Small angle neutron scattering has been used to study the radius of gyration and thermodynamics of dilute blends of deuterated polystyrene (PSD) in a strongly interacting matrix of poly(vinylmethylether) (PVME) and in a weakly interacting matrix of protonated polystyrene (PSH). The PSD chain is found to be slightly expanded in the PVME matrix over the PSH matrix with the radius of gyration for PSD being 123 Angstrom A in PVME vs 115 Angstrom A in PSH. The Flory interaction parameter, chi/nu(0), for the PSD/PVME blend is found to be in approximate agreement with an extrapolation of data from studies of chi/nu(0) for PSD/PVME at high concentration to the dilute concentrations studied in this work. The concentration dependence of chi/nu(0) is close to linear and shows no strong change in slope down to phi=0.02, the lowest concentration studied in this work. Analysis of the temperature dependence of chi/nu(0) and the second virial coefficient, A(2) indicates that phase separation should occur for PSD/PVME in the range of 200 degrees C for a sample with phi(PSD)congruent to 5%.