x′, y′, z)

(2)

where ρα(x, y, z) is the local charge density arising from the atomic charge distribution of ionic species α (α = EMI+ or BF4− = + or −), ∑α is the sum over ionic species, and A0 (=4x0y0) is the electrode surface area. B



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Figure 2. (a) ΔΔΦcell vs percent oxidation for IL supercapacitor. Error bars mark ±σ, where σ is one standard deviation. In the case of random oxidation configurations, i.e., randomly distributed OH groups on the electrodes, ΔΔΦcell tends to increase with electrode oxidation. For a given percent oxidation, ΔΔΦcell for regularly distributed OH groups is considerably higher than that for randomly distributed OH groups. (b) ΔΦcell as a function of duration t of the production run for 10 independent MD trajectories for the charged IL supercapacitor at 25% oxidation. For each trajectory, ΔΦcell at t is the cell voltage averaged from 0 to t. The dashed and dashed-dotted lines mark μ and μ ± σ, respectively, where μ and σ are the average and standard deviation of ΔΦcell at t over the 10 trajectories. The convergence of ΔΦcell along a single trajectory is slow; in most cases, it takes more than 9 ns to obtain convergence. Variance of the converged results of individual trajectories is also substantial.

In Figure 2a, results for ΔΔΦcell are shown as a function of the degree of electrode oxidation for the IL supercapacitor. Overall, ΔΔΦcell of the supercapacitor with randomly distributed OH groups (solid circles) on electrode surfaces increases with oxidation, although this increase is not linear. We note the existence of three regions that show differing ΔΔΦcell behavior with oxidation. The first region, from 0% to ∼10% oxidation, is characterized by rapidly increasing ΔΔΦcell. In the second region, from ∼10% to ∼30% oxidation, ΔΔΦcell does not change significantly as the electrodes become more oxidized. The third and last region, from ∼30% to 100% oxidation, is a region of markedly increasing ΔΔΦcell. Though not presented here, the OE supercapacitor shows a similar trend, except that the first region of rapidly increasing ΔΔΦcell is absent. Another interesting aspect of Figure 2a is the strong dependence of ΔΔΦcell on the spatial distribution of OH groups. Although regular distributions were simulated only at the 25% and 40% oxidation, their high ΔΔΦcell values (triangles) compared to the random distributions (solid circles) are striking. By contrast, the alternate random distribution (open circle) at 25% has average ΔΔΦcell similar to that of the primary random distribution (solid circle). This dependence of ΔΔΦcell on the spatial arrangement of oxidation will be analyzed below. For perspective, we briefly pause here to consider the MD statistics employed in the present study. This is to assess at the outset the (statistical) reliability of our work on ΔΔΦcell and related quantities, for which one MD configuration yields just one data point in the sample. Such information will also be useful for future simulation studies of IL systems. In Figure 2b, we have analyzed ΔΦcell as a function of time after equilibration for each of 10 10-ns trajectories of the charged IL supercapacitor at 25% oxidation. Two noteworthy aspects are apparent. First, ΔΦcell fluctuates significantly during the first several nanoseconds of simulation and does not converge until t ≈ 9 ns in most cases. This highlights the need for long simulations when calculating electric potential and related quantities in ILs. Though not shown here, we note that extending the single trajectory simulation to 20 ns has little influence on its ΔΦcell value according to the few cases we have tested. Second, even when ΔΦcell converges at t ≈ 9 ns, the final values are quite varied, spanning a range of ∼0.4 V among the 10 trajectories. This underscores the need to consider

multiple trajectories for reliable MD statistics. Although the standard deviation of ΔΦcell shown in Figure 2b is the largest of all charged systems studied, most of the other systems have comparable standard deviations. It would thus be prudent to consider both long and many trajectories in order to adequately sample phase space, especially for viscous IL systems. 3.2. Ion Structure. Here we consider ion number densities, averaged over x and y nα̅ (z) = A 0−1

x0

y0

0

0

∫−x ∫−y

dx′ dy′ nα(x′, y′, z)

(3)

where nα(x, y, z) is the local number density of ionic species α and the center-of-mass of ions represents the position of α. The results for selected number densities around the electrodes with randomly distributed OH groups are exhibited. (Information on all 11 cases we studied is given in Figure S3 of the Supporting Information.) In this paper, we restrict our attention to counterion densities, viz., EMI+ near electrode 2 and BF4− near electrode 1, that usually play a central role in screening the electrode charges. The two top panels of Figure 3 show that for low oxidation (≲ 25%), the first solvation layer is

Figure 3. Number densities of (a) anions near electrode 1 located at z = −3.3 nm and (b) cations near electrode 2 at z = 3.3 nm (units: nm−3). The top and middle panels in each column show the results for the discharged and charged cases, respectively, while the bottom panel shows their difference. C



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formed by IL ions about ∼3.5 Å away from the discharged electrodes. For both cations and anions, the number density of this first solvation layer decreases as oxidation increases from 0% to ∼25%. Additionally, between 10% and 25%, a second solvation structure develops at a distance ∼1 Å away from the first solvation layer. As the electrode becomes more oxidized, this second peak, which grows in height and moves away from the electrode, becomes the main solvation layer, while the structure associated with the original first solvation layer continues to decrease and eventually disappears. While the two top panels in Figure 3 exhibit similar behavior in peak height with oxidation, the trend of peak position differs for cations and anions. In the case of cations, their main solvation structure shifts continuously away from the electrode as OH groups are introduced. This overall outward shift is attributed to the increase in volume occupied by OH groups, hindering access of cations to the electrode. The anions, however, show a biphasic behavior: their primary solvation layer initially moves toward the electrode, from ∼0% to ∼40%. We ascribe this inward shift to the formation of hydrogen bonds between anion F and hydroxyl H atoms. However, in view of the large size of, and significant F−F separation in, anions, one can imagine that not every OH group can form a hydrogen bond with anions when the density of OH groups on the electrode surface exceeds a certain critical value. In this case, through steric hindrance, some OH groups will repel anions. This results in gradual exclusion of anions from the first solvation layer, as evidenced by the small shoulder appearing in the 25% case and more pronounced in the 40% case (top panel in Figure 3a). As in the cation case, this leads to the outward shift of the anion layer. For additional insight into the biphasic behavior of the anion number density, we have examined hydrogen bonds between BF4− anions and OH groups of electrodes. MD results at discharged electrode 2 (i.e., surface charge density σS = 0) are exhibited in Figure 4. We notice that the number of anions that form hydrogen bonds with OH groups is not a monotonic function of the density of OH groups on the electrode. Initially, the number of anions hydrogen bonded to OH grows with increasing electrode oxidation, because more OH groups become available to form such bonds. However, beyond ∼20% oxidation, the number of such anions decreases, even

though the density of OH groups continues to grow. The aforementioned steric hindrance between anions and OH groups is responsible for this decreasing trend of anion−OH hydrogen bonds. The reduction in anion−OH hydrogen bonds is accompanied by the formation of hydrogen bonds among the electrode OH groups, which starts at ∼20% oxidation (results not shown here). Returning to the ion number density, we notice that characteristics of n̅α(z) for the charged supercapacitor (two middle panels of Figure 3), both peak heights and positions, are similar to those for the discharged system. Because of electrostatic interactions with the electrode charges, the electrolyte becomes significantly more structured than the discharged case. The inward shift of anion number density near electrode 1 with increasing graphene oxidation is also less pronounced and restricted to 0%−25% oxidation in the charged system due to the dominance of electrode charge−anion Coulomb attraction over OH-anion hydrogen bonding. In bottom panels of Figure 3, we examine the change Δn̅α in ion number density from the discharged to the charged supercapacitor: Δn̅α = n̅α,charged − nα̅ ,discharged. This describes the reorganization of ion density in response to electrode charging. As the supercapacitor is charged, the number density of both cations and anions increases (i.e., Δn̅α > 0) at the negative and positive electrodes, respectively. This is as expected, since cations and anions there are counterions. We notice that the magnitude of the increase in ion density diminishes for the systems with higher oxidation insofar as the oxidation level is below ∼50%. This trend is ascribed to attractive Coulomb (and hydrogen-bonding) interactions between OH groups and IL ions that hinder ion density reorganization. This has an important consequence for the charge screening ability of IL ions, in particular, anions, which we turn to next. 3.3. Electrolyte Charge Density. MD results for electrolyte charge densities ρ̅α(z) (eq 2) are displayed in Figure 5. Their general trends with electrode oxidation in Figure 5c,d mirror those of n̅α(z) in Figure 3. Nevertheless, there are several noteworthy differences. First, since atomic charge distributions of ions were used for ρ̅α(z) while the position of center-of-mass was employed for n̅α(z), the peak positions of ρ̅α(z) are closer to the electrode than those of nα̅ (z). Second, in the discharged case, the magnitude of the first peak of the anion charge density ρ̅−(z) at z ≈ −3.0 nm initially increases with oxidation (top panel of Figure 5c), whereas n−̅ (z) shows the opposite trend (top panel of Figure 3a). We ascribe this ρ̅−(z) behavior to enhanced alignment of F sites of anions near the electrode surface through the formation of hydrogen bonds with OH groups. Another interesting feature is that anion charge density shows sign changes; despite its overall negative charge, ρ̅−(z) is positive-valued in some regions. This arises from the highly symmetric and charge-separated nature of the BF4− charge distribution. Specifically, positively charged B of charge +1.1504e at the core and negatively charged shell consisting of four F atoms each with charge −0.5376e make opposite contributions to the local charge density.16,51 The lack of such a clear charge separation in cations results in the absence of sign changes for ρ̅+(z). To understand how the electrode oxidation by hydroxyl groups influences screening of electrode charges by IL, we investigate reorganization of IL charge distribution Δρ̅IL(=Δρ̅+ + Δρ̅−) in response to electrode charging, where Δρ̅α = ρ̅α,charged − ρ̅α,discharged. The results in the bottom panels of Figure 5a,b show that IL charge reorganizationwhich gauges

Figure 4. Number of anions hydrogen bonded to OH groups of discharged electrode 2 at z = 3.3 nm. A hydrogen bond is assumed to be formed between F of BF4− and H of OH if their separation is less than or equal to 2.28 Å and the angle between two directions, O-to-H and O-to-F, is less than or equal to 20°. The latter condition yields ∼28° or less for the angle between the O-to-H and H-to-F directions. The majority of the hydrogen-bonded anions are characterized by either one or two hydrogen bonds. D



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Figure 5. Charge density of IL ions (units: e nm−3). Overall charge densities near electrodes 1 and 2 are shown in parts a and b, respectively. Anion charge density near electrode 1 and cation charge density near electrode 2 are displayed in parts c and d, respectively.

Figure 6. Probability distribution P(r) of accessible surface area at 25% electrode oxidation. The red and blue lines represent results for the random and regular Cox configurations (right panel), respectively. In both configurations, the dark-colored dots denote the position of Cox atoms whose OH groups are in the direction facing the IL, whereas the light-colored dots represent Cox atoms whose OH groups face in the opposite direction. Inset: ion number densities (units: nm−3). In Monte Carlo simulations of accessible surface area, disks of radii between 0.001 and 1 nm were considered, with centers at (x, y) coordinates generated randomly. If a disk of radius r did not enclose the position of any solvent-facing Cox (i.e., any darkcolored dot), the move was considered a success. Otherwise, the move was considered a failure. N(r) is the number of successes, and P(r) is obtained as −dN(r)/dr with proper normalization. For each of the 1000 radii considered, 3 × 106 throws were performed.

its screening efficiencyoccurs mainly in a narrow region of width 0.3−0.4 nm (“screening zone”), close to the electrodes. The degree of charge reorganization, measured by the amplitude of Δρ̅IL in the screening zone, is the largest at 0% oxidation and generally decreases as the oxidation level increases at both electrodes. This is a direct consequence of the ion density reorganization discussed above, which tends to weaken with electrode oxidation. While the decreasing trend of IL’s screening efficiency is monotonic at electrode 1, electrode 2 shows a more complex behavior. The degree of IL charge reorganization at electrode 2 is nearly the same for 10% and 25%, suggesting that the decrease in screening efficiency between 10% and 25% oxidation may not be as significant as that between 0% and 10%. At ∼70% oxidation, the screening zone begins to move away from the electrode due to the volume excluded by the OH layer, and the gap of the so-called double layers starts to grow. This means that screening of the electrode charges by IL starts at a longer distance from the electrode and thus becomes less effective than that in lower

oxidation cases. These two factors, degree of IL charge reorganization and location of the screening zone, both of which vary with the level of electrode oxidation, are responsible for the ΔΔΦcell trend for electrodes with randomly distributed OH groups in Figure 2a. Comparison of Δρ̅IL with the corresponding change of its counterion charge density (i.e., anions at electrode 1 and cations at electrode 2) shows that Δρ̅IL is dominated by the anions. Even at electrode 2, a large difference between Δρ̅IL and Δρ̅+ there (bottom panels of columns b and d in Figure 5) indicates that BF4− is the major contributor, although they are co-ions in this case. This dominance of anions in charge reorganization is ascribed to easy alignment of their charges, enabled by the highly symmetric nature of their charge distribution with a clear separation of the positively charged core and negatively charged shell mentioned above. We thus expect that the anion dominance will diminish with less symmetric anions. E



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tot Figure 7. Specific capacitance of GO supercapacitors: (a) ctot S and (b) cM . Results for IL and OE are plotted in red and green, respectively.

Before we proceed to capacitance, we briefly consider the large difference in ΔΔΦcell observed between the random and regular distributions of OH groups on electrodes in Figure 2a above. To this end, we have examined the GO surface accessibility of the ions. For convenience, the accessible surface area at a given position on the electrode is measured by the maximum radius r of a disk centered there that does not overlap with any of Cox whose OH group is in the direction facing the electrolyte. In Figure 6, the probability distribution of maximum disk size at 25% oxidation obtained via the Monte Carlo method is exhibited. The random Cox configuration shows a considerably broader distribution at large r than the regular distribution. The average values of r and r2 are 2.0 Å and 4.9 Å2 for the random configuration and 1.7 Å and 3.3 Å2 for the regular configuration; thus, the accessible surface area for the former is about 50% larger than the latter. This indicates that the electrode with a random distribution of OH groups is much more accessible to ions than that with a regular distribution. The ion density profiles in the inset off Figure 6 confirm that ions can approach the former electrode more closely, thereby shielding its charge better than the latter. This difference in surface accessibility is mainly responsible for the big difference in ΔΔΦcell between the random and regular configurations of Cox. 3.4. Specific Capacitance. Finally, we consider the influence of electrode oxidation on capacitance. Capacitance is typically cast in terms of electrode area (surface-areanormalized) or mass (mass-normalized) cStot =

|σS| ; ΔΔΦcell

tot cM = cStot

A0 2M

Table 1. MD Results for Specific Capacitance of Graphene Oxide Supercapacitorsa IL % oxidation 0 5 10 20 25 30 40 60 70 80 100

OE

ctot S

ctot M

ctot S

ctot M

2.60 2.35 2.30 2.31 2.26, 2.23 (1.86) 2.25 2.18 (1.92) 2.04 1.94 1.94 1.86

16.95 14.32 13.16 11.72 10.86, 10.75 (8.98) 10.32 9.07 (7.96) 7.18 6.34 5.91 5.03

2.24 2.26 2.22 2.22 2.22, 2.14 (1.99) 2.22 2.10 (1.95) 1.98 1.84 1.81 1.72

14.58 13.80 12.69 11.27 10.71, 10.30 (9.57) 10.18 8.73 (8.10) 6.98 6.02 5.51 4.64

a

Results for regular distributions of OH groups are given in 2 parentheses. Units: surface-area-normalized capacitance ctot S , μF/cm ; , F/g. mass-normalized capacitance ctot M

with electrode oxidation. At given oxidation, electrodes with a regular Cox configuration are characterized by considerably lower capacitance than those with a random configuration. As discussed above, this is a consequence of the lower surface accessibility of ions afforded by the regular distribution. For insight into the robustness of our analysis, we also studied the charged IL supercapacitors with σS = ± 0.215e/nm2, corresponding to total electrode charges of ±2.5e. While their MD statistics in some cases are limited compared to those employed for supercapacitors with σS = ± 0.43e/nm2, both charge densities yield similar capacitance behaviors with electrode oxidation (Figure S5 in the Supporting Information). Likely sources of the differences between the two are differing MD statistics and sampling errors and the dependence of capacitance on σS. Nevertheless, a good overall agreement between the two suggests that our results are robust.

(4)

where 2M is the mass of its two electrodes. To avoid confusion, we note that while the area of a single electrode is considered in the surface-area-normalized ctot S , the mass of both of the parallel electrodes is taken into account in the mass-normalized capacitance ctot M in the present study. The results obtained with σS = ± 0.43e/nm2 are shown in Figure 7 and compiled in Table 1. For completeness, results for the OE supercapacitor are also presented there. Whether the capacitance is normalized to the electrode surface area or mass, specific capacitance decreases with oxidation because ΔΔΦcell generally increases (Figure 2a). Since M increases with oxidation whereas A0 does not, ctot M decreases more rapidly than ctot S . Though limited to electrode oxidation by OH, the decreasing trend of capacitance obtained here is in qualitative agreement with several experimental studies.28−34 It also lends support to the conjecture that pseudocapacitance may play a substantial role in other measurements,26,27 in which capacitance was found to increase

4. CONCLUDING REMARKS In this paper, we have studied parallel-plate GO supercapacitors containing EMI+BF4− via MD. It was found that capacitance decreases with increasing oxidation. This was attributed to two factors: decreasing reorganization ability of IL ions and widening gap of double layers. Specific interactions between ions and OH groups, such as hydrogen bonding, hinder ion reorganization, while steric hindrance arising from oxygen atoms of OH groups shifts the screening zone of IL away from the electrodes. It was also found that capacitance depends on F



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the oxidation configuration. This was attributed to differing accessibility of ions to the electrode surface. The analysis of individual MD trajectories as a function of the simulation time revealed that calculations of electric potential in ILs converge very slowly. It usually takes ∼9 ns after equilibration to obtain convergence for most of the trajectories we simulated. Additionally, converged results of individual trajectories show significant variations. Thus, averaging over multiple trajectories of extended simulation time is needed for reliable estimation of electric potential and related quantities. We conclude by placing our work in perspective. One of its limitations is the absence of electronic polarizability, especially in the GO model description. There have been a few simulation studies13−15,19−22 in which polizability of pure graphene electrodes was accounted for explicitly. It was found that although the electrode polarizability does not have a major effect on capacitance,19,22 it does influence detailed behaviors of electrolytes.20 For example, electrolyte dynamics become substantially slower with the inclusion of electrode polarizability.20 Similar deceleration of solvent response was observed previously in solvation dynamics in both conventional solvents61 and ILs.62 In view of these findings, we expect that while the electrode polarizability would not change the qualitative aspect of our results, e.g., the trend of specific capacitance with electrode oxidation, it would nonetheless affect their quantitative aspects. It would thus be worthwhile in the future to incorporate both electrode and electrolyte polarizability into the fully atomistic description for quantitative simulation study. Also not included in our descriptions are possible chemical processes, such as electron transfer between the electrolyte and electrodes (pseudocapacitance) and dissociation of OH groups. Structural defects of GO electrodes, e.g., holes, that can form during the actual reduction of GO were also ignored. While a considerable effort via both theory and experiments would be needed in order to construct a computationally efficient model description that properly captures these features, it would be desirable to cosider them in the simulations of GO supercapacitators. Finally, oxidation of graphene electrodes was effected solely via OH groups in our model. Although hydroxyl groups are one of the predominant oxidation species in GO, other functionalities, especially epoxides, have also been observed experimentally.25,63 Since the epoxide oxygen has a partial negative charge, whereas a hydroxyl group consists of neighboring negative and positive partial charges, we would expect a significant difference in their specific interactions with electrolytes and thus their influence on capacitance. Applying the same computational method, we are currently studying graphene electrodes oxidized with epoxide groups and with a mixture of hydroxyl and epoxide groups.

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AUTHOR INFORMATION

Corresponding Authors

*Y.J. E-mail: [email protected]. *H.J.K. E-mail: [email protected]. Present Addresses ∥

Samsung Advanced Institute of Technology, SEC, Yongin 446-712, Korea. ⊥ Carnegie Mellon University, Pittsburgh, PA 15213. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by the National Science Foundation through NSF Grant No. CHE-1223988. This work was also supported in part by the National Research Foundation of Korea through grants NRF-2010-0014525 and NRF-2007-0056095, and by the KISTI Supercomputing Center through grants KSC-2011-C1-15 and KSC-2012-C2-47. A.D. acknowledges financial support from the ARCS Foundation. Y.S. acknowledges financial support from the BK 21 Program of Korea.

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S Supporting Information *

DFT results for two OH groups attached to graphene, and MD results for the electric potential profile, cell voltage, number and charge densities of IL ions near electrodes, and specific capacitance determined with two different electrode charge densities. This material is available free of charge via the Internet at http://pubs.acs.org/. G



Article

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