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

Abstract

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 λ N ( 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 λ N ( 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 λ N ( k ) ( s ) tends towards a constant value λ p ( k ) ( s ) behaving as k 1 / 2 . In the other analysed case k ∼ N , in the same limit, λ N ( 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.