Scattering function of semiflexible polymer chains under good solvent conditions

TL;DR

This study uses advanced Monte Carlo simulations to analyze the scattering functions of semiflexible polymers in good solvents, exploring the effects of chain stiffness, dimensionality, and stretching forces on their conformational properties.

Contribution

It provides a detailed computational analysis of semiflexible polymer scattering, validating and extending models like the Kratky-Porod worm-like chain in different dimensions and under stretching.

Findings

Kratky-Porod model applies in 3D for stiff chains with limited Kuhn segments

In 2D, crossover effects invalidate the Kratky-Porod description

Pincus blob size influences scattering behavior under stretching

Abstract

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 $N = 25600$ steps on the square and simple cubic lattices, variable chain stiffness is modeled by introducing an energy penalty $\epsilon_b$ for chain bending; varying $q_b=\exp (- \epsilon_b/k_BT)$ from $q_b=1$ (completely flexible chains) to $q_b = 0.005$, 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 $n_K$ does not exceed a limiting value $n^*_K$ (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 $<X^2> - <X>^2$, $<R_{g,\bot}^2>$ are used.