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Related Experiment Video

Updated: May 7, 2026

Origami Inspired Self-assembly of Patterned and Reconfigurable Particles

Origami Inspired Self-assembly of Patterned and Reconfigurable Particles

Published on: February 4, 2013

Combinatoric analysis of heterogeneous stochastic self-assembly.

Maria R D'Orsogna¹, Bingyu Zhao, Bijan Berenji

¹Department of Mathematics, CSUN, Los Angeles, California 91330-8313, USA.

The Journal of Chemical Physics

|October 5, 2013

Summary

This study presents a stochastic model for particle self-assembly, revealing discrepancies with classical models. Kinetic Monte-Carlo simulations and analytic solutions offer new insights into cluster formation dynamics.

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Area of Science:

Physical Chemistry
Materials Science
Statistical Mechanics

Background:

Heterogeneous nucleation and self-assembly are fundamental processes in various scientific disciplines.
Classical mass-action models often simplify the complex dynamics of these phenomena.

Purpose of the Study:

To develop and analyze a fully stochastic model for heterogeneous nucleation and self-assembly.
To compare the predictions of the stochastic model with classical mass-action approaches.

Main Methods:

Derivation of a discrete master equation for cluster size probability distribution.
Kinetic Monte-Carlo simulations to determine cluster concentrations.
Development of analytic expressions and recursion relations for cluster densities in the slow detachment limit.

Main Results:

The stochastic model provides a detailed probability distribution of cluster sizes.
New analytic expressions and recursion relations were derived for cluster densities.
Significant discrepancies were identified between the stochastic model and classical mass-action equations.

Conclusions:

The stochastic model offers a more comprehensive understanding of nucleation and self-assembly dynamics.
Classical mass-action equations may not fully capture the intricacies of these processes.
The findings provide a foundation for more accurate modeling of self-assembling systems.