Rheological complexity in simple chain models

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 β to be tracked over a wide range of state points. The smoothness of β as a function of packing fraction η is a testimony both to the accuracy of the analytical methods and the appropriateness of ( η 0 − η ) as a measure of the distance to the ideal glass transition at η 0 . Relatively direct comparison is made with experiment by viewing β as a function of the KWW relaxation time τ 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 α -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 β 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.