Percolation and jamming properties in an object growth model on a triangular lattice with finite-size impurities

• Published in: Journal of statistical mechanics 2024-09, Vol.2024 (9), p.93213
• Main Authors: Dujak, D, Karač, A, Budinski-Petković, Lj, Jakšić, Z M, Vrhovac, S B
• Format: Article
• Language: English
• Subjects: impurities; percolation; seeded growth; triangular lattice
• ISSN: 1742-5468; 1742-5468
• DOI: 10.1088/1742-5468/ad7851

A percolation model with nucleation and object growth is studied by Monte Carlo simulations on a triangular lattice with finite-size impurities. The growing objects are needle-like objects and self-avoiding random walk chains. Results are obtained for three different shapes of impurities covering three lattice sites—needle-like, angled and triangular. In each run through the system, the lattice is initially randomly occupied by impurities of a specified shape at a given concentration ρ imp . Then, the seeds for the object growth are randomly distributed at a given concentration ρ . The percolation and jamming properties of the growing objects are compared for the three different impurity shapes. For all the impurity shapes, the percolation thresholds θ p ∗ have lower values in the growing needle-like objects than in the growing self-avoiding random walk chains. In the presence of needle-like and angled impurities, the percolation threshold increases with the impurity concentration for a fixed seed density. The percolation thresholds have the highest values in the needle-like impurities, and somewhat lower values in the angled impurities. On the other hand, in the presence of the triangular impurities, the percolation threshold decreases with the concentration of impurities.