Frequency Exponent of Ionic Conductivity in One-Dimensional Random Lattices

Abstract

The temperature dependent frequency exponent s^′ in the ionic conductivity Re σ(ω)=σ(0)+A^′ω^s′ is investigated by the relaxation mode theory in one-dimensional random lattices with exponential, uniform and normal distributions of activation energies: For the exponential distribution, Bernasconi ηl. analytically obtained s^′≈ s_B=(1-T/T_m)/(1+T/T_m) in the effective medium approximation within the range T<T_m. The present theoretical investigation concludes that (1) the obtained result s^′ is reproduced by s_B approximately for T<0.5T_m, and (2) the exponential distribution is not essential to obtain s^′≈ s_B: s^′ can be approximated by s_B better in the case of uniform distribution.