Free-energy functional method for inverse problem of self assembly

Area of Science:

• Physics
• Materials Science
• Computational Chemistry

Background:

• The inverse self-assembly problem aims to determine interparticle interactions based on observed structures.
• Existing methods may lack efficiency or broad applicability for complex systems.

Purpose of the Study:

• To introduce a novel theoretical framework for solving the inverse self-assembly problem.
• To reconstruct interparticle potentials from specified particle arrangements.

Main Methods:

• The approach utilizes a variational principle combined with Percus's method.
• A functional is constructed from free energy, and the interaction potential maximizes this functional.
• Monte Carlo simulations are employed to validate the predicted potentials.

Main Results:

• The theory successfully predicts interparticle potentials for various 2D crystal structures, including square, honeycomb, and kagome lattices.
• Simulations demonstrate the formation of these target lattices from random configurations using the derived potentials.

Conclusions:

• The developed theoretical approach offers a robust method for the inverse self-assembly problem.
• The successful prediction and validation of potentials for 2D lattices confirm the theory's efficacy.