S. Enders, A. Hinrichs, R. Horst and B. A. Wolf
"Influence of Molar Mass Distribution on the Compatibility of Polymers"
J. Macromol. Sci., Pure and Appl. Chem. 1996, A33, 1097-1111.
Abstract: Phase equilibria were calculated by means of a new method (direct minimization of the Gibbs energy of mixing) for polymer blends consisting of monodisperse polymer A and polydisperse polymer B. The results obtained for a Schulz-Flory distribution of B (molecular nonuniformity U = (M(w)/M(n)) - 1 = 1 and 100 components of model B) agree quantitatively with that of computations on the basis of continuous thermodynamics. The influence of U-B on the miscibility of A and B in 1:1 mixtures was studied for constant M(w) of B, quantifying the incompatibility of the polymers by the length of the tie lines. The outcome of these calculations demonstrates that the typical effect of an augmentation of U-B (keeping M(w) and the overall composition constant) consists in an enlargement of the mutual solubility of A and B. However, for an almost compatible pair of polymers (i.e., interaction parameters g are only slightly larger than the critical values for U-B = 0), this statement remains true only in the case of sufficiently small U-B. In order to gain some understanding of these findings, calculations were also performed for ternary systems (A and two species B). They demonstrate that it is the distance of the overall composition in the Gibbs phase triangle to the critical line (connecting the critical points for different U-B) which governs the changes in compatibility. Normally the critical point comes closer to the overall composition as U-B is raised, except for low g values where the critical point - after an initial approach - drifts apart as U-B becomes larger.
preprint number: 167