Scattering function of semiflexible polymer chains under good solvent conditions

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 $q_b=\exp (-{\epsilon }_b/k_{B}T)$ 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 $n_K^{\ast }$ (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 $<X^2>-<X{>}^2$, $<R_{g,\perp }^2>$ are used.

23 pages, 16 figures, 1 table

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