Spinodal decomposition in filled polymer blends exhibiting upper critical solution temperature behavior

By extending the Sanchez-Lacombe lattice-fluid model for mixtures to the case of polymer blends containing solid fillers, we calculate the excess thermodynamic quantities arising from the presence of fillers. These results are then used to derive the spinodal stability condition of a filled polymer blend. In the low-compressibility limit, this condition reduces to a remarkably simple analytical expression that is derived self-consistently within the present framework. Comparison between the exact and approximate spinodal curves shows excellent agreement, with deviations in the spinodal temperature of less than 4K, thereby validating the proposed approximation. The obtained analytical approximation enables a straightforward evaluation of the spinodal temperature without the extensive numerical calculations required to determine the exact spinodal condition. Both the exact and approximate spinodal conditions yield good quantitative agreement with experimental data for filled and unfilled blends.