Understanding Dynamics in Binary Mixtures of Entangled cis-1,4-Polybutadiene Melts at the Level of Primitive Path Segments by Mapping Atomistic Simulation Data onto the Tube Model

Abstract

We study dynamics in bidisperse melts of linear cis-1,4-polybutadiene composed of probe and matrix chains at the level of the segment survival probability function ψ(s,t) which is computed directly in the course of long atomistic molecular dynamics simulations [Stephanou et al. J. Chem. Phys. 2010, 132, 124904]. By controlling precisely the matrix chain length and composition, the effect of contour length fluctuations (CLFs) and constraint release (CR) on melt dynamics is quantified. Our study shows that (a) the values of the static topological properties of the probe chains (e.g., the average value of their primitive path (PP) contour length and its fluctuation) remain unaltered in the different matrices, but (b) their dynamical properties (including ψ(s,t) and its average over all segments s, ψ(t), the time autocorrelation function of the PP contour length, and the time autocorrelation function of the chain end-to-end vector) vary significantly from matrix to matrix. As the length of the matrix chains decreases, the functions ψ(s,t) and ψ(t) describing the reptation relaxation of the probe chains are found to decrease more rapidly. Furthermore, the relaxation of longer probe chains is seen to be delayed as the concentration of shorter matrix chains decreases. Overall, our direct computational study proves that CR is the dominant relaxation mechanism in melts of long and short cis-1,4-polybutadiene chains accounting for the majority of differences observed in their relaxation dynamics in different environments (since CLFs appear to be unaffected by compositional differences); as a result, it has a profound effect on the linear viscoelastic properties of the melt, such as the spectra of storage and loss moduli. By further analyzing the mean-square displacement of atomistic segments in the different matrices, we find that while the tube diameter is constant in the mixtures with MS ≤ Me where MS is the molecular weight of short chains and Me the entanglement molecular weight, it gradually increases in the mixtures with MS < Me. How the simulation results compare with laboratory measurements on melts of bidisperse polymers reported in the literature is also discussed.