LATTICE CLUSTER THEORY FOR PEDESTRIANS - THE INCOMPRESSIBLE LIMIT ANDTHE MISCIBILITY OF POLYOLEFIN BLENDS

The high pressure (incompressible), high molecular weight limit of the lattice cluster theory is derived as a first approximation to describ e the influence of monomer molecular structure and nonrandom mixing ef fects on the thermodynamic properties of binary polymer blends. In par ticular, the noncombinatorial free energy of mixing and the small angl e neutron scattering effective interaction parameter chi(exp) emerge i n this limit as rather simple, compact analytical expressions that dep end on a single microscopic energy and on two geometrical indices obta ined 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 rapi d use of the theory with minor additional effort than the application of Flory-Huggins theory. Our theory is applied to a few polyolefin ble nds in order (a) to illustrate a new mechanism for the occurrence of l ower critical solution temperature (LCST) phase diagrams in incompress ible systems, (b) to provide a partial explanation of why blends of po ly(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.