The miscibility in several polymer blend mixtures (polymethylmethacrylate/polystyrene, (1,4-cis) polyisoprene/polystyrene, and polymethylmethacrylate/polyoxyethylene) has been investigated by using Molecular Dynamics simulations performed for fully atomistic representations of short chains. The trajectories obtained from simulation boxes representing the mixtures have been analyzed in terms of the collective scattering structure function. The Flory-Huggins parameter is determined from fits of the simulation results for this function to the random phase approximation expression. The numerical values of this parameter and its variation with temperature obtained with this procedure show a general qualitative and semi-quantitative agreement with existing experimental data for the different systems, though with significant error bars. These results together with those previously obtained for the polyvinylmethylether/polystyrene blends with the same method are compared with data yielded by other computational simpler approaches, which are considerably more sensitive to different parameter choices. (C) 2009 Published by Elsevier Ltd.