Percolation and jamming properties in limited grain growth of linear objects

Abstract

The physical and chemical properties of the nanocrystals are highly shape dependent, and shape control has become very important. The seeded growth method enables seeds to grow in a predetermined way. We have already proposed such amodel that can reproduce the granular growth on a triangular lattice and for different growth shapes. In this paper, however, we have introduced a limitation on seed growth up to a certain length. This method can be used when the growth of all seeds have to be limited to the same length, or for a mixture with the different growth limits.The main goal is to investigate how the growing limits affect the values of the percolation threshold and jamming density, and whether large objects significantly affect the percolation threshold. We used growing needle-shaped objects (k-mers) made by a self-avoiding random walk filling the nodes of the triangular lattice. Objects can grow until they reach the growth limit k' defined as the maximum number of lattice nodes belonging to one object. For k' ≥10 percolation is reached for all investigated seed densities. We obtained that the values of the percolation threshold and jamming density are identical for k' ≥10k .Above these values, the percolation threshold and jamming remain unchanged, regardless of the growth limit.Our results also show that when significant growth is allowed, long objects are very rare and do not influence the results.