Tunable Cooperative Motion, Rigidity, and Glassy Dynamics in Knotted Ring Polymer Melts

We present a molecular dynamics study of the influence of knot complexity and molecular mass on glass formation upon cooling in knotted ring polymer melts. We find that cooperative motion, rigidity, and glassy dynamics can be tuned over a wide range by knots. By leveraging these knotting constraints, we assess the validity of prevalent models of glass formation, including the string model based on the extent of cooperative particle motion, the localization model emphasizing fluctuations in local particle mobility, and the shoving model derived from emergent elastic properties in relation to the material stiffness. In line with our previous findings on polymeric and other glass-forming liquids, we demonstrate that all of these models of glass formation provide a quantitative description of segmental relaxation as a function of knot complexity, molecular mass, and temperature, despite their apparently distinct conceptual foundations. Our study thus provides additional evidence for an underlying unity among various theoretical frameworks of glass formation and for the presence of quantitative relations between the characteristic properties emphasized by these models. Furthermore, we discuss dynamic and elastic heterogeneities in relation to fragility and stiffness variations of knotted ring polymer melts, with a focus on how these trends relate to other glass-forming liquids, where fragility is tuned over a large range.