Glass Transition and Ionic Conductivity in Cellulose Acetate

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 ...

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