High-precision computer simulations of entangled polymer chains: 1. Determination of entanglement parameters of bond-fluctuation model

High-precision computer simulations of bond-fluctuation (BF) model (volume fraction φ=0.5) are performed in the transition region between the non-entanglement and the entanglement regime. Defects of the model called X-traps are newly found which result in serious errors in the long-time behavior of the system. For samples free from X-traps, diffusion coefficient D of the center of mass, relaxation times τ_α for Rouse coordinate R_α (α=1,2) and τ_L for the end-to-end vector L are determined for chains of length N=16–180 within few percent of statistical errors. Their N-dependence changes around N=100 at which entanglement coupling is supposed to begin. By comparing D obtained by the simulations with experimental data of polystyrene melts and solutions, the average chain length per entanglement N_e was estimated to be 89, which is much larger than 30–42 reported by Paul et al. (J Phys II 1991;1:37). To see the origin of the discrepancy, statistical errors and system size effects are studied in detail and it was found that, to determine D within few percent of error, the number of independent chain samples N_sample should be larger than 10 000 and the size of simulation cells ℓ_cell should be larger than 4R_g; these conditions are not satisfied in the previous simulations. Critical chain length N_c^η for entanglement of BF model is estimated to be N_c^η=170 using the empirical relationship N_c^η/N_e=1.92 for polystyrene melts. It is argued that N_c^η=170 is a universal parameter of entanglement but N_e=89 is a specific value for polystyrenes and it may change with the materials with which comparisons are made.