Glass Formation in Ring Polymer Melts Having Variable Knot Complexity and Molecular Mass

Abstract

The variation of polymer topology provides an alternative way to tune the properties of polymer materials without varying the chemistry of the monomers composing the polymer and provides a powerful approach to creating new functional materials and testing ideas about molecular transport in polymer fluids having broad theoretical significance in polymer science. Here, we focus on flexible ring polymer melts by coarse-grained molecular dynamics simulations, where the rings have a fixed knot complexity defined by the minimal crossing number m c , and explore how basic thermodynamic and segmental dynamic properties are impacted by varying m c and polymer molecular mass M. We find that increasing m c has a similar influence on the density, thermal expansion coefficient, radius of gyration, and overall average polymer shape, along with the characteristic temperatures of glass formation and fragility, as we recently found upon increasing the number of star arms f in star polymer melts where f defines the corresponding measure of topological complexity. The common trend in the thermodynamic and segmental dynamic properties of these distinct topological classes of polymers can be understood from the generalized entropy theory, based on how increasing m c and f alters molecular packing frustration, as quantified by the dimensionless thermal expansion coefficient and isothermal compressibility. These findings confirm in a striking way that molecular packing frustration is a key factor in determining the characteristic properties of glass-forming liquids. Notably, the effect of ring knotting was hardly considered in previous simulation and experimental studies of ring polymers, which is akin to ignoring f in the case of star polymers, so we suggest that knotting might be a source of some variability in measurements on ring polymers, in addition to linear polymer contaminants.