How Pure Components Control Polymer Blend Miscibility

Fundamental insight regarding what drives polymer blend immiscibility/miscibility requires understanding the enthalpic and entropic contributions to the free energy of mixing. In this modeling investigation we show that two quantities, connected to the molecular characterization parameters, serve as separate “controls” on these thermodynamic mixing functions. The g parameter is defined as g = εij/(εiiεjj)1/2, with ε representing a segment–segment interaction energy, which may be obtained using minimal data on the mixture (for example, a phase separation temperature), appears to be correlated with the enthalpy of mixing. Characterization of the pure components, for example by fitting equation of state data, yields εii values. In this work we present evidence that |εii – εjj| controls the entropy of mixing. Furthermore, by analyzing the separate ideal and excess contributions to the entropy of mixing, we demonstrate that it is the excess contribution in particular that is strongly influenced by the value of |εii – εjj|, becoming increasingly unfavorable as |εii – εjj| increases. This sheds further light on a correlation noted in recent work of ours [White; Macromolecules 2012, 45, 1076−1084], that for LCST-type blends an increasingly favorable εij (meaning an increasing value of g) is needed to offset a greater mismatch in εii and εjj values (meaning an increasing |εii – εjj| difference) in order to maintain even partial miscibility. Given the importance of the excess entropy of mixing in driving miscibility, especially for LCST-type blends, we conclude that knowledge of |εii – εjj| can lead to a degree of a priori insight in assessing the mixture thermodynamics in the absence of any mixture data.