Research Article
www.advmat.deSoft Actuators Made of Discrete Grains
Sophia Eristoff, Sang Yup Kim, Lina Sanchez-Botero, Trevor Buckner,
Osman Doğan Yirmibeşoğlu, and Rebecca Kramer-Bottiglio*
microscale actuation. However, thesematerial-based actuators are often slow or
only expand or contract axially, preventing
use in applications that require volumetric
expansions. To address such limitationsof existing actuating materials, actuators
based on the liquid-to-gas phase change ofsolvent inclusions encapsulated in a hyperelastic matrix have been realized. Phasechange actuators are capable of inducing
rapid volumetric expansion similar to
fluidic actuators, without being tethered toan external fluid source.[29–32]
Accepting the advantages of phasechange actuators, we now turn ourattention to granular media. Granularassemblies, consisting of discrete grains,
can be tuned to accomplish a variety ofdifferent responses. For example, favorable
self-assembly of granular media can beachieved via modulating interparticle
interactions and external stimuli,[33–36] andgranular assemblies with different packing
configurations have been shown to yield
different bulk properties.[36–39] Furthermore, granular media can
exhibit optimized changes in stiffness during jamming transitions, enabling tunable moduli.[16,40–44] When unjammed, thebulk material is compliant, and when jammed, the bulk material
can achieve the stiffness of the grains. Finally, when mixed into
carrier fluids, granular media can impart thixotropic behavior
on the carrier fluid due to dynamic jamming,[45–48] enabling 3D
printing of previously unprintable materials. With all the advantageous properties granular media has to offer, the technology
has seen application in soft robotics,[49–52] medical devices,[53–55]
flexible airfoils,[56] and programmable aggregate architecture.[57]Here, we bring together the unique advantages of phasechange soft actuators and granular media to introduce soft
granular actuators made of discrete, volumetrically expanding
grains. A single active grain consists of multiple solvent cores
encapsulated in a hyperelastic silicone shell (Ecoflex 00-30).
At elevated temperatures, the encapsulated solvent vaporizes
and increases the internal pressure of the hyperelastic shell,
inducing volumetric expansion of the grain. The grains are
independently capable of rapid, high-force microscopic actuation, and are also easily arranged into granular assemblies toform larger-scale bulk actuators. Furthermore, agglomerates ofactive grains can self-assemble from disordered arrangements
to conform around objects and exhibit variable moduli. Finally,
the use of grains suspended in a carrier solvent or resin enables
compatibility with granular self-assembly and 3D printing techniques, offering the potential to print volumetrically expanding
actuators into freeform patterns across scales.

Recent work has demonstrated the potential of actuators consisting of bulk
elastomers with phase-changing inclusions for generating high forces andlarge volumetric expansions. Simultaneously, granular assemblies have beenshown to enable tunable properties via different packings, dynamic moduli
via jamming, and compatibility with various printing methods via suspension
in carrier fluids. Herein, granular actuators are introduced, which represent
a new class of soft actuators made of discrete grains. The soft grains consistof a hyperelastic shell and multiple solvent cores. Upon heating, the encapsulated solvent cores undergo liquid-to-gas phase change, inducing rapid
and strong volumetric expansion of the hyperelastic shell up to 700%. The
grains can be used independently for micro-actuation, or in granular agglomerates for meso- and macroscale actuation, demonstrating the scalability of
the granular actuators. Furthermore, the active grains can be suspended ina carrier resin or solvent to enable printable soft actuators via establishedgranular material processing techniques. By combining the advantages ofphase-change soft actuation and granularity, this work presents the opportunity to realize soft actuators with tunable bulk properties, compatibility with
self-assembly techniques, and on-demand reconfigurability.

1. Introduction
Soft robots have garnered interest due to their potential ability
to change shape in response to changing tasks or environments,[1–5] be robust to impacts and falls,[6–8] conform to thehuman body without restriction on the natural mechanics ofmotion,[9–13] and grasp delicate and diverse objects.[14–17] Furthermore, soft robots embed safety at the material level, and are
generally accepted as a path toward human-safe co-robotics.[18,19]
Fluidic actuators are the most common artificial muscle technology employed in the soft robotics literature,[2,20–22] however,fluidic actuators typically require actuator-source tethering, limiting the mobility of the robot.[19–21,23,24] Alternatively, stimuliresponsive materials, such as hydrogels[25] and shape-memory
polymers,[26–28] have been proposed to realize untethered,
S. Eristoff, S. Y. Kim, L. Sanchez-Botero, T. Buckner, O. D. Yirmibeşoğlu,R. Kramer-Bottiglio
School of Engineering and Applied Science
Yale University
9 Hillhouse Ave., New Haven, CT 06511, USA
E-mail: rebecca.kramer@yale.edu
S. Y. Kim
Department of Mechanical Engineering
Sogang University
35 Baekbeom-ro, Seoul 04107, Republic of Korea
The ORCID identification number(s) for the author(s) of this article
can be found under https://doi.org/10.1002/adma.202109617.

DOI: 10.1002/adma.202109617

Adv. Mater. 2022, 34, 2109617

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www.advmat.deFigure 1. Overview of the volumetrically expanding grains. A) Working mechanism of a grain. When placed on a hot plate of 200 °C, the grain exploits
the liquid-to-gas change of the encapsulated solvent cores, leading to a rapid volumetric expansion up to 730%. B) A group of grains, showcasing
the scale of the high-throughput synthesis process. C) A mixture of the grains and uncured matrix resin enables 3D printing of freeform actuators.

2. Results
Figure 1 shows an overview of granular actuators and theirscalable design space. A grain consists of a soft hyperelastic
shell with multiple embedded solvent cores (Figure 1A). At
elevated temperatures, a grain will volumetrically expand due tothe liquid-to-gas phase change of the solvent cores. Post actuation, the grain’s shell elastically recovers as the solvent coresevacuate. The active grains are prepared via a high-throughput
double emulsion process, yielding large numbers of grains(Figure 1B). Incorporating the grains into uncured silicone
resin enables printability, opening up the design space for
freeform actuators (Figure 1C).
We first characterized the multicore hyperelastic grains
and their manufacturing parameters (Figure 2). To synthesize
grains, perfluorodecalin (PFD) is first emulsified in uncured
silicone (Ecoflex 00-30). Thereafter, the resulting PFD/silicone
mixture is poured into an aqueous medium of sodium alginate,
where the mixture is then emulsified a second time (Figure S1,
Supporting Information). Once the uncured silicone is broken
down sufficiently, the shear-thinning thixotropic properties of
the aqueous sodium alginate enables static-state solidification.[58] This double emulsion results in silicone grains withmultiple solvent cores suspended in the aqueous continuous
phase, which can be rinsed away after the silicone cures.
Optical microscopy images under transmittance light reveals
the spherical shape of the grains (Figure 2A). The size of thegrains is tunable by either modulating the viscosity of thesodium alginate medium or the shear rate during the second
emulsification process (Figure S2, Supporting Information). In
general, the higher the viscosity of the medium or the shear
rate, the lower the mean diameter of the resulting grains,which is in agreement with existing emulsion processes.[58–60]
When prepared at 500 rpm in a 3 wt% sodium alginate aqueous
medium, the size distribution of the grains exhibits a normal
distribution with a mean diameter of 162 µm (Figure 2B). Thermogravimetric analysis (TGA) reveals that each grain contains

Adv. Mater. 2022, 34, 2109617

around 8 wt% PFD solvent when compared against neat silicone control spheres (Figure 2C), and cross-sectional scanningelectron microscopy (SEM) images confirmed internal grainpockets where PFD was contained (Figure 2D). The neat control spheres absorbed <1 wt% of PFD when soaked in a PFD
bath for 24 h, underscoring the need to encapsulate solvent
within the grains.
To quantify actuation performance, we conducted actuation force measurements on a single grain using a dynamic
mechanical analyzer (DMA) (Figure 2E). Elevating the temperature above the vaporization point of PFD (142 °C), the active
grain produced a rapid actuation force of 62 kPa. In comparison, both neat control spheres and control spheres were soaked
in PFD generated marginal forces <2 kPa, which is presumably
due to the thermal expansion of the Ecoflex 00-30 matrix. The
rapid expansion of a grain is attributed to the snap-through of
its hyperelastic spherical shell as,
1 1
P = C  − 7 λ λ 

(1)

where P and λ are the internal pressure and the stretch ratioof the grain respectively, and C is the material constant derived
from various elastic properties (Equation (1), and Figures S3and S4 and Section S1, Supporting Information).[61,62] Notably,
the structural instability of the hyperelastic spherical shell gives
rise to the near-instantaneous expansion of the grain via snapthrough behavior, an actuation strong and fast enough to elicit
jumping (Figure 2F and Movie S1, Supporting Information).
The expanded grain obtained a rough surface texture as theindividual pockets of solvent expanded, distinguished from thesmooth wall of pristine grains, and underwent shape recovery
as the encapsulated solvent evacuated (Figure 2G). The grains
exhibited a volume increase of ≈125% due to plastic deformation at higher temperatures, which agrees with prior works.[63]Post-actuation, the grains are unable to undergo subsequentactuation sequences due to silicone permeability at high strains,
thus leading to evacuation of the solvent cores.

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www.advmat.deFigure 2. Characterization of the volumetrically expanding grains. A) Optical microscopy image of the multicore hyperelastic grains. B) Size distributionof the grains, controlled by a shearing speed during emulsification and viscosity of the sodium alginate medium (see Figure S2, Supporting Information). C) TGA results of the grains and control spheres prepared using identical materials and processes but without PFD inclusions. Control spheres
are also soaked in a PFD bath but uptake a marginal amount of PFD. D) Cross-sectional SEM images of a grain and a control sphere. Multiple cavities
in the grain serve to contain PFD solvent. E) Actuation force results of a grain and a neat control sphere with and without being soaked in PFD solvent.
The grain exhibits rapid volumetric expansion past the boiling point of PFD, in stark contrast to control spheres. F) Time-lapse images of a jumping
grain taken at 500 frames per second. G) Optical microscopy images of a grain prior to and post actuation. Multiple cores and cavities are visible.

The scalability of granular actuators—actuators made up ofmultiple or many volumetrically expanding grains—was investigated by embedding active grains into a silicone elastomer
to realize a composite material (Figure 3). Since a concentration of the grains can be directly mixed into uncured silicone
resin, the composite manufacturing process is easy to scale
up and readily tailorable to control the bulk actuator properties (Figure 3A). Upon heating, the composite exhibits a rapid
sequence of multiple actuation events as each embedded grain
expands individually (Figure 3B and Movie S1, Supporting
Information). Expansion stress measurement results revealthat the actuation force of a composite actuator with a grain

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fraction of 60 wt% is 150 times greater than that of the control
specimens embedded with neat control spheres (Figure 3C).
It is possible to modify the stress and strain properties of thecomposite by modulating the grain fraction, Wc (Figure 3D).
Additionally, adjusting the grain fraction gives rise to different
measured volumetric expansions, where higher grain fractions
induce larger volumetric expansions (Figure 3E).
The active grains can be incorporated into a low-viscosity solvent like ethanol or water to enable drop-on-demand printing,as shown in previous works,[64–66] or even arranged without
any liquid external media (in air). However, here we focus on
incorporating grains into an elastic medium to showcase the2109617 (3 of 8)© 2022 Wiley-VCH GmbH

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www.advmat.deFigure 3. Characterization of the soft granular composite. A) Optical microscopy image of the composite actuator with embedded grains. B) Expansionof the granular composite when exposed to forced hot air. C) Actuation force results for the granular composite and control composites that replace thegrains with neat control spheres (no PFD cores). The control composite with embedded control spheres shows negligible actuation. D) Actuation force
results for the granular composite with varying grain concentrations, Wc. Increasing the Wc leads to an increase in actuation forces. E) Volumetric expansion results of the granular composite with varying grain concentrations, Wc. Increasing Wc leads to an increase in volumetric expansion, up to 1200%.

scalability and extrusion-based 3D printability of the grains(Figure 4). Our composite actuator with embedded active grains
unlocks printable soft actuation, which has remained elusive inexisting phase-change actuators. Typically, phase-change actuators exhibit low uncured viscosity due to the incorporated liquidsolvent, rendering it impossible to achieve 3D printing of thematerial without the addition of viscosity enhancers.[29–31] However, in our method, the grains provide not only the solvent
inclusions but also the viscosity enhancement of an otherwise
unprintable low viscosity carrier resin, increasing the thixotropic response with increasing grain fraction (Figure 4A). The
amplitude sweep in Figure 4B shows the linear viscoelastic
region and the yielding region for our high fraction uncured
granular composites (60 wt%) with a storage modulus (G′) of
2830 Pa and a dynamic yield stress (σy) of 123 Pa. The ink canflow after the yield point but rapidly regains its structure after
extrusion (Section S2, Supporting Information). The shaperetention κ = h/w, where h and w are height and width of theprinted filament respectively, remains >0.9 at a grain fraction
Wc = 60 wt% (Figure 4C), which is sufficient for 3D printing(Figure 4D and Movie S1, Supporting Information), thus enabling the freeform fabrication of soft actuators with highly
varied designs.
We present the practical utility of both the granularity andactuation properties of the grains in Figure 5. The microscopic
actuation of a single grain can be used to lift a mass 2000 times
its own weight in less than 2 ms (Figure 5A and Movie S1,Adv. Mater. 2022, 34, 2109617

Supporting Information). When individual actuating grains arepatterned onto a microscale soft cylinder and placed on a heatsource, the grains in contact with the heat source sequentiallyexpand to induce rolling locomotion (Figure 5B and Movie S1,
Supporting Information). Furthermore, a collection of grains
can be integrated into a soft pouch to give rise to a jamming
gripper (Figure 5C and Figure S5 and Movie S1, Supporting
Information).[16] The enclosed grains exhibit compliance atatmospheric pressure and when under vacuum pressure, thegrains undergo jamming behavior, increasing the stiffness ofthe system and enabling gripping of the object. Because thegrains can be utilized both as discrete components and incomposite form, they serve as effective soft actuators across avariety of scales and applications (Figure 5D and Figures S6–S9and Section S3, Supporting Information).
To demonstrate the potential for our granular composite
actuator to be printed onto arbitrary structures, Figure 5E
shows short segments of the granular composite printed
directly onto a soft cylinder, enabling local curvatures along theinert filament. The working principle of the actuating filament
can be extended to control the morphing of a 2D soft silicone
film (Figure 5F and Movie S1, Supporting Information). Finally,
the granular composite can be printed directly onto inanimate
fabrics[67] to, for example, provide pronounced motion for gait
or gripping behavior (Figure 5G and Movie S1, Supporting
Information). Exploiting the scalability, dynamic tunability,and flow properties of granular media, coupled with the rapid

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www.advmat.deFigure 4. Printability of grains in a soft granular composite. A) Rheological behavior of Ecoflex 00-30 resin and grain mixtures. Shear thinning behaviorof the mixture becomes apparent as the grain concentration, Wc, increases. B) Effect of the applied shear stress on the resin and grain mixture viscosity.
Higher Wc enables printability. C) Shape retention of the mixture after printing on a flat surface as a function of Wc. D) 3D printing and actuation ofsoft granular actuators in a variety of shapes.

and strong volumetric expansions of phase-change actuators,
actuating grains offer the potential to collectively broaden thedesign space of robotic systems.

3. Conclusion
We have developed granular actuators that exploit the advantageous properties of both granular media and phase-change
actuators. Consisting of a hyperelastic shell and multiple PFD
solvent inclusions, a single volumetrically expanding grain produces micro-actuation via thermally driven phase change ofthe solvent. The expanding grains can be used independently
for micro-actuation, or in collectives for larger-scale actuation. Additionally, collections of grains exhibit variable bulk
mechanical properties based on their configuration, assembly,
and boundary conditions (e.g., jamming). When suspended ina carrier solvent or resin, the grains favorably modify the rheological properties in a way that enables stable 3D printing ofbulk soft actuators. Via printing, inanimate objects can be easily
augmented with widely varied soft actuator designs, displaying
the multifaceted potential of the soft granular actuator.

Adv. Mater. 2022, 34, 2109617

Naturally, there are areas for improvement with this technology. By modulating particle size and interparticle interactions, we hypothesize control over particle self-assembly
behavior, collectively enhancing granular actuator properties
and manufacturing techniques by enabling optimized packing
configurations and the opportunity to employ drop-on-demand
techniques. We also expect to move beyond single-stroke actuation sequences to repeatable actuation of the grains by optimizing the constituent materials to prevent solvent evacuation.
Additionally, we see a need for precise, localized commandof actuator grains. Utilizing a range of solvents with distinct
vaporization temperatures could enable controlled actuation
sequences, while an addressable heating interface could allow
us to specifically actuate certain grains within a cluster.
We see various potential applications for granular actuators in future works. Actuating grains can be switched froma solid-like to liquid-like state via confinement pressure,allowing the actuator to be rearranged into a variety of configurations on-demand, which implies a potential for rapid
prototyping and high customization of soft actuators. We
envision adaptable soft robots, with granular actuators thatcan flow within the body to sites where forces are needed.

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www.advmat.deFigure 5. Multiscale design space of the grains in various applications. A) Actuation of a single grain allows lifting an object >2000 times heavier
in less than 2 ms. B) Adhering grains onto a soft body realizes an all-soft locomoting system that can rotate due to the expansion of each grain.
C) Under vacuum pressure, a collection of grains in a silicone pouch may undergo jamming behavior, enabling gripping of objects. D) Application
space of the grains. Individual grains and granular composites act as effective actuators across scales. E) Printing the granular composite onto
1D inert soft filaments provides substantial morphing depending on patterning. F) Granular composite can be printed onto a 2D silicone laminae to
direct its actuated curvature. G) Conventional fabrics can be granted motion when the granular composite is printed in a pattern.

Additionally, due to the printability of the granular composite, we foresee intricate, 3D actuators patterned alongsideother components to achieve new levels of robotic material
integration. Finally, we envision a generalized, easy-to-use,volumetrically expanding actuator that can replace the needfor tethered air supplies. Given the vastly versatile potentialof granular actuators, we are optimistic that this new classof actuation will open up broader design spaces for diverse
robotic systems across scales.
Adv. Mater. 2022, 34, 2109617

4. Experimental Section
Materials: Platinum-cure silicone polymer Ecoflex 00-30, Platinum
silicone cure accelerator Plat-Cat, Silc Pig silicone dye, silicone thinner,and SIL-Poxy adhesive were purchased from Smooth-On (Macungie,
PA). Sodium alginate was purchased from Modernist Pantry (Eliot, ME,USA) and PFD (95% purity, vapor pressure of 0.88 kPa at 25 °C) was
purchased from Sigma Aldrich (St. Louis, MO, USA).
Preparation of Grains: The sodium alginate solution was prepared bymixing a designated mass of sodium alginate into a volume of distilled

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www.advmat.dewater. Higher concentrations of sodium alginate in water resulted inhigher viscosity of the medium; a concentration of 3 wt% was used inthis work (Figure S10, Supporting Information). This sodium alginate
solution was mixed using an overhead mixer (IKA Eurostar 20) until
completely homogeneous. Grains were created by mixing Ecoflex
00-30, cure accelerator, silicone thinner, red silicone dye (for better
visualization), and PFD in a planetary mixer (ARE-310 Thinky) for 1 min
at 2000 rpm. Subsequently, the polymer mixture was poured into thesodium alginate solution and mixed in the ARE-310 Thinky for another10 min, at a designated speed (nominally 500 rpm). The mixture wasplaced in an oven at 80 °C for 1 h to cure. Finally, the mixture wasfiltered through an ASTM E-11 standard sieve and thoroughly rinsed with
distilled water. Grains were stored in a suspension of PFD to prevent
ambient evaporation of solvent prior to intended use.
Experimental: TGA was performed using a TGA Q50 from TA
Instruments over a temperature range of 30–300 °C, at a rate of
10 °C min−1 in N2 atmosphere. A grain size of ≈1 mm diameter was used
for TGA analysis.
Actuation force measurements were performed using a DMA fromTA Instruments (model 850) with a parallel compression plate fixture of
23 mm in diameter. Specimens were placed into a shallow aluminumdish machined such that the upper compression plate of the DMA fit
neatly within its inner diameter. Each test began by equilibrating thechamber temperature to 40 °C. Next, contact with the specimen was
ensured as an initial preload of 500 Pa was applied relative to thecross-sectional area of the specimen, and was allowed to stabilize for2 min to mitigate the effects of any strain relaxation. After this point,
the parallel plates remained stationary in an isostrain configuration.
The temperature of the DMA chamber was then increased to 200 °C at
a rate of 10 °C min−1 in a nominal air atmosphere. As the specimens
activated, the blocked expansion force was measured. A grain size of≈1 mm diameter was used for actuation force analysis of single grains. A
grain size of ≈200 µm diameter was used for actuation force analysis ofcomposite actuators. Since increasing the dimensions of the composite
actuator sample, namely the thickness, could enable higher measured
expansion stresses, the specimens must be normalized with regard tosample thickness (Figure S11, Supporting Information).
SEM images were obtained using a Hitachi SU-70 at 2 kV.
Rheological behavior of the uncured composite actuator was analyzed
using an Anton Paar MCR 302 rheometer in a parallel plate geometry
with a diameter of 25 mm and gap size of 1.5 mm. Shear rate was varied
from 1 to 100 Hz with clockwise rotational motion at room condition.
Dynamic oscillatory tests were performed with increasing amplitude
stress up to 1000 Pa at a frequency of 1 Hz. A grain size of ≈200 µm
diameter was used for rheological analysis of composite actuators.
High speed videos were captured at 500 frames per second using a
Micro LAB110 from Vision Research.
3D Printing of Grains: A customized 3D printer attached with a Tefloncoated 18G (inner diameter: 1.041 mm) nozzle was used for additive
manufacturing. A mixture of 60 wt% grains in uncured Ecoflex 00-30 was
loaded into a 50 mL syringe and extruded using a high precision fluid
dispenser. A grain size of ≈200 µm diameter was used. The pot lifeof the premixed material in the syringe was limited to a time of up to
45 min. However, this limited print time could be resolved by using
an active mixing system commonly seen in literature.[68–70] Completed
prints were then left to cure at room temperature for 4 h prior toactuation. The experimental setup with the modified printer is shown in
Figure S12, Supporting Information, and the print parameters are
displayed in Table S1, Supporting Information. Flow rate calculations
and the printing process are discussed in Section S4, Supporting
Information. Printed primitive shapes and their dimensions are shownin Figure S13, Supporting Information.
Demonstrations: The all-soft microscopic rolling system was preparedby adhering a group of grains onto a soft cylinder made of Ecoflex
00-30 by using SIL-Poxy adhesive. The jamming gripper was prepared byembedding grains of ≈3–5 mm in diameter into an Ecoflex 00-30 pouch.
A standard vacuum pump was used for demonstrative purposes. For
the composite actuator, a mixture of uncured Ecoflex 00-30 and grains

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were prepared at 60 wt% of grain concentration (Wc). A grain size of≈200 µm diameter was used. The actuation of both the grains andcomposite actuator was achieved by placing them onto a hot plate set
to a temperature of 200 °C or applying forced hot air. The authors notedthat in the robotic fabric demonstration some slight discoloration of thefabric was visible due to heating, and that heat-resistant fabrics might
mitigate this issue.

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

Acknowledgements
This material was based upon work supported by the NSF under grant
no. EFMA-1830870. S.E. was partially supported by a NASA SpaceTechnology Graduate Research Fellowship (80NSSC21K12690). S.Y.K.
was supported by an NSF CAREER award (CMMI-1812948). L.S.-B. was
supported by an NSF Human-Centered Computing award (IIS-1954591).
T.B. and O.D.Y. were supported by a NASA Early Career Faculty award(80NSSC17K0553). The authors thank Prof. Minjiang Zhong and Prof.
Eric Brown for access to testing equipment. The authors thank Dr. Amir
Mohammadi Nasab for assistance in editing the manuscript.

Conflict of Interest
The authors declare no conflict of interest.

Author Contributions
S.Y.K. and S.E. contributed equally to this work. S.Y.K. and R.K.-B.
conceived the idea. S.Y.K. and S.E. performed the materials design
and manufacturing. S.Y.K., S.E., L.S.-B., and T.B. performed thematerial characterization. S.Y.K., S.E., L.S.-B., and O.D.Y. performed
the demonstrations. O.D.Y. performed the additive manufacturing. All
authors participated in writing the manuscript.

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

Keywords
double emulsion, granular actuators, multicore
multiphase composites, phase-change actuators,
actuators, soft robotics

microcapsules,
printable soft

Received: November 25, 2021
Revised: February 5, 2022
Published online: March 10, 2022

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