Brownian Dynamics Simulation of Dilute Polymer Chains.

Abstract

Local motion of polymers is extremely important while studying the behavior of single strand DNA in DNA unzipping and replication, understanding rheological properties of polymers in confined in narrow gaps for head-disk interface design for hard disk drives, and designing membrane structure for small molecule permeation through a dense polymeric membrane. So, in order to understand the mechanism of energy dissipation of dilute polymer solutions at high frequencies, I carry out a Brownian dynamics study of a linear bead-spring chain in which the beads represent individual backbone atoms, a stiff Fraenkel spring potential maintains the distance between atoms near 1.53 , a bending potential maintains tetrahedral bonding angles, a torsional potential imposes realistic barriers to torsional transitions, and white noise represents the Brownian force from the solvent. With this model, I find that the end-to-end vector autocorrelation function from the simulation is in excellent agreement with the theoretical Rouse model predictions. Nevertheless, the autocorrelation function of the bond orientation vectors—which delineates the relaxation of the stress tensor—exhibits a much slower decay then predicted by the coarse-grain Rouse theory except near the longest relaxation time even for chains with as many as 50 bonds. I find that both the bending and torsional potentials slow down the contributions of local relaxation modes, bringing the relaxation of short chains (less than 50 bonds) closer to single exponential behavior than to the Rouse spectrum, in qualitative agreement with observations of birefringence relaxation [Lodge et al. (1982) J. Poly. Sci. 20, 1409]. Also, my normal mode predictions using the bead-spring model provides an excellent fit to data for 2400 and 6700 base single-strand DNA molecules [Shusterman et al. (2004) Phy. Rev. Lett. 92(4), 048303] and the fit yields 12 Kuhn steps per spring and a value of 0.12 for the standard hydrodynamic interaction parameter—very close to the values typical of conventional polymers such as polystyrene. Thus, my results are generally in agreement with a recent notion of a “dynamical Kuhn length” in which torsional barriers to chain motion, can suppress high frequency contribution to viscoelasticity [Larson (2004) Macromol. 37, 5110].