Battery design

The devices exploit pouch cells in which arrays of small-scale storage components are connected by conducting frameworks with extraordinary stretchable characteristics. A schematic illustration of the system, an exploded view of the multilayer construction of a unit cell, and a representation of the ‘self-similar’ interconnect geometries appear in Fig. 1a–c, and Supplementary Fig. S1. The current collectors consist of photolithographically patterned circular disks of aluminium (600 nm) and copper (600 nm). Layers of polyimide (PI; 1.2 μm) encapsulate interconnecting traces between these disks in a way that places the metals close to the neutral mechanical plane (Fig. 1d, left panel). Thin (0.25 mm), low modulus (60 kPa) sheets of silicone elastomer form top and bottom substrates that support these structures (Fig. 1d, middle panel) and other components of the batteries. The overall construct consists of a square array of 100 electrode disks, electrically connected in parallel. Moulded pads of slurries based on LiCoO 2 and Li 4 Ti 5 O 12 serve as active materials at the cathode and anode23,24, respectively (Fig. 1d, right panel, and Supplementary Fig. S2). The two sheets laminate together in a way that involves spatial offsets between the active materials to avoid electrical shorts between them and to eliminate the need for a separator. A spacer, made of the same silicone elastomer and applied around the periphery of the system, prevents direct contact of the top and bottom sheets. A gel electrolyte injected into the gap provides media for ionic transport. Thin encapsulating layers of an acryloxy perfluoropolyether elastomer bonded to the outer surfaces help to prevent moisture from diffusing into the battery and solvents in the gel from leaking out25. Long-term operation requires more sophisticated packages consisting of for example, buckled bilayer sheets of aluminium/PI that bond to the outer surfaces of the battery (Supplementary Fig. S3). The materials and fabrication details appear in the Methods section.

Figure 1: Aspects in battery layout and design. (a) Schematic illustration of a completed device, in a state of stretching and bending. (b) Exploded view layout of the various layers in the battery structure. (c) Illustration of ‘self-similar’ serpentine geometries used for the interconnects (black: 1st level serpentine; yellow: 2nd level serpentine). (d) Optical images of the Al electrode pads and self-similar interconnects on a Si wafer (left panel; top down view; ~4 unit cells), after transfer printing on a sheet of silicone (middle panel; top down view, in a bent geometry), and with moulded slurries of LiCoO 2 (right panel; top down view, in a bent geometry). (e) Optical images of the Cu electrode pads and self-similar interconnects on a Si wafer (left panel; top down view; ~4 unit cells), after transfer printing on a sheet of silicone (middle panel; top down view, in a bent geometry), and with moulded slurries of Li 4 Ti 5 O 12 (right panel; top down view, in a bent geometry). Scale bars in d and e are 2 mm. Full size image

The devices must accommodate two competing design goals: (1) high areal capacity, which requires large coverage of the active regions, and (2) high mechanical stretchability, which requires large distances between these regions. Strategic features of relief on the elastomer substrates provide a partial solution to this challenge, as demonstrated recently in photovoltaic modules26,27. A disadvantage is that levels of stretchability beyond ~30% can be difficult to achieve without sacrificing coverage. Here, we take a different, but complementary, approach in which the focus is on deformable interconnects with advanced designs. In particular, we introduce layouts that use ‘self-similar’ structures of wires in serpentine configurations to offer, simultaneously, high system-level stretchability, and low interconnect resistances. A conventional serpentine consists of circular arcs connected by straight lines. ‘Self-similar’ designs follow from iteratively applying this basic geometry, beginning with a unit cell as illustrated schematically in the red box of Fig. 1c. Here, reducing the scale of the cell, and then connecting multiple copies of it in a fashion that reproduces the layout of the original cell geometry, corresponds to one iteration. The yellow line in Fig. 1c represents a 2nd order serpentine geometry, created in this manner. Although higher orders can be designed and implemented easily, the 2nd order construct satisfies requirements for the applications considered here, as described in detailed experimental and theoretical study below.

Mechanical characteristics of the ‘self-similar’ interconnects

Three-dimensional finite element analysis (see Supplementary Methods) and experimental measurements illustrate the essential mechanics. Test samples fabricated for this purpose consist of free-standing, multilayer traces, with materials and multilayer stack designs (PI (1.2 μm)/Cu (0.6 μm)/PI (1.2 μm)) that match those used in the batteries, between circular pads that bond to posts moulded onto underlying elastomer substrates. The self-similar geometry leads to hierarchical buckling physics that ensures ultra-low strains in the materials, even under extreme stretching3,28. For the entire range of tensile strains examined, from 0 to 300%, the configurations predicted by FEA agree remarkably well with optical images collected during the experiments, as shown in Fig. 2 and Supplementary Movies 1 and 2. Both symmetric and anti-symmetric buckling modes exist (see Supplementary Fig. S4 for detailed illustrations of the two modes). The trace consists of three columns of serpentine wires connected by two horizontal straight lines. We refer to the construct that corresponds to the ‘short’ wavelength serpentine within each column as the 1st level; the 2nd level corresponds to the large-scale serpentine shape, with ‘long’ wavelength. For the symmetric buckling mode (Supplementary Fig. S4a), the left and right columns undergo mainly an overall bending deformation along the vertical direction, resulting in the collective upward motion of the entire middle column of serpentine wires. In this sense, the out-of-plane displacement is symmetric with respect to the centre line (x=0) in the ‘Front view’ of Supplementary Fig. S4a. For the anti-symmetric buckling mode (Supplementary Fig. S4b), the serpentines in the left and right columns mainly undergo an overall twisting deformation along the vertical direction. Here, the two ends of middle serpentine move in opposite directions (that is, one moves up, and the other moves down). In this case, the out-of-plane displacement is anti-symmetric with respect to the centre line (x=0) in the ‘Front view’ of Supplementary Fig. S4b. The critical buckling strains obtained by FEA for the symmetric (0.078%) and anti-symmetric (0.087%) modes are much lower than those (>0.172%) for all other buckling modes. This result is consistent with experimental observation of only these two modes. In both cases, the physics associated with stretching involves a mechanism of ‘ordered unravelling’, which begins at the 2nd level, at a well-defined, critical buckling strain, ~0.08% for the example investigated here. Next, the 2nd level gradually ‘unravels’ via bending and twisting as the applied strain increases from 0.08% to ~150%, during which there is essentially no further deformation in the 1st level. The motions in the 1st level start when the 2nd level is almost fully extended, corresponding to an applied strain of ~150% in this case. As the ‘unravelling’ of the 1st level serpentine approaches its end, the strain in the materials begin to increase rapidly, thereby defining the practical limit in stretchability.

Figure 2: Experimental and computational studies of buckling physics in interconnects with self-similar serpentine layouts. Optical images and corresponding finite element analysis (FEA) of symmetric (left column) and anti-symmetric (middle column) deformation modes, for various levels of applied tensile strain (ε). The colour in the FEA results represents the maximum principal strains of the metal layer. The scale bar is 2 mm. The right column shows the interconnect structures after releasing the applied strain. Full size image

For applied strains below this limit, the deformation mechanisms of ordered unravelling processes ensure low levels of strain in the materials (Supplementary Fig. S5). For a representative failure strain of 1% for copper, FEA predicts a stretchability of 321%, which is in good agreement with the experimental observations (300%<ε stretchability <350%) (simulations suggest that the copper reaches its failure point before the PI). For reversible behaviour (that is, the interconnects return to their initial configuration after release), the maximum material strain must be less than the yield strain. For a representative yield strain of 0.3% for copper, FEA suggests reversibility for applied strains up to ~168%. This value is lower than experimental observations, where reversibility occurs even for strains of between 200% and 250% (Fig. 2). The likely explanation for this discrepancy is that yield occurs first in only small portions of the interconnect (for example, one element in the FEA). In this case, the effects on reversibility might not be easily observed in experiments.

These levels of stretchability (>300%) and reversibility (>200%) significantly exceed those of previous reports in stretchable batteries and/or battery electrodes; they are also greater than those of any other reports of stretchable interconnects that use lithographically defined patterns of conventional metals. The importance of the self-similar designs can be assessed through comparisons of stretchability to otherwise similar, but conventional serpentine structures: the former exhibits a stretching range of 321%, while the latter is 134%, determined by FEA (Supplementary Fig. S6). Furthermore, even for the same total length (l total ), span (L), amplitude (h), and cross-section (width w and thickness t), the self-similar design again outperforms the conventional serpentine, both in stretchability (809% versus 682%) and reversibility (528% versus 284%) (Supplementary Fig. S7). We note that in all cases of uniaxial stretching, the Poisson effect leads to compression in the orthogonal direction. The buckling profiles in these regions have behaviours that are consistent with FEA (Supplementary Fig. S8).

Electrochemical and mechanical behaviour of the battery

After choosing a set of dimensions that offers excellent system-level stretchability, with good areal capacity density, and modest interconnect resistance, we observed the best electrical performance for layouts in which the diameters of the disks for the cathode and anode are 2.20 mm and 1.58 mm, respectively, and the offset distances are 0.51 mm. This configuration corresponds to an areal coverage of 33% for the cathode, 17% for the anode, and 50% for the entire battery (in the undeformed configuration) (Supplementary Fig. S9). The interconnects have thicknesses of 600 nm and widths of 50 μm. For these parameters, the resistance between adjacent disks is 24 Ω, and that between the connexion lead and the most distant disk is 45 Ω. The leads for external connexion are thin and narrow to avoid strain at the interface, and facilitate connexion to flexible (but not stretchable) cables that connect to external characterisation equipment. The gel electrolyte combines the flow properties of viscous liquids with the cohesive properties of a solid, thereby allowing it to accommodate large strains while maintaining ionic conduction pathways.

Electrochemical properties of the battery electrodes without and with 300% uniaxial strain appear in Fig. 3a. The results show two well-defined plateaus at around 2.35 V corresponding to potentials of Co3+/4+ and Ti4+/3+ redox couples29. The mass of the LiCoO 2 (specific capacity 145 mAh g−1) at each unit is ~95 mg, and thus areal capacity density of 1.1 mAh cm−2 at a charge/discharge rate of C/2. The mass of Li 4 Ti 5 O 12 (specific capacity 160 mAh g−1) is ~90 mg, which corresponds to 5–10% more anode capacity than cathode30. Slurry disks with thicknesses larger than those described here yield improved areal capacity density, but with reduced rate capability due to the concentration polarisation in the disks31,32. The output resistance of the battery is ~70 Ω (Supplementary Fig. S10), and the leakage current is 1–10 μA, which arises from two main sources: the internal ohmic self-discharge between the slurry disks at the anode and cathode and Faradaic effects, including shuttle reactions associated with impurities in the slurry materials, residual oxygen and/or moisture. Experimental measurements described in the Supplementary Methods and Supplementary Fig. S11 show that use of separators and enhanced packaging schemes can reduce the capacity loss from 161 μA h to 23 μA h in 44 h. Figure 3b shows the coulombic efficiency (red) and cycling performance (black) of the encapsulated battery. The coulombic efficiency rises from ~60% for the first cycle to over 90% after three cycles. The initial loss can be attributed to the formation of a solid-electrolyte-interphase, and lithium is consumed in side reactions with impurities in the electrolyte. The gradually degrading capacity retention results not from the cycle fade (Supplementary Fig. S12) but more likely from the calendar fade due to some combination of reaction with residual water in the packaging materials, moisture penetration and electrical discontinuity of slurry particles that detach from the disks, which are not hot pressed and can be sometimes observed in the electrolyte gel. Further increasing the baking temperature and optimising the composition of the slurries, such as increasing the binder ratio, could reduce the latter behaviours. Improved conditions for device assembly could reduce effects of the former. Varying the depth of discharge from 100% to 75% did not have a significant effect on the degradation characteristics (Supplementary Fig. S13). Figure 3c shows the output power of the battery, when connected to a resistor 2.02 kΩ), during biaxial stretching and releasing. The slight decrease in output power with strain likely results from increased internal resistances that arise from the significantly increased separations between slurry disks with strains at these large levels. The battery provides sufficient power to operate commercial light-emitting diodes, with turn on voltages of 1.7 V (Supplementary Fig. S14), as shown in Fig. 3d. The battery could be stretched by up to 300% (Fig. 3e, Supplementary Movie 3), folded (Fig. 3f) and twisted (Fig. 3g) without noticeable dimming of the light-emitting diode. Furthermore, FEA demonstrates that the effective modulus (66.8 kPa) of the full composite structure of the battery is only slightly higher than the modulus (60.0 kPa) of the silicone substrate materials. As a result, the battery is not only stretchable but also exceptionally soft and compliant. The battery modulus is, in fact, lower than that of the human epidermis (140–600 kPa)8, thereby offering the potential for integration onto the skin and biological tissues, without significant mechanical loading. Figure 3h shows that the battery is compliant when mounted on human skin.

Figure 3: Electrochemical and mechanical properties of the battery. (a) Galvanostatic charging and discharging of the battery electrodes without (black) and with 300% uniaxial strain (red). (b) Capacity retention (black) and coulombic efficiency (red) over 20 cycles with a cutoff voltage of 2.5–1.6 V. (c) Output power as a function of applied biaxial strain. (d) Operation of a battery connected to a red light-emitting diodes (LED) while (e) biaxially stretched to 300%, (f) folded, (g) twisted and (h) mounted on the human elbow. Full size image

Stretchable wireless charging system for the battery

In many practical cases such as implanted devices the ability to charge the battery without establishing physical connexions to external supplies can be valuable. Even in systems where the charging terminals are accessible, such as in skin-mounted systems there is value in wireless charging, simply because the process of establishing physical contacts can be mechanically destructive to thin, stretchable components (or to the underlying soft tissue). Approaches that involve physical contact also have the danger of electrical shock to surrounding materials (for example, the skin itself). The versatility of the materials and designs enable integration of wireless power transmission systems, monolithically with the battery itself. The design and an actual device appear in Fig. 4a and b, respectively. A secondary coil couples the electromagnetic flux from a primary coil, and a Schottky diode provides rectification. The Schottky diode (packaged in epoxy, with a modulus of ~4.0 GPa) has a modulus of more than 4 orders of magnitude larger than that of the silicone substrate, but its size (length 0.62 mm, width 0.32 mm and height 0.31 mm) is only a few per cent (~2%) of the overall size (~30 mm × ~20 mm) of the wireless system. As a result, the influence on the overall stretchability is still negligible, as demonstrated by finite element simulations shown in Supplementary Figs S15 and S16. The parallel capacitor smooths oscillations in the output voltages; its small size and thickness enable natural integration into the overall system. Larger capacitors can smooth the oscillations to an even greater extent (Supplementary Fig. S17). The coil and rectifier add a series resistance of 2.3 kΩ (Supplementary Fig. S18), which functions as a parallel resistance with the secondary coil, shunting away current from the battery. The resistance of the serpentine secondary coil is 1.92 kΩ m−1; a coil with similar overall geometry but without the serpentine shape is calculated to be 1.22 kΩ m−1. The efficiency of the charging system can be improved by increasing the width and thickness of the wires, but at the expense of reduced stretchability and increased modulus. Specific application requirements will define the right tradeoffs. In this case, the output power from the primary coil was 187 mW. With a working distance of 1 mm between the primary and secondary coil, the power received on the secondary coil is 9.2 mW, corresponding to an efficiency of 4.9%. Increasing the secondary coil thickness to 7 μm improves the efficiency from 4.9 to 17.2%. At this thickness, the coil retains stretchability to strains of 25% (Supplementary Fig. S19). The capacitor has a capacitance of 1.7 nF, in a structure that uses a 1.2-μm thick layer of PI as the dielectric, with a layer of thiol molecules on the bottom Au electrodes to enhance adhesion. Figure 4c shows the input and output of this wireless power transmission device. An input voltage at a frequency of 44.5 MHz matches the self-resonant frequency of the secondary coil, which depends on the coil area, number of turns, distance between each turn and wire resistance. For a peak-to-peak input voltage of 9.1 V (Fig. 4c, black curve), the DC output voltage is 3.0 V (Fig. 4c, red curve). The charging curves of a small-scale battery using the wireless coil appear in Fig. 4d. The battery voltage (Fig. 4d, orange curve) rises to 2.5 V in about 6 min. The charging current in the circuit (Fig. 4d, blue curve) decreases from 0.5 mA to below 0.2 mA. We used a partial differential equation to model the charging circuit, and a numerical program to calculate the charging current curve. Simulation of this process agrees well with the experimental data (see Supplementary Methods and Supplementary Fig. S20).