A master-equation approach to simulate kinetic traps during directed self-assembly

Richard Lakerveld, George Stephanopoulos, Paul I. Barton

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


Robust directed self-assembly of non-periodic nanoscale structures is a key process that would enable various technological breakthroughs. The dynamic evolution of directed self-assemblies towards structures with desired geometries is governed by the rugged potential energy surface of nanoscale systems, potentially leading the system to kinetic traps. To study such phenomena and to set the framework for the directed self-assembly of nanoparticles towards structures with desired geometries, the development of a dynamic model involving a master equation to simulate the directed self-assembly process is presented. The model describes the probability of each possible configuration of a fixed number of nanoparticles on a domain, including parametric sensitivities that can be used for optimization, as a function of time during self-assembly. An algorithm is presented that solves large-scale instances of the model with linear computational complexity. Case studies illustrate the influence of several degrees of freedom on directed self-assembly. A design approach that systematically decomposes the ergodicity of the system to direct self-assembly of a targeted configuration with high probability is illustrated. The prospects for extending such an approach to larger systems using coarse graining techniques are also discussed.

Original languageEnglish (US)
Article number184109
JournalJournal of Chemical Physics
Issue number18
StatePublished - May 14 2012
Externally publishedYes

ASJC Scopus subject areas

  • General Physics and Astronomy
  • Physical and Theoretical Chemistry


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