Molecular-dynamics simulation of a glassy polymer melt: Incoherent scattering function

We present simulation results for a model polymer melt, consisting of short, nonentangled chains, in the supercooled state. The analysis focuses on the monomer dynamics, which is monitored by the incoherent intermediate scattering function. The scattering function is recorded over six decades in time and for many different wave-vectors which range from the size of a chain to about three times the maximum position of the static structure factor. The lowest temperatures studied are slightly above Tc, the critical temperature of mode-coupling theory (MCT), where Tc was determined from a quantitative analysis of the β- and α-relaxations. We find evidence for the space-time factorization theorem in the β-relaxation regime, and for the time-temperature superposition principle in the α-regime, if the temperature is not too close to Tc. The wave-vector (q-) dependence of the nonergodicity parameter, of the critical amplitude, and the α-relaxation time are in qualitative agreement with calculations for hard spheres. For q larger than the maximum of the structure factor the α-relaxation time τq already agrees fairly well with the asymptotic MCT-prediction τq ∼ q -1/b. The behavior of the relaxation time at small q can be rationalized by the validity of the Gaussian approximation and the value of the Kohlrausch stretching exponent, as suggested in neutron-scattering experiments.