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

Abstract 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mrow> <mml:mrow> <mml:mi>imp</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> . 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi>θ</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">p</mml:mi> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:mrow> </mml:math> 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.