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Submitted to Scientific Reports
Kirigami-based stretchable lithium-ion batteries
Zeming Song1#, Xu Wang1#, Cheng Lv1, Yonghao An1, Mengbing Liang2, Teng Ma1, David He1,2,
Ying-Jie Zheng3, Shi-Qing Huang3, Hongyu Yu4,5, and Hanqing Jiang1,*
1School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ
85287, USA
2Desert Vista High School, Phoenix, AZ 85048, USA
3MOE Key Lab of Disaster Forecast and Control in Engineering, Jinan University, Guangzhou
510632, China
4School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ
85287, USA
5School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287, USA
#These authors contribute equally.
*Email: [email protected]
Keywords: Lithium-ion Batteries, Kirigami, Stretchable, Samsung Gear 2
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Abstract:
We have produced stretchable lithium-ion batteries (LIBs) using the concept of kirigami,
i.e., a combination of folding and cutting. The designated kirigami patterns have been
discovered and implemented to achieve great stretchability (over 150%) to LIBs that are
produced by standardized battery manufacturing. It is shown that fracture due to cutting and
folding is suppressed by plastic rolling, which provides kirigami LIBs excellent electrochemical
and mechanical characteristics. The kirigami LIBs have demonstrated the capability to be
integrated and power a smart watch, which may disruptively impact the field of wearable
electronics by offering extra physical and functionality design spaces.
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Introduction
Energy storage devices, such as supercapacitors and lithium-ion batteries (LIBs) that are
able to sustain large strains (much greater than 1%) under complex deformations (for instance,
bending, tension/compression, and torsion) are indispensable components for flexible,
stretchable electronics, and recently emerging wearable electronics, such as flexible displays1, 2, 3,
4, stretchable circuits5, hemispherical electronic eyes6, and epidermal electronics7. Various
approaches have been employed to achieve flexible and stretchable energy storage devices, such
as thin film based bendable supercapacitors8, 9, 10, 11 and batteries10, 12, 13, 14, 15, 16, buckling-based
stretchable supercapacitors17, 18, and island-serpentine-based stretchable LIBs19. Recently, an
origami-based approach was adopted to develop highly foldable LIBs, where standard LIBs were
produced followed by designated origami folding20. The folding endows the origami LIB with
a high level of foldability by changing the LIB from a planar state to a folded state. However,
the previously developed origami-based foldable devices20, 21 have two disadvantages. First,
their foldability is limited from the folded state to the planar state. Although it can be tuned by
different folding patterns, the same constraint is still prescribed by the planar state. Second, the
folded state involves uneven surfaces, which introduces inconvenience when integrating with
planar systems, though this issue can be somewhat circumvented. The approach introduced
here combines folding and cutting, by the name of kirigami, to define patterns that form an even
surface after stretching and the stretchability is not limited by the planar state. The folding and
cutting lead to high level of stretchability through a new mechanism, "plastic rolling", which has
not yet been discovered and utilized in the stretchable electronics/systems. The LIBs were
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produced by the standard slurry coating (using graphite as an anode and LiCoO2 as a cathode)
and packaging procedure, followed by a designated folding and cutting procedure to achieve a
particular kirigami pattern. Kirigami batteries are also compatible with emerging battery
fabrication skills such as direct printing or painting22. Following kirigami patterns, the printed or
painted kirigami batteries is expected to perform similarly as batteries fabricated in conventional
way. Over 150% stretchability has been achieved and the produced kirigami LIBs have
demonstrated the ability to power a Samsung Gear 2 smart watch, which shows the potential
applications of this approach. The kirigami-based methodology can be readily expanded to
other applications to develop highly stretchable devices and thus deeply and broadly impact the
field of stretchable and wearable electronics.
Results
Battery design using Kirigami patterns. Three kirigami patterns are utilized, as illustrated in
Fig. 1, with (a) a zigzag-cut pattern, (b) a cut-N-twist pattern, and (c) a cut-N-shear pattern.
The zigzag-cut pattern (Fig. 1a) represents one of the most commonly seen kirigami patterns and
is produced by cutting a folded stack of foil asymmetrically between the neighboring creases,
which creates zigzag-liked cuttings in the longitudinal direction. The zigzag pattern can be
stretched beyond its length in the planar state, which is the advantage of kirigami. To
accommodate stretching, the out-of-plane deformation (or equivalently, buckling) occurs at the
vicinity of cuts. The level of stretchability depends on the length of the cut and is a function of
buckling amplitude. To eliminate the out-of-plane deformation, one of the advantages of
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kirigami compared with the origami pattern, the cut-N-twist pattern (Fig. 1b) is utilized, in which
a folded stack of foil is symmetrically cut at all creases, and then unfolded to a planar state,
followed by twisting at the two ends. The twisted structure is shown in the bottom panel of Fig.
1b and analogous to a twisted telephone cord. This pattern represents a locked structure in the
sense that the out-of-plane deformation, induced by stretching, is constrained and rotation occurs
at the cuts to accommodate stretching. The packing density of cut-N-twist pattern is defined by
the width of each face. To increase the packing density, the cut-N-shear pattern (Fig. 1c) is
introduced, where folding is employed after symmetric cutting and then the folded structure is
subjected to shear, thus the packing density doubles compared with that for the cut-N-twist
pattern. The stretching is also achieved by the rotations of the cuts and no out-of-plane
deformation is involved.
Now we demonstrate kirigami LIBs, specifically the LIBs using cut-N-twist here and
cut-N-shear and zigzag-cut patterns in the Supporting Information. Conventional materials and
approaches of LIBs preparation were used, with graphite (Fisher Scientific Inc.) and LiCoO2
(LCO, MTI Corp.) as the anode and cathode active materials, respectively. Conventional
slurries of these active materials were prepared and used to coat the current collectors, where
copper (Cu) and aluminum (Al) served as the anode and cathode current collectors, respectively.
The Cu and Al current collectors were first cut to the three patterns (Fig. 1) based on the specific
geometries as provided in the Supplementary Fig. S1, followed by slurry coating. To prepare
packaging, polypropylene (Celgard 2500) as separator and aluminized polyethylene (PE)
(Sigma-Aldrich) as packaging materials were also cut using the same kirigami pattern; thus all
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the layers of a LIB have the same pattern. Then these layers were perfectly laminated in the
order of packaging material, cathode electrode, separator, anode electrode, and packaging
material (Supplementary Fig. S2), and delivered to an Argon-filled glovebox for packaging.
The impulse sealer was used to seal the sides of the each cell (Supplementary Fig. S1) except one
side for the electrolyte (1 M LiPF6 in EC:DMC:DEC (1:1:1), MTI Corp.) injection, followed by
sealing the last side of the battery cell. The key to achieve excellent packaging is that the
cutting of all layers of a battery cell must be uniform and the alignment must be perfect. We
have designed a customized puncher for cutting. The cutting quality can be significantly
improved by using laser cutting in the future.
Electrochemical and mechanical characteristics. Figure 2 shows electrochemical and
mechanical characterization results for LIBs using cut-N-twist pattern. Using the most compact
state (Fig. 2a) as the reference, Fig. 2b, displaying the LIB at its most stretched state, shows that
the stretchability of a kirigami LIB is over 100%. It should be noted that there is no significant
change on the thickness of this LIB between the most compact state (h = 1.31 mm) and at the
most stretched state (h = 1.07 mm). Figure 2c shows the electrochemical cycling results of a
kirigami LIB at its most compact state (for the 1st to 5th cycles), followed by that at its most
stretched state (for the 6th to 10th cycles), then that at its most compact state again (for the 11th to
15th cycles), and then that at its most stretched state again (for the 16th to 20th cycles), and finally
that at its most stretched state (for the 21st to 100th cycles) under C/3 charge/discharge rate.
Well-defined plateaus at around 3.7V are observed along with fairly stable charge/discharge
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behaviors under compact and stretched states. The present mass loading (see caption of Fig. 2c)
gives this kirigami LIB 30 mAh energy capacity. Figure 2d shows reasonable cyclic stability of
the LIBs up to 100 cycles with over 85% capacity retention and 99.8% Coulombic efficiency.
It should be emphasized that this result represents the stability of this kirigami LIB at mixed
states, i.e., both compact and stretched states. Figure 2e shows the rate performance of this
kirigami battery when the charge/discharge rate varied in the sequence of C/3, C/2, C and C/3
again at both compact and stretched state. When discharge rates increase, as expected, the
capacity decreases from 29.3 mAh for C/3 rate to 26.5 mAh for C/2 rate, and 21.4 mAh for
discharge rate C. However, the capacity recovered to the 27.6 mAh when the discharge rate
resumed to C/3 after 30 cycles charge/discharge at the both compact the stretched state under
varies C-rates, which indicates great rate performance of this kirigami battery. Figure 2f
provides the results for electrochemical impedance spectroscopy (EIS) studies during the first
discharge cycle at the most compact state before stretching and stretched state after 100 cycles of
mechanical stretching. No significant changes in the impedance were found.
The mechanical characteristics of the fully charged kirigami LIB using cut-N-twist are
then examined. As shown in Fig. 2g, at different stretchability, the output voltage remained
steady at 3.83 V. Supplementary Movie S1 shows the dynamic process of this deformation.
Figure 2h shows the maximum output power of the kirigami LIB as a function of stretchability,
stretche , under different cycles of stretching. Here the internal resistance of the battery was
measured to be about 1.8 Ω. Over 3,000 stretching cycles and a stretchability stretche of up to
90%, it is found that the output power is stable and shows no noticeable decay. The maximum
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output power is 4.1 W and is sufficient to operate commercial light-emitting diodes (LEDs). As
shown in the Supporting Information (Supplementary Figs. S3 and Supplementary Movie S1),
LEDs driven by this kirigami LIB do not show noticeable dimming upon cyclic stretching for a
few hours. Ultimate tensile strength of LIBs using cut-N-twist pattern is 13.3 MPa with load
frame Instron-Model 4411.
Figures 2i and 2j show the scanning electron micrographs (SEMs) for the anode current
collectors (e.g., Cu foil) at the cuts before charging, and after discharge and 100 cycles of
mechanical deformation. The similar SEM images are given for the cathode current collectors
(e.g., Al foils) in Figs. 2k and 2l. There are no cracks after cyclic mechanical stretching, which
contribute to the robust electrochemical and mechanical characterizations.
Numerical calculation of crack and plastic behavior. This phenomenon is consistent with the
theoretical analysis and a simplified model is shown in Fig. 3a, where two pre-existing cracks are
presumably caused by initial folding and/or cutting and located at the present positions when a
pair of concentrated moment M is applied at the end of the strip with length L and width H.
The concentrated moment M is used to characterize the applied stretching deformation that
causes bending about the folding creases. Angle θ is used to denote the relative positions of
two strips with θ = 0 for the initial folded position. When the moment M is applied, there exist
two modes of deformation. The first mode causes the growth of the pre-existing cracks from a
to a + ∆a, while maintaining the angle θ unchanged, which refers as “crack growth”. The
second mode leads to plastic deformation of the thin foil at the vicinity of the fold by altering θ
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to θ + ∆θ, which is referred to as “plastic rolling”.
The critical condition for “crack growth” is given by the Griffith's criterion. The driving
force, or the release of the elastic energy due to the propagation of cracks, 2 /A a Eσ , equates
the resistance of the crack growth, defined by 2g. Here A is a non-dimensional geometrical
factor that depends on angle θ, i.e., ( )A A θ= ; σ is the normal traction applied on the crack
surface and related to the moment M by 26 /M Hσ = ; E is the elastic modulus; and g [unit:
Newton/meter] is the surface energy. Thus the critical moment for "crack growth" is given by
( )crack growth 2 / 2 / 3crM H E Aag= . For “plastic rolling”, the rate of energy dissipation due to the
plastic deformation during the rolling about the creases provides the resistance, given by
( )2 21 tan / 4Hβ θ+ ; and the driving force is the rate of release of potential energy due to the
increase of θ, given by M/2. Here β [unit: Newton/meter2] is the dissipated energy per unit area
due to plastic rolling, which is related to the extent of the plastic deformation (i.e., hard crease
versus soft crease) and can be associated with the yield stress of plastic materials. The critical
condition for "plastic rolling" is given by ( )plastic rolling 2 21 tan / 2crM Hβ θ= + . When M is
applied, the smaller one between crack growthcrM and plastic rolling
crM is activated as the critical
moment during deformation, which leads to either “crack growth” mode, when
crack growth plastic rollingcr crM M< , or “plastic rolling” mode, when plastic rolling crack growth
cr crM M< .
Finite element simulations were conducted using commercial package ABAQUS to
analyze these two deformation modes. Because in a LIB, Al foil tends to crack due to its lowest
fracture toughness, the material parameters of Al were used in the analysis, with the surface
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energy g 0.868 N/m , elastic modulus E 69 GPa, and Poisson’s ratio ν 0.3323, 24. The
geometry is H = 3 mm, and L = 10 mm to match with the experiments. The pre-existing crack
is assumed small as compared with the width H. β, dissipated plastic energy per area, is
calculated by folding a 10 µm-thick Al foil (the same thickness as that used in LIB) with
different folding radius via finite element simulations. Details of this analysis are given in the
Supporting Information.
Figure 3b shows the “safe zone” (i.e., crack growth plastic rolling/ 1cr crM M > ) and the “fracture zone”
(i.e., crack growth plastic rolling/ 1cr crM M < ) as a function of θ for various a and β. For example, a = 0.03
mm (i.e., 1% of H, the width of strip) and β = 20 MPa, corresponding in creating a sharp crease
of a 10 µm-thick Al foil with bending diameter of 70 µm (see Supplementary Fig. S9), "safe
mode" is activated for all angle of θ. The results also show that for a larger β (or equivalently
shaper crease) or a (i.e., larger initial crack), "fracture mode" tends to occur. It is important to
note from the Supplementary Fig. S9 that for the present battery setup (i.e., bending diameter
ranging from 500 µm to 800 µm), β is one the order of 1 MPa, which indicates that it is always
the scenario to activate the "safe mode". Thus this analysis verifies that the robust
electrochemical and mechanical performance of the kirigami LIB is due to the activated "safe
mode".
LIBs using the other two kirigami patterns were also produced and characterized. Very
similar electrochemical and mechanical characteristics were exhibited during testing (Detailed
results provided in Supporting Information). Supplementary Figs. S4 and S5 are for the
characterizations of LIBs using the cut-N-shear and zigzag-cut patterns, respectively. The
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dynamic stretching deformations for LIBs using cut-N-shear and zigzag-cut patterns are shown
in the Supplementary Movies S2 and S3, respectively. It is worth mentioning that the LIB
using cut-N-shear pattern has doubled the energy capacity compared to the cut-N-twist pattern
for a given length, and its stretchability is up to 150%.
Connecting kirigami battery with Samsung Gear 2 smart watch. We demonstrated that the
stretchable kirigami LIB is able to power a Samsung Gear 2 smart watch. The original LIB
with energy capacity 300 mAh was removed from the Samsung Gear 2 and a kirigami LIB using
cut-N-twist pattern was connected to the device. The same geometry as that in Fig. 2 was used.
The mass loading for active materials are 0.26 g for graphite, 0.65 g for LCO, which gives the
energy capacity 80 mAh. At the compact state, the kirigami LIB is 51.3 mm in length, 27 mm
in width, and 2.6 mm in thickness. The produced kirigami LIB was sewn between two elastic
bands at its two ends and wrapped around the wrist, allowing the elastic bands to function as an
elastic watch strap. By sewing the kirigami LIB to the elastic band at the two ends, the LIB can
be stretched and contracted, driven by the elasticity of the band. The Supplementary Movie S4
shows a series dynamic deformation on the elastic "watch strap" and thus on the kirigami LIB,
and some snapshots are provided in Fig. 4. Figure 4a shows that when the elastic band and the
kirigami LIB were at their most compact states, the Samsung Gear 2 was just turned on. Then,
while the elastic band was stretched from the wrist to the upper arm, the Samsung Gear 2 was
working normally (Fig. 4b). It is estimated from the circumferences of the wrist and upper arm,
the kirigami LIB was subjected to a strain of 30%, lower than its full stretchability. While the
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elbow bent (Fig. 4c) and straightened (Fig. 4d), the smart watch was able to maintain normal
functionality, and even display a video. During bending and straightening of the elbow, the
biceps introduced an additional 15% strain to the kirigami LIB. Finally, the kirigami LIB was
removed from the elastic bands and stretched directly while powering the smart watch (Figs. 4e
and 4f).
To further evaluate the performance of the kirigami battery, standby and calling tests of
the smart watch powered by the kirigami battery were carried out. For a fully charged kirigami
battery with 80 mAh capacity that was connected with a Samsung Gear 2 smart watch, the
standby time was measured to be 24.5 hours. When the smart watch was paired with a
Samsung Galaxy S5 cell phone with a Bluetooth connection when they were separated by 30 cm,
the smart watch was able to make calls through the Bluetooth connection. The calling time was
measured to be 90 minutes. To simulate the standby and calling tests, quantitative discharge
characterizations were also conducted by applying the corresponding constant discharge currents
for standby (2.9 mA) and calling (48 mA) using an Arbin electrochemical workstation. The
stopping voltage of the smart watch was measured to be 3.6 V. Details of the measurement of
the discharge currents and stopping voltage are provided in the Supplementary Information. As
shown in Fig. 4g for the simulated standby test, the calling time (when the voltage drops to the
stopping voltage 3.6 V) is 25.8 hours, which is consistent with the direct test. For the simulated
calling test (Fig. 4h), the calling time is 90 minutes, which perfectly matches the direct test. It
should be noticed that the discharge currents for standby and calling are relatively low C-rate for
the present kirigami battery with 80 mAh capacity, specifically discharge current for standby 2.9
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mA ≈ C/30 and that for calling 48 mA ≈ C/2. Given the stable rate performance as shown in
Fig. 2d (though for a kirigami battery with different capacity), a stable cyclic charge/discharge
performance can be expected. These experiments demonstrate the promises of using a kirigami
LIB to replace present rigid and bulky batteries and to power a commercial smart watch, which
has been a bottle-neck in developing compact wearable devices. It is worth mentioning that if
the kirigami LIB is scaled up to cover the entire area of the elastic band (25 cm in length, 3 cm in
width) with a battery thickness of 0.3 cm, the energy capacity is about 700 mAh, which
significantly exceeds the current LIB used in most smart watches, and the energy density is about
160 Wh/Kg, which is comparable to the current LIB used in smart watches or smart phones.
By using the space of watch strap instead of using the limited space of watch body, the kirigami
battery may disruptively impact the field of wearable electronics by offering extra physical and
functional design space. Furthermore, to test the compatibility of the Kirigami battery
integrated with real watchband, a Cut-N-Twist battery was embedded in a watchband made of
Sorta-Clear 40 (Smooth-On, Inc.). Movie S5 shows the watchband integrated with Kirigami
battery powering the Samsung Gear 2.
Thermal test of kirigami battery and Samsung Gear 2 battery. The Kirigami battery is thin
film based. It is has much higher surface-to-volume ratio than bulky battery, which is beneficial
for heat radiation. The thermal test of Kirigami battery and Samsung Gear 2 bulky battery were
conducted. Figure S10 and S11 illustrates the test and the result. In the test both batteries
discharged at 48mA for one hour. Obvious temperature rise was observed for the Gear 2 bulky
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battery, while the Kirigami battery was consistent with the ambient temperature during the
discharge period.
Discussion
The demonstration of stretchable kirigami LIBs in a Samsung smart watch only
represents one application of this type of stretchable energy sources that fully utilize the
mainstream manufacturing capability. Other applications may include smart bracelets and
smart headbands among many others. It is expected that the kirigami LIBs are able to resolve
one of the bottlenecks in the development of wearable devices by providing a scalable solution
for a stretchable energy source to profoundly change the form factor. The methodology
involved in kirigami-based approach, i.e., competing mechanisms between “crack growth” and
“plastic rolling” also provide a much broader spectrum of employing the concept of kirigami to
other fields, such as in microelectromechanical systems (MEMS) where robust interconnects can
be placed at the cut/fold locations and the functional devices are fabricated on the rigid faces,
which leads to stretchable devices using standardized procedures. These areas appear
promising for further research.
Methods
Fabrication of kirigami lithium-ion batteries. The multilayer stacking structures as shown in
Supplementary Fig. S2 were used to fabricate the lithium-ion batteries (LIBs), where graphite
(Fisher Scientific Inc.) and LiCoO2 (LCO, MTI Corp. ) as active materials for anode and cathode
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electrodes, respectively; copper (Cu) and aluminum (Al) as the anode and cathode current
collectors, respectively; polypropylene (Celgard 2500) as separator, 1 M LiPF6 in
EC:DMC:DEC (1:1:1) as electrolyte, and the aluminized polyethylene (PE) (Sigma-Aldrich) was
the packaging material. Cathode slurries were prepared by mixing the LCO, PVDF (MTI
Corp.), Carbon black (Super C45) and N-Methyl-2-pyrrolidone solvent (CreoSalus) with a ratio
of 8:1:1:5 by weight. Then the slurry was uniformly coated on a 10 µm-thick Al foil (Reynolds
Wrap), and then dried on a hot plate at 130 oC for 5 hours in ambient environment. Anode
slurries were prepared by mixing the graphite (Fisher Scientific), carbon black (Super C45),
Carboxymethyl cellulose (Fisher Scientific), Styrene Butadiene Rubber (Fisher Scientific) and
DI water with a ratio of 95:2.5:1.25:1.25:200 by weight. After that the slurry was uniformly
coated on a 20 µm-thick Cu foil (CF-T8G-UN, Pred Materials International, Inc.), and then dried
on a hot plate at 120 oC for 5 hours in ambient environment. A mass ratio for graphite:LCO
was around 1:2.5. Finally the anode and cathode electrodes were pressed to make condensed
electrodes. The multilayer structure shown in Supplementary Fig. S2 was subjected to folding
and cutting following the kirigami patterns given by Supplementary Fig. S1.
Electrochemical characterization. An Arbin electrochemical workstation with a cutoff voltage
of 2.5–4.2 V at room temperature was used to conduct cyclic galvanostatic charge and discharge
of the kirigami batteries at the most compact and the stretched states. The maximum output
power of the fully charged battery was calculated by 2
2 i
VR
, where V is the open circuit voltage
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and Ri is the internal resistance as a function of system-level mechanical strain and cycles of
mechanical loading. The values of voltage of the kirigami batteries were measured using a
voltmeter. The electrochemical impedance spectroscopy (EIS) characterizations were
performed by applying a small perturbation voltage of 5 mV in the frequency range of 0.1 Hz to
100 kHz during the first discharge cycle before and after stretching, using a Gamry Echem
Analyst. The analysis of the impedance spectra was conducted using equivalent circuit
software provided by the manufacturer.
Measurement of the discharge currents for standby and calling of the Samsung Gear 2
watch. The discharge current for standby was measured to be about 2.9 mA when the smart
watch was tuned on and remained at the standby mode as the kirigami battery was connected.
To measure the discharge current for calling, the Samsung Gear 2 watch was paired with a
Samsung Galaxy S5 cell phone with a Bluetooth connection when they were separated by 30 cm.
A phone call was made via the cell phone and accepted from the smart watch end. The
discharge current for calling was then measured to be about 48 mA.
Measurement of the stopping voltage of the Samsung Gear 2 watch. After the smart watch
stopped working, the kirigami battery was disconnected from the watch. The voltage leftover
in the battery was then measured. The stopping voltages of both standby and calling test were
measured to be about 3.6V.
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Measurement of the Kirigami battery and Samsung Gear 2 battery temperature. The
temperature was measured by thermal couple. Two thermal couples were used during one
measurement. One was attached to the battery. The other was attached to the testing table
(ambient). Data was collected every 3 miniutes.
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References
1. Chen, Y. et al. Flexible active-matrix electronic ink display. Nature 423, 136-136 (2003). 2. Gelinck, G. H. et al. Flexible active-matrix displays and shift registers based on solution-processed organic
transistors. Nat. Mater. 3, 106-110 (2004). 3. Kim, S. et al. Low-Power Flexible Organic Light-Emitting Diode Display Device. Adv. Mater. 23, 3511-+
(2011). 4. Yoon, B. et al. Inkjet Printing of Conjugated Polymer Precursors on Paper Substrates for Colorimetric
Sensing and Flexible Electrothermochromic Display. Adv. Mater. 23, 5492-+ (2011). 5. Kim, D. H. et al. Stretchable and foldable silicon integrated circuits. Science 320, 507-511 (2008). 6. Ko, H. C. et al. A hemispherical electronic eye camera based on compressible silicon optoelectronics.
Nature 454, 748-753 (2008). 7. Kim, D. H. et al. Epidermal Electronics. Science 333, 838-843 (2011). 8. Pushparaj, V. L. et al. Flexible energy storage devices based on nanocomposite paper. Proc. Natl. Acad. Sci.
U. S. A. 104, 13574-13577 (2007). 9. Scrosati, B. Nanomaterials - Paper powers battery breakthrough. Nat. Nanotechnol. 2, 598-599 (2007). 10. Hu L. B. et al. Highly conductive paper for energy-storage devices. Proc. Natl. Acad. Sci. U. S. A. 106,
21490-21494 (2009). 11. Gao K. Z. et al. Paper-based transparent flexible thin film supercapacitors. Nanoscale 5, 5307-5311 (2013). 12. Wang, J. Z. et al. Highly flexible and bendable free-standing thin film polymer for battery application.
Mater. Lett. 63, 2352-2354 (2009). 13. Hu, L. B., Wu, H., La Mantia F., Yang, Y. A., Cui, Y. Thin, Flexible Secondary Li-Ion Paper Batteries. Acs
Nano 4, 5843-5848 (2010). 14. Ihlefeld, J. F. et al. Fast Lithium-Ion Conducting Thin-Film Electrolytes Integrated Directly on Flexible
Substrates for High-Power Solid-State Batteries. Adv. Mater. 23, 5663-+ (2011). 15. Koo, M. et al. Bendable Inorganic Thin-Film Battery for Fully Flexible Electronic Systems. Nano Lett. 12,
4810-4816 (2012).
19
16. Gaikwad, A. M., Steingart, D. A., Ng, T. N., Schwartz, D. E., Whiting, G. L. A flexible high potential
printed battery for powering printed electronics. Appl. Phys. Lett. 102, 233302 (2013). 17. Yu, C. J., Masarapu, C., Rong, J. P., Wei, B. Q., Jiang, H. Q. Stretchable Supercapacitors Based on Buckled
Single-Walled Carbon Nanotube Macrofilms. Adv. Mater. 21, 4793-+ (2009). 18. Li, X., Gu, T. L., Wei, B. Q. Dynamic and Galvanic Stability of Stretchable Supercapacitors. Nano Lett. 12,
6366-6371 (2012). 19. Xu, S. et al. Stretchable batteries with self-similar serpentine interconnects and integrated wireless
recharging systems. Nat. Commun. 4, 8 (2013). 20. Song, Z. et al. Origami Lithium-ion Batteries. Nat. Commun. 5:3140 doi: 10.1038/ncomms4140 (2014). 21. Tang, R. et al. Origami-enabled Deformable Silicon Solar Cells. Appl. Phys. Lett. 104, 083501 (2014). 22. Singh, N. et al. Paintable battery. Sci. Rep. doi:10.1038/srep00481 (2012). 23. Wessel, J. K. in The handbook of advanced materials: enabling new designs. Ch. 9, 363 (John Wiley &
Sons 2004). 24. Bainbridge, I. F., Taylor, J. A. The Surface Tension of Pure Aluminum and Aluminum Alloys. Metallurgical
and Materials Transactions A 44, 3901-3909 (2013).
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Acknowledgements
We acknowledge the financial support from the Office of Associate Dean for Research at Ira A.
Fulton School of Engineering, and Office of Knowledge Enterprise and Development, Arizona
State University. H.J. acknowledges the support from NSF CMMI-1067947 and
CMMI-1162619.
Author Contributions
Z. S., X, W., H. Y. and H. J. designed the experiments. Z. S., X. W., C. L. Y. A., M. L., T. M., D.
H., Y. J. Z., S. Q. H., H. Y, and H. J. carried out experiments and analysis. Z. S., X, W., C. L., H.
Y. and H. J. wrote the paper.
Competing Financial Interests statement
The authors declare no competing financial interests.
Supporting Information
Supporting Information is available from the Nature Online Library or from the author.
Received: ((will be filled in by the editorial staff)) Revised: ((will be filled in by the editorial staff))
Published online: ((will be filled in by the editorial staff))
21
Figure 1. Illustrations of three kirigami patterns. (a) A zigzag-cut pattern, where the out-of-plane deformation occurs to accommodate stretching. (b) A cut-N-twist pattern, where the rotation is involved to accommodate stretching and no out-of-plane deformation. (c) A cut-N-shear pattern, where the packing density doubles compared with that of the cut-N-twist pattern. Rotation is involved to accommodate stretching and no out-of-plane deformation.
Figure 2. Electrochemical and mechanical characterizations of a kirigami lithium-ion battery (LIB) using cut-N-twist pattern. (a) Photograph of a LIB at its most compact state. (b) Photograph of a LIB at its most stretched state. (c) Galvanostatic charge and discharge at the most compact state (1st to 5th cycles), the most stretched state (6th to 10th cycles), the most compact state again (11th to 15th cycles), and the most stretched state again (16th to 20th cycles) under C/3 charge/discharge rate. The mass loading of LiCoO2 (LCO) (specific capacity 145 mAh g-1) and graphite (specific capacity 372 mAh g-1) were 95 mg and 255 mg, respectively, which gave LIB the capacity of 30 mAh. (d) Energy capacity (left axis, black) and Coulombic efficiency (right axis, red) as a function of cycle number for C/3 charge/discharge rate. The mass accounts for all the materials involved in a cell, which is 1.49 g. (e) Rate performance when the charge/discharge rates varied from C/3, C/2, to C, and C/3 again for both compact and stretched states. (f) Electrochemical impedance spectroscopy (EIS) analysis during the first discharge cycle at the most compact state before stretching and stretched state after 100 stretching cycles. EIS studies were performed by applying a small perturbation voltage of 5 mV in the frequency range of 0.1 Hz to 100 kHz. Typical impedance spectrum, with high-to-middle frequency range flat curve and a relative straight line representing the low frequency range, was observed. No obvious semicircle was observed because of the low internal resistant. There are not significant changes in the impedance before and after mechanical deformation. (g) Photograph of stretching a kirigami LIB while it was connected to a voltmeter. (h) Maximum output power of the kirigami LIB as a function of stretchability over 3,000 cycles of stretches. (i) Scanning electron micrographs (SEM) of anode current collector Cu at the cut before charge. (j) SEM of anode current collector Cu at the cut after discharge and 100 cycles of stretching. (k) SEM of cathode current collector Al at the cut before charge. (l) SEM of cathode current collector Al at the cut after discharge and 100 cycles of stretching.
Figure 3. Theoretical analysis of kirigami crack growth versus plastic rolling. (a) Illustration of the two deformation modes, i.e., crack growth and plastic rolling. (b) "Safe zone" and "fracture zone" that are characterized by the ratio of critical moments, i.e.,
crack growth plastic rolling/cr crM M , as a function of angle θ, for various α and β.
22
Figure 4. Powering a Samsung Gear 2 smart watch by a kirigami lithium-ion battery (LIB) using cut-N-twist pattern. The kirigami LIB sewn between two elastic bands was (a) at the wrist, (b) at the upper arm, (c) at the upper arm with elbow straightened, (d) at the upper arm with elbow bent. The kirigami LIB was removed from the elastic bands and stretched directly. (e) At the compact state and (f) at the stretched state. (g) Galvanostatic discharge to simulate the standby test with discharge current 2.9 mA. (h) Galvanostatic discharge to simulate the calling test with discharge current 48 mA. The stopping voltage is 3.6 V.
Figure 1
(a)
Stretch
Cut asymmetrically
Folded foil
Left view Right view
Unfold
Figure 1(b)
Unfold
Cut symmetrically
Folded foil
Twist
Figure 1
(c)
Fold
Shear
Cut symmetrically
Folded foil
(a)
Figure 2
(b)
(c)
Figure 2
(d)
0 5 10 15 20 25 30 351.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5Charge
Discharge
Vol
tage
(V)
Capacity (mAh)
1st to 5th cycle (Most compact state)
6th to 10th cycle (Most stretched state)
11th to 15th cycle (Most compact state)
16th to 20th cycle (Most stretched state)
0 5 10 15 20 50 75 1000
10
20
30
40
50
Stretched state for the rest 80 cycles
Most stretched state
Most compact state
Most stretched state
Capacity
Cap
acity
(mA
h)
Cycle number
Most compact state
0
20
40
60
80
100
Coulombic efficiencyC
oulo
mbi
c ef
ficie
ncy
(%)
(e)
Figure 2
(f)
0 10 20 30 40 50 60 70 80 900
10
20
30
40
50
60
70
80
90
-Z"
()
Z' ()
Most compact state before stretching Most stretched state after 100 cycles of stretching
0 10 20 30 400
8
16
24
32
C/3
C
C/2
Cap
acity
(mA
h)
Cycle number
Most compact state Most stretched state
C/3
Figure 2
(g)
(h)
90%stretch =0% 40%
0 200 400 600 800 10003.0
3.2
3.4
3.6
3.8
4.0
4.2
Max
imum
out
put p
ower
(W)
Cycle of stretching
stretch
=0% stretch=40% stretch=90%
(i)
Figure 2
(j)
1mm
(k) (l)
1mm 1mm
1mm
(a)
Figure 3(b)
0 10 20 30 40 50 600
1
2
3
4
a = 0.03 mm = 20 MPa
a = 0.24 mm = 20 MPa
a = 0.03 mm = 50 MPa
Fracture zone
Safe zone
crack growth
plastic rollingcr
cr
M
M
Angle (o)initial folding position
a = 0.24 mm, = 50 MPa
a
a
HL
MM
a + a
MM
a + a
a
MM
a
(a)
Figure 4
(b)
(c)
Figure 4
(d)
(e)
Figure 4
(f)
Figure 4
(g)
(h)
0 20 40 60 80 1002.0
2.5
3.0
3.5
4.0 48 mA
3.6 V
Voltage (V)
Vol
tage
(V)
Time (Minute)
89 minutes
0
10
20
30
40
50
Current (mA)
Cur
rent
(mA
)
0 5 10 15 20 25 302.0
2.5
3.0
3.5
4.0 2.9 mA3.6 V
25.8 hours
Vol
tage
(V)
Time (Hour)
Voltage (V)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Current (mA)
Cur
rent
(mA
)
1
Supporting Information
for
Kirigami based stretchable lithium-ion batteries
Zeming Song1#, Xu Wang1#, Cheng Lv1, Yonghao An1, Mengbing Liang2, Teng Ma1, David He1,2,
Ying-Jie Zheng3, Shi-Qing Huang3, Hongyu Yu4,5, and Hanqing Jiang1,* 1School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ
85287, USA
2Desert Vista High School, Phoenix, AZ 85048, USA
3MOE Key Lab of Disaster Forecast and Control in Engineering, Jinan University, Guangzhou
510632, China
4School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ
85287, USA
5School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287, USA
#These authors contribute equally.
*Email: [email protected]
2
Geometry of the Three Kirigami Patterns for Lithium-Ion Batteries (LIBs)
In order to ensure the quality of the packaging, specifically, no short between anode and
cathode, and large areal coverage, the following geometries were used to produce the three
kirigami batteries with these three patterns, namely, zigzag-cut, cut-N-twist, and cut-N-shear
patterns. The annotation shown in the Fig. S1 is the size of the current collector with electrode
materials. For the LIB stack, the size of the separator is 1mm larger than that of the current
collector at each edge to ensure the separation of the two electrodes and the size of the package
materials is 2 mm even larger than that of the separator at each edge to ensure the film sealing of
the battery.
(a)
(b)
(c)
battery cell
battery cell
battery cell
3
Supplementary Figure S1. Geometries of the three kirigami batteries. (a) Zigzag-cut pattern,
(b) cut-N-twist pattern, and (c) cut-N-shear pattern. The dashed line shows a battery cell.
Supplementary Figure S2. Exploded view of the multilayer structure of lithium-ion
batteries.
Copper tab
Anode current collector Anode electrode
Separator
Cathode electrode
Cathode current collector
Aluminum tab
Packaging material
Packaging material
4
Lighting up a Light-Emitting Diodes (LED) by a Kirigami Lithium-Ion Battery (LIB) using
Cut-N-Twist Pattern
(a)
(b)
(c)
Supplementary Figure S3. A kirigami lithium-ion battery (LIB) using cut-N-twist pattern
is lighting up a light-emitting diodes (LED) while (a) at the most compact state, (b) being
stretched by 30%, and (c) being stretched by 70%.
5
Electrochemical and Mechanical Characterization of a Kirigami Lithium-Ion Battery using
Cut-N-Shear Pattern
Similar to Fig. 2 in the main text, the kirigami lithium-ion batteries (LIBs) were produced by
following the geometry given by Supplementary Fig. S1c. Then the electrochemical and
mechanical characterizations were performed.
Figure S4 shows electrochemical and mechanical characterization results for LIBs using
cut-N-shear pattern. Figures S4a and S4b show the images the LIB at the most compact and
stretched states. Fig. S4b shows that a LIB using cut-N-shear pattern can be stretched up to 150%
by using the most compact state (Fig. S4a) as the reference. Meanwhile the thickness change,
from 4.30 mm at the most compact state to 2.7 mm at the most stretched state is noticeable.
Figure S4c shows the electrochemical cycling results of a LIB using the cut-N-shear pattern at its
most compact state (for the 1st to 5th cycles), followed by that at its most stretched state (for the
6th to 10th cycles), then that at its most compact state again (for the 11th to 15th cycles) and finally
followed by that at its most stretched state again (for the 16th to 20th cycles) under C/3
charge/discharge rate. Fairly stable charge/discharge behaviors under the compact and
stretched states are observed. The present mass loading (see caption of Fig. S4c) gives this
kirigami LIB 75 mAh energy capacity. Figure S4d shows the cyclic stability of the LIBs up to
20 cycles. Figure S4e shows the excellent rate performance of this kirigami battery when the
charge/discharge rate varied in the sequence of C/3, C/2, C and C/3 again at both compact and
stretched state. Figure S4f provides the results for electrochemical impedance spectroscopy
(EIS) studies during the first discharge cycle at the most compact state before stretching and
stretched state after 100 cycles of stretching. No significant changes in the impedance were
found.
6
Then the mechanical characteristics of the fully charged kirigami LIB using cut-N-shear are
examined. As shown in Fig. S4g, at different stretchability, the output voltage remained steady
at 3.87 V. Supplementary Movie S2 shows the dynamic process of this deformation. Figure
S4h shows the maximum output power of the kirigami LIB as a function of stretchability, stretche ,
under different cycles of stretching. The internal resistance of the battery is measured to be
about 1.5 Ω. Over 3,000 stretching cycles and up to a stretchability stretche of 83 %, there is
insignificant decrease of the power. The maximum output power is 4.7 W and is sufficient to
operate commercial light-emitting diodes (LEDs). As shown in the Supplementary Movie S2,
LEDs driven by this kirigami LIB do not show noticeable dimming upon cyclic stretching.
Ultimate tensile strength of LIBs using cut-N-shear pattern 11.5 MPa with load frame
Instron-Model 4411.
Figures S4i and S4j show the scanning electron micrographs (SEMs) for the anode current
collectors (e.g., Cu foil) at the cuts before charging, and after discharge and 100 cycles of
mechanical deformation. The similar SEM images are given for the cathode current collectors
(e.g., Al foils) in Figs. S4k and S4l. There are no cracks after cyclic mechanical stretching.
7
(a)
(b)
0 20 40 60 801.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Charge
1st to 5th cycle (Most compact state) 6th to 10th cycle (Most stretched state) 11th to 15th cycle (Most compact state) 16th to 20th cycle (Most stretched state)
Vol
tage
(V)
Capacity (mAh)
Discharge
(c)
8
0 5 10 15 200
20
40
60
80
Most stretched stateMost compact state
Most stretched state
Capacity
Cap
acity
(mA
h)
Cycle number
Most compact state
0
20
40
60
80
100
Coulumbic efficiency
Cou
lum
bic
effic
ienc
y (%
)
0 5 10 15 200
20
40
60
80
Most stretched stateMost compact state
Most stretched state
Capacity
Cap
acity
(mA
h)
Cycle number
Most compact state
0
20
40
60
80
100
Coulumbic efficiency
Cou
lum
bic
effic
ienc
y (%
)
(d)
(e)
0 10 20 30 400
20
40
60
80
C/3
C
C/2
Cap
acity
(mA
h)
Cycle number
Most compact state Most stretched state
C/3
0 10 20 30 400
20
40
60
80
C/3
C
C/2
Cap
acity
(mA
h)
Cycle number
Most compact state Most stretched state
C/3
9
0 1 2 3 4 5 6 7 8 90
2
4
6
8
10
12
14
16
18
20 Most compact state before stretching Most stretched state after 100 cycles of stretching
-Z"(Ω
)
Z' (Ω)
(f)
(g)
0 200 400 600 800 10003.0
3.2
3.4
3.6
3.8
4.0
4.2
4.4
4.6
4.8
Max
imum
out
put p
ower
(W)
Cycle of stretching
estretch=0% estretch=40% estretch=83%
(h)
10
(i)
(j)
(k)
11
(l)
Supplementary Figure S4. Electrochemical and mechanical characterization of a kirigami
lithium-ion battery (LIB) using cut-N-shear pattern. (a) Photograph of a LIB at its most
compact state. (b) Photograph of a LIB at its most stretched state. (c) Galvanostatic charge
and discharge at the most compact state (1st to 5th cycles), the most stretched state (6th to 10th
cycles), the most compact state again (11th to 15th cycles), and the most stretched state again (16th
to 20th cycles) under C/3 charge/discharge rate. The mass loading of LiCoO2 (LCO) (specific
capacity 145 mAh g-1) and graphite (specific capacity 372 mAh g-1) were 240 mg and 650 mg,
respectively, which gave LIB the capacity of 75 mAh. (d) Energy capacity (left axis, black) and
Coulombic efficiency (right axis, red) as a function of cycle number for C/3 charge/discharge
rate. The mass accounts for all the materials involved in a cell, which is 2.98 g. (e) Rate
performance when the charge/discharge rates varied from C/3, C/2, to C, and C/3 again for both
compact and stretched states. When discharge rates increase, as expected, the capacity
decreases from 73.2 mAh for C/3 rate to 66.5 mAh for C/2 rate, and 56.6 mAh for discharge
rate C. However, the capacity recovered to the 70.8 mAh when the discharge rate resumed to
C/3 after 30 cycles charge/discharge at the both compact the stretched state under varies C-rates,
which indicates excellent rate performance of this kirigami battery. (f) Electrochemical
12
impedance spectroscopy (EIS) analysis during the first discharge cycle at the most compact state
before stretching and stretched state after 100 stretching cycles. EIS studies were performed by
applying a small perturbation voltage of 5 mV in the frequency range of 0.1 Hz to 100 kHz.
Typical impedance spectrum, with high-to-middle frequency range flat curve and a relative
straight line representing the low frequency range, was observed. No obvious semicircle was
observed because of the low internal resistant. There are not significant changes in the
impedance before and after mechanical deformation. (g) Photograph of stretching a kirigami
LIB while it was connected to a voltmeter. (h) Maximum output power of the kirigami LIB as
a function of stretchability over 3,000 cycles of stretches. (i) Scanning electron micrographs
(SEM) of anode current collector Cu at the cut before charge. (j) SEM of anode current
collector Cu at the cut after discharge and 100 stretching. (k) SEM of cathode current collector
Al at the cut before charge. (l) SEM of cathode current collector Al at the cut after discharge
and 100 stretching.
13
Electrochemical and Mechanical Characterization of a Kirigami Lithium-Ion Battery using
Zigzag-Cut Pattern
Similar to Fig. 2 in the main text, the kirigami lithium-ion batteries (LIBs) was produced by
following the geometry given by Supplementary Fig. S1a. Then the electrochemical and
mechanical characterizations were performed.
Figure S5 shows electrochemical and mechanical characterization results for LIBs using
zigzag-cut pattern. Figures S5a and S5b show the pictures of the LIB at the most compact and
stretched states. The LIB using zigzag-cut pattern has relatively small stretchability,
approximately 46% measured from the most compact state (Fig. S5a) to the most stretched state
(Fig. S5b), and out-of-plane deformation can be observed when stretched (Fig. S5b). Similar
cyclic charge/discharge curves are shown in Fig. S5c and S5d. The present mass loading gives
this kirigami LIB 55 mAh energy capacity. The rate performance of this kirigami battery when
the charge/discharge rate varied in the sequence of C/3, C/2, C and C/3 again at both compact
and stretched state was given by Fig. S5e. Electrochemical impedance spectroscopy (EIS)
studies during the first discharge cycle at the most compact state before stretching and stretched
state after 100 cycles of stretching are shown in Fig. S5f. No significant changes in the
impedance were found.
The mechanical characteristics of the fully charged kirigami LIB using zigzag-Cut are then
examined. Figure S5g shows that at different stretchability, the output voltage remained steady
at 3.86 V. Supplementary Movie S3 shows the dynamic process of this deformation. Figure
S5h shows the maximum output power of the kirigami LIB as a function of stretchability, stretche ,
under different cycles of stretching. Here the internal resistance of the battery is measured to be
14
about 1.7 Ω. Over 3,000 stretching cycles and up to a stretchability stretche of 35%, there is no
obvious output power decay. The output power of 4.7 W is sufficient to operate commercial
light-emitting diodes (LEDs). As shown in Supplementary Movie S3, LEDs driven by this
kirigami LIB do not show noticeable dimming upon cyclic stretching. Ultimate tensile strength
of LIBs using zigzag-cut pattern is 10.8 MPa with load frame Instron-Model 4411.
Figures S5i and S5j show the scanning electron micrographs (SEMs) for the anode current
collectors (e.g., Cu foil) at the cuts before charging, and after discharge and 100 cycles
mechanical deformation. The similar SEM images are given for the cathode current collectors
(e.g., Al foils) in Figs. S5k and S5l. Again, no cracks are observed after cyclic mechanical
stretching.
15
(a)
(b)
0 10 20 30 40 50 601.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5Charge
1st to 5th cycle (Most compact state) 6th to 10th cycle (Most stretched state) 11th to 15th cycle (Most compact state) 16th to 20th cycle (Most stretched state)
Vol
tage
(V)
Capacity (mAh)
Discharge
(c)
16
0 5 10 15 200
20
40
60
Most stretched stateMost compact state
Most stretched state
Capacity
Cap
acity
(mA
h)
Cycle number
Most compact state
0
20
40
60
80
100
Coulombic efficiency
Cou
lom
bic
effic
ienc
y (%
)
0 5 10 15 200
20
40
60
Most stretched stateMost compact state
Most stretched state
Capacity
Cap
acity
(mA
h)
Cycle number
Most compact state
0
20
40
60
80
100
Coulombic efficiency
Cou
lom
bic
effic
ienc
y (%
)
(d)
0 10 20 30 400
10
20
30
40
50 C/3
C
C/2
Cap
acity
(mA
h)
Cycle number
Most compact state Most stretched state
C/3
0 10 20 30 400
10
20
30
40
50 C/3
C
C/2
Cap
acity
(mA
h)
Cycle number
Most compact state Most stretched state
C/3
(e)
17
0 5 10 15 20 25 30 350
5
10
15
20
25
30
35
-Z" (Ω
)
Z' (Ω)
Most compact state before stretching Most stretched state after 100 cycles of stretching
(f)
(g)
0 200 400 600 800 10003.0
3.2
3.4
3.6
3.8
4.0
4.2
4.4
4.6
4.8
Max
imum
out
put p
ower
(W)
Cycles of stretching
estretch=0% estretch=20% estretch=35%
(h)
18
(i)
(j)
(k)
19
(l)
Supplementary Figure S5. Electrochemical and mechanical characterization of a kirigami
lithium-ion battery (LIB) using zigzag-cut pattern. (a) Photograph of a LIB at its most
compact state. (b) Photograph of a LIB at its most stretched state. (c) Galvanostatic charge
and discharge at the most compact state (1st to 5th cycles), the most stretched state (6th to 10th
cycles), the most compact state again (11th to 15th cycles), and the most stretched state again (16th
to 20th cycles) under C/3 charge/discharge rate. The mass loading of LiCoO2 (LCO) (specific
capacity 145 mAh g-1) and graphite (specific capacity 372 mAh g-1) were 174 mg and 457 mg,
respectively, which gave LIB the capacity of 55 mAh. (d) Energy capacity (left axis, black) and
Coulombic efficiency (right axis, red) as a function of cycle number for C/3 charge/discharge
rate. The mass accounts for all the materials involved in a cell, which is 2.10 g. (e) Rate
performance when the charge/discharge rates varied from C/3, C/2, to C, and C/3 again for both
compact and stretched states. When discharge rates increase, as expected, the capacity
decreases from 52.7 mAh for C/3 rate to 50.1 mAh for C/2 rate, and 43.8 mAh for discharge
rate C. However, the capacity recovered to the 51.7 mAh when the discharge rate resumed to
C/3 after 30 cycles charge/discharge at the both compact the stretched state under varies C-rates,
which indicates excellent rate performance of this kirigami battery. (f) Electrochemical
20
impedance spectroscopy (EIS) analysis during the first discharge cycle at the most compact state
before stretching and stretched state after 100 stretching cycles. EIS studies were performed by
applying a small perturbation voltage of 5 mV in the frequency range of 0.1 Hz to 100 kHz.
Typical impedance spectrum, with high-to-middle frequency range flat curve and a relative
straight line representing the low frequency range, was observed. No obvious semicircle was
observed because of the low internal resistant. There are not significant changes in the
impedance before and after mechanical deformation. (g) Photograph of stretching a kirigami
LIB while it was connected to a voltmeter. (h) Maximum output power of the kirigami LIB as
a function of stretchability over 3,000 cycles of stretches. (i) Scanning electron micrographs
(SEM) of anode current collector Cu at the cut before charge. (j) SEM of anode current
collector Cu at the cut after discharge and 100 stretching. (k) SEM of cathode current collector
Al at the cut before charge. (l) SEM of cathode current collector Al at the cut after discharge
and 100 stretching.
21
Theoretical Analysis of the Two Competing Mechanisms, "Crack Growth" versus "Plastic
Rolling"
According to the Griffith’s criterion for linear elastic fracture, potential energy takes this
form , crack growth 2 2~ /a EσΠ , where σ is the normal stress on the crack, a is the size of the crack
and E is the elastic modulus. The energy releasing rate due to the crack growth is then given by
crack growth 2/ ~ /J a a Eσ= ∂Π ∂ . Here J is the J-integral which equals to the energy release per
unit area. For the present scenario that has different geometrical setup as that in the Griffith's
criterion, the geometry factors are taken into account. The form of J is speculated to be
2 /A a Eσ , where A characterizes the geometrical effects and is determined by finite element
simulations. A is assumed to be a function of θ .
In finite element simulations using commercial package ABAQUS, the values of σ , a
and E are fixed while θ changes from 0 to / 3π . Plane stress model was applied as the
structure has very low thickness compared to its in-plane dimensions. Mesh was refined around
the crack tip, which is shown in Supplementary Fig. S6 for / 4θ π= . About 200,000 CPS4R
(4-node bilinear plane stress quadrilateral, reduced integration) elements were used to obtain
accurate and converged results. J-integral was obtained by numerical integration along the
elements on a circle with the crack tip as its center. After obtaining the values of J-integral for
different angle θ , the value of A can be calculated by the expression of J as mentioned
22
above, i.e. 2 /J A a Eσ= . Substitute A into the expression of crack growthcrM and the final
expression of crack growthcrM is thus obtained.
Supplementary Figure S6. Mesh of finite element model for / 4θ π= .
23
During the plastic rolling (i.e., the angle θ changes), the plastic zone is highlighted by the
shaded area as shown in Supplementary Fig. S7. The area of the plastic zone is 2 tan / 4H θ .
So the critical moment plastic rollingcrM for plastic rolling can be obtained by
( ) ( )plastic rolling plastic rolling 2 2 2/ tan / 4 / 1 tan / 2crM H Hθ β θ θ β θ= ∂Π ∂ = ∂ ∂ = + .
Supplementary Figure S7. Plastic zone generated during "plastic rolling".
24
For plastic rolling, β, the dissipated plastic energy density, was calculated by simulating
folding a thin foil by a prescribed folding thickness. This problem was modeled by bending a
thin film around a rigid circular die (Supplementary Fig. S8). The diameter of the rigid circular
die corresponds to the folding thickness. The material parameters of Al were used in the
analysis. Contact was defined between the deformable thin foil and the rigid die. 1,571 B22
(3-node quadratic beam) elements are used in the analysis. Once the thin foil enters the plastic
zone, the plastic energy density can then be calculated.
Supplementary Figure S8. Plastic zone generated during "plastic rolling".
25
Supplementary Fig. S9 shows β as a function of the ratio between the folding thickness and
foil thickness /folding foilH h . It is found that as the ratio /folding foilH h increases, β decreases.
For the real battery setup, Al foil is 10 µm in thickness, while the entire battery cell is 500 µm -
800 µm in thickness depending on the mass loading of the active materials, which gives the ratio
/folding foilH h about 50 to 80. Within this range, Supplementary Fig. S9 shows that β is on the
order of 1 MPa.
0 20 40 60 80
1
10
100
folding
foil
Hh
β (M
Pa)
Kirigami battery
β = 20 MPa
Supplementary Figure S9. The dissipated plastic energy per area (β) as a function of the
extent of the folding crease that is characterized by the ratio between folding thickness and
foil thickness.
26
(a) (b)
Supplementary Figure S10. Thermal test of Kirigami battery and Samsung Gear 2 bulky
battery. (a) Kirgami battery discharged at 48mA for one hour. (b) Samsung Gear 2 bulky battery
discharged at 48mA for one hour.
Supplementary Figure S11. Thermal test result of Kirigami battery and Samsung Gear 2
bulky battery.
0 10 20 30 40 50 6020
21
22
23
24
25
Tem
pera
ture
(o C)
Discharge time (minutes)
Ambient temperature Samsung Gear 2 battery temperature Kirigami battery temperature
Discharge current: 48mA
d e m o d e m o d e m o d e m o
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d e m o d e m o d e m o d e m o
d e m o d e m o d e m o d e m o
d e m o d e m o d e m o d e m o
d e m o d e m o d e m o d e m o
d e m o d e m o d e m o d e m o
d e m o d e m o d e m o d e m o
0 10 20 30 40 50 6020
21
22
23
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25
Tem
pera
ture
(o C)
Discharge time (minutes)
Ambient temperature Samsung Gear 2 battery temperature Kirigami battery temperature
Discharge current: 48mA
d e m o d e m o d e m o d e m o
d e m o d e m o d e m o d e m o
d e m o d e m o d e m o d e m o
d e m o d e m o d e m o d e m o
d e m o d e m o d e m o d e m o
d e m o d e m o d e m o d e m o
d e m o d e m o d e m o d e m o
d e m o d e m o d e m o d e m o