Size and Dynamics of a Tracer Ring Polymer Embedded in a Linear Polymer Chain Melt Matrix

Using dynamic Monte Carlo simulations based on the bond-fluctuation model, we systematically investigate the static and dynamic properties of a tracer ring polymer in a melt composed of linear polymers. Our results reveal that the mean-square radius of gyration of a cyclic polymer is independent of the topological constraints between the ring and linear chains. The scaling exponent (ν) of the radius of gyration Rg ∼ NRν, where NR is the ring chain length, increases from 0.5 to 0.6 as the length of the linear matrix chains, NL, decreases, which lies between the two values reported by Iyer et al. [ Macromolecules 2007, 40, 5995] and Lang et al. [ Macromolecules 2012, 45, 7642]. We find that both the structural relaxation time and self-diffusion coefficient are nearly independent of NL for a short ring chain (NR = 20) and the scaling exponents of NL for the self-diffusion coefficient are between −1 and −2 for large NR (NR ≥ 100), which cannot be understood by existing mechanisms, including the restraint reptation mechanism, the once-threaded mechanism, and the constraint release mechanism. Furthermore, we propose a “touch-threading” mechanism, which could be regarded as an important supplement to the above mechanisms, to describe the structural relaxation and translational diffusion of a tracer ring in a linear melt. In addition, when NL is large, the structural relaxation and translational diffusion of the tracer ring are decoupled, resulting in a breakdown of the extended Stokes–Einstein relation. These results provide fundamental insights into the properties of the ring-linear blends.