Deterministic growth model of Laplacian charged particle aggregates

TL;DR

This paper presents a deterministic Laplacian growth model for charged particle aggregates, exploring how parameters influence cluster morphology and phase transitions between different structural zones.

Contribution

It introduces a comprehensive deterministic model for charged particle aggregation, analyzing phase diagrams and morphological transitions based on electrostatic parameters.

Findings

Identified three distinct growth zones with different morphologies.

Demonstrated a continuous change in fractal dimension within the ramified zone.

Observed a crossover from linear to compact structures at the zone boundary.

Abstract

The results of the computer simulation of the aggregates growth of the similarly charged particles in the framework of deterministic Laplacian growth model on a square lattice are presented. Cluster growth is controlled by three parameters ${p, E,\lambda}$, where $p$ - Laplacian growth parameter, $E$ - energy of a particle sticking to a cluster, $\lambda$ - the screening length of electrostatic interactions. The phase diagram of cluster growth is built in the co-ordinates ${E,\lambda}$. The zones of different cluster morphology are selected: I-the zone of finite X-like structures,II-the zone of infinite ramified structures, controlled by electrostatic interactions, III-the zone of infinite structures with electrostatic interactions effectively switched off. Simple electrostatic estimations of the locations of the zone boundaries are presented. It is shown that in general case within the zone II the continuous change of $D_f$, controlled by parameters ${p, E,\lambda}$, takes place. In the degeneration limit when the given model transforms into deterministic version of the Eden model (at $p=0$), the crossover from linear $(D_f=1)$ to compact $(D_f=2)$ structures is observed when passing through the boundary between the zones I and II.