Composition dependence of chi from neutron scattering, compressibility, and a purely interaction chi

We demonstrate that the concept of a bare chi parameter as exchange energy is meaningful only within the context of a lattice theory. We introduce a simple ensemble to describe a compressible system. The ensemble shares many features present in the ensemble describing an incompressible system. This allows us to express the intensity in terms of fluctuations in only one species, a feature also present in the incompressible model. We demonstrate that the perplexing features seen experimentally and theoretically in the wings of small-angle-neutron-scattering (SANS) measured χSANS are spurious and unrelated to the energetics, and result from a definition that leaves behind some nonenergetic contribution, which dominates the behavior in the wings and controls the sign of the curvature. It is easy to identify an appropriate χscatt that properly characterizes the interactions without any superfluous composition dependence. We use our recently developed lattice theory, which gives rise to genuine composition dependence in χscatt due to nonrandomness. For a symmetric blend, χscatt depends only weakly on compressibility. This is not true of an asymmetric blend, where compressibility effects can be strong. In particular, we demonstrate that a linear χscatt results from the asymmetry in the model and not from the compressibility.