Comparison of Some Random-Barrier, Continuous-Time Random-Walk, and Other Models for the Analysis of Wide-Range Frequency Response of Ion-Conducting Materials

• Published in: The journal of physical chemistry. B 2009-07, Vol.113 (27), p.9175-9182
• Main Author: Macdonald, J. Ross
• Format: Article
• Language: English
• Subjects: B: Macromolecules, Soft Matter
• ISSN: 1520-6106; 1520-5207
• DOI: 10.1021/jp9026095

Several theoretical models are fitted to an exact wide-frequency-range data set representing a new random-free-energy, effective-medium expression for mobile-ion response at low temperatures. A continuous-time, random-walk K1 model, indirectly involving a stretched-exponential temporal correlation function, led to the best fit, much superior to those of two dielectric-dispersion models as well. Two types of approaches are compared for analyzing 0.4Ca(NO3)2·0.6KNO3 (CKN) experimental data covering a very wide frequency range: a simplified conventional approach, usually involving only some or all of the real part of conductivity, denoted type 1, and an approach involving nonlinear least-squares fitting of full complex data over its entire range, denoted type 2. The type-2 analysis uses a composite fitting model involving the K1 and involves 10 free parameters needed to well represent electrode polarization, conductive-system dispersion, nearly constant loss, and limiting far-infrared vibrational effects. It confirmed that the latter were purely dielectric and led to σ′′ and ε′′ boson peaks; included a mobile-charge explanation of the nearly constant loss region; and yielded reasonable values of the K1-model fractional exponent, β1, and plausible values of a completely blocking double-layer capacitance. The good type-2 fit parameter estimates were used to generate extrapolated model response over a 20-decade range at complex conductivity and complex relative permittivity levels, as well as their accurate slopes over that range. The maximum slope of the log−log σ′ curve failed to approximate well the value of 2 usually inferred from data of the present type but instead led to a novel double peak with peak slope values of about 1.6 and 1.7 before decreasing to zero at the limiting far-infrared plateau region of σ′ response. Nearly constant loss was found to be well described by the series combination of the bulk high-frequency-limiting dielectric constant of the material and a translational ionic-motion constant-phase-element expression, one whose inclusion was also needed for representing low-frequency electrode polarization effects. Further, this combination should dominate the full response at sufficiently low temperatures.