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

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.

arXiv comment16 pages, 12 figures. Accepted for publication in Physical Review E

References in corpus (2)

• Optimized Interactions for Targeted Self-Assembly: Application to Honeycomb Lattice
• Designed Interaction Potentials via Inverse Methods for Self-Assembly

Cited by in corpus (23)

• Colloidal Gels: Equilibrium and Non-Equilibrium Routes
• Self-Assembly of Monatomic Complex Crystals and Quasicrystals with a Double-Well Interaction Potential
• Vacancy-stabilized crystalline order in hard cubes
• Inverse design of simple pairwise interactions with low-coordinated 3D lattice ground states
• Algorithmic design of self-assembling structures
• Synthetic Diamond and Wurtzite Structures Self-Assemble with Isotropic Pair Interactions
• Inverse Statistical Mechanics: Probing the Limitations of Isotropic Pair Potentials to Produce Ground-State Structural Extremes
• Designing isotropic interactions for self-assembly of complex lattices
• Negative Poisson's ratio materials via isotropic interactions
• Inverse Design of Simple Pair Potentials for the Self-Assembly of Complex Structures
• Glass Formation and Crystallization of a Simple Monatomic Liquid
• Probing the Theoretical and Computational Limits of Dissipative Design
• Neuroevolutionary learning of particles and protocols for self-assembly
• Simulating complex crystal structures using the phase-field crystal model
• Novel Ground-State Crystals with Controlled Vacancy Concentrations: From Kagomé to Honeycomb to Stripes
• Soft matter crystallography -- complex, diverse, and new crystal structures in condensed materials on the mesoscale
• Phase Behavior of Materials with Isotropic Interactions Designed by Inverse Strategies to Favor Diamond and Simple Cubic Lattice Ground States
• Structural characterization and statistical-mechanical model of epidermal patterns
• Free-Energy Functional Method for Inverse Problem of Self Assembly
• On energy ground states among crystal lattice structures with prescribed bonds
• Effective potentials induced by mixtures of patchy and hard co-solutes
• Valence-free open nanoparticle superlattices
• Free-Energy Functional Approach to Inverse Problems for Self-Assembly of Three-Dimensional Crystals