Projection of atomistic simulation data for the dynamics of entangled polymers onto the tube theory: calculation of the segment survival probability function and comparison with modern tube models

Abstract

State-of-the-art tube models for the dynamics of entangled polymer melts are usually validated on the basis of the agreement of their predictions for the linear viscoelastic properties (LVE data) of the system against experimentally measured data. We present here a more direct and fundamental test of these models based on their comparison against molecular dynamics (MD) simulation data for the dynamics of primitive paths (PPs) in the system under study. More precisely, we show how one can take advantage of a recently developed computational methodology (P. S. Stephanou, C. Baig, G. Tsolou, V. G. Mavrantzas and M. Kröger, J. Chem. Phys., 2010, 132, 124904) for calculating the most important function of all tube models, the segment survival probability ψ(s,t) and its average Ψ(t) (the overall tube survival probability), by projecting MD data of atomistically detailed samples onto the level of the primitive paths, to directly probe mechanisms proposed for chain relaxation, such as contour length fluctuation (CLF) and constraint release (CR). The simulation data for ψ(s,t) and Ψ(t) can be used next to evaluate refinements of the original Doi–Edwards reptation theory based on a modified diffusion equation for ψ(s,t) incorporating the terms proposed to account directly or indirectly for these effects (CLF and CR). The functions ψ(s,t) and Ψ(t) determined directly from the atomistic MD simulation data account automatically for all these relaxation mechanisms, as well as for any other mechanism present in the real melt. We present and discuss results from such an approach referring to model, strictly monodisperse cis- and trans-1,4-polybutadiene and polyethylene melts containing on average up to 6 entanglements per chain, simulated in full atomistic detail for times up to a few microseconds (that is, comparable to the chain disentanglement time τ_d). From the same simulations we also present results for two other measures of the PP dynamics in the framework of the reptation theory, the time auto-correlation function of the PP contour length L and the time auto-correlation function of the chain end-to-end vector R. Our methodology, which serves as a bridge between molecular simulations and analytical tube theories, helps quantify chain dynamics in entangled polymers and understand how it is influenced by factors like melt polydispersity and chain molecular architecture, or the presence of interfaces. It can also be straightforwardly extended to polymeric liquids under non-equilibrium conditions (e.g., subjected to a flow field) to understand the interplay between flow and entanglements.