CHEMPHYSCHEM ARTICLES DOI: 10.1002/cphc.201402220

Temperature Effects on the Capacitance of an Imidazolium-based Ionic Liquid on a Graphite Electrode: A Molecular Dynamics Simulation Xiaohong Liu, Yining Han, and Tianying Yan*[a] Temperature-dependent electric double layer (EDL) and differential capacitance–potential (Cd–U) curves of the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate (BMIM + /PF6) were studied on a graphite electrode by molecular dynamics simulations. It was found that all Cd–U curves were asymmetric camel-shaped with higher Cd at negative polarization, attributed to the specific adsorption of BMIM + . In addition, the maxima of Cd at the negative polarization decrease monotonically with temperature due to the thicker EDL,

whereas at the positive polarization they gradually increase from 450 to 550 K and decrease at 600 K. Such temperature effects at positive polarization may be understood in terms of the competition between two aspects: the weakening specific adsorption of BMIM + allows more effective screening to the positive charge and overall increasing EDL thickness. Although the former dominates from 450 to 550 K, the latter becomes dominant at 600 K.

1. Introduction Room-temperature ionic liquids (ILs), composed exclusively of bare ions, have received numerous attention in electrochemical capacitors or supercapacitors.[1] ILs can be constructed by a variety of combinations of cations and anions, different substituent functional groups on ions, as well as mixtures of different ILs. Thus, an IL is considered as a “designer solvent”, which can provide desirable electrochemical properties, such as a wide electrochemical window and high ionic conductivity. Recently, a supercapacitor of IL electrolytes with carbon materials, such as a three-dimensional porous graphene electrode, delivered an energy density comparable to that of a lead–acid battery.[2] The central aspect of a supercapacitor is the electric double layer (EDL) structure, which is often complicated by various conformations of ILs,[3] ionic correlations,[4] specific adsorption,[5] morphology of the electrode,[6] and so forth. A good understanding of the relationship between ILs and the EDL structure is highly demanded for the purpose of improving the capacitance. Experimentally, the EDL is often probed by the potential-dependent differential capacitance (Cd) by using electrochemical impedance spectroscopy (EIS).[7] Though an ambiguity is imposed by the quality of the electrode surfaces, the stability of the reference electrode, and the purity of ILs,[8] the trend of experimental Cd is often found to increase with elevated temperature.[8, 9] Lockett et al.[8, 9] and Kislenko et al.[10] attributed such anomalous temperature-dependent Cd to the [a] X. Liu, Y. Han, Prof. Dr. T. Yan Tianjin Key Laboratory of Metal- and Molecular-based Material Chemistry Key Laboratory of Advanced Energy Materials Chemistry Collaborative Innovation Center of Chemical Science and Engineering Institute of New Energy Material Chemistry College of Chemistry, Nankai University, Tianjin 300071 (PR China) E-mail: [email protected]

 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

weakening of ionic association, which thus causes more effective screening of electrode potential at high temperature, as proposed for the capacitance behavior of inorganic molten salt.[11] On the other hand, Roling and co-workers found from EIS measurements that there are two distinct capacitive processes, and the Cd of both capacitive processes decreases with elevated temperature.[12] Based on the observation of two capacitive processes, the authors questioned the apparent increase of Cd with temperature as an artifact caused by the single-frequency measurement in EIS.[12] Similar contradiction also exists in computer simulations of the EDL and the capacitance properties of ILs. In the computer simulations of N-methyl-N-propylpyrrolidinium bis(trifluoromethane)sulfonyl imide (pyr13 + /TFSI) and N-methyl-N-propylpyrrolidinium bis(fluorosulfonyl)imide (pyr13 + /FSI) on atomically flat graphite electrodes,[13] it is found that Cd decreases with increasing temperature. On the other hand, Kislenko and coworkers performed computer simulations of 1-butyl-3-methylimidazolium hexafluorophosphate (BMIM + /PF6) on a graphite electrode, and found that the integral capacitance (Ci) increases with elevated temperature at a certain potential. Thus, there is still a debate on the trend of temperature-dependent capacitance in both experiments and computer simulations, due to the complex interfacial EDL between the IL and electrode. It should be mentioned that the anomalous temperature dependence of capacity for ILs is in apparent contradiction to the predictions of the mean field theory (MFT) of the EDL.[3, 14] Such a contradiction is reasonable because MFT does not take into account the ionic correlations, which are important to account for the short-range overscreening effect.[4] It may be of interest to investigate the temperature-dependent Cd with ionic correlation theory[4] or density functional theory.[15] For a more comprehensive discussion on the effects of temperature on the caChemPhysChem 2014, 15, 2503 – 2509

2503

CHEMPHYSCHEM ARTICLES

www.chemphyschem.org

pacitance of ILs, we refer to a recent review article by Fedorov and Kornyshev.[1b] The present work aims at studying the temperature dependence of the EDL structure and capacitance of BMIM + /PF6 by molecular dynamics (MD) simulations. In our previous studies, we demonstrated the effect of specific adsorption of imidazolium (im)-based IL on a graphite electrode both computationally[5a, 16] and experimentally.[5b] The current MD simulation study continues the above studies, with focus on the effects of temperature. In the current study, MD simulations were performed on the IL BMIM + /PF6 confined in two oppositely charged graphite electrodes at four different temperatures, that is, 450, 500, 550, and 600 K. We found that the maxima of Cd decrease with elevated temperature at the negative polarization. However, the situation is more complicated for the positive polarization. Specifically, the maxima of Cd increase slightly at the positive polarization from 450 to 550 K, and then decrease at 600 K. The temperature-dependent Cd may be understood by the specific adsorption of BMIM + on the graphite surface,[5, 16] and the effects of temperature will be illustrated in the Results and Discussion section. Finally, we compare the Ci with previous MD simulations of the same system by Kislenko et al.[10, 17]

and < Qþ ðz Þ >¼ QðL=2Þ þ

Z

L=2

1ðz0 Þdz0

z

in which Q(L/2) and Q(L/2) denote the constant opposite charges on the two electrodes located at z = 50 and 50 , respectively; A = 42.608  41.8115 2 is the electrode surface area, and e0 is the permittivity of free space. 2.1. Differential Capacitance at Different Temperatures from 450 to 600 K Figure 1 a shows the simulated s–U relation between the electrode surface charge density (s) and the electrode potential (U) of BMIM + /PF6/graphite electrode at four different temperatures of 450, 500, 550, and 600 K. The s–U curves were fitted segmentally by polynomials, which are connected by error functions.[20] Subsequently, Cd–U curves at the above four temperatures were obtained by differentiating the fitted s–U curves in Figure 1 a, that is, Cd = ds/dU, and are depicted in Figure 1 b. Clearly, the Cd–U curves for BMIM + /PF6 at these temperatures all display an asymmetric camel-shaped feature,

2. Results and Discussion In this study, the IL/electrode model consists of two infinite parallel graphite (0001) electrodes of opposite constant charge densities, with a rectangular supercell of 42.608–41.8115  along the x–y dimensions using periodic boundary conditions. The two electrodes are separated by a fixed distance L = 100  along the z dimension, with 439 pairs of BMIM + /PF6 filled between the electrodes. Such an arrangement allows the two electrodes to be treated independently.[5a, 13a, 18] For a planar electrode located at z =  50 , the electric potential on the electrode surface is shown by Equation (1):

U ¼ UðL=2Þ  Uð0Þ ¼ 

Z

L=2

E ðzÞdz

ð1Þ

0

in which U(0) = 0 is the potential of the reference point taken in the middle of the two electrodes, and E(z) denotes the electric field across the bulk electrolyte, with E(0) = 0 due to the complete screening of the electrode electric field.[5a] For the MD simulation, E(z) can be calculated from the ensemble average ionic charge density 1(z) using Gauss law, as proposed by Pratt and co-workers [Eq. (2)].[19] EðzÞ ¼ ð< Q ðzÞ >  < Qþ ðzÞ >Þ=ð2 Ae0 Þ where

< Q ðz Þ >¼ QðL=2Þ þ

Z

z

1ðz 0 Þdz0

L=2

 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

ð2Þ Figure 1. a) Surface charge density (s) versus electrode potential (U) for BMIM + /PF6 at 450 (g), 500 (a), 550 (d), and 600 K (c); an increment of 2 mC cm2 has been added successively to the data of 500, 550, and 600 K to distinguish them as a guide to the eye. The lines in (a) are fitted to the s–U relation at individual temperatures. b) Differential capacitance (Cd) of BMIM + /PF6 IL as a function of electrode potential at 450 (g), 500 (a), 550 (d), and 600 K (c).

ChemPhysChem 2014, 15, 2503 – 2509

2504

CHEMPHYSCHEM ARTICLES

www.chemphyschem.org

with potential of zero charge (PZC) at 0.084, 0.076, 0.071, and 0.079 V, respectively, at 450, 500, 550, and 600 K. A notable feature of all four Cd–U curves is that Cd at the negative polarization is higher than that at positive polarization, though the size of the PF6 anions (4.76 ) is smaller than that of the cations (5.70 ),[5a] ascribable to the specific adsorption of BMIM + by shortening the thickness of the EDL.[5a, 17, 21] Such specific adsorption is caused by the p-stacking interaction between the aromatic im-ring and the sp2 graphite surface, as described in our previous computational[5a, 16] and experimental[5b] studies. There are several features in + , butyl head carbon of BMIM + , deCd at different temperatures, as Figure 2. Number density profiles of the im-ring geometrical center of BMIM noted as gc and C4 in the inset of (a), and center-of-mass position of PF6 for BMIM + /PF6 under electrode surface can be seen from Figure 1 b: densities of 0 (a,c,e) and  6 mC cm2 (b,d,f) at 450 (g), 500 (a), 550 (d), and 600 K (c). The two electro1) at the negative polarization, des are located at 50  (neutral or negatively charged) and + 50  (neutral or positively charged). the maxima of Cd gradually decrease at elevated temperatures from 450 to 600 K; 2) at the positive polarization, the maxima at surface charge densities of s = 0 (Figure 2 a,c,e) and of Cd are slightly complicated: specifically, the maxima of Cd  6 mC cm2 (Figure 2 b,d,f) at 450, 500, 550, and 600 K. The electrode potentials of the Cd maxima correspond approxigradually increase at elevated temperatures from 450 to 550 K, and decrease at 600 K; and 3) the maxima of Cd shift to mately to the surface charge densities of s =  6 mC cm2. a higher potential at elevated temperature, as can be seen for We note that a symmetric density profile between two neutral both the negative and positive polarizations. The shift of electrodes of s = 0 mC cm2 is a necessary condition to check maxima of Cd with temperature is consistent with the studies whether the MD simulation time is long enough to ensure statistically averaged results, as shown in the top row of by experiment,[9d] MFT,[3, 14, 22] and MD simulation.[13a] Such Figure 2. It can be seen that density oscillation extends several a trend may be understood in terms of the driving force of tens of angstroms into the bulk, attributed to the overscreenthermal energy with increasing temperature, which causes ing effect.[4, 23] Apart from that, it can be inferred from Figure 2 broader distributions of counterions in the EDL at high temthat a higher temperature modulates the density profiles perature. Thus, systems at high temperature require high poslightly, whereas the main features are retained at all the temtential to compensate this driving force resulting from thermal peratures. Specifically, all the peak values decrease with elevatenergy. Apart from that, it is of interest to note that the cured temperature, thus indicating a less structural EDL at higher rent simulations demonstrate both trends of temperature-detemperature due to the higher thermal energy at elevated pendent Cd. Though the negative polarization decreases monotonically with elevated temperature, the positive polarizatemperature, in agreement with a previous study.[24] tion demonstrates a more complicated behavior with a slight A distinct feature is that the gc of the im-ring remains in increase at intermediate temperature from 450 to 550 K, and close contact with the neutral and negatively charged electhen a decrease at 600 K. Thus, it is desirable to closely inspect trode surface, as depicted in Figure 2 a,b. This is reasonable bethe effects of temperature on both positive and negative pocause the positive charge on the BMIM + cation is distributed larizations, as will be discussed below. largely on the im-ring. Upon charging from s = 0 to 6 mC cm2, the first peak shifts from z = 3.6 to 3.5 , with 1(z) increasing from approximately 0.0125 to 0.021 3 for 450 K 2.2. Density Profiles and Orientational Distribution at and 0.0096 to 0.016 3 for 600 K. The overall increased accuDifferent Temperatures from 450 to 600 K mulation is around 1.6–1.7 for the four temperatures. On the The influence of temperature on the EDL and Cd of pure positively charged electrode of s = 6 mC cm2, it is seen from  + BMIM /PF6 IL was investigated by analyzing the number denFigure 2 b that the gc is repelled to give a peak at 3.9  with much lower 1(z) of less than 0.005 3. On the other hand, the sity profiles, 1(z), of the geometrical center (gc) of the im-ring + + of BMIM , the butyl head carbon of BMIM (see gc and C4 de1(z) values of the C4 atom of BMIM + do not undergo such  noted in the inset of Figure 2 a), and the center of mass of PF6 drastic enhancement or depression as the surface charge den 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

ChemPhysChem 2014, 15, 2503 – 2509

2505

CHEMPHYSCHEM ARTICLES

www.chemphyschem.org

sity switches from s = 0 to  6 mC cm2, as depicted in Figure 2 c,d. Interestingly, the C4 atom peaks at 3.5 , that is, a closer contact to the electrode of s = 6 mC cm2 compared with that of 3.6  to a neutral electrode. Figure 2 e,f shows the 1(z) of the center of mass of PF6 . For PF6 , the overall increment of 1(z) from a neutral electrode to s = 6 mC cm2 is around 1.7– 1.8, which is higher than that (1.6–1.7) for BMIM + from a neutral electrode to s = 6 mC cm2. Thus, there is more space in the interfacial region to accommodate PF6 , contributed by the + along the surface normal direction z of the “latent void” donated by the Figure 3. Orientational ordering, P2(q), of the BMIM im-ring normal electrode under electrode surface densities of 0 (a) and  6 mC cm2 (b), or between the nitrogen–nitrogen vector + [20, 25] Also, on the im-ring of BMIM + and z under electrode surface densities of 0 (c) and  6 mC cm2 (d), at 450 (g), 500 butyl chain of BMIM . PF6 is repelled much more (a), 550 (d), and 600 K (c). strongly upon negative charging, with the first peak position switching from 4.1 to 4.6  from a neutral electrode to s = the higher temperature the less structural feature, similar to 6 mC cm2, and the peak value of 1(z) decreases from 0.0175– 1(z) in Figure 2. 0.019 to approximately 0.004 3 at the four temperatures. At the positive polarization of s = 6 mC cm2, PF6 is in closer conIt can be deduced that BMIM + tends to lie flat on the electact with the electrode with higher 1(z) of the first peak to it, trode because the first peak of 1(z) is located at 3.6  to the as expected. electrode surface, shown in Figure 2 a,c, and the im-ring has To further illustrate the effect of temperature on ionic oriena parallel alignment on the electrode surface, as indicated by tations at the graphite surface, the orientational distributions Figure 3 a,c. Upon charging, the configuration of BMIM + + of BMIM at 450, 500, 550, and 600 K are shown in Figure 3. switches from a flat to a slant configuration, that is, a gc–C4 The orientational distribution is defined as the ensemble averpattern with the gc in closer contact with the negatively age of the second Legendre polynomial [Eq. (3)]:[16] charged electrode and a C4–gc pattern with C4 in closer contact with the positively charged electrode, as shown in Figure 2 b,d. Such an EDL structure is in good agreement with ð3Þ P2 ðqÞ ¼< ð3 cos2 ðqÞ1Þ=2 > previous simulations using a coarse-grained BMIM + model.[20, 25] Thus, the reconstruction of the EDL must involve two processes for a conformational ion such as BMIM + , that is, a translation motion as seen in the changes in 1(z) and a reorin which q is the angle between the im-ring normal direction ientational motion as discussed above. Such reorientational vector and the electrode surface normal (z), as shown in the motion may correspond to a slow capacitive process detected inset of Figure 3 a, or between the nitrogen–nitrogen (NN) by EIS, in addition to the fast process contributed by the ionic vector on the im-ring and z, as shown in the inset of Figure 3 c. translational motion.[12, 26] Clearly, the im-ring of BMIM + in the innermost layer is preferentially oriented parallel to the uncharged electrode surface, as shown by the values of P2(q) approximating unity in Fig2.3. Effects of Temperature on the EDL Structure of BMIM + / ure 3 a,b in the first layer, accompanied by the values of P2(q) PF6 on the Graphite Electrode approximating 0.5 in Figure 3 c,d. Notably, such a feature persists even at a positively charged electrode at s = 6 mC cm2, as Based on the above inspections of Figures 2 and 3, we can illustrate the qualitative evolution of the EDL at elevated temshown in Figure 3 b,d. Of course, the probability for a BMIM + perature. Figure 4 depicts the temperature-dependent EDL of ion to be in close contact with a positively charged surface is BMIM + /PF6 in a qualitative manner. BMIM + ions in the innerrather low, as shown in Figure 2 b. However, it tends to take a parallel alignment between the im-ring and surface as long most layer preferentially lie flat on the neutral electrode suras they are close to each other, due to the p-stacking interacface according to the 1(z) of the im-ring gc and C4 of BMIM + [5, 16] + tion. The overall orientational distributions of BMIM are (see Figure 2), as well as the P2(q) of BMIM + (see Figure 3). broader at elevated temperatures, both on the negatively Such parallel alignment of BMIM + in the innermost layer even charged electrode and the positively charged electrode, with persists at charge densities of  6 mC cm2, thus indicating the  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

ChemPhysChem 2014, 15, 2503 – 2509

2506

CHEMPHYSCHEM ARTICLES

www.chemphyschem.org from 450 to 550 K. Thus, the effects of elevated temperature are twofold: they depress Cd at the negative polarization but increase Cd slightly at the positive polarization, as displayed pictorially in the right column of Figure 4. The benefit of the more effective screening by PF6 on the positively charged electrode surface cannot be maintained at high temperature, and the maximum of Cd at the positive polarization decreases at 600 K (see Figure 1 b). Note that although the trend of temperature-dependent Cd at negative polarization is clear, the effect of temperature at the positive polarization is subtle, and attributed to the above-mentioned competition. 2.4. Comparison with Previous Simulations of BMIM + /PF6 on the Graphite Electrode

Figure 4. Schematic illustration of the temperature-dependent EDL structure of BMIM + /PF6 on positively and negatively charged electrodes, in which with BMIM + is depicted as a polar head of the im-ring with methyl as . a butyl tail, and PF6 is depicted as

strong specific adsorption between BMIM + and the graphite surface by p-stacking interaction between the im-ring and graphite surface, as shown in the middle of Figure 4, upon charging the electrode. The effect of specific adsorption on Cd has been well discussed in our previous studies.[5] Briefly, on the one hand, it brings a closer contact between BMIM + and the electrode surface, and thus shortens the effective thickness of the EDL to bring a higher Cd at the negative polarization; on the other hand, the specific adsorption of the cations contributes to the surface charge and thus raises the electrode potential on the positively charged electrode, which depresses the Cd at positive polarization.[5a] Increasing temperature weakens the specific adsorption of BMIM + on the graphite electrode, as seen by a broader density and the orientational distributions of BMIM + (see Figure 2 and Figure 3). In this case, BMIM + moves away from the electrode surface, and thus generates a thicker EDL structure. Thus, a thicker effective EDL is the unavoidable result at the negative polarization, and the maxima of Cd decay monotonically with elevated temperature on the negatively charged electrode, as shown in Figure 1 b. Of course, a thicker effective EDL with elevated temperature also applies at the positive polarizations. On the other hand, it is also notable that the specific adsorption of BMIM + on the graphite electrode is weakened at elevated temperature, and allows more effective screening of the positively charged electrode by PF6 . Thus, on positive polarization there is competition between two aspects at elevated temperature, that is, more effective screening by PF6 and elongated EDL. Although the former enhances Cd, the latter depresses it. The net result is that the maxima in Cd at the positive polarization increase slightly with elevated temperature  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Notably, Kislenko et al. conducted MD simulations on the EDL and capacitance properties of the same BMIM + /PF6/electrode system.[10, 17] A general conclusion from their studies, that is, that capacitance increases with elevated temperature, seems to be in apparent contradiction with our current study. We note that Kislenko et al. estimated integral capacitance, Ci = s/(UUPZC), in their studies.[10, 17] Of course, Ci is different from the Cd = ds/dU shown in Figure 1 b, though sometimes it is ambiguous to distinguish the above two definitions of the capacitance.[27] Nevertheless, it is of interest to depict Ci, from the raw simulation data shown in Figure 1 a, utilizing the UPZC at four different temperatures. Figure 5 shows Ci–U curves of the current study at temperatures of 450, 500, 550, and 600 K. It can be seen that the overall trend of Ci follows that of Cd in Figure 1 b, whereas capacitance at the negative polarization is higher than that at the positive polarization. In terms of the temperature effects, it can be seen that Ci decreases with elevated temperature at the negative polarization, following the trend of Cd. The anomalous Ci values around 0.25 V are caused by the crossover of the Cd curves around the PZC, as shown in Figure 1 b, and manifest in Ci upon integration from UPZC. On the other hand, the effect of

Figure 5. Integral capacitance (Ci) of BMIM + /PF6 on graphite as a function of electrode potential at 450, 500, 550, and 600 K. The individual data marked with open circles at 2.2 and 1.8 V, corresponding to the electrode surface charge density of s =  8.2 mC cm2, are taken directly from Ref. [16], whereas those marked with open circles, corresponding to 300, 350, and 400 K at s = 1.7 mC cm2 are deduced from Ref. [9] using UPZC = 0.10 V at 300 K.[10b, 17]

ChemPhysChem 2014, 15, 2503 – 2509

2507

CHEMPHYSCHEM ARTICLES temperature is relatively ambiguous for the positive polarization, as also reflected by the crossovers of Cd at the positive polarization branch in Figure 1 b. A similar trend in Ci was also observed in the MD simulation of pyr13 + /FSI on the graphite electrode.[13b] Nevertheless, the Ci values around 2 V, which correspond to the maxima positions of Ci at the positive polarization in Figure 1 b, show an increment from 450 to 500 and 550 K, and then a decrease at 600 K, that is, the same trend as the maxima in Cd around 2 V in Figure 1 b. Also shown in Figure 5 are the Ci–U data from Kislenko et al.[10, 17] Note that the Ci values for 300 K at 2.2 and 1.8 V, corresponding to an electrode surface charge density of s =  8.2 mC cm2, are taken directly from Ref. [16], whereas those corresponding to 300, 350, and 400 K at s = 1.7 mC cm2 were deduced from Ref. [9] using UPZC = 0.10 V at 300 K.[10b, 17] Despite the scattering of Kislenko’s Ci data,[10, 17] we note that numerical values are within the same range in Kislenko’s work and our current study. Furthermore, there is actually good agreement between the current study and Kislenko’s studies on the same system, at least qualitatively. 1) It can be seen that the overall trend of Ci is higher at the negative polarization than that at the positive polarization for temperatures ranging from 450 to 600 K, as found in the Cd shown in Figure 1 b. Moreover, Kislenko’s Ci results at 300 K show the same trend, with higher Ci at the negative polarization than that at the positive polarization. 2) The trend of Ci at low positive potential, corresponding to s = 1.7 mC cm2, increases with elevated temperature for 300, 350, and 400 K.[10] Such a trend is retained in the current study, specifically at s = 2 mC cm2, for 450 and 500 K, but the Ci decreases when the temperature increases to 550 K. Thus, on combining Kislenko et al.’s work and the current study, we see that the Ci around 0.5 V increases in the temperature range from 300 to 500 K, and then decreases as the temperature reaches 550 K, though the high Ci value for 400 K seems to be probably caused because the 300 K UPZC[10b, 17] was used directly in estimating Ci at 400 K. Finally, we note that complete Cd–U and/or Ci–U curves are more desirable to estimate the temperature effects on the capacitance and EDL properties.

3. Conclusions The effects of temperature on the EDL structure and capacitance of the IL BMIM + /PF6 on the graphite electrode have been studied by MD simulations at four temperatures, that is, 450, 500, 550, and 600 K. It was found that the feature of asymmetric camel-shaped Cd–U curves with higher Cd values at the negative polarization than at the positive polarization was well maintained for all the temperatures investigated in this study, and was attributed to the specific adsorption of BMIM + on graphite.[5, 16] In addition, the current study showed that the maximum of Cd at the negative polarization decreases at elevated temperature, whereas at the positive polarization it first slightly increases from 450 to 550 K, and then decreases at 600 K. The decreasing Cd at negative polarization with increasing temperature is associated with a thicker EDL structure induced by diminishing specific adsorption of BMIM + on the graphite surface. On the other hand, the weakening specific  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

www.chemphyschem.org adsorption of BMIM + allows a relatively higher packing density of PF6 and causes more effective screening of the surface charge, and thereby increases Cd at positive polarization at temperatures ranging from 450 to 550 K. The benefit of the weakening specific adsorption of BMIM + is depressed at the high temperature of 600 K, attributed to the high thickness of the EDL at the positive polarization, and results in the lowest Cd at positive polarization. Thus, for the IL BMIM + /PF6 with a graphite electrode, the temperature effect at the positive polarization may be understood in terms of the competition between two aspects: 1) the weakening of the specific adsorption of BMIM + , which allows more effective screening of the positively charged surface by PF6 ; and 2) the overall increasing EDL thickness at higher temperature. Although the former predominates at temperatures ranging from 450 to 550 K, the latter becomes predominant at 600 K. The current study also demonstrated that the maxima of Cd shift to the higher potential at elevated temperature for both the negative and positive polarizations to balance the broader EDL at higher temperature. Finally, we note that it is more appropriate to investigate the temperature effects on capacitance properties by using the capacitance curve based on the entire potential window.

Experimental Section We performed MD simulations of pure BMIM + /PF6 IL between two oppositely charged electrodes composed of frozen graphene layers on both sides of the simulation cell. The separation between the two inner graphene layers was set to 100 , which allowed the EDL and the differential capacitance on the two oppositely charged walls to be studied separately.[18b] The simulation process was similar to that in our previous studies.[5a, 16] Briefly, the BMIM + /PF6 bulk phases contained 439 cation–anion pairs for all systems (i.e. the overall number density of all systems was identical for clearer comparison) and these systems were run at T K (T = 450, 500, 550, and 600 K) under a pressure of 1 bar. The force-field parameters were taken from Pdua’s work,[28] and the carbon atoms of the graphite (0001) surface interacted with BMIM + /PF6 through the Lennard-Jones potential corresponding to the sp2 hybrid carbon atoms in the AMBER force field.[29] The van der Waals and the real space electrostatic interaction cutoff distance was set to 12 . The smoothed particle-mesh Ewald (SPME) algorithm[30] elongated up to 700  in the z direction (i.e. the direction perpendicular to the graphite electrode surface) was used to handle the longrange electrostatic interactions in reciprocal space, whilst a slab correction[31] was induced along the z direction for such an essential two-dimensional periodic system along the x–y directions. For each system, 11 MD runs were performed with a fixed charge density s on the two inner graphene layers from 11 to + 11 mC cm2, with an increment of 1 mC cm2. Charges with opposite signs were put on the carbon sites of the two inner graphene layers in contact with the BMIM + /PF6 , so that the whole system was charge neutral. For each simulation, after initial annealing from 1000 to T K within 20 ns, a trajectory of 50 ns was gradually generated at T K, coupled to a Nos–Hoover chain thermostat[32] to generate a converged EDL because the dynamics of the IL was slow.[33] The integration time step was 2 fs with a SHAKE/RATTLE algorithm[34] applied on constraining all the CH bonds. The simulation was performed with a homemade MD package and the image charges were not considered in the current work. ChemPhysChem 2014, 15, 2503 – 2509

2508

CHEMPHYSCHEM ARTICLES Notably, the electronic capacitance (CQ) is important for graphite.[35] For a capacitance model that takes into account CQ, the total capacitance (CT) is represented as a series of CQ and double layer capacitance (Cd) values, that is, 1/CT = 1/CQ + 1/Cd, in which Cd is given in Figure 1 b. It is demonstrated that for graphite and graphene the CQ is a U-shaped curve,[35] with the minimum located at the PZC, and CQ increases dramatically with elevated potential. Thus, CQ is only important at low potential and mainly alters the bellshaped Cd to camel-shaped CT. For the camel-shaped Cd found in this study, the effect of CQ is expected to be small and does not alter the overall Cd curve in a fundamental manner.

Acknowledgements This work was supported by NSFC (21373118, 21073097), the Natural Science Foundation of Tianjin (12JCYBJC13900), NCET-100512, and the MOE Innovation Team of China (IRT13022). The simulations were performed on TianHe-1(A) at the National Supercomputer Center in Tianjin. Keywords: differential capacitance · electric double layer · ionic liquids · molecular dynamics · temperature effects [1] a) Y. Z. Su, Y. C. Fu, Y. M. Wei, J. W. Yan, B. W. Mao, ChemPhysChem 2010, 11, 2764 – 2778; b) M. V. Fedorov, A. A. Kornyshev, Chem. Rev. 2014, 114, 2978 – 3036; c) R. Burt, G. Birkett, X. S. Zhao, Phys. Chem. Chem. Phys. 2014, 16, 6519 – 6538. [2] a) Y. Zhu, S. Murali, M. D. Stoller, K. J. Ganesh, W. Cai, P. J. Ferreira, A. Pirkle, R. M. Wallace, K. A. Cychosz, M. Thommes, D. Su, E. A. Stach, R. S. Ruoff, Science 2011, 332, 1537 – 1541; b) L. Zhang, F. Zhang, X. Yang, G. Long, Y. Wu, T. Zhang, K. Leng, Y. Huang, Y. Ma, A. Yu, Y. Chen, Sci. Rep. 2013, 3, 1408. [3] A. A. Kornyshev, J. Phys. Chem. B 2007, 111, 5545 – 5547. [4] M. Z. Bazant, B. D. Storey, A. A. Kornyshev, Phys. Rev. Lett. 2011, 106, 046102; Erratum ibid. 2012, 109, 129903. [5] a) X. Si, S. Li, Y. Wang, S. Ye, T. Yan, ChemPhysChem 2012, 13, 1671 – 1676; b) Q. Zhang, Y. Han, Y. Wang, S. Ye, T. Yan, Electrochem. Commun. 2014, 38, 44 – 46. [6] a) C. Merlet, B. Rotenberg, P. A. Madden, P.-L. Taberna, P. Simon, Y. Gogotsi, M. Salanne, Nat. Mater. 2012, 11, 306 – 310; b) Z. Hu, J. Vatamanu, O. Borodin, D. Bedrov, Phys. Chem. Chem. Phys. 2013, 15, 14234 – 14247. [7] A. J. Bard, L. R. Faulkner, Electrochemical Methods: Fundamentals and Applications, 2nd ed., Wiley, New York, 2001, pp. 383 – 386. [8] V. Lockett, M. Horne, R. Sedev, T. Rodopoulos, J. Ralston, Phys. Chem. Chem. Phys. 2010, 12, 12499 – 12512. [9] a) V. Lockett, R. Sedev, J. Ralston, M. Horne, J. Phys. Chem. C 2008, 112, 7486 – 7495; b) F. Silva, C. Gomes, M. Figueiredo, R. Costa, A. Martins, C. M. Pereira, J. Electroanal. Chem. 2008, 622, 153 – 160; c) R. Costa, C. M. Pereira, F. Silva, Phys. Chem. Chem. Phys. 2010, 12, 11125 – 11132; d) M. T. Alam, J. Masud, M. M. Islam, T. Okajima, T. Ohsaka, J. Phys. Chem. C 2011, 115, 19797 – 19804; e) C. Cannes, H. Cachet, C. DebiemmeChouvy, C. Deslouis, J. de Sanoit, C. L. Naour, V. A. Zinovyeva, J. Phys. Chem. C 2013, 117, 22915 – 22925; f) V. Ivanisˇtsˇev, A. Ruzanov, K. Lust, E. Lust, J. Electrochem. Soc. 2013, 160, H368 – H375; g) L. Siinor, R. Arendi, K. Lust, E. Lust, J. Electroanal. Chem. 2013, 689, 51 – 56.

 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

www.chemphyschem.org [10] a) S. A. Kislenko, R. H. Amirov, I. S. Samoylov, Phys. Chem. Chem. Phys. 2010, 12, 11245 – 11250; b) S. A. Kislenko, R. H. Amirov, I. S. Samoylov, J. Phys. Conf. Ser. 2013, 418, 012021. [11] M. Holovkoa, V. Kapkoa, D. Hendersonb, D. Bod, Chem. Phys. Lett. 2001, 341, 363 – 368. [12] M. Drschler, N. Borisenko, J. Wallauer, C. Winter, B. Huber, F. Endres, B. Roling, Phys. Chem. Chem. Phys. 2012, 14, 5090 – 5099. [13] a) J. Vatamanu, O. Borodin, G. D. Smith, J. Am. Chem. Soc. 2010, 132, 14825 – 14833; b) J. Vatamanu, L. Xing, W. Li, D. Bedrov, Phys. Chem. Chem. Phys. 2014, 16, 5174 – 5182. [14] Y. Han, S. Huang, T. Yan, J. Phys. Condens. Matter 2014, 26, 284103. [15] D. Jiang, D. Meng, J. Wu, Chem. Phys. Lett. 2011, 504, 153 – 158. [16] S. Wang, S. Li, Z. Cao, T. Yan, J. Phys. Chem. C 2010, 114, 990 – 995. [17] S. A. Kislenko, I. S. Samoylov, R. H. Amirov, Phys. Chem. Chem. Phys. 2009, 11, 5584 – 5590. [18] a) R. M. Lynden-Bell, M. Del Ppolo, Phys. Chem. Chem. Phys. 2006, 8, 949 – 954; b) G. Feng, J. S. Zhang, R. Qiao, J. Phys. Chem. C 2009, 113, 4549 – 4559; c) R. M. Lynden-Bell, A. I. Frolov, M. V. Fedorov, Phys. Chem. Chem. Phys. 2012, 14, 2693 – 2701. [19] M. A. Wilson, A. Pohorille, L. R. Pratt, J. Phys. Chem. 1987, 91, 4873 – 4878. [20] N. Georgi, A. A. Kornyshev, M. V. Fedorov, J. Electroanal. Chem. 2010, 649, 261 – 267. [21] G. Feng, R. Qiao, J. Huang, S. Dai, B. G. Sumpter, V. Meunier, Phys. Chem. Chem. Phys. 2011, 13, 1152 – 1161. [22] M. Kilic, M. Bazant, A. Ajdari, Phys. Rev. E 2007, 75, 021502. [23] M. V. Fedorov, A. A. Kornyshev, Electrochim. Acta 2008, 53, 6835 – 6840. [24] K. Kirchner, T. Kirchner, V. Ivanisˇtsˇev, M. V. Fedorov, Electrochim. Acta 2013, 110, 762 – 771. [25] M. V. Fedorov, N. Georgi, A. A. Kornyshev, Electrochem. Commun. 2010, 12, 296 – 299. [26] a) M. Drschler, B. Huber, B. Roling, J. Phys. Chem. C 2011, 115, 6802 – 6808; b) B. Roling, M. Drschler, B. Huber, Faraday Discuss. 2012, 154, 303 – 311; c) J. Wallauer, M. Drschler, B. Huber, B. Roling, Z. Naturforsch. B 2013, 68, 1143 – 1153. [27] a) B. Roling, M. Drschler, Electrochim. Acta 2012, 76, 526 – 528; b) H. Wang, L. Pilon, Electrochim. Acta 2012, 63, 55 – 63. [28] a) J. N. A. Canongia Lopes, J. Deschamps, A. A. H. Pdua, J. Phys. Chem. B 2004, 108, 2038 – 2047; b) J. N. A. Canongia Lopes, J. Deschamps, A. A. H. Pdua, J. Phys. Chem. B 2004, 108, 11250. [29] W. D. Cornell, P. Cieplak, C. I. Bayly, I. R. Gould, K. M. Merz, J. Ferguson, M. David, D. C. Spellmeyer, T. F. Caldwell, W. James, A. K. Peter, J. Am. Chem. Soc. 1995, 117, 5179 – 5197. [30] U. Essmann, L. Perera, M. L. Berkowitz, T. Darden, H. Lee, L. G. Pedersen, J. Chem. Phys. 1995, 103, 8577 – 8593. [31] I. Yeh, M. L. Berkowitz, J. Chem. Phys. 1999, 111, 3155 – 3162. [32] a) G. J. Martyna, M. L. Klein, M. E. Tuckerman, J. Chem. Phys. 1992, 97, 2635 – 2643; b) G. J. Martyna, M. E. Tuckerman, D. J. Tobias, M. L. Klein, Mol. Phys. 1996, 87, 1117 – 1157. [33] a) T. Yan, Y. Wang, C. Knox, J. Phys. Chem. B 2010, 114, 6886 – 6904; b) T. Yan, Y. Wang, C. Knox, J. Phys. Chem. B 2010, 114, 6905 – 6921. [34] a) J. Ryckaert, G. Ciccotti, H. J. C. Berendsen, J. Comput. Phys. 1977, 23, 327 – 341; b) H. C. Andersen, J. Comput. Phys. 1983, 52, 24 – 34. [35] a) N. B. Luque, W. Schmickler, Electrochim. Acta 2012, 71, 82 – 85; b) E. Paek, A. J. Pak, G. S. Hwang, J. Electrochem. Soc. 2013, 160, A1 – A10; c) A. A. Kornyshev, N. B. Luque, W. Schmickler, J. Solid State Electrochem. 2014, 18, 1345 – 1349. Received: April 8, 2014 Published online on July 1, 2014

ChemPhysChem 2014, 15, 2503 – 2509

2509

Temperature effects on the capacitance of an imidazolium-based ionic liquid on a graphite electrode: a molecular dynamics simulation.

Temperature-dependent electric double layer (EDL) and differential capacitance-potential (C(d)-U) curves of the ionic liquid 1-butyl-3-methylimidazoli...
401KB Sizes 0 Downloads 3 Views