Scaling behavior of proton mobility in sulfonated block copolymers

Abstract

An in-depth analysis of proton mobilities in model ionic block copolymers has been carried out. The system of interest is a series of sulfonated poly(styrene-b-methylbutylene) (PSS-PMB) copolymers. Dilute solutions of PSS-PMB copolymers in methanol were examined where the PSS domains have an ability to conduct protons by offering sufficiently protonated conditions. A nearly monodisperse molecular weight distribution of PSS-PMB copolymers yields highly uniform spherical ionic micelles. In particular, on virtue of the self-assembly nature of block copolymers, the system revealed well-defined ionic PSS domains with different thicknesses ranging from 3.0 to 7.8 nm. The proton transport in PSS–PMB copolymers was found to be facilitated by the decrease in the ionic domain sizes with proton mobilities (μ) ranging from 1.96 × 10⁻⁴ to 8.48 × 10⁻⁴ cm² V⁻¹s⁻¹. Notably, a unique scaling relationship between the μ values and the micelle radii (R_H), μ ∝ R_H^−1.67, was described, which was rationalized by the different proximity of acid groups at the surfaces of ionic domains. The validity of the scaling behavior was verified by examining body-centered cubic forming concentrated solutions. Interestingly, when the same analysis was applied to the hydrated samples possessing different domain geometries, i.e., cylindrical ionic domains, the scaling behavior was also revealed, although an obtained exponent is significantly low as −0.35.