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.

Automated summary

Our study reveals that due to fluctuations at short time scales, the characteristic number of segments in entangled polymers deviates from the average number of segments, leading to a non-trivial relationship between the plateau modulus and these two parameters.