Abstract
Using polygonal magnetic particles, we conduct experiments to explore the space-filling properties of anisotropic blocks with long-range interactions. In contrast to previous studies, we obtain the surprising finding that our systems’ structures do not depend on the shape of building blocks: a single state, the hexagonal plastic crystal, appears as a universal attractor for a wide range of different polygons. This robust particle-shape independency appears as the interactions go beyond nearest neighbors. Particle shape plays an essential role in system relaxation, and determines the basic relaxation dynamics through a microscopic control parameter, internal roughness, produced by particle vertices. Thus our study reveals a new pattern-forming paradigm, in which particle shape plays little role in the static structure but determines the essential relaxation dynamics. Due to the ubiquity of long-range interactions and anisotropic building blocks, our discovery may shed new light on diverse problems involving structure formation, self-assembly, and packing.
Highlights
Using polygonal magnetic particles, we conduct experiments to explore the space-filling properties of anisotropic blocks with long-range interactions
Another important factor is the interactions among particles: by coupling fine-tuned interactions with carefully-designed particle shapes, different building blocks may assemble into various types of structures including liquid and plastic crystals[7,8,9], superlattices[10,11,12], quasi-crystals[6,13,14], and glass[5]
The entropic effect due to geometric constraints from neighboring blocks plays an essential role in structure formation[28,29,30], which has led to amazing systems such as directional bonding and chiral structures[31,32,33,34,35], open lattices[36,37], and clathrate structures[38]
Summary
We conduct experiments to explore the space-filling properties of anisotropic blocks with long-range interactions. The shape of building blocks is of fundamental importance: it can influence the packing efficiency as demonstrated by the famous experiment of packing ellipsoidal M&M’s candies versus its spherical counterparts[4], it may produce unique frustration structures as illustrated by depositing special ‘kite’ tiles under gravity[5], and it could even help to realize highly-unusual phases such as quasicrystals with specially-designed blocks[6] Another important factor is the interactions among particles: by coupling fine-tuned interactions with carefully-designed particle shapes, different building blocks may assemble into various types of structures including liquid and plastic crystals[7,8,9], superlattices[10,11,12], quasi-crystals[6,13,14], and glass[5]. The opposite regime of coupling long-range interactions with anisotropic building blocks remains largely unexplored (note that ‘long-range interactions’ in this work mean the interactions going beyond the nearest neighbors) In this open regime dominated by non-entropic effect, are there any new physics, novel structures and unconventional material properties? In this open regime dominated by non-entropic effect, are there any new physics, novel structures and unconventional material properties? This fundamental question remains to be addressed from both experimental and theoretical fronts
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