A framework to self-consistently combine a classical equation of state (EoS) and a molecular force field to model polymers and polymer mixtures is presented. The statistical associating fluid theory (SAFT-𝜸 Mie) model is used to correlate the thermophysical properties of oligomers and generate robust and transferrable coarse-grained (CG) molecular parameters which can be used both in particle based molecular simulations and in equations of state (EoS) calculations. Examples are provided for polyethylene, polypropylene, polyisobutylene atactic polystyrene, 1,4-cis-butadiene, polyisoprene, their blends and mixtures with low molecular weight solvents. Different types of liquid-liquid phase behavior are quantitatively captured both by the EoS and by direct molecular dynamics simulations. The use of CG models following this top-down approach extends the time and length scales accessible to molecular simulation while retaining quantitative accuracy as compared to experimental results.