Shape Allophiles Improve Entropic Assembly

TL;DR

This paper explores how specially shaped particles called shape allophiles can be used to control entropic forces, enabling the self-assembly of complex structures like square and triangular lattices.

Contribution

It introduces the concept of shape allophiles for entropic assembly and demonstrates their effectiveness in stabilizing specific lattice structures.

Findings

Shape allophiles can successfully reassemble into desired lattice structures.

Allophilic shaping influences the fraction of particles that entropically bind.

The approach generalizes from squares to triangles for lattice assembly.

Abstract

We investigate a class of "shape allophiles" that fit together like puzzle pieces as a method to access and stabilize desired structures by controlling directional entropic forces. Squares are cut into rectangular halves, which are shaped in an allophilic manner with the goal of re-assembling the squares while self-assembling the square lattice. We examine the assembly characteristics of this system via the potential of mean force and torque, and the fraction of particles that entropically bind. We generalize our findings and apply them to self-assemble triangles into a square lattice via allophilic shaping. Through these studies we show how shape allophiles can be useful in assembling and stabilizing desired phases with appropriate allophilic design.