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Updated: Jan 8, 2026
06:55
Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
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Stochastic closed Frank model in two dimensions: Chiral symmetry breaking driven by diffusive control over bounded
José Cândido de Souza Filho1,2, Alejandro López-Castillo2
1Universidade Estadual de Maringá (UEM), Departamento de Tecnologia (DTC), Campus Umuarama, PR 87506-370, Brazil.
Physical Review. E
|December 23, 2025
Summary
Simulations of the closed Frank model show that increasing neighborhood size accelerates the achievement of the global homochiral state (GHS). Larger neighborhoods reduce simulation time and increase GHS success rates in chiral systems.
Area of Science:
- Chemical Physics
- Computational Chemistry
- Theoretical Chemistry
Background:
- The emergence of homochirality is fundamental to life.
- Understanding the factors influencing homochiral state formation is crucial.
Purpose of the Study:
- To investigate the impact of neighborhood size on achieving the global homochiral state (GHS).
- To analyze the dynamics of domain formation and spatial distribution in chiral systems.
Main Methods:
- Simulated the closed Frank model using a stochastic Ehrenfest urn method on a surface.
- Varied neighborhood sizes to observe effects on reaction-diffusion processes.
- Initiated simulations with random particle distributions and zero enantiomeric excess.
Main Results:
- Increasing neighborhood size enhances the probability and speed of reaching the GHS.
- Domain formation is observed, with GHS arising from spatiotemporal concentration fluctuations in larger neighborhoods.
- In simulations not reaching GHS, a steady state with coexisting domains and equal reaction rates at interfaces is established.
Conclusions:
- Neighborhood size is a critical parameter in models of homochirality.
- Spatiotemporal fluctuations play a key role in driving systems towards homochirality.
- The model provides insights into the spatial organization and dynamics of chiral systems.
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