Actual Structure of Dissolved Zinc Ion Restricted in Less Than 1

ARTICLE pubs.acs.org/JPCC

Actual Structure of Dissolved Zinc Ion Restricted in Less Than 1 Nanometer Micropores of Carbon Takahiro Ohkubo,* Masayasu Nishi, and Yasushige Kuroda Department of Chemistry, Faculty of Science, Okayama University, 3-1-1Tsushimanaka, Kita-ku, Okayama 700-8530, Japan

bS Supporting Information ABSTRACT: The structures and properties of hydrated ions confined in solid nanospaces are not substantially understood, although they are indispensable for the development of new devices such as electrical double-layer capacitors. We describe the hydration structure around a Zn2+ restricted in slit-shaped micropores of two kinds of activated carbon fibers (ACF) by the analysis of X-ray absorption fine structure (XAFS) spectra. The proportion of dissolved species against the total adsorbed amounts of Zn2+on ACF was decreased with the reduction of the average micropore width of ACF. We could trace the actual structure of “nanosolution” around a Zn2+ restricted in less than 1 nm pore by extended XAFS (EXAFS) spectra with applying these values. Our results strongly indicate that the dehydrated structure can be stably formed inside the micropore whose pore size is less than the total diameter of the symmetrically hydrated ion, where the dehydrated ions can be stabilized by the strong potential well of the micropore.

’ INTRODUCTION Molecules restricted in solid nanospaces have been the subject of many studies because of their intensive possibility for new science and technology. However, the structure and properties of restricted molecules in nanoscale space are not substantially understood. A lot of researchers have tried to reveal the specific properties of nanorestricted molecules. For instance, Kaneko et al. have reported that the molecules such as nitrogen, oxygen, and other fundamental molecules adsorbed in hydrophobic nanospaces tend to form a highly ordered structure.1 Also, it was suggested that water and alcohol molecules adsorbed in the slit-shaped carbon micropores form highly ordered structures even at room temperature as revealed by an in situ X-ray diffraction (XRD) technique.2
5 These specific phenomena originate from the strong stabilization by the enhanced potential well in nanospaces. Therefore, the phase transition in solid nanospaces is also characteristic, which is significantly different from that in the bulk phase.6
9 The Frank
Wen model,10 which is the most famous and fundamental model representing a hydrated ion, is obviously helpful to understand the properties of electrolytic solution. However, we wonder if such a model can be applied to special conditions such as a nanorestricted condition. In recent years, studies on ions or ionic solutions restricted in solid nanospaces have been carried out to understand the fundamental chemistry of ions.11,12 For example, the transport properties of ions coexisting with porous materials are different from that in bulk phase because of the dehydration effect inside the nanospaces. 13,14 Holt et al. 15 and Duan and Majumdar16 reported the dynamic properties of ions restricted in nanoscale spaces whose pore diameter is less than 2 nm. They concluded that the mobility of ions restricted in the nanospaces is faster than that in bulk phase. These studies strongly indicate that the variation in the local structure around an ion can play an r 2011 American Chemical Society

important role to give the anomalies of such dynamic properties. On the other hand, the local structure around an ion also has been studied from theoretical aspects. Feng et al. reported that the strong potential well by a polarizable slit-shaped subnanometer space can compensate the free energy penalty even if the ions such as Na+ lose about 20% of their hydration shell.17 Ohba et al. showed the specific structures around Ca2+ confined in the slit-shaped micropore by a molecular simulation technique.18 The hydrated structure around Ca2+ restricted in 0.5 nm pore is quite distorted, which depends upon the pore geometry, indicating the variation of chemical or physical properties of hydrated ions from that in bulk aqueous solution. Consequently, the exposure of electrolytic solution to a nanorestricted condition can provide a new direction in solution chemistry. The nanorestricted structures of pure solvents such as water have been studied by a lot of methods. For example, Iiyama et al. showed the dependence of the cluster growth of water molecules with pore widths of activated carbon fiber (ACF) by in situ smallangle X-ray scattering.19 Kimura et al. showed the variation of heat of water adsorption with the pore width of ACF.20 Therefore, the ordered structure and cluster formation of water molecules in carbon micropores of ACF are sensitive to the pore width. Consequently, the structure of ionic solution confined in micropores should depend on the pore width. Then, we examined the pore-width dependence of the restricted hydration structure using two kinds of ACF having different pore widths. The X-ray absorption fine structure (XAFS) technique is quite effective in determining the local structure around a target atom. Received: May 10, 2011 Revised: June 21, 2011 Published: June 21, 2011 14954

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Figure 1. Powder XRD profiles of Zn(OAc)2-deposited ACF: (a) P7
Zn and (b) P20
Zn. The wavelength of monochromatic X-ray used for the measurements is 0.10011 nm.

Then, at first, we applied XAFS to study the nanoscale RbBr solution confined in the slit-shaped hydrophobic micropores of ACF21
23 and single-wall carbon nanohorn,24 showing a hydration anomaly. However, we have not succeeded in revealing a precise model for actually dissolved species in the micropores. If d-block ions such as Zn2+ can be applied as a probe ion for the purpose to study the restricted hydration structure around a metal ion, it is possible to analyze the structure from XAFS spectra more precisely because s-block ions such as Rb+ are not sensitive to the local distortion around an ion from the aspect of the XAFS technique. Accordingly, this article describes the micropore-size dependence of the restricted hydration structure around a Zn2+ of zinc acetate [Zn(OAc)2], which was evidenced with XAFS technique.

’ EXPERIMENTAL METHODS Two kinds of pitch-based ACF (P7 and P20; AD0 ALL Co. Ltd.) were used, which have considerably uniform slit-shaped hydrophobic nanospaces.25
29 In this study, we used as-prepared P7 and P20 because a lot of studies showed that pitch-based ACF has the least amount of surface functional groups. Thus, the adsorption amount on any surface functional groups of ACF can be negligible than the value on the nanospaces. Also, we used zinc

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acetate [Zn(OAc)2] dihydrate (99.9% Wako Co. Ltd.) as an electrolyte. A 50 cm3 amount of electrolytic aqueous solution (0.5 mol/dm3) was stirred with 200 mg of P7 or P20 over 24 h to impregnate the electrolyte into the slit-shaped micropores. After the deposition of Zn(OAc)2 followed by washing and drying in the desiccator, water vapor was adsorbed to provide the corresponding solution only in the carbon nanospaces at the relative pressure over 0.9. Powder XRD profiles for each sample were corrected with synchrotron-irradiated X-ray at SPring-8 to investigate the adsorbed structure of the electrolyte on ACF. Here, the wavelength of the monochromatic X-ray was estimated by the analysis of standard patterns from CeO2. The high-resolution nitrogen adsorption isotherms on ACF at 77 K were measured by BELSORP-max (BEL Japan, Inc.), and the porosity for each sample was determined by the subtracting pore effect (SPE) method for the high-resolution Rs-plot.30,31 Beside these experiments, we determined the adsorption isotherms of water on ACF at 303 K by the same apparatus. The pretreatment conditions were the same as the conditions for nitrogen adsorption isotherm measurements. Also, solution-phase adsorption isotherms of Zn2+ on ACF were measured at 303 K. We added 50 mg of ACF, which was sufficiently dried in a desiccator, into a glass tube with an aqueous solution of Zn(OAc)2 having appropriate concentrations followed by sealing with a gas burner and shaking for 24 h at 303 K in a water bath. The suspension was filtered, and residual zinc ions were analyzed by the titration experiment. The adsorbed amount of zinc ions was determined by the differences of the concentrations between before and after the adsorption of the metal ions. The electrolyte-deposited samples were installed in an XAFS glass cell with windows of Kapton film. The extended XAFS (EXAFS) measurements were performed on the Zn K-absorption edge at the National Laboratory for High Energy Accelerator Research Organization (KEK). The EXAFS spectra of the corresponding solutions were measured for comparison. The determination of each structure was carried out by the curve fitting of reverse Fourier transforms of the definite shell with the formula of EXAFS spectra, χ(k), including the structural parameters around a central atom:32 χðkÞ ¼ S0 2 NjFðkÞje
2σ k e
2r=λðkÞ 2 2

sin½2kr þ ϕðkÞ kr 2

ð1Þ

Here, k is the photoelectron wavenumber, S02 is the amplitude reduction factor, N is the coordination number, F(k) is the backscattering amplitude of a central atom, σ is the Debye
Waller factor, r is the distance between a central atom and a neighboring shell, λ(k) is the mean free path length of a photoelectron, and ϕ(k) is the total phase shift by the photoelectron. The calculated parameters of F(k), λ(k), and ϕ(k) obtained by FEFF6 procedure,33 which is included in IFEFFIT code,34 were used in the curve fittings. Also, S02 could be estimated as 0.78 if the coordination number for the first shell of bulk aqueous solution of Zn(OAc)2 was defined as 6 including 4.6 water molecules and 1.4 acetate ions.35 In addition, we analyzed X-ray absorption near edge structure (XANES) spectra of P7
Zn and P20
Zn adsorbed by water by linear least-squares fitting of reference spectra. Here, each spectrum from both electrolyte-deposited ACF samples and reference ones was normalized by each absorbance at E = 9671.0 eV, which is an isosbestic point during the adsorption process of water to form P7
Zn
H2O from P7
Zn
evac. Here, we denote Zn(OAc)2deposited ACF as P7
Zn and P20
Zn. Also, we describe the 14955

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Table 1. Parameters of Pore Structure of ACF a aR (m2 g
1)

aext (m2 g
1)

W0 (mL g
1)

w (nm)

P7

904

25

0.278

0.63

P20

1780

73

0.880

1.03

sample

a

The parameters are total surface area aR, external surface area aext, micropore volume W0, and average slit-shaped pore width w.

Figure 3. Adsorption isotherms of Zn2+ on P7 (blue circle) and P20 (red square) at 303 K and ratios of the adsorbed amount on P20 against that on P7 ().

Figure 2. Adsorption isotherms of water on P7 (a) and P20 (b) at 303 K: adsorption (black circle) and desorption (white circle) branches on original ACF and adsorption (solid red square) and desorption (outlined red square) branches on Zn(OAc)2-deposited ACF.

samples evacuating at 423 K or adsorbed by water at saturated vapor pressure conditions by using “
evac” or “
H2O” such as P7
Zn
evec or P7
Zn
H2O, respectively, in the following discussion. Figure S1 in the Supporting Information shows quick XAFS (QXAFS) spectra36 at Zn K-edge for P7
Zn during the adsorption process of water for 30 min. Here, the acquisition time of each spectrum is 2 min and the background absorption of each spectrum are subtracted to obtain EXAFS spectra without any normalization. Therefore, we could use the isosbestic point as a standard value for the normalization of EXAFS spectra. In this study, we used IFEFFIT code and REX2000 program37 for the curve fittings of EXAFS and XANES spectra, respectively.

’ RESULTS AND DISCUSSION Figure 1a,b shows powder XRD profiles of P7
Zn and P20
Zn, respectively. Three kinds of broad peaks around 15,

28, and 49° could be assigned to the graphitic structure of ACF. However, any peaks assigned to the crystal structure of Zn(OAc)2 could not be observed. Therefore, our results indicate that the electrolyte is highly dispersed in micropores of ACF. The characteristic parameters of each ACF obtained by the analysis of nitrogen adsorption isotherms at 77 K (Figure S2 in the Supporting Information) were collected in Table 1. Eventually, the average pore widths of slit-shaped pore on P7 and P20 were estimated as 0.63 and 1.03 nm, respectively, by using the parameters from the analysis of the SPE method for the highresolution Rs-plots (Figure S3 in the Supporting Information). The water adsorption isotherms on ACF and Zn(OAc)2-deposited ACF at 303 K were of typical type V, as shown in Figure 2a,b. The adsorbed amount of water on P7 deposited by Zn(OAc)2 at lower pressure region was larger compared with that on original P7, although the saturated adsorbed amounts of water on electrolytedeposited P7 and P20 were smaller than those of original ones. The tendency at lower pressure region indicates that the electrolyte restricted inside the micropores can strongly stabilize the adsorbed water. The adsorbed amounts at higher relative pressure region of Zn(OAc)2-deposited P7 and P20 were, on the other hand, smaller than those of original ACF. As we will discuss with XANES spectra, all Zn(OAc)2 restricted in the micropore of ACF cannot be dissolved by the addition of water vapor because of the limitation of the pore geometry. Therefore, the decrease in the adsorption amount at higher pressure region for electrolyte-deposited P7 is the result of less diffusivity of water into the micropore because the adsorbed electrolytes might throttle the diffusion of water molecules in the micropore. Figure 3 shows adsorption isotherms of Zn2+ on each ACF at 303 K and ratios of the adsorbed amount on P20 against that on P7 for each equilibrium concentration. Both isotherms were of type I, showing rapid uptakes initially tending to be saturated at the higher equilibrium
concentration region. Also, the adsorbed amounts of Zn2+ on P20 for all equilibrium concentrations except for the lowest one are about 2 times larger than that on P7. Because the amount of functional groups that can chemically adsorb metal ions on P7 is smaller than that on P20,20 more than 2 times a larger amount of Zn2+ can be adsorbed on P20 at the lowest concentration with strong interactions between a metal ion and the surface functional groups. Here, the ratios of the 14956

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Figure 4. Zn K-edge XANES spectra of P7
Zn (a) and P20
Zn (b) at the saturated vapor pressure region of water: experimental data (solid line), component in evacuated condition on each ACF (red triangle), component of bulk aqueous solution of Zn(OAc)2 (blue diamond), and sum of the components in both evacuated condition and bulk aqueous solution (open circle).

adsorbed amount of Zn2+ are similar to those of the total surface area of P20 against that of P7, indicating that the adsorbed densities of Zn2+ per unit area of the carbon surface are similar to each other. At the same time, this result also suggests that the adsorbed density of Zn2+ on P7 per unit pore volume is larger than that on P20 because the micropore volume of P20 is more than 3 times larger as shown in Table 1. Hence, the results strongly indicate that the strong potential well formed inside the micropore of P7 can produce the appropriate space for Zn2+ to enhance the adsorption. However, a few water molecules hydrating to a Zn2+ in bulk aqueous solution must dehydrate from the ion when the hydrating ion penetrates inside the micropore of P7 because the average pore width of P7 is less than 0.7 nm, which is smaller than the diameter of symmetrically hydrated Zn 2+ assuming that the average distance between a Zn2+ and an oxygen atom of water and the average radius of a water molecule are 0.209 and 0.140 nm, respectively.38 Feng et al. recently reported that the energy loss of dehydration can be supported by the van der Waals attractions between ions and pore walls, image charge effects, and the interaction between ions.17 Therefore, we can expect that the hydration structure around a Zn2+ inside the micropore of P7 can be varied by the dehydration of water molecules. Figure 4a,b shows the XANES spectra of P7
Zn
H2O and P20
Zn
H2O, respectively. We analyzed the spectra of P7
Zn
H2O and P20
Zn
H2O by linear least-squares fitting39,40

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Figure 5. Fourier transforms of Zn K-edge EXAFS spectra of P7
Zn (a) and P20
Zn (b): in evacuated state (black line), in water-adsorbed state (red line), and bulk aqueous solution of Zn(OAc)2 (blue line).

of each spectrum from P7
Zn
evec or P20
Zn
evec with that from bulk aqueous solution of Zn(OAc)2. The ratio of the proportional constants obtained by the fitting can reflect the composition between dissolved and insoluble Zn(OAc)2 inside the micropore. Figure 4a,b also shows the reference and fitting spectra for comparison. Each fitting spectrum by the linear combination of reference spectra is well agreed with the experimental one, indicating that it is enough for P7
Zn
H2O or P20
Zn
H2O to assume only the dissolved and insoluble species. From the fitting analysis, we could estimate the proportion of the dissolved species inside the micropore of P7 and P20 as 21.9 and 36.5% even at saturated vapor pressure region. The tendency is well agreed with the results of water adsorption isotherm shown in Figure 1a,b; as the adsorbed water inside the micropore of P7 is hard to penetrate because of the less diffusivity, the proportion of the dissolved species formed on P7 is less than that on P20. Then, we analyzed Fourier transforms of Zn K-edge EXAFS function, k3χ(k), on P7
Zn and P20
Zn samples. Here, χ(k) is the EXAFS oscillation. Figure 5 shows Fourier transforms of Zn K-edge k3χ(k) on P7 or P20
Zn
evac and P7 or P20
Zn
H2O. Each figure also shows the function obtained from bulk aqueous solution of Zn(OAc)2 at room temperature for comparison. The first shell for each sample can be ascribed to the Zn
O shell. The distance to the first shell for P7
Zn
H2O is similar to that of the evacuated phase, although the peak intensity is weaker. As shown in Figure 4a, the electrolytes formed in the micropore of P7 are mainly composed by the insoluble species where the first shell is composed only by the oxygen atoms of acetate ions. Therefore, 14957

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Table 2. Structural Parameters Obtained by Least-Squares Fit of EXAFS Spectra a sample

NZn
O

rZn
O (10
1 nm)

σ2Zn
O (10
5 nm2)

ΔE0 (eV)

P7
Zn
evac

4.6 ( 0.5

1.96 ( 0.01

5.96 ( 1.36

3.0

P7
Zn
H2O

4.7 ( 0.5

1.99 ( 0.01

7.41 ( 1.36

3.0

P7
Zn
NSN

5.1

2.10

12.6

P20
Zn
evac

4.6 ( 0.6

1.96 ( 0.01

6.52 ( 1.59

2.4

P20
Zn
H2O

5.1 ( 1.0

1.99 ( 0.02

8.71 ( 2.52

2.1

P20
Zn
NSN

6.0

2.04

Zn(OAc)2
evac

4.5 ( 0.6

1.96 ( 0.02

4.41 ( 1.42

2.4

Zn(OAc)2(aq) (0.5 M)

6

2.06 ( 0.01

9.46 ( 1.93

1.0

12.5

The parameters are coordination number N, interatomic distance r, Debye
Waller factor σ, and edge-energy shift ΔE0. The first and second elements in the subscripts denote the central and scattering atoms, respectively. a

the result shows that the average structure at nearest neighboring of P7
Zn
H2O is similar to that of evacuated state. On the other hand, the structure around the second shell for P7
Zn
H2O is not similar to that of evacuated state but bulk aqueous solution. Comparing the shapes of Fourier transforms for second shells around r = 0.28 nm, it can be expected that the second shell of P7
Zn
H2O is ordered as compared with that of bulk aqueous solution, because the Fourier transform of bulk aqueous solution is broader than that of P7
Zn
H2O. Thus, even if water molecules adsorb and fill the micropore deposited by the electrolyte, water molecules are hard to hydrate to the nearest neighboring of the ion and to form the ordered structure at the higher shell in the micropores of P7. Table 2 summarizes the structural parameters on the first shell of each sample. We fitted the theoretical EXAFS function, k3χ(k), to the reverse Fourier transforms of the experimental curve with the fitting parameters such as N, r, σ, and edge-energy shift, ΔE0. Here, we determined the parameters with one shell model for all first shells. As we already discussed above, the structural parameters for P7
Zn
H2O and P20
Zn
H2O samples involve the information only from dissolved and insoluble Zn(OAc)2. To estimate the structural information only from the dissolved species, we assume that the parameters of water-adsorbed species are the linear combination of two components, which depends on the proportion of each component obtained by the analysis of XANES spectra. Here, the assumption is quite enough to estimate the precise parameters for the dissolved species in micropores because the QXAFS spectra shown in Figure S1 in the Supporting Information possess the isosbestic point during the adsorption process of water, indicating the existence of only two structural states around a Zn2+ ion confined in micropores of ACF. Specifically, the structural parameter for water-adsorbed species obtained by the curve fitting, X, can be assumed as linear combination of each parameter, which is multiplied by the proportion, where we assume that the reference parameters for evacuated species are not varied even after the adsorption of water. X ¼ ð1
cdissol ÞXevac þ cdissol Xdissol

ð2Þ

Here, cdissol is the proportion of the dissolved species, and Xevac and Xdissol are the structural parameters for evacuated and dissolved species, respectively. For instance, the coordination number of the dissolved electrolyte in the micropore of P7, Xdissol, can be estimated as 5.1 where we use X = 4.7, cdissol = 0.219, and Xevac = 4.6. As the parameters obtained here are the information only from the dissolved species that subtracts the structure information from insoluble electrolytes, we can discuss the actual structure of

“nanosolutino”,11,21 which is defined as aqueous solution restricted in nanospaces. The other parameters for actual nanosolution are also summarized in Table 2, where we use P7
Zn
NSN or P20
Zn
NSN for actual nanosolution. The actual coordination number of the dissolved species on P7 is smaller than that on P20 or bulk aqueous solution, indicating the dehydration of a water molecule from a Zn2+. Also, the actual interatomic distance between Zn2+ and O atoms for the nanosolution formed in the micropore of P7 is longer than that on P20 or bulk aqueous solution. As both dehydration of a water molecule and the increase in the coordination distance are typically endothermic, the structure of actual nanosolution formed in the micropore of P7 is thermodynamically disadvantage. The recent calculation reported by Feng et al. indicates the moderate dehydration of the ions such as Na+ and Cl
inside the slit pore whose pore width is 0.82 nm, where the ions tend to lose 19
26% of their hydrated water molecules. If we assume the number of hydrated water as 4.6, which was reported by Ohtaki and Radnai,35 0.9
1.2 water molecules can dehydrate from the ion. Therefore, the coordination number of P7
Zn
NSN well sustains the theoretical results showing the moderate dehydration inside less than 1 nm pore. Hence, it is expected that the strong potential well formed in the micropore of P7 can supplement the endothermic variation and strongly stabilize the dehydrated Zn2+ in the narrower micropore. Thus, the present results obviously demonstrate that the structure around a Zn2+ confined in the micropore whose average pore width is less than 1 nm can be dehydrated under the strong compensation by the pore potential even if the structural information is subtracted from the insoluble electrolytes.

’ CONCLUSIONS We describe the actual hydration structure around a Zn2+ restricted in slit-shaped micropores of two kinds of ACF by the analysis of XAFS spectra. The results of the adsorption isotherms indicate that the strong potential well formed inside the carbon micropore whose average pore width is 0.63 nm can produce the appropriate space for Zn2+ to enhance the adsorption even though the ion must dehydrate a water molecule to penetrate into the micropore. The results of XAFS spectra show that the proportions of dissolved species against the total adsorbed amounts of Zn2+on ACF were 21.9 and 36.5% in the nanospaces whose slit-shaped pore widths are 0.63 and 1.03 nm, respectively. When we apply these proportion values for the analysis of EXAFS spectra, we can obtain the actual hydration structure around a Zn2+ ion showing the dehydration around the ion in less than 1 nm micropore, although the hydration number in the 14958

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The Journal of Physical Chemistry C micropore whose average pore width is 1.03 nm is the same with that of bulk aqueous solution. Our results strongly indicate that the dehydrated structure can be stably formed inside the micropore whose pore size is less than the total diameter of the symmetrically hydrated ion, where the dehydrated ions can be strongly stabilized by the potential well of the carbon micropore.

’ ASSOCIATED CONTENT

bS

Supporting Information. QXAFS spectra, adsorption isotherms of nitrogen, and Rs-plots. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Tel/Fax: 81-86-251-7843. E-mail: [email protected].

’ ACKNOWLEDGMENT This work was partially supported by Grant-in-Aid for Scientific Research (A) (No. 21245006) and for Young Scientists (B) (No. 20750013) from Japan Society for the Promotion of Science (JSPS), TEPCO Research Foundation, Kao Foundation for Arts and Sciences, and Wesco Scientific Promotion Foundation. Also, this work has been performed under the approval of the Photon Factory Program Advisory Committee (Proposal Nos. 2008G064 and 2010G148) and the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No. 2009B1765). ’ REFERENCES (1) Noguchi, D.; Hattori, Y.; Yang, C.-M.; Tao, Y.; Konishi, T.; Fujikawa, T.; Ohkubo, T.; Nobuhara, Y.; Ohba, T.; Tanaka, H.; Kanoh, H.; Yudasaka, M.; Iijima, S.; Sakai, H.; Abe, M.; Kim, Y.-J.; Endo, M.; Kaneko, K. ECS Trans. 2007, 11, 63–75. (2) Iiyama, T.; Nishikawa, K.; Otowa, T.; Kaneko, K. J. Phys. Chem. 1995, 99, 10075–10076. (3) Iiyama, T.; Nishikawa, K.; Suzuki, T.; Kaneko, K. Chem. Phys. Lett. 1997, 274, 152–158. (4) Ohkubo, T.; Iiyama, T.; Nishikawa, K.; Suzuki, T.; Kaneko, K. J. Phys. Chem. B 1999, 103, 1859–1863. (5) Ohkubo, T.; Iiyama., T.; Kaneko, K. Chem. Phys. Lett. 1999, 312, 191–195. (6) Miyahara, M.; Gubbins, K. E. J. Chem. Phys. 1997, 106, 2865–2880. (7) Watanabe, A.; Iiyama, T.; Kaneko, K. Chem. Phys. Lett. 1999, 305, 71–74. (8) Kaneko, K.; Watanabe, A.; Iiyama., T.; Radhakrishnan, R.; Gubbins, K. E. J. Phys. Chem. B 1999, 103, 7061–7063. (9) Radhakrishnan, R.; Gubbins, K. E.; Watanabe, A.; Kaneko, K. J. Chem. Phys. 1999, 111, 9058–9067. (10) Frank, H. S.; Wen, W. Y. Discuss. Faraday Soc. 1957, 24, 133–140. (11) Fox, B. S.; Balaj, O. P.; Balteanu, I.; Beyer, M. K.; Bondybey, V. E. Chem.—Eur. J. 2002, 8, 5534–5540. (12) Chmiola, J.; Yushin, G.; Gogotsi, Y.; Portet, C.; Simon, P.; Taberna, P. L. Science 2006, 313, 1760–1763. (13) Mizuhata, M.; Sumihiro, Y.; Deki, S. Phys. Chem. Chem. Phys. 2004, 6, 1944–1951. (14) Mizuhata, M.; Ito, F.; Deki, S. J. Power Sources 2005, 146, 365–370. (15) Holt, J. K.; Park, H. G.; Wang, Y.; Stadermann, M.; Artyukihin, A. B.; Grigoropoulos, C. P.; Noy, A.; Bakajin, O. Science 2006, 312, 1034–1037. (16) Duan, C.; Majumdar, A. Nature Nanotechnol. 2010, 5, 848–852.

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