Trap avoiding walk: a model for polymer growth

Abstract

To describe the irreversible growth of a linear polymer chain, we introduce a random walk called trap avoiding walk (TAW). This walk is strictly self-avoiding, can grow successfully to any specified length, and does not have the restriction that it should not end inside a cage. This has been achieved by allowing a TAW to avoid only those cages which prevent it from growing to its full length. The physical justification for such a walk is that a polymer can, in general, grow inside a cage and get chemically terminated there. Monte Carlo results of the TAW on a square lattice for lengths up to N=105 are presented. The critical exponents V, V₀, V_I of the mean square end-to-end distance for the total ensemble of TAWs and for its subensembles of walks ending outside and inside cages are found to have the values 0.571±0.005, 0.578±0.007, and 0.61±0.05, respectively.