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Optimized interactions for targeted self-assembly: application to a honeycomb lattice.

Mikael C Rechtsman1, Frank H Stillinger, Salvatore Torquato

  • 1Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.

Physical Review Letters
|December 31, 2005
PubMed
Summary

We developed a new method to design interaction potentials for self-assembling materials. This approach allows for the creation of specific disordered or ordered structures, including quasicrystals.

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Area of Science:

  • Statistical Mechanics
  • Materials Science
  • Computational Physics

Background:

  • Traditional self-assembly focuses on forming ordered crystalline structures.
  • Designing interaction potentials for specific many-particle configurations is challenging.
  • Extending self-assembly to include amorphous and quasicrystalline structures is an active research area.

Purpose of the Study:

  • To develop an inverse statistical-mechanical methodology for designing interaction potentials.
  • To enable the spontaneous formation of target many-particle configurations, including disordered and ordered structures.
  • To illustrate the method's capability by designing a potential for a specific 2D lattice.

Main Methods:

  • An inverse statistical-mechanical approach was devised.

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  • The methodology optimizes interaction potentials to achieve target configurations.
  • Computational techniques were applied to derive a specific pair potential.

    • Main Results:

    • The developed methodology successfully designs interaction potentials for target configurations.
    • An optimized isotropic pair potential was generated.
    • The potential spontaneously yields the three-coordinated honeycomb lattice as the ground state in 2D.

    Conclusions:

    • The inverse statistical-mechanical method offers a powerful tool for designing self-assembling materials.
    • This approach extends self-assembly to a broader range of structures beyond traditional crystals.
    • The generated honeycomb lattice serves as a 2D analog to the diamond lattice, relevant for photonic band gap applications.