Ordered self-similar patterns in anisotropic stochastic growth

Zhenwei Yao, Monica Olvera De La Cruz*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We propose an anisotropic stochastic growth model to rationalize the anisotropic self-assembly of supramolecules to form elongated two-dimensional ribbon structures in a recent experiment. The model exhibits distinct growth scenarios that are critically controlled by the ratio of the transverse and the longitudinal growth rate. In the regime of suppressed transverse growth, the model generates the experimentally observed elongated structures through layer-by-layer growing. We further observe the convergence of rough clusters toward smooth regular elliptic patterns by averaging over a number of independent growth processes. Remarkably, these resulting elliptic clusters are self-similar in each instantaneous moment in the growth process. Statistical analysis suggests that the realization of such ordered patterns does not rely on the delicate coordination of different parts in the cluster growth. The self-similarity phenomenon derived from this idealized model may have wider implications, notably in the designed clustering of various elementary building blocks with anisotropic interactions.

Original languageEnglish (US)
Pages (from-to)5960-5965
Number of pages6
JournalJournal of Physical Chemistry B
Issue number26
StatePublished - Jul 7 2016

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry
  • Surfaces, Coatings and Films
  • Materials Chemistry

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