1

Supplementary Information for “A multifunctional shape morphing

elastomer with liquid metal inclusions”

Michael J. Ford1, Cedric P. Ambulo2, Teresa A. Kent1, Eric J. Markvicka3,4, Chengfeng Pan1, Jonathan

Malen1, Taylor H. Ware2, Carmel Majidi1,3,5

1Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213

2Department of Bioengineering, University of Texas at Dallas, Richardson, TX 75080

3Robotics Institute, Carnegie Mellon University, Pittsburgh, PA 15213

4Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE

68588

5Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213

Detailed LM-LCE synthesis: 12g of 4-bis-[4-(3-acryloyloxypropypropyloxy) benzoyloxy]-2-

methylbenzene (RM257, Wilshire Technologies, Fig. S1 in SI) were dissolved in 4.5 g of toluene by

heating in an 85 oC oven. The saturated solution was allowed to cool to room temperature before adding

0.675 g of the tetra-functional thiol crosslinking monomer, pentaerythritol tetrakis(3-mercaptopropionate)

(PETMP, Sigma Aldrich), and 3.17 g of the di-functional thiol spacer monomer, 2,2-(ethylenedioxy)

diethanethiol (EDDET, Sigma Aldrich). For composites synthesized with photoinitiator, 0.576 g of

PETMP and 2.88 g of EDDET were added along with 0.144 g of the photoinitiator 2-hydroxy-4′-(2-

hydroxyethoxy)-2-methylpropiophenone (HHMP, Sigma Aldrich). After vigorous mixing, the mixture

was returned to the 85 oC oven for 10 min. 1.5 g of the catalyst dipropylamine (DPA, Sigma Aldrich)

diluted 1:50 by weight in toluene was added after allowing the uncured mixture to cool to room

temperature. If air bubbles were present, the mixture would be placed under vacuum for 60 s. Catalyst

was stirred into the mixture slowly, and the viscous mixture was poured into high density polyethylene

molds. The reaction proceeded for > 5 h until the composite was a stiff gel before placing the molds in an

85 oC vacuum oven for > 8 h to completely remove solvent. Composites were mechanically sintered for

internal joule-heating by applying pressure to the sample until the sample was conductive. After sintering,

any LM residue on the surface was cleaned with isopropyl alcohol.

Detailed thermo- and electro-mechanical characterization: Dogbone samples with dimensions of

about 30 mm 10 mm 1 mm were stretched at 10 mm/min using an Instron 5969. Elastic moduli were

calculated at 2-3 % strain after at least 3 cyclic pre-strain cycles to a nominal strain of < 10 %. For

electromechanical characterization, entire samples were mechanically sintered. A USB DAQ (USB-6002,

NI) was used to collect analog data from the Instron 5969 while also recording resistance data from a

voltage divider. The data were collected with MATLAB, 2018a (MathWorks, Inc.).

DMA was performed on rectangular samples measuring 23 6 1 mm3 with an active testing gap of

approximately 18 mm. Samples were tested at 0.4 % strain at 1 Hz and heated from -15 to 120 °C at a rate

of 2 °C min-1. All samples underwent annealing at 80 °C and were then cooled to room temperature 24

www.pnas.org/cgi/doi/10.1073/pnas.1911021116

2

hrs prior to testing. The temperature corresponding to the peak of tan δ curve was used to measure Tg and

Tm.

Thermal actuation of the composite samples was characterized for rectangular samples measuring

approximately 20 4 0.75 mm3 were tested in tensile mode. To measure the actuation strain of the

unprogrammed LM-LCEs, constant stresses of 10, 20 and 40 kPa were applied to each composite sample.

0 kPa stress was applied to programmed LM-LCEs. Each sample was heated and cooled three times from

25 °C to 150 °C at a rate of 2 °C min-1. The blocking stress at failure for programmed LM filled samples

with dimensions of 20 mm 4 mm 0.75 mm was evaluated through iso-strain testing using DMA. The

samples were fixed to a set strain of 0.01 % and heated from 25 °C to 150 °C at a rate of 2 °C min-1.

Detailed transient hot wire thermal conductivity: The cylindrical heat diffusion equation defines the

thermal conductivity, k, as k = q/4πξ where q is the linear heat rate (W/m), calculated using measured

current and resistance values, and ξ = d(ΔT)/(d[ln(t)]). Pt wire with 25 µm diameter and length of 10-40

mm was embedded into samples before curing or sandwiched and clamped between samples after curing.

A Keithley 2700 Digital Multimeter and a Keithley 6221 DC/AC Current Source in a four-point

measurement configuration was used to apply a 40 mA or 80 mA current, I, while the voltage, V, is

recorded. The resistance, R, as a function of time, t, follows Ohm’s Law where R(t) = V(t)/I, which was

used to calculate ΔT(t) = [R(t)/R0 – 1]/β and q = I2R0/l where R0 is the initial resistance of the wire; β =

3.75 × 10−3 K−1 is the coefficient of thermoresistance of Pt; and l is the length of the wire. The change in

temperature vs. time was thus measured and fitted using a nonlinear regression algorithm in MATLAB

2014a to determine k.

The thermal conductivity was measured 100 times for each sample, with multiple (n > 3) samples

measured for unstrained thermal conductivity. Bruggeman effective medium theory was used to fit the

unstrained data. For strained thermal conductivity measurements, where thermal conductivity is

anisotropic, unfilled LCEs and 50 vol. % LM-LCE composites were stretched above 100 % strain by hand.

Upon releasing the strain, the sample relaxed but remained elongated at about 50-60 % strain due to liquid

crystal reorientation. The Pt wire was sandwiched and clamped between two pre-stretched samples.

Thermal conductivity was measured axially and transverse to the direction of strain to determine the

anisotropic thermal conductivity, where given a strain in the x-direction, kaxial = ky = kz with the thermal

conductivity in a particular direction equal to the geometric mean of the thermal conductivities extending

radially outward from the wire. Similarly, ktransverse = (kxkz)1/2 = (kxkaxial)1/2, or kx = ktransverse2/kaxial. A

modified Bruggeman formulation for elongated inclusions, (kp-kc)/(kp-km)×(km/kc)L, where kp is the thermal

conductivity of the particle inclusions; kc is the thermal conductivity of the composite; km is the thermal

conductivity of the LCE matrix; and L is the depolarization factor (L = 1/3 for spherical particles, returning

the using the original Bruggeman formula).20,21 For the strained model, the thermal conductivity of the

stretched LCE matrix was used for km, and the strain was set to 0.6. For thermal images, a FLIR C2 thermal

camera was used.

Thermal diffusion in the composite is expected to occur on the time scale of τ = (L/k + 1/h) × L ×

C, where L is the thickness; k is the thermal conductivity; h is the heat transfer coefficient of the

surrounding medium, and C is the volumetric heat capacity. The LCE specific heat capacity was measured

by monitoring thermal equilibration of a hot sample with room temperature water to be about 1000 J kg-1

K-1. A value of 330 J kg-1 K-1 was used for EGaIn, estimated using values of liquid indium and gallium

and the rule of mixing. This value is similar to the specific heat capacity of gallium and gallistan. The rule

of mixing was used to determine the heat capacity of the composite. A broad range of time constants is

given in the text given the uncertainty in the specific heat values.

3

Additional experimental details: For cycling frequency and long-term cycling at 1 Hz, 10 % duty cycle

was used with the actuation time indicating the amount of time the power was on. For cycling frequency,

the power supply was set with a supply voltage of 1.8 V. For long-term cycling at 0.007 Hz, the power

supply was set with a supply voltage of 1.5 V with a duty cycle of 16.7%. For long-term cycling at 1 Hz,

the power supply was set with a supply voltage of 8 V to achieve 2.5 % reversible strain. For specific

work determination, the composite was heated slowly by ramping the supply voltage until the weight was

fully lifted

For the multifunctional composite demonstrated in Fig. 1H, the composite acted as a transducer, sensing

the change in local electric field of the composite due to touch. Materials incapable of modifying the

electric field (e.g., insulators like wood) did not trigger a change in capacitance.

Descriptions for supplementary video.

Supplementary Video S1. This video includes a demonstration of multifunctionality of the conductive

composite, highlighting Joule-heated actuation and compatibility for capacitive touch sensing and digital

circuitry. LM-LCE composites were linked to an LED, to a microcontroller for capacitive sensing, and to

a power supply for Joule-heated actuation. When touch sensing was activated, Joule-heating was triggered

by the microcontroller and the LED turned on.

Supplementary Video S2. This video highlights actuation strain capabilities. The LM-LCE composite is

actuated to full actuation. Clips to record actuation strain as a function of actuation frequency are also

shown for frequencies of 10 Hz, 3 Hz, and 0.005 Hz.

Supplementary Video S3. This video features actuation and heat dissipation underwater. Heat dissipation

in water is better than in air for LM-LCEs, allowing for fast actuation. Colored lines are provided for

reference.

Supplementary Video S4. This video shows robustness and resilience of LM-LCEs. LM-LCEs can

operate in sub-freezing temperatures, while being punctured, and while being struck with a hammer. LM-

LCEs can also be stretched without inadvertently sintering LM droplets.

Supplementary Video S5. This video highlights the LM-LCE potential for soft robotic applications. A

soft crawling entity was fabricated using an LM-LCE as the active actuator with a thin layer of Sylgard

184 silicone adhered to the LM-LCE to force bending actuation. The crawler propels forward due to

asymmetric friction.

Supplementary Video S6. This video shows examples of LM-LCE composites that were programmed

with UV light to form zero-stress actuation of 3-D structures. Patterns were formed by stretching by hand

and masking particular regions of the composite. Corresponding patterns are indicated in the video.

Supplementary Video S7. This video features a linearly-programmed LM-LCE composite that undergoes

asymmetric Joule-heating. The video provides an example of how asymmetric Joule-heating can result in

unique shape-morphing.

Supplementary Video S8. This video includes a gallium-based LCE composite, rather than EGaIn. The

composite can be frozen to solidify the gallium microparticles, which rigidifies the composite. The

composite can be heated above the transition temperature of gallium but below the transition temperature

of the LCE matrix to allow the composite to stretch. By heading above the transition temperature of the

LCE, the composite can actuate. Gallium particles can be selectively melted by Joule-heating to produce

unique shape-morphing like bending and buckling shown in the example in the video.

4

Fig. S1. Chemical structures and schematic of the LCE network and shape change. The mesogen (blue

oval) is RM257; the spacer (green line) is EDDET; and the crosslinker (pink lines) is PETMP. The

mesogens order anisotropically and order is disrupted above the nematic-to-isotropic transition

temperature to enable macroscopic shape change.

5

Fig. S2. Linear response at low strains for each volume fraction composite and the unfilled LCE. The

blue dots represent the collected data and the orange lines represent linear fitting to determine the tensile

modulus.

6

Fig. S3. Representative cooling traces for 50 vol. % LM-LCE macroscopic length change for different

values of applied stress. As the applied stress increases, the normalized length change as a function of

temperature increases, a property typical for LCEs. The average values and standard deviations of

normalized length change were 1.70 ± 0.04 at 40 kPa and 1.58 ± 0.08 at 10 kPa for n = 3 measurements.

7

Fig. S4. Change in temperature versus time collected from transient hot wire experiments (colored data

points) along with fittings (gray traces) to determine thermal conductivity. Shown are examples of

multiple curve fittings for each volume fraction of liquid metal tested. Pt wires were of lengths between

10-40 mm. Note that 0-30 vol. % LM-LCE composites were tested at 40 mA whereas 50 vol. % LM-

LCE was tested at 80 mA for consistency in the magnitude of the change in temperature.

8

Fig. S5. Histograms of transient hot wire experimental results for each volume percent. Shown are all

unstrained data for each composition along with the normal distribution fittings.

9

Fig. S6. Resistance as measured while holding a power of 6.5-7 W (fixed voltage) for an extended

period of time, demonstrating suitability for long-term joule-heated actuation. The resistance was

measured from data collected from the Korad KA3010d precision variable adjustable power supply.

10

Fig. S7. Displacement and input power during Joule-heating of a 50 vol. % LM-LCE actuator. The

sample was heated for 8s followed by 35s of cooling (0.02 Hz). The stress during cycling was 30-35

kPa.

11

Fig. S8. Displacement data for 10 Hz cycling as tracked by digital video. The red and blue circles

indicate peak fitting to determine the displacement, which is less than 1 px in many of the actuation

cycles.

12

Fig. S9. The normalized displacement of a hanging weight was tracked for the first 1200 and last 1200

seconds of cycling. The composite retained >90 % of its initial normalized displacement (equivalent to

2.5 % reversible strain) after 100,000 cycles. Normalized displacement is defined as the displacement

normalized by the average of the first 100 displacements following equilibration of cycling.

13

Fig. S10. Representative normalized length change versus temperature during cooling for programmed

50 vol. % LM and unfilled linearly programmed LCE with 0 kPa stress applied.

14

Fig. S11. Representative trace of blocking stress for a programmed 50 vol. % LM-LCE. Blocking

stresses of 50 vol. % LM-LCEs were measured to failure (119 ± 36 kPa for n=4 measurements, failing at

74 ± 6 oC)

15

Fig. S12. A thermal image of asymmetric joule-heating overlaid atop a photograph of the linearly

programmed LM-LCE composite. The left side of the composite is heated while the right side remains at

a lower temperature.

16

Fig. S13. a) Differential scanning calorimetry at 10 oC/min for a gallium-LCE composite. The melting

transition onset is at 29.5 oC, above room temperature and below the LCE nematic-to-isotropic

transition. Undercooling below room temperature is necessary for recrystallization. b) Stress-strain

measurements of the gallium-LCE composites at room temperature when gallium is in the solid state

(left) and the liquid state (right) with each colored line representing subsequent measurements beginning

with the blue trace. For solid gallium microparticles, the composite is rigid and begins to tear at small

strains (<10 %) as apparent in the stress-strain traces where the first cycle (blue) has a higher modulus at

small strains than the subsequent cycles.

17

Fig. S14. Schematic for UV programming of pre-programmed LM-LCE composites. Patterns for each

individual shape-changing composite are shown in Supplementary Video S6.