  Obtaining a rigorous and reliable method for linking computer simulations of
polymer blends and composites at different length scales of interest is a
highly desirable goal in soft matter physics. In this paper a multiscale
modeling procedure is presented for the efficient calculation of the static
structural properties of binary homopolymer blends. The procedure combines
computer simulations of polymer chains on two different length scales, using a
united atom representation for the finer structure and a highly coarse-grained
approach on the meso-scale, where chains are represented as soft colloidal
particles interacting through an effective potential. A method for combining
the structural information by inverse mapping is discussed, allowing for the
efficient calculation of partial correlation functions, which are compared with
results from full united atom simulations. The structure of several polymer
mixtures is obtained in an efficient manner for several mixtures in the
homogeneous region of the phase diagram. The method is then extended to
incorporate thermal fluctuations through an effective chi parameter. Since the
approach is analytical, it is fully transferable to numerous systems.
