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https://doi.org/10.1038/s41467-021-23992-2

OPEN

Static-state particle fabrication via rapid
vitriﬁcation of a thixotropic medium

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Sang Yup Kim 1,2, Shanliangzi Liu1,3, Sungwoo Sohn1, Jane Jacobs1, Mark D. Shattuck
Jan Schroers 1, Michael Loewenberg5 & Rebecca Kramer-Bottiglio 1 ✉4, Corey S. O’Hern1,

Functional particles that respond to external stimuli are spurring technological evolution
across various disciplines. While large-scale production of functional particles is needed fortheir use in real-life applications, precise control over particle shapes and directional properties has remained elusive for high-throughput processes. We developed a high-throughput
emulsion-based process that exploits rapid vitriﬁcation of a thixotropic medium to manufacture diverse functional particles in large quantities. The vitriﬁed medium renders stationary
emulsion droplets that preserve their shape and size during solidiﬁcation, and energetic ﬁelds
can be applied to build programmed anisotropy into the particles. We showcase massproduction of several functional particles, including low-melting point metallic particles, selfpropelling Janus particles, and unidirectionally-magnetized robotic particles, via this staticstate particle fabrication process.

1 Department of Mechanical Engineering and Materials Science, Yale University, New Haven, CT, USA. 2 Department of Mechanical Engineering, Sogang University,
Seoul, Republic of Korea. 3 School of Mechanical Engineering, Purdue University, West Lafayette, IN, USA. 4 Department of Physics, City University of New York, New
York, NY, USA. 5 Department of Chemical and Environmental Engineering, Yale University, New Haven, CT, USA. ✉email: rebecca.kramer@yale.edu

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P

articles are extensively used in various disciplines, such as
medicine1–3, materials science4–6, and robotics7,8. Such
minute fragments of matter are often incorporated into bulk
materials to achieve multifunctional composites9–11, dispersion
inks12,13, and granular metamaterials14, which yield gained functionalities responsive to external stimuli. Thus, mass manufacturingof functional particles is becoming increasingly important totranslate particulate material discoveries to large-scale applications.
One widespread method to mass-produce particles from bulk
matter is emulsion processing15–17 that consists of emulsifying abulk liquid in a continuous phase via either shear mixing or sonication, then solidifying the distributed phase. Although rapid andscalable, previous emulsion processes have not addressed the needfor high process yield18, monodispersity19,20, or anisotropy21,22.
Similarly, micro-ﬂuidic particle fabrication processes can addressthese critical demands, but produce small numbers of particles(large quantity production is time-consuming and costly).
Throughout an emulsion process, sedimentation or creamingof the distributed phase (emulsion droplets) after their creationand prior to their solidiﬁcation result in droplet coalescence,causing irregular clumps of particles and potentially ruining theoverall particle batch23,24. This phenomenon is usually prevented
by stirring the continuous phase until the distributed droplets are
fully solidiﬁed25–27, but this redundant shearing causes the droplets to collide and deform, ultimately leading to low process yieldand high particle heterogeneity. One proposed solution to thischallenge is to ﬁx and isolate each droplet in place by vitrifying
the continuous phase after emulsiﬁcation. This static-state particle fabrication process can eliminate coalescence and droplet
deformation, but existing methods require secondary steps tovitrify the continuous phase (e.g. freezing28–30, adding thickening
agent31,32) which are too complex and laborious to scale production volume.
Here, we report a method of fabricating particles via a scalable,
static-state emulsion process. The method uses a shear-thinning
thixotropic medium as the continuous phase that reduces its
viscosity with increasing shear and then rapidly vitriﬁes when theshearing stops. This rheological response of the continuous phaseenables both dynamic-state emulsiﬁcation (during shear mixing)
and static-state solidiﬁcation (with the mixer disengaged), allwithin the same batch and without additional processing steps.
Moreover, once the particles are held in place in the continuous
phase, energetic ﬁelds can penetrate the continuous phase to
induce anisotropy in the solidifying particles, enabling scalable
programming of the intrinsic particle properties. Our method
herein is highly generalizable as long as the continuous phaseexhibits thixotropy, and in this study, gelatinized corn starch inwater is used as the medium, which carries the additional
advantage of being eco-friendly with sustainable by-products.
Results and discussion
Overview of the static-state particle fabrication. Figure 1 shows
the overview of our static-state particle fabrication process thatenables scalable manufacturing and programming of functional
particles. The target material is placed in bulk in the corn starch/water medium and broken up by shearing (Fig. 1a). As the shear
rate ω increases, the viscosity ηc of the continuous phase drops andemulsiﬁes the target material. The shearing is stopped after theemulsiﬁcation and ηc increases by ~100 times to rapidly vitrify thecontinuous phase. The emulsion droplets are seized by networksof starch within the vitriﬁed medium and remain suspended
without creaming, sedimentation, or colliding with each otherduring the subsequent solidiﬁcation (Fig. 1b). This static-state
condition unlocks scalable programming of anisotropy in particles
when a mixture of nanoparticles and a polydimethylsiloxane
2(PDMS) resin is utilized as the target material (Fig. 1c). The
arrangement of nanoparticles, inside stationary resin droplets, iscontrolled by an external energetic ﬁeld to realize anisotropic
particles. In addition, prepared particles are easily retrieved byadding an enzyme to catalyze the hydrolysis of starch.
Scalable manufacturing of low-melting point alloy particles.
We ﬁrst demonstrate our method using Field’s metal (FM), a
Bi–In–Sn alloy with a low melting temperature of 62 °C, as the
distributed phase, as shown in Fig. 2. A bulk of molten FM isemulsiﬁed in a medium at 90 °C and solidiﬁed as the medium
cools below the melting temperature of the FM (see Methods fordetails). Previously, FM has been a challenging material toemulsify due to its high speciﬁc gravity (ca. 7.9), which causes
rapid sedimentation before the droplets of molten FM cool andfreeze33. However, using our method, the weight of the FM
droplets is supported by the vitriﬁed medium, allowing the particles to stay suspended during solidiﬁcation (see Supplementary
Movie 1). Utilizing a thixotropic medium also substantiallyenhances the quality of the produced FM particles. FM particles
fabricated from our static-state fabrication process show a highdegree of sphericity and surface smoothness (Fig. 2a). Thismorphology provides evidence that, in the absence of shear forces, the surface tension of the emulsion droplets dominates
during solidiﬁcation. Particle size analysis reveals a unimodal
distribution with a standard deviation ca. 19%, and a process yield(the ratio of the total mass of retrieved particles to that of the
input material) of >95%. Such a narrow size distribution anda high process yield are marked improvements compared toconventional emulsion-based processes, of which the process
yield ranges from 50 to 80%34,35.
The underlying mechanism behind our static-state method is
examined by comparing particles produced using the static- anddynamic-state methods. FM particles are deformed into ellipsoids
when they are solidiﬁed within a viscous starch/water mediumthat is under continued shearing (Fig. 2b). Such particle
morphology indicates that our static-state method eliminates
the capillary stress applied to the emulsion droplets during theirsolidiﬁcation, thereby preserving the spherical particle shape.
When water alone is used as the continuous phase, irregularities
in particle shape and size are further intensiﬁed (Fig. 2c). FM
particles fabricated within a low-viscosity Newtonian medium(water) have a variety of shapes (e.g. ellipsoid, platelet, spiky
sphere), and their sizes have a large standard deviation. We
hypothesize that such heterogeneous particle shapes and sizes
originate from high energy collisions of molten and solidiﬁed FM
droplets, which is effectively mitigated when starch is present in
the medium. The weakly perturbed environment of our staticstate process also alters the microstructure of FM, enabling
precise control of the particle quality (Supplementary Fig. 1 andSupplementary Note 1).
Vitriﬁcation of a thixotropic medium. We further investigate
the underlying mechanism to optimize the processing parameterswhich will enable mass manufacturing of complex particles(Fig. 3). We draw speciﬁc data from the starch/water medium
case previously described, but the principles can be expanded to
the generalized system. The viscosity ηc of the continuous phase iscontrolled by the weight fraction ϕ of starch in the medium andthe shearing rate ω (Fig. 3a). The increase of ηc in response to ω isnearly 2 orders of magnitude, which enables immediate vitriﬁcation once the shearing is stopped. In addition, higher ϕincreases ηc due to the higher density of gelatinized starch in themedium, and correspondingly, depolymerization of the starch(hydrolysis) decreases ηc. Therefore, to retrieve prepared particles,

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Fig. 1 Overview of the static-state particle fabrication process. a The viscosity of the starch/water medium ηC decreases with the presence of a shear
force (shear rate ω) in the emulsiﬁcation stage, and abruptly increases to the initial value when the shearing is stopped. This abrupt increase in ηC gives riseto the vitriﬁcation of the medium, ﬁxing the distributed phase (emulsion droplets) in place. b Stationary droplets isolated in the vitriﬁed medium undergo
the static-state solidiﬁcation devoid of deformation forces or coalescence, enabling the droplets to preserve their shape and size during the solidiﬁcation.
c Scalable programming of anisotropy in particles is realized by emulsifying a mixture of nanoparticles and a PDMS resin to composite droplets. The
nanoparticle inclusions are arranged by an external energy ﬁeld inside the stationary polymer droplets, followed by curing of the polymer resin.

Fig. 2 Field’s Metal particles fabricated under different conditions. a Static-state process in starch/water medium is devoid of any external force orinternal particle coalescence during the solidiﬁcation stage. Produced solid particles preserve the spherical shape of the emulsiﬁed droplets, and the particle
size distribution is narrow with the mean particle diameter d = 317 μm with the standard deviation s = 22%. The particle size distribution is shown in thevolume fraction, Q achieved from the image analysis, or in the cumulative mass, PQ achieved from the sieve analysis. b Dynamic-state process in starch/water medium mitigates internal particle coalescence but the continued shear force results in deformed particle shapes. c Dynamic-state process in water
medium gives rise to both particle deformation and coalescence, resulting in particles with irregular shapes and a wide size distribution of s = 65%.

we utilize hydrolysis of starch by adding enzyme, thereby
upholding the eco-friendly and biocompatible process initiallygranted from using starch.
However, distributed droplets are still prone to sediment
within the vitriﬁed medium unless their weight can be supportedby the viscoelastic stress of the vitriﬁed medium. To measure themaximum value of the viscoelastic stress, the stress relaxation of
the starch/water medium is examined (Fig. 3b). The stress applied
to the medium is gradually reduced until it reaches a plateau as afunction of time, and the value of the plateau point increases with

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Fig. 3 Characterization of the static-state particle fabrication process. a Rheological behavior of the starch/water medium. Either increasing a starchconcentration ϕ in the medium or decreasing a shearing rate ω increases the viscosity of the medium ηC . Hydrolysis of the starch reduces the viscosity ηC ,thereby facilitating the particle cleaning procedure. b Stress relaxation of the starch/water medium. The vitriﬁcation stress σv is deﬁned where the residual
stress plateaus after 1 h. c Vitriﬁcation diameter dv of Field’s Metal (FM) particles in the starch/water medium. Increasing ϕ results in a higher dv attributed
to the increased σ v . d A relation of the concentration ϕ and the mean particle diameter d for polymer resins and FM. Two types of polymer resins are used:high-viscosity Dragon Skin 10 and low-viscosity Semicosil 964. Error bars denote one standard deviation. e Time-lapse images of simulated particle
collision and coalescence behavior. Each particle is differently color-coded for clarity. f Coalescence probability Pc as a function of the viscosity ηC . Starchconcentration ϕ in correspondence to ηC reveals that a higher starch concentration in the medium mitigates the coalescence of the distributed phase.

increasing starch concentration ϕ. We use this plateau as the
maximum value of the viscoelastic stress because it indicates thatthe medium remains stationary as long an external stress is lessthan the plateau value. We deﬁne this plateau value as thevitriﬁcation stress σv (see Methods for details), and since σvmonotonically increases with ϕ, the medium can thus be tuned tosupport heavier droplets.
Static-state condition of distributed droplets. The vitriﬁcationstress σv, the density of the emulsion droplets ρdroplet , and thedensity of the medium ρmedium allow a prediction of the maximum
droplet size that will remain suspended within the medium as,
ΔρVg < Aσ v

ð1Þwhere Δρ ¼ ρdroplet  ρmedium , V is the droplet volume, g is thegravitational acceleration, and A is the droplet cross-sectional area.
Equation (1) can be simpliﬁed as d < 1:5σ v Δρ1 g 1 using thedroplet diameter d, and therefore, droplets that do not exceed thisspeciﬁc size (hereby deﬁned as the vitriﬁcation diameter, dv) canbe indeﬁnitely suspended within the vitriﬁed medium. Figure 3cshows dv of FM droplets (ρdroplet = 7,880 kg/m3) distributed
within the starch/water medium, which reveals the ability of thevitriﬁed medium to hold the heavy metallic droplets in place
without sedimentation. For example, dv of the FM droplets is~200 μm at ϕ = 10 wt%, and only ~ 0.1 μm at ϕ = 5 wt%.
We examine how to control the diameter of emulsiﬁed
droplets, such that the mean droplet diameter d is smaller than
dv. The droplet diameter can be controlled during theemulsiﬁcation primarily by tuning either the viscosity of thecontinuous phase ηC or the shearing rate ω. Figure 3d reveals thatd decreases with increasing starch concentration ϕ under a ﬁxed
4ω, because higher ϕ leads to higher ηC. Therefore, higher ϕ isgenerally advantageous for enabling vitriﬁcation because it
decreases d while simultaneously increasing dv (see Fig. 3c). For
example, under a given ﬁxed ω, the FM droplets produced at ϕ =7.5% are too large for the vitriﬁed medium to support their weight(d = 317 μm vs dv = 50 μm), but increasing to ϕ = 12.5% allows
for droplet suspension in the vitriﬁed medium (d = 230 μm vsdv = 360 μm). In the case of a ﬁxed ϕ, increasing ω can reduce d(Supplementary Fig. 2). Hence, both ϕ and ω can be controlled tosatisfy the critical process condition of d < dv.
Extension to polymeric distributed phase. To expand our
method to polymeric particles, two types of polymer resins withdifferent viscosities ηD are used as the distributed phase: Semicosil
964 (SC, ηD = 0.7 Pa s) and Dragon Skin 10 (DS, ηD = 23 Pa s).
Compared to FM particles, polymeric particles are lower density(ρdroplet ~ 1,000 kg/m3), enabling dv to reach tens of millimeters
while maintaining compatibility with the vitriﬁcation process. For
the emulsiﬁcation, particle size analysis shows that SC particles
are signiﬁcantly smaller than DS particles under identical emulsiﬁcation conditions (see Fig. 3d). This is presumably due to thedifference in surface tension γ (Supplementary Fig. 3), as capillarystress ηC ω applied to the distributed phase can emulsify the
distributed phase as long as ηC ω > γd1 is satisﬁed36,37. For thesame reason, both DS and FM particles are unable to be fabricated at ϕ < 5 wt%, in contrast to SC particles which are successfully fabricated but then agglomerate (Supplementary Fig. 4).
Mitigation of droplet agglomeration under shearing. Such
agglomeration of SC particles at low ϕ suggests that the presence

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of starch mitigates particle coalescence, which is also demonstrated from the FM particles in Fig. 2c. To understand theparticle coalescence process, we perform discrete element method
simulations to model collisions of dispersed droplets in a shear
ﬁeld and calculate the coalescence frequency Ω = C ´ PC , where C
is the collision frequency and Pc is the coalescence probability24.
Figure 3e shows a time-lapse simulation of individual particles
moving in a shear ﬁeld and agglomerating when gelatinizedstarch is absent (no inter-particle ﬁlm drainage), due to particle
collisions (Supplementary Movie 2). However, increasing ηCappears to have only a marginal effect on the collision frequency C (Supplementary Fig. 5) because C is mostly a functionof particle density and shear rate alone38.
Therefore, the coalescence frequency Ω is primarily dependent
on the coalescence probability PC , which is in turn a function of theviscosity of the medium ηC . Not all particle collisions lead tocoalescence; the form of the coalescence probability PC can be
described by
PC ¼ etc =ti

ð2Þwhere t i ~ ω1 is the duration of a collision event, t c ~ d 2 ηC f 1 is
the time required for droplets to coalesce, and f is the interaction
force between particles39. The relation between PC and ηC in Fig. 3f
reveals that PC sharply increases with decreasing ηC when the initialηC < 10 Pa s, which is consistent with the experimental results in
Fig. 3d that show the departure of d of SC particles at ϕ < 5.0 wt%.
These results indicate that the beneﬁt of exploiting a thixotropic
medium occurs during both the emulsiﬁcation and solidiﬁcation
stages, and that our fabrication method is highly generalizable tovarious types of thixotropic media (e.g. hydrogel, syrup).
Scalable programming of anisotropic particles. To showcase the
far-reaching impacts of our static-state particle fabrication
method, we demonstrate the scalable programming of anisotropy
in particles, as shown in Fig. 4. Anisotropic particles have promising applications in functional and intelligent materials, but
their fabrication processes have thus far been unfeasible to scaleup40,41. Our static-state method addresses these challenges ofmass-production by exploiting the relative difference in the d v of
metallic particles in a polymer resin and polymeric particles in a
thixotropic medium. By emulsifying a mixture of metallic
nanoparticles and uncured polymer resin, the metallic inclusions
can be arranged inside larger polymer droplets using a variety of
external forces before the polymer cures (Fig. 4a). The vitriﬁed
medium ﬁxes the geometry and location of the composite droplets during this process, ensuring that each anisotropic particle
maintains its size and shape as the internal inclusions ﬂow insidethe uncured resin.
We demonstrate two types of anisotropic particles—Janus
particles and unidirectionally magnetized particles. Janus particles
are made by leveraging the difference in densities between metaland polymer resin (ρmetal >>ρresin ), which causes sedimentation of
metallic inclusions (d > d v ) within uncured polymer droplets due
to gravity (Fig. 4b and Supplementary Movie 3). Figure 4c shows
Janus particles composed of small Ag inclusions (ρinclusion =10,490 kg/m3) arranged on one side of a larger PDMS droplet(ρdroplet ~ 1,000 kg/m3). These Janus particles can be used as selfpropelling particles when they are placed in hydrogen peroxide,because the Ag catalyzes a process that generates oxygen bubbles(Fig. 4d and Supplementary Movie 4). In addition, when Ag
inclusions are replaced with ferromagnetic Fe inclusions, prepared
Janus particles can elicit a controlled group assembly under anexternal magnetic ﬁeld, Bz (Fig. 4e). Similarly, mixtures of active
and Brownian particles are predicted to generate unexpected

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topological defects and spacings, which could lead to dynamic selfassembly of crystalline and metamaterial structures42.
Unidirectionally magnetized particles are made by applying an
external magnetic ﬁeld, Bz to uncured composite droplets withferromagnetic Fe inclusions, as shown in Fig. 5. The magnetic
ﬁeld, Bz aligns the internal inclusions along the ﬁeld, otherwise ahigh viscosity of the polymer resin upholds d < d v and allows theinclusions to remain randomly distributed (Fig. 5a). Figure 5bshows the imposed order inside a unidirectionally magnetizedparticle and a control particle with a random inclusion
distribution when no magnetic ﬁeld is applied during solidiﬁcation. The programmed magnetism of each particle enables
external control over single particle motions (Fig. 5c andSupplementary Movie 5), and furthermore collective particle
behaviors (Fig. 5d). Likewise, the anisotropy of these massproduced particles allows for controllable robotic motions, which
are not achievable using isotropic particles. We anticipate ourstatic-state particle fabrication process to shift paradigms indesigning and manufacturing intelligent particles that have beenmostly relied on microﬂuidic processes of low process yields.
In sum, we present a method to manufacture particles using
the rapid vitriﬁcation of a thixotropic medium. The vitriﬁcationof the shear-thinning medium allows the distributed droplets tosolidify, devoid of shearing forces typically required during theemulsion process. This lack of applied shear results in asigniﬁcant improvement in the consistency of particle shapeand size within a given batch, with a notable process yield rate
higher than 95%. Furthermore, we used the static-state process tomass-produce anisotropic Janus particles and unidirectionallymagnetized particles. The presented method is a technicalbreakthrough for future academic research into particulatecomposites, dispersion inks, and granular metamaterials, due toits simple implementation and high adaptability to many existing
intelligent particle designs. Moreover, the process is eco-friendly(no synthetic materials used) and energy-efﬁcient (no extra power
consumption from redundant stirring), which will streamline thetechnology transfer of this static-state particle fabrication toindustry-scale manufacturing.
Methods
Materials. Corn starch granules (MFG 2006779) were purchased from Argo
(Oakbrook, IL), and used to prepare starch/water mediums by mixing with DIwater at various concentrations of 5–25 wt% and gelatinizing the granules at 95 °C
for 1 h. Amylase enzyme (SKU: 5BHBZZ7100B) was purchased from BSG (Shakopee, MN). Field’s Metal blocks (SKU: LMP144) were purchased from RotoMetals(San Leandro, CA) and used as-is. Two-part silicone resin EcoFlex 00-30 and onepart RTV silicone resin Semicosil 964 were purchased from Smooth-On(Macungie, PA) and Wacker (Adrian, MI), respectively. Iron powder (<10 μm)(SKU: 267953) and silver-coated ferrite particles (~25 μm) (SM25P20) were purchased from Sigma Aldrich (St. Louis, MO) and Potters Industries, LLC respectively, and used as ﬁllers of anisotropic particles. Hydrogen peroxide and Triton X100 (SKU: X100) were purchased from Sigma Aldrich (St. Louis, MO) and used asreaction medium and surfactant for propelling Janus particles.
Preparation of Field’s Metal particles. A bulk of 10 g Field’s Metal was added to
the gelatinized starch/DI-water medium of 200 ml and melted for 2 min at 95 °C. A
shear mixer broke up the molten Field’s Metal at various shear rates and removed
off after 10 min. Two types of shear mixer were used to emulsify the molten Field’sMetal: a 10-speed overhead mixer (RW16, IKA) with a 3-bladed stirrer of 56 mm indiameter (Item# UX-50703-31, IKA), and a 6-speed lab homogenizer (LabGEN
850, Cole-Parmer) with a 20 mm saw-tooth generator (Item# UX-04727-41, ColeParmer). Applied shear rates are ranging from 600 rpm to 9,500 rpm when using
the overhead mixer, and from 17,500 rpm to 24,000 rpm when using the homogenizer. The entire medium containing micro-droplets of the molten Field’s Metal
was cooled down at room temperature to solidify the molten metal.
An aqueous solution of 5 wt% amylase enzyme of 100 ml was then added to theresulting batch and the temperature was raised to 40 °C to catalyze hydrolysis of thecontained gelatinized starch. The hydrolysis reaction was performed for 1–2 h under agentle shearing (i.e., a magnetic stir bar or a tube rotator) to ensure the contact
between the enzyme and the starch. Depolymerization of the starch from thehydrolysis caused Field’s Metal particles to rapidly sediment and the particles were

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Fig. 4 Scalable programming of Janus particles. a Illustration of preparing composite droplets to program anisotropy. b Manufacturing conditions for thecomposite droplets to evolve as Janus particles, determined by a relation between the vitriﬁcation diameter dv and the mean diameter d of the droplet.
Polymer droplets are ﬁxed in a vitriﬁed starch network (dv > d) while the nanoparticle inclusions sediment (dv < d). c Optical micrograph of a Janus particle
and its SEM and EDS images. The SEM image is false-colored to emphasize the presence of Ag on one side. d Self-propelling of the Janus particle inhydrogen peroxide. e Alignment of ferromagnetic Janus particles by an external magnetic ﬁeld, Bz.

Fig. 5 Scalable programming of unidirectionally magnetized particles. a Manufacturing conditions for the composite droplets to evolve as unidirectionallymagnetized particles. An external magnetic ﬁeld, Bz forces previously vitriﬁed nanoparticle inclusions (dv > d) to align along the magnetic ﬂux within thepolymer droplet. b Optical micrographs of a unidirectionally magnetized particle and a control particle prepared without a magnetic ﬁeld. c Rotating motionof the single magnetized particle using an external magnetic ﬁeld, Bz. d Collective actuated behavior of a group of the magnetized particles.

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easily retrieved. Such a hydrolysis step was especially important for fabricatingsmaller/polymeric particles because long-chains of the pristine starch remain adhered
to the particles until being cut into the short-chain glucose. Retrieved particles wereadditionally washed using DI-water for 3 times and dried at room condition.
Experimental methods. Rheological behavior of thixotropic gelatinized starch/DIwater medium was measured using RSA-G2 from TA Instruments with a parallel
plates ﬁxture of 15 mm in diameter. Frequency sweep was performed at 80 °C withan oscillatory strain of 1.0%, and a solvent trap was used to prevent the prematureevaporation of DI-water during the measurements. Stress relaxation was performedat room temperature with the initial strain of 1.0% and σ v is predicted from atrendline, at t = 1 h, achieved of the logarithmic experimental data. The surface
tension of polymer resins in water was measured via a pendant drop method atroom temperature. A drop of the resin formed at an ID 0.34 mm syringe nozzle(23 G, BSTEAN) was imaged using a Grasshopper camera (Part# GS3-U3-51S5MC, FLIR) and an imaging software ImageJ analyzed the radii of the drop. The same
method was applied, but the water at 70 °C, to measure the surface tension of themolten Field’s Metal. Optical micrographs of particles were obtained by Smartzoom 5 from Zeiss and scanning electron micrographs (SEM images) wereobtained using SU-70 from Hitachi where energy-dispersive X-ray spectroscopy(EDS) was also performed at 10.0 kV. XRD data were obtained using Rigaku
SmartLab X-ray diffractometer equipped with Cu Kα radiation under BraggBrentano focusing mode at step 0.02° over a 2θ range of 10° to 100°. The phase
identiﬁcation of the particles was analyzed using PDXL software.
The particle size distribution was achieved by two different methods: sieve
analysis and imaging analysis. Sieve analysis was performed by sieving a batch of
fabricated particles using a set of sieves and constructing a relevant cumulative
distribution curve. The mesh sizes of used sieves were 850, 355, 212, 106, 75, 45 μm
purchased from DUAL MFG (Franklin Park, IL) and the cumulative distribution
curve was predicted referencing the Weibull cumulative probability function as,ðxλÞkFðxÞ ¼ 1  e

ð3Þwhere k is the Weibull shape factor and λ is the scale factor.
Imaging analysis for the size distribution was performed on the particles
collected on each sieve, respectively. Backlight optical micrographs of the collectedparticles were taken, and the Image J software was used to calculate the frequencyof particle sizes pertinent to each sieve. The overall particle distribution Q(xk) was
obtained by multiplying this particle size frequency (from the imaging analysis)
with the weight fraction (from the sieve analysis) as,
pk x3kQðxk Þ ¼ wi ´ nði ¼ 1; 2; ¼ ; 6 and 1 ≤ k ≤ nÞ
∑ pj x3j

McMaster) to unidirectionally align the iron powders and remained for 3 h to allow
the polymer resin to cure. Both Janus particles and unidirectionally magnetizedparticles were cleaned via the aforementioned procedure that uses amylase enzyme.
Demonstration of robotic anisotropic particles. Self-propelling particles wererealized by placing Janus particles in a 100 mm PYREX petri dish, and 30 wt%
hydrogen peroxide solution was poured to initiate a reaction that creates oxygen
bubbles on the side of the Janus particle surfaces covered with silver-coated ferrite
particles. A surfactant Triton X-100 (0.5 wt%) was added to the solution to spur theoxygen bubbles on to be detached from the particle surface. Since the heavier ferrite
particles settle and become deposited from the very bottom of polymer droplets, wehypothesize the amount of the ferrite particles required to impart the selfpropelling ability will be notably less than what is used in this study (0.5 g per 1 ml
resin). The magnetized particles were actuated by placing into a rotating
magnetic ﬁeld.

Data availability
The data that support the ﬁndings of this study are available from the corresponding
authors upon reasonable request.

Received: 5 February 2021; Accepted: 18 May 2021;

References
1.
2.
3.
4.

5.

ð4Þ

6.

where wi is the weight fraction of particles collected on a sieve i (total 6 sieves), pj is
the frequency of particle at size xj in the sieve i. As a result, the mean particle
diameter d and normalized standard deviation s were achieved as,

7.

j¼1

N

d ¼ ∑ xk Qðxk Þ

ð5Þ

sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
N
2
N
s 1
s ¼  ¼  ∑ x2k Qðxk Þ  ∑ xk Qðxk Þ
d d k¼1
k¼1

ð6Þ

k¼1

8.
9.
10.
11.

where N is the total number of particles.
12.
Simulation of particle collisions. 2D simulation of particle collisions lacking astarch inter-particle layer was performed by assuming the particles moving in themedium as deformable sticky particles. Deformable particles were modeled using
polygons in which the vertices were freely jointed, but the area was conserved.
Stickiness, that gives rise to particle coalescence after their collision, was includedin the simulation via an energy term proportional to the particle surface.
The total number of particle collisions with respect to viscosities of the medium
was obtained in a 3D setting by assuming no collisions to cause particle coalescence.
Therefore, the total number of particles in a controlled 3D space was maintained thesame over time. See Supplementary Note 2 for details.
Preparation of anisotropic particles. Self-propelling Janus particles were fabricated by emulsifying a mixture of 1 ml semicosil-964, 0.3 ml toluene (solvent) and
0.5 g silver-coated ferrite particles in 50 ml gelatinized starch/water medium (10 wt% of starch concentration). The emulsiﬁcation was performed at room temperaturefor 30 s using the homogenizer applying a shearing rate of 600 rpm. The resulting
vitriﬁed emulsion then underwent a resting period of 3 h to allow the silver-coatedferrite particles to sediment and the polymer resin to cure.
Unidirectionally magnetized stretchable particles were fabricated by emulsifying
a mixture of 2 ml Eco-Flex 00-30 (two parts mixed at 1:1 by weight) and 0.8 g ironpowder in 50 ml gelatinized starch/water medium (10 wt% of starchconcentration). The emulsiﬁcation was performed at room temperature for 1 minusing the overhead mixer that applies a shearing rate of 600 rpm. The resulting
vitriﬁed emulsion was placed on top of a 50 mm neodymium magnet (5862K43,

13.
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16.

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Acknowledgements
This material is based upon work supported by the National Science Foundation under
grant no. CMMI-1454284. We also acknowledge R. Adam Bilodeau for assistance withthe manuscript text.

Author contributions
S.Y.K. and R.K.B. conceived the idea. S.Y.K., S.L. and J.J. performed the manufacturing
and demonstration. S.Y.K. and M.L. performed characterization and analytical study.
C.S.O. and M.D.S. conceived and performed the computer simulations. S.S. and J.S.
performed material characterization on metallic particles. All authors participated inwriting the manuscript.

Competing interests
The authors declare no competing interests.

Additional information
Supplementary information The online version contains supplementary material
available at https://doi.org/10.1038/s41467-021-23992-2.
Correspondence and requests for materials should be addressed to R.K-B.
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