3386
2009, 113, 3386–3389 Published on Web 02/11/2009
Electrical Double Layer Structure in Ionic Liquids: An Understanding of the Unusual Capacitance-Potential Curve at a Nonmetallic Electrode Md. Mominul Islam, Muhammad Tanzirul Alam, Takeyoshi Okajima, and Takeo Ohsaka* Department of Electronic Chemistry, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Mail Box G1-5, 4259 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan ReceiVed: December 27, 2008; ReVised Manuscript ReceiVed: January 29, 2009
This study describes the causes of a U-like capacitance-potential (C-E) curve observed at nonmetallic electrode/ionic liquids (ILs) interfaces, in contrast to those observed at metal electrodes and expected according to the Kornyshev theory (Kornyshev, A. A. J. Phys. Chem. B 2007, 111, 5545). Several C-E curves were measured at glassy carbon (GC) and highly oriented pyrolytic graphite (HOPG) electrodes in three different ILs with inherent ionic concentrations of 6.4, 3.3, and 1.7 M. The minimum capacitance value (2.2 µF cm-2) at the HOPG electrode is significantly lower than those at GC or metal electrodes (>10 µF cm-2). The degree of curvature of the “U-like” curve measured at the GC electrode decreases in the ILs with low inherent ionic concentrations. This observation is in agreement with the theoretical curves deduced by considering both semiconductor and Kornyshev theories and the inherent properties (concentrations, sizes of ions, dielectric constant, etc.) of ILs used. The capacitance at the GC electrode exhibits a complex potential dependence, being different from those at HOPG and metal electrodes that were explained using semiconductor and Kornyshev theories, respectively. Depending on the characteristics of ILs, both concepts of semiconductor theory and Kornyshev’s model may be required to explain the C-E curves at the GC electrode. Introduction In the feature article,1 Kornyshev has developed the theory of an electrical double layer (EDL) structure at electrode/ionic liquids (ILs) interfaces based on local density approximation dependent mean-field theory and has pointed out that the characteristic of the capacitance-potential (C-E) curve should be bell-shaped (convex parabola) (curves 1 and 5, Figure 1a), provided that the electrode is a flat metal, the ions of ILs are nonadsorbing in character, and the parameter “gamma” (γ) is greater than 1/3 (γ physically signifies the degree of incompressibility of IL media as defined below). Later, the same group2,3 and Oldham4 supported the Kornyshev’s model by the computer simulation results. Very recently, we have justified5 that the theoretical C-E curve could be obtained experimentally with a proper choice of the practically available ILs and electrode substrate. The C-E curve is virtually bell-shaped (curve 1, Figure 1a) with metal (platinum and gold) electrodes in ILs composed of cation and anion of comparable sizes.5 Interestingly, this is not the case with the nonmetallic, for example, glassy carbon (GC) and highly oriented pyrolytic graphite (HOPG) electrodes. The C-E curves measured in the same set of ILs or in other ILs were commonly observed to be opposite in shape (concave parabola) (curve 2, Figure 1b).5-12 Locket et al.11 have, however, compared the C-E curve obtained at the GC electrode with the so-called camel-shaped one, another characteristic shape of the C-E curve * To whom correspondence should be addressed. Tel: +81-45-9245404. Fax: +81-45-9245489. E-mail:
[email protected].
10.1021/jp8114447 CCC: $40.75
proposed by Kornyshev.1 To date, no reason has been conferred to explain such an unusual observation at the nonmetallic electrodes. The EDL structure in ILs is in lack of a solvent dipole and composed of only ions (Figure 1b-d) of a high concentration (e.g., 6 M). At the vicinity of an electrified interface, the ions of ILs are packed up as much as possible at the proximity of the electrode surface to deliver the full countercharge to the charge density of the electrode surface.5 Thus, at a particular potential, the thickness of EDL (Figure 1) and hence the absolute value of C would be expected to depend on the characteristics of ILs, that is, the size of ions and the γ of ILs. With a bulky cation-anion pair, for example, all cations that are requested by the electrode charges cannot be accumulated in the nearest single layer of the electrode (Scheme 1). Hence, the rest of the cations may reside in the several consecutive layers (Figure 1c).5 This is known as “lattice saturation” and actually results in the bell-shaped C-E curve, and C is described by eq 1.1
1 1 1 ) + C Cc Cd
(1)
with
Cc )
ε* 4πd
×
(2)
and
Cd ) CD ×
( 2u )
cosh
1 + 2γ sinh (u ⁄ 2) 2
2γ sinh2(u ⁄ 2) (3) ln[1 + 2γ sinh2(u ⁄ 2)]
where Cc and Cd signify the compact and diffuse layer 2009 American Chemical Society
Letters
J. Phys. Chem. C, Vol. 113, No. 9, 2009 3387
Figure 1. Schematic diagrams of possible C-E curves (a) and EDL structures (b, c, and d) in ILs at various conditions as explained in the text. Panels (b) and (c) represent the accumulations of small- and large-sized ions, respectively, in response to the negative charges (seven charges) on the electrode, whereas panel (d) represents the accumulations of large-sized ions in response to four negative charges. The symbol (T) represents the effective thickness of the EDL.
SCHEME 1: Structures of Cations and Anions of ILs Used in This Study
interface may be presumed as a series of capacitances of the space charge layer (Csc) within the electrode, Cc, and Cd (inside of the solution) as follows16-20
1 1 1 1 + + ) C Csc Cc Cd
( 2u )
Csc ) C0 cosh C0 )
capacitances, respectively. CD ) ε/4πLD, and LD is the Debye length. The ε*, ε, and d represent the effective dielectric constant of the compact layer, the high-frequency dielectric constant of the IL, and the distance of the closest approach of ions to the electrode, respectively and u ) eΦ/kBT, where Φ is the total potential drop across the EDL and the value of (kB × T/e) is 25.69 mV at 25 °C;1 γ ) 2c0/cmax, where c0 is the average bulk number density of cations or anions and cmax is the maximal possible local concentration of ions (both cations and anions), respectively. In practice, the C-E curves measured at the metal electrodes (platinum, gold, and mercury) in ILs with a small cation-anion pair (Scheme 1) have been reported to be different from the so-called bell-shaped curve (e.g., the distorted shape of curve 3 or 4, Figure 1a).6-9 What is the main remaining factor to be considered for a clear understanding of the EDL in ILs? The answer is the density-of-state of the electrode substrate. Free-electron densities of gold (metal), GC (semimetal), HOPG (semimetal), and the semiconductor are reported to be 6 × 1022, 2 × 1020, 5 × 1018, and 1013-1017 cm-3.13-15 Such a different electronic density of the electrode substrate may essentially result in different C-E curves (Figure 1a). This may be speculated by considering the accumulation of cations with different sizes in the hypothetical EDL in response to different electrode charges (potential) and the resulting thicknesses of the EDL (Figure 1b-d). At a semiconductor electrode, the C value is mainly determined by the space charge density of the electrode itself. However, the total C at the semiconductor or semimetallic electrode/IL
(
2εε0e2c kBT
)
(4) (5)
1⁄2
(6)
where ε0 is the permittivity. The u, Cd, and Cc are defined above, and other symbols have their usual meanings. C0 is the capacitance at the minimum and completely depends on the characteristics of the electrode material [the dielectric constant (ε′) and electronic charge carrier density (c)]. Here, eq 5 represents a change of Csc with u (potential). In this study, to clarify the causes of observation of U-like C-E curves (curve 2, Figure 1a) at the HOPG and GC electrodes in ILs, we measured several C-E curves in three different ILs with different inherent ionic concentrations (Scheme 1). To clarify the role of the nonmetallic electrode on the EDL formation in ILs, the HOPG electrode was chosen since its surface is well-defined and contains a negligible number of functional groups and because its free-electron density is two orders of magnitude lower than that of the GC electrode (described above). The experimental results were supported by the theoretical C-E curves calculated by considering the concept of the electronic density of the electrode substrate. Chemicals 1-Ethyl-2-methylimidazolium tetrafluoroborate ([EMI+][BF4-]), N,N-diethyl-N-methyl-N-(2-methoxyethyl)ammonium bis(trifluoromethanesulfonyl)imide ([DMOA+][N(Tf)2-]), and N,N,N-trioctylN-methylammonium bis(trifluoromethanesulfonyl)imide ([MTOA+][N(Tf)2-]) with a purity of more than 99% and less than 0.005% water and halides were obtained from Kanto Chemical Co., Inc. (Japan). Highly pure N2 (99.99%) gas was supplied by Nippon Sanso Co., Inc. (Japan). The electrochemical measurements were carried out according to the procedures described in our previous papers.5-9 Before their use, ILs were
3388 J. Phys. Chem. C, Vol. 113, No. 9, 2009
Letters (v) The slope of the wings of this curve is ∼1.5 µF cm-2 V , which is comparable with that (1.6 µF cm-2 V-1) at the SAPG electrode in aqueous solution.17 Previously, Randin and Yeager16,17 reported a similar shape of the C-E curves measured at the SAPG electrode in aqueous NaF solutions at concentrations of 0.9-10-5 M. The values of C at the minimum (1.7-3.0 µF cm-2) were found to be incomparable with those obtained at the metal electrodes (>15 µF cm-2) and the value (0.72 µF cm-2 in 10-5 M NaF solution) calculated according to the Gouy-Chapman model.15 Moreover, the C-E curves are less sharp compared to the metal electrodes; for example, the slopes of the wings of the C-E curve measured at SAPG16,17 and the metal23 electrodes have been reported to be 1.6 and 20 µF cm-2 V-1, respectively. Such an observation has been reasonably explained based on the concept of the “space charging” (semiconducting) behavior of the SAPG electrode.16,17 In the present study, the C-E curve measured at the HOPG electrode in the highly concentrated (3.4 M) ionic medium (i.e., IL) is comparable in all respects with those obtained at the SAPG electrode in aqueous solutions. The obtained minimum C value (2.2 µF cm-2) at the HOPG electrode (Figure 2) is roughly comparable with the value (4.5 µF cm-2) of C0 of a SAPG electrode17 calculated using eq 6 [note that the insignificant variation in the minimum capacitance obtained by different research groups9,16,17 may result from the nonideality (cracks that originate the capacitance dispersion in the measurement) of the HOPG surface]. Thus, the obtained U-like C-E curve at the HOPG electrode could be explained using the theory of the semiconductor electrode, where the C value is mainly determined by the space charge density of the electrode itself, that is, Cc and Cd may negligibly contribute to the total value of C (eq 4). Hence, the minimum value of C and its change with potential at the HOPG electrode may be quantitatively explained by eqs 6 and 5, respectively, instead of eqs 1-3 given by Kornyshev.1 Figure 3 illustrates the C-E curves measured at the GC electrode in three ILs with inherent ionic concentrations of 6.4 ([EMI+][BF4-]), 3.3 ([DMOA+][N(Tf)2-]), and 1.7 M ([MTOA+][N(Tf)2-]). Similarly to the HOPG electrode (Figure 2), the C-E curve measured in [EMI+][BF4-] is almost U-like in shape, with a minimum at -0.2 V (Figure 3a). The shape of this curve is also comparable with those at the GC electrode in different ILs6 and aqueous H2SO4 and NaF solutions (pH 6).18 The potential corresponding to the minimum has been generally defined as the PZC. On the other hand, interestingly, the C-E curves are found to translate down with a distortion of the left wing (i.e., diminishing the curvature nature) as the inherent ionic concentrations of ILs decrease in the order of 6.4 > 3.3 > 1.7 M (Figure 3) or the cation size increases as [EMI+] < [DMOA+] < [MTOA+]. -1
Figure 2. Typical C-E curve measured at the HOPG electrode in N2-saturated [DMOA+][N(Tf)2-].
Figure 3. C-E curves measured at the GC electrode in N2-saturated (a) [EMI+][BF4-], (b) [DMOA+][N(Tf)2-], and (c) [MTOA+][N(Tf)2-].
dried under vacuum at 80 °C overnight and deaerated by bubbling with a dried N2 gas for 1 h. Results and Discussion The C-E curve measured at the HOPG electrode is a symmetrical U-shaped one (Figure 2). Several features concerning the obtained curve may be noted. (i) The shape of this curve is comparable with those found at various carbon electrodes,5-12,16-18,21,22 including GC and HOPG electrodes in ILs5-12 and inorganic molten salt,21,22 as well as at stress-annealed pyrolytic graphite (SAPG) in aqueous solution.16 (ii) The shape of the measured C-E curve is opposite of those (generally bell-shaped) obtained at platinum and gold electrodes in the same IL5 [note that in imidazolium-cationbased ILs (ImILs), distorted U-like curves have been observed at gold, platinum, and mercury electrodes6-9]. (iii) The minimum C value at -0.15 V is significantly smaller (2.2 µF cm-2) than those (>10 µF cm-2) at the metal and GC electrodes in ILs (Figure 3).5-12 (iv) The obtained minimum C value (2.2 µF cm-2) is comparable to those at the HOPG electrode (3.0 µF cm-2) in ImILs6 and at the SAPG electrode (ca. 2.6-3.0 µF cm-2) in aqueous solution.16,17
From the observed similarity in the shape of the C-E curve at the GC electrode (especially curve a in Figure 3) to that at the HOPG electrode (Figure 2), at a glance, one may presume that the space charging may control the total C at the GC electrode. On the contrary, special attention should be given to the observation of the “flattering phenomenon” of the left wing (especially curve c in Figure 3). The minimum C value (5.3-12.5 µF cm-2) obtained at the GC electrode in all of the ILs is fairly larger than that at the HOPG electrode. In addition, in contrast to the case at the HOPG electrode, the minimum C at the GC electrode significantly varies with the characteristics of ILs. It may also be noted that the minimum C at the GC electrode has been reported to be 8 µF cm-2, calculated based
Letters
J. Phys. Chem. C, Vol. 113, No. 9, 2009 3389 less steep than that of the Csc-E curve. At more negative potentials than the PZC, the accumulations of small- and largesized ions may be exemplified with the hypothetical EDLs shown in panels b and c of Figure 1, respectively, where the EDLs are necessarily packed up with one and two layers of cations to compensate for seven negative charges on the electrode. From the above discussion, it is clear that all of the components of capacitances in eq 4 (i.e., Csc, Cc, and Cd) should be taken into account to explain the whole C-E curve obtained in [MTOA+][N(Tf)2-]. On the contrary, the term Cd would be essentially neglected in the case of [EMI+][BF4-]. Thus, the capacitance at the GC electrode in ILs exhibits a complex potential dependence, being different from that at HOPG16,17,19,20 and metal electrodes.5
Figure 4. Csc-E curve (theoretical) derived for the GC electrode according to eqs 5 and 6 in which C0 was taken as 8.0 µF cm-2 at 25 °C.18 The inset shows the calculated C-E curves for the EDL formed at the GC electrode/[EMI+][BF4-] (a), [DMOA+][N(Tf)2-] (b), and [MTOA+][N(Tf)2-] (c) interfaces. The data of the curves marked by numbers 1 (solid line) and 2 (dashed line) were created by series additions (eq 4) of Csc and Cc (curves 1) and Csc, Cc, and Cd (curves 2), respectively. Data were created by assuming that the sizes of the cation and anion of a particular IL used are the same.24
on the semiconductor theory (i.e., eq 6).18 Therefore, the capacitance behavior at the GC electrode is rather complex. By electrochemical pretreatments of the GC electrode, the C value has been found to increase in ILs.6 Randin and Yeager18 have found that C at the GC electrode depends on the solution pH. In acidic solution, the C has been found to be significantly smaller than that observed in basic solution. As described above, the free-electron density (i.e., value of c in eq 6) of the GC substrate is about two orders of magnitude greater than that at the HOPG electrode. Furthermore, the surface of the GC electrode used in our study would not be smooth. Thus, different electronic densities,13-15 the presence of functional groups6,18 and the capacitance dispersion phenomenon11 due to roughness at the GC surface may be partially associated with the observed larger C at the minimum compared to that at the HOPG electrode. On the other hand, the translation and flattering phenomena of the C-E curves in different ILs used may be explained by considering a significant contribution of the EDL formed inside of the solution to the total C (eq 4). The present analysis directs us to consider the space charging inside of the electrode and the packing of ions inside of the solution in explaining the characteristic C-E curves at the GC electrode in ILs. On the basis of the above-mentioned analysis, we have attempted to calculate the theoretical C-E curves using eq 4 for the EDL formed at the GC electrode. In the calculation, the known values of the parameters that appeared in eqs 1-6 were used.24 The typical results are shown in Figure 4. Similarly to the Csc-E curve, all of the theoretical C-E curves are concave parabolic in shape. Interestingly, in agreement with the experimental results (Figure 3), a downward translation of the curves takes place for the ILs with a bulky cation (inset in Figure 4). In each case, the curves obtained by neglecting Cd (curves a1, b1, and c1 in Figure 4) are steeper than those (curves a2, b2, and c2 in Figure 4) obtained by considering the value of Cd.24 On the other hand, these curves (curves a1, b1, and c1) are generally
Acknowledgment. The present work was financially supported by a Grant-in-Aid for Scientific Research on Scientific Research (A) (No. 19206079) to T. Ohsaka from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. References and Notes (1) Kornyshev, A. A. J. Phys. Chem. B 2007, 111, 5545. (2) Fedorov, M. V.; Kornyshev, A. A. Electrochim. Acta 2008, 53, 6835. (3) Oldham, K. B. J. Electroanal. Chem. 2008, 613, 131. (4) Fedorov, M. V.; Kornyshev, A. A. J. Phys. Chem. B 2008, 112, 11868. (5) Islam, M. M.; Alam, M. T.; Ohsaka, T. J. Phys. Chem. C 2008, 112, 16568. (6) Alam, M. T.; Islam, M. M.; Okajima, T.; Ohsaka, T. J. Phys. Chem. C 2008, 112, 16600. (7) Alam, M. T.; Islam, M. M.; Okajima, T.; Ohsaka, T. Electrochem. Commun. 2007, 9, 2370. (8) Alam, M. T.; Islam, M. M.; Okajima, T.; Ohsaka, T. J. Phys. Chem. C 2007, 111, 18326. (9) Alam, M. T.; Islam, M. M.; Okajima, T.; Ohsaka, T. J. Phys. Chem. C 2008, 112, 2601. (10) Nanjundiah, C.; McDevitt, S. F.; Koch, V. R. J. Electrochem. Soc. 1997, 144, 3392. (11) Lockett, V.; Sedev, R.; Ralston, J.; Horne, M.; Rodopoulos, T. J. Phys. Chem. C 2008, 112, 7486. (12) Silva, F.; Gomes, C.; Figueiredo, M.; Costa, R.; Martins, A.; Pereira, C. M. J. Electroanal. Chem. 2008, 622, 153. (13) Cline, K. K.; McDermott, M. T.; McCreery, R. L. J. Phys. Chem. 1994, 98, 5314. (14) Tsuziku, T.; Saito, K. Jpn. J. Appl. Phys. 1966, 5, 738. (15) Bard, A. J.; Faulkner, L. R. Electrochemical Methods, Fundamental and Application, 2nd ed.; Wiley Inc.: New York, 2001. (16) Randin, J.-P.; Yeager, E. J. Electrochem. Soc. 1971, 5, 711. (17) Randin, J.-P.; Yeager, E. J. Electroanal. Chem. 1972, 36, 257. (18) Randin, J.-P.; Yeager, E. J. Electroanal. Chem. 1975, 58, 313. (19) Gerischer, H. J. Phys. Chem. 1985, 89, 4249. (20) Gerischer, H.; McIntyre, R.; Scherson, D.; Storck, W. J. Phys. Chem. 1987, 91, 1930. (21) Graves, A. D. J. Electroanal. Chem. 1970, 25, 349. (22) Graves, A. D.; Inman, D. J. Electroanal. Chem. 1970, 25, 357. (23) Islam, M. M.; Okajima, T.; Ohsaka, T. J. Phys. Chem. B 2004, 108, 19425. (24) Islam, M. M.; Ohsaka, T. Manuscript in preparation. The values of Cc (eq 2) and Cd (eq 3) were estimated by using the real parameters (inherent concentrations of ILs, the size of the cations, and values of ε) of [EMI+][BF4-], [DMOA+][N(Tf)2-], and [MTOA+][N(Tf)2-]. The diameters of [EMI+], [DMOA+] and [MTOA+] were considered to be 6.0, 6.6, and 14.4 Å, respectively (Ue, M.; Murakami, A.; Nakamura, S. J. Electrochem. Soc. 2002, 149, 1385). Typically, the values of Cc that are assumed to be independent of the potential were calculated to be 19, 13, and 5 µF cm-2 in [EMI+][BF4-], [DMOA+][N(Tf)2-], and [MTOA+][N(Tf)2-], respectively. To calculate the value of Cd, the value of γ (eq 3) was arbitrarily chosen to be 0.7 for all of the cases, and the temperature was 25°C.
JP8114447
