Self-assembly by anti-repellent structures for programming particles with momentum

Abstract

Self-assembled configurations are versatile for applications in which liquid-mediated phenomena are employed to ensure that static or mild physical interactions between assembling blocks take advantage of local energy minima. For granular materials, however, a particle's momentum in air leads to random collisions and the formation of disordered phases, eventually producing jammed configurations when densely packed. Therefore, unlike fluidic self-assembly, the self-assembly of dry particles typically lacks programmability based on density and ordering symmetry and has thus been limited in applications. Here, we present the self-assembly of particles with momentum, yielding regular arrays with programmable density and symmetry. The key is to embed anti-repellent structures, i.e. traps, that can capture kinetic particles individually and then robustly hold them against collisions with other momentum granules during a dynamic assembly procedure. By using anti-repellent traps, physical interactions between neighbouring particles can be inhibited, resolving many phenomena related to the uncertainty of space-sharing events in granular packing. With our self-assembly strategy, highly dense yet unjammed configurations are demonstrated, which conserve the inherent randomness in the location information of each granule in the trap and are useful for robust multilevel authentication systems as unique applications.

Fig. 1. Overview of the cell-type PUF platform for hierarchical physical unclonable functions.

a Concept illustration of a self-assembled functional unit array utilising anti-repelling structures. The right panel shows three features of our concept. b Anti-repellent sticky trap for capturing momentum granules with both elastic and sticky surfaces. c Symmetry and density programmability using trap patterns. By observing at different scales, hierarchical physical unclonable functions for multilevel authentication systems can be constructed. Scale bars: 1 mm.

Fig. 2. Sticky trap fabrication system and dynamic collision tests.

a Illustration of our light-writing setup to manufacture patterned sticky traps from UV-curable resins. b Indentation tests for the mechanical properties of NOA73 structures with different curing states. Stage 1 denotes slightly uncured conditions (~100 mJ/cm²), while Stage 2 denotes fully cured phases. c Measured pull-off forces, where the structures in Stage 1 showed higher adhesion, playing a key role in the anti-repellent traps. d Monitoring scenes of collision events of glass beads under various impact conditions, including i) the vertically dropped granule on traps in Stage 1, ii) collision-resistive behaviour of a trapped granule on a trap in Stage 1, and iii) stronger collision-resistive behaviour of granules on traps after shape adaptation. Note that for shape adaptation, the beads and the traps in contact in Stage 1 are further cured by flood UV exposure. Scale bar: 1 mm.

Fig. 3. Analyses of granule adhesion under dynamic conditions.

Distributions of directly adhered or bounced granules after the free fall drop test: a on a sticky surface (Stage 1) and b on an elastic surface (Stage 2). Quantitative analyses of the assembly rates of granules on an array of 200 traps at different RPM. Granule mass of: c 5 g and d 10 g.

Fig. 4. Programmability of polydisperse granules and the analysis of inherent randomness in each granule’s contact information.

a Polydispersity of glass beads employed in this study. b Plotted distributions of monitored contact points of each granule on two types of pillars with different diameters: 200 μm (left) and 600 μm (right). c Quantitative analysis of the density and contact number characteristics of densely packed granules on traps with various interspace distances. The colour indicates the void fraction of unit cells, and the black lines are drawn when two granules are in contact. d The inherent randomness in the location of contact points, where the displacement vectors $\overrightarrow{V}$_m,m+1 feature evenly distribute elements of θ’ and φ', visualising randomness in our array.

Fig. 5. The role of observation frames and the existence of the lock’s hierarchy.

a Lock’s hierarchy in pixel-based correlation algorithms, revealing stricter genuine locks when observation frames (OFs) are increased. b Comparison of pixel-to-pixel correlation algorithm and vector-based algorithm in the contact points analysis, where the latter maintains unique contact information for all granules regardless of the OFs. Heatmaps of cross-correlation of 200 keys in different OFs, where two OFs with c low magnification and low pixel resolution (OF#1, LMLR) and d high magnification and high pixel resolution (OF#3, HMHR) can build different challenge-response pairs independently.

Fig. 6. Example of hierarchical mPUFs for multilevel authentication systems.

a Constructed hierarchical mPUFs with various private keys and the utilisation of different OFs for multilevel authentication via a single physical key. b Conceptual illustration of the stored hierarchical locks in a data centre. c Conceptual illustration of the multilevel authentication procedure with a single physical key via different OFs.

Fig. 7. mPUF generation with customised unit granules to enhance randomness.

Assembly results using custom-designed, polygonal, and letter-shaped granules. In the test, hard and soft polyurethane acrylate (PUA) resins with the moduli of 320 MPa and 19.8 MPa, respectively, are employed for shaped particles. To visualise the challenge-response pair in authentication, fluorescent dyes (Rhodamine B) are added to the manufacture of soft PUA particles, which can be seen in fluorescent microscopic images. Those combinations of different shapes and materials enhance the randomness for robust mPUFs. Scale bars: 1 mm.