Self-assembly of the simple cubic lattice with an isotropic potential

TL;DR

This paper demonstrates that an isotropic pair potential can be designed to cause particles to self-assemble into a simple cubic lattice, challenging the assumption that low-coordinated structures require directional interactions.

Contribution

The authors develop a method to design isotropic potentials that induce self-assembly of specific low-coordinated crystal structures, including the simple cubic lattice.

Findings

Successfully designed an isotropic potential for simple cubic lattice

Standard liquid state theories cannot predict the correct potential

Extended the approach to other non-close-packed structures

Abstract

Conventional wisdom presumes that low-coordinated crystal ground states require directional interactions. Using our recently introduced optimization procedure to achieve self-assembly of targeted structures (Phys. Rev. Lett. 95, 228301 (2005), Phys. Rev. E 73, 011406 (2006)), we present an isotropic pair potential $V(r)$ for a three-dimensional many-particle system whose classical ground state is the low-coordinated simple cubic (SC) lattice. This result is part of an ongoing pursuit by the authors to develop analytical and computational tools to solve statistical-mechanical inverse problems for the purpose of achieving targeted self-assembly. The purpose of these methods is to design interparticle interactions that cause self-assembly of technologically important target structures for applications in photonics, catalysis, separation, sensors and electronics. We also show that standard approximate integral-equation theories of the liquid state that utilize pair correlation function information cannot be used in the reverse mode to predict the correct simple cubic potential. We report in passing optimized isotropic potentials that yield the body-centered cubic and simple hexagonal lattices, which provide other examples of non-close-packed structures that can be assembled using isotropic pair interactions.