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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: hanqing.jiang@asu.edu

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: hanqing.jiang@asu.edu

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

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

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d e m o d e m o d e m o d e m o

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Tem

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(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