Critical properties of semi-flexible polymer chains situated within the simple cubic lattice

Abstract

We have studied the critical properties of semi-flexible polymer chains whose elastic properties are brought out by the stiffness parameter s, and which are modelled by self-avoiding random walks (SAWs) in three-dimensional space. By applying the PERM Monte Carlo method, we have simulated the polymer chains by SAWs along the bonds of the simple cubic lattice, for a set of specific values for the stiffness parameter s. More precisely, we have examined behaviour of critical exponent νN, associated with the mean squared end-to-end distance of polymer chains of length N, as a function of s. Thus, we have established that νN monotonically decreases with N for s ⩾ 0.6, whereas the critical exponent νN displays a non-monotonic behaviour for s < 0.6. Values of νN, obtained for various s, have been extrapolated in the range of very long chains, and we have shown that obtained values ν = limN→∞νN do not depend on the polymer flexibility. Besides, we have calculated approximately the partition function for SAWs of length N, and examined its asymptotic behaviour, which turns out to be governed by the entropic critical exponent γ (associated with the total number of different polymer configurations), and the growth constant μ. We demonstrate that μ is a linear function of s, while γ does not depend on the polymer flexibility. Finally, we discuss and compare our results to those obtained previously for polymers on Euclidean lattices.