Explaining the Absence of High-Frequency Viscoelastic Relaxation Modes of Polymers in Dilute Solutions

Abstract

Using multiscale modeling, including molecular dynamics simulations, with both united-atom and coarse-grained force fields, as well as Brownian dynamics simulations with still higher levels of coarse-graining, we explain the long-mysterious absence of high frequency modes in the viscoelastic spectrum of isolated polymer chains in good solvents, reported years ago by Schrag and co-workers. The relaxation spectrum we obtain for a chain of 30 monomers at atomistic resolution is, remarkably, a single exponential, while that of a coarse-grained chain of 100 monomers is well fit by only two modes. These results are very surprising in view of the many degrees of freedom possessed by these chains, and in view of the many relaxation modes present in melts of such chains. However, the result agrees perfectly with experimental observations of Schrag and co-workers. We also performed Brownian dynamics (BD) simulations in which the explicit solvent molecules are replaced by a viscous continuum, using chain models of varying degrees of resolution, both in the presence and absence of hydrodynamic interactions (HI). Although the local dynamics is suppressed by the addition of bending, torsion, side groups and excluded volume interactions (as suggested in Jain and Larson(15)), none of the BD simulations predict a single exponential relaxation for a short polymer chain. The comparison of the relaxation of the bond vectors from different models indicates an additional slow-down in the presence of explicit solvent molecules, which is critical to obtain a single exponential relaxation for short chains. Our results indicate that the chain dynamics at small length scales (down to a few Kuhn steps) are significantly different from the predictions of models based on a continuum solvent, and finally help explain the experimental results of Schrag and co-workers.