Measurement of Flory-Higgins interaction parameter between unlike polymers via solution light scattering near "optical θ" state

Abstract

The optical 8 technique proposed by Inagaki et al. for the measurement of the polymer-polymer interaction parameter via ternary solution light scattering was critically examined. A modification of their method through a combination of Flory-Krigbaum theory and Yamakawa theory was developed so that the technique can be applied to both symmetric and moderately asymmetric ternary systems. From the light scattering results of Inagaki et al., the Flory-Huggins interaction parameter between polystyrene and poly(methy1 methacrylate) was determined to be 0.009 i 0.001 at 30 C. I. Introduction Over 30 years ago, Stockmayer and Stanley' measured the Flory-Huggins (F-H) interaction parameter between polystyrene (PS) and poly(methy1 methacrylate) (PMMA) via a ternary (PS/PMMA/butanone) solution light scat- tering technique. The main difficulty of their method is that generally the contribution of solvent-polymer inter- actions to the second virial coefficient of the ternary so- lution is overwhelmingly larger than that of the poly- mer-polymer interaction, thus rendering the obtained polymer-polymer interaction parameter poor in accuracy. Another inadequacy of the method, as pointed out by Krigbaum and Flory? lies in its mean-field or lattice-model theoretical frame,3 which disregards totally the excluded volume effect. Recently, Inagaki et al.495 devised an in- triguing modification to the technique. Under the so-called optical 0 state achieved by using a solvent with refractive index intermediate to those of the polymers and carefully selecting operation conditions such as temperature, blend composition, and polymer molecular weights, the scattering components resulting from solvent-polymer interactions exactly cancel each other according to Stockmayer's theoretical scheme; thus the second virial coefficient be- comes (presumably) proportional to the polymer-polymer interaction parameter and a better accuracy is realized. However, the excluded volume effect was still not con- sidered during their theoretical development. Rather, the correction for the excluded volume effect was done after the preliminary values (based on Stockmayer's mean-field theoretical frame) of the polymer-polymer interaction parameter at different blend compositions and polymer molecular weights were obtained. The symmetry of the polymers used (PS and PMMA) with respect to the solvent (bromobenzene), i.e., the component polymers were not strongly interacting with each other and had similar ex- pansion factors, chain lengths, and solvent-polymer in- teraction parameters, allowed the excluded volume effect to be taken into account by applying binary polymer so- lution theories. This ad hoc correction of excluded volume effect, although maybe in principle justifiable for their specific ternary system, imposes a severe constraint on the application of the technique due to the simultaneous re- quirements of symmetry and the optical 0 condition. It is the attempt of this paper to examine more closely and then extend this optical 0 technique to less sym- metric ternary systems by introducing corrections for ex- cluded volume effect from the beginning of the theoretical development.