Relaxation and Stiffening Dynamics of a Single Semiflexible Polymer Chain

Abstract

Both synthetic and biological polymers are a challenge to study because of the many features and functional roles they carry. A good understanding of the macromolecule's dynamical properties is essential for biological processes such as the cytoskeleton dynamics of actin or in creating novel materials such as biodegradable nanocomposites. Here we focus on the Brownian dynamics of single semiflexible polymer chains, speci cally the relaxation and stiffening behaviors. To date, the transient modeling of dilute solutions has concentrated mainly on flexible chains. Semiflexible polymers, with a persistence length comparable to or larger than their contour length show distinct properties in solution.

Brownian dynamics simulations based on a discretized version of the Kratky-Porod chain model were employed. First, the relaxation of a bead-rod polymer chain from an initially straight configuration was followed. Through a scaling-law analysis, universal relaxation laws were determined covering all time scales. A correlation describing the properties studied by the single parameter of chain length was noticed. Based on this, we were able to confirm and explain the chain's stress and optical properties, as well as derive a nonlinear stress-optic law valid for semiflexible chains at any time period. Also, we determine the relaxation for long semiflexible chains exhibit two intermediate-time behaviors, as a result of the interplay of Brownian and bending forces on the link tensions.

A second project involved the relaxation dynamics of a worm-like bead-spring chain. Existing relaxation simulations of this bead-spring model are limited to the stress behavior. Here we monitor the short and intermediate-time relaxation behaviors of a nearly extended semiflexible chain. We also look at the effects of the Kuhn length on a chain of constant length.

Finally, the interesting behavior of the coil-helix-rod stiffening transition was studied. When subjected to external forces or a change in solution conditions the macromolecule may stiffen. Being able to control the chain stiffness is of technological importance especially for nanotechnology devices where the constraint of the walls limits the entropy available to the chain. We have successfully simulated the transient conformational behavior and subsequently understand the chain dynamics involved through analysis of the chain's length, width, and stress.