Persistence length of semi-flexible polymer chains on Euclidean lattices

Abstract

We have studied the persistence length behavior of semi-flexible linear polymers, represented by self-avoiding random walks (SAWs) on the square (d=2) and simple cubic (d=3) lattice. By employing the PERM Monte Carlo algorithm we have generated SAWs, changing the chain stiffness (characterized by the parameter s, related to each bend of a SAW). We have examined two quantities that measure persistence length of N-step SAWs: (1) ℓN, which is defined as an average length of straight parts of polymer chains, and (2) λN, defined as the mean projection of the end-to-end distance vector on the SAW’s first step. For each particular s, we have found that ℓN is a linear function of 1/N in both dimensions, d=2 and d=3, while λN is a linear function of 1/NΦeff, where Φeff≈0.3 in d=2 and Φeff≈0.82 in d=3. Sequences of ℓN and λN have been extrapolated in the range of very long chains, and we have established that, for each examined s, they converge to s dependent constants ℓp=ℓN→∞ and λp=λN→∞. We analyze dependence of ℓp and λp on the polymer stiffness s, and make a comparison between our findings and former results for studied quantities.