Conformations and Transverse Fluctuations of a Semi-Flexible Chain in Two Dimensions

We study conformations and transverse fluctuations of a semi-flexible polymer using Langevin Dynamics simulation in two dimensions(2D). By showing that the end-to-end distance $\langle R_N^2 \rangle $ for a semiflexible chain characterized by its contour length $L$ and the persistence length $\ell_p$ follows the scaling relation $\langle R_N^2 \rangle \sim L^{1.5}\ell_p^{0.5}$, as proposed by Schaefer {\em et al.} and Nakanishi, we verify the absence of the Gaussian regime, thus disprove the validity of the worm-like chain (WLC) theory in 2D. We also verify that the bond autocorrelation function exhibits a power law $\langle \vec{b}_i\cdot \vec{b}_{i+s} \rangle \sim s^{-\beta}$ instead of an exponential decay as predicted by the WLC model. We further show that the normalized transverse fluctuations $\sqrt{\langle l_{\bot}^2\rangle}/L$ for the semiflexible chains of different persistence length and contour length collapse onto the same master plot as a function of $L/\ell_p$, which exhibits $\sqrt{\langle l_{\bot}^2\rangle}/L \sim (L/\ell_p)^{0.5}$ and $\sqrt{\langle l_{\bot}^2\rangle}/L \sim (L/\ell_p)^{-0.25}$ at two extreme limits $L/\ell_p \rightarrow 0$ and $L/\ell_p \rightarrow \infty$, respectively and exhibits a maximum for $L/\ell_p \sim 1.0$.