Correspondence relation with respect to entanglement among different simulation models: comparison between bead-spring and bond fluctuation model

A novel index for comparing different simulation model polymers with respect to entanglement is proposed. It is the number of elements $\text{N}{}_{\mathrm{<mtext>e</mtext>}}{}^{\mathrm{\ast }}$ of ring polymers whose average number of entanglement per molecule is unity; $\text{N}{}_{\mathrm{<mtext>e</mtext>}}{}^{\mathrm{\ast }}$ can be calculated with a small-scale computer simulation. We also proposed a method to equilibrate the entangled ring polymers. As an example we calculated $\text{N}{}_{\mathrm{<mtext>e</mtext>}}{}^{\mathrm{\ast }}$ with a molecular dynamics simulation using a bead-spring (BS) model which is equivalent to the model proposed by Kremer and Grest [J Chem Phys 92 (1990) 5057], and with a Monte Carlo simulation using bond fluctuation (BF) model. We obtained $\text{N}{}_{\mathrm{<mtext>e</mtext>}}{}^{\mathrm{\ast }}\text{=82±1}$ for BS model with volume fraction φ=0.43 and $\text{N}{}_{\mathrm{<mtext>e</mtext>}}{}^{\mathrm{\ast }}\text{=59±1}$ for BF model with φ=0.5. By comparing with the recent result of our group, N_e=89 for BF model with φ=0.5, we can assume that $\text{N}{}_{\mathrm{<mtext>e</mtext>}}\text{≃1.5}\text{N}{}_{\mathrm{<mtext>e</mtext>}}{}^{\mathrm{\ast }}\text{.}$ If this assumption holds for BS model, its N_e is estimated to be 120, which is 3.4 times greater than the estimated value by Kremer and Grest. The origin of this difference is discussed.