Plateau Moduli of Several Single-Chain Slip-Link and Slip-Spring Models

Abstract

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 the literature, and show that our theoretical expressions reasonably explain the simulation results.

arXiv comment26 pages, 3 figures, to appear in Macromolecules

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• Multi-chain Slip-spring Model for Entangled Polymer Dynamics
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Cited by in corpus (1)

• Dissipative particle dynamics simulation plus slip-springs for entangled polymers with various slip-spring densities