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Extensive Monte Carlo simulations are presented for the bond-fluctuation model on three-dimensional simple cubic lattices. High statistics data are obtained for polymer volume fractions Φ in the range $0.025 \leqslant \Phi \leqslant 0.500$ and chain lengths N in the range $20 \leqslant N \leqslant 200$, making use of a parallel computer containing 80 transputers. The simulation technique takes into account both excluded volume interactions and entanglement restrictions, while otherwise the chains are non-interacting and athermal. The simulation data are analysed in terms of the de Gennes scaling concepts, describing the crossover from swollen coils in the dilute limit to gaussian coils in semidilute and concentrated solution. The crossover scaling functions for the chain linear dimensions and for the decay of the structure factor are estimated and compared to corresponding theoretical and experimental results in the literature. Also the dynamics of the chains is studied in detail, and evidence for a gradual crossover from the Rouse model to a D ∼N-2 law for the diffusion constant is presented. This crossover is consistent with scaling only if a concentration-dependent segmental “friction coefficient" is introduced. Within this framework general agreement between these data, other simulations and experiment is found

We present Molecular Dynamics simulations of the thermal glass transition in a dense model polymer liquid. We performed a comparative study of both constant volume and constant pressure cooling of the polymer melt. Great emphasis was laid on a careful equilibration of the dense polymer melt at all studied temperatures. Our model introduces competing length scales in the interaction to prevent any crystallisation tendency. In this first manuscript we analyse the structural properties as a function of temperature and the long time or α-relaxation behaviour as observed in the dynamic structure factor and the self-diffusion of the polymer chains. The α-relaxation can be consistently analysed in terms of the mode coupling theory (MCT) of the glass transition. The mode coupling critical temperature, T c , and the exponent, γ, defining the power law divergence of the α-relaxation timescale both depend on the thermodynamic ensemble employed in the simulation.

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The bond fluctuation model on the simple cubic lattice is studied by Monte Carlo simulations on a multitransputer array, for polymer volume fractions φ in the range 0.025≤φ≤0.500 and chain lengths N in the range 20≤N≤200. Extensive data are presented on the dynamics of monomer displacements, center-of-gravity displacements, and relaxation times. This study is complementary to previous work, in which the crossover scaling properties of the chain linear dimensions, structure factor, and self-diffusion constant were tested for the same athermal model. The simulation technique takes both excluded volume interactions and entanglement constraints into account, but ignores hydrodynamic forces. Our results describe the crossover from Rouse behavior of swollen chains (τ∼N1+2ν, ν being the exponent describing the radius R of the chains, R∼Nν ) to reptation, τ∼N3. Since the excluded volume screening length is found to be smaller than the tube diameter by a factor of about 3, the rescaled times Wτ/N1+2ν decrease first as a function of the scaled chain length Ñ∼Nφ1/(3ν−1), before they increase due to the onset of reptation. Additional evidence for reptative behavior is found by identifying the several successive crossovers in the time-dependent displacements predicted by de Gennes.