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Role of zero clusters in exchange-driven growth with and without input
Emre Esenturk1,2, Colm Connaughton1,3,4
1Mathematics Institute, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom.
Physical Review. E
|June 25, 2020
Summary
The exchange-driven growth model shows distinct behaviors for active versus passive cluster dynamics. Passive systems exhibit power-law growth, while active systems reach a finite equilibrium size, even with continuous monomer input.
Area of Science:
- Physical Chemistry
- Statistical Mechanics
- Materials Science
Background:
- The exchange-driven growth model simulates composite particle (cluster) kinetics via pairwise monomer exchange.
- Two variants exist: active (zero-size clusters gain monomers) and passive (zero-size clusters are removed).
Purpose of the Study:
- To analyze the distinct large-time behaviors of active and passive exchange-driven growth models.
- To investigate isolated and non-isolated (monomer input) systems.
Main Methods:
- Mean-field kinetic modeling.
- Analysis of cluster size distributions and typical cluster size evolution over time.
- Comparison of isolated and non-isolated system dynamics.
Main Results:
- Passive systems: Cluster size distribution shows self-similar evolution with power-law growth.
- Active systems (isolated): Distribution reaches a time-independent equilibrium with finite typical size.
- Active systems (non-isolated): Distribution approaches the isolated equilibrium but with time-increasing amplitude.
Conclusions:
- The active/passive distinction fundamentally alters long-term cluster growth dynamics.
- Active systems demonstrate a robust equilibrium behavior, even under continuous monomer supply.
- The model provides insights into self-organization and size-distribution evolution in interacting particle systems.
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