Free-Energy Functional Method for Inverse Problem of Self Assembly

Abstract

A new theoretical approach is described for the inverse self-assembly problem, i.e., the reconstruction of the interparticle interaction from a given structure. This theory is based on the variational principle for the functional that is constructed from a free energy functional in combination with Percus's approach [J. Percus, Phys. Rev. Lett. vol.8, 462 (1962)]. In this theory, the interparticle interaction potential for the given structure is obtained as the function that maximizes the functional. As test cases, the interparticle potentials for two-dimensional crystals, such as square, honeycomb, and kagome lattices, are predicted by this theory. The formation of each target lattice from an initial random particle configuration in Monte Carlo simulations with the predicted interparticle interaction indicates that the theory is successfully applied to the test cases.

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Cited by in corpus (6)

• Designing convex repulsive pair potentials that favor assembly of kagome and snub square lattices
• Inverse Design of Multicomponent Assemblies
• 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
• Design of two-dimensional particle assemblies using isotropic pair interactions with an attractive well
• Free-Energy Functional Approach to Inverse Problems for Self-Assembly of Three-Dimensional Crystals