Scaling of the ODT of Block Copolymers in Compressed CO$_{2}$

It is well-known that diblock copolymers with sufficient $\chi N$ form periodic microphase-separated domains upon cooling through an order-disorder transition (ODT). We have investigated the scaling behavior of the ODT as a function of polymer volume fraction, \textit{$\phi $}, of several nearly symmetric poly(styrene-$b$-2-vinylpyridine) and poly(styrene-$b$-isoprene) diblock copolymer/diluent systems in relation to the well-known dilution approximation. Using compressed CO$_{2}$ in the place of conventional liquid diluents allowed$_{ }$the determination of the scaling parameter, \textit{$\alpha $}, for highly concentrated systems where \textit{$\phi $ }ranges from 0.85 to 1.0 at high temperatures. The scaling was determined by combining optical birefringence measurements of the ODT ($\chi _{ODT})$ with the ellipsometric swelling measurements (\textit{$\phi $}) of the constituent homopolymers at increasing CO$_{2}$ pressures. We show that sorption of small volume fractions of CO$_{2}$ results in significant reductions in the observed ODTs. Yet, \textit{$\alpha $ }was clearly shown not to be universal even for a specific diblock copolymer. For styrene-b-isoprene copolymers, it appears that \textit{$\alpha $ }is an increasing function of copolymer molecular weight. In contrast, the styrene-b-2-vinylpyridine copolymers studied show no obvious correlation with molecular weight, with \textit{$\alpha $ } taking on both positive and negative values.