Composition Dependence of the Flory–Huggins Interaction Parameters of Block Copolymer Electrolytes and the Isotaksis Point

Abstract

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 comprises 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 (N f 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 in order 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 o 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 3 composition at which phase behavior is independent of salt concentration (f EO , salt =0.27). We refer to this composition as the "isotaksis point".

Sub-3-Nanometer Domain Spacings of Ultrahigh-χ Multiblock Copolymers with Pendant Ionic Groups

“…63 For example, poly(styrene-b-ethylene oxide) with lithium bis-(trifluoromethane-sulfonyl)imide (LiTFSI) systems observe an increase of χ with salt concentration. 60 In contrast, the χ of PESxLi polymers solely depends on the molecular interactions of the polar and nonpolar blocks. Thus, the current experimental results of the PESxLi system should not be directly compared to the salt/copolymer systems.…”

“…Various salt-containing block copolymers have been extensively investigated both theoretically − and experimentally. − In these salt/copolymer systems, the value of χ depends on the salt concentration and solvation energy . For example, poly­(styrene- b -ethylene oxide) with lithium bis­(trifluoromethane-sulfonyl)­imide (LiTFSI) systems observe an increase of χ with salt concentration . In contrast, the χ of PES x Li polymers solely depends on the molecular interactions of the polar and nonpolar blocks.…”

Effect of Added Salt on Disordered Poly(ethylene oxide)-Block-Poly(methyl methacrylate) Copolymer Electrolytes

“…Lacking a better alternative, we use the random phase approximation (RPA) to interpret the measured scattering profiles; this is similar to the approach used in the study of other disordered block copolymer/salt mixtures. 25,36,[42][43][44] The RPA theory predicts the absolute scattering intensity of a monodisperse AB diblock copolymer…”

“…The non-monotonic relationship between χ eff and salt concentration may be explained by a competition between ion solvation, screening, and entropic effects. 17,23,42,48 At low salt concentrations, ion solvation effects dominate, which drives ordering, while at high salt concentration, entropic effects dominate, which drives disordering. Above m = 0.44 mol Li/ kg polymer, χ eff decreases with added salt.…”

Comparing Experimental Phase Behavior of Ion-Doped Block Copolymers with Theoretical Predictions Based on Selective Ion Solvation

“…This asymmetry can be accounted for empirically by postulating a composition-dependent parameter m, but the physical origin of this dependence remains unclear. 55 In contrast, the iPSCF model predicts asymmetric behavior with composition-27 independent inputs listed in Table 2-a more detailed analysis can be found in the Supporting Information. We emphasize that our simple model produces asymmetric phase behavior with respect to copolymer composition using only the Born solvation model, without accounting for complex interactions such as ionic correlations or Li-EO complexation.…”