Conformation and structure of ring polymers in semidilute solutions: A molecular dynamics simulation study

Abstract

Scaling is one of the most fundamental concepts in theoretical polymer physics. For linear polymers in semidilute solutions under a good solvent condition, there has been a well established scaling behavior of mean-square radius of gyration of chains with the concentration, i.e., R g 2 ~ ϕ β , with β = −0.25, which receives strong support from experiments, computer simulations and scaling arguments. However, a clear-cut conclusion about the scaling behavior of dimensions of nonconcatenated and unknotted ring polymers in the semidilute solution with the concentration has not been achieved. Values of the corresponding scaling exponent β are diversely reported in literature, ranging from −0.25 to −0.59 and in contradiction within experimental, simulation and theoretical studies. As an endeavour for clarifying this issue, we carried out extensive molecular dynamics (MD) simulations based on the Kremer-Grest model of ring polymers with chain lengths N up to 5120 in semidilute solutions, and compared our results about ring conformations with almost all of experimental, simulation and theoretical data available in literature. Our MD simulation results lead to a conclusion that the mean-square radius of gyration of ring polymers scales with the concentration in semidilute regime as R g 2 ∼ φ − 0.59 ± 0.01 . This conclusion is in a good agreement with a previous finding by a lattice Monte Carlo simulation. Surprisingly, by looking into the experimental and other simulation results reported previously with sufficient caution, we tend to conclude that in reality almost all of their data can be described reasonably well by the same scaling law, R g 2 ~ ϕ − 0.59 . Furthermore, the scaling exponent obtained (−0.59) can be successfully explained by a scaling argument based on concept of correlation length. Finally, effects of the concentration on shape properties and packing behavior of ring polymers in the semidilute solutions have also been illuminated within our MD simulations. • Scaling behavior of ring dimensions in semidilute solutions with the concentration has been revisited. • Comparison of our results with experimental, and other simulation and theoretical results has been conducted. • Effect of concentration on shape and packing behavior of ring polymers in semidilute solutions has been illuminated.