화학공학소재연구정보센터
Macromolecules, Vol.54, No.3, 1338-1353, 2021
Plateau Moduli of Several Single-Chain Slip-Link and Slip-Spring Models
We calculate the plateau moduli of several single-chain slip-link and slip-spring models for entangled polymers. In these models, the entanglement effects are phenomenologically modeled by introducing topological constraints such as slip-links and slip-springs. The average number of segments between two neighboring slip-links or slip-springs, N-0, is an input parameter in these models. To analyze experimental data, the characteristic number of segments in entangled polymers N-e estimated from the plateau modulus is used instead. Both N-0 and N-e characterize the topological constraints in entangled polymers, and naively, N-0 is considered to be the same as N-e. However, earlier studies showed that N-0 and N-e (or the plateau modulus) should be considered as independent parameters. In this work, we show that due to the fluctuations at the short time scale, N-e deviates from N-0. This means that the relation between N-0 and the plateau modulus is not simple as naively expected. The plateau modulus (or N-e) depends on the subchain-scale details of the employed model, as well as the average number of segments N-0. This is due to the fact that the subchain-scale fluctuation mechanisms depend on the model rather strongly. We theoretically calculate the plateau moduli for several single-chain slip-link and slip-spring models. Our results explicitly show that the relation between N-0 and N-e is model-dependent. We compare theoretical results with various simulation data in literature and show that our theoretical expressions reasonably explain the simulation results.