Computer simulations of the static scattering from model polymer blends

To understand the unusual composition and wave vector, q, dependent Flory interaction parameters, chi, obtained from small angle neutron scattering (SANS), we have calculated the three partial structure factors for symmetric binary polymer blends with relatively strong interactions between dissimilar monomers using molecular dynamics simulations. In agreement with past work we find that the radii of gyration of the chains are altered on blending. The following new results emerged from our simulations. The single-chain form factors in the blends follow Gaussian statistics at all distances larger than a monomer diameter, confirming the Flory-de Gennes conjecture that correlations in condensed polymer phases are screened over short length scales. The R-g's deduced from these form factors are in agreement with simulation-determined values and illustrate conclusively that the single chain term in the incompressible random-phase approximation (i-RPA) is altered on blending. The three partial structure factors obtained from the simulations, each of which follows an Ornstein-Zernike behavior, have different q dependences and extrapolate to different values in the thermodynamic limit. The different q dependences can be explained qualitatively by a compressible RPA formalism proposed by Tang and Freed. We then show that any form chosen to combine these partial structure factors into a single total scattering function will, in general, not have a q dependence that is describable by the incompressible RPA. This explains the experimentally observed q dependence of the chi parameter derived from the i-RPA. Finally, a thermodynamic analysis on the zero wave-vector limit of the partial structure factors shows that their absolute values are different from each other due to the effects of density fluctuations, as well as the different partial molar volumes of the two species in the blend. These results serve to emphasize the important role played by compressibility on the scattering obtained from simple polymer mixtures with large excess volumes on mixing.