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, chi(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, chi(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 chi(eff,SC) for a given copolymer composition and chain length. The theory of Sanchez was used to determine chi(eff) from-chi(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 degrees 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, 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".