The determination of relaxation parameters and their distributions using thermally stimulated discharge current measurements

For any elemental peak obtained by the thermally stimulated depolarization current technique, there is a relationship between the activation energy W, the pre-exponential factor τ₀, the temperature of the maximum current T_m and the heating rate b. This relationship can yield useful information concerning the values and the distribution of the relaxation parameters. Numerical simulations, using concrete experimental data obtained for nylon 11, are used to demonstrate the analysis for organic dielectrics. Lower limits for the incertitude intervals of W and τ₀ represent the natural or minimum incertitude intervals expected for an elemental relaxation process. Taking advantage of the fact that the natural incertitude interval in activation energies is ΔW≅kT_m (k is Boltzmann's constant), the natural incertitude interval for τ₀ is deduced as Δτ₀≅τ₀. For example, assuming T_m = 300 K and Δτ₀ = 0, the interval ΔT_m for two resolved neighbour elemental peaks, in other words the interval in which T_m can have values as W varies in the limits on the natural incertitude interval, increases from 7.1 to 11.9 K as W decreases from 1.05 to 0.59 eV. An experimental thermogram can be decomposed into a limited number of elemental peaks having W and τ₀ distributed in the limits of the natural or minimum incertitude intervals (ΔW≅kT_m and Δτ₀≅τ₀). The distribution function for a relaxation parameter cannot be determined unambiguously for the case when the width of the distribution is comparable with the natural standard deviation for the given conditions. Only one parameter or only one distribution must be avoided considering any analysis as variable.