Linear Viscoelasticity from Molecular Dynamics Simulation of Entangled Polymers

Abstract

The linear viscoelastic (LVE) spectrum is one of the primary fingerprints of polymer solutions and melts, carrying information about most relaxation processes in the system. Many single chain theories and models start with predicting the LVE spectrum to validate their assumptions. However, until now, no reliable linear stress relaxation data were available from simulations of multichain systems. In this work, we propose a new efficient way to calculate a wide variety of correlation functions and mean-square displacements during simulations without significant additional CPU cost. Using this method, we calculate stress-stress autocorrelation functions for a simple bead-spring model of polymer melt for a wide range of chain lengths, densities, temperatures, and chain stiffnesses. The obtained stress-stress autocorrelation functions were compared with the single chain slip-spring model in order to obtain entanglement related parameters, such as the plateau modulus or the molecular weight between entanglements. Then, the dependence of the plateau modulus on the packing length is discussed. We have also identified three different contributions to the stress relaxation: bond length relaxation, colloidal and polymeric. Their dependence on the density and the temperature is demonstrated for short unentangled systems without inertia.

Polymer and spherical nanoparticle diffusion in nanocomposites

“…However searching for the reptation power laws 1 as predicted by reptation theory, through molecular dynamics simulations, is difficult [32][33][34][35][36][37][38] . For example by using the Kremer-Grest model 31 the reptation regime can not be reached for very long polymers 33 .…”

Whither tube theory: From believing to measuring

“…The tube theory in 2007 is still facing many key questions which cannot be answered within the model. Here we list just a few key ones [7]:…”

“…Computers are becoming cheap and powerful enough to perform reliable molecular dynamics simulations of toy polymers (i.e. Lennard-Jones beads connected by FENE springs [8]) well into entangled timescales [7]. However, so far molecular dynamics simulations have been used mainly as an additional experimental technique, i.e.…”

“…It also allows one to separate e¤ective bonded stress from the other contribution by subtracting it from total stress (dotted line). Most likely, it can be attributed to colloidal relaxation by collisions with other non-bonded particles (see [7], [13] for density dependence of colloidal relaxation).…”

The tip of iceberg in nonlinear polymer rheology: Entangled liquids are “solids”

“…The readers can get a comprehensive review of the relevant literature in a recent publication. 4 A great number of experiments have accumulated for more than three decades to indicate that the de Gennes-Doi-Edwards tube model 3,5 is very successful in describing polymer dynamics in the linear response regime, including diffusion and linear viscoelastic behavior in bulk and at surfaces, and that much is reliably known about linear viscoelasticity at a phenomenological level, although some recent theoretical activities indicated [6][7][8] that the tube theory may have serious limitations even in the simplest case of stress relaxation after small step strain.…”