IMMITTANCE SPECTROSCOPY Models data fitting and analysis J

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IMMITTANCE SPECTROSCOPY Models, data fitting, and analysis J. Ross Macdonald IMSPEMAS Workshop Warsaw 9/2003

IMMITTANCE SPECTROSCOPY Models, data fitting, and analysis J. Ross Macdonald IMSPEMAS Workshop Warsaw 9/2003

MATERIAL/ELECTRODE CHARACTERIZATION WITH IS • • Bulk resistivity and dispersion Bulk dielectric constant Mobile

MATERIAL/ELECTRODE CHARACTERIZATION WITH IS • • Bulk resistivity and dispersion Bulk dielectric constant Mobile charge concentrations Mobilities and valence numbers Bulk dissociation and recombination rates Electrode reaction rate constant Electrode adsorption rate constant Other fit-model parameters

IMMITTANCE SPECTROSCOPY • Impedance Spectroscopy • Dielectric Spectroscopy • Data Analysis • CNLS; INVERSION

IMMITTANCE SPECTROSCOPY • Impedance Spectroscopy • Dielectric Spectroscopy • Data Analysis • CNLS; INVERSION • LEVM ---- LEVMW V. 8

CNLS-LEVMW • CNLS: Complex nonlinear least squares fitting. Fit complex data to a model

CNLS-LEVMW • CNLS: Complex nonlinear least squares fitting. Fit complex data to a model whose parts satisfy the Kronig-Kramers transform relations • LEVMW: Windows version of LEVM, a free general CNLS fitting and inversion program. Download it and its manual from http: //www. physics. unc. edu/~macd/ • LEVMW can accurately fit data to K 0, K 1, and many other models. It allows temporal response to be calculated from frequency response and vice versa

ELECTRODE EFFECTS AND SLOPES

ELECTRODE EFFECTS AND SLOPES

BULK K 0 AND K 1 FIT RESULTS

BULK K 0 AND K 1 FIT RESULTS

NEARLY CONSTANT LOSS

NEARLY CONSTANT LOSS

CONCLUSIONS • The Moynihan original modulus formalism dispersion model is theoretically and experimentally incorrect

CONCLUSIONS • The Moynihan original modulus formalism dispersion model is theoretically and experimentally incorrect and should be replaced by the corrected modulus formalism. • The corrected modulus formalism is isomorphic to the Scher-Lax microscopic model and leads to virtually independent of temperature and ionic concentration.

 • The variable-correlation assumption of the OMF and NCM is unsupported by fits

• The variable-correlation assumption of the OMF and NCM is unsupported by fits of experimental data using the CK 1 CMF model. • The cutoff model is much superior to all coupling models and requires no ad hoc assumptions. • Nearly-constant-loss behavior is likely to be associated with coupling between vibrating ions and induced dipoles of the bulk material. A microscopic model of the process is needed.

MATERIAL CHARACTERIZATION • Conduction character Intrinsically conducting: a. Completely blocking electrodes b. Partially blocking

MATERIAL CHARACTERIZATION • Conduction character Intrinsically conducting: a. Completely blocking electrodes b. Partially blocking electrodes Intrinsically insulating: a. Dielectric: no mobile charge b. Leaky dielectric: surface or bulk impurity conduction • Charge characteristics Supported: strong supporting electrolyte, as in liquids Unsupported: no supporting electrolyte, as in glasses, solid electrolytes, semiconductors