  Two coarse-grained models for polymer chains in dense glass-forming polymer
melts are studied by computer simulation: the bond-fluctuation model on a
simple cubic lattice, where a bond-length potential favors long bonds, is
treated by dynamic Monte Carlo methods, and a bead-spring model in the
continuum with a Lennard-Jones potential between the beads is treated by
Molecular Dynamics. While the dynamics of both models differ for short length
scales and associated time scales, on mesoscopic spatial and temporal scales
both models behave similarly. In particular, the mode coupling theory of the
glass transition can be used to interpret the slowing down of the undercooled
polymer melt. For the off-lattice model, the approach to the critical point of
mode coupling is both studied for constant pressure and for constant volume.
The lattice model allows a test of the Gibbs-Di Marzio entropy theory of the
glass transition, and our finding is that although the entropy does decrease
significantly, there is no ``entropy catastrophe'', where the fluid entropy
would turn negative. Finally, an outlook on confinement effects on the glass
transition in thin film geometry is given.
