**Molecular Dynamics Simulations of Ring Shapes on a Ring Fraction in
Ring-Linear Polymer Blends**

K Hagita and T Murashima, MACROMOLECULES, 54, 8043-8051 (2021).

DOI: 10.1021/acs.macromol.1c00656

Threading of a linear chain through a ring has been known to have a strong effect on slowing the dynamics of the ring. To enhance the toughness of soft materials using ring-linear polymer blends, it is important to understand the effects of parameters such as the average of the squared radius of gyration (< R-g(2)>) of the rings, the number of linear chains penetrating a ring (n(P)), and the n(P) dependence of the shape indexes on the ring fraction f(ring). Using the Kremer-Grest model for flexible chains, we simulated rings of length N-ring = 70 and 140 for 0.2 < f(ring) <= 0.97. The exponent a for the relation < R-g(2)> proportional to f(ring)(-alpha) was 0.06 and 0.09 for N-ring = 70 and 140, respectively. The increase in alpha for the increasing N-ring was similar to the experimental results for polystyrene reported in the study by Iwamoto et al. (Macromolecules 2018, 51, 1539-1548 and 6836-6847). < R-g(2)> of the rings increases as f ring decreases. This increase in the size of the rings results in an increase in the average number of linear chains < n(P)> that penetrate the rings. < n(P)>. was also observed to increase with the increasing N-ring. In particular, for f(ring) = 0.2 and N-ring = 140, multiple linear chains penetrated the ring. We also confirmed that the Kremer-Grest model with the bending potentials proposed by Everaers et al. to map this model to polystyrene shows good agreement with the exponent a found experimentally by Iwamoto et al.

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