Electrochemical and Solid-State Letters, 8 共7兲 A373-A377 共2005兲
A373
1099-0062/2005/8共7兲/A373/5/$7.00 © The Electrochemical Society, Inc.
High Capacitance of Electrodeposited MnO2 by the Effect of a
Surface-Active Agent
S. Devaraj and N. Munichandraiah*,z
Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560 012, India
Manganese dioxide has been electrochemically deposited on a Ni substrate from a neutral electrolyte in the presence of a
surface-active agent, namely, sodium lauryl sulfate 共SLS兲, for supercapacitor application. The potentiodynamically prepared oxide
provides higher capacitance than the potentiostatically and galvanostatically prepared oxides. Owing to adsorption of the surfactant molecules at the interface during electrodeposition, the manganese dioxide possesses higher specific surface area. Specific
capacitance of 310 F g−1 obtained for the oxide prepared in the presence of SLS over an extended charge-discharge cycling is
higher by about 25% in relation to the oxide prepared in the absence of SLS.
© 2005 The Electrochemical Society. 关DOI: 10.1149/1.1922869兴 All rights reserved.
Manuscript submitted January 4, 2005; revised manuscript received March 8, 2005. Available electronically June 1, 2005.
Among several types of materials studied for electrochemical
capacitors, various forms of carbon, conducting polymers, and transition metal oxides have received wide interest.1 RuO2·xH2O, which
belongs to the third category, has a specific capacitance as high as
740 F g−1 due to a solid-state redox mechanism.2 Because RuO2 is
expensive, there has been increasing interest to investigate alternate
transition metal oxides with capacitance close to that of
RuO2·xH2O. MnO2 has been studied as a promising material,3-15
because it is inexpensive, safe, environmentally friendly, and also
widely used in batteries.16 The charge-storage mechanism in MnO2
has been reported recently,17 and accordingly a theoretical specific
capacitance of 1370 F g−1 is expected. However, this value can be
obtained in practice only when the mass of MnO2 is at the level of
a few micrograms per cm2 area. At such a low thickness range, the
utilization of the active material is high. As thin layers of MnO2 are
uneconomical for practical capacitors, studies with a mass range of
0.4-0.5 mg cm−2 have been extensively reported.9 At this mass
range, a maximum specific capacitance of about 240 F g−1 has been
obtained.18 With an increase in mass per unit area, the specific capacitance of MnO2 decreases.17 Similar results for RuO2·xH2O have
been reported recently.19
The problem associated with low values of specific capacitance
of thick layers of MnO2 is the following. The MnO2 deposits or
coatings generally do not possess high porosity, and the electrolyte
cannot permeate into the coating. Only the outer layer of the electrode is exposed to the electrolyte. Consequently, the electrochemical utilization of the material decreases with an increase in thickness. Nevertheless, utilization of thick layers of the active material is
preferable for obtaining capacitance as high as possible in a given
volume and area of the electrodes. Indeed, it would be ideal if specific capacitance of MnO2 is improved from its presently reported
value of 240 F g−1 to a value equivalent to that of RuO2·xH2O,
namely, 740 F g−1.2 In view of this, it is attempted in the present
investigation to enhance capacitance of MnO2 at a mass range of
0.4-0.5 mg cm−2.
In general, the physical and morphological nature of electrochemically deposited materials depends on the experimental conditions used during preparation, including the presence of foreign molecules in the electrolyte. A surface-active molecule possesses a polar
group attached to the end of a long hydrophobic tail. Adsorption of
these molecules at the electrode/electrolyte interface influences the
properties of the double-layer and also the kinetics and mechanism
of electrochemical processes. During an electrocrystallization process, the relative rates of nucleation and growth of crystals greatly
influence the surface morphology of the deposit. The adsorbed surfactant molecules can favor one of these two steps. If the rate of
nucleation exceeds the growth rate, a high surface area of the de-
* Electrochemical Society Active Member.
z
E-mail: [email protected]
posit is expected. Inspite of interesting applications of surfactants in
electrochemistry and electrodeposition, only a few studies are reported in the literature.20 For instance, high surface area PbO2 deposits have been prepared by the addition of a commercial surfactant, namely, Teepol, to the electrolyte.21 In a recent study,22
electrolytic manganese dioxide 共EMD兲 has been prepared in an
acidic electrolyte in the presence of several surfactants and evaluated for rechargeable alkaline manganese dioxide-zinc battery application. The EMD prepared in the presence of Triton X-100 has been
shown to provide higher discharge capacity in relation to the EMD
prepared otherwise. To the best of the authors’ knowledge, there are
no reports in the literature on studies of capacitance of MnO2 by
electrodeposition in the presence of surfactants.
The aim of the present study is to electrochemically deposit
MnO2 in the presence of a suitable surface-active agent and to
evaluate the electrodes for capacitor properties. Accordingly, MnO2
electrodeposited in the presence of sodium lauryl sulfate 共SLS兲 is
shown for the first time to provide a specific capacitance of
310 F g−1 against 240 F g−1 obtained for MnO2 deposited in the
absence of SLS.
Experimental
Analytical grade MnSO4·H2O, H2SO4, K2SO4 were purchased
from Merck, Na2SO4 from BDH, Li2SO4 from Spectrochem. Reagent grade SLS 共C12H25NaOSO3兲 from Merck was used as the
surface-active agent. A high purity Ni foil 共thickness: 0.18 mm兲 of
battery grade was used as the substrate for MnO2 deposits. All solutions were prepared in doubly distilled water. A glass cell of about
150 mL capacity with suitable ground-glass joints to introduce a Ni
working electrode, Pt foil auxiliary electrodes, and a saturated
calomel reference electrode 共SCE兲 was used for electrochemical
deposition of MnO2 and also for characterization studies. All potential values are reported against SCE.
A Ni foil 10 mm wide and 8 cm in length was sectioned out of a
sheet, 2 cm2 area at one of the ends was exposed to the electrolyte
and the rest of its length was used as a tag for taking electrical
contact. The Ni substrate was polished with emery; washed copiously, dried in vacuum at 60°C for about 30 min and weighed before using it for electrodeposition of MnO2. A mixed electrolyte of
0.5 M MnSO4·H2O + 0.5 M Na2SO4 was used for MnO2 deposition. For deposition of MnO2 in the presence of the surface-active
agent, the required quantity of SLS was added followed by a thorough stirring of the electrolyte till a clear solution was obtained.
Experiments were carried out using several concentrations of SLS
up to 100 mM in the electrolyte. As the effective concentration of
SLS was found to be 100 mM, a majority of the studies were carried
out using this concentration. The deposition of MnO2 on Ni was
carried out by galvanostatic, potentiostatic, and potentiodynamic
techniques. Subsequent to the deposition of the required quantity of
MnO2, the electrode was separated from the cell, rinsed with doubly
distilled water, dried at 100°C in air, and weighed.
Downloaded 01 Oct 2011 to 137.132.123.69. Redistribution subject to ECS license or copyright; see http://www.ecsdl.org/terms_use.jsp
A374
Electrochemical and Solid-State Letters, 8 共7兲 A373-A377 共2005兲
Figure 1. Cyclic voltammograms recorded during deposition of 共i兲 MnO2
and 共ii兲 MnO2共s兲 on a Ni substrate in 0.5 M MnSO4 + 0.5 M Na2SO4 in the
absence and the presence of SLS, respectively, at 20 mV s−1 sweep rate.
A Sartorius balance of model CP225D-OCE with 0.01 mg sensitivity was used for weighing the electrodes. The powder X-ray
diffraction 共XRD兲 patterns of the samples were recorded using Philips XRD X’PERT PRO diffractometer using Cu K␣ as a source. The
scanning electron microscope 共SEM兲 images were recorded using
JEOL JSM-5600LV scanning electron microscope. BrunauerEmmett-Teller 共BET兲 surface area measurements were carried out
using SMARTSORB-92/93 surface area analyzer utilizing N2 gas.
The electrochemical studies were carried out using a potentiostat/
galvanostat EG&G PARC model Versastat II or Solartron model
1286.
Results and Discussion
The electrochemical preparation of MnO2 from an aqueous solution of Mn2+ salt has been extensively studied and reported.23 The
reaction occurs according to
Mn2+ + 2H2O → MnO2 + 4H+ + 2e−
关1兴
MnO2 thus formed usually deposits as a film on the anode. A large
variety of studies on electrodeposition of MnO2 from acidic electrolytes have been reported,24 and the mechanism of deposition using
cyclic voltammmetric method has been studied in our laboratory.25 These studies have been carried out using an inert electrode
such as Pt. However, it is imperative to employ an inexpensive
substrate instead of an expensive Pt-group metal for a cost-effective
application. Accordingly, Ni was used as the substrate for MnO2
deposition in the present study. However, it was found that Ni undergoes corrosion and also oxidation during oxidation of Mn2+ to
MnO2 in the acidic electrolytes. To avoid these problems, therefore,
a neutral, mixed aqueous solution of 0.5 M MnSO4
+ 0.5 M Na2SO4 was used with varying concentrations of SLS from
0 to 100 mM. The oxides deposited from a solution in the absence
of SLS and in the presence of SLS are hereafter referred to as MnO2
and MnO2共s兲, respectively.
Cyclic voltammograms recorded during preparation of MnO2
and MnO2共s兲 on Ni are shown in Fig. 1. Although the voltammograms in the absence 共curve i兲 and the presence of SLS 共curve ii兲 are
similar in shape, the current is higher in the later case. The anodic
peaks at about 1.25-1.30 V correspond to the oxidation of Mn2+ to
MnO2 共Reaction 1兲, and the cathodic peaks at about 0.9-1.0 V correspond to the reduction of MnO2 to MnOOH.25 The effect of SLS
in the 0.5 M MnSO4·H2O + 0.5 M Na2SO4 electrolyte is clearly re-
Figure 2. 共a兲 XRD patterns of 共i兲 MnO2 and 共ii兲 MnO2共s兲, 共b兲 SEM image of
MnO2 and 共c兲 SEM image of MnO2共s兲. The 共hkl兲 planes corresponding to ␦
form of MnO2 are given on the XRD patterns.
flected in the voltammograms. As adsorption of Mn2+ ions at the
interface precedes the electron-transfer process 共Reaction 1兲, it is
inferred that SLS molecules favor this process, which results in
higher anodic peak current during the preparation of MnO2共s兲.
Since the kinetics of oxidation of Mn2+ to MnO2 depends on the
electrochemical method, namely, galvanostatic, potentiostatic, or potentiodynamic method employed, it was intended to study the influence of these techniques on the capacitance of MnO2 and MnO2共s兲.
Several electrodes were prepared by varying current density 共galvanostatic current density, cd = 2.5 - 10 mA cm−2兲, potential 共potentiostatic, potential = 0 - 1.5 V兲 and sweep rate 共potentiodynamic,
␯ = 10 - 200 mV s−1兲 with nearly identical masses of MnO2 关or
MnO2共s兲兴 and their capacitances were evaluated using cyclic voltammetry and galvanostatic charge-discharge cycling as described
later. From these experiments, it was found that the MnO2 and
MnO2共s兲 prepared by the potentiodynamic method in the potential
range between 1.1 and 1.5 V at a sweep rate of 20 mV s−1 gave
maximum specific capacitance values. The reason could be the partial reduction of MnO2 关or MnO2共s兲兴, which starts occurring at
about 1.1 V during cathodic half-cycle. During repeated cycling, the
partial reduction and then further oxidation or deposition of the fresh
oxide layer on the previous layer could have resulted in a high
porosity of the oxides. Accordingly, the electrodes prepared using
the potentiodynamic method between 1.1 and 1.5 V at 20 mV s−1
were employed for the rest of the studies.
It has been known that MnO2 exists in several crystallographic
forms, and an oxide prepared by electrochemical oxidation in acidic
electrolytes, which is generally called the EMD, has the ␥ structure.
In order to examine the effect of the neutral medium and the surfactant in the solution, the XRD patterns of the MnO2 and MnO2共s兲
were recorded and shown in Fig. 2a. The data suggest that both
Downloaded 01 Oct 2011 to 137.132.123.69. Redistribution subject to ECS license or copyright; see http://www.ecsdl.org/terms_use.jsp
Electrochemical and Solid-State Letters, 8 共7兲 A373-A377 共2005兲
samples are crystalline with identical structures. Thus, the effect of
surfactant on the crystallographic structure of MnO2共s兲 is absent.
Furthermore, it is inferred from the position of the diffraction peaks
共Fig. 2a兲 that MnO2 and MnO2共s兲 are in ␦ form.26 This result differs
from the earlier reports, which suggest either ␥-form27 or amorphous nature6 for the EMD. From the SEM micrographs 共Fig. 2b
and c兲, it is seen that the surface of MnO2共s兲 共Fig. 2c兲 appears
rough, suggesting higher surface area than the smoother surface of
MnO2 共Fig. 2b兲. For surface area measurements, thick layers of
MnO2 and MnO2共s兲 were deposited and the oxides were scraped out
of the substrate. The specific surface area of MnO2 and MnO2共s兲
powders are 34.0 and 76.4 m2 g−1, respectively. These results support that MnO2共s兲 possesses greater surface area than MnO2.
The charge-storage mechanism in MnO2, as has been reported,17
is due to a redox reaction, which involves insertion of cations from
the electrolyte into MnO2 lattice. This single-electron transfer process corresponds to about 1162 C per gram of MnO2. As the kinetics of reversible insertion/extraction of the cation varies with the
electrolyte, it was intended to select an appropriate electrolyte for
capacitor studies. For this purpose, cyclic voltammograms of a
MnO2 electrode were recorded in Li2SO4, Na2SO4, and K2SO4 solutions of different concentrations between 0 to 1.0 V. It was found
that the voltammograms were rectangular in shape when recorded in
Na2SO4 solution. However, there was an increase in current in
Li2SO4 and K2SO4 solutions during cathodic half-cycle at potentials
at about 0 V, thus deviating from the rectangular shape as shown in
Fig. 3. This observation is found to be similar for both MnO2 共Fig.
3a兲 and MnO2共s兲 共Fig. 3b兲. Furthermore, there was a decrease in
voltammetric current with an increase in the concentration of
Na2SO4 from 0.1 M. Thus, a solution of 0.1 M Na2SO4 was used
for all characterization studies. Furthermore, the effect of varying
concentrations of SLS in 0.5 M MnSO4 was studied by depositing
MnO2共s兲 in the presence of 10, 50, and 100 mM SLS and recording
cyclic voltammograms in 0.1 M Na2SO4. It was found that the
100 mM concentration is the saturation limit of SLS in
0.5 M MnSO4 + 0.5 M Na2SO4 and the voltammetric current increases with an increase in concentration of the SLS. Thus, MnO2共s兲
electrodes
prepared
from
0.5 M MnSO4 + 0.5 M Na2SO4
+ 100 mM SLS electrolyte were used for characterization studies.
The results of cyclic voltammetry for these optimization studies
were also confirmed by galvanostatic charge-discharge studies.
Cyclic voltammograms of MnO2 and MnO2共s兲 electrodes each
with mass of 0.42 mg cm−2 and also a bare Ni electrode in 0.1 M
Na2SO4 are shown in Fig. 4a for comparison. There is no significant
current density on the bare Ni electrode, thus suggesting that the
contribution of the substrate to the measured capacitance of MnO2
or MnO2共s兲 is negligibly small. The current 共Icv兲 of the MnO2共s兲 is
higher than the MnO2. The specific capacitance 共C兲 was calculated
using the following equation
C = Icv /共␯m兲
关2兴
where ␯ is the sweep rate used for recording the cyclic voltammogram and m is the mass of MnO2 or MnO2共s兲. The values of C
obtained from Fig. 4a for MnO2 and MnO2共s兲 are 232.4 and
291.4 F g−1, respectively. Thus, there is an increase of C by about
25% for MnO2共s兲 in comparison with MnO2.
The electrodes were subjected to galvanostatic charge-discharge
cycling between 0 and 1.0 V with several values of cd. The variation
of potential during the first few cycles, typically at a cd of
0.5 mA cm−2 is shown in Fig. 4b. There is a linear variation of the
potential during charge and discharge regions for both MnO2 and
MnO2共s兲. Both electrodes exhibit about 57 mV ohmic drop at the
beginning of discharge, thus, suggesting that the surfactant has no
influence on the iR drop of the electrodes. Similar magnitudes of iR
drop are reported for MnO2.18 The specific capacitance obtained
from the discharge data was calculated using the equation give below
A375
Figure 3. Cyclic voltammograms recorded at a scan rate of 5 mV s−1 of 共a兲
MnO2 and 共b兲 MnO2共s兲 in 0.1 M Li2SO4 共i兲, 0.1 M Na2SO4 共ii兲 and
0.1 M K2SO4 共iii兲. Masses of MnO2 and MnO2共s兲 are 0.44 and 0.4 mg cm−2,
respectively.
C = It/共⌬Em兲
关3兴
where I is discharge current, t is discharge time, ⌬E is potential
window 共i.e., 1.0 V兲. The values of C obtained from the second
cycle 共Fig. 4b兲 for MnO2 and MnO2共s兲 are 246.8 and 310.2 F g−1,
respectively. These values are in close agreement with those obtained from the cyclic voltammetric data 共Fig. 4a兲.
Both MnO2 and MnO2共s兲 electrodes were subjected to an extended cycle-life test with a cd of 0.5 mA cm−2, and the variation of
specific capacitance with cycle number is shown in Fig. 4c. It is seen
that the specific capacitance of MnO2 is 240 F g−1 during the initial
stages of cycling. This value agrees with the studies reported in
the literature.18 There is a decrease in capacitance on cycling and
220 F g−1 is obtained for the 500th cycle. Thus, there is a decrease
of about 10.5% of capacitance after 500 charge-discharge cycles. On
the other hand for MnO2共s兲, a specific capacitance of 310 F g−1 is
obtained during the initial cycles, and it decreases marginally to
288 F g−1 at 500th cycle and 275 F g−1 at 1000th cycle. Thus the
decrease in capacitance during the first 500 cycles is only about 7%
for MnO2共s兲 against about 10.5% for MnO2.
The variation of specific capacitance of the electrodes with the
mass of the material is shown in Fig. 5a. At all loading levels, the
specific capacitance of MnO2共s兲 is higher than MnO2. At a mass of
0.03 mg cm−2, the specific capacitance of MnO2共s兲 is 1330 F g−1,
Downloaded 01 Oct 2011 to 137.132.123.69. Redistribution subject to ECS license or copyright; see http://www.ecsdl.org/terms_use.jsp
A376
Electrochemical and Solid-State Letters, 8 共7兲 A373-A377 共2005兲
Figure 4. 共a兲 Cyclic voltammograms recorded at a scan rate of 5 mV s−1, 共b兲
charge-discharge curves at 0.5 mA cm−2, and 共c兲 cycle-life data at
0.5 mA cm−2 of MnO2 共i兲 and MnO2共s兲 共ii兲 in 0.1 M Na2SO4. Curve 共iii兲 in
共a兲 is cyclic voltammogram of a bare Ni electrode at 5 mV s−1. Mass of
MnO2 or MnO2共s兲 is 0.42 mg cm−2.
which is close to the value theoretically expected.17 For getting this
value from MnO2, it is anticipated that still thinner deposits are
required. The electrodes were subjected to charge-discharge cycling
at different current densities, and the variation of specific capaci-
Figure 5. 共a兲 Dependence of specific capacitance on mass, 共b兲 dependence of
specific capacitance on current density of charge-discharge cycling, and 共c兲
Ragone plots of MnO2 and MnO2共s兲 in 0.1 M Na2SO4. Mass of MnO2 or
MnO2共s兲 used for obtaining the data in 共b兲 and 共c兲 is 0.41 mg cm−2. In 共c兲,
the current density in mA cm−2 used for charge-discharge cycling is indicated at each data point.
tance with current density is shown in Fig. 5b. For both electrodes,
there is a decrease in specific capacitance with an increase in current
density, similar to the reports in the literature.19
Downloaded 01 Oct 2011 to 137.132.123.69. Redistribution subject to ECS license or copyright; see http://www.ecsdl.org/terms_use.jsp
Electrochemical and Solid-State Letters, 8 共7兲 A373-A377 共2005兲
Evaluation of supercapacitors for their specific power 共SP兲 and
specific energy 共SE兲 have been of interest in the literature,28 because
a high SP is expected from electrochemical supercapacitors. Although SP and SE are properties of a device, these parameters have
been evaluated for active materials also similar to the calculation of
specific capacitance. For instance, SP and SE of RuO2·xH2O have
been calculated and reported as Ragone plots from single-electrode
studies.29 In the present study, the values of SP and SE were calculated using Eq. 4 and 5, respectively
SP = I⌬E/共2m兲
关4兴
SE = It⌬E/共2m兲
关5兴
where t is the discharge time. The calculations of SP and SE for
RuO2·xH2O have also been carried out using Eq. 4 and 5,
respectively.29 In the present study, the variation of SE with SP is
shown as Ragone plots in Fig. 5c. It is seen that the SP of MnO2共s兲
is greater than that of MnO2 at all SE values. At a SE of
12.5 Wh kg−1, for instance, the SP obtained for MnO2共s兲 is
14 kW kg−1 against 7.5 Wh kg−1 for MnO2.
Conclusions
Thus MnO2共s兲, which is electrochemically deposited in the presence of SLS, yields superior capacitor properties than MnO2 prepared in the absence of SLS. The anionic surfactant, SLS molecules
adsorbed on the positively charged Ni electrode surface alter the
structure of the double-layer and the kinetics of Reaction 1. Smaller
particle size, greater porosity, higher specific surface area, and
higher efficiency of utilization of MnO2共s兲 in relation to MnO2 are
the factors responsible for obtaining higher specific capacitance. For
the first time, a specific capacitance of 310 F g−1 for MnO2共s兲 is
obtained in the present study at a loading level of about 0.40.5 mg cm−2.
A377
Acknowledgments
The authors thank Dr. C. Shivakumara for the XRDs, K. R. Kannan for the SEMs, and K. C. Suresh and G. Ravi for surface area
measurements.
Indian Institute of Science assisted in meeting the publication costs of
this article.
References
1. S. Sarangapani, B. V. Tilak, and C. P. Chen, J. Electrochem. Soc., 143, 3791
共1996兲.
2. J. P. Zheng and T. R. Jow, J. Electrochem. Soc., 142, L6 共1995兲.
3. H. Y. Lee and J. B. Goodenough, J. Solid State Chem., 144, 220 共1999兲.
4. S. C. Pang, M. A. Anderson, and T. W. Chapman, J. Electrochem. Soc., 147, 444
共2000兲.
5. H. Y. Lee, S. W. Kim, and H. Y. Lee, Electrochem. Solid-State Lett., 4, A19
共2001兲.
6. C. C. Hu and T. W. Tsou, Electrochem. Commun., 4, 105 共2002兲.
7. M. Toupin, T. Brousse, and D. Belanger, Chem. Mater., 14, 3946 共2002兲.
8. Y. U. Jeong and A. Manthiram, J. Electrochem. Soc., 149, A1419 共2002兲.
9. J. K. Chang and W. T. Tsai, J. Electrochem. Soc., 150, A1333 共2003兲.
10. Y. T. Wu and C. C. Hu, J. Electrochem. Soc., 151, A2060 共2004兲.
11. J. K. Chang, C. T. Lin, and W. T. Tsai, Electrochem. Commun. 6, 666 共2004兲.
12. Y. S. Chen, C. C. Hu, and Y. T. Wu, J. Solid State Electrochem. 8, 467 共2004兲.
13. B. Djurfors, J. N. Broughton, M. Brett, and D. G. Ivey, J. Mater. Sci., 38, 4817
共2003兲.
14. Y. S. Chen and C. C. Hu, Electrochem. Solid-State Lett., 6, A210 共2004兲.
15. C. C. Hu and C. C. Wang, J. Electrochem. Soc., 150, A1079 共2004兲.
16. A. Yamada and J. B. Goodenough, J. Electrochem. Soc., 145, 737 共1998兲.
17. M. Toupin, T. Brousse, and D. Belanger, Chem. Mater., 16, 3184 共2004兲.
18. M. S. Wu and P. C. J. Chiang, Electrochem. Solid-State Lett., 7, A122 共2004兲.
19. B. O. Park, C. D. Lokhande, H. S. Park, K. D. Jung, and O. S. Joo, J. Power
Sources, 134, 148 共2004兲.
20. C. Hu, X. Dang, and S. Hu, J. Electroanal. Chem., 572, 161 共2004兲.
21. N. Munichandraiah and S. Sathyanarayana, J. Appl. Electrochem., 17, 22 共1987兲.
22. M. Ghaemi, L. Khosravi Fard, and J. Neshati, J. Power Sources, 141, 340 共2005兲.
23. A. Kozawa, in Batteries, Vol. 1, Manganese Dioxide, K. V. Kordesch, Editor, p.
385, Marcel Dekker, New York 共1974兲.
24. W. H. Kao and V. J. Weibel, J. Appl. Electrochem., 22, 21 共1992兲.
25. S. Rodrigues, N. Munichandraiah, and A. K. Shukla, J. Appl. Electrochem., 28,
1235 共1998兲.
26. O. Bricker, Am. Mineral., 50, 1296 共1965兲.
27. Y. Chabre and J. Pannetier, Prog. Solid State Chem., 23, 1 共1959兲.
28. B. E. Conway, Electrochemical Supercapacitors, Kluwer Academic Publishers/
Plenum Press, New York 共1999兲.
29. C. Lin, J. A. Ritter, and B. N. Popov, J. Electrochem. Soc., 146, 3155 共1999兲.
Downloaded 01 Oct 2011 to 137.132.123.69. Redistribution subject to ECS license or copyright; see http://www.ecsdl.org/terms_use.jsp