A theoretical study of isotope blends:: No concentration dependence of the SANS χ parameter

The small-angle neutron scattering (SANS) interaction parameter chi(NS) in isotope blends almost always exhibits pronounced upward curvature when plotted as a function of concentration at any given temperature. Optimized cluster theory (OCT), which accounts for blend compressibility and for fluctuations, is used to address this effect in blends of conventional and perdeuterated polyethylene. Structure factors are calculated for symmetric systems having a concentration independent chi(bare) = 2.09 x 10(-4) and chains of N = 3290 or N = 8746 monomers. When analyzed in terms of incompressible RPA approach, exactly as done in experiments,the model returns an interaction parameter that; is practically indistinguishable from chi(bare) for all blends concentrations between 0.01 and 0.99. Trivial departures from the energetic chi(bare) are attributed to equation-of-state effects. These results, combined those from compressible lattice models, show clearly that compressibility has no significant role in determining the composition dependence of the interaction parameter. The experimental behavior of isotope blends cannot be ascribed to any theoretical reason (i.e., compressibility or density fluctuations) and is therefore attributed to measurement errors.