Static dynamics approach to relaxation modes and times for deformed polymers

We discuss relaxation of conformational fluctuations around deformed polymer states. To this end, Brownian dynamics simulations of bead-spring models including a finite extensibility of the springs as well as excluded volume and hydrodynamic interactions between the beads have been performed. Complete spectra of relaxation times as well as corresponding relaxation modes are obtained from the simulation data by applying the static dynamics formalism, which rigorously describes the initial decay of correlations between the bead positions. As shown here, this procedure amounts to using a generalized Rouse-Zimm-like model which is governed by linear effective equations of motion having the same initial decay of correlations as the full nonlinear bead-spring model used in the simulations. In thermal equilibrium, the well-known scaling laws in the presence of excluded volume and hydrodynamic interactions between the beads are recovered, but, in addition, the static dynamics method also yields numeric values for the nonuniversal prefactors of the respective laws. The method is equally applicable to a broad range of problems, where the polymer is deformed by the action of flows or forces. Two examples of recent interest are considered: a tethered polymer pulled at its free end and one which is stretched by a uniform flow. It is shown that in both cases, the relaxation process is dominated by a finite extensibility of the springs.