Rheological complexity in simple chain models

Abstract

Dynamical properties of short freely jointed and freely rotating chains are studied using molecular dynamics simulations. These results are combined with those of previous studies, and the degree of rheological complexity of the two models is assessed. New results are based on an improved analysis procedure of the rotational relaxation of the second Legendre polynomials of the end-to-end vector in terms of the Kohlrausch-Williams-Watts (KWW) function. Increased accuracy permits the variation of the KWW stretching exponent beta to be tracked over a wide range of state points. The smoothness of beta as a function of packing fraction eta is a testimony both to the accuracy of the analytical methods and the appropriateness of (eta(0)-eta) as a measure of the distance to the ideal glass transition at eta(0). Relatively direct comparison is made with experiment by viewing beta as a function of the KWW relaxation time tau(KWW). The simulation results are found to be typical of small molecular glass formers. Several manifestations of rheological complexity are considered. First, the proportionality of alpha-relaxation times is explored by the comparison of translational to rotational motion (i.e., the Debye-Stokes-Einstein relation), of motion on different length scales (i.e., the Stokes-Einstein relation), and of rotational motion at intermediate times to that at long time. Second, the range of time-temperature superposition master curve behavior is assessed. Third, the variation of beta across state points is tracked. Although no particulate model of a liquid is rigorously rheologically simple, we find freely jointed chains closely approximated this idealization, while freely rotating chains display distinctly complex dynamical features.

Molecular dynamics simulations of glassy polymers

“…In the continuum, the simplest model are highly flexible bead-spring models, where spherical monomers are tethered together by springs and have nonbonded, Lennard-Jones (LJ) interactions [31,30,32]. More chemical realism can be introduced by making the chains semiflexible, through the addition of a bond-angle potential [59] and, possibly also, of a torsional potential [60,61,62]. Due to their simplicity, these generic models allow for an efficient simulation.…”

“…[59][60][61] Due to their simplicity, these generic models allow for an efficient simulation. This is important if one wants to vary the cooling rate 62 or the strain rate 27 over decades, to explore systematically the impact of model parameters, such as chain length or chain flexibility, [58][59][60][61] or to obtain good statistics for comparison with theory. 63 Computational expedience is also important for exploratory studies of more complex systems, such as inhomogeneous polymer systems (e.g., polymer films, nanocomposites, semi-crystalline polymers) or glassy polymer mixtures (e.g., dynamically asymmetric polymer-polymer mixtures or polymersolvent systems).…”

Effect of chain flexibility on master curve behavior for diffusion coefficient

“…3,7,[28][29][30] Previously, freely jointed and freely rotating, tangent site chains were explored. In the current paper, rotational restrictions on the dihedral angle ("torsional" chains) are introduced resulting in well defined gauche and trans states.…”

Dynamic heat capacity of the east model and of a bead-spring polymer model.

“…The specific model that we are using is a bead-spring polymer model, as in previous equilibrium work [29,30,31,32,33,34]. This is a coarse grained model, in that the chemical details of the monomers are ignored; instead, the polymer chains are simply chains of single atom monomers (the beads) chained together with unbreakable bonds (the springs).…”