Glass Transition and Ionic Conductivity in Cellulose Acetate

Abstract

For many polymers an effective glass transition Tg′ can be defined via a change in slope of logσ[Ω−1cm−1] vs T−1[°K−1]. Measurements for dry cellulose acetate (CA), previously doped by soaking (48 h) in 0.1M alkali-chloride solutions, indicate that Tg′ depends on ion and polymer properties. A model based on fluctuation theory and ``free volume'' concepts is developed. The main assumptions are: (1) ions partially fill void space reducing the available local free volume; and (2) reduction in local free volume about an ion can be accounted for in the statistical expression 〈(V−V0)2〉av=RTV0/B by subtracting an effective ion volume Vi from the total volume (per mole) V of a reference aggregation of particles of most probable volume V0. (B is the bulk modulus, R the gas constant.) With simplified distribution functions, we obtained the expressions Tg≈Bδ2/6RV0 and Tg′=Tg−2a(δ/m)m2Wi+am2Wi2, where a = B/6V0R, Wi is ionic volume (per mole) from x-ray measurements on crystals, m = Vi/Wi, and δ is a measure of free volume. For CA, the best fit is Tg′≈Tg−0.3Wi+0.14Wi2 corresponding to a fractional free volume fg≈δ/V0, which may be as much as 12%. Below Tg′, activation energies for conduction by alkali-chloride-doped CA were found to be given by Eb[kcal / mole]≈ 15+0.7Wi≈16.1+2.45(1024α), where α[cm3/ion] is the electronic polarizability of the ion. Above Tg′, the energy Ea was approximately 29 kcal/mole, independent of the ion. Alternative interpretations in terms of internal pressure and polarization effects are discussed.