The local persistence length of semi-flexible self-avoiding walks on the square lattice

Abstract

By applying the pruned-enriched Rosenbluth Monte Carlo simulation method, we have studied the local persistence length of semi-flexible linear polymers presented by self-avoiding walks (SAWs) on the square lattice, where the stiffness property is characterised by the weight s assigned to each bend of the walk. In this model, the local persistence length λN(k) of N-step SAWs is formulated as an ensemble average of the projection of the end-to-end position vector onto the oriented kth step of the SAW path. We have found that the persistence length λN(k)(s) decreases with s and increases with k and N. Regarding the chain position parameter k, we have scrutinised two particular cases: the first case is when k has a constant (fixed) value, independent of the chain length, and the second one is the situation when k is comparable with the SAW length k∼N . For fixed k, we have learnt that in the limit N→∞ , the persistence length λN(k)(s) tends towards a constant value λp(k)(s) behaving as k1/2 . In the other analysed case k∼N , in the same limit, λN(k)(s) diverges as N ϕ , with φ=1/2 . We have also examined the dependence of the studied quantity on s and discussed our results in the context of previous findings and predictions related to the persistence length behaviour of SAWs in Euclidean spaces.