  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 cristallisation tendency. In this first manuscript we we analyse
the structural properties as a function of temperature and the long
alpha-relaxation behaviour as observed in the dynamic structure factor and the
self-diffusion of the polymer chains. The relaxation can be consistently
analysed in terms of the mode coupling theory (MCT) of the glass transition.
The mode coupling critical temperature and the exponent gamma, defining the
power law divergence of the alpha-relaxation timescale both depend on the
thermodynamic ensemble employed in the simulation.
