Analysis of the incoherent intermediate scattering function in the framework of the idealized mode-coupling theory: A Monte Carlo study for polymer melts

In this Monte Carlo simulation, we calculate the incoherent intermediate scattering function φqˢ(t) for a three-dimensional dense polymer melt after having made long relaxation runs in order to eliminate the history of the cooling procedure sufficiently. This function shows the signature of a two-step process in the temperature interval T{∈}[0.16,0.21] (the temperature is measured in units of an energy parameter introduced in the Hamiltonian of the model) whose time evolution was quantitatively analyzed in the framework of the idealized mode-coupling theory (MCT) within the {β}-relaxation regime. As a result of this analysis the temperature interval splits into high- and low-temperature parts. In the high-temperature part (T{≥}0.19), the idealized theory accounts very well for the decay of φqˢ(t) over about three decades in time, whereas φqˢ(t) relaxes much faster than the idealized MCT anticipates in the low-temperature region (T0.19). Since this discrepancy between the idealized MCT and the simulation data can qualitatively be rationalized by taking hopping processes into account, we try to estimate the critical temperature Tc from the fits with the idealized MCT, yielding Tc{}0.150.