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

Functional particles that respond to external stimuli are spurring technological evolution across various disciplines. While large-scale production of functional particles is needed for their 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 mass-production of several functional particles, including low-melting point metallic particles, self-propelling Janus particles, and unidirectionally-magnetized robotic particles, via this static-state particle fabrication process.


Supplementary Note 1 | Microstructure of FM particles
Here we detail structural and microstructural characteristics of Field's Metal particles fabricated under both static-state and dynamic-state conditions. A particle fabricated under dynamic-state conditions in a water medium exhibits an irregular shape with a rough surface ( Supplementary Fig.   1a), while a particle fabricated under static-state conditions exhibits a spherical shape with a smooth surface ( Supplementary Fig. 1c). We believe that the difference in shape and surface texture originates from particle collisions during solidification and corresponding phase segregation 1 . Supplementary Fig. 1b shows surface features ranging from 50 to 500 nm covering the particle fabricated under dynamic-state conditions, which may be due to: a) multiscale particle collisions, b) cracked/shattered surface oxides during particle collisions, and/or c) uneven integration of materials while particles are merging. X-ray diffraction (XRD) analysis reveals pronounced Bi2O3 peaks in particles fabricated through the dynamic-state condition (marked by solid circles in Supplementary Fig. 1e), which supports the hypothesis that oxide fragments contribute to the surface features.
Oxide fragments are also seen in the mixed EDS elemental mapping (far right in Supplementary Fig. 1b) as black dots. We note that the tendency of oxidation quantified by Gibbs free energy of oxidation follows the order of In2O3 > SnO2 > Bi2O3 2 . Thus, Bi2O3 is not expected to form on the surface of Bi-Sn-In alloys as a significant oxide 3 . This observed deviation from the expected thermodynamic condition indicates an opportunity to form unusual oxide products using the dynamic-state process. In contrast, the XRD pattern from particles fabricated under static-state conditions shows a lower quantity of Bi2O3, which is in agreement with the expected oxidation of this material system 2 .
8 Micrographs with EDS elemental mappings from both particles (in Supplementary Fig. 1b and d) reveal typical ternary eutectic microstructures. Based on the curved boundaries between phases, we describe these microstructures as non-faceted / non-faceted type eutectic in a smaller category. The combined results from the XRD and EDS mappings suggest that both ternary eutectics consist of BiIn2, Sn0.8In0.2 and In0.75Sn0.25 phases, which is in agreement with other studies 4,5 .

Supplementary Note 2 | Simulation of particle collisions
To visualize the coalescence of particles following the collision, we simulate 2D deformable sticky particles. Deformable particles are modeled using polygons in which the vertices are freely jointed, but the area(mass) is conserved 6,7 . To add stickiness, we include an energy term proportional to the perimeter (surface). This term is the 2D equivalent of surface tension. The surface energy between particles and fluid is 10 times that of the energy between two particles. The deformable sticky particles are placed in a periodic Lees-Edwards 8 shear flow. Because of the shear stress on the particles in the flow, they are deformed into an elliptical shape (see t = 3sec). When particles collide, they may stick and coalesce due to the lower energy of the particle-particle interface. The shear flow also competes with the stickiness to elongate and potentially break the clusters up.
To calculate an effect of the medium's viscosity on the collision frequency of moving particles, We simulate 180 spheres of diameter 1 μm × (1 + 0.25 × N(0,1)), where N(0,1) is zero mean standard deviation of one random number. The particles are placed at random in a small parallelepiped Lx × Ly × Lz of 62.8 μm × 61.9 μm × 10.0 μm. The Lz direction is fixed to 10 times the mean particle diameter, Lx is determined by requiring a fixed fraction (1 / 300) of the 9 experimental domain, and Ly is set so that the 180 spheres give a number density of 5 × 10 6 particles/ml. Gravity points downward in the Ly direction. We use Lees-Edwards shear boundary conditions 8 to create a simple shear in the Ly direction with shear rate  = 16. The shear flow is specified for the fluid and the particles follow by a Stokian drag force:

Supplementary Discussion 1 | Relaxation time of the droplet interface in a vitrified medium
The vitrification time-time required for a medium to recover its zero-shear value after shearing stops-and the relaxation time of droplet interface are additional factors that can determine the shape of droplets. For example, if a medium reaches the vitrification earlier than the relaxation of distributed droplets' interface (vitrification time < relaxation time), the droplets could gain irregular shapes.
All the particles which we fabricated in this study were nearly perfect spheres, indicating that the surface tension of the droplet interface was the dominant force to determine the shape of the droplets. This particle morphology indicates that the droplets had sufficient time to relax in the medium until their solidification (vitrification time > relaxation time), presumably because of the stark difference in length scales of the medium (approx. 10 2 ml) and the droplets (approx. 10 -5 ml).

Supplementary Discussion 2 | Processable maximum volume fraction of the distributed phase
The maximum volume fraction of the distributed phase processable by an emulsion process is dependent on the characteristics of phase inversion 9,10 , and physical properties (e.g. viscosity, surface tension, density) of both the distributed and continuous phase. While we did not explicitly characterize this value for each of the material systems we present, we hypothesize the maximum volume fraction of the target material in a vitrifying medium would be similar to that in a nonvitrifying medium, if the mediums have similar viscosities prior to vitrification (during shear).
However, vitrification of the medium will yield more monodisperse particles by preventing collisions and coalescence during particle solidification.