The high pressure (incompressible), high molecular weight limit of the lattice cluster theory is derived as a first approximation to describe the influence of monomer molecular structure and nonrandom mixing effects on the thermodynamic properties of binary polymer blends. In particular, the noncombinatorial free energy of mixing and the small angle neutron scattering effective interaction parameter chi(exp) emerge in this limit as rather simple, compact analytical expressions that depend on a single microscopic energy and on two geometrical indices obtained easily from the monomer united atom structures. These analytical expressions, in conjunction with the geometrical indices summarized in a table for a wide range of vinyl monomer structures, enable the rapid use of the theory with minor additional effort than the application of Flory-Huggins theory. Our theory is applied to a few polyolefin blends in order (a) to illustrate a new mechanism for the occurrence of lower critical solution temperature (LCST) phase diagrams in incompressible systems, (b) to provide a partial explanation of why blends of poly(isobutylene) with other polyolefins often yields LCST behavior, and (c) to explain the rather large negative entropic portions of chi(exp) observed for many binary polyolefin blends.