Conformations, transverse fluctuations, and crossover dynamics of a semi-flexible chain in two dimensions

We present a unified scaling description for the dynamics of monomers of a semiflexible chain under good solvent condition in the free draining limit. We consider both the cases where the contour length L is comparable to the persistence length l(p) and the case L >> l(p). Our theory captures the early time monomer dynamics of a stiff chain characterized by t(3/4) dependence for the mean square displacement of the monomers, but predicts a first crossover to the Rouse regime of t(2 nu/1 +) (2 nu) for tau(1) similar to l(p)(3), and a second crossover to the purely diffusive dynamics for the entire chain at tau(2) similar to L-5/2. We confirm the predictions of this scaling description by studying monomer dynamics of dilute solution of semi-flexible chains under good solvent conditions obtained from our Brownian dynamics (BD) simulation studies for a large choice of chain lengths with number of monomers per chain N = 16-2048 and persistence length l(p) = 1-500 Lennard-Jones units. These BD simulation results further confirm the absence of Gaussian regime for a two-dimensional (2D) swollen chain from the slope of the plot of < R-N(2)>/2Ll(p) similar to L/l(p) which around L/l(p) similar to 1 changes suddenly from (L/l(p)) -> (L/l(p))(0.5), also manifested in the power law decay for the bond autocorrelation function disproving the validity of the worm-like-chain in 2D. We further observe that the normalized transverse fluctuations of the semiflexible chains for different stiffness root < l(perpendicular to)(2)>/L as a function of renormalized contour length L/l(p) collapse on the same master plot and exhibits power law scaling root < l(perpendicular to)(2)>/L similar to (L/l(p))(eta) at extreme limits, where eta = 0.5 for extremely stiff chains (L/l(p) >> 1), and eta = -0.25 for fully flexible chains. Finally, we compare the radial distribution functions obtained from our simulation studies with those obtained analytically. (C) 2014 AIP Publishing LLC.