Longitudinal Relaxation of Initially Straight Flexible and Stiff Polymers
Physical Review Letters
The relaxation mechanism of an initially straight flexible or stiff polymer chain of length N in a viscous solvent is studied through Brownian dynamics simulations covering a broad range of time scales. After the short-time free diffusion, the chain's longitudinal reduction R 2 k 0 ÿ R 2 k Nt 1=2 at early intermediate times is shown to constitute a universal behavior for any chain stiffness caused by a quasisteady T Nt ÿ1=2 relaxation of tensions associated with the deforming action of the
... action of the Brownian forces. Stiff chains with a persistence length E N are shown to exhibit a late intermediate-time longitudinal reduction R 2 k 0 ÿ R 2 k N 2 E ÿ3=4 t 1=4 associated with a T N 2 E ÿ3=4 t ÿ3=4 relaxation of tensions affected by the deforming Brownian and the restoring bending forces. The present study considers the conformational relaxation of a single flexible or stiff polymer chain from an initial straight configuration in a viscous solvent. This problem commonly arises when strong flows are turned off in both industrial and biological applications. The problem is also motivated by recent experiments with single DNA molecules relaxing after being fully extended by applied forces as well as by the recent development of microdevices involving stretched tethered biopolymers . Our interest lies in understanding the relaxation mechanism for flexible and stiff polymers, and thus our results are applicable to a wide array of both synthetic polymers, such as polyacrylamides, Kevlar, and polyesters as well as biopolymers, such as DNA, actin filaments, microtubules, and rodlike viruses. In recent years considerable progress has been made in understanding the properties of semiflexible polymers near equilibrium [2 -5]. In this regime the transverse fluctuations of semiflexible polymers were found to scale as t 3=4 , while the longitudinal fluctuations scale as t 7=8 [2,3]. With this study, we want to understand the relaxation mechanism of a specific problem far from equilibrium where a complete theory of the relaxation process is lacking. We show that the early longitudinal relaxation, being associated with a quasisteady relaxation of link tensions of a Brownian nature, is valid for any chain stiffness. Stiff chains are shown to exhibit a late longitudinal relaxation associated with the cumulative effect of the deforming Brownian forces and the restoring bending forces on the link tensions. The techniques we develop to understand the relaxation mechanism may be useful for a wide array of problems in polymer rheology. To describe the polymer chain, Brownian dynamics simulations are employed based on a discretized version of the wormlike chain model described in our previous publication  . This method considers a bead-rod model with fixed bond lengths and ignores hydrodynamic interactions among beads as well as excluded-volume effects  . The polymer chain is modeled as N B N 1 identical beads connected by N massless links of fixed length b (which is used as the length unit). The position of bead i is denoted as X i , while the link vectors are given by d i X i1 ÿ X i . The polymer stiffness is accounted by a bending potential proportional to the square of the local curvature, bend E P Nÿ1 i1 1 ÿ d i d i1 =b 2 .