Scattering function of semiflexible polymer chains under good solvent conditions

Using the pruned-enriched Rosenbluth Monte Carlo algorithm, the scattering functions of semiflexible macromolecules in dilute solution under good solvent conditions are estimated both in d = 2 and d = 3 dimensions, considering also the effect of stretching forces. Using self-avoiding walks of up to N = 25 600 steps on the square and simple cubic lattices, variable chain stiffness is modeled by introducing an energy penalty εb for chain bending; varying qb = exp (−εb/kBT) from qb = 1 (completely flexible chains) to qb = 0.005, the persistence length can be varied over two orders of magnitude. For unstretched semiflexible chains, we test the applicability of the Kratky-Porod worm-like chain model to describe the scattering function and discuss methods for extracting persistence length estimates from scattering. While in d = 2 the direct crossover from rod-like chains to self-avoiding walks invalidates the Kratky-Porod description, it holds in d = 3 for stiff chains if the number of Kuhn segments nK does not exceed a limiting value \documentclass[12pt]{minimal}\begin{document}$n^*_K$\end{document}nK* (which depends on the persistence length). For stretched chains, the Pincus blob size enters as a further characteristic length scale. The anisotropy of the scattering is well described by the modified Debye function, if the actual observed chain extension ⟨X⟩ (end-to-end distance in the direction of the force) as well as the corresponding longitudinal and transverse linear dimensions ⟨X2⟩ − ⟨X⟩2, \documentclass[12pt]{minimal}\begin{document}$\langle R_{g,\bot }^2 \rangle$\end{document}⟨Rg,⊥2⟩ are used.