A numerical method for the study of nucleation of ordered phases

Ling Lin, Xiuyuan Cheng, Weinan E, An Chang Shi, Pingwen Zhang

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


A numerical approach based on the string method is developed to study nucleation of ordered phases in first-order phase transitions. Among other things, this method allows an efficient computation of the minimum energy path (MEP) during the nucleation process. The MEP provides information about the size, shape and free energy barrier of the critical nucleus. To improve the efficiency of the string method, a special initialization process is proposed. Constraints from physical models are treated using two methods, a generalized coordinates method and a projection method. Strategies for choosing the computational domain and defining the nucleus boundary are also introduced. The validity of our approach is illustrated by two nontrivial examples from soft condensed matter physics, namely the nematic-isotropic transition of liquid crystals and the ordered-to-ordered phase transition of diblock copolymers.

Original languageEnglish (US)
Pages (from-to)1797-1809
Number of pages13
JournalJournal of Computational Physics
Issue number5
StatePublished - Mar 1 2010

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


  • Block copolymer
  • Critical nuclei
  • Liquid crystal
  • Minimum energy path (MEP)
  • Nucleation
  • Ordered phase
  • String method


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