ARTICLE pubs.acs.org/JPCC
Graphene-Based Supercapacitors: A Computer Simulation Study Youngseon Shim,† YounJoon Jung,*,† and Hyung J. Kim*,‡,§,|| †
Department of Chemistry, Seoul National University, Seoul 151-747, Korea Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States § School of Computational Sciences, Korea Institute for Advanced Study, Seoul 130-722, Korea ‡
ABSTRACT: Energy density of supercapacitors based on a single-sheet graphene electrode is studied via molecular dynamics (MD) computer simulations. Two electrolytes of different types, pure 1-ethyl-3-methylimidazolium tetrafluoroborate (EMI+BF4) and an 1.1 M solution of EMI+BF4 in acetonitrile, are considered as a prototypical roomtemperature ionic liquid (RTIL) and organic electrolyte, respectively. Structure of ions near the electrode surface varies significantly with its charge density, especially in pure RTIL. Specific capacitance normalized to the electrode surface area is found to be higher in EMI+BF4 than in acetonitrile solution by 5560%. This is due to strong screening of the electrode charge by RTIL ions in the former. The RTIL screening behavior is found to be rather insensitive to temperature T. As a result, the capacitance of supercapacitors based on pure EMI+BF4 decreases by less than 5% as T increases from 350 to 450 K. The difference in size and shape between cations and anions and the resulting difference in their local charge distribution as counterions near the electrified graphene surface yield cathodeanode asymmetry in the electrode potential in RTIL. As a consequence, specific capacitance of the positively charged electrode is higher than that of the negatively charged electrode by more than 10%. A similar degree of disparity in electrode capacitance is also found in acetonitrile solution because of its nonvanishing potential at zero charge. Despite high viscosity and low ion diffusivity of EMI+BF4, its overall conductivity is comparable to that of the acetonitrile solution thanks to its large number of charge carriers. The present study thus suggests that as a supercapacitor electrolyte, RTILs are comparable in power density to organic electrolytes, while the former yield considerably better energy density than the latter at a given cell voltage.
1. INTRODUCTION Electric double layer capacitors (EDLCs), also referred to as supercapacitors, have emerged as an attractive energy storage device to complement and even replace batteries in applications that require rapid energy draw, i.e., high power density.15 Commonly used electrode materials for EDLCs are carbonbased, such as activated carbon, carbon nanofibers, and carbon nanotubes, because of their commercial availability at relatively low cost and good properties, such as large surface area, high capacitance, and long cycle life.4,6 However, the electrochemically available surface area of these materials during charging is often limited because charge propagation via ion transport in and out of small micropores is usually not efficient.4 Thus, in some cases, small mesopores are incorporated in order to improve charge transport in microporous materials.4 Low electrical conductivity poses another difficulty in achieving high power density with activated carbon. Two-dimensional graphene materials made of atomic carbon sheets7 provide an exciting alternative to activated carbon for use in energy-related devices because of their excellent properties, including large surface area, superior stiffness, high electrical conductivity, and chemical and thermal inertness.810 The large surface area of graphene, substantially higher than the BET surface area11 of activated carbon, can lead to a significant increase in the energy storage capability of supercapacitors. In addition, since its active surface forms effectively a large flat structure, ion transport in graphene is much more efficient than r 2011 American Chemical Society
in activated carbon. Therefore, electrodes based on graphitic materials hold immense potential to significantly improve both power and energy densities of energy storage devices, such as rechargeable lithium ion batteries12 and EDLCs,1318 and to increase efficiency of energy conversion in, e.g., solar cells.19,20 In this article, we investigate supercapacitors based on a singlesheet graphene electrode via MD simulations. While organic electrolytes are commonly considered for supercapacitors, roomtemperature ionic liquids have also received significant attention, thanks to their attractive properties, in particular, wide electrochemical window, high ion density, nonvolatility, nonflammability, and good thermal stability.6,21,22 For instance, RTILs’ large electrochemical window allows high cell voltage that can lead to a substantial increase in energy storage capacity of EDLCs, compared to conventional electrolytes.13,23 Recently there have been several computational efforts to obtain microscopic understanding of supercapacitors using RTILs as an electrolyte.2432 These studies have shed light on, e.g., ion structure and distributions near electrodes of various geometry and their influence on capacitance. However, we are not aware of any prior analysis of RTILs vis-a-vis organic electrolytes in terms of their performance as supercapacitor electrolytes. In order to gain molecular-level insight into this important issue with attention focused on Received: April 13, 2011 Revised: October 12, 2011 Published: October 12, 2011 23574
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Figure 1. Model supercapacitor system employed in MD. A single-sheet graphene electrode is interfaced on both sides with an electrolyte (in the present case, pure EMI+BF4). For convenience, the supercapacitor system is terminated on either side by introducing another graphene sheet as a confining wall at a distance 6.43 nm from the central electrode. All graphene sheets, i.e., both the central electrode and confining walls, are rigid, flat, and parallel to each other.
similarities and differences in their roles in supercapacitors, we embark on a systematic analysis of pure EMI+BF4 and an acetonitrile solution of EMI+BF4 as prototypes of these two liquid classes. In this initial study, we consider only half-cell properties, i.e., electric potential and capacitance of a single graphene electrode in an electrolyte. Analysis of full supercapacitor cells in parallel plate electrode geometry will be reported elsewhere.33 The outline of this paper is as follows: In section 2, we give a brief account of the models and methods employed in the present simulation study. In section 3, we examine the structure of, and charge distributions resulting from, EMI+ and BF4 ions (and also acetonitrile molecules in the case of the organic electrolyte) and their screening behaviors in the presence of a uniformly charged graphene electrode. A detailed comparison of the EMI+BF4 and acetonitrile solution cases is made for the electric potential and capacitance of supercapacitors. For insight into power density, the electrolyte conductivity is also analyzed via linear response theory. The influence of temperature on the energy and power densities of the RTIL-based supercapacitor is also considered there. Concluding remarks are offered in section 4.
2. SIMULATION METHODS Our model supercapacitor system is composed of a flat, singlesheet graphene electrode that interfaces with an electrolyte on either side (Figure 1). In the discharged configuration of the supercapacitor, the electrode is immersed in either a pure RTIL consisting of 512 pairs of EMI+ and BF4 or an organic electrolyte composed of 100 pairs of EMI+ and BF4 and 1024 CH3CN molecules. Hereafter, the former and latter systems will be simply referred to as the RTIL and organic electrolyte supercapacitors, respectively. We note that the organic electrolyte considered here models a 1.1 M solution of EMI+BF4 with mole fraction 0.089 in acetonitrile. The combined electrode electrolyte system was placed between two confining graphene walls in the xy plane situated at z = (6.43 nm, such that the electrode surface positioned at z = 0 was parallel to the walls (Figure 1). Outside of the confining walls was a vacuum. All graphene sheets, viz., the central electrode and two confining
walls, were modeled as a rigid and flat layer of 448 sp2-hybridized carbon atoms with dimensions 3.432 3.398 nm2. To describe the positively and negatively charged electrodes as well as the fully discharged case, three different uniform surface charge densities, σS = ( 0.86e/nm2 and 0, were considered for the central graphene via partial charge assignments to its C atoms. The corresponding total surface charges were (10e for the charged electrode cases. The two confining graphene walls were electrically neutral regardless of the charge state of the central electrode. The numbers of RTIL cations and anions were adjusted to meet the charge neutrality of the entire simulation system. For instance, in the case of the positive electrode with 10e, we employed 507 cations and 517 anions for pure EMI+BF4, while the acetonitrile solution contained 95 cations and 105 anions. The Lennard-Jones parameters employed for C atoms of the graphene are ε = 43.2 K and σ = 0.34 nm.34 During the simulations, the graphenes were held rigid with carbon carbon bond length lCC = 0.1415 nm.35 For RTIL, the flexible all-atom description of refs 28 and 36, based on the EMI+ model in refs 37 and 38 and BF4 in refs 39 and 40, was used. For CH3CN, we used the fully flexible six-site description of ref 41. Electronic polarizability42 for both the graphene and electrolytes was ignored in our present study.43,44 We simulated molecular dynamics of the system in the canonical ensemble at 350 K using the DL_POLY program.45 The simulation cell was composed of the supercapacitor system described above, placed in an orthorhombic box of 3.432 3.398 30.0 nm3. The long-range electrostatic interactions were computed via the Ewald method, resulting in essentially no truncation of these interactions. The trajectories were integrated via the Verlet leapfrog algorithm using a time step of 1 fs. Simulations were carried out with 10 ns equilibration, followed by a 10 ns trajectory from which ensemble averages were computed. To examine the temperature effect on energy storage, we also studied the RTIL supercapacitor at 450 K. Compared to the 350 K case, the density of EMI+BF4 was reduced by 5% to account for thermal expansion.46
3. RESULTS AND DISCUSSION Structure. We begin with electrolyte structures and their variations with the electrode surface charge density σS. We 23575
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Figure 3. Average number density nα(z) of (a) EMI+, (b) BF4 and (c) CH3CN in the organic electrolyte supercapacitor using a 1.1 M acetonitrile solution of EMI+BF4 at 350 K. (d) P(θ) of CH3CN in the first peak of R the first solvation layer, i.e., z < 0.4 nm, in (c) with normalization dθP(θ) = 1. The notation is the same as in Figure 2. In (d), θ is the angle between the normal to the electrode surface and the molecular orientation of acetonitrile defined as the C-to-C direction from its nitrile to methyl groups.
Figure 2. Average number density of (a) EMI+ and (b) BF4 ions in the RTIL supercapacitor at 350 K. The corresponding results at 450 K are shown in (c) and (d). z is the distance from the graphene electrode measured in nanometers. N represents the fully discharged case with an electrically neutral electrode, while (+) and () denote, respectively, the positively and negatively charged electrode configurations with the surface charge density σS = (0.86e/nm2, where e is the elementary charge. In the inset, the same results for z e 1.5 nm are shown for clear exposition of nα(z) near the electrode. In (e) and (f), nα(z) around the electrically neutral and negative electrodes at 350 K is presented, respectively.
mention at the outset that the electrode surface is fully solvated (viz., wetted) in the present study, irrespective of T, σS, or electrolytes we employed. For convenience, we employ a Cartesian coordinate system, where the graphene electrode surface spans the xy plane (x0 < x < x0 and y0 < y < y0) with the origin at its center and its normal defines the z direction (cf. Figure 1). We introduce the ion densities averaged over x and y n̅ α ðzÞ ¼ A0 1
Z x Z y 0 0 x0 y0
dx0 dy0 nα ðx0 , y0 , zÞ
ð1Þ
A0 ¼ 4x0 y0 where A0 is the surface area of the graphene electrode with x0 = 1.716 nm and y0 = 1.699 nm, nα(x,y,z) is the local number density of solvent species α (α = EMI+, BF4, or CH3CN) at (x,y,z), and the center-of-mass of ions and molecules is used to represent the position of α. The results for the average ion and molecule densities nα(z) are displayed in Figures 2 and 3. nα(z) for z < 0
are not shown because it is invariant under z f z due to symmetry of our supercapacitor system. We first consider the results for the RTIL supercapacitor in Figure 2. Regardless of the electrode charge density σS, electrolyte structures show significant fluctuations along z. These fluctuations, particularly strong in the vicinity of the electrode surface, extend up to z ≈ 3 nm. Similar spatial fluctuations are also present near the confining walls at z = (6.43 nm. This indicates that on average ions form layered structures near flat surfaces24,27,32,47 and that this ordering persists over a considerable distance from the surfaces. Nevertheless, the ion densities become essentially constant in the region 3.5 nm j z j 4.5 nm, irrespective of σS. This suggests that RTIL there is nearly bulklike and thus the presence of confining walls at z = (6.43 nm would not affect our analysis based on the results obtained for |z| j 4 nm. It is also worthwhile to mention that RTIL distributions near the central electrode and near the confining walls differ even when the former is electrically neutral with σS = 0. This is due to the fact that both sides of the central electrode are exposed to RTIL, while only one side of the confining walls interfaces with the electrolyte. Comparison of panels a and b and panels c and d of Figure 2 reveals that temperature has little influence on RTIL distributions. Except for a very minor reduction in their structure, nα(z) of both cations and anions remain essentially unchanged as T increases from 350 to 450 K. With this in mind, we consider ion structures in the first solvation shell (more accurately, solvation layer), which is defined as the region associated with the local density maximum located closest to the electrode surface. In the case σS = 0, the first peak in local densities of the cations and anions result at z = 0.37 and 0.38 nm, respectively (Figure 2ad). The average ring orientation of EMI+ in the first solvation shell, i.e., z j 0.45 nm, 23576
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Figure 4. Snapshots of EMI+ and BF4 ions close to (a) electrically neutral (σS = 0), (b) positively charged (σS = σ(+)), and (c) negatively charged (σS = σ()) graphene electrodes in the RTIL supercapacitor at 350 K. Only the ions with their center-of-mass located within 0.45 nm from the electrode surface are shown.
is nearly parallel to the graphene surface, forming a π-stacking structure (cf. Figure 4a below); the average angle between the normal vector of the electrode surface, i.e., z axis, and that of EMI+ rings there is found to be about 10. Also notable is that RTIL structures vary markedly with σS, especially near the electrode surface. Electrostatic interactions with the surface charge induce reorganization of ions, which leads to major structural enhancement and reduction for counterions and co-ions, respectively, near the charged electrode, compared to the σS = 0 case. Therefore, around the positive electrode with σS = 0.86e/nm2(σ(+)) that yields a total surface charge 10e, the distribution of counterions BF4 exhibits a strong first solvation shell peak at z = 0.37 nm. By contrast, near the negatively charged electrode with σS = 0.86e/nm2(σ()) and a total surface charge 10e, BF4 ions, which are now co-ions, are characterized by the first solvation shell peak that is much lower in height and located further from the electrode (z = 0.54 nm) than the σS = σ(+) case. EMI+ ions show essentially the same trend even though the extent of their peak location variations is considerably less than that of smaller anions. The first solvation shell peak positions of the former are z = 0.37 and 0.35 nm for the σ(+) and σ() cases, respectively. Another noticeable feature is that, on average, counterions and co-ions form alternating layers around the electrified graphene surfaces (Figure 2f).24,27,32,47 This is reminiscent of alternating concentric shell structures of counterions and co-ions around a central charge found in bulk RTILs.48,49 For further insight, snapshots of RTIL ions close to the graphene electrode surface are shown in Figure 4. It clearly illustrates the population changes of the cations and anions with σS. It is noteworthy that there is a non-negligible number of co-ions present close to the electrifed graphene surfaces. We also mention in passing that in the presence of a neutral electrode, cations are mainly surrounded by anions and vice versa in their immediate vicinity.
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Figure 5. Snapshots of ions and solvent molecules close to the electrode with (a) σS = 0, (b) σS = σ(+), and (c) σS = σ() in the organic electrolyte supercapacitor at 350 K. As in Figure 4, only the ions and molecules with their center-of-mass located within 0.45 nm of the electrode surface are shown here.
We turn to the organic electrolyte supercapacitor case in Figure 3. One of the most salient features is that for the neutral electrode the first solvation shells of ions are formed considerably further from the electrode than that of acetonitrile. As a consequence, there are virtually no ions present with their centerof-mass located within 0.5 nm of the neutral graphene surface, whereas acetonitrile distribution exhibits a main peak at about z = 0.36 nm. This is well illustrated by the snapshot in Figure 5a. Even when the graphene is charged with a significant surface charge density σ((), only a very small number of counterions are present in the close neighborhood of the electrode, compared to CH3CN molecules there (Figure 5b,c). Thus the “covering” (i.e., wetting) of flat graphene electrode surface is effected primarily via acetonitrile molecules irrespective of σS, at least in the charge density range we studied. This is attributed to the low ionic concentration of the electrolyte solution, which is 1.1 M in the present case, as well as to the highly dipolar character of acetonitrile. We note that the ionic concentration in this range is typically used in real supercapacitors. In Figure 3d, we have analyzed the orientation of acetonitrile, in particular, its probability distribution P(θ), where θ is the angle between the z axis and the orientation of the CC bond of CH3CN in the direction from the nitrile to methyl groups. We considered only the acetonitrile molecules with their center-ofmass located in the region z < 0.4 nm, corresponding to the first peak of the first solvation shell in Figure 3c. The average θ value is θ ≈ 70 in the presence of the neutral electrode, indicating that the nitrile C of acetonitrile is closer to the graphene surface than its methyl C. Thus on average, the CC axis of CH3CN in the z < 0.4 nm region is slightly tilted from the orientation parallel to the electrode surface, probably due to steric hindrance arising from its methyl group. As expected, the tilted orientation is favored even more near the positively charged electrode because 23577
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Figure 6. Average local charge density Fα(z) (units: e/nm3) of (a) EMI+ and (b) BF4 in the RTIL supercapacitor at 350 K. In (c), the total charge density, F+(z) + F(z), is shown.
of Coulomb attraction between the electrode and the nitrile group of CH3CN; the resulting average value for θ is about 60. In the case of the negatively charged electrode with σ(), however, Coulomb repulsion between the two pushes out the nitrile group, resulting in the average orientation of acetonitrile parallel to the electrode surface in the first peak of the first solvation layer. This orientation change is accompanied by a significant reduction in the first peak height. Electric Potential. We proceed to the electric potential of the supercapacitors. For convenience, we decompose the total electric potential Φ into two components, Φσ and ΦIL, arising from the graphene surface charge and RTIL ions, respectively. In the case of the organic electrolyte supercapacitor, there is an additional contribution ΦCH3CN from acetonitrile. We calculated ΦIL(z) by integrating the Poisson equation24,26 ΦIL ðzÞ ¼ 4π Fα ðzÞ ¼ A0 1
∑ α¼(
Z z 0
Z x Z y 0 0 x0 y0
ðz z0 ÞF α ðz0 Þ dz0
ð2Þ
dx0 dy0 Fα ðx0 , y0 , zÞ
where Fα(x,y,z) is the local charge density arising from the atomic charge distribution of ionic species α, F α(z) is its average at z, and α = ( denotes sum over ionic species. ΦCH3CN was obtained in a similar way. The results for Fα(z) of the RTIL supercapacitor at 350 K are exhibited in Figure 6. The corresponding results for 450 K are nearly the same as 350 K (cf. Figure 2ad) and thus are not shown there. Both cation and anion charge densities are characterized by strong oscillations in z near the electrode surface. Surprisingly, the oscillations of the anion charge density are accompanied by sign changes, especially in the presence of a positively charged or neutral electrode. This is attributed to the extended nature of ion charge distributions.28 Specifically, despite its overall negative charge, the B and F sites of BF4 ions have, respectively, partial positive (+1.1504e) and negative (0.5376e) charges and thus play antagonistic roles in their
Figure 7. Average local charge density Fα(z) (units: e/nm3) of (a) EMI+, (b) BF4, and (c) CH3CN in the organic electrolyte supercapacitor at 350 K. The total charge density, F+(z) + F(z) + FCH3CN(z), is displayed in (d).
Figure 8. ΦIL(z) (solid line) and Φσ(z) (dotted line) in (a) pure EMI+BF4 and (b) the acetonitrile solution at 350 K. In (b), the contribution to Φ from acetonitrile, ΦCH3CN(z), is shown in a dasheddotted line. For easy comparison of different components, the results for Φσ(z) rather than Φσ(z) are exhibited, so that it has the same sign as ΦIL(z). Units for electric potential: V.
contributions to local charge density. While the degree of charge separation is not as pronounced as BF4, the charge distribution of EMI+ has a similar extended character. Comparison with Figure 2 discloses that for z j 1 nm, charge densities of electrolytes show much more rapid oscillations with z than their number densities. By contrast, the oscillatory behavior of the former nearly disappears for z J 1 nm, while structural order persists well beyond z = 1 nm. The finite character of atomic charge distributions of ions is also responsible for this interesting difference between the electrolyte charge and number densities. We note that the relaxation of charge oscillations over ∼1 nm observed here is in reasonable accord with the long-range charge screening length, 0.51 nm, obtained for dipolar solvation in other EMI+-based RTIL systems in different model descriptions.48,49 Several interesting aspects of Figure 6, in particular, rapid oscillations for z j 1 nm and flattening for z J 1 nm, are shared by the corresponding cation and anion charge densities in the 23578
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Figure 9. Profile of total electric potential Φ(z) (in units of V) in the supercapacitor. Electrolytes employed are (a) pure EMI+BF4 at 350 K, (b) pure EMI+BF4 at 450 K, and (c) 1.1 M acetonitrile solution of EMI+BF4 at 350 K. For clarity, Φ(z) at the electrode is set at 0 V for all cases. For comparison, MD results for Φ(z) for a conventional capacitor with pure acetonitrile used as a dielectric material at 350 K are displayed in (d).
acetonitrile solution in Figure 7. The charge density arising from CH3CN in Figure 7c shows a similar oscillatory behavior. One important difference is that while F+(z) and F(z) approach a positive and a negative value as z increases, the acetonitrile charge density converges to 0. This is fully expected since acetonitrile molecules are dipolar, i.e., electrically neutral. Because of the low ionic concentration, spatial fluctuations of the electrolyte charge density are governed primarily by acetonitrile for z j 0.7 nm. The results for Φσ(z) and ΦIL(z) are presented in Figure 8, while those for Φ(z) are in Figure 9. In the RTIL supercapacitor case, ΦIL(z) tracks Φσ(z) very closely except for z j 0.3 nm. Also their magnitudes are vey similar in nearly the entire electrolyte region. Thus screening of the electrode surface charge is effected essentially completely via RTIL ions located mainly in the first solvation shell. The resulting total electric potential Φ(z) is very small in magnitude and varies little with z outside of the first solvation shell region (Figure 9a). In other words, the RTIL supercapacitor behaves like an ideal electric double layer capacitor for z J 0.5 nm. As expected from nα(z) in Figure 2, a rise in T from 350 to 450 K has nearly a negligible effect on Φ(z) in RTIL (Figure 9b). For additional insight, we have analyzed the ion numbers and charges in the electrolyte volume extending from the electrode surface to a surface at z (cf. eqs 1 and 2) Nα ðzÞ ¼ A0 QIL ðzÞ ¼ A0
Z z 0
dz0 n̅ α ðz0 Þ
∑ α¼(
Z z 0
ð3Þ
dz0 Fα ðz0 Þ
NCH3CN(z) and QCH3CN(z) are defined similarly. The reader is reminded that the position of the center-of-mass of α is used for
Figure 10. Number of (a) cations and (b) anions in EMI+BF4, contained in the volume spanning from the graphene electrode surface to z in the RTIL supercapacitor at 350 K. Their difference N+(z) N(z) is presented in (c).
nα(z) and Nα(z), whereas their extended atomic charge distribution is employed for Fα(z) and QIL(z). Panels a and b of Figure 10 show that populations of counterions increase in a stepwise manner with z, viz., a very abrupt and steep rise near z = 0.35 nm, followed by a relatively plateau behavior in the 0.4 nm j z j 0.7 nm region and a rapid increase for z J 0.75 nm. This is more evidence that counterions form a well-defined layered structure close to the charged electrodes in the RTIL supercapacitor (cf. Figure 2). The results for the difference between cation and anion populations, ΔN(z) = N+(z) N(z), in the RTIL supercapacitor at 350 K are shown in Figure 10c. Pronounced oscillations of ΔN(z) up to z ≈ 3 nm in the presence of charged electrodes are the direct consequence of alternating layered structures of counterions and co-ions mentioned above (cf. Figure 2f). Since the total surface charge of the graphene is (10e, the full screening occurs when ΔN(z) = -5, viz., the total charge in the volume spanning from z to z, including the electrode charge, is 0. The results in Figure 10c confirm that the complete screening obtains at z ≈ 0.35 nm for both the positive and negative electrodes. Interestingly, counterions continue to accumulate more than co-ions in the RTIL as z increases beyond 0.35 nm until |ΔN(z)| reaches a maximum of ∼15 around z = 0.4 nm. Therefore, the total charge in the volume 0.4 nm < z < 0.4 nm, including the electrode charge, becomes positive in the case of the negatively charged electrode and negative in the positively charged electrode case! This is responsible for |QIL(z)| > 5e for 0.4 j z j0.5 nm in Figure 11a. Returning to Figure 9a, we notice a significant gap in the magnitude of Φ(z) between the positive and negative electrodes for z J 1 nm. The magnitude of the potential drop ΔΦS(= Φ(z = 0) Φ(z ≈ 4 nm)) at the electrode with respect to the bulk electrolyte shows a sizable difference between the two. MD yields ΔΦ(+) = 1.12 V with σS = σ(+) and ΔΦ() = 1.42 V with σ() at 350 K, while PZC (potential of zero charge), i.e., the potential drop for the neutral electrode, is 0.07 V (Table 1). The corresponding 23579
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Figure 11. (a) QIL(z) in the RTIL supercapacitor at 350 K. (b) QIL(z) and QCH3CN(z) and (c) their sum in the organic electrolyte supercapacitor. In (b), QIL(z) and QCH3CN(z) are plotted in the solid and dotted lines, respectively.
Table 1. Electrode Potential ΔΦS and Specific Capacitance cS solvent
σS (e/nm2)
ΔΦS (V)a
cS (μF/cm2)
EMI+BF4 at 350 K
0.86
1.12
5.78
EMI+BF4 at 450 K
0.86 0.86
1.42 1.14
5.09 5.54
0.86
1.48
4.98
0.86
2.00
3.62
0.86
2.00
3.28
CH3CN/EMI+BF4 at 350 K
ΔΦS at PZC is 0.07 and 0.10 V for the RTIL and organic electrolyte supercapacitors, respectively.
a
values at 450 K are nearly the same, viz., 1.14, 1.48, and 0.10 V, respectively. The difference in size and molecular structure between the cations and anions is believed to be mainly responsible for the |ΔΦ(+)| |ΔΦ()| disparity, which is about 0.3 V irrespective of T. Smaller BF4 anions shield the positively charged electrode more efficiently via their F sites with a partial negative charge (0.5376e) than bulkier EMI+ cations screen the negatively charged electrode. This is manifested as a large peak of height 13e in QIL(z) at z ≈ 0.2 nm around the positively charged electrode in Figure 11a. By contrast, the corresponding value around the negatively charged electrode is QIL(z) = 3.5e. This enables anions to reduce the electric field at short distances arising from the electrode surface charge better than cations. Since ΔΦS is given by the integration of the electric field, better reduction of the electric field at short distances yields smaller magnitude for ΔΦS. The results for the organic electrolyte supercapacitor in Figures 8b and 9c exhibit interesting differences from those for the RTIL supercapacitor. To be specific, while ΦIL(z) tracks Φσ(z) analogous to the RTIL supercapacitor case, the difference in their magnitude in the organic electrolyte supercapacitor, which is about 46 V for z J 0.5 nm, is much bigger than the RTIL supercapacitor. This exposes the weak screening of the
Figure 12. Nα(z) of (a) EMI+, (b) BF4 and (c) acetonitrile in the organic electrolyte supercapacitor. In (d), the corresponding difference in Nα(z) between the cations and anions is shown.
electrode charges by ions in the organic electrolyte, compared to the RTIL. The low ionic concentration of the former is directly responsible for the weak screening. It is also noteworthy that acetonitrile makes an important contribution to Φ for small z. Through alignment of its dipole moment (cf. Figures 7c,d and 11b,c), acetonitrile mainly governs the electrolyte charge density and thus the shielding in the region z j 0.7 nm as noted above and reduces |ΔΦS| by 24 V. It should nonetheless be stressed that its cumulative charge QCH3CN(z) vanishes as z increases beyond ∼1 nm because acetonitrile molecules are electrically neutral. This means that the screening of the electrode charge at large distances is governed by ions as expected from Figure 8b. According to Figure 12d, full screening occurs close to z = 1 nm for the organic electrolyte supercapacitor. Another difference from the RTIL case is that the positive and negative electrodes of the organic electrolyte supercapacitor are characterized by the same |ΔΦS| (=2 V) (Figure 9c) despite their substantial difference in ion charge density (Figure 7a,b) and populations (Figure 12a,b) at small z. Analogous to the RTIL capacitor, however, ΔΦS of the organic electrolyte supercapacitor does not vanish at PZC. Specifically, ΔΦS = 0.1 V at PZC with respective contributions of 0.3 and 0.2 V from ions and acetonitrile. By contrast, PZC is 0 in neat acetonitrile, indicating that the nonvanishing PZC in the organic electrolyte supercapacitor is induced by the ions. We ascribe this to a significant difference between EMI+ and BF4 in nα(z) (Figure 3a,b) and Fα(z) (Figure 7a,b) in the acetonitrile solution, arising from their differing size and shape. For completeness, we have also analyzed a conventional capacitor, consisting of a single-sheet graphene electrode and a dielectric material modeled as acetonitrile. Its MD result for Φ(z) in the presence of a positive electrode charged with σ(+) is shown in Figure 9d. One prominent feature is that Φ(z) shows a bimodal character, i.e., a rapid drop near the electrode and a linear decrease with z in the region z J 0.5 nm. We notice that the Φ(z) behavior for z j 0.5 nm is very similar, though lesser in extent, to that of the organic electrolyte supercapacitor in 23580
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The Journal of Physical Chemistry C Figure 9b. This provides additional evidence that acetonitrile plays a crucial role near the electrode in the organic supercapacitor. Linear decay in Φ(z) for z J 0.5 nm in the conventional capacitor, on the other hand, is a manifestation of incomplete screening of the electrode charge due to the dipolar character of the solvent, revealing its clear distinction from EDLCs. Specific Capacitance. We turn to specific capacitance of the RTIL and organic electrolyte supercapacitors, normalized to the total electrode surface area exposed to the electrolyte 1 ∂qS ∂σS σS S ¼ 1=2 ≈ ð4Þ c ¼ S S 2A0 ∂ΔΦ ∂ΔΦ 2ΔΔΦS PZC
PZC
ΔΔΦS ¼ ΔΦS ΔΦS ðat PZCÞ where qS (=σSA0) is the total electrode charge, A0 is the graphene surface area (eq 1), and cS is evaluated at PZC. The factor 2 in the denominator of eq 4 arises because both sides of the graphene electrode interface with the electrolyte (cf. Figure 1). The results for cS are compiled in Table 1. For the RTIL supercapacitor, c(+) and c() are, respectively, 5.78 and 5.09 μF/ cm2 at 350 K and 5.54 and 4.98 μF/cm2 at 450 K. A few comments are in order here: First, since the RTIL distribution (Figure 2ad) and thus potential drop hardly change with T as noted several times above, so does the electrode capacitance. For the present supercapacitor system based on EMI+BF4, an increase in temperature by 100 K leads to a reduction of specific capacitance by only j4%. Second, the aforementioned difference in solvation of the positively and negatively charged electrodes, induced by the difference in size and shape of cations and anions, and resulting discrepancy in the magnitude of their ΔΦS yield non-negligible cathode-anode asymmetry50,51 in cS. Our finding that c(+) > c() is in good agreement with prior theory50,51 and MD study,28,27,32 but is at variance with ref 26, where the opposite result (c(+) < c()) was obtained for a similar system with a lower electrode surface charge density, 0.5125e/nm2. Third, despite the complete neglect of electronic polarizability in our model description for both the electrode and electrolytes, the MD results we obtained for our graphene-based supercapacitors are comparable to experimental results for closely related systems. For example, the specific capacitance of a highly oriented pyrolytic graphite (HOPG) electrode in N,N-diethyl-N-methyl-N-(2-methoxyethyl)ammonium bis(trifluoromethanesulfonyl)imide was found to be 2.25 μF/cm2.15 As in the RTIL supercapacitor case, the organic electrolyte supercapacitor also exhibits cathodeanode asymmetry in capacitance. The simulation results for T = 350 K are c(+) = 3.62 μF/ cm2 and c() = 3.28 μF/cm2. The nonvanishing PZC discussed above is responsible for this asymmetry in the organic electrolyte supercapacitor. Interestingly, the relative difference in electrode capacitance is ∼10% for both capacitors. Nevertheless, it should be noticed that specific capacitance of the organic electrolyte supercapacitors is smaller than that of the RTIL supercapacitors by 1.82.2 μF/cm2. This corresponds to a ∼35% diminution in the acetonitrile solution, compared to the pure EMI+BF4 case. As analyzed above, this decrease is attributed primarily to the weak ionic screening of the electrode charges in the acetonitrile solution. The result that RTIL supercapacitors exceed organic electrolyte supercapacitors in electrode capacitance is one of the major findings of the present work. This means that in addition to their wide electrochemical window, RTILs offer another important
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Figure 13. Time correlation function of the ionic current normal to the electrode surface in (a) RTIL and (b) organic electrolyte supercapacitors at 350 K.
advantage over organic electrolytes in energy density; viz., use of RTILs would improve the capacitance of the supercapacitors significantly, compared to organic electrolytes, even at the same cell potential. Another important finding is that specific capacitance of RTIL supercapacitors is rather insensitive to temperature, provided that the electrode surface is fully wetted by ions. As such, RTILs would provide a promising class of electrolytes for efficient energy storage in a broad temperature range. Ion Conductivity. To obtain insight into power density of the RTIL and organic electrolyte supercapacitors, we briefly consider electrolyte conductivity in the direction perpendicular to the electrode surface. In the GreenKubo formulation based on linear response theory, ion conductivity along the z direction, i.e., normal to the electrode surface, is related to the time correlation function of collective ionic current Jz(t) as σ GK ¼
1 Z VkB T
∞ 0
dt CJJ ðtÞ
ð5Þ
CJJ ðtÞ ¼ ÆJz ð0ÞJz ðtÞæ Jz ðtÞ ¼
N
∑ qi vz, i ðtÞ i¼1
where V is the volume of the system, kB is Boltzmann’s constant, qi and vz,i are the charge and z-component of center-of-mass velocity of ith ion and Æ...æ represents an equilibrium ensemble average. For comparison, we also consider the conductivity estimated via the NernstEinstein equation σ NE ¼
∑
1 nα q2α DGK, α kB T α ¼ (
DGK, α ¼ Nα1
∑ i∈α
Z ∞ 0
ð6Þ
dt Ævz, i ð0Þvz, i ðtÞæ
where qα, nα, and Nα are, respectively, the charge, number density, and total number of ions of species α, i ∈ α means sum over all ions of species α, and DGK,α is their translational diffusion coefficient along z. We note that σGK reduces to σNE if the contribution of cross correlation in CJJ(t) is ignored completely in eq 5. The results for CJJ(t) are displayed in Figure 13 and those for the conductivities and diffusion coefficients are compiled in Table 2. We first consider the RTIL supercapacitor case. Figure 13a shows that its CJJ(t) varies little with the electrode charge density σS. Though not presented there, we mention that the temporal behaviors of CJJ(t) at 450 K, including the 23581
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The Journal of Physical Chemistry C
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Table 2. Translational Diffusion Coefficient and Ion Conductivity Normal to the Electrode Surfacea solvent EMI+BF4
CH3CN/EMI+BF4
σS (e/nm2)
DGK,+
DGK,
σNE
σGK
0.86
0.20 (0.52)
0.21 (0.44)
0.59 (1.0)
0.27 (0.29)
0.0
0.20 (0.47)
0.21 (0.42)
0.59 (0.96)
0.27 (0.28)
0.86
0.20 (0.47)
0.21 (0.41)
0.59 (0.95)
0.26 (0.27)
0.86
1.3
1.4
0.73
0.32
0.0
1.3
1.3
0.72
0.33
0.86
1.3
1.3
0.72
0.32
a
The system temperature is T = 350 K. Results for the RTIL supercapacitor at 450 K are given in parentheses. Diffusion coefficients and conductivities are measured in units of 109 m2 s1 and S/m, respectively.
4. CONCLUDING REMARKS In this article, we have studied supercapacitors based on a single-sheet graphene electrode via MD. Two different electrolytes, i.e., neat EMI+BF4 and a 1.1 M acetonitrile solution of EMI+BF4, were considered. One of our key findings is that specific capacitance of the electrode normalized to its surface area is 5560% higher when pure EMI+BF4 is employed as an electrolyte than the acetonitrile solution. Strong and effective screening of electrode charges by RTIL ions close to the electrode is mainly responsible for high capacitance of the RTIL supercapacitor. Specific capacitance of the positively charged
electrode was found to be considerably larger than that of the negatively charged electrode in both EMI+BF4 and acetonitrile solution. This cathodeanode asymmetry50,51 is ascribed to differing screening effciency arising from the difference in size and molecular structure between the cations and anions. To gain insight into power density, we analyzed ion conductivity. It was found that ion conductivity in the direction normal to the electrode surface is larger in the acetonitrile solution than in pure EMI+BF4 but only by ∼20%. This result suggests that all other things being equal, the two electrolytes would be largely comparable in power density. The effect of temperature on the supercapacitor performance was also examined. Interestingly and importantly, specific capacitance and ion conductivity of the RTIL supercapacitors were found to vary little with T. This finding, together with the results summarized above in this section, indicates that RTILs are a viable candidate to replace conventional electrolytes in energy storage devices, which has promising potential for a good and reliable performance in energy storage and delivery over a significant temperature range. It would thus be very worthwhile in the future to extend the present study to other supercapacitor systems composed of differing RTILs and/or electrodes to find optimal conditions, configurations, and combinations of electrolytes and electrode materials for efficient energy storage.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected];
[email protected]. Present Addresses
)
frequency and relative amplitude of oscillations, are very close to those at 350 K. Thus regardless of σS and T we considered, the ion conductivity along z determined via eq 5 remains largely unchanged (σGK = 0.260.29 S/m). DGK,α, on the other hand, shows a marked increase with T. This difference in the T dependence arises primarily from the presence of the T1 factor in σGK in eq 5, which is absent in DGK,α. Another noteworthy aspect is that σNE obtained with the neglect of the cross correlation in CJJ(t) overestimates the actual conductivity, viz., σGK, by more than a factor of 2. This reveals an important role played by the cross correlation in the determination of conductivity; it cancels a significant part of the contribution from the self-correlation component of CJJ(t) and thus reduces ion conductivity substantially. It is worthwhile to note that the relaxation behavior of CJJ(t) in Figure 13a is very similar to that in pure EMI+PF6 studied in ref 52 even though anionic species are different. CJJ(t) of the acetonitrile solution in Figure 13b shows an interesting departure from that of RTIL. Specifically, relaxation dynamics of the former become decelerated and its librational character attenuated with increasing t, compared to the latter. While this kind of relaxation behavior sometimes leads to “superdiffusion”,53,54 we found that when integrated over t, CJJ(t) for the present organic electrolyte supercapacitor system yields a proper plateau behavior and thus well-defined conductivity. As in the RTIL supercapacitor case, σGK is considerably smaller than σNE, confirming the importance of the cross-correlation effect. Comparison of the RTIL and organic electrolyte supercapacitor results at 350 K shows a couple of noteworthy features. First, the ion translational diffusion coefficients along z in acetonitrile solution are more than 6-fold greater than those in EMI+BF4 because the latter is considerably more viscous than the former. Second, the conductivities of the RTIL and organic electrolyte are comparable. This is due to the high ion density, i.e., large number of charge carriers, in the former, which compensates for low mobility of its individual charge carriers.
Carnegie Mellon University.
’ ACKNOWLEDGMENT This work was supported by the National Research Foundation of Korea (NRF) grants funded by the Korean Government (MEST) (Nos. 2011-0001212 and 2011-0018038). Y.S. acknowledges the financial support from the BK 21 Program of Korea. ’ REFERENCES (1) Conway, B. E. Electrochemical Supercapacitors: Scientific Fundamentals and Technological Applications; Plenum: New York, 1999. (2) K€otz, R.; Carlen, M. Electrochim. Acta 2000, 45, 2483–2498. (3) Pandolfo, A. G.; Hollenkamp, A. F. J. Power Sources 2006, 157, 11–27. (4) Frackowiak, E. Phys. Chem. Chem. Phys. 2007, 9, 1774–1785. (5) Abru~ na, H. D.; Kiya, Y.; Henderson, J. C. Phys. Today 2008, 61, 43–47. 23582
dx.doi.org/10.1021/jp203458b |J. Phys. Chem. C 2011, 115, 23574–23583
The Journal of Physical Chemistry C (6) Simon, P.; Gogotsi, Y. Nat. Mater. 2008, 7, 845–854. (7) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Science 2004, 306, 666–669. (8) Meyer, J. C.; Geim, A. K.; Katsnelson, M. I.; Novoselov, K. S.; Booth, T. J.; Roth, S. Nature 2007, 446, 60–63. (9) Gomez-Navarro, C.; Weitz, R. T.; Bittner, A. M.; Scolari, M.; Mews, A.; Burghard, M.; Kern, K. Nano Lett. 2007, 7, 3499–3503. (10) Allen, M. J.; Tung, V. C.; Kaner, R. B. Chem. Rev. 2010, 110, 132–145. (11) Brunauer, S.; Emmett, P. H.; Teller, E. J. Am. Chem. Soc. 1938, 60, 309–319. (12) Ishikawa, M.; Sugimoto, T.; Kikuta, M.; Ishiko, E.; Kono, M. J. Power Sources 2006, 162, 658–662. (13) Vivekchand, S. R. C.; Rout, C. S.; Subrahmanyam, K. S.; Govindaraj, A.; Rao, C. N. R. J. Chem. Sci. 2008, 120, 9–13. (14) Stroller, M. D.; Park, S.; Zhu, Y.; An, J.; Ruoff, R. S. Nano Lett. 2008, 8, 3498–3502. (15) Islam, M. M.; Alam, M. T.; Okajima, T.; Ohsaka, T. J. Phys. Chem. C 2009, 113, 3386–3389. (16) Zhu, Y.; Stoller, M. D.; Cai, W.; Velamakanni, V.; Piner, R. D.; Chen, D.; Ruoff, R. S. ACS Nano 2010, 4, 1227–1233. (17) Liu, C.; Yu, Z.; Neff, D.; Zhamu, A.; Jang, B. Z. Nano Lett. 2010, 10, 4863–4868. (18) Kim, T. Y.; Lee, H. W.; Stoller, M.; Dreyer, D. R.; Bielawski, C. W.; Ruoff, R. S.; Suh, K. S. ACS Nano 2011, 5, 436–442. (19) Wang, X.; Zhi, L. J.; M€ullen, K. Nano Lett. 2008, 8, 323–327. (20) Wang, X.; Zhi, L. J.; Tsao, N.; Tomovic, Z.; Li, J. L.; M€ullen, K. Angew. Chem., Int. Ed. 2008, 47, 2990–2992. (21) Ue, M. In Electrochemical Aspects of Ionic Liquids; Ohno, H., Ed.; John Wiley & Sons: Hoboken, NJ, 2005; Chapter 17. (22) Armand, M.; Endres, F.; MacFarlane, D. R.; Ohno, H.; Scrosati, B. Nat. Mater. 2009, 8, 621–629. (23) Balducci, A.; Dugas, R.; Taberna, P. L.; Simon, P.; Plee, P. D.; Mastragonstino, M.; Passerini, S. J. Power Sources 2007, 165, 922–927. (24) Pinilla, C.; Del Popolo, M. G.; Kohanoff, J.; Lynden-Bell, R. M. J. Phys. Chem. B 2007, 111, 4877–4884. (25) Yang, L.; Fishbine, B. H.; Migliori, A.; Pratt, L. R. J. Am. Chem. Soc. 2009, 131, 12373–12376. (26) Kislenko, S. A.; Samoylov, I. S.; Amirov, R. H. Phys. Chem. Chem. Phys. 2009, 11, 5584–5590. (27) Feng, G.; Zhang, J. S.; Qiao, R. J. Phys. Chem. C 2009, 113, 4549–4559. (28) Shim, Y.; Kim, H. J. ACS Nano 2010, 4, 2345–2355. (29) Lauw, Y.; Horne, M. D.; Rodopoulos, T.; Nelson, A.; Leermakers, F. A. M. Phys. Rev. Lett. 2009, 103, 117801. (30) Lauw, Y.; Horne, M. D.; Rodopoulos, T.; Nelson, A.; Leermakers, F. A. M. J. Phys. Chem. B 2010, 114, 11149–11154. (31) Trulsson, M.; Algotsson, J.; Forsman, J.; Woodward, C. E. J. Phys. Chem. Lett. 2010, 1, 1191–1195. (32) Vatamanu, J.; Borodin, O.; Smith, G. D. J. Am. Chem. Soc. 2010, 132, 14825–14833. (33) Shim, Y.; Kim, H. J.; Jung, Y. Faraday Discuss. DOI: 10.1039/ C1FD00086A. (34) Hummer, G.; Rasaiah, J. C.; Noworyta, J. P. Nature 2001, 414, 188–190. (35) Odom, T. W.; Huang, J.-L.; Kim, P.; Lieber, C. M. Nature 1998, 391, 62–64. (36) Shim, Y.; Kim, H. J. ACS Nano 2009, 3, 1693–1702. (37) Canongia Lopes, J. N.; Deschamps, J.; Padua, A. A. H. J. Phys. Chem. B 2004, 108, 2038–2047. (38) Canongia Lopes, J. N.; Deschamps, J.; Padua, A. A. H. J. Phys. Chem. B 2004, 108, 11250. (39) de Andrade, J.; B€oes, E. S.; Stassen, H. J. Phys. Chem. B 2002, 106, 13344–13351. (40) Wu, X.; Huang, S.; Wang., W. Phys. Chem. Chem. Phys. 2005, 7, 2771–2779. (41) Nikitin, A. M.; Lyubartsev, A. P. J. Comput. Chem. 2007, 28, 2020–2026.
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(42) Schmickler, W. Chem. Rev. 1996, 96, 3177–3200. (43) Yan, T.; Burnham, C. J.; Del Popolo, M. G.; Voth, G. A. J. Phys. Chem. B 2004, 108, 11877–11881. (44) For the effect of solute polarizability in RTIL, see, e.g.:Jeong, D.; Shim, Y.; Choi, M. Y.; Kim, H. J. J. Phys. Chem. B 2007, 111, 4920–4925. (45) Forester, T. R.; Smith, W. DL_POLY user manual; CCLRC, Daresbury Laboratory: Daresbury, Warrington, U.K., 2001. (46) Taguchi, R.; Machida, H.; Sato, Y.; Smith, R. L. J. Chem. Eng. Data 2009, 54, 22–27. (47) Pinilla, C.; Del Popolo, M. G.; Lynden-Bell, R. M.; Kohanoff, J. J. Phys. Chem. B 2005, 109, 17922–17927. (48) Shim, Y.; Choi, M. Y.; Kim, H. J. J. Chem. Phys. 2005, 122, 044510. (49) Shim, Y.; Jeong, D.; Manjari, S. R.; Choi, M. Y.; Kim, H. J. Acc. Chem. Res. 2007, 40, 1130–1137. (50) Fedorov, M. V.; Kornyshev, A. A. J. Phys. Chem. B 2008, 112, 11868–11872. (51) Oldham, K. B. J. Electroanal. Chem. 2008, 613, 131–138. (52) Shim, Y.; Kim, H. J. J. Phys. Chem. B 2008, 112, 11028–11038. (53) Liu, B.; Goree, J. Phys. Rev. E 2007, 75, 016405. (54) Ott, T.; Bonitz, M.; Donk o, Z.; Hartmann, P. Phys. Rev. E 2008, 78, 026409.
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