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We calculate the plateau moduli of several single-chain slip-link andslip-spring models for entangled polymers. In these models, the entanglementeffects are phenomenologically modeled by introducing topological constraintssuch as slip-links and slip-springs. The average number of segments between twoneighboring slip-links or slip-springs, $N_{0}$, is an input parameter in thesemodels. To analyze experimental data, the characteristic number of segments inentangled polymers $N_{e}$ estimated from the plateau modulus is used instead.Both $N_{0}$ and $N_{e}$ characterize the topological constraints in entangledpolymers, 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) shouldbe considered as independent parameters. In this work, we show that due to thefluctuations at the short time scale, $N_{e}$ deviates from $N_{0}$. This meansthat the relation between $N_{0}$ and the plateau modulus is not simple asnaively expected. The plateau modulus (or $N_{e}$) depends on thesubchain-scale details of the employed model, as well as the average number ofsegments $N_{0}$. This is due to the fact that the subchain-scale fluctuationmechanisms depend on the model rather strongly. We theoretically calculate theplateau moduli for several single-chain slip-link and slip-spring models. Ourresults explicitly show that the relation between $N_{0}$ and $N_{e}$ ismodel-dependent. We compare theoretical results with various simulation data inthe literature, and show that our theoretical expressions reasonably explainthe simulation results.

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