Liquid-liquid phase separation in multicomponent polymer systems .26. Blends of two polydisperse polymers

A method for computing phase diagrams of polydisperse A/B polymer blends is proposed, based on Flory-Huggins-Staverman thermodynamics, and employed to obtain cloud-point curves (CPCs), shadow curves, spinodals and coexistence curves for a series of systems. Often bimodal CPCs and shadow curves result, even for systems with a concentration-independent interaction parameter g. The importance of coexistence curves, as opposed to CPCs, for judging the A/B miscibility, recently observed in polydisperse blends, is confirmed in this study. Particular attention is here paid to the critical state. Analytical relations are derived for the critical point (CP) and the critical slopes of the CPC and shadow curve, as well as for the criterion of CP stability, all in terms of various molar-mass averages of A and B. The latter criterion then yields conditions for the existence of heterogeneous double CPs and triple CPs, important as markers announcing the proximity of a three-phase region. Interestingly, the sign of the critical CPC slope depends solely on the relative magnitude of the r(z)/r(w) ratios for the two polymers A and B. Hence, a CP located at the CPC's top should not be interpreted as a proof of both polymers' monodispersity. The validity of derived analytical relations is confirmed by numerically computed phase diagrams.