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), 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.

Dissipative particle dynamics simulations of a single isolated polymer chain in a dilute solution

“…This suppression of higher modes for short polymer chains is surprising, but is consistent with previous experiments 26 and simulations 24,27 .…”

“…Further, the DPD simulations for relatively higher values of a ij (a ij ≥ 25) clearly predict an abrupt cut-off in the relaxation spectrum of the chain, which is also observed in earlier experimental studies 26 . For a short chain of 10 Kuhn steps, the relaxation spectrum is approximately reduced to a single time scale, which is remarkably consistent with experiments and a recent MD simulation 27.…”

Effectiveness of DPD Simulations to Predict the Dynamics of Polymer Chains in Solutions at Equilibrium and Steady Shear Flows

“…Hence, there have been only a handful of MD studies that investigate polymer physics, and that too for a few tens of monomers, which barely constitute a few Kuhn steps. [ 12 ] Thus, techniques operating at the mesoscopic length scales, far away from the atomistic length and time scales, have become popular (and practically feasible) for polymer physics. Instead of MD simulations, a lot of researchers have performed Brownian dynamics (BD) simulations of single, isolated polymer chains, to understand the behavior with or without flow.…”

“…This indicates a lack of understanding of the role of the dynamics of the surrounding solvent molecules when the chain is exposed to a flow field. Another, possibly solvent‐related related problem, lies in the abrupt cut‐off of the relaxation spectrum, observed from experiments [ 37 ] as well as MD simulations of short chains, [ 38 ] where the higher modes in the polymer chains are virtually absent. Issues like these cannot be addressed by BD simulations, where the solvent is replaced by a continuum.…”

Accurate Closure for the Configuration Dynamics and Rheology of Dilute Polymer Chains in Arbitrary Flows

“…The framework set by the Rouse and Zimm models was closely followed by computational techniques, which also modeled the polymer chain by beads connected by springs. While only a few beads and springs − and dumbbells , were used in the early days when computational power was limited, in recent years, the phenomenal rise in computer power has allowed analysis of highly detailed models that retain hundreds or thousands of degrees of freedom using Brownian dynamics (BD) or molecular dynamics (MD) simulations. − A summary of the findings of earlier works is given in various review articles. − Most of those investigations were restricted to extensional and shear flows, while a few have explored planar mixed flows ranging from extensional to purely rotational . In a fast extensional flow, the chain attains a nearly completely extended final state, while in a fast shearing flow, which contains equal amounts of extension and rotation, the long-time behavior consists of incessant end-over-end tumbling events.…”