Can a single function for χ account for block copolymer and homopolymer blend phase behavior?

Most theoretical treatments of polymer-polymer phase behavior assume that homopolymer mixtures and block copolymer melts are controlled by a common segment-segment interaction parameter knows as χ. This publication describes the results of small-angle neutron scattering (SANS) experiments conducted as a function of temperature and composition from homogeneous mixtures of poly(ethylene) (PE) and poly(ethylenepropylene) (PEP) of equal molecular weight. Analysis of these SANS measurements based on the random phase approximation indicates that χPE/PEP is independent of composition and linear in T^-1. The associated symmetric phase diagram calculated with Flory-Huggins theory contains a stability curve that is consistent with the divergence in single phase susceptibility obtained by SANS. This function χPE/PEP(T) is compared with functions for χPE-PEP(T) associated with the homologous PE-PEP diblock copolymers, extracted both from the temperature dependence of the disordered state scattering structure factor, and from the N dependence of the order-disorder transition (ODT) temperature T_ODT, where N is the degree-of-polymerization. Analysis of these data using mean-field and fluctuation theories leads to four distinct expressions for χPE-PEP(T) , none of which is consistent with χPE/PEP(T). We attribute this disparity to the effects of polarization and stretching of diblock molecules in the vicinity of the ODT. A simple model calculation that corrects the prediction for (χN)_ODT based on the experimentally determined shift in the SANS peak location corroborates this deduction. We conclude that current theories cannot account for block copolymer and homopolymer phase behavior based on a single function for χ, and suggest that this deficiency may be rectified with a more sophisticated block copolymer theory that properly accounts for chain stretching.