2006/01/19 by Mikael C. Rechtsman, Salvatore Torquato, Frank H. Stillinger · 7 citations
Materials Science · Physics and Astronomy · #Block Copolymer Self-Assembly #Machine Learning in Materials Science #Material Dynamics and Properties #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.73.011406
published as Phys. Rev. E 73, 011406 (2006) · 28 pages, 23 figures
openalex publication_date 2006/01/19 · arxiv created 2006/03/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We formulate statistical-mechanical inverse methods in order to determine optimized interparticle interactions that spontaneously produce target many-particle configurations. Motivated by advances that give experimentalists greater and greater control over colloidal interaction potentials, we propose and discuss two computational algorithms that search for optimal potentials for self-assembly of a given target configuration. The first optimizes the potential near the ground state and the second near the melting point. We begin by applying these techniques to assembling open structures in two dimensions (square and honeycomb lattices) using only circularly symmetric pair interaction potentials; we demonstrate that the algorithms do indeed cause self-assembly of the target lattice. Our approach is distinguished from previous work in that we consider (i) lattice sums, (ii) mechanical stability (phonon spectra), and (iii) annealed Monte Carlo simulations. We also devise circularly symmetric potentials that yield chainlike structures as well as systems of clusters.