Research Article
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Effect of Filler Aspect Ratio on Stiffness and Conductivity
in Phase-Changing Particulate Composites
Amir Mohammadi Nasab, Trevor L. Buckner, Bilige Yang, and Rebecca Kramer-Bottiglio*
magnetorheologicalcomposites,[11,14]
fluids[6,7] and elastomers,[15] electrorheoVariable stiffness in elastomers can be achieved through the introduction oflogical fluids,[16] and elastomers,[17] shape
low melting point alloy particles, such as Field’s metal (FM), enabling onmemory polymers,[18] shape memory
demand switchable elasticity and anisotropy in response to thermal stimulus.
alloys,[12,19,20] thermoplastics,[21] liquid
Because the FM particles are thermally transitioned between solid and liquid
crystal elastomers,[22–24] and phasephases, it is beneficial for the composite to be electrically conductive sochanging filler-composites.[3,9,25,26] Amongthe stiffness may be controlled via direct Joule heating. While FM is highly
these approaches to achieve variable stiffness, electrically responsive methods, in
conductive, spherical particles contribute to a high percolation threshold. In
particular, are advantageous for electrothis paper, it is shown that the percolation threshold of FM particulate commechanical and untethered robotic sysposites can be reduced with increasing particles aspect ratio. Increasing thetems.[27] Exploring electrically actuatedaspect ratio of phase-changing fillers also increases the rigid-to-soft modulus
methods, magnetorheological and elecratio of the composite by raising the elastic modulus in the rigid state whiletrorheological systems often require thesupport of bulky external hardware suchpreserving the low modulus in the soft state. The results indicate that lower
as electromagnets and high-voltage power
quantities of high aspect ratio FM particles can be used to achieve both elecsupplies. However, thermally responsive
trical conductivity and stiffness-switching via a single solution and without
systems, such as phase-changing filler
introducing additional conductive fillers. This technique is applied to enable
composites empowered with direct Joulea highly stretchable, variable stiffness, and electrically conductive composite,heating (resistive-heating), may enable
which, when patterned around an inflatable actuator, allows for adaptable
more compact robotic systems.
Phase-changing
fillercomposites
trajectories via selective softening of the surface materials.
achieve variable stiffness through solidliquid phase transition of their inclusions, and their variable stiffness property can be tuned based
1. Introduction
on the choice and volume fraction of the inclusions and thematrix. The incorporation of fillers also enhances mechanMaterials and structures that can reversibly switch their stiffical strength, elastic modulus, or thermal conductivity of theness between “rigid” and “soft” in response to external stimuli
composites in most cases. However, achieving electrical conare required in many emerging applications in soft robotics,[1–4]ductivity in phase-changing filler composites for direct Joulemedical devices,[5] the automotive industry,[6,7] and wearable
heating is a challenge. Recently, several groups have utilized
electronics.[8] Specifically in soft robotics, these materials can be
external heaters, such as helical conductive wires and serpenused as artificial muscles or stiffness-tunable tendons and ligatine channels of liquid metal, along with thermally responsive
ments.[9,10] Variable stiffness materials are load-bearing in one
materials, to decrease the stiffness of a structure by increasingor several directions in their rigid state, but when transitioned
the temperatures past the melting point or glass transition
to their soft and often stretchable state, let their hosting structemperature of the variable stiffness material.[28,29] As anothertures undergo shape change. By using variable stiffness materials, complex configurations and motion trajectories can beapproach, conductive fillers such as carbon black[30] andachieved with a reduced number of actuators in robotic shapegraphite[31] have been incorporated into phase-changing or
morphing structures.[11,12]
thermoset polymer matrices to impart electrical conductivity,
usually resulting in materials with high electrical resistivity but
Variable stiffness can be achieved through different
no elastic response.
methods[1] using granular materials,[13] fluid-polymer
In a recent work, a three-component particle–fiber–elastomer
composite
was fabricated with high stiffness tunability and
A. Mohammadi Nasab, T. L. Buckner, B. Yang, R. Kramer-Bottiglio
electrical conductivity.[32] Conductive nickel-coated carbon
School of Engineering & Applied Science
Yale University
fibers bridge between the spherical particles of a low melting
9 Hillhouse Ave., New Haven, CT 06511, USA
point alloy in the elastomer matrix and create conductive pathE-mail: rebecca.kramer@yale.edu
ways in the material. Although the stiffness tunability range in
The ORCID identification number(s) for the author(s) of this article
this work is as high as ≈30×, the presence of rigid nickel-coatedcan be found under https://doi.org/10.1002/admt.202100920.
carbon fibers limits the material’s stretchability to ≈20% in its
soft state.
DOI: 10.1002/admt.202100920

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Figure 1. Variable stiffness silicone composite with enhanced electrical and mechanical properties. a) Schematics and microscopic images of silicone
composites containing spherical and HAR FM particles. b) Microscopic images of the FM particles with ARs ranging from 1 to 19.5. c) Cold–hot
modulus ratio and electrical conductivity of the composites containing Ecoflex 30 and FM particles versus ARs of inclusions at 40 vol% of inclusions.
Each data point is acquired based on testing five samples and error bars represent ±1 standard deviation. d) Two specimens of the variable stiffness
composites containing spherical (left) and HAR (right) inclusions are shown in the stiff (cold) state, bearing load, and in the soft (hot) state, being
stretched. The composites are rigid at room temperature (25 °C) and soft when T > 62 °C. An external heat source (heat gun) is needed to soften thecomposite containing spherical particles, however the composite containing the HAR particles is heated via electrical current applied to both endsof the specimen. Video S1 (Supporting Information) shows the temperature distribution in the sample with HAR particles while being Joule-heated,
captured with an IR camera. Both composites here contain 55 vol% FM in Ecoflex 30.

Here, we study filler aspect ratio (AR) as a way to impartelectrical conductivity and stiffness-switching via a single solution without introducing additional conductive fillers in phasechanging filler composites. For this study, we adapted our previous variable stiffness material[25] composed of a silicone matrix(Ecoflex 30) and Field’s metal (FM; eutectic alloy of bismuth,
indium, and tin with a low melting point at Tm = 62 °C) particles. The elastic modulus of FM drastically and rapidly drops
from 9.25 GPa[33] when heated above its melting temperature
via solid–liquid transition. When FM particles are embedded inan elastomer, the elasticity of the composite is modulated by
the phase of the embedded particles. On its own, FM is highly
conductive, with a resistivity of 5.2 × 10−7 Ωm (about 31× thatof copper). However, achieving the percolation threshold forelectrical conductivity in a filler composite using only sphericalparticles is challenging without introducing other composite
defects. The incorporation of high aspect ratio (HAR) particles
reduces the percolation threshold for creating electrical pathways and, at the same time, increases the elastic modulus of
the composite. In the following sections, we present fabrication
methods for creating both spherical and HAR particles (fibers)of FM ranging from AR = 5.6 to 19.5 (Figure 1a,b), characterize

Adv. Mater. Technol. 2021, 2100920

the mechanical and electrical properties of silicone composites
containing these particles, and demonstrate the applicationof a highly stretchable, variable stiffness, and electrically conductive composite in a robotic structure with reprogrammableactuation trajectories.

2. Results and Discussion
Increasing the AR of fibers in a composite material increases
the material stiffness in composites with fixed filler contents[34,35] Figure 1c shows that if the volume content of the FM
fillers is kept constant at 40%, the modulus of the composite
containing the particles with AR = 19.5 is ≈2× the modulus of
the composite containing the spherical FM inclusions. Because
the incorporation of HAR particles in a composite matrix creates line contacts between the inclusions, in contrast to point
contacts in the case of spherical inclusions, it also reduces
the percolation threshold for creating conductive pathways[36](Figure 1a), thereby enhancing electrical conductivity.[37–39]
Figure 1c shows that at 40 vol% of FM inclusions, composites containing spherical particles (AR = 1) are not electrically

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Figure 2. Electrical properties. a) Electrical conductivity of silicone composites containing FM inclusions with varying AR versus the volume content of the inclusions. Each data point is acquired based on testing fivesamples and error bars represent ±1 standard deviation. b) Percolationthreshold of the silicone composites versus AR of inclusions obtained byfitting the data shown in (a) to the equation σ = σ0(Vf − Vc)t.[38]conductive, while increasing the AR of fillers from 5.6 to19.5 enhances the electrical conductivity of composites by≈7 orders of magnitude.
When heated, FM inclusions undergo a solid–liquid phasechange and the stiffness of the composite decreases. Figure 1dshows that strips of the variable stiffness composite containing
either the spherical particles or HAR particles can hold a 100 gweight in their rigid state. The composite containing the spherical particles will need an external source of heat to soften, but
the composite containing the HAR particles can be softened
through Joule-heating on demand by applying an electricalcurrent to both ends of the strip. Video S1 (Supporting Information) shows this softening process when the input power
applied to both ends of the strip is 8 W (2 V and 4 A).
We systematically characterized the electrical conductivity
and percolation thresholds of composites containing HAR particles. Figure 2a shows that by either increasing the vol% or
the AR of fillers, the electrical conductivity of the composite
increases. It can also be seen that the percolation thresholddecreases with increasing the AR of fillers. The electrical conductivity of polymer composites obeys a power law dependence, σ = σ0(Vf − Vc)t, predicted by percolation theory for filler
concentrations which is sufficiently close to the percolationthreshold. Equation σ = σ0(Vf − Vc)t only applies to the volume
fractions greater than the percolation threshold, Vf > Vc, whereVf, Vc, σ0, and t are the volume fraction of filler, the percolationthreshold, a constant, and the critical exponent, respectively(See Supporting Information for more details).[38] The percolation threshold is ≈50 vol% when AR = 5.6, and it decreases to≈40 vol% when the AR = 19.5 (Figure 2b).
Figure 3 compares the mechanical properties and electricalconductivity of the composites containing HAR particles with
AR = 5.6 and 19.5 in rigid and soft states versus different volume
fractions of FM inclusions. By increasing either the volume
fraction or AR of FM fillers, both the elastic modulus and cold–
hot modulus ratio are also increased (Figure 3a,b). Our resultsfor elastic moduli of composites as cast in Figure 3a are inagreement with the theoretical results from the Halpin-Tsai andAdv. Mater. Technol. 2021, 2100920

Guth (see Supporting Information for more details) composite
models.[34,35] We find that Halpin-Tsai can reasonably model theelastic modulus of composites containing inclusions with AR =19.5, which is in agreement with prior literature.[32] However,
the model overestimates the modulus in composites containing
inclusions with AR = 5.6, so the Guth model has been implemented to model the latter case.
If the composite is first softened and then strained to 150%,
the oxide layer on the inclusions’ surface will rupture, allowing
the inclusions to reflow and coalesce to create an interconnected FM network. Subsequently, when the network structurecools and solidifies, the elastic modulus of the composite in
the rigid state is increased even further. We chose 150% as theactivation strain because all composites with different volume
fractions of HAR FM particles were activated in our experiments beyond this threshold. The increase in the elastic modulus is not observed when the composites are softened but notstrained, which we attribute to the presence of the thin oxide
layer (≈4 nm, E =116 GPa[40]) at the surface of the particles. FM
oxide is composed of ≈90 wt% indium oxide (In2O3), ≈10 wt%
tin oxide (SnO2), and a negligible amount of bismuth oxide(Bi2O3) in which indium oxide is the dominant chemical compound with a melting temperature at ≈1910 °C.[41] The failure
strain of the oxide layer is dependent on its thickness and has
been reported 0.003 for a 16.8 nm thick film.[42] Therefore, we
surmise that the FM oxide does not melt, but rather a large
strain must be applied in the soft state to break the oxide layer
encompassing the molten core of the particles and “activate”
the composites. This activation process also enhances the electrical conductivity in the composites and is more drastic, up to≈5 orders of magnitude, for composites with lower content of
the HAR FM inclusions (Figure 3c,d and Figure S1, Supporting
Information).
We note that the experimental results for the elastic modulusof the composites containing particles with AR = 19.5 do notfollow the trend predicted by Halpin-Tsai theoretical equations
when the content of FM inclusions exceeds 55 vol% (shaded
region in Figure 3a). We attribute this drop in the elastic
modulus of the composites to an increasing presence of voids(Figure 3e), since the maximum packing fraction in a randomly
dispersed 3D mixture decreases with increasing AR of inclusions.[37] The porosity of the composites has been calculated byweighing the samples with known dimensions and then comparing the density of the samples with the theoretical density
obtained from the rule of mixtures. Figure 3e shows that theporosity of the composites including more than 55 vol% of FM
particles with AR = 19.5 is more than 25%, which significantly
affects the elongation at break of the composite at rigid andsoft states. The elongation at break for composites containing
inclusions with AR = 19.5, shown in Figure 3f, reduces by about
100% in the soft state when the FM content increases from 55
to 60 vol% and above.
Porosity further affects the stability of samples undergoing
thermal cycling. The standard deviation of the elastic modulusof the activated composites reported in Figure 3a is less than
20% for all composites containing AR = 5.6 particles, and also
for composites containing AR = 19.5 particles at FM volume
fractions lower then 50%. This standard deviation, which is ameasure of the soft-to-rigid reversibility of the composites, isdirectly affected by the porosity of the structure, as structures

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Figure 3. Comparing mechanical and electrical properties of composites containing FM inclusions with AR = 5.6 and 19.5. a) Elastic modulus of composites in the rigid state versus FM volume content before and after activation. The Halpin-Tsai (green line) and Guth (black line) theoretical models
are in good agreement with the experimental results. Data points represent five samples that were each cycled five times between cold and hot states.
b) Cold–hot modulus ratio of composites versus volume content of FM inclusions before and after activation. c) Electrical conductivity of composites
versus volume content of FM inclusions with AR = 5.6 before and after activation. d) Electrical conductivity of composites versus volume content of FM
inclusions with AR = 19.5 before and after activation. e) Porosity of the composite containing inclusions with AR = 19.5 versus the volume content of FM.
f) Elongation at break versus volume fraction of FM inclusions with AR = 19.5 in the rigid and soft states. Error bars represent ±1 standard deviation.

with higher porosity are more prone to FM leakage and reduced
soft-to-rigid reversibility. Figure S2 (Supporting Information)shows the elastic modulus of representative composite samples
containing particles with AR = 19.5 after activation in the rigid
and soft states.
Finally, we employ the results of our study to introduce
a material that is both electrically conductive and possesses
variable stiffness properties, which we apply to a soft inflatable cylindrical actuator to program its actuation trajectories
via selective softening of the surface materials (Figure 4). The
sidewall of the actuator was fabricated from a thin silicone
membrane embedded with inextensible parallel threads, andboth ends of the actuator were capped and sealed with lasercut acrylic disks. The actuator could only extend in the longitudinal direction when pressurized due to constraints appliedby the inextensible threads in the radial direction. Three composite strips, containing 50 vol% of FM inclusions with AR =19.5, were located axisymmetrically around the sidewall of theactuator and glued using uncured silicone as the bonding agent(Figure 4a). The actuator was pressurized with 10 kPa air pressure and held its straight configuration when all the strips werein the rigid state (Figure 4b). When one of the strips was softened by applying 2.5 A electrical current, an average powerrate of ≈0.005 W mm−3, the sidewall under the compliant strip
could extend, and as a result, the actuator bent toward the opposite direction (Video S2, Supporting Information). Figure 4c–eAdv. Mater. Technol. 2021, 2100920

shows the actuator bending, with a curvature of ≈0.1 cm−1,
toward left, right, and back when the right, left, and front strips
were softened, respectively.

3. Conclusions
We studied the effect of filler aspect ratio in phase-changing filler
composites on modulus range and electrical conductivity. Basedon these findings, the composite developed herein contains asingle type of inclusion that contributes to both variable stiffness
properties and electrical conductivity, allowing high mechanicalstrains (≈300% for Vf < 55%) when heated and softened. Incorporation of FM HAR particles substantially increases the coldhot modulus ratio of the composite compared to the case ofusing spherical inclusions. Using HAR particles also reduces
the percolation threshold for electrical conductivity, which is very
challenging to achieve using spherical particles alone. Adjacentinclusions are in sufficient contact to create electrical pathways,
and when the composite is softened and stretched for the firsttime, the inclusions coalesce and create longer structures, whichfurther increases the elastic modulus of the composite in the coldstate. For example, the cold–hot modulus ratio of a composite
containing 55 vol% of FM inclusions with AR = 19.5 increased
from ≈25 to ≈45 after activation. We showcased the applicationof this composite in controlling the trajectory of a soft body while

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Figure 4. Three strips of the composite are positioned and glued axisymmetrically around the sidewall of an inflatable cylindrical actuator (a). The
actuator is made of a silicone membrane with embedded inextensible parallel threads to constrain the radial expansion of the structure. When all thecomposite strips are in the rigid state and the actuator is pressurized with 10 kPa air pressure (b), the actuator holds its straight configuration. However,when the right, left or front strip is softened, the actuator bends toward c) left, d) right, or e) back, respectively. The red strip in the schematic shows
the location of the compliant strip.

being softened with electrical current on-demand. We expect that
HAR phase-changing fillers will be widely used in the future forcreating stiffness tunable composites in robotics due to theirease of implementation and manufacture.

4. Experimental Section
Fabrication and Characterization of HAR Particles: The fabrication
process of the HAR FM particles is illustrated in Figure S3, Supporting
Information. An ingot of FM (Roto144F, RotoMetals, Inc.) was submerged
in a 200 mL glass beaker filled with deionized water and the mixture washeated up on a hot plate for ≈20 min at 100 °C to melt the FM. In thenext step, a 3 mL syringe was used to collect 2 mL of the molten metal
and the hot water. A blunt tip needle with the appropriate inner diameter(50 to 270 μm) was inserted on the syringe tip, and the contents of thesyringe were injected into a 500 mL beaker containing water at room
temperature. In this process, long fibers of FM were created due to theinstant solidification of the molten metal stream entering the cold water.
The above procedure was repeated till all the molten FM content wascollected with the syringe and transformed into long FM fibers. Next,a mechanical homogenizer (Cole-Pramer LabGEN 850) with a 20 mm
diameter saw-tooth generator attachment was inserted into the mixtureof the water and long FM fibers at 5000 rpm for 30 s to smash thelong FM fibers into short FM fibers (HAR particles). The supernatant
was removed from the beaker and the particles were dried in a vacuum
oven at 55 °C for ≈12 h to remove as much of the remaining moisture
as possible. The resulting dry particles may agglomerate together likesandstone and needed to be shaken apart and sieved. AR of the particles
was controlled by the inner diameter of the needle used for injecting
the molten FM into cold water. The clearance between the stator androtor of the homogenizer saw-tooth generator was fixed at ≈0.7 mm andtherefore was not actively used to modulate the AR of the particles. The
length and diameter of the particles were measured using the visual
processing software ImageJ, and AR was calculated as length/diameterfor each individual particle. Length was measured along the full curveof a given particle as the particles were not always straight. The average
ARs and the standard deviations for different batches are reported in
Figure 1b.
Fabrication of Spherical Particles: Spherical particles were
manufactured via a process modified from ref. [43]. An ingot of FM(Roto144F, RotoMetals, Inc.) was submerged in a 500 mL glass beaker
filled with 200 mL of a thixotropic mixture, made from an aqueous

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solution of confectionery sodium alginate powder with a loading of
2 wt%. The mixture was then warmed up to ≈70 °C by placing the beakerinside of a heated oil bath (95 °C). Once fully melted, the FM ingot was
broken apart using a mechanical homogenizer (Cole-Parmer LabGEN
850) with a 20 mm diameter saw-tooth generator attachment for 60 s
at a specified rpm depending on the particle size desired (higher rpms
corresponded with smaller diameter particles). After homogenization,
the medium shear-thickened in place, which prevented the Field’s metal
droplets from settling or aggregating while they were allowed to cool.
The mixture was then diluted in a large container by stirring in additional
water, at which point the FM particles were able to settle and collectat the bottom of the container. The supernatant was removed from thebeaker and the particles were dried in a vacuum oven at 55 °C for ≈12 h
to remove as much of the remaining moisture as possible. The resulting
dry particles may agglomerate together like sandstone and needed to be
shaken apart and sieved.
Fabrication of Composite: HAR FM particles and Ecoflex 30 (Smooth-onInc.) were hand-mixed for ≈1 min to distribute the particles evenly
throughout the silicone matrix. The mixture was then cast into acrylic
molds with appropriate dimensions for the mechanical and electricaltesting. The molds were placed in a vacuum oven at room temperaturefor 2 min to degas the mixture. Next, the samples were cured in an ovenat 60 °C for 12 hs.
Fabrication of Inflatable Cylindrical Actuator: The cylindrical actuator
was made by first creating a thin silicone (EcoFlex 30, Smooth-On)
membrane with embedded parallel polyester threads at 3 mm spacing,
and then wrapping the membrane into a cylinder of 1-inch diameter.
The membrane was positioned in a way that the inextensible threads
constrained the expansion of the actuator in the radial direction. Acrylic
caps with holes were laser-cut and Luer lock connectors were glued tothe caps using instant adhesive (Loctite 401). The acrylic caps were thenattached on both ends of the cylinder with silicone adhesive (Sil-poxy,
Smooth-On). The detailed fabrication process of the silicone membrane
embedded with the inextensible treads is described in previous work.[44]Three 90mm × 10mm × 3 mm composite strips were then positioned
axisymmetrically around the sidewall of the actuator and glued using
Ecoflex 30 as the bonding agent. Copper shims were wrapped aroundboth ends of the composite strips to be used as electrodes. One drop of
liquid metal (eGaIn) was used between the electrodes and the composite
to reduce the contact resistance between the strips and the copper
electrodes. Fabric reinforcements were added over the electrode sites tocreate a strain-free region to provide reliable electrical connections.
Mechanical Testing: For stiffness characterization, tensile testing
was conducted on 50mm × 10mm × 3 mm rectangular samples of

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the FM-Ecoflex 30 composite using an Instron 3345 testing systemequipped with a 50 N load cell. Fabric reinforcements were adhered toboth ends of each sample for enhancing the grip in the Instron machine,which resulted in a stretchable portion of 30mm × 10mm × 3 mm foreach sample. The samples were loaded in tension with a constantdisplacement rate of 2 mm min−1, up to a strain of 5%, and thenunloaded to the stress-free state. Bluehill Universal testing software wasused to automatically calculate the elastic moduli of samples from thestress–strain measurements.
Electrical Testing: Strips of copper shim were wrapped around the endsof each 60mm × 5mm × 2 mm rectangular sample of the FM-Ecoflex 30
composite, resulting in a stretchable portion of 50mm × 5mm × 2 mm.
The samples were left in an oven at 80 °C for 15 min and then both ends
were slightly squeezed to enhance the electrical connection between thecopper stripes and the FM inclusions. The samples were placed inside
a Petri dish and uncured Ecoflex 30 were poured into the Petri dish to
submerge the samples, such that they can be embedded in a thin skin ofsilicone on both sides to prevent melted FM leaking in later steps. Next,
the Petri dish was left in an oven at 60 °C for 6 h. Finally, the samples
were carved out of the cured sheet. A four-point probe technique wasadopted to measure the electrical resistivity of the samples using a
digital multimeter (BK Precision 5492B) at room temperature in two
different scenarios of 1) the pristine state and 2) after stretching thesamples up to 150% for the first time in the soft state and releasing
them to come back to their original lengths and cooling down.

Supporting Information
Supporting Information is available from the Wiley Online Library orfrom the author.

Acknowledgements
This material is based upon work supported by the National Science
Foundation under Grant No. EFMA-1830870.

Conflict of Interest
The authors declare no conflict of interest.

Data Availability Statement
The data that support the findings of this study are available from thecorresponding author upon reasonable request.

Keywords
conductive composite, shape morphing, variable elasticity, variable
stiffness
Received: July 23, 2021
Revised: August 30, 2021
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