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We present a unified scaling description for the dynamics of monomers of asemiflexible chain under good solvent condition in the free draining limit. Weconsider both the cases where the contour length $L$ is comparable to thepersistence length $\ell_p$ and the case $L\gg \ell_p$. Our theory captures theearly time monomer dynamics of a stiff chain characterized by $t^{3/4}$dependence for the mean square displacement(MSD) of the monomers, but predictsa first crossover to the Rouse regime of $t^{2\nu/{1+2\nu}}$ for $\tau_1 \sim\ell_p^3$, and a second crossover to the purely diffusive dynamics for theentire chain at $\tau_2 \sim L^{5/2}$. We confirm the predictions of thisscaling description by studying monomer dynamics of dilute solution ofsemi-flexible chains under good solvent conditions obtained from our Browniandynamics (BD) simulation studies for a large choice of chain lengths withnumber of monomers per chain N = 16 - 2048 and persistence length $\ell_p = 1 -500$ Lennard-Jones (LJ) units. These BD simulation results further confirm theabsence of Gaussian regime for a 2d swollen chain from the slope of the plot of$\langle R_N^2 \rangle/2L \ell_p \sim L/\ell_p$ which around $L/\ell_p \sim 1$changes suddenly from $\left(L/\ell_p \right) \rightarrow \left(L/\ell_p\right)^{0.5} $, also manifested in the power law decay for the bondautocorrelation function disproving the validity of the WLC in 2d. We furtherobserve that the normalized transverse fluctuations of the semiflexible chainsfor different stiffness $\sqrt{\langle l_{\bot}^2\rangle}/L$ as a function ofrenormalized contour length $L/\ell_p$ collapse on the same master plot andexhibits power law scaling $\sqrt{\langle l_{\bot}^2\rangle}/L \sim(L/\ell_p)^\eta $ at extreme limits, where $\eta = 0.5$ for extremely stiffchains ($L/\ell_p \gg 1$), and $\eta = -0.25$ for fully flexible chains.

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