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

Abstract

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 R g ∼ N R ν, where N R is the ring chain length, increases from 0.5 to 0.6 as the length of the linear matrix chains, N L, decreases, which lies between the two values reported by Iyer et al. [Macromolecules2007405995] and Lang et al. [Macromolecules2012457642]. We find that both the structural relaxation time and self-diffusion coefficient are nearly independent of N L for a short ring chain (N R = 20) and the scaling exponents of N L for the self-diffusion coefficient are between −1 and −2 for large N R (N R ≥ 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 N L 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.

Structure of Polymer Rings in Linear Matrices: SANS Investigation

“…However, the simulation only considered symmetric blends RxLx, and thus, the behavior of asymmetric blends may differ from the symmetric case. Based on their MC simulations that are in agreement with our results, Mo et al observed that only for short matrices, a significant dependence of ring swelling on the host length occurs . As for the Mavrantzas results, the number of threadings is high.…”

“…Aside from the MD simulations, Monte-Carlo simulations are also reported . They also found large numbers of threadings, agreeing with Mavrantzas’ atomistic MD simulations.…”

“…Aside from the MD simulations, Monte-Carlo simulations are also reported. 12 They also found large numbers of threadings, agreeing with Mavrantzas' atomistic MD simulations. Again, except for very short hosts, the number of threadings is rather independent of the linear host size.…”

Topological transition in multicyclic chains with structural symmetry inducing stress-overshoot phenomena in multicyclic/linear blends under biaxial elongational flow

“…15,20 Thus, the constraint release mechanism of rings is much slower than theoretically expected. Moreover, since these penetrations lead to slow ring polymer dynamics, 21,22 the rheological properties of ring/linear blends differ from those of both the pure ring and linear melts. Specifically, a small number of linear chains drastically increases the viscosity of the ring melts, 23,24 whereas a low ring volume fraction increases the viscosity of the linear melt up to the overlapping concentration of the rings.…”

Topological Transition in Multicyclic Chains with Structural Symmetry Inducing Stress-Overshoot Phenomena in Multicyclic/Linear Blends under Biaxial Elongational Flow

“…Rings are penetrated and interlocked by the surrounding rings, − while in linear chain contaminants they are penetrated by linear chains. , Thus, the constraint release mechanism of rings is much slower than theoretically expected. Moreover, since these penetrations lead to slow ring polymer dynamics, , the rheological properties of ring/linear blends differ from those of both the pure ring and linear melts. Specifically, a small number of linear chains drastically increases the viscosity of the ring melts, , whereas a low ring volume fraction increases the viscosity of the linear melt up to the overlapping concentration of the rings .…”