Composition dependence of the flory-huggins interaction parameters of block copolymer electrolytes and the isotaksis point

The thermodynamics of block copolymer/salt mixtures were quantified through the application of Leibler's random phase approximation to disordered small-Angle X-ray scattering profiles. The experimental system is comprised of polystyrene-block-poly(ethylene oxide) (SEO) mixed with lithium bis(trifluoromethanesulfonyl)imide salt (LiTFSI), SEO/LiTFSI. The Flory-Huggins interaction parameter determined from scattering experiments, χ_SC, was found to be a function of block copolymer composition, chain length, and temperature for both salt-free and salty systems. In the absence of salt, χ_0,SC is a linear function of (Nf_EO)^-1 in the presence of salt, a linear approximation is used to describe the effect of salt on χ_eff,SC for a given copolymer composition and chain length. The theory of Sanchez was used to determine χ_eff from χ_eff,SC to predict the boundary between order and disorder as a function of chain length, block copolymer composition, salt concentration, and temperature. At fixed temperature (100 °C), N_crit, the chain length of SEO at the order-disorder transition in SEO/LiTFSI mixtures, was predicted as a function of the volume fraction of the salt-containing poly(ethylene oxide)-rich microphase, f_EO,salt, and salt concentration. At f_EO,salt > 0.27, the addition of salt stabilizes the ordered phase; at f_EO,salt < 0.27, the addition of salt stabilizes the disordered phase. We propose a simple theoretical model to predict the block copolymer composition at which phase behavior is independent of salt concentration (f_EO,salt = 0.27). We refer to this composition as the "isotaksis point".