Using the uncertainty principle to design simple interactions for targeted self-assembly

Abstract

We present a method that systematically simplifies isotropic interactions designed for targeted self-assembly. The uncertainty principle is used to show that an optimal simplification is achieved by a combination of heat kernel smoothing and Gaussian screening. We use this method to design isotropic interactions for self-assembly of complex lattices and of materials with functional properties. The interactions we derive are significantly simpler than those previously published, and it is realistic to discuss explicit experimental implementation of the designed self-assembling components.

5 pages, 2 figures

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Cited by in corpus (10)

• Perspective: Inverse methods for material design
• Designing convex repulsive pair potentials that favor assembly of kagome and snub square lattices
• Inverse Design of Multicomponent Assemblies
• Dimensionality and design of isotropic interactions that stabilize honeycomb, square, simple cubic, and diamond lattices
• Inverse Design of Simple Pair Potentials for the Self-Assembly of Complex Structures
• Designing Pairwise Interactions that Stabilize Open Crystals: Truncated Square and Truncated Hexagonal Lattices
• Breadth versus depth: Interactions that stabilize particle assemblies to changes in density or temperature
• Phase Behavior of Materials with Isotropic Interactions Designed by Inverse Strategies to Favor Diamond and Simple Cubic Lattice Ground States
• Using the uncertainty principle to design simple interactions for targeted self-assembly
• Design of two-dimensional particle assemblies using isotropic pair interactions with an attractive well