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Cite this: Energy Environ. Sci., 2011, 4, 2152
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The governing self-discharge processes in activated carbon fabric-basedsupercapacitors with different organic electrolytes
Qing Zhang,a Jiepeng Rong,a Dongsheng Mab and Bingqing Wei*a
Received 14th December 2010, Accepted 15th March 2011
DOI: 10.1039/c0ee00773k
Electrochemical power devices with a long lifespan, long-term energy retention and great cycle stability
are extremely important for periodic energy store/supply, especially for solar energy storage for space
equipment and for power electronics in integrated circuits. In this report, we have systematically
investigated the effects of the charging current density and temperature over the self-discharge (SDC)
process of activated carbon fabric-based (ACF) supercapacitors with 1 M LiPF6/EC–DEC (v/v ¼ 1)
and 1 M TEABF4/PC as electrolytes, respectively. The experimental results have shown that a different
control mechanism governs the SDC process in each electrolyte system. Significant energy retention (in
excess of 70%) was obtained in the ACF–TEABF4 system after 36 h. SDC at room temperature. A dual-
mechanism control model is proposed for the first time which describes perfectly the SDC process of the
supercapacitor using 1 M TEABF4/PC as the electrolyte over different charge current densities and at
different SDC temperatures.
1. Introduction
Due to the intrinsic electrochemical reaction, rechargeable
lithium-ion batteries have always suffered from the drawback of
rapid capacity reduction and short lifespan, even though they can
have high energy density and retainability.1–3 Hence, with
outstanding cycling stability and long lifetime, supercapacitors
(SCs) based on the double-layer mechanism have become
a promising candidate in periodical energy storage, as they have
ultra-long service life and high reliability.4–7 However, poor
aDepartment of Mechanical Engineering, University of Delaware, Newark,DE, 19716, USA. E-mail: [email protected] System Design Laboratory (ISDL), Texas Analog Center ofExcellence (TxACE), The University of Texas at Dallas, Richardson,TX, 75080, USA. E-mail: [email protected]
Broader context
Electrochemical power devices with a long lifespan, long-term energ
periodic energy store/supply, especially for solar energy storage for s
Supercapacitors (SCs) are an electrochemical power source with a
rapid self-discharge (SDC) process remains a big challenge. In order
retain sufficient energy for a long enough time, we have systematical
(ACF) supercapacitors with two electrolytes. We have found that tw
two electrolyte systems. A dual-mechanism control model is propose
the supercapacitor using 1 M TEABF4/PC as electrolyte over differ
Significant energy retention (in excess of 70%) was then obtaine
understanding will provide guidance in designing next-generation
products.
2152 | Energy Environ. Sci., 2011, 4, 2152–2159
energy retention due to the rapid self-discharge (SDC) process is
one of the biggest challenges remaining for SCs. SC systems with
various configurations of electrodes and electrolytes may expe-
rience different SDC mechanisms. It is therefore necessary to
understand the fundamentals of SDC mechanisms in different
electrode/electrolyte systems, to better control and tailor the
SDC process. By doing this, applications of SCs could be
expanded: for example, they could be used in integrated circuits,
or they could replace the bulky (and heavier) lithium-ion
batteries used as solar-energy storage devices on space equip-
ment. However, in order to do this, the SDC process of SCs needs
to be controllable, in order that they can retain sufficient energy
for a long enough time period.
Different types of carbon materials (activated carbons,7,8 aero-
gels,9,10 xerogels,11,12 carbon nanotubes,13 and graphene14,15) have
y retention and great cycle stability are extremely important for
pace equipment and for power electronics in integrated circuits.
significant power density, but poor energy retention due to the
to understand the fundamentals of the SDC process and make it
ly investigated the SDC process of activated carbon fabric-based
o different control mechanisms govern the SDC processes in the
d for the first time which describes perfectly the SDC process of
ent charge current densities and at different SDC temperatures.
d in the ACF–TEABF4 system after 36 h. This fundamental
SCs, and should eventually lead to reliable commercial SC
This journal is ª The Royal Society of Chemistry 2011
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been studied for their electrochemical performance with aqueous
and aprotic electrolytes. Activated carbon fibers (ACFs), with
their high specific surface areas,16 controllable pore size distri-
bution17,18 and a wide temperature tolerance with organic elec-
trolytes,19,20 have been examined for application in double-layer
SCs, and were selected as the standard electrode materials for the
evaluation of the SDC processes in the current study.
For conventional dielectric capacitors, the potential driving
model with leakage over an ohmic resistance was well-developed
decades ago:21 V ¼ Vinitial e�t/RC (where V is potential difference,
i.e. the voltage of the capacitor, Vinitial is the voltage from which
SDC starts, R is the ohmic equivalent load resistance, and C is
the capacitance of the capacitor). It can be used to perfectly fit
the SDC process under only electric field driving, but without the
consideration and involvement of ions. Usually, the SDC process
in this type of capacitor can be completed in microseconds,
therefore allowing negligible energy retention in dielectric
capacitors. The time constant, s ¼ RC, is the intrinsic charac-
teristic of the dielectric capacitor, and determines its SDC rate.
t ¼ s corresponds to the moment that the voltage decreases to
37% of the initial voltage (as e�1 ¼ 0.37).
Introduction of a double layer and organic electrolytes has
radially enhanced the energy density of capacitors relative to
dielectric capacitors. Taking an average capacitance value of
25 mF cm�2 and a specific area of 1000 m2 g�1,21,22 the ideal
attainable energy at 1 V operating potential would be
250 kJ kg�1, which is comparable to the energy density of
lithium-ion batteries. However, the involvement of ions and
various electrode structures makes SDC behavior more difficult
to understand. Although previous studies have pointed out that
the SDC process of SCs cannot be entirely attributed to the
leakage resistance model as in dielectric capacitors,23 very few
analytical results or mechanistic models have been presented that
allow one to understand the phenomenon.
In this report, in order to have a better understanding of the
SDC process and the design of SCs with adequate energy
retainability, two types of SCs built with the ACF electrodes but
with different organic electrolytes – 1 M lithium hexa-
fluorophosphate in ethylene carbonate–diethyl carbonate
(LiPF6/EC–DEC) and 1 M tetraethyl ammonium tetra-
fluoroborate in propylene carbonate (TEABF4/PC) – were
systematically studied with various charge current densities (IC)
and at different temperatures. A dual-mechanism control model
is proposed for the first time, enabling us to better understand the
>70% energy retention of the ACF–TEABF4 system.
Fig. 1 SDC of ACF–LiPF6 at 25 �C after two-and-a-half cycles of
charge/discharge with 100 mA g�1.
2. Experimental
Two types of supercapacitors (SCs) were assembled in a standard
2032 coin cell configuration with ACF (Challenge Carbon
Technology Co., Taiwan) as electrodes, 1 M LiPF6/EC–DEC
(Ferro Corporation) and 1 M TEABF4 (Alfa-Aesar) dissolved in
battery-grade PC (Alfa-Aesar) solvent as electrolyte, respec-
tively. The ACF electrode is the same as we used in a previous
study on supercapacitors operable over a wide temperature
range.19 The ACF electrode has a pore size distributed around
10 �A (in the micropore region) and partly at 25 �A (in the meso-
pore region), and has an excellent BET surface area of
This journal is ª The Royal Society of Chemistry 2011
1340 m2 g�1. All of these structural features suggest that ACF
electrode would be a very good choice to build double-layer SCs.
The galvanostatic charge/discharge examinations were carried
out using anArbinbattery testing system.To certify the stability of
the initial voltage, first we carried out two-and-a-half charge/
discharge cycles with various charge current densities from
10mAg�1 to1000mAg�1 and from0 to2.0V, and thenallowed the
cell to experience the SDC process (Fig. 1). All the charging cycles
were carried out at 25 �C,while the SDCprocesses were conducted
at three different temperatures: �25 �C, 25 �C, and 75 �C,respectively. An alcohol based circulation cooling system (Poly-
Science) was used to conduct the low-temperature (�25 �C) SDC
measurements. The high-temperature (75 �C) SDCmeasurements
were conducted in a hot-box (Thermo, Electron Corporation) to
examine the temperature effects on the SDC process. Detailed
experimental parameters are summarized in Table 1.
3. Results and discussion
3.1 General SDC rule for both ACF-based SCs
By comparing the SDC processes of the two SCs under the same
temperature and charge current density IC (Fig. 2), we found that
ACF–TEABF4 SC not only displays a much lower discharge
rate, but also enters a discharge plateau which stays at a voltage
higher than 1.2 V for 48 h. The onset and the presence of the SDC
plateau reflects a low driving force from the potential, despite
appearing at a high voltage. This obvious difference indicates
that different SDCmechanisms operate in the two electrolytes, as
discussed below.
Capacitors in a charged condition are in a state of highly
positive free energy compared to the discharged or partially
charged states. Hence, virtual forces corresponding to certain
mechanisms exist and drive the SDC process.21 In our experi-
ments, the permitted high voltage window of organic electrolytes,
and glovebox operation, have eliminated the probability of
faradic reactions as demonstrated by the straight charge/
discharge lines (V vs. t) displayed in Fig. 1, which shows a pure
double layer behavior. Hence, the two possible driving forces
involved in the process might be: the potential differenceV by the
potential driving model lnV f t; and the ion concentration
variation vC/vx by the diffusion-control model V f t1/2.
Energy Environ. Sci., 2011, 4, 2152–2159 | 2153
Table 1 SDC experimental parameter set-up
Capacitor (electrode/electrolyte)
Charge current density IC/mA g�1 a
25 �C (RT) �25 �C 75 �C
ACF–1 M LiPF6/EC–DEC 1000, 500, 250, 100, 50, 25, 10 100 100ACF–1 M TEABF4/PC 500, 250, 100, 50, 25b 100 100
a All charged to 2.0 V at 25 �C, followed by SDC. b Unstable SDC under 1000 mA g�1 and 10 mA g�1.
Fig. 2 SDC of ACF–LiPF6 and ACF–TEABF4 at IC ¼ 100 mA g�1,
T ¼ 25 �C.
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More detailed SDC curves as a function of the charge current
density for the two SCs built with the same ACF as electrodes but
with different electrolytes are shown in Fig. 3(a) and 3(b). The
nominal voltage (here 2.0 V) should be replaced with the actual
voltage from which point the SDC process starts, i.e. the initial
voltage (Vinitial), because of an internal resistance (IR) drop from
2.0 V at the commencement of the SDC process. As can be seen
from Fig. 3 and the insets, the initial voltage, Vinitial, increases
with decreasing charge current density IC, and varies depending
on the type of electrolyte being used.
A near-zero to fairly large IR drop with increasing IC indicates
a strong influence of IC on the SC pre-discharge states, i.e. Vinitial.
According to the V¼Q/C relation between voltageV and charge
Q in capacitors, an IR drop in voltage should be ascribed to the
variation in the quantity of ions accumulated within the double
layers. A lower IC allows more time for ions to distribute and
form a more stable double-layer (DL) structure than when the
ions stack together quickly to form an unstable state at high IC.
Therefore, as shown in Fig. 3, as the DL structure becomes more
stable with decreasing IC, the corresponding IR drop decreases
for both SCs.
The initial voltage shows an approximate linear behavior with
IC in both SC systems; however, their SDC curves differ from
each other, indicating a possible change in the mechanism of
SDC control.
Fig. 3 SDC curves of (a) ACF–LiPF6 and (b) ACF–TEABF4 systems
under different charge current densities IC, at T ¼ 25 �C; insets in (a) and
(b) are Vinitial vs. IC.
3.2 SDC processes of the ACF–1 M LiPF6/EC–DEC system
3.2.1 SDC mechanism of ACF–LiPF6. By redrawing each
SDC curve by setting t to t1/2, shown in Fig. 4(a), within the
voltage range down to 37% of the initial voltage, we find that
2154 | Energy Environ. Sci., 2011, 4, 2152–2159
almost all the curves display a linear relation between V and t1/2.
This linear relation is confirmed by performing fittings (Fig. 4(b))
on the original data curves. According to the diffusion control
model V ¼ Vinitial � mt1/2, the high correlation coefficient R2 (all
higher than 0.99) resulting from the fittings shows that the
diffusion control model can explain the SDC process in the
ACF–LiPF6 system.
The value of ‘‘m’’, which is the slope of the fitting curves, also
called the diffusion parameter,21,23 is shown in Fig. 4(c), together
with Vinitial. It can be seen in the figure that the initial voltage
decreased by 61.7% when IC increased from 10 to 1000 mA g�1,
and m decreases in a similar fashion. Since SDC in ACF–LiPF6
SC is under diffusion control (as confirmed by the fitting), the
corresponding driving force comes from the variation in
This journal is ª The Royal Society of Chemistry 2011
Fig. 4 Diffusion control simulation of ACF–LiPF6 SDC: (a) SDC curved by (V � t1/2); (b) Comparison between the original experiment data (black
lines) and the diffusion-control simulation (blue lines) (1000, 100 and 10 mA g�1 are shown here); (c) Initial voltage and diffusion parameter as functions
of charge current density IC.
Fig. 5 Variation of the energy barrier Eb at different charge current densities.
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Fig. 6 ACF–TEABF4 simulation by: (a) (Vf t1/2), (b) (lnVf t); and by
the proposed dual-mechanism control model; (c) IC ¼ 25 mA g�1 and (d)
IC ¼ 500 mA g�1. Black curve: original; Red curve: lnV f t; Blue curve:
Vf t1/2. Simulations were performed for all charge current densities; only
25 mA g�1 and 500 mA g�1 are shown here, as examples.
2156 | Energy Environ. Sci., 2011, 4, 2152–2159
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concentration of the ions (vC/vx), which is proportional to V
because of Q ¼ CV. Hence, as V decreases, m decreases
accordingly.
3.2.2 Deviation at the beginning of SDC with a lower IC. At
the beginning of the SDC process, a small deviation was
observed at small IC, comparing the original experimental curve
with the fitted one (Fig. 4(b), shadowed area), implying a rela-
tively unusual situation at the beginning of the SDC process.
Similarly to the effects of low IC upon the IR drop, this slowness
of ion discharging from the double layer also results from the
more equilibriated state of ions at the electrode–electrolyte
interfaces when charged with a lower IC. The lower IC (and the
correspondingly more stable ion distribution) lead to not only
the small IR drop (i.e. high Vinitial), but also the formation of
a higher energy barrier Eb, which prevents ions from moving
from the established double layer despite the correspondingly
higherVinitial, as illustrated in Fig. 5. Eb increases with decreasing
IC, as confirmed by the increasing trend of deviation, as seen in
Fig. 4(a) and 4(b).
3.3 SDC process of the ACF–1 M TEABF4/PC system
3.3.1 SDC mechanism of ACF–TEABF4. For the SDC
process of the ACF–TEABF4 system, it is hard to understand the
behavior if only a single control mode is considered. As shown in
Fig. 6(a) and 6(b) with the charge current densities of 25 mA g�1
and 500 mA g�1 as examples, neither the diffusion-control model
(Vf t1/2) nor the potential drivingmodel (lnVf t), fitwell with the
experimental data, respectively. However, the fact that the lower
portion overlaps between the original data and the simulation
curves derived from the diffusion controlmodel (Vf t1/2) in Fig. 6
(a) implies that a transition occurs, with diffusion control domi-
nating as the SDC process reaches a certain point. Thus, we
considered a possible dual-mechanism (DM)model by separating
the SDC process of the ACF–TEABF4 system into two parts, and
fitting each of themwith the potential drivingmodel (lnVf t) and
the diffusion control model (Vf t1/2), respectively.
As seen in Fig. 6(c) and 6(d), the red curve represents the fitting
from the potential driving model (lnV f t) and the blue curve
from the diffusion control model (V f t1/2). The nearly perfect
matches demonstrate that SCs built with ACF and TEABF4/PC
experienced a transition of governing mechanisms, from the
potential driving model to the diffusion control model during the
SDC process – thus a dual-mechanism (DM) control model is
proposed.
The ‘‘cut-off point’’ VC corresponds to the voltage around
which the mechanism transition occurred. With decreasing IC, an
increase ofVC was found based on the DMmodel proposed here.
Based on the knowledge that ions can discharge/diffuse only
when the SDC driving forces outstrips the drag, the DM model
and the transition of control models relies on the competition
between the two driving forces corresponding to the two control
models.
As is well known, the SDC process is fundamentally a direc-
tional migration of ions across opposing electrodes. For the more
stably-arranged ions, a larger driving force will be needed to
enforce ion migration. This can be interpreted as follows: at the
beginning of an SDC process, as demonstrated by the DMmodel
This journal is ª The Royal Society of Chemistry 2011
Fig. 7 Absolute voltage drop and drop percentage of ACF–TEABF4 with SDC for (a) 12 h, (b) 24 h, (c) 36 h. (d) Percentage drop every 12 h.
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fitting, the corresponding driving force is scaled with the poten-
tial difference of the SC as measured. Due to the equilibrium
distribution of ions under a low IC, a stronger electric driving
force, scaled by the large potential difference, would be required
Fig. 8 SDC behavior at different temperatures with charge current density
TEABF4 at �25 �C, 25 �C, 75 �C; (c) Simulation by the diffusion control mod
mechanism model for ACF–TEABF4 SDC at �25 �C and 75 �C.
This journal is ª The Royal Society of Chemistry 2011
at the initial part of SDC dominated by potential driving model.
Thus, the potential driving model will lose control at a relatively
high voltage when subjected to a low IC, which is shown as an
increase of VC with decreasing IC according to the DM analysis.
of IC ¼ 100 mA g�1: (a) ACF–LiPF6 at �25 �C, 25 �C, 75 �C; (b) ACF–
el for ACF–LiPF6 SDC at �25 �C and 75 �C; (d) Simulation by the dual-
Energy Environ. Sci., 2011, 4, 2152–2159 | 2157
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3.3.2 The slow SDC process and explanation using the dual-
mechanism model. For the ACF–TEABF4 SCs, the most signif-
icant practical feature is their great energy retention as shown in
Fig. 7; more than 70% energy was preserved after 36 h SDC, even
when charged with a high current density of 500 mA g�1 (Fig. 7
(a–c)). This remarkably high energy retention makes the appli-
cations of SCs in periodic energy storage promising and realistic.
It is interesting to note that an extreme point at IC¼ 100mAg�1
was observed at all three voltage drop percentage lines (Fig. 7),
suggesting that the fastest SDC process is at this middle point.
With the DM model, this phenomenon can be explained as the
combined effects of the two mechanisms:
(1) The beginning of the SDC process is dominated by the
potential driving model (red curves in Fig. 6(c and d)), and the
corresponding driving force results from the electric field scaled
by the potential difference V. Hence, charging with a lower ICwill give a higher initial voltage, and a faster SDC process. As
long as the SDC is driven by the electric field and scaled by V, the
percentage voltage drop should increase with decreasing IC.
(2) The large (up to 15%) voltage drop in the first 12 h,
compared with the subsequent small voltage drops (only �5%
and 3%) (Fig. 7(d)), indicates that the SDC process becomes
much slower as the diffusion control model gradually takes
control. Thus, the earlier the diffusion model takes control, the
slower the SDC process becomes.
Combining the two effects above and considering the increase
of VC when the diffusion model takes control at small IC, it
reaches a maximum at a middle point.
3.3.3 Temperature effect on the SDC process. Environmental
temperature has a significant effect on the SDC process for both
SCs, the SDC process is faster at a high temperature (75 �C) andslower at a lower temperature (�25 �C), as can be seen from
Fig. 8(a and b). However, the SDC mechanisms applied at room
temperature are still valid within the wide temperature window
for both SC systems. This conclusion is based on the excellent
curve fittings in the two SC systems, i.e. the diffusion-control
model applied to the ACF–LiPF6/EC–DEC system as shown
in Fig. 8(c), and the DM-control model applied to the
ACF–TEABF4/PC system as shown in Fig. 8(d).
It should be noted that the blue line representing the diffusion
control begins at a lower VC at 75 �C and a higher VC at �25 �C,as shown in Fig. 8(d). The effects of elevating the temperature to
75 �C include decreasing electrolyte viscosity and increasing the
thermal energy of ions, which means that the drag force would be
lower than at 25 �C. Thus, the potential driving mechanism can
be sustained to a lower VC at 75 �C, whereas, at �25 �C, the
Table 2 Initial voltages and capacitances of the two SCs
Charge curr
25
ACF–1 M LiPF6/EC–DEC Vinitial/V 1.97C/F g�1 66.2
ACF–1 M TEABF4/PC Vinitial/V 1.96C/F g�1 37.7
C: specific capacitance.
2158 | Energy Environ. Sci., 2011, 4, 2152–2159
electrolyte is more viscous and the ions move less easily due to
their lower thermal energy, so the potential-driven mechanism
loses control at a higher VC – exactly the situation shown in
Fig. 8(d).
Moreover, a wide voltage fluctuation was observed in ACF–
TEABF4 SC at �25 �C (Fig. 8(b), blue line), indicating that both
TEA+ and BF4� ions in PC solvent are difficult to move at
�25 �C. The absence of this phenomenon in the ACF–LiPF6 SC
provides evidence of a difference between the two electrolytes,
such as the ion mobility difference. Hence, the different prop-
erties of the two electrolytes be the main reason for the different
SDC mechanisms operating, which is surely worthy further
study.
SDC is a spontaneous and self-driving process. In capacitor
systems, where no chemical reactions take place, such as the two
SCs in our experiments, the driving forces can be ascribed to only
two factors: the potential field V and concentration variation
vC/vx; one leads to SDC by a potential-driven mechanism and
the other by a diffusion-control mechanism. Which one takes
control depends on the outcome of competition between the two
mechanisms. For the ACF–LiPF6 SC, the diffusion takes control
up to the voltage reaches 37% of the initial value; the driving
force from vC/vx outweighs the potential driving force to a great
extent for this SC, and only diffusion-control operates. In
contrast, in the ACF–TEABF4 SC, even though the initial
voltage decreases slightly compared to ACF–LiPF6 (Table 2), its
capacitance decreases by a larger percentage. Because Q ¼ CV,
the decrease in capacitance means that fewer ions accumulate
within the double layers, i.e. there is a lower concentration
variation. Thus, we may assume that in the capacitor system of
ACF–TEABF4, both V and vC/vx decrease, but with vC/vx
decreasing more, thus SDC of ACF–TEABF4 first is dominated
by the potential driving mechanism then switched to the diffu-
sion-control mechanism. Based on the discussion and assump-
tion above, we may expect that potential-driven SDC is likely to
occur in SCs with a high voltage and a low capacitance, and high-
energy retention should be expected from SCs with a low ion
mobility controlled by diffusion.
4. Conclusions
In summary, we have demonstrated that different electrode/
electrolyte configurations are responsible for different SDC
processes. The diffusion control model governs the SDC process
in the ACF–LiPF6/EC–DEC system, while the dual-mechanism
control model controls the SDC process in the ACF–TEABF4/
PC system. It is also evident that both models are suitable under
ent density IC/mA g�1
50 100 250 500
1.95 1.90 1.77 1.5952.2 43.2 33.7 22.51.92 1.85 1.44 1.2835.7 31.5 14.3 8.3
This journal is ª The Royal Society of Chemistry 2011
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different charge current densities and extendable to a wide
discharge temperature window. Most importantly, an excellent
energy retention capability can be achieved by tailoring the
electrode/electrolyte configuration – more than 70% energy
retention was observed after 36 h SDC in the ACF–TEABF4/PC
system, suggesting that SCs are very promising candidates for
periodic energy storage/supply that require high reliability and
long lifetime.
Acknowledgements
This work is supported in part by the US National Science
Foundation (NSF) under the Contracts CMMI-0925678 and
CMMI-0926093, and in part by the Semiconductor Research
Corporation (SRC) under Contract 2009-RJ-2020G.
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