Doubly folded random walks for unentangled polymers: a tree percolation model

We study the properties of two-dimensional unentangled polymer chains in a dense environment of many other cross-linked polymer molecules incorporating the excluded volume effect. A kinetic random-walk model is introduced in which the different possible directions of a step are chosen sequentially in a clockwise direction with a pre-assigned probability. While the spanning probability and other bulk properties of this walk shows a percolation-like transition, the detailed structural properties are found to be different. A spiraling behavior is observed beyond the percolation threshold. We also study two other variants of kinetic random walks.