Stress and configuration relaxation of an initially straight flexible polymer

Abstract

The stress and conformational relaxation of an initially straight flexible polymer is studied through Brownian dynamics simulations covering a broad range of time scales and polymer lengths. At short times $t\,{\ll}\, N^{-2}$, the strong stress component scales as $\sigma_{11}\,{\sim}\, N^3$ (‘1’ is the direction of the original alignment), while the weak component is $\sigma_{22} \,{\sim}\, N$ (where $N$ is the polymer length). At intermediate times $N^{-2}\,{\ll}\, t\,{\ll}\, N^{2}$, the stress decay is shown to be anisotropic: $\sigma_{11} \,{\sim}\, N^2 t^{-1/2}$ while $\sigma_{22} \,{\sim}\, N^{1/2} t^{-1/4}$. At long times $t\,{\gg}\, N^2$, both stress components show the same exponential decay associated with the reduction of the chain's length, while their magnitudes are still different; $\sigma_{11}\,{=}\, \mbox{\it O}(N)$ while $\sigma_{22} \,{=}\, \mbox{\it O}(1)$. The configuration relaxation is studied over the same extended time periods by employing scaling laws for the evolution of the eigenvalues of the gyration tensor. After the short-time free diffusion, the configuration relaxation is anisotropic at intermediate times: the chain's width grows as $R_{\perp} \,{\sim}\, N^{-1/4} t^{3/8}$ while its length is reduced as $R_{\parallel}(0)\,{-}\,R_{\parallel} \,{\sim}\, t^{1/2}$. During long times, the polymer length shows an exponential decay towards the equilibrium coil-like shape. The polymer chain remains aligned along the original direction until late in long times where the chain rotation is shown to be significant. The chain is shown to be far from equilibrium during the entire transient relaxation. By focusing on the chain's longitudinal relaxation, a quasi-steady equilibrium of the link tensions in shown to exist along the chain's length; the mechanism is identical to that found in Grassia & Hinch (1996) based on a sideways motion model. This mechanism also explains the ability of the FENE model to describe the longitudinal relaxation of the flexible bead-rod chain. A comparison with experimental findings from initially straight single tethered DNA molecules is also included.